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C OMPUT E RAI DE DDE S I GN
500
BACHELORI NMECHANI CALENGI NEERI NG www. i mt s i n s t i t u t e . c o m
IMTS (ISO 9001-2008 Internationally Certified) COMPUTER AIDED DESIGN
COMPUTER AIDED DESIGN
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COMPUTER AIDED DESIGN
CONTENTS:
UNIT I:
01-18
Introduction: – CAD/CAM defined – the produced cycle and CAD/CAM – automation and
CAD/CAM. Computer Technology:
– Introduction –Control
Processing Unit- Type of memory – input/output – data representation – computer programming language – operating the computer system.
UNIT II:
19-32
Computer fundamentals of CAD: – Introduction- the design process- the application of computer for design-creating the manufacturing data base - benefits of CAD. Hardware of CAD: – the design workstation – the graphics terminal – operation input devices – plotter and other o/p devices – secondary storage.
UNIT III:
33-58
Computer graphics: – Raster scan graphics – co-ordination system database structure for graphic modeling – transformation of geometric – 3D transformation mathematics of projection – clipping – hidden surface removal. IMTSINSTITUTE.COM
UNIT IV:
59-77
Geometric modeling: – Requirements of geometric modeling – geometric models – geometric construction methods – other modeling methods – curve – representation – desirable modeling facilities – rapid prototyping. CAD standards: – Standardization in graphics – graphics kernel system – other graphics standards – exchange of modeling data.
UNIT V:
78-116
Introduction to a drafting system: – basic facilities in AutoCAD – basic geometric commands – layers – display control commands – editing a drawing – dimensioning. Introduction to modeling system: general facilities of
unigraphics – example of solid
modeling finite element analysis – finite element modeling –FEM software.
UNIT QUESTIONS:
117-121
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UNIT I 1.1 CAD/CAM defined 1.2 The product cycle and CAD/CAM 1.3 Automation and CAD/CAM 1.4 Introduction (Computer Technology) 1.5 Central Processing Unit (CPU) 1.6 Types of memory 1.7 Input /Output 1.8 Data Representation 1.9 Computer Programming Language 1.10 Operating the Computer System
Introduction
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1.1 CAD/CAM defined CAD/CAM is a term which means computer-aided design and computer-aided manufacturing. It is the technology concerned with the use of digital computers to perform certain functions in design and production. This technology is moving in the direction of greater integration of design and manufacturing. CAD can be defined as the use of computer system to assist in the creation, modification, analysis, or optimization of a design. The CAD hardware typically includes the computer, one or more graphics display terminal, keyboards, and other peripheral equipment. The CAD software consists of the computer programs and application programs. CAM can be defined as the use of computer systems to plan, manage, and control the operations of a manufacturing plant. The application of computer-aided manufacturing:
Computer monitoring and control: These are the direct applications in which computer is connected directly to the manufacturing process for the purpose of monitoring or controlling the process.
Manufacturing support applications: These are the indirect applications in which the computer is used in support of the production operation in the plant.
The difference between monitoring and control
In computer monitoring the flow of data between the process and the computer is in one direction only.
Computer
Process data
Process
FIGURE 1.1 Computer monitoring
In control, the computer interface allows for a two-way communication flow of data.
Process data
Computer
Control signals
FIGURE 1.2 Computer control
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Computer-aided manufacturing also include indirect applications in which the computer serves a support role in the manufacturing operation of the planet. In these applications, the computer is not linked directly to the manufacturing process. The computer is used “off-line”.
Process data
Computer
Control signals
Process
FIGURE 1.3 CAM for manufacturing support The dashed lines are used to indicate that the communication and control link is an off-line connection, with human beings often required to communicate the interface.
Some examples of CAM for manufacturing support
Numerical control part programming by computers.
Computer-automated process planning.
Computer-generated work standards.
Production scheduling.
Material requirements planning.
Shop floor control.
1.2 The product cycle and CAD/CAM The various steps in the product life cycle are presented in FIGURE 1.4.
Product concept
Customers and markets
Design engineering
Order new equipment and tooling
Quality control Production FIGURE 1.4 Product cycle (design and manufacturing)
Drafting
Process planning
Production scheduling
The cycle is driven by customers and markets which demand the product. Depending on the particular customer group, there will be differences in the way the product cycle is activated.
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In some cases, the design functions are performed by the customer and the product is manufactured by a different firm. In other cases, design and manufacturing is accomplished by the same firm. Whatever the case, the product cycle begins with a concept, an idea for a product. This concept is cultivate, refined, analyzed, improved, and translated into a plan for the product through the design engineering process. The plan is documented by drafting a set of engineering drawings showing how the product is made and how the product should perform. The next activities involve the manufacture of the product. Scheduling provides a plan that commits the company to the manufacture of certain quantities of the product by certain dates. Once all these plans are formulated, the product goes into production, followed by quality testing, and delivery to the customer. Computer-aided design and automated drafting are utilized in the conceptualization, design, and documentation of the product. Computer are used
in process planning, and scheduling,
in production to monitor and control the manufacturing operation,
Quality control: – to perform inspection and performance test on the product and its components.
As given in FIGURE 1.5 CAD/CAM is overlaid on virtually all of the activities and functions of the product cycle.
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Computeraided design
Product concept
Customers and markets
Quality control
Computer-aided quality control
Computer-automated drafting and documentation
Design engineering
Drafting
Order new equipment and tooling
Process planning
Production
Production scheduling
Computer controlled robots, machines, etc.
Computeraided process planning
Computerized scheduling, material requirements planning, shop floor control
FIGURE 1.5 Product cycle revised with CAD/CAM overlaid.
In design and production operations of a modern manufacturing firm, the computer has become a useful tool. 1.3 Automation and CAD/CAM Automation was defined as the technology concerned with the application of complex mechanical, electrical, and computer-based systems in operation and control of production. Production activity can divide into four categories:
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Categories
Description
1. Continuous-flow process
2. Mass production of discrete products
Continuous dedicated production of large amounts of bulk product. Dedicated production of large quantities of one product.
3. Batch production
Production of medium lot sizes of the same product or components. The lots may be produced once or repeated periodically.
4. Job shop production
Production of low quantities, often one of a kind, of specialized products. The products are often customized and technologically complex.
The relationships among the four types in terms of product variety and production quantities can be conceptualized as shown in Figure1.6. There is some overlapping of the categories as the figure indicates.
Continues -flow process Production quantity
Mass production Batch Production
Product variety
Job production
Figure1.6 Four production types related to quantity and production variation Automation achievements for the four types of production.
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1. Continuous-flow process:
Flow process form beginning to end.
Sensor technology available to measure important process variables.
Use of sophisticated control and optimization strategies. Flow computer-automated plants.
2. Mass production of discrete products:
Automated transfer machines.
Dial indexing machines.
Partially and fully automated assembly lines.
Industrial robots for spot welding, parts handling, machine loading, spray painting, etc.
Automated materials handling systems.
Computer production monitoring.
3. Batch production:
Numerical control (NC), direct numerical control (DNC), computer numerical control (CNC).
Adaptive control machine.
Robots for arc welding, parts handling, etc,
Computer-integrated manufacturing systems.
3. Job shop production:
Numerical control, computer numerical control.
The automated production systems implemented today make use of computers. However the cost of computers has decreased and their capabilities have increased, the economics feasibility of using computers in manufacturing and design has developed. The economics of high productions quantities have tended to Stimulate some of the most productive achievements in automation.
The difference between automation and CAD/CAM Let us consider the mathematical model of the product life cycle. This is a model of the amounts of time expended in designing, planning, and producing a typical product. Let T1 be the time required to produce 1 unit of product. This would be the sum of all the individual process times for each component in the product plus the time to assemble, inspect, and package a single product. Let T2 be the time associated with planning and setting up for each batch of production. T 2 would include the ordering of raw material by the purchasing department, time required in production planning to schedule the batch, setup times for each operation, and so forth. If the batch size is very large, the batch
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time can be spread among many units of production. If the batch is very small, the batch time would become relatively important. Finally, let T3 be the time required for designing the product and for all the other activities that are accomplished once for each different product. These include process planning, cost estimating and pricing, building of special tools and fixtures, and various other functions which must be done to get the product ready for production. Tow additional parameters are needed to complete the model. Let B equal the of batches produced throughout the product’s life cycle. And let Q be the number of units produced in each batch. We assume, for simplicity, that the batch size, Q, will always be the same for each batch. Accordingly, the total number of units produced during the life cycle is BQ. The aggregate time spent on the product thought its life cycle can be defined as TTLC = BQT1 + BT2 + T3 Where TTLC is the total time during the product life cycle. The total can be allocated evenly among the total number of units produced, BQ, to determine the average time spent on each unit of product during its life cycle. Calling this average time TLC, we have TLC = T1 + T2 / Q + T3 / BQ The goal of the both CAD/CAM and automation is to reduce the various time elements in the product life cycle.
Computer Technology
1.4 Introduction
Computers are now in common use in both scientific and commercial field. Present computers are compact in size, reliable, available at low cost with high computing power which makes them to use in many applications. A computer system consists of hardware and software. The hardware includes Central Processing Unit (CPU) , Mass storage devices, input and output device, where as the software includes operating system (OS), modeling software, application software for design analysis and synthesis.
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CPU
Input/Output
Control Unit
Arithmetic and Logic Unit
Memory
FIGURE 2.1. Basic hardware components of a computer There are three basic hardware components of a computer 1. Central Processing Unit. 2. Memory Unit. 3. Input/Output section. The central processing unit consists of two sub sections namely Control Unit, Arithmetic and Logic Unit. The control unit controls and co-ordinates the functions of all the other sections of the computer. It controls the information between CPU and Input/Output devices, and also between other sections of computer. It also commands the other sections of computer to perform their functions. ALU carries out arithmetic and logic manipulation of data such as add, subtract, divide and compare the data according to perform written. The software consists of the programs and instructions stored in memory and in external storage units.
1.5 Central Processing Unit (CPU)
The central processing unit (CPU) regulates the operation of all system components and performs the arithmetic and logical operations on the data. The CPU consists of two operating units: 1. Control Unit 2. Arithmetic-Logic (ALU)
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The control unit coordinates the various operations specified by the program instructions. These operations include receiving data which enter the computer and deciding how and when the data should be processed. The control unit directs the operation of the arithmetic-logic unit. It sends data to the ALU and tells the ALU what functions to perform on the data and where to store the results. The arithmetic and logic unit performs operations such as addition, subtraction, and comparisons. These operations are carried out on data in binary form. The logic section can also be used to alter the sequence in which instructions are executed when certain conditions are indicated and to perform other functions. Both the control unit and the arithmetic-logic unit perform their functions by utilizing register. Computer memory is small memory devices that can receive, hold, and transfer data. Each register consists of binary cells to hold bits of data. The arrangement of register in the computer’s CPU
Address
Program counter
connections
Input data connection
Memory address register
Instruction register
Output data connection
Accumulator
Status register
Arithmetic-logic unit
FIGURE 2.2 Typical arrangement of register in the computer’s CPU
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The functions of register units
Program counter: The program counter holds the location or address of the next instruction. An
instruction word contains two parts: an operator and operand. The operator defines the type of arithmetic or logic operation to be carried out. The operand usually specifies the data on which the operation is to be performed. The program counter is incremented to go on the next instruction word.
Memory address register: This unit is used to hold the address if data held in memory. A computer may have
more then single memory addresses register.
Instruction register: The instruction register is used to hold the instruction for decoding.
Accumulator: An accumulator is a temporary storage register used
during an arithmetic or logic operation.
Status register: Status register are used to indicate the internal condition of the CPU. A status
register is a 1-bit register (called a flags).
Arithmetic-logic unit (ALU): The ALU provides the circuitry required to perform the various calculations and
manipulations of data. A typical configuration of the arithmetic-logic unit is illustrated in FIGURE 2.3. The has two input for data, data outputs, and status outputs used to set the status register or flags.
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Functions inputs
Data input A Data output C Data input B
ALU
Status output FIGURE 2.3
The two inputs, A and B, enter the ALU and the logical or mathematical operation is performed as defined by the function input. The ALU places the result of the operation on A and B in the output, C, for transfer to the accumulator.
1.6 Types of memory
The memory section consists of binary storage units which are organized into bytes. Computer words can typically be 4, 8, 12, 16, 32, or 64 bits long. Each word has an address in the memory. The CPU calls words from memory by referring to the word address. The time required to find the correct address and fetch the contents of that memory location is called access time. The memory section stores all the instruction and data of a program. Thus the CPU must transfer these instructions and data to and from the memory throughout the execution of the program. Types of memory 1. Main Memory (Primary storage). 2. Auxiliary memory (secondary storage). Main Memory (Primary storage) The main memory or primary storage is terms which designate storage areas that are physically a part of the computer and connected directly to the CPU. Primary storage can be divided into three
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Main data storage, such as magnetic core or solid-state memory. Fast access rate, low storage capacity, and very high cost.
Control storage, which commonly contains the micro programs that that assist the CPU circuitry in performing its functions.
Local storage, the high-speed working register used in the arithmetic and logical operations.
Auxiliary memory (secondary storage) Programs and data files are not generally kept in primary storage but are stored on large-capacity auxiliary devices and loaded into main memory as required. Main storage is very expensive, and has a rather limited capacity, so the entire file is stored on an auxiliary device and individual records are accessed as needed by the program. There are two types of secondary storage: 1. Sequential access storage: A sequential access storage unit is distinguished by the fact that to read one particular record in the file, all records preceding it must also be read. 2. Direct access storage: With this storage method, individual records can be located and read immediately without reading any other records. Sequential access storage is suitable for applications that do not require a high level of file activity. Direct access storage is best suited to files where a high level of activity is involved. List of hardware devices used for computer storage technology
Magnetic tape storage is a prime example of sequential access storage technology.
Magnetic drum storage is a random access storage device with high access rates.
Magnetic disk storage is a direct access storage device.
1.7 Input /Output
The purpose of the input/output section of the computer is to provide communication with peripheral devices used with the computer system.
There are inverse function 1. Programs and data are read into the computer. The I/O section must interpret the incoming signals and hold them temporarily until they are placed in main memory or into the CPU.
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The result of the calculations and data processing operation must be transmitted to the appropriate peripheral equipment.
Common peripheral devices used for computer input/output 1. Card Readers: A card reader transfers data form the punched card (data–recording medium) to the computer system. 2. Card punches: A card punch records the output from the computer onto punched cards. Its speed range form 100 to 300 cards per minute. 3. Magnetic tape unit: Magnetic tape unit can be used for program and data storage, and they can be interfaced to the computer as both input and output units. The tape is moved past a read/write head, usually at constant speed. 4. Keyboard input devices: Input devices employ a typewriter like keyboard. It inputs data and programs directly to the computer 5. The keypunch: The keypunch is an electromechanical keyboard device which converts operator keystrokes into machine-readable holes on cards. The cards are then submitted through a card reader to the computer. 6. Punched tape punches: Data from a computer system can be outputted onto punched paper tape. Data from main storage are converted into the appropriate code and punched on the tape as it is fed through the punching unit. 7. Alphanumeric displays: An alphanumeric display consists of a typewriter like keyboard and a display screen, usually a cathode ray tube (CRT). 8. Teleprinters: A teleprinter consists of an electromechanical or electronic typewriter keyboard and a hard-copy printing device. 9. Magnetic ink character recognition (MICR): MICR readers are electronic devices that operate by interpreting the sensed waveforms of the individual magnetic ink characters.
10. Optical character recognition (OCR): In this a mechanical drum is used to rotate documents past an optical scanning station. A light source and lens system can distinguish the patterns of the character. 11. Optical bar-code reader (OBR): An optical bar code reader senses; the configuration of shaded bars of different widths and correlates them to previously defined characters. It can read 50 to 400 characters per second. 12. Line printers: The volume of output is sufficient to justify a high-speed line printer. These units print entire lines at one cycle at rate that may exceed 1000 line per minute. The recent high-
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speed printers combine laser and xerography technologies to achieve print speeds of about 10,000 lines per minute.
1.8 Data Representation
The symbols used by the computer are based on electrical signals that can take one of two states. The smallest unit of data is the bit. It has two possible values 1 or 0. The conversion process between the higher-level characters and the basic units of data used by the computer (the bit). The binary number system The bit, or binary digit, is the basic unit of data which can be interpreted by the digital computer. It uses only two digits 0 and 1. The meaning of successive digits in the binary system is based on the 0
1
2
number 2 raised to successive powers. The first digit is 2 , the second 2 , the third 2 and so forth. Data is represented in a computer system by either the presence or absences of electronic signals in its circuitry. This is called binary or two-state representation of data. Binary and Decimal Number System Equivalence
Binary
Decimal
0000
0
0001
1
0010
2
0011
3
0100
4
0101
5
0110
6
0111
7
1000
8
1001
9
The conversion of binary to decimal systems
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2+
1+
0*2
0
1 * 2 = 4 + 0+ 1 = 5
A minimum of four digits are required in the binary system to represent any single-digit number in the decimal system. By using more then four binary digits, higher valued decimal numbers or other highlevel data can be represented. An alternative way to represent decimal numbers larger than nine involves separate coding of each digit, using four binary digits for each decimal digit. This coding system is known as binary-coded decimal (BCD). Common binary coding schemes Binary-Code Decimal (BCD) system uses a total of 7 bits. The first 6 represent the data itself. The last bit position is used as a parity check. The first 4 bits are called numeric bits. The fifth and sixth bit is called zone bits. The zone bits are both zero when numeric characters are represented. Combination of the zone and numeric bits can be used to code the alphabetic and special characters. EBCDIC The maximum number of character a computer code can represent is 2 raised to the power 6
equal to the number of bits. Thus BCD allows for 2 = 64 distinct characters. EBCDIC (Extended BinaryCoded Decimal Interchange Code) uses an 8-bit code plus a parity bit so that it can define 256 distinct characters. These include upper and lowercase alphabetic, the numerals, many special characters and control characters for I/O devices. ASCII American Standard Code for Information Interchange was developed for telecommunications to simplify machine-to-machine and system-to-system communications. It is a 7-bit code, which provides 128 bits patterns for character representation.
1.9 Computer Programming Language
Data and instructions are communicated to the computer in the form binary words. In executing a program, the computer interprets the configuration of bits as an instruction. The sequences of these binary-coded instructions define the set of calculations and data manipulation by which computer executes the programs. Three levels of computer programming languages: 1. Machine language 2. Assembly language 3. Procedure-oriented (high level) languages Machine and assembly languages
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The language used by the computer is called machine language. It is written in binary, with each instruction containing an operation code and an operand. The operand might be a memory address, a device address, or data. In machine language programming, storage locations are designated for the program and data, and these are used throughout the program to refer to specific data or program steps. Machine language instructions are different for each computer. Programming in machine language is tedious, complicated, and time consuming. To alleviate the difficulties in writing programs in binary, symbolic languages have been developed which substitute English like language mnemonics instructions. Mnemonics are easier to remember than binary, so they help speed up programming process. A language consisting of mnemonics instructions is called an assembly language. Assembly languages are considered to be low-level language. It is converted into machine languages before the computer can execute them. The conversion is carried out by a program called an assembler. High level language High level language consists of English-like statements and traditional mathematical symbols. Each high-level statement is equivalent to many instructions in machine language. The advantage of high-level language is that it is not necessary for the programmer to be familiar with machine language. High- level languages must also be converted to machine code. This is accomplished by a special program called a compiler. The compiler takes the high-level program, and converts it into a lower-level code, such as the machine language. If there are any statements errors messages are printed in a special program listing by the compiler. There are many different high-level languages FORTRAN FORTRAN stands for FORmula TRANslation. It was developed in the mid-1950s for scientists, engineers, and mathematicians.
COBOL COBOL stands for COmmon Business-Oriented Language. It was developed around 1959. It has become a major computer language for business data processing applications. BASIC BASIC stands for Beginner’s All-purpose Instruction Code. It was developed in the 1960s at Dartmouth College to be an east-to-learn language. It was developed as an interactive language.
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APL APL stands for A Programming Language. It was designed for interactive problem solving. A significant feature is that it permits users to define complex algorithms efficiently. The primary data structure in APL is in the form of arrays and an extensive set of array operators is provided. RPG RPG stands for Report Program Generator. It is a language designed for writing programs that produce printed reports as output. It is widely used in business environment, where it updates data files, performs analysis of data and generates documents and reports. PL/I PL/I are a general purpose programming language. It is a flexible language which meets the needs of a wide variety of programmers. PASCAL PASCAL is high-level language developed in the early 1970s. The objectives in developing the language were to facilitate the teaching of computer programming as a discipline of knowledge and to accomplish programming implementations which are reliable and efficient on modern computers.
1.10 Operating the Computer System
Technological improvements have been made computer system much easier to operate and much more efficient. For example, in early system, the CPU was forced to be idle a slow input/output device transferred data to and form main memory. In modern computer systems, input/output and data processing operations can occur simultaneously to make the operation of the computer system more efficient. Techniques which facilitate the operation of the computers system by the user. 1. I/O control system and operating systems 2. Virtual storage 3. Time sharing 4. Distributed processing
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UNIT II
2.1
Introduction
2.2
The Design Process
2.3 2.4
The Application of Computers for Design Creating the Manufacturing Database
2.5 Benefits of Computer-Aided Design 2.6 Introduction (Hardware) 2.7
The Design Workstation
2.8
The Graphics Terminal
2.9
Operator Input Devices
2.10
Plotters and Other Output Devices
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Computer Fundamentals of CAD 2.1
Introduction
The CAD SYSTME DEFINED Computer –aided design involves any type of design activity which makes use of the computer to develop, analyzer, or modify an engineering design. Fundamental reasons for implementing a CAD 1. To increase the productivity of the designer. 2. To improve the quality of design. 3. To improve communications. 4. To create a data base for manufacturing.
The Design Process The process of designing consists of six steps or phases: 1. Recognition of need 2. Definition of problem 3. Synthesis 4. Analysis and optimization 5. Evaluation 6. Presentation
Recognition of need involves the realization by someone that a problem exists for which
some corrective action should be taken in a current machine.
Definition of the problem involves thorough specifications of the item to be designed.
Synthesis and analysis are closely related and highly iterative in the design process. The
process the repeated until the design has been optimized within the constraints imposed on the designer.
Evaluation design has been accomplished on drawing boards, with the design
documented in the form of detailed engineering drawing. Fig.2.1 shows the basic steps in the design process.
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Fig.2.1 Basic Steps in the Design Process
The Application of Computers for Design The various design-related tasks which are performed by a modern compute-aided design system and can be grouped into four functional areas:
1. Geometric modeling 2. Engineering analysis 3. Design review and evaluation 4. Automated drafting Design process, illustrated in Fig. 2.2.
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Fig. 2.2 Application of Computers to the Design Process
Geometric modeling Geometric modeling is concerned with the computer compatible mathematical description of the geometry of an object. The basic methods for representing the object in geometric modeling are wireframe.
Engineering analysis The analysis may involve stress-strain calculations, heat transfer computations, or the use of differential equations to describe the dynamic behavior of the system being designed. Two examples are i. Analysis of mass properties ii. Finite-element analysis Design review and evaluation A procedure called layering is often helpful in design review. This procedure can be preformed in stage to check each successive step in the processing of the part. Another related procedure for design review is interference checking. One of the most interesting evaluation features available on some computer aided design systems is kinematics Automated drafting It involves the creation of hard-copy engineering drawing directly from the CAD data base.
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Parts classification and coding It involves the grouping of similar part designs into classes, and relating the similarities by means of a coding scheme.
2.4
Creating the Manufacturing Database The important reason for using a CAD system is that it used to develop the database need for
manufacture the product. The conventional manufacturing is used in industry, engineering drawings were prepared by design draftsmen and then used by develop the process plan. The activities involved in designing the product were separated from the activities associated with process of planning. The manufacturing database is an integrated CAD/CAM database. It includes all the data on the product generated during design (geometry data, material specification, parts lists and bill of materials, etc.) as well as additional data require for manufacturing, much of which is based on the product design (Fig. 2.3). CAD
CAM
Tool and fixture design
Geometric Modeling
Engineerin g analysis
Interactiv e graphics
Data base
Numerical control Programmin g
Production
Computer –aided process planning
Design review and evaluation
Production
Automated drafting
Fig 2.3 Desirable Relationship of Cad/Cam Database to Cad And Cam planning 2.5 Benefits of Computer-Aided Design
and scheduling
There are many benefits of computer-aided design, only some of which can be easily measured. Some benefits are intangible, reflected in improved work quality, more pertinent and usable information and improved control, all of which are difficult to quantify. Other benefits are tangible, but the saving from them shows far downstream in the production process. The benefits of CAD: 1. Productivity improvement in design
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2. Design Analysis 3. Fewer design errors 4. Greater accuracy in design calculations 5. Standardization of design, drafting, and documentation procedures 6. Drawings are more understandable 7. Improve procedures for engineering 8. Benefits in manufacturing
Productivity improvement in design: The productivity improvement in CAD as compared to traditional design process in dependent on:
Complexity of the engineering drawing
Level of detail required in the drawing
Degree of repetitiveness in the designed parts
Extensiveness of library of commonly used entities
Design analysis: The design analysis helps to consolidate the design process into a more logical work pattern. Rather than having a back-and-forth exchange between design and analysis groups, the same person can perform the analysis while remaining at the CAD workstation. This helps to improve the concentration of designers, since they are interacting with their designs in real-time sense. This helps designs can be created which are closer to optimum and time saving. Its finds way from the designer’s drawing board to design analyst’s queue and back again. Fewer design errors: The Cad system provides an intrinsic capability for avoiding design, drafting, and documentation errors. In manual compilation data entry, transposition, and extension errors are occurred and it eliminated virtually. Errors are further avoided by perform time-consuming repetitive duties such as multiple symbols placement, and sorts by area and by like item, at high speeds with consistent and accurate result. Greater accuracy in design calculations: The accuracy delivered by interactive CAD systems is three-dimensional curved space designs provide by manual calculation methods that is no real comparison. Computer-based accuracy pays off in many ways,
Parts are labeled by the same recognizable nomenclature and number throughout all drawings.
A change entered on single item can appear throughout the entire documentation package.
Standardization of design, drafting, and documentation procedures: The single database and operating system is common to all workstation in the CAD system. Consequently, the system provides natural standards for design/drafting procedures. With interactive CAD, drawings are
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“standardized” are drawn .
no confusion in proper procedure because the entire format is “built into” the system program.
Drawings are more understandable: In general, visualization of drawing related directly to projection used. Orthographic view is less comprehensible than the isometric. Finally, animation of images on CRT screen allows for even greater visualization capability. The various relationships are illustrated in Fig. 2.4.
Orthographic
Oblique
isometric
perspective
Fig. 2.4 Improvement in Visualization of Images of Various Drawing Types and Complete Graphics Features.
Improve procedures for engineering: Control and implementation of engineering changes is significantly improved with CAD. Original drawings and reports are in database of CAD system. This makes them more accessible than document kept drawing Vault and quickly checks the new information. Since data storage is extremely compact, historical information from previous drawings can be easily retained in the system’s database, for easy comparison with current design and drafting needs. Benefits in manufacturing:
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The following benefits are derived largely from the CAD/CAM database, whose initial frame work is established during CAD.
Numerical control part programming
Tool and fixture design for manufacturing
Computer aided process planning
Assembly lists (generated by CAD) for production
Computer-aided inspection
Robotics planning
Group technology
Shorter manufacturing lead times through better scheduling
Hardware in Computer-Aided Design
2.6 Introduction The hardware is restricted to CAD system that utilizes interactive computer graphics. Typically, a stand-alone CAD system would include the following hard ware components: 1. One or more design workstations. These would consists of:
A graphics terminal
Operator input devices
2. One or more plotters and other output devices 3. Central processing unit (CPU) 4. Secondary storage These hardware components would be arranged in as given in Fig.2.5. The various hardware components and the alternatives and options can be obtained in each category.
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Secondary storage
Graphics terminal
CPU
Input devices
Output plotters, etc
Fig.2.5 Configuration of Hardware Components in a Stand-Alone Cad System
2.7
The Design Workstation It represents the significant in determining how convenient and efficient it is for a designer to use
the CAD system and its function s are:
It must interface with the central processing unit.
It must generate a steady graphic image for user.
It must provide the digital descriptions for the graphic image.
It must translate computer commands into operating functions
It must facilitate communication between the user and system.
The use of interactive graphics has been found to be the best approach to accomplish these functions. Atypical interactive graphics workstation would consist of the following hardware components: Hardware Components
2.8
A graphics terminal
Operator input devices
The Graphics Terminal
The current technology in interactive computer graphics terminals are: 1. Image generation in computer graphics 2. Graphics terminals for computer-aided design
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3. Color and animation in computer graphics
Image generation in computer graphics: Nearly all computers graphics terminals available today use the cathode ray tube (CRT) as the display device (Fig 2.6). A heated cathode emits a high-speed electron beam onto a phosphor-coated glass screen. The electrons energize the phosphor coating, causing it to glow at the points where the beam makes contact. By focusing the electron beam, changing its intensity, and controlling its point of contact against the phosphor coating through the use of a deflector system, the beam can be made to generate a picture on CRT screen.
Fig 2.6 Cathode Ray Tube
The two basic techniques used in current computer graphics terminals for generating the image on the CRT screen are: ďƒ˜
Stroke writing
ďƒ˜
Raster scan
Stroke writing: Other names for the stroke-writing techniques include line drawing, random position, vector writing, and directed beam. It moves from one point on the screen to the next, where each point is defined by its x and y coordinates. The process is portrayed in Fig. 2.7.
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Fig 2.7 Stroke Writing For Generating Images in Computer Graphics
Raster scan: The other name for raster scan technique includes digital TV and scan graphics (Fig. 2.8). Here the viewing screen is divided into larger number of discrete phosphor picture elements called pixels. The number of separate pixels are typically range from 256×256 (a total over 65,000) to 1024×1024 ( a total over 1,000,000).Color screen provides for them pixels to have different brightness.
Fig 2.8 Raster Scan Approach For Generating Images Graphics
Graphics terminal for computer-aided design It includes the type of phosphor coating on the screen, whether color is required, the pixel density, and the mount of computer memory available to generate the picture. The three types are:
Directed-beam refresh
Direct-view storage tube(DVST)
Raster scan(digital TV)
Color and animation in computer graphics The capabilities for multicolored images and animated pictures in computer graphics are largely dependent on the hardware considerations and the relative capabilities for the three types of commercial graphics terminals for color and animation. Advantages:
Finite-element analysis results displayed in color shows the improved clarity of information provided by color in displaying the results in of a finite elements in analysis.
Wire –frame model of jet engine with different sections of the assembly displayed in various colors.
Color display of industrial plant model for industrial building, showing packing lot, landscaping and etc.
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Solid modeling assembled for water cooled power frame and display various color.
Operator Input Devices
Operator input devices are provided at the graphics to facilitate convenient communication between the user and system. Workstations generally have several types of input devices to allow the operator to select the various preprogrammed input functions. These functions permit the operator to create or to modify an image on CRT screen or to enter alphanumeric data into system and it results complete part on the CRT screen as well as a complete description of the part in the CAD database. These devices are can be divided into three general categories: 1. Cursor control devices 2. Digitizers 3. Alphanumeric and other keyboard terminals The cursor control devices and digitizer are both used for graphics interaction with the system. Keyboard terminals are used as input devices for commands and numerical data. There are two basic types of graphical interaction accomplish by means of cursor control and digitizing:
Creating and positioning new items on the CRT screen
Pointing at or otherwise identifying locations on the screen, usually associated with existing images.
Cursor Control The cursor normally takes the form of a bright spot on the CRT screen that indicates where lettering or drawing will occur. The computer is capable of reading the current position of the cursor. Varity of cursor control devices
Thumbwheels
Direction keys on a keyboard terminal
Joysticks
Trackball
Light pen
Digitizers The digitizer is an operator input devices which consists of a large, smooth board and an electronic tracking device which can be moved over the surface to follow existing lines. It is
common
technique in CAD system for taking x, y coordinates from a paper drawing. Keyboard terminal Several forms of keyboard terminals are available as CAD input devices. The most familiar type is the alphanumeric terminal. The alphanumeric terminal may be CRT or hard-copy terminal. The alphanumeric terminal is used to enter commands, functions, and supplemental data to the CAD system. This information is displayed for verification on the CRT or typed on paper. The system also communicates back to the user in a similar manner.
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Plotters and Other Output Devices
There is various output devices used in conjunction with a computer-aided design system. These output devices include:
Pen plotters
Hard-copy units
Electrostatic plotters
Computer-output-to-microfilm (COM) units
Pen plotters The accuracy and quality of the hard-copy plot produced by a pen plotter is considerably greater then the apparent accuracy and quality of the corresponding image on the CRT screen. Two types of pen plotters 1. Drum plotters 2. Flat-bed plotters Hard-Copy Unit A hard-copy unit is a machine that can make copies from the same image data displayed on the CRT screen. The image on the screen can be duplicated in a matter of seconds. The copies can be used as records of intermediate steps in the design process or when rough hard copies of the screen are need quickly. The hard copies are not suitable for final copies.
Electrostatic plotters The electrostatic plotter is almost as fast and accurate image on the CRT screen. The limitation is that the data must be in the raster format. If the data are not in raster format, some type of conversion is required to change them into required format. Advantage is which is shared with the drum-type pen plotter is that the length of the paper is virtually unlimited. Computer-output-to-microfilm (COM)units COM units reproduce the drawings on microfilm rather then as full-size engineering drawings. It is expensive equipment. One advantage is storage capacity and speed. Disadvantage of the COM process are that the user cannot write notes on the microfilm as is possible with a paper copy.
2.11
Secondary Storage Secondary storage devices are magnetic disk and magnetic tape. The purpose in using
secondary storage is to reduce the cost of main computer memory. The secondary storage con be used for engineering drawing files, CAD software which can be transferred to main memory as needed, and temporary files for CPU output which will be downloaded to individual graphics terminals, plotters, or other output devices.
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Disk has the advantage of fairly rapid retrieval, owing to their random access configuration. Because of this feature, the CPU can load and swap programs and files between primary and secondary memory as needed. Magnetic tape would be used for storing programs and files which are less frequently used by the system. Storage on magnetic tape is less expensive then on disks. It would be suitable for disk backup, permanent archival files, and data transfer to output devices or other computers.
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UNIT III
3.1 Raster Scan Graphics
3.2 Co-ordinate Systems
3.3 Database Structure for Graphic Modeling 3.4 Transformation of Geometry 3.5 3D Transformation
3.6 Mathematics of Projection
3.7
Clipping
3.8
Hidden Surface Removal
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Computer Graphics
3.1 Raster Scan Graphics
This involves the conversion of the vectorial information of the drawing into its equivalent raster format such that the frame buffer can be filled with that information. This process is termed as rasterisation and involves one of the most important and basic components of a graphic software unit. The two most common forms of geometric elements present in a graphics display are straight lines and circles. Converting a line vector into its equivalent pixel position is an arduous task involving a large amount of computation. Each drawing consists of a large number of vectors to be displayed.
3.1.1
DDA Algorithm
DDA or Digital Differential Analyser is one of the first algorithms developed for rasterizing the vectorial information. The equation of a straight line is given by Eq. 3.1 Y = mX + C
(3.1)
Using this equation for direct computing of the pixel positions involves a large amount of computational effort. Hence it is necessary to simplify the procedure of calculating the individual pixel positions by a simple algorithm.
For this purpose consider drawing a line on the screen as shown in Fig.3.1, form (x1, y1) to (x2, y2), then
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y
y2 y1
x1
x x2
Fig. 3.1 A Straight Line Drawing
y2 - y1 m= x1 - x2
(3.2)
and c = y1 - m x1
(3.3)
The line drawing method would have to make use of the above three equations in order to develop a suitable algorithm.
Eq. 3.1 for small increments can also be written as ∆y = m∆ x
(3.4)
By taking a small step for ∆x, ∆y can be computed using Eq. 3.4. However, the computations become unnecessarily long for arbitrary values of ∆x. Let us now workout a procedure to simplify the calculation method. Let us consider a case of line drawing where m > 1. Choose an increment for ∆x as unit pixel. Hence ∆x = 1. Then from Eq. 3.4. Yi+1 = Yi + m
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(3.5)
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The subscript i takes the values starting from1 for the starting point till the end point is reached. Hence the pixel positions for completely drawing the line on the display screen. This is called DDA algorithm. If m ≤ 1, then the roles of x and y would have to be reversed. Choose ∆y = 1
(3.6)
Then from Eq. 3.4, we get xi+1 = xi + 1 ∕ m
(3.7)
The following is the flow chart showing the complete process for the implementation of the above procedure.
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Calculate dx = x2 - x1 dy = y2 – y1 Yes
If |dx| > |dy| No
ST = | dy |
dx = dx / ST dy = dy / ST
X = xi Y = yi
Set pixel at X, Y No Yes
X = X + dx Y = Y + dy
End loop?
Stop
Fig. 3.2 Chart for Line Drawing Calculation Procedure
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3.1.2 Bresenham’s Algorithm Bresenham’s method is an improvement over DDA since it completely eliminates the floating point arithmetic except for the initial computations. All other computations are fully integer arithmetic and hence are more efficient for raster conversion. The basic argument for positioning the pixel here is the amount of deviation by which the calculated position is from the actual position obtained by the line equation in terms of d1 and d2 shown in Fig. 3.3.
Fig. 3.3 the position of individual pixel for calculation using Bresenham procedure
Let the current position be (Xi, Yi) at the ith position as shown in Fig. 3.3. Each of the circles in Fig. 3.3 represents the pixels in the successive position.
Then Xi+1 = Xi + 1
(3.8)
Also Yi = mXi + c
(3.9)
and Y = m (Xi + 1) + c
(3.10)
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These are shown in Fig. 3.3. Let d1 and d2 be two parameters, which indicate where the next pixel is to be located. If d1 is greater then d2 , then the y pixel is to be located at the +1 position else, it remains at the same position as previous location. d1 = Y -Yi = m (Xi + 1) + c - Yi d2 = Yi+1 – Y = Yi+1 - m (Xi + 1) – c
(3.11) (3.12)
d1 - d2 = 2 m (Xi + 1) - 2 Yi + 2c – 1
(3.13)
Equation 3.13 still contains more computations and hence we would now define another parameter p which would define the relative position in terms of d1 - d2. Pi = (d1 - d2) ∆X
(3.14)
Pi = 2∆Y Xi + 2∆X Yi + b
(3.15)
where b = 2∆Y + 2c ∆X -∆Y Similarly we can write Pi+1 = 2∆Y (Xi + 1) - 2∆X Yi+1
(3.16)
Taking the difference of two successive parameters, we can eliminate the constant terms from Eq. 3.16, to get Eq. 3.17. Pi+1 - Pi = 2∆Y - 2∆X (Yi+1 – Yi) Pi+1 = Pi + 2∆Y - 2∆X (Yi+1 – Yi)
(3.17) (3.18)
The same can also be written as Pi+1 = Pi + 2∆Y when Yi+1 + Yi Pi+1 = Pi + 2∆Y - 2∆X
(3.19)
when Yi+1 + Yi + 1
(3.20)
From the start point (x1, y1) y1 = m x1 + c c = y1 - ∆X
x1
∆Y Substituting this in Eq. 3,15 and simplifying, we get P1 = 2∆Y - 2∆X
(3.21)
Hence from Eq. 3.17, when Pi is negative, then the next pixel location remains the same as precious one and Eq. 3.19 becomes valid. Otherwise, Eq. 3.20 becomes valid.
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Using these equations it is now possible to develop the algorithm for drawing the line on the screen as shown in the flowchart (Fig. 3.4). The procedure just described is for the case when m > 1. The procedure can be repeated for the case when m < 1 by interchanging X and Y similar to the DDA algorithm.
Calculate dx = x2 - x1 dx= y2 â&#x20AC;&#x201C; y1 C1 = 2dy C2 = 2(dy - dx)
x = x1 y = y1 p1 = 2dy - dx
Put a pixel at (x1, y1)
x = x +1
No
Yes
If Pi < 0
No
P(i+1) = P(i) + C2 Y(i+1) = Y(i) + 1
P(i+1) = P(i) + C1 Y(i+1) = Y(i) Yes
End of loop? Fig. 3.4 Flow Chart Line Drawing Calculation Using Bresenham Procedure
End
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3.1.3 Antialiasing Lines The rasterisation algorithms will generate the pixel points by rounding off to the nearest integer. As a result the inclined lines have the jagged effect often called the staircase effects as shown in Fig. 3.5. The effect will be more pronounced in the case of the lines with small angles as also shown in Fig. 3.5.
Fig. 3.5 The Staircase Effect Pixel When Drawing Inclined Lines It is possible to improve the appearance by increasing the screen resolution as shown in Fig. 3.6.
Fig. 3.6 the staircase effect of pixel when drawing inclined lines decreases with increased resolution
The effect can be decreased by antialiasing based on the sampling theory. Each of the geometric elements has a certain thickness compared to the size of the pixel. As can be seen in Fig. 3.7, the finite line thickness is overlapping the pixel with different areas. In this method, the intensity of the pixel is made proportional to the area of the pixel covered by the line thickness. Though this improves the appearance of the line, but computationally is more intensive.
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Fig. 3.7 Antialiasing of Pixel Proportional to the Portion of Pixel Occupied by the Line Raster display of lines utilizes unequal number of pixels to represent lines depending upon their orientation in space. For example from Fig. 3.8, it can be seen that the same number of pixels are representing a small length when it is horizontal or vertical while the length of an inclined line is more for the same number of pixels. This makes the horizontal or vertical lines more bright compared to the inclined lines. This can also be taken care of by making the brightness of the pixels different depending upon the inclination of the line.
Fig. 3.8 unequal number of lines displayed with the same number of pixel 3.2 Co-ordinate Systems Co-ordinate system is used for defining the geometry of the parts. In order to specify the geometry of a given solid, it is necessary to use a variety of co-ordinate systems.
3.2.1 World Co-ordinate system (WCS)
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This refers to the actual co-ordinate system used as master for the component. It may also be called as model co-ordinate system. Figure 3.9 shows typical components, which needs to be modeled.
Fig. 3.9 A Typical Component to Be Modeled Figure 3.10 shows the component with its associated world co-ordinate system X, Y and Z.
Fig. 3.10 A Typical Component with its Associated WCS The user will have the flexibility of inputting the data in other co-ordinate systems as well such as polar co-ordinates or spherical co-ordinates. The software will actually convert this information into the certain system before it stores the data. 3.2.2 User Co-ordinate system WCS is the default co-ordinate system, when the user starts modeling. Sometimes it becomes difficult to define certain geometries if they are to be defined from the WCS. These co-ordinates systems are termed as user co-ordinates systems (UCS) or working co-ordinates systems. 3.2.3 Display Co-ordinate
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This refers to the actual co-ordinates or screen co-ordinates system to be used for displaying the image on the screen. The actual screen co-ordinates relate to the pixels whether the actual values of the screen or the virtual image that can be displayed to help in the image display. The virtual size will be larger than the actual pixels of the screen resolution. 3.2.4 View Generation The display screen is two-dimension. The screen is therefore divided into a number of views ports wherein the various views are presented. For example the most common views required for representing the component details fully are the front, top and right side views as shown in Fig. 3.11
Fig. 3.11 A Typical Component Showing the Orthogonal View Planes
The views generated in the process along with their co-ordinates systems as referred to the WCS are shown in Fig. 3.12.
Fig. 3.12 Generated Orthogonal Views of the Components Shown in Fig.3.11
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3.3 Database Structure for Graphic Modeling
The major functions of a database are to manipulate the data
onscreen, such as zooming
and panning; to interact with the user, essentially for the purpose of editing functions like trimming, filleting, stretching, etc.; to evaluate the properties like areas, volumes, inertias, etc. to provide additional information like manufacturing specifications. Graphic data bases may contain graphical information such as point co-ordinates, alphanumerical information as manufacturing requirements or some procedural type wherein the concerned data is to be fitted in a certain form. The information contain in the database are interdependent and uses pointers for accessing data in the various interconnected files. The data in a drawing file is of two types. 1. Organisational data
Identification number
Drawing number
Design origin and status of changes
Current status
Designer name’
Date of design
Scale
Type of projections
Company
2. Technical data
Geometry
Dimensions
Tolerances
Surface finishes
Material specifications or reference
Manufacturing procedures
Inspections procedures
The graphic data can be stored in sequential form. In sequential form the disadvantage is that whenever one has to access the data, the retrieval is not simple. So, the geometric modelers have to opt for combinations of random and sequential form. In random access files all the files are linked by pointers. The advantage by using random access files reduces the data storage.
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Some portion of the drawing database is stored in RAM. This increases the response time of the system for modifications. To get an idea how the data for a component may be stored, refer to Fig. 3.13.
Fig. 3.13 Data Structure For Geometric Models The solid is first broken into edges, which are further broken into surfaces and the vertices for completely defining the object. A face meets another face to form an edge. Edge may be considered as curves such as lines and arcs. Edges meet the points (vertices) at the end. When data is organized in a database it is required to ensure the basic integrity of the data in terms of eliminating redundancy and security problems. The most common form in which the graphical database is organized is in terms of number of tables that are interlinked by relations. This form of database is termed as relational database and is shown in Fig.3.14. Solid body
Face list
Edges
Vertices
X
Fig 3.14 Relational Data Structure for Geometric Models
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3.4 Transformation of Geometry The transformations actually convert the geometry from one co-ordinate system to the other. The main types of pure transformations with which we are likely to come across are the following.
Translation
Reflection or Mirror
Scaling
Rotation
These transformations are symbolically shown in Fig. 3.15.
Fig 3.15 Some of the Possible Geometric Transformation
Three dimensions can be represented by its co-ordinates (X, Y, Z). The sane can also be represented by a vector starting from the origin of the co-ordinates system. P*
= [ x , y, Z ]
(3.22)
[P] =
x y z
(3.23)
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3.4.1 Translation It is the most common and easily understood transformation in CAD. This moves a geometric entity in space in such a way that the new entity is parallel at all points to the old entity. A representation is shown in Fig. 3.16 for an object.
Fig 3.16 Translation of a Group of Points Let us now consider a point on the objects, represented by P which is translated along X and Y axes by dX and dY to a new position P*. The new co-ordinates after transformation are given by following equations. P* = [x* , y*
]
(3.24)
x* = x + dX
(3.25)
y* = y + dy
(3.26)
Putting Eqs. 3.25 and 3.26 back into Eq. 3.24, we can write [P*] =
x*
=
Y*
x + dX
(3.27)
y + dy
This can also be written in matrix form as follows. [P*] = x* Y*
= x + dX = y + dy y
x
+ dY
dX
(3.28)
This is normally the operation used in the CAD systems as MOVE command.
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3.4.2 Scaling Scaling is the transformation applied to change the scale of an entity. As shown in Fig. 3.17, this alters the size of the entity by the scaling factor applied. For example, in the Fig. 3.17, to achieve scaling, the original co-ordinates would be multiplied uniformly by the scaling factor. P* = [X*, Y*] = [Sx × X, Sy × dY]
(3.29)
Fig 3.17 Scaling of a Plane Figure
This equation can also be represented in a matrix form as follows. [P*] =
0
Sx 0 [P*]
=
X
Sy
(3.30)
Y
[ TS ] . [ P ]
(3.31)
[ TS ] =
Sx 0
0 Sy
(3.32)
There is a possibility to have differential scaling when S x ≠ Sy. Normally in the CAD system uniform scaling is allowed for object manipulation. 3.4.3 Reflection or Mirror Reflection or mirror is a transformation, which allows a copy of the object to be displayed while the object is reflected about a line or a plane. The transformation required in this case is
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that the axes co-ordinates will get negated depending upon the reflection required. For examples from Fig. 3.18, the new P* = [X*, Y*] = [X, -Y]
(3.33)
This can be given in a matrix form as [P*] =
1 0
0 -1
x (3.34)
y
[P*] = [ Tm ] . [ P ] Where [ Tm ] =
1 0
0 -1
(3.35)
Thus the general transformation matrix will be [M] =
Âą1 0
0 Âą1
(3.36)
Hence, -1 in the first positions refers to the reflection about Y axis where all the X coordinate values get negated. When the second term becomes -1 the reflection will be about the X axis with all Y co-ordinate value getting reversed. Both the value are -1 for reflection about X and Y axes.
Fig 3.18 Example for reflection Transformation
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3.4.4 Rotation Rotation is another important geometric transformation. The final position and orientation of a geometric entity is decided by the angle of rotation (Ɵ) and the base point which the rotation is to be done. Consider a point P located in XY plane, being rotated in the counter clockwise direction to the new position, P* by an angle Ɵ as shown in Fig. 3.19.
Fig 3.19 Rotation Transformation Then the new position P* is given by P* = [ x* , y* ] The original position is specified by x = r cos α y = r sin α The new position P* is specified by x* = r cos( α + Ɵ ) = r cos Ɵ cos α – r sin Ɵ sin α = x cos Ɵ – y sin Ɵ Y* = r sin( α + Ɵ ) = r sin Ɵ cos α + r sin Ɵ sin α = x sin Ɵ + y cos Ɵ
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This can be written in a matrix form as
[ P* ] =
=
x* y*
[ P* ] = [ TR ] . [ P ]
cosƟ
–sinƟ
sinƟ
cosƟ
x
(3.37)
y
Where [ TR ] =
cosƟ
–sinƟ
sinƟ
cosƟ
(3.38)
The above is the transformation matrix for rotation which can be applied in any plane in the following way.
y*
=
z*
cosƟ
–sinƟ
sinƟ
cosƟ
=
z* x*
cosƟ
–sinƟ
sinƟ
cosƟ
y
(3.39)
z (3.40)
z x
3.5 3D Transformation The 2D transformation can be extended to 3D by adding the Z axis parameters. The transformation matrix will now be 4 4. The following are the transformation matrices to be used for this purpose.
Translation
x* y*
=
1
0
0
dX
x
0
1
0
dY
y
z*
0
0
1
dZ
z
1
0
0
0
1
1
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(3.41)
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Scaling
x*
SX
0
0
0
x
0
Sy
0
0
y
z*
0
0
Sz
0
z
1
0
0
0
1
1
y*
=
(3.42)
Reflection
x* y*
=
±1
0
0
0
x
0
±1
0
0
y
z*
0
0
±1
0
z
1
0
0
0
1
1
(3.43)
3.6 Mathematics of Projection In the realm of drawing, there are a number of methods available for depicting the details of a given object. It is possible to have a Variety of representation from the same object depending upon the nature of the projections. Orthographic Projection The most common form of projection used in engineering drawings is the orthographic projection. This means that the projection lines or projectors are all perpendicular to the projection plane. It includes a total of six projection planes in any direction required for complete description. Isometric Projection An isometric projection is obtained b aligning the projection plane so that it intersects each co-ordinate axis in which the object is defined at the same distance from the origin. All the three principal axes are foreshortened equally in an isometric projection so that relative proportions are maintained while showing the pictorial view.
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Clipping Clipping is a vary important element for displaying graphical images. This helps in
discarding a part of the geometry outside the viewing window, such that all transformation that are to be used out for zooming and panning of the image on the screen are applied only on the necessary geometry. This improves the response of the system. For example in Fig. 3.20 the image shown inside the window with dark lines is the only part that will be visible. All the geometry outside this window will be clipped.
Fig 3.20 Reflection Transformation about an Arbitrary Line
Cohen Sutherland Clipping Algorithm in 2D In this method all the lines are classified to see if they are in, out or partially in the window by doing an edge test. The end points of the line are classified as to where they are with reference to the window by means of a 4 digit binary code as shown in Fig. 3.21.
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Fig 3.21 The 4 Digit Coding Of The Line End Points For Clipping
The code is termed as TBRL. The code is identified as follows. T = 1 if point is above top of window = 0 otherwise B = 1 if point is above below of window = 0 otherwise R = 1 if point is above right of window = 0 otherwise L = 1 if point is above left of window = 0 otherwise
The full 4 digit codes of the line end points with reference to the window are shown Fig. 3.21.
Having assigned the 4 digit code, the system first examines if the line is fully in or out of the window by the following conditions.
The line is inside the window if both the end points are equal to “0000”.
The line is outside the window if both the end points are not equal to “0000”.
For those lines which are partly inside the window, they are split at the window edge and discard the line segment outside the window.
As can be seen from Fig. 3.22, the clipping procedure described above procedures a result, which can mean more then one geometry. This ambiguity can be removed by the use of polygon clipping algorithm developed by Sutherland and Hodgman.
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Fig 3.22 Identical Line Clipping Of Two Different Geometric
Sutherland and Hodgman Polygon Clipping Algorithm in 2D The basic idea used in polygon clipping is that an n sided polygon is represented by n vertices. On each of the polygon two tests are conducted. If the line intersects the window edge, the precursor point is added to the output list. If the next vertex is outside the window, it is discarded or else added to the output list. This process is repeated for all the edges of the polygon. The resulting output is an m sided polygon, which can be displayed as shown in Fig. 3.23.
Fig 3.23 clipping product for different geometric by polygon clipping
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Advantage The advantage of this algorithm is that it can be used for clipping a window that need not be a rectangle. Further, this can be easily extended to 3D. 3.8
Hidden Surface Removal Removing hidden lines and surfaces greatly improves the visualization of objects. There
are many approaches to the hidden surface removal and it is difficult to cover all of them here. Hence some basic approaches are highlighted here while the details can be seen in other specified literature. The following hidden surface algorithms are discussed here: 1. Back-face removal 2. Z-buffer ( depth buffer ) Back-face removal The basic concept used in this algorithm is that only those faces that are facing the camera are visible. The normal from a polygon face indicates the direction in which it is facing. Thus a face can be seen if some component of the normal N (Fig. 3.24) is along the direction of the projector P. this method allows to identify the invisible faces for individual objects only.
Fig 3.24 Back-Face Removal Using the Face Normal and Projecting Ray
Z-buffer (depth buffer)
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This method utilizes the principle that for each of the pixel location, only that point which has the smallest Z-depth, is displayed For this purpose this constructs two arrays. Z (x, y) the dynamic nearest Z-depth of any polygon face currently examined corresponding to the (x, y) pixel co-ordinates. I (x, y) the final output color intensity for each pixel which gets modified as the algorithm scans through all the faces that have been retained after the back-face removal algorithm.
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UNIT IV
4.1
Requirements of Geometric Modeling
4.2
Geometric Models
4.3
Geometric Construction Methods
4.4
Other Modeling Methods
4.5
Curve Representation
4.6
Desirable Modeling Facilities
4.7
Rapid Prototyping (RP)
4.8
Standardization in Graphics
4.9
Graphical Kernel System (GKS)
4.10
Other Graphic Standards
4.11
Exchange of Modeling Data
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Geometric Modeling 4.1
Requirements of Geometric Modeling The geometric model generated should be as clear and comprehensive as possible so
that the other modules of the modeling and manufacturing system are able to use this information in the most optimal way. The functions that are expected of geometric modeling are the following:
Design analysis
Drafting
Manufacturing
Production engineering
Inspection and quality control
The modeling system should be able to describe the parts, assemblies, raw material used and the manufacturing requirements. From geometric models, it would possible to obtain manufacturing, assembly and inspection plans and command data for numerically controlled machine tools.
4.2
Geometric Models
The geometric models can be categorized into two types. 1. Two Dimensional 2. Three Dimensional Two dimensional model, utility is limited because of their inherent difficult in representing complex objects. Their utility lies in many of the low end drafting packages or in representing essentially two dimensional manufacturing applications such as simple turning jobs, sheet metal punching or flame or laser cutting. The three dimensional geometric modeling has the ability to provide ass the information required for manufacturing applications. There are a number of ways in which the three dimensional representing can be arrived at. The three principal classifications can be 1. The line model 2. The surface model 3. The solid or volume model These are represented in Fig. 4.1.
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Fig. 4.13D Geometric Representation Techniques The line model is the simplest and is used in low-cost designing systems. This is also called wire frame representation. The surface model is constructed essentially from surfaces such as planes, rotated curved surfaces and even very complex surface. These are often capable of clearly representing the solid from the manufacturing point of view. The solid or volume model consisting of the complete description of the solid in a certain form is the most ideal representation, as all the information required for manufacturing can be obtained with this technique.
4.3
Geometric Construction Methods The geometry construction method makes use of the normal information available at the
product design stage and also be as simple as possible in construction. In addition, the current day interactive interfaces provided between the software and the user minimize the hassles associated with the geometry input 3d Modeling Methods
4.3.1
ď&#x201A;ˇ
Linear extrusion or translation sweep
ď&#x201A;ˇ
Rotational sweep
Sweep or Extrusion
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In linear extrusion, initially a two dimensional surface is generated and than swept along a straight line thus generating three dimensions. It is possible to repeat the same technique for generating reasonably complex geometry. The sweep direction can be any three dimensional space curves and need not be a straight line. Advantage of sweep is that in view of the varied facilities available normally in the two dimensional modelers, they can also be utilized for modeling the three dimensional solids. Another type of construction technique is the rotational sweep, which can be utilized only for axis-symmetric jobs. This type is used for all axis-symmetric such as bottles used for various applications. 4.3.2
Solid Modeling The best method of three dimensional solid constructions is the solid modeling technique,
often called the primitive instancing or constructive solid geometry (CSG). Some typical primitives utilized in the solid modelers are shown in Fig. 4.2. Though these are the analytical solid primitives generally used, the modeling will not be restricted only to these.
Fig. 4.2 various solid modeling primitives The complex objects are created by adding or subtracting the primitives. For combining the primitives to form the complex solid, the basic set operators, also called Boolean operators are used. Types of Boolean operators
Union
Intersection and
Difference
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The effect of these operators on the primitives is shown in Fig. 4.3 for the simple case of a block and cylinder shown in their 2D relationship.
Fig. 4.3 The Boolean Operator And Their Effects On Model Construction
4.3.3
Free Form Surfaces There may be surfaces, which cannot be defined by any of the analytical techniques
available. A few examples are the car bodies, ship hulls, some die cavity surfaces and decorative surfaces styled for aesthetics. The only way these surfaces can be modeled is through a series of control points and other boundary conditions, which specify the nature of the surface desired. Some of the types of surfaces that are normally employed in CAD system are ruled surfaces, Bezier surface, B-spline surface and NURBS. 4.3.4
Skinning or Lofting In this method, a number of 2D arbitrary or regular profiles are placed along an arbitrary
3D space curve and then skinning is done on all these profiles. This method is useful for modeling engine manifolds, turbine blades, airframes, volute chambers and the like. 4.3.5
Miscellaneous Construction Methods
Geometry construction techniques ď&#x201A;ˇ
Filleting This is the ability to automatically generate the fillet radius between two surfaces,
either analytical or sculptured. The radius could be uniform or vary linearly, depending upon the meshing surface. ď&#x201A;ˇ
Tweaking
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This is the ability to alter a model already created using any of the earlier approaches. In this, a face or a vertex in the model would be interactively moved to see the effect in the modification of the geometry.
4.4
Other Modeling Methods Depending upon the requirements of the particular problem other schemes are used for
specific applications.
4.4.1
Variant Method The complete part is located in the memory in the form of a sample drawing without the
dimensions. The job is identified by means of a part code. The skeleton part drawing would be displayed on the CRT screen. The user would then have to simplify fill in the blank dimensions as directed by the program. This approach is very convenient when one is interested in making a group of similar components or for making vary small corrections in only their size and not shape. After the input of dimension on the menu drawing, the actual proportionate drawing would be generated.
4.4.2
Symbolic Programming Input a partâ&#x20AC;&#x2122;s drawing through a series of symbols, which show the direction of movement
in SYMBOLIC FAPT TURN system. As shown in Fig 4.4, the keyboard consists of a number of directions keys for drawing lines, circles and special features like chamfer, corner and thread.
The operator would start inputting the drawing from one end showing the direction in which the part contour moves.
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Fig 4.4 Part Model Product Using the Symbolic Programming
4.4.3
Form Features In this modeling system, all features that are available for a particular type of job are
catalogued into what are called feature or form elements. The actual job id therefore o be treated as an assembly of these form elements properly dimensioned in the correct order. The complete system would be highly interactive with proper graphic menus made available. Typical axi-symmetric component is shown in Fig.4.5
Fig.4.5 Form Elements Used For Model Generation In The Case Of Axi-Symmetric Component Typical form features useful for modeling a majority of axi-symmetric components with all the additional milling features such as holes, slots, etc, are shown in Fig. 4.6. Here the user would start assembling the features from one end as required in the final component.
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Fig.4.6 Form Features For Modeling Axi-Symmetric Components with Milled Features It is possible to incorporate any type of features, both internal and external. The major advantage of this kind of modeling is that the feature elements are more convenient for the people involved in the manufacturing process than the geometric elements and the modeling process is generally faster. Further advantage of this method is that it can be easily used to external functions, such as identifying the manufacturing requirements, process planning and CNC part program generation to the technological processing. 4.5
Curve Representation Representation of curve geometry can be carried out in two forms. Implicit form Parametric form The implicit form is convenient for two dimensional curves of first and second order.
Typical curves that can be covered are lines, arcs, and circles.
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In parametric form, the curve can is represented as X = x (t), Y = y (t) and
Z = z (t)
Where X, Y, Z are the co-ordinates values on the space curve, with the corresponding functions x, y, z being the polynomial in a parameter, t. Implicit forms of few curves have been derived. Circles The parametric form of a circle whose centre lies at the origin of the co-ordinate system (Fig. 4.7) is given by X = r cos Ө Y = r sin Ө
Y
(X, Y)
O
Ө
X Fig. 4.7 Circle
Where r is the radius of the circle. The implicit form of the circle is given by 2
2
x +y =r
2
A circle other than the one located at the origin of the co-ordinates system, can be obtained by the transformation such as translation and rotation. Ellipse The parametric form of an ellipse whose center lies at the origin of the co-ordinates systems (Fig.4.8) is given by X= a cos Ө Y = b sin Ө Where a and b are the semi major and minor axes of the ellipse. The Implicit form of the ellipse is given by x
2
2
+ 2
a
y
=1 2
b
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(X, Y) Ó¨
b o
a
Fig. 4.8 Ellipse
Splines Splines are the more general form of curves that can be defined through a set of vertices. A spine is a piecewise parametric representation of the geometry of a curve with a specified level of parametric continuity. Cubic Splines use a parametric equation of third order with the second order continuity maintained at the intersection points of the curves. Bezier Curves To obtain a more free form design for aesthetic surfaces such as the car exterior surface, the modeling techniques have to provide more flexibility for changing the shape. This can be achieved by the use of Bezier curves named after P. Bezier curve uses the given vertices as control points for approximating the generated curve. The curve will pass through the first and last point with all other points acting as control points.
B-Splines One of the problems associated with the Bezier curves is that, with an increase in the number of control points, the order of the polynomial representing the curve increase. To reduce the complexity, the curve is broken into more segments with better control exercised with individual segments, whiling maintaining a simple continuity between the segments. An alternative is to use a B-spine to generate a single piecewise parametric polynomial curve through any number of control points according to the degree of the polynomial selected by the designer. B-Splines exhibit a local control. Uniform cubic B-Splines are curves with parametric intervals defined at equal lengths.
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Desirable Modeling Facilities
The desirable modeling facilities are categorized into following heads.
4.6.1
Geometric modeling features
Editing or manipulation features
Drafting features
Display control facilities
Programming facility
Analysis features
Connecting
Geometric Modeling Features Various geometric modeling and construction facilities that one should expect to have in
any good system are the following: 1. Various geometric methods, such as Cartesian and polar co-ordinates, absolute and incremental dimensions, various types of units, grid, snap, object snap, layer etc. 2. All 2D analytical features, such as points, lines, arcs, circles etc. 3. Majority of the 3D wireframe modeling facilities including 3D lines, 3D faces, and tapered sweep. 4. Solid modeling with various basic primitives such as block, cylinder, sphere, etc, along with the ability to apply the Boolean operators on any solid that can be constructed using the other techniques . 5. Skinning around regular and arbitrary surfaces. 6. Sculptured surfaces of the various types like Bezier, coons and other free form surfaces. 7. Comprehensive range of transformation facilities for interactively assembling the various solid models generated by the modeler with features such as surface filleting and trimming. 4.6.2
Editing or Manipulation Features Improving the productivity of the designer, the facilities desired in this category are the
following. 1. Transformations such as move, copy, rotate, scale, compress, and mirror or to any arbitrary co-ordinate frame.
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2. The editing features used to alter the already drawn geometric entities. 3. Symbols in drawing refer to often repeated set in a number of drawings, which may consist of a number of geometric entities that are grouped together and stored as a symbol. 4.6.3
Display Control Facilities This range of features is inclusive of all the facilities needed for interacting with the
modeling system so as to obtain the necessary feedback at the right time during the modeling stage. Following are facilities required
4.6.4
Windows
Perspective views
Zoom
Orthographic views
Pan
Isometric views
Hidden
Axonometric views
Shading
Sectioning
Animation
Clipping of images
Drafting Features The facilities refer to the way in which the developed model can utilized for the purpose of
transmitting the information in hard copy from other applications. The ability to draw various types of lines and provide ample notes in the form of text addition at various locations in the drawing should be available. The text handling capability in terms of font changing and different methods of text presentation should also be available. Many types of views should be obtained from the solid model of the geometry stored in the database. The dimension types that should be available are – linear, radius, circular, leader, baseline dual dimension etc. 4.6.5
Programming Facility It is possible to program specifically for an application, making use of all the features
available in the system for either modeling or for any specific application, based on the information generated during the modeling. The availability of such a program helps the user to input the least amount of information for any required design provided the application programs are written well using the programming language.
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Analysis Features This kind of analysis facilities that are required to be carried on the product models being
generated should be considered. The simplest and most sophisticated features may be available under this category. The simplest facilities may be calculating perimeter, area, volume, mass etc. the geometric model created as above could be conveniently passed onto the FEA through an intermediate processor called a Finite Element Modelers (FEM). Another important feature essential in the modeling systems used by the mechanical engineering industries is the assembly facility with the associated interference checking. 4.6.7
Connecting Features It is necessary that the internal data format in which the data is stored by the modeling
system should be well documented and should also have very good connectivity with other allied modules. Integrated database is useful wherein all the various modules share the common database. 4.7
Rapid Prototyping (RP) Rapid Prototyping (Rp) is means through which the product geometry as modeled in the
earlier stages is directly utilized to get the physical shape of the component. RP technologies are generally based on a layered manufacturing concept. Machining can be effective in many RP applications. The technologies involved are the following.
Stereo lithography
Selective laser sintering
3-D printing
Solider process
Fused Deposition Modeling
Laminated object manufacturing
CAD Standards 4.8
Standardization in Graphics
Interface at various levels:
GKS
PHIGS (Programmer’s Hierarchical Interface for Graphics )
(Graphical User Interface)
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GKS-3D
DXF
(Drawing Exchange Format)
VDI
(Virtual Device Interface)
VDM
(Virtual Device Metafile)
GKSM
STEP (Step for the Exchange of Product Model Data)
IGES
CORE
(Initial Graphics Exchange Specification)
The operation of these standards with applications programs is depicted in Fig. 4.9.
Graphics Database
DXF, IGES, STEP, SET
Applications ProgramGKS, PHIGS, CORE
Graphics Functions
Device Driver
VDI, VDM
Device Driver
Fig. 4.9 Various Standards in Graphical Programming
Device
4.9
Device
Graphical Kernel System (GKS) DIN released the version of GKS. Taking all the existing graphic packages, ISO has
standardized the GKS as a 2D standard. The main objectives that were put forward for GKS are the following. 1. To provide the complete range of graphical facilities in 2D, including the interactive capabilities.
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2. To control all types of graphics devices such as plotters and display devices in a consistent manner. 3. To be small enough for a variety of programs. The major contributions of GKS for the graphics programming are in terms of layer model, as shown in Fig.4.10.
Application program Application oriented layer Language-Independent Layer GKS Operating system Other resources
Graphical resources
Fig.4.10 Layer Model of Graphics Kernel System The co-ordinates frames available to the user are of the following types.
World co-ordinate (WC)
Normalized device co-ordinates (NDC)
Device co-ordinate (DC)
The input methods in GKS environment are
LOCATOR
VALUATOR
CHOICE
PICK
STRING
STROKE
For drawing line, the concept of PEM is used. PEN has the attributes of color, thickness, and line type. Lines can be drawn with any PEN that can be defined.
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GKS is defined in terms of a number of levels describing the level of support in terms of facilities. The highest level is 2c, through level 2b is the most commonly available facility with marginal difference in terms of the length of input queue. 4.10
Other Graphic Standards
GKS 3D The GKS has been subsequently enhanced to provide a separate standard for the three dimensions as GKS 3D, which maintains compatibility with the 2D standard. PHIGS PHIGS is a 3D standard. Some of the features that are specific to PHIGS and are not well supported by GKS are the following:
Vary high interactivity
Hierarchical structuring of data
Real time modification of graphic data
Support for geometric animation
Adaptability to distributed user environment
NAPLPS NAPLPS stands for The North American Presentation Level Protocol Syntax. The NAPLPS is a means of encoding the graphic data consisting of both graphics and text into an electronically transferable format (ASCII).
4.11
Exchange of Modeling Data The data format used by all the software should be the same. The database formats are
identified on the basis of the modeling requirements and is therefore not possible to have identical format for all the systems. It is possible to identify a certain format for drawing exchange and make it a standard so that the various systems can convert their internal format tot his standard format or vice versa. Standards are 4.11.1 Initial Graphics Exchange Specification (IGES) The IGES is the most comprehensive standard and is designed to transmit the entire product definition including that of manufacturing and any other associated information.
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In IGES the records are present with 80 column fields, with columns 1 to 72 providing the data and columns 73 to 80 providing a sequence number for the record with identification as to the location of the sub-function. a)
Flag section This is optional and is used to indicate the form in which the data is specified.
The format has been standardized in three modes 1. ASCII mode 2. Binary form 3. compressed ASCII form b)
Start Section This section contains a man-readable prologue to the file.
c)
Global section This contains information about details of the product, the person originating the product,
name of the company originating it, date, the details of the system which generated it, drafting standard used and some information required for its post processing on the host computer. d)
Directory entry section For each entity present in the drawing is fixed in size and contains 20 fields of 8
characters each. The purpose of this section is to provide an index for the file and to contain attribute information. Some the attribute information such as color, line type, transformation matrix etc. e)
Parameter Data Section This contains the data associated with the entities. It may contain any contain any
number of records. Entities are
f)
geometric entities
annotation entities
structure entities
Terminate Section This contains the sub-totals of the records. This would always contain a single record.
4.11.2 Standard for the Exchange of Product Model Data (STEP)
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The broad scope of STEP is as follows. 1. The standard method of representing the information necessary for completely defining a product thought its entire life. 2.
Standard methods for exchanging the data electronically between two different systems.
The step document is split into eight major areas.
Overview
Description methods
Implementations methods
Conformance and tools
Integrated-generic resources
Applications information models
Applications protocols
Application interpreted constructs
4.11.3 Drawing Exchange Format (DXF) It is not a industry standard developed by any standards organization, but in view of the widespread use of AutoCAD made it a default standard for use of verity of CAD/CAM vendors. The overall interchange file is simply an ASCII text file extension of .DXF and specially formatted text. The overall organization of a DXF file is as follows. HEADER section This section contains general information about the drawing similar to the Global section of IGES. It consists of the AutoCAD database version number and a number of system variables. CLASSES section It holds the information for application-defined classes, whose instances appear in the BLOCKS, ENTITIES and OBJECTS sections of the database. A class definition is permanently fixed in the class hierarchy.
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TABLES section This contains definitions for the symbol tables which directly relate to the objects types available in AutoCAD.
Line type table
Layer table
Text style table
View table
User co-ordinate system table
View port configuration table
Dimension style table
Application identification table
Block reference table
BLOCKS section This contains block definitions and drawing, including block reference. ENTITIES section This contains the graphical objects in the drawing. All objects that are not entities or symbol table record or symbol tables are stored in this section.
OBJECT section This contains the non-graphical objects in the drawing, all objects that are nor entities or symbolic table records or symbolic tables are stored in this section. Examples of entries in the objects section are dictionaries that contain mline (multiple line) style and groups. A DXE file is composed of many groups, each of which occupies two lines the file. The first line is a group code. The second line is the group value
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UNIT V 5.1 Introduction 5.2 Basic Facilities in AutoCAD 5.3 Basic Geometric Commands 5.4 Layers 5.5 Display Control Commands 5.6 Editing a Drawing 5.7 Dimensioning 5.8 Introductions (Finite Element Modeling) 5.9 General Facilities of Unigraphics 5.10 Examples of Solid Model 5.11 Introduction (Finite Element Modeling) 5.12 Finite Element Modeling 5.13 FEM Software
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Introduction to Drafting System 5.1 Introduction Drafting is one of the first computer applications used by many users. AutoCAD is widely used for CAD software for drafting application. 5.2 Basic Facilities in AutoCAD The release 2000 screen is shown in Fig. 5.1, which has the familiar windows look and feel, in terms of the various buttons and an easier interface.
Fig 5.1 AutoCAD 2000 Screen Appearance It has a set of drop down windows for various menu options. New Open
This allows for starting a new drawing. This allows for opening an old drawing for editing.
Save
This allows for saving the current drawing.
Save As
This allows for saving the current drawing with a new
Export This allows for exporting the current drawing into other for other programs such as 3D studio. The following formats are possible.
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BMP - Device-independent bitmap file DWG – AutoCAD drawing file DWF – AutoCAD drawing web format file DXF – AutoCAD drawing interchange file SAT – ASCI solid object file SLT - Solid object stereo-lithography file WMF – Windows Metafile 5.2.1 Screen Display The total display screen is divided into number of areas as shown in Fig. 5.1. The status line is the bottom most line. On the right side a column is displayed for providing with the possible menu selections. This column can be removed from the screen if necessary by changing the options in the AutoCAD setup. At the bottom, a command area is provided which is generally designated for 3 lines. In this portion the interaction between the user and AutoCAD takes place. The rest of the screen is designated as the Drawing Area. The actual drawing being made is drawn in the area. When the cursor is moved into various regions, its shape would change depending upon the screen area. 5.2.2 Menu AutoCAD is a completely menu driven system. Also the number of menu commands available is many. The menu items are made available through a large number of options such as:
Direct command entry
Through the side bar menu
Through the pop-up windows from the top menu bar or
Through the button bars located in any position of the screen (Fig. 5.2.)
Fig. 5.2 Standard Tool Bar in AutoCAD 2000
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5.2.3 Planning for a Drawing While planning a drawing in AutoCAD one has to carefully organize some of the information. This is carried out in the set up operations.
Units This lets us set up the units in which the AutoCAD would have to work. Internally AutoCAD would be working in default co-ordinates called as drawing units (Fig. 5.3).
Fig. 5.3.Specification of Drawing Units in AutoCAD 2000 Types of units to work with in the drawing 1. scientific 2. decimal 3. engineering 4. Architectural 5. fractional Co-ordinates system The co-ordinates system used by all the CAD packages is generally the rectangular Cartesian co-ordinates system which follows the right hand rules. AutoCAD also uses the rectangular co-ordinates system designated as X, Y, Z axes. Limits
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It is normally necessary to specify the limits of the drawing that one is about to use. It is like choosing the right size of drawing sheet for making the drawing. The actual size of the drawing would have to be specified using the keyboard. This would be achieved by using the LIMIT command. Grid Working on a plain drawing area is difficult since there is no means for the user to understand or correlate the relative positions or straightness of the various objects or entities made in the drawing. The GRID command control the display of a grid of alignment dots to assist the placement of objects in the drawing. Snap When the cursor is moved it can go through an infinite number of points on the screen. This infinite resolution is not required or necessary for any drawing work. The resolution of the cursor movement can be controlled using the SNAP command. The SNAP mode can be made operational by using the toggle control during the execution of any of the other command in AutoCAD by using <F9> or ^B keys simultaneously. Ortho The ORTHO command allows to control â&#x20AC;&#x153;orthogonalâ&#x20AC;? drawing mode. While drawing lines, the cursor moves to a point which makes it perpendicular to the point or in the same direction. The ORTHO mode can be made operational by using the toggle control during the execution of any of the other command in AutoCAD by using <F8> or ^O keys simultaneously. Help AutoCAD provides complete help at any point of working in the program. Help can be obtained for general commands or specifically for any of the individual commands. 5.2.4
Object Properties All objects in AutoCAD when created would have certain properties such as color, line
type and the layer on which they would be residing. The default setting would be visible in the object properties button bar as shown in Fig. 5.4.
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Fig. 5.4 Object Properties Button Bar Description of the properties is as follows Line type AutoCAD allows the user to draw various types of lines in a drawing. This dot-dash line type of each entity can be controlled either individually or by layer. To change the line type of existing objects, use the
CHANGE command. To control
layer line types, use the LAYER command. The LINETYPE command sets the line type (Fig. 5.5) for new entities. It can also load line type definitions from a library file.
Fig. 5.5 Popup Window for Changing the Line Type
5.3
Basic Geometric Commands The various entities that can be used for making an AutoCAD drawing in 2D are as follows.
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Point
Poly line
Lines
Dough nut
Arc
Sketch
Circle
Text
Ellipse
Block
Polygon
The popup window for drawing commands is shown in Fig.5.6.
Fig.5.6 Popup Window for Drawing Commands AutoCAD provides a default option as <> in each of the command response. The value or option shown in the angle brackets is the most recently set value. To have the same value one has to simplify press the <ENTER> key. Point It is used to specify a point or a node in the drawing for any given purpose. The point coordinates can be inputted into the system in a number of ways. By the direct input of co-ordinate values in their respective order, i.e. X, Y, and Z. If Z co-ordinates are not specified, it is considered as the current Z level given through the ELEVATION command.
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It is also possible to specify the co-ordinates in incremental format as the distances from the current
cursor position in the drawing area. The distance is specified by using the “@”
parameter. Command: POINT<CR> Co-ordinates of point: @34.5, 12.0<CR> The first value refers to the length of the line or polar radius, while the second quantity refers to the angle at which the line is drawn from the current point. Line The LINE command allows you to draw straight lines. You can specify the desired endpoints using either 2D or 3D co-ordinates or a combination. To erase the latest line segment without exiting the LINE command, enter “U” (UNDO) when prompted for a “To” point. You can continue the previous line by responding to the “From point:” with a space or RETURN. If you are drawing a sequence of lines that will become a closed polygon, you can reply to the “To point” prompt with “C” to draw the last segment. Circle The CRICLE command is used to draw a full circle. You can specify the circle in many ways. For specifying a circle we need at least two values. There are at least five ways 1. Center point and radius 2. Center point and diameter 3. Two points on the circumference across diameter 4. Three points on the circumference 5. Tangential to two other already drawn entities and radius To specify the radius, you designate a point to be on the circumference or make use of the “DRAG” facility in response to the “Diameter/<Radius>” prompt to specify the circle size visually on screen. Arc The ARC command draws an arc as specified by any of the following methods. 1. three points on the arc 2. start point, center, end point’ 3. start point, center, included angle 4. start point, center, length of chord
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5. start point, end point, radius 6. start point, end point, included angle 7. start point, end point, starting direction 8. Continue of previous line or arc. The ARC is always drawn in the counter clockwise direction.
5.4
Layers Drawing normally consists of lot of information which is of varying types such as
geometric and alpha-numeric. It is difficult to see all this information in one frame because of the clustering effect it produces. To deal this layer concept is used in drawing. A layer is basically one which contains some information which can be geometric and alpha-numeric. The reason of distributing all the information present in the drawing into various layers is that at any given time some of the layers can be deleted from view (OFF) or can be made visible (ON). This helps in organizing the information in a drawing. In AutoCAD a layer has certain properties and rules
Each layer has a name which can be up to 31 characters. Default name is 0. Only numbers could be used for naming the layers.
A layer could be ON or OFF. ON – information present would be visible on screen. OFF – information is not lost from the drawing, it would
not be visible
in the drawing.
A layer is either current or inactive. Only one layer can be current at any given time. If the current layer is ON the given information being entered would be visible on the screen.
Each layer has a color associated with it. All information entered in to the layer would get the color. It does not mean that more than one color can be present in a single layer. The color can be altered by using CHANGE command or by using COLOR command.
5.5
Display Control Commands
ZOOM ZOOM is used to change the scale of display (Fig.5.7). This can be used to magnify a part of the drawing to any higher scale for closely observing some fine details in the drawing.
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Fig. 5.7 Popup Window for Various Display and Zoom Options
Options available in ZOOM Scale<X>
A numeric factor. A value less then 1 zooms out and
greater then 1 zooms
in. All
Zooms out to original limits.
Dynamic
Graphically selects any portion of the drawing as your next screen view.
Center Pick a center point and a picture top and bottom by selecting two end points of a height. Left
Pick a lower left corner and a height of how much drawing information you want to display to fill up the screen.
Previous
Restores the last ZOOM setting.
Choosing the dynamic option displays all the drawing up to limits in a small window so that the entire drawing is visible in the display screen.
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The current visible window would be shown as a rectangle linked to the cursor. By pressing the left button of the mouse and moving the mouse would make the window smaller or larger than the previous display. Once the window rectangle size is satisfactory, pressing the mouse left button again fixes the size of the rectangle. The mouse can now be moved to any position to place the display window on the drawing. Then pressing the right mouse button would correspondingly show the image in the window in the full size of the screen. This is a very convenient option and requires normally small number of steps to come up with the required image to be shown to the requisite scale. PAN The PAN command allows you to move the display window in any direction without changing the display magnification. This means the display being seen is through a window in an opaque sheet covering the drawing limits. The window can be moved to any location within the display limits, although no dynamic movement is possible. This shows details that are currently off the screen. OBJECT SNAP The snap convert the original drawing area into finite GRID points with the SNAP spacing selected. SNAP is useful for drawing a new object into the drawing by itself. It may be required to start a line from an unknown precise tangent point on a circle. All that the user may know is a specific area where the tangent may be laying. Then by selecting the OSNAP option the system would be able to automatically calculate the tangent point in the region selected. The various OSNAP options CENter
ENDpoint INTersection
Center of Arc or Circle
Closest endpoint of Line/arc Intersection of Lines/Arc/Circles
INSertion
Insertion point of Text/Block/Shape/Attribute
MIDpoint
Midpoint of Line/Arc
NODe
Nearest point entity
NONe
None (off)
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Tangent to Arc or Circle
TEXT HANDLING AutoCAD provides a large range of text entering capabilities including various fonts and other text handling features (Fig. 5.9)
Fig. 5.9 Sample Fonts Available In AutoCAD In each of the fonts, it is possible to have lettering with various attributes which are specified during the selection of the style as shown in the dialogue box (Fig. 5.10). The selection results are also shown in the dialog box.
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Fig. 5.10 Font Specifications that Are Given Through the Popup Window It is also possible to combine the attributes to get complex attributes. It is possible to change the width factor, greater then 1 makes the letters elongated and less then 1 makes them compressed. The text can be slanted by any angle. 5.6 Editing a Drawing Editing capabilities are the most useful part of AutoCAD to exploit the productivity potential making use of the already existing objects in the drawing. Editing facilities are listed Array
Places multiple copies of objects with a single command.
Break
Cuts existing objects and/or erases portions of objects.
Change
Change spatial properties of some objects like location, text height, and circle.
Copy
Makes copies of objects.
Erase
Allows selecting objects in the drawing file and erasing them.
Mirror
Create a mirror image of objects.
Move
Picks up existing objects to any angular specifications.
Rotate
Turns existing objects to any angular specifications.
Scale
Scale objects up or down to your specifications.
To use any of the editing functions, it is necessary to make a selection of the objects in the drawing on which the editing function would be applied. As any of the editing commands are issued, AutoCAD responds first with the object selection option.
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5.6.1 Basic Editing Commands MOVE The MOVE command is used to move one or more existing drawing entities from one location in the drawing to another (Fig. 5.11).
Fig. 5.11 Moving Object in the Drawing COPY The COPY command is used to duplicate one or more existing drawing entities at another location without erasing the original (Fig. 5.12).
Fig. 5.12 Copying of Object in the Drawing
CHAMFER The CHAMFER command creates a bevel between two intersecting lines at a given distance from their intersection (Fig. 5.13).
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Fig. 5.13 Chamfer as used in Drawing
FILLET The FILLET command connects two lines, arcs or circles with a smooth arc of specified radius. It adjusts the lengths of the original lines or arcs so they end exactly on the fillet arc (Fig. 5.14).
Fig. 5.14 Fillet as used in Drawing
OFFSET The OFFSET command constructs an entity parallel to another entity at either a specified distance or through a specified point (Fig. 5.15). You can OFFSET a line, arc, circle, or poly line. Offset lines are parallel, while the offset circles and arcs make concentric circles and arcs respectively.
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Fig. 5.15 Offset as used in Drawing ARRAY The ARRAY command makes multiple copies of selected objects, in a rectangular or circular pattern. For a rectangular array, you are asked for the number of columns and rows and the spacing between them (Fig. 5.16).
Fig. 5.16 Rectangular Array of Objects For a polar or circular array (Fig. 5.17), center point needs to be supplied. Following this, you must supply two of the following three parameters.
The number of items in the array.
The number of degrees to fill.
The angle between items in the array.
Optionally, you can rotate the items as the array is drawn.
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Fig. 5.17 Polar Array of Object Rotated while Copying
Dimensioning
After creating the various views of the model or after preparing the drawing, it is necessary to add dimensions at the appropriate places. AutoCAD provides semi-automatic dimensioning capability with a way of associating the dimensions with the entities. As a result, once dimensioning is created, there is no need to redo it after modifications to the drawing. The following screen (Fig. 5.18) shows the typical appearance of the dimension menu.
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Fig. 5.18 Dimension Style Option While dimensioning, the information to be specified is as follows.
Where is the dimension?
Where the dimension text should go?
How big and what style the text will be?
If tolerance range is to be included?
How big and what the arrows look like?
To set these values, a number of variables are available in AutoCAD whose values need to be set in the prototyping drawing. These variables actually control the way the dimensions appear in the drawings. AutoCAD gives great control over the way dimensions may appear in the drawings. It is therefore necessary that users should be familiar with these in order to customize the dimensioning to the best of the methods used in the design office. Each of these can be further specified based on dimension families or for all of them. The dimension families are specified as follows.
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Diameter
Radial
Angular
Ordinate
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The procedure to be followed for dimensioning in AutoCAD is as follows. a)
b)
Set up the following basic parameters for dimensioning.
Arrow head type
Arrow head size
Extension line offset
Placement of dimension text
Identify what you want to measure.
c)
Specify where the dimension lines and text are to be located.
d)
Approve AutoCAD’s measurements as dimension text or type in your own text. An example made in AutoCAD is given in Fig. 5.19.
Fig. 5.19 Example Drawing Made in AutoCAD
Introductions to a Modeling System
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5.8 Introductions There are large numbers of modeling systems that are generally used by the industry. The following are the major CAD/CAM system.
Unigraphics
CATIA
Pro Engineer
I-DEAS
Unigraphics modeling system help in modeling. Unigraphics is one of the powerful CAD systems with hybrid modeling facilities The modeling methods embedded with unigraphics is the following.
Solid Modeling
Surface Modeling
Wire frame Modeling
Feature-Based Modeling
5.9 General Facilities of Unigraphics Unigraphics works under the X-windows environment. The typical appearance if the screen for unigraphics version 14.0 is shown in Fig. 5.20. The total screen is divided into a number of areas and each has a specific function to be served.
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Fig. 5.20 Unigraphics Screen Appearance before Starting Modeling Menu bar Menu bar is the horizontal menu of options displayed at the top of the main window like the Windows look and feel. The options that are displayed provide different groups of categories. Each of these options has a pull-down menu which may or may not have further sub-topics File
To organize the saving and other file handling functions
Edit
To carryout the modification to the model created
Toolbox
The various toolboxes that is available for creating the model
Arrange
This allows to group objects, assigning attributes to objects and parts
Assembles
The assembly functions
View
Menu items for controlling the viewing
Layout To create various layouts of the screen for better visualization WCS
To organize the work co-ordinates system
Layer
To control the layers usage
Info
To get information about the objects in the model
Preferences
To control the various options
Applications
To select the actual applications to be used such as modeling/drafting, manufacturing, etc,
Macro Allows to perform repetitive complex and lengthy tasks all of which can be grouped into a macro User Tools
This options allows to launch special user tools such as macros, or GRIP programs
Web
The main drawing window can be saved as an image for publishing on the web
Help
To get the help
Pull Down Menus Pull-down menus appear below the menu bar when a particular set is selected. The users then need to select any one of the options within. Cascade Menus
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Some options on a pull down menu display a sub-menu of additional options when selected. Sub-menus of this type are called cascade menus and their presence id indicated by a small triangle to the right of the menu option name. Cue Line The cue line, located just below the menu bar, which displays prompt messages about input that is expected by the current option. These messages indicated the next action the user is expected to take.
Status Line The status line, located to the right of the cue line, displays information messages about the current option or the most recently completed function. Dialogue Area 1 Dialogue area 1 is where the top level menu buttons would be displayed based on the selection from the main menu bar. This area is located just below the cue line and to left of the graphics window. In Fig. 5.20 the modeling icons are displayed in the dialogue area 1. Dialogue Area 2 Dialogue area 2 that is below dialogue area 1, displays the subordinate window to the dialogue displayed in dialogue area 1. Graphics Window The graphics window contains the main unigraphics applications –specific graphics that is where the modeling tasks will be visible. This window displays the current part name as its title and contains the following components.
Zoom scale
System ready indicator
Co-Ordinate System The co-ordinate system used is the Cartesian right handed co-ordinate system like any other CAD system.
▪ Absolute co-ordinate system
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The world co-ordinate system is called Absolute coordinate system in unigraphics and it refers to the master co-ordinates system used for the component. Fig. 5.21 shows the component with its associated absolute co-ordinate system X, Y and Z. This is basically the co-ordinate system in which the part database is stored.
Fig. 5.21 Co-ordinates system used in unigraphics ▪ Work co-ordinate system The user co-ordinate system is called Work co-ordinate system or WCS unigraphics which is generally manipulated by the user to permit easy entry of the modeling data. In Fig. |
|
|
5.21 the X , Y , Z is the WCS defined for modeling slots. It is possible to change the WCS with the following type of facilities. Change the location of the origin but not the direction of the axes. Change the direction of the axes, but not the location of the origin Change both origin locations and axes direction of the WCS. Point Sub Function The point sub function allows the user to enter co-ordinates of the particular point in question. The user has to utilize these functions almost every time any graphic data needs to be inputted during modeling. Typical appearance of the function is shown in Fig. 5.22. The point can be specified directly in the form of the X, Y, Z co-ordinates with reference to the WCS in operation or can be picked up from the objects that are already modeled, such as the end, mid, center, quadrant or intersection.
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Most of the time the unigraphics will be able to pick the right choice, which in any case will be highlighted to allow the user to pick.
Fig. 5.22 Point Subfunction Dialogue Window Used In Unigraphics
Geometric Facilities in Unigraphics Geometric facilities is available in unigraphics accessed through the subfunctions ‘create curve’ and ‘create feature‘menus as shown in Fig. 5.23. Each of these buttons represents the facilities such as solid primitives block, cylinder, cone, sphere, tube or features such as hole, slot, groove, boss or the operating tools such as linear and rotary sweep, Boolean operations, trim, etc.
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Fig. 5.23 Geometry Creation Dialogue Windows in Unigraphics Curve creation allows two dimensional objects to be incorporated in the model being designed. The basic curves included are the following. Lines, polygons
Splines
Arc, circles, ellipses
Fillet and chamfer
The solid specified then performing the Boolean Operation are called the Target and the Tool. Target Solid is that solid upon which the operation is performed. Tools solid is that which operates upon the Target and becomes a part of the solid at the end of the operation. In addition to the conventional geometrical modeling facilities, Unigraphics also provides for sketching capability. 5.10 Examples of Solid Model We will now go through the modeling process of developing a complex solid as shown in Fig. 5.24 using Unigraphics. As can be observed from Fig 5.24 the modeling starts from the left side, with the first solid being the block. After making the block, the origin of the WCS is moved to the center of the cylindrical portion to the left side. Construct a cylinder at the point.
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Fig 5.24 An Example for Geometric Modeling in Unigraphics The screen should then look as shown in Fig. 5.25. At this point in order to see that the solids are present, the user may use the option of shaded display or hidden line removed display. The two solids in the display can be joined by calling the Boolean operator addition.
Fig. 5.25 Geometric Modeling Step 1 for Fig.5.24 In the next step, the stepped block on the extreme right needs to be created. So move the WCS origin to the bottom most corner of the step and create to lower block. Next create the smaller block above lower block taking care to see that the block will end at the center of the cylinder. This can then be joined to the solid body created earlier. Next move the WCS to the center of the cylinder and create a hole by subtracting a cylinder of the size. The shape of the object should now look similar to the one shown in Fig. 5.26
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Fig. 5.26 Geometric Modeling Step 2 for Fig.5.24 It is better to confirm the shape of the object as created by getting the shaded image as shown in Fig.5.27 and rotating the object on screen to see the various sides of the objects.
Fig.5.27 Shaded View of the Present Model In Geometric Modeling step 2 for Fig. 5.24 The next step involves the
creation of the conical hole in the middle of the top
surface of the cylindrical portion. So move WCS to that point and subtract a cone of the correct proportions. The next operation to be done is the two holes at the center of the big block created in the beginning. After moving the WCS to that position subtract the two cylinders to get the hole and the counter bore for that. Then it is necessary to add a side block to the bottom block. For this purpose first create a block and then trim it using the trim body option. After trimming, that body is united to the main body created. The model should now be visible as in Fig. 5.28.
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Fig. 5.28 Shaded View of the Present Model In Geometric Modeling step 3 for fig.5.24 Next create a hole in the side block that was just joined by using a cylinder subtraction method. Next step is to create the right side stepped blocks as individual blocks. The model should be similar to that shown in Fig. 5.29. It is good idea to change the color of the different solids during the modeling process to clearly identify the modeling operation. This can be done by picking up the option object display from the Edit menu option.
Fig. 5.29 Geometric Molding Step 4 for Fig. 5.24 After this, all the blocks will be united with the main body. This completes the basic modeling operation and the result should be seen as in Fig. 5.30.
Fig. 5.30 Shaded View of the Present Model In Geometric
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Modeling step 5 for Fig 5.24. The last operation that needs to be done is the creation of the fillet radii at the various edges on the model. This can be done with the help of the blending option. The final result after successful blending is shown in Fig. 5.31.
Fig. 5.31 Shaded View of the Final Model In Geometric Modeling of Fig.5. 24
View option is available to have modeling view on a screen simultaneously than the single view of the modeling process. This can be done by using the view option in the menu bar. The model in a four port view on screen is shown in Fig. 5.32. The next step will be the drafting functions, which requires that the model be converted for drafting by using the associated drafting functions. The next step involved is the placement of views in the drawing sheet. It is necessary to get the dimension in place.
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Fig. 5.32 Modeling Screen Being Divided Into Multiple View Ports
Once the drafting is completed, the border and title block can be drafted using the curve creation facilities. Unigraphics provides the assembly option which provides a concurrent top-down product development approach. Parametric modeling of assemblies provides additional power for describing mating relationships between components and for specifying groups of common fasteners and other duplicated parts. The assembly being associative with the component models, any modifications dome to the components automatically reflects in the assembly.
Finite Element Analysis 5.11 Introduction Finite elements modeling (FEM) is a convenient to carry out a very power analysis tool. The finite element, modeling process allows for discrediting to intricate geometrics into small fundamental volumes called finite elements. It is then possible to write the governing equations and martial properties for these elements.
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Application of FEM is not limited to mechanical systems alone but to a range engineering problems such as
Stress analysis
Dynamic studies
Fluid flow analysis
Heat flow analysis
Seepage analysis
Magnetic flux studies
Acoustic analysis
With the FEM software it is possible to try a number of alternative designs before actually going for a prototype manufacture. Based ob this knowledge it is possible to modify the mould to get the right the component in the first attempt itself.
5.12 Finite Element Modeling In order to understand the concept of finite element modeling, we will consider a one dimensional problem which is easier to visualize. The same concepts can be extended to two and three
dimensional problems similarly. Consider a taper beam as shown in Fig.5.33 with unidirectional force acting in the direction of X.
X
Fig. 5.33 One Dimensional Body with a Force in the X-direction
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Since the displacement, stress, strain and loading are functions of X only, they can be written as follows: Displacement functions,
u = u(x)
(5.1)
Stress function,
σ = σ(x)
(5.2)
Strain function,
ε = ε(x)
(5.3)
Load function,
F = F(x)
(5.4)
The strain is defined as
ε = du / dx
(5.5)
And stress and strain are related by E, i.e. the young modulus of elasticity as given in Eq. 5.6. σ = Eε
(5.6)
The total force T acting on the body consists of three components, the body force f, and the traction force T and point load P. The body force acts on every point of the body. The traction force is that which acts on the surface such as friction. Since the cross-section is non uniform, in order to discretise, we may convert it into a stepped shaft of different diameters each of which are uniform in size (Fig.5.34).
Fig.5.34 Discretising the Non Uniform Body into Four Sections Each of these sections is then converted into a rectangular shaft maintaining the same total area. These are then called as finite elements and are numbered with circles as 1, 2, 3 and 4 as shown in Fig. 5.35. The nodes are numbered elements and are numbered 1 to 5 and are used as the point of application of the point forces.
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Fig.5.35 Equivalent Stepped Shaft after Descretising with No Volume Change The components has 5 nodes, it has 5 degrees of freedom. For each of the nodes there will be displacement and forces acting which are shown as Q and F vectors (Fig. 5.36). The global vectors therefore are the following.
Fig.5.36 displacement and forces acting on the nodes of the discretised model Global displacement, Q = Q {Q1, Q2, Q3, Q4} Global force, F = F {F1, F2, F3, F4}
(5.7) (5.8)
(5.9)
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(5.10) The global displacement vector {Q} can be written as
{Q} =
Q1 Q2 Q3 Q4
(5.11)
Where Qi are the displacement vectors at the individual nodes. The displacement equation can therefore be written as [k] = {Q} = {F}
(5.12)
Solving the Eq. 5.12 with the necessary boundary conditions and loading conditions will give rise to the solution of the composite problem.
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5.13 FEM Software The total process of solving a particular problem using the finite element method had to be done by individuals. This has been changed by the availability of commercial comprehensive finite element analysis (FEA) software that runs on the desktop computers to make the job of engineering relatively simple in applying the FEA. The commercial FEA solver will generally have the same three-stage approach as shown in Fig. 5.37
Physical Problem Nodes Elements
FEM Preprocessor
Boundary condition Loads Material properties
Finite Element Analysis
FEM postprocessor
Global Matrices Compute Results
Deformed shapes Modal Shapes Counter Plots Results
Fig. 5.37 steps involved in the use of finite element for solving physical problem 5.13.1 Preprocessor The preprocessor of the FEM software allows for the following functions.
Modeling of the geometry.
Generating the finite element mesh by making a suitable approximation to the geometry.
Calculate the notes and elemental properties.
Allows for the specification of the support condition and loading condition for the individual element position.
Allow the material properties to be specified.
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One of the possibilities is direct linkage in the which the geometric model from the CAD system goes into the preprocessing part of the finite element software. For this purpose generally some neutral data format is used. Another possibility is that of preprocessor present with in the CAD software, which will convert the geometric model in to the finite element mesh and then transmit that data into the preprocessor of the finite element software. This requires that the element type available in the FE software the same as CAS software. Typical elements available in the FE software are shown in Fig. 5.38.
Fig. 5.38 Typical elements available in commercial FEA software Another possibility is that the CAD package as a complete specialized preprocessor built in which can do the mesh generation. Along with the specification of all the boundary conditions as well. Then it can directly link with the solver component of the FE software. A typical geometry and the corresponding mesh shown in Fig 5.39 and Fig.5.40
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Fig. 5.39 A spanner model directly in the preprocessor of LUSAS FEA Software.
Fig.5.40 Spanner as in Fig.5.39 with the generated mesh using LUSAS FEA Software After the conversion, it is to be solved using solver available with in the FE Software. The result will be generated after all the equations as assembled or solved. 5.13.2 Post Processing Post processing was ability to go through a large amount of data generated during the solving process and convert into an easily understood from for the design purpose. For this purpose many facilities will be available within the FE Software. An example generated using the LUSAS software shown in Fig.5.41
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Fig.5.41 Can Plate Showing The Geometry, The Finite Element, Mesh Used
Along With The
Boundary Conditions Generated Using LUSAS Its shows an complete with the geometry and finite element mesh generated. It is supported from the left side as shown by the arrows in Fig.5.41. the load acting is on the bottom right edge of the clamp, again shown with arrows. This model is now ready for running the analysis. After a successfully running of the analysis the result generated can be post processed to various forms depending upon the requirements envisaged in the design process. The total list of result types in LUSAS is shown below. Structural Analysis
Displacement
Velocity
Stress
Acceleration
Strain
Strain Energy
Loading
Named Variables
Reaction
State Variables.
Terminal Analysis
Potentials
Fluxes
Gradients
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For example the Von Mises stress contour plot for the cam plate is shown in Fig.5.42
Fig.5.42 Stress Contours of the cam plate as in Fig.5.42 generated using LUSAS FEA Software.
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UNIT QUESTIONS UNIT 窶的 QUESTIONS
. Self Assessment Questions
2. 3. 4. 5. 6.
CAD/CAM is a term which means___________________. CPU is a term which means _______________________. Define Automation. BCD stands for __________________. Define High level language.
Unit Questions
1. 2. 3.
Explain the product life cycle. Explain central processing unit. Explain computer programming language.
UNIT-II QUESTIONS
Self Assessment Questions 1. CRT is a term which means___________________. 2. Give types of Pen Plotters 3. List the secondary device.
Unit Questions
1. 2. 3.
Explain designing process. Explain Benefits of Computer-Aided Design. Explain Input Devices.
UNIT-III QUESTIONS
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Self Assessment Questions
1. 2. 3.
Z-buffer or ____________________.
1.
Explain raster scan display.
List types of pure transformations. Reflection or ___________________.
Unit Questions
2. Explain clipping. 3. Explain 3D transformation.
UNIT-IV QUESTIONS
Self Assessment Questions 1. List the types of geometric models. 2. Give representation of curve. 3. Give the types of Boolean operators.
Unit Questions
1. 2. 3.
Explain geometric models. Explain exchange of modeling data. Explain graphic standards.
UNIT-V QUESTIONS
Self Assessment Questions
1. 2. 3.
FEM stands for_________________________. User co-ordinate system is called_______________________. What is copy command?
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Unit Questions 1. Explain display control command. 2. Explain FEM software. 3. Explain general facilities of unigraphics.
Answer For Self Assessment Questions
UNIT I ANS1. : Computer-aided design and Computer-aided manufacturing.
ANS2. : Central Processing Unit ANS3. : Automation was defined as the technology concerned with the application of complex mechanical, electrical, and computer-based systems in operation and control of production. ANS4. : Binary-Code Decimal ANS5. : High level language consists of English-like statements and traditional mathematical symbols. Each high-level statement is equivalent to many instructions in machine language.
UNIT II
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ANS1. : Cathode Ray Tube. ANS2. : Two types of pen plotters Drum plotters Flat-bed plotters ANS3. :
Secondary storage devices are 1. Magnetic disk 2. Magnetic tape UNIT III ANS1. : Z-buffer (depth buffer)
ANS2. :
Translation
Scaling
Reflection or Mirror
Rotation
ANS3. : Reflection or mirror
UNIT IV ANS1. : Two dimensional and Three dimensional ANS2. : Implicit form and
Parametric form
ANS3. : Union, Intersection and Difference
UNIT V ANS1. : Finite elements modeling
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