[SPIRO]rat by rat[LAB]EDUCATION_Grasshopper3D / Rhinoceros3D Plug-in by RAT LAB

DEVELOPED BY

ABOUT [SPIRO]rat is a free plugin for Grasshopper (plugin for McNeel Rhinoceros3D) developed by rat[LAB] EDUCATION in INDIA. It generates Epitrochoids and Hypotrochoids by representing the motion of pen in a classic spirograph. An infinite number of patterns can be generated through this plugin using Rhino3D and Grasshopper3D which can be translated into spatial formations. rat[LAB] EDUCATION is an initiative by rat[LAB] to start a new discourse in architecture & parallel design disciplines with the use of ‘computational design’ & it’s various subsets. Spread across various cities / countries, we are establishing a global dialogue in the domain of computational design by actively organizing and participating in workshops, lectures, presentations & symposiums. While rat[LAB] has taken a top-down approach of exploring computational design through industry collaborations, a parallel, bottom-up approach is also in place to involve students of all levels, from design & related backgrounds. rat[LAB]’s educational mission has led to formations of national and international workshops, programmes, discourses and collaborations which has now opened up new avenues of academic exchange. rat[LAB] has started Design Technology Tools section on their platform where new developments, tool-kits, workflows and associations will be showcased. [SPIRO]rat is now available at: www.rat-lab.org/designtechtools More information about rat[LAB]EDU: www.rat-lab.org/education rat[LAB] - Research in Architecture & Technology, is an independent research organization and network of designers & researchers specializing in computational design or similar technology-related domains. Operated as a cloud-based organization with an international network of researchers & computational designers spread across UK, USA, Europe & Asia, and a studio in New Delhi, India, the research cell functions as a global collaborative and multidisciplinary laboratory facilitating design research that leads to novel spatial tectonics and smart built environments. More info at: www.rat-lab.org [SPIRO]rat Project Team: Sushant Verma – Co-Founder, rat[LAB] Studio [ Tool Conceptualization ] Praneet Mathur - Developer and Programmer [ Tool Development ] Darshi Kapadia - Graphics and Documentation [ Tool Testing & Documentation ]

CONTENTS 1. History and Introduction

2. Mathematical Relations

3. [SPIRO]rat as a Learning Tool

4. Installation

5. Understanding the Tool

6. FAQs and Common Issues

7. Workflows

8. License, Catalogue and Appendix

1.The Spirograph - History and Introduction The spirograph is a classic tool that consists of a ring and a wheel. The wheel in placed inside the ring. After the pen is placed inside one of the holes present on the wheel, it is made to rotate with the help of the ‘teeth’ present on the edges of the ring and a wheel – much like a gear. The wheel rotates on its own axis while revolving around the center of the ring. This motion generates radially symmetric patterns. One can create different patterns with different sizes of ring and wheels.

Figure 1(Left)-Traditional Spirograph [Source: Kannanshanmugam, shanmugamstudio, Kollam (CC BY 3.0)] Figure 2(Right)- Pattern Generated from a Digital Spirograph Setup as produced by [SPIRO]rat

One of the earliest spirographs was constructed between 1845 and 1848 by P.H. Desvignes, who worked in Vienna, for preventing forgeries in bank notes [i]. The mathematician Bruno Abakanowicz invented the spirograph between 1881 and 1900 to calculate the area closed by a curve [ii]. One of the first spirographs to be advertised as a toy, ‘Marvelous Wondergraph’ [iii] came out in 1900s. A book called ‘The Boy Mechanic – A wondergraph’ was also launched which contained instructions. It was further developed by A British engineer Denys Fisher who exhibited the Spirograph in 1965 at the Nuremberg International Toy Fair and produced it in Britain [iv]. In 2013 the Spirograph brand was re-launched worldwide by Kahootz Toys with products that returned to the use of the original gears and wheels [v] .

References i - https://collection.sciencemuseum.org.uk/objects/co60094/spirograph-and-examples-of-patterns-drawn-using-itspirograph ii - L’Europe mathématique: histoires, mythes, identités edited by Catherine Goldstein, Jeremy Gray, Jim iii- ‘The Boy Mechanic - a wondergraph’ , 1913 iv- https://www.kahootztoys.com v- https://www.kahootztoys.com

2. Mathematical Relations

A B

The spirographs form mathematical curves that are knows as Epitrochoids and Hypotrochoids[1]. 1. Consider a circle A and B of radius RA and Rb and center CA and Cb respectively. 2. Consider a point P at a distance d from the Cb. One must note that the point could lie anywhere on the on a circle of radius d with Cb as the center. Any point on this circle would generate the same pattern. 3. The circle B rolls along the circle A, that is - P rotates around Cb while revolving around CA. 4. Tracing the path of point P during this motion gives us a hypotrochoid curve. The patterns generated are always radially symmetric. 5. Alternately, the circle B can roll on the outside of the circle A forming an epitrochoid curve. 6. The pattern formed depends on the number of times the circle rotates with respect to the number of times it revolves. 7. In the spirograph tool, this is controlled by the ‘teeth’ present of the edge of the inner wheel and outer ring. These interlock like in gears. They are available in sizes that correspond to the number of teeth present on them. Hence this number is always a positive integer. 8. For a ring size SA and wheel size Sb – the number of sides s, in the curve or the number of radial axes is determined by s = [ LCM[2] (SA, Sb) / Sb ] 9. The number of revolutions, r1, is determined by r1= [ LCM (SA, Sb) / SA ] 10. The number of rotations, r2 ,is determined by r2 = [ LCM (SA, Sb) /Sb ] - [ LCM (SA, SB) / SA ]

1- Epitrochoids and Hypotrochoids are a curves of the variety roulettes 2 - LCM = Lowest Common Multiple

3. [SPIRO]rat as a learning tool With computation and parametric design becoming an important part of the design industry, it is important for students to understand the design processes and workflows associated with it. Beginners and amateurs are often misguided with a large volume of visual information available on the web and limited technical information for understanding. In such cases, designs tend to be driven by â&#x20AC;&#x2DC;what the tool can doâ&#x20AC;&#x2122; rather than using the tool to aid the design process. Much like other design processes â&#x20AC;&#x201C; a computational design process must start in the same way - an idea, concept or thought. Computation aids this beginning in visualization, generating iterations, handling complexities, documentation and manufacturing. The computer is only a tool that helps realize the design. The larger aim of creating a Grasshopper3D Plug-in is to create an academic and knowledge-sharing exchange that can take place to create awareness and spread technical knowledge. Many designers still lack the relationship between mathematics and geometry which restricts them in their creative outputs and thought process. By exploring a simple tool such as spirograph, many of these aspects can be understood but it lacks a technical guidance. [SPIRO]rat, as a tool, along with the example files and elaborate documentation, serves as the first step to spread technical knowledge of understanding one of many aspects that define the relationship between mathematics and geometry. [SPIRO]rat plugin reflects and encourages this workflow of computational design processes. It takes the idea of a classic tool and digitalizes it for better understanding and control of the outcome. The tool not only gives patterns as outputs but also possibilities of parameters to get desired patterns and data corresponding to generated pattern. This helps understand the mathematical relationship between parameters. Once the basic relationships are understood one can explore with customized patterns and shapes. The workflow strongly encourages more control over the generated design.

Some Applications of Spirographs: https://www.dezeen.com/2016/06/22/shawn-yang-giant-spirograph-lab-machine-home-accessories-homewaregraduate-design/ https://maxwelldemon.com/2010/01/14/spirographs-and-the-third-dimension/

4. Installation

[SPIRO]rat is available free for all versions of Rhinoceros 5 and 6 from Food4Rhino.com To install [SPIRO]rat: • Close all instances of Rhinoceros • Download and run the [SPIRO]rat setup. Ignore all antivirus alerts, if any. • Follow instructions in the setup to install [SPIRO]rat to your system. The installation is located at C:\Users\ (Username)\AppData\Roaming\Grasshopper\Libraries\[SPIRO]rat by default. The installation folder also contains Example Scripts and Documentation for [SPIRO]rat. You may quickly access the documentation and example files from within Grasshopper by Right-Clicking on any [SPIRO]rat component and clicking on the menu item with the plugin logo and name; Then click on Documentation or Example Files.

If you have a version of [SPIRO]rat previously installed at the default location, PLEASE UNINSTALL ANY PREVIOUS VERSIONS BEFORE INSTALLING AN UPDATED VERSION OF [SPIRO]rat. To uninstall [SPIRO]rat, open ‘Add or Remove Programs’ from the Control Panel or Settings App and uninstall from there.

5. Understanding the Tool 5.1

Understanding Parameters:

1. 2. 3. 4.

Plane – The plane of which the graph is to be made Ring Size – Size of the outer ring (integer) Wheel size – Size of inner ring (integer) Hole Parameter – The position of point between the center and the edge of the wheel as a factor (real number greater than 0 and less than 1) 5. Inside / Outside (Hypotrochoids/Epitrochoids) – Define if the wheel is to move inside or outside the ring (Boolean) 6. Wheel Rotations – Number of times the wheel rotates around its center (number of type integer) 7. Wheel Revolutions – Number of times the wheel revolves around the center of the ring (integer) 8. Resolution – It determines the precision of the curve made (integer greater than 0 and less than 7). Technically, Resolution is ‘x’ where the number of points plotted using the spirograph setup is ‘10x‘. Curves are further drawn using these points. Higher Resolution takes longer to compute. Ideal Resolution should be 3 or 4 9. Length of Curve – Length of the graph made 10. Sides – The number of ‘arms’ in the one graph 11. Spirograph - Data type that contains the curve of the graph made and the parameters associated with it 5.2 Components Components are divided into 4 categories under the [SPIRO]rat tab: 1. 2. 3. 4.

Derive Set Draw Modify

1. Derive 1.1 Get Possibilities – Gives a list of possible combinations of wheel and ring sizes for a given number of sides from a standardized database, along with one randomly selected possibility. The seed controls the random values selected from the list of possibilities.

1.2 Get Wheel Possibilities – Gives a list of possible wheel sizes for a given combination of number of sides and ring size from a standardized database, along with one randomly selected possibility.

1.3 Get Ring Possibilities – Gives a list of possible ring sizes for a given combination of number of sides and wheel size from a standardized database, along with one randomly selected possibility.

1.4 Array Spirographs – Generates multiple hole parameters randomly when keeping ring size and wheel size constant.

2. Set 2.1 Set Spirograph – Defines a Spirograph Setup in the grasshopper canvas. This Setup can further be used as data in a workflow. The Spirograph data-type contains all necessary information about the Spirograph setup required by other components to draw/modify the pattern curves/points.

2.2

Stats â&#x20AC;&#x201C; Returns all information contained in a spirograph setup along with some useful statistics.

2.3 Show Gears â&#x20AC;&#x201C; Draws the ring circle, wheel circle and hole point at any given step for a spirograph setup. Last step must be a value from 0 to 1 that defines the step up to which the spirograph setup is plotted. Last Step = 1 represents the complete plot. You may animate the Last Step Slider to get an animation of the plotting process for the spirograph.

2.4 3D Spirograph â&#x20AC;&#x201C; Generates a 3D curve for the equation y=sin((n/d) *x). Demonstrates how spirographlike curves are not confined to only 2D space. Use values as described for each input parameter.

3. Draw 3.1 Draw – Generates a closed curve from the plot of a spirograph setup. Resolution controls the accuracy of the output curve.

3.2 Draw Steps – Generates part of the complete curve from the plot of a spirograph setup. Resolution controls the accuracy of the output curve. Last step must be a value from 0 to 1 that defines the step up to which the spirograph setup is plotted. Last Step = 1 represents the complete plot. You may animate the Last Step Slider to get an animation of the plotting process for the spirograph.

3.3 Get Points – Generates the path points from the plot of a spirograph setup. Resolution controls the number of points plotted.

3.4 Get Step Points – Generates the path points from the plot of a spirograph setup up to the last step. Resolution controls the number of points plotted. Last step must be a value from 0 to 1 that defines the step up to which the spirograph setup is plotted. Last Step = 1 represents the complete plot. You may animate the Last Step Slider to get an animation of the plotting process for the spirograph.

4. Modify 4.1 Build Panels – Builds Surfaces from a spirograph pattern curve. USE A BOOLEAN TOGGLE TO RUN. This component may take a long time to compute in certain cases. Works best with simple spirograph patterns with a smaller number of sides.

4.2 Build Strips – Builds a surface from widened strips of the spirograph pattern curve. Width defines the offset on both sides of the curve. USE A BOOLEAN TOGGLE TO RUN. This component may take a long time to compute in certain cases. Works best with simple spirograph patterns with a smaller number of sides.

4.3

Get Symmetry Planes – Generates planes of symmetry for the pattern curve of the spirograph.

4.4 Color Code – Colors multiple spirograph curves randomly to help distinguish between multiple spirograph setups.

Spirograph Parameter Accessed from under the ‘Params’ tab in the ‘Primitive’ section, a Spirograph Parameter can contain the Spirograph Datatype. Users may store multiple spirograph setups in a parameter and may also internalize data. This parameter is useful when handling multiple spirograph setups and managing data. Right-click on an empty Spirograph parameter and select “Set One Spirograph” to set a single setup using the dialog prompt shown below.

The ‘Set one Spirograph’ Dialog box shown above can be used to setup a basic spirograph. It allows the user to choose one of the three world planes, a ring size, wheel size, hole parameter and choose whether the wheel is to be place inside or outside the ring. The user may also edit the values of any internalized data using this dialog, if the internalized data contains a single valid spirograph on one of the three world planes. Information The Information Component displays information about the [SPIRO]rat plugin. It has no function and cannot store/modify any data. You may place this component in your scripts while sharing to give credits to the creators of [SPIRO]rat.

Ring / Wheel Size In traditional spirographs, the wheel or ring number is determined by the number of teeth along the circumference. Since teeth are not required to make a digital spirograph function, the Wheel or Ring Size directly controls the radius. This gives results similar to traditional spirographs due to the fact that the number of teeth is directly proportional to the circumference, which is in turn directly proportional to the radius. Hole Parameter

1 1

Hole number ‘8’ of Wheel ‘50’ is at ~0.47 between the center of the wheel and the edge. When used with Ring ‘105’, the pattern above is produced.

Hole Parameter 0.47, Wheel size 50 and Ring size 105 produces the same pattern digitally.

The Hole Parameter controls the position of the hole in the wheel that draws the pattern. In traditional spirographs, each hole is placed at an increasing distance from the center of the wheel as the hole number increases. To simplify this mechanism in digital spirographs, the Hole Parameter simply defines a point at a position between the center of the wheel and it’s edge, where the center = 0 and the edge = 1. Last Step

Last Step = 0.000

Last Step = 0.200

Last Step = 0.400

Last Step = 0.600

Last Step = 0.800

Last Step = 1.000

The Last Step defines the current position in the drawing procedure time-line from 0 to 1. The user may scrub the Last Step slider to preview how the pattern is drawn. The slider my also be animated to produce frames of making the pattern. All ‘Draw’ Components use a ‘Resolution’. as explained previously, this controls the number of points plotted to make the spirograph pattern. This in turn also determines the maximum decimal places that can be used for the Last Step parameter. For example, if the Resolution is 4, the maximum decimal places in the Last Step will be 4. At Last Step = 0.4282, all points up to the 4,282nd point (out of 10,000 points) will be plotted to generate the pattern. Shown here is a series of 6 steps from 0 to 1. 3D Spirograph As mentioned previously, the 3D Spirograph component functions based on a mathematical function given as follows: x

This equation is used to plot polar points which are then interpolated to generate a curve. The component allows you to control the values of ‘n’, ‘d’ and ‘x’ in this equation. The ratio ’n/d‘ defines the overall form of the output curve. This ratio is directly controlled by the ‘N’ and ‘D’ parameters. Basic trigonometric logic can be used for a rough idea of the output form.‘X’ parameter defines the upper limit of ‘x’ in the equation. Resolution in turn controls the number of values to be used for ‘x’ in the equation. Higher resolution implies more number of points and a more accurate curve.For each step in ‘x’, the component plots a polar point with the XY rotation defined by the current value of ‘x’, the Z rotation defined by ‘Z’ parameter and the offset defined by the value of ‘y’ above for ‘x’. All the points plotted are then used to make a curve which is given as output. Shown below is an example output from the 3D Spirograph Component.

FAQs and Common Issues • High resolution values cause the script to become very slow or crash - Keep the Resolution at 3 or 4. Resolution is ‘x’ where the number of points plotted using the spirograph setup is 10x. For example, if the resolution is set to 4, exactly 1,000 points will be plotted using the spirograph and a curve will be interpolated using these points to get the pattern curve.

Resolution = 3

Resolution = 4

• Build Panels and Build Strips components take too long to compute or don’t compute - Both these components perform time-taking and complex tasks using the curve generated from the Draw component. For best results, ensure the number of sides of the spirograph pattern is not more than 20. Simpler patterns will compute quicker. Also ensure you are not using a large list or tree of spirograph curves. Toggle the Run Boolean parameter only after ensuring these conditions. These components may return unexpected results in rare conditions which can be fixed by adjusting the input parameters slightly. • ‘Get Possibilities..’ components don’t work in some cases - These components work using a generative database of ring and wheel combinations for various number of sides. In case these components are showing an error, it is because the combination of input parameters does not match any entry in the database. In most reasonable cases, scrubbing one of the input sliders should help finding other possibilities. The reason behind this issue is that the spirograph logically depends on the LCM/GCD function which makes reverse calculations extremely complicated. • Size of the spirograph pattern changes drastically when using Get Ring/Wheel Size components As mentioned above, the functioning of these components is limited. When a parameter is changed, the components randomly select an entry from the database, which may often be a multiple of another entry of a smaller/larger size. • The pattern generated is too small / Decimal values aren’t working - [SPIRO]rat works best with units set to Millimeters and does not accept non-integer values for the ring and wheel sizes. The reason for this, once more, is the core mathematics behind spirographs which is based on the LCM/GCD function. Since decimal values cannot have a GCD, only integer values can be used. Scaling the pattern after generation may help solve any issues related to this. You may also use multiples of the input values to generate scaled up patterns. • Unable to use 3D Spirograph with any other components to produce sensible geometry - The 3D Spirograph component generates pure mathematical geometry (Please refer to it’s description to know more). It is an experimental component with the purpose of only demonstrating possibilities of mathematics in geometry and design. If you wish to use 3D spirographs for designing, this component may not be very useful. • Build Strips and Color Code components aren’t present in my grasshopper ribbon - Both these components were built for Rhinoceros versions above 6.10, due to changes in the SDK. Please update your Rhinoceros to use them. 14

5.3 Workflow 5.3.1 Draw Spirograph

1. 2. 3. 4. 5. 6.

5.3.2 Draw Steps

1. 2. 3. 4. 5. 6.

Start a Rhinoceros File Start a new definition in Grasshopper Create a new Point parameter at the origin (0, 0, 0) Use the point to define an XY Plane Place a ‘Set Spirograph’ Component and plug in the XY plane to the ‘Plane’ or P parameter Double click on the canvas and type ‘100<200<500’ to create a number slider that returns an integer value between 100 and 500, with a default value of 200 7. Connect this number slider to the ‘Ring Size’ or R Parameter 8. Double click on the canvas and type ‘5<75<350’ to create a number slider that returns an integer value between 5 and 350, with a default value of 75 9. Connect this number slider to the ‘Wheel Size’ or W Parameter 10. Double click on the canvas and type ‘0.01<0.65<0.99’ to create a number slider that returns a number between 0.01 and 0.99, with a default value of 0.65 11. Connect this number slider to the ‘Hole Parameter’ or H Parameter 12. Create a Boolean Toggle, connect it to the ‘Inside/Outside’ or I/O Parameter and set it to True 13. Place a ‘Draw Steps’ Component from the [SPIRO]rat tab and connect the ‘Spirograph’ or S parameter to the output Spirograph from the ‘Set Spirograph’ Component 14. Double click on the canvas and type ‘2<3<4’ to create a number slider that returns an integer value between 2 and 4, with a default value of 3 15. Connect this number slider to the ‘Resolution’ or R Parameter 16. Double click on the canvas and type ‘0.000<0.5<1’ to create a number slider that returns a number between 0.000 and 1.000, with a default value of 0.500 17. Connect this number slider to the ‘Last Step’ or L Parameter

5.3.2 Build Panels

1. 2. 3. 4. 5. 6.

Start a Rhinoceros File Start a new definition in Grasshopper Create a new Point parameter at the origin (0, 0, 0) Use the point to define an XY Plane Place a ‘Set Spirograph’ Component and plug in the XY plane to the ‘Plane’ or P parameter Double click on the canvas and type ‘0.01<0.65<0.99’ to create a number slider that returns a number between 0.01 and 0.99, with a default value of 0.65 7. Connect this number slider to the ‘Hole Parameter’ or H Parameter 8. Create a Boolean Toggle, connect it to the ‘Inside/Outside’ or I/O Parameter and set it to True 9. Place a ‘Get Possibilities’ Component 10. Double click on the canvas and type ‘2<11<15’ to create a number slider that returns an integer value between 2 and 15, with a default value of 11 11. Connect this number slider to the ‘Number of Sides’ or N Parameter 12. Double click on the canvas and type ‘50’ to create a number slider that returns an integer value between 0 and 100, with a default value of 50 13. Connect this number slider to the ‘Seed’ or S Parameter 14. Connect the ‘Random Ring Size’ or R output parameter to the ‘Ring Size’ or R input parameter of the ‘Set Spirograph’ Component 15. Connect the ‘Random Wheel Size’ or W output parameter to the ‘Wheel Size’ or W input parameter of the ‘Set Spirograph’ Component 16. Place a ‘Draw’ Component from the [SPIRO]rat tab and connect the ‘Spirograph’ or S parameter to the output Spirograph from the ‘Set Spirograph’ Component 17. Double click on the canvas and type ‘2<3<4’ to create a number slider that returns an integer value between 2 and 4, with a default value of 3 18. Connect this number slider to the ‘Resolution’ or R Parameter 19. Place a ‘Build Panels’ Component and connect the ‘Curve’ or C output parameter from the ‘Draw’ Component to the ‘Curve’ or C input parameter 20. Create a Boolean Toggle, connect it to the ‘Run’ or ‘>’ Parameter but do not switch it to True immediately 21. Change the input values like number of sides, seed, hole parameter, etc. to get a spirograph pattern you are happy with 22. Switch the ‘Run’ Boolean toggle to True in order to build panel surfaces from the spirograph curve

License Copyright © 2019 rat[LAB] Studio - Research in Architecture and Technology Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the ‘Software’), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute and/or sublicense copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED ‘AS IS’, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. Proudly Made in India.

This document was created on 25-Apr-2019 18

RING SIZE: 105 (I) WHEEL SIZE: 45 HOLE PARAMETER: 0.65 STRIP WIDTH: 5

RING SIZE: 105 (I) WHEEL SIZE: 50 HOLE PARAMETER: 0.65 STRIP WIDTH: 1

RING SIZE: 105 (I) WHEEL SIZE: 32 HOLE PARAMETER: 0.65 STRIP WIDTH: 1

RING SIZE: 105 (O) WHEEL SIZE: 45 HOLE PARAMETER: 0.65 STRIP WIDTH: 3

RING SIZE: 105 (O) WHEEL SIZE: 50 HOLE PARAMETER: 0.65 STRIP WIDTH: 3

RING SIZE: 105 (O) WHEEL SIZE: 32 HOLE PARAMETER: 0.65 STRIP WIDTH: 1

RING SIZE: 150 (I) WHEEL SIZE: 95 HOLE PARAMETER: 0.73 STRIP WIDTH: 2

RING SIZE: 180 (O) WHEEL SIZE: 40 HOLE PARAMETER: 0.95 STRIP WIDTH: 4

RING SIZE: 180 (I) WHEEL SIZE: 40 HOLE PARAMETER: 0.95 STRIP WIDTH: 4

RING SIZE: 105 (O) WHEEL SIZE: 95 HOLE PARAMETER: 0.73 STRIP WIDTH: 2

RING SIZE: 144 (O) WHEEL SIZE: 40 HOLE PARAMETER: 0.95 STRIP WIDTH: 1

RING SIZE: 105 (I) WHEEL SIZE: 95 HOLE PARAMETER: 0.73 STRIP WIDTH: 1

RING SIZE: 144 (I) WHEEL SIZE: 40 HOLE PARAMETER: 0.95 STRIP WIDTH: 1

RING SIZE: 105 (O) WHEEL SIZE: 95 HOLE PARAMETER: 0.73 STRIP WIDTH: 1

RING SIZE: 105 (O) WHEEL SIZE: 32 HOLE PARAMETER: 0.65 STRIP WIDTH: 1

RING SIZE: 105 (I) WHEEL SIZE: 45 HOLE PARAMETER: 0.75

RING SIZE: 105 (I) WHEEL SIZE: 50 HOLE PARAMETER: 0.65

RING SIZE: 105 (I) WHEEL SIZE: 32 HOLE PARAMETER: 0.65

RING SIZE: 105 (I) WHEEL SIZE: 95 HOLE PARAMETER: 0.73

RING SIZE: 150 (O) WHEEL SIZE: 45 HOLE PARAMETER: 0.65

RING SIZE: 150 (O) WHEEL SIZE: 32 HOLE PARAMETER: 0.65

RING SIZE: 150 (I) WHEEL SIZE: 95 HOLE PARAMETER: 0.73

RING SIZE: 150 (I) WHEEL SIZE: 45 HOLE PARAMETER: 0.65

RING SIZE: 105 (O) WHEEL SIZE: 50 HOLE PARAMETER: 0.65

RING SIZE: 105 (O) WHEEL SIZE: 32 HOLE PARAMETER: 0.65

RING SIZE: 105 (O) WHEEL SIZE: 95 HOLE PARAMETER: 0.73

RING SIZE: 144 (O) WHEEL SIZE: 40 HOLE PARAMETER: 0.95

RING SIZE: 150 (I) WHEEL SIZE: 32 HOLE PARAMETER: 0.65

RING SIZE: 150 (O) WHEEL SIZE: 95 HOLE PARAMETER: 0.73

RING SIZE: 180 (O) WHEEL SIZE: 40 HOLE PARAMETER: 0.95

RING SIZE: 180 (I) WHEEL SIZE: 40 HOLE PARAMETER: 0.95

RING SIZE: 200 (I) WHEEL SIZE: 150 HOLE PARAMETER: 0.6

RING SIZE: 144 (I) WHEEL SIZE: 40 HOLE PARAMETER: 0.95

RING SIZE: 105 (O) WHEEL SIZE: 45 HOLE PARAMETER: 0.65

RING SIZE: 200 (I) WHEEL SIZE: 125 HOLE PARAMETER: 0.6

RING SIZE: 180 (I) WHEEL SIZE: 80 HOLE PARAMETER: 0.6

RING SIZE: 190 (I) WHEEL SIZE: 90 HOLE PARAMETER: 0.6

RING SIZE: 150 (O) WHEEL SIZE: 90 HOLE PARAMETER: 0.6

RING SIZE: 120 (I) WHEEL SIZE: 80 HOLE PARAMETER: 0.6

RING SIZE: 200 (I) WHEEL SIZE: 140 HOLE PARAMETER: 0.6

RING SIZE: 200 (I) WHEEL SIZE: 130 HOLE PARAMETER: 0.6

RING SIZE: 210 (O) WHEEL SIZE: 170 HOLE PARAMETER: 0.6

RING SIZE: 210 (I) WHEEL SIZE: 165 HOLE PARAMETER: 0.6

Use #SPIROrat #ratLABeducation

to have your work showcased on our webpage www.rat-lab.org/designtechtools The following graphics have been made using [SPIRO]rat along with other tools 20

S. No.

Term

Page No.

3D Spirograph

Array Spirographs

Build Panels

Build Strips

Color Code

Components

Derive

Draw

Draw Curve

Draw Steps

Epitrochoid

Get Points

Get Possibilities

Get Ring Possibilities

Get Step Points

Get Symmetry Planes

Get Wheel Possibilities

Hole Parameter

5, 10

Hypotrochoid

Inside/Outside

Last Step

Modify

Parameters

Plane

Resolution

5, 12

Ring Size

5, 10

Run

5, 12

Set

Set Spirograph

Show Gears

Sides

Spirograph

Spirograph Parameter

Spirograph Statistics

Symmetry Planes

Wheel Revolutions

Wheel Rotations

Wheel Size

5, 10

Workflow

11 25