Dipyramid Documentation
Alexander Yu
Arch 490.1
AIM
One of the main goals of the module is to be rigid in order to resist a vertical load. The other goal to create a curved form out of rigid modules that can be defined by a series of parameters
Rigid Module 1.1
Predictable Curved Global Form 1.2
Alexander Yu
Arch 490.1
FORM
Equilateral Triangle
Elongated to create an isosceles triangle
Symmetrical triangular form to allow for aggregation on either side of module
Removed a face because the only one is needed to define the angle of the top face
Alexander Yu
Arch 490.1
Figure 2.1
Two of the isosceles triangles were joined together in order to create a component that would be able to define a curve as seen in Angles 7.1, 7.2
FORM
The basic form is two tetrahedrons with a shared base. (Figure 3.1) The angles and side lengths of this module is controlled by 5 control points (figure 3.3) The tetrahedron was further simplified to two fixed sides, (represented in the red), connected by adjustable edges, (represented in the grey) (figure 3.4) This allows the aggregation to be controlled by a single parameter.
Alexander Yu
Arch 490.1
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
COMPONENTS
The adjustable edge length controls the angle of the vertical panel. (Figure 4.1)
Fixed Length
Adjustable Length
Fixed Length
Figure 4.1
Alexander Yu
Arch 490.1
COMPONENTS
The adjustable edge is shown at different lengths, and the resulting angle of the vertical side. (Figure 5.1 - 6)
C
Figure 5.1
C
Figure 5.4
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Arch 490.1
C
Figure 5.2
C
Figure 5.5
Figure 5.3
C
Figure 5.6
GLOBAL FORM Sum of interior angles = (n-2)180 Each interior angle = ((n-2)180)/n Each exterior angle = (180-((n-2)180)/n)/2
The angle at which the two flaps of the trapezoid are bent out at determine the radius of the “global” cylinder form. These angles are then used to determine relationships between the components as seen in Figure 7.1
Figure 6.1
Figure 6.2
Alexander Yu
Arch 490.1
Number of Sides
Fold Angle (°)
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
45 36 30 25.7 22.5 20 18 16.4 15 13.8 12.9 12 11.25 10.6 10 9.5 9 Table 6.3
GLOBAL FORM
The length of “C� determines the angle that the vertical side is leaning. The angle that the vertical side is leaning at in turn defines the angle between the vertical panels. Finally, this angle informs the curvature of the global form.
C
LEAN ANGLE
Figure 7.1 OUT
C
C
Figure 7.2 Alexander Yu
Arch 490.1
LEAN
Figure 7.3
GEOMETRY
Given A=3.5”, B=2”, J=2.5”, ANGLE Find C Cylinder Calculations
A
J B
B
RADIUS R=((J/2)/sin(ANGLE)) LEAN = R-Rcos(ANGLE) = R(1-cos(ANGLE) = ((J/2)/(sin(ANGLE))(1-cos(ANGLE) OUT =SQRT(B2-(J/2)2) - LEAN 2 2 =SQRT(B -(J/2) ) - ((J/2)/(sin(ANGLE))(1cos(ANGLE) Inverted Triangle Calculations
C
=SQRT(A2-(J/2)2) =SQRT(TRUE HEIGHT2 - LEAN2) 2 2 =SQRT(A -(J/2) 2 ((J/2)/(sin(ANGLE))(1-cos(ANGLE)
TRUE HEIGHT FLOOR HEIGHT
C
=SQRT(OUT2 + FLOOR HEIGHT2)
C =A2 + B2 - 2(J/2)2 - 2SQRT(B2 -(J/2)2) (((J/2)/sin(ANGLE))(1-cos(ANGLE))
Alexander Yu
Arch 490.1
CONTROLLING THE GLOBAL FORM By increasing the length of side “C”, it is possible to morph the global form from cylindrical to fully open.
Figure 8.1
Alexander Yu
Arch 490.1
Figure 8.2
CONTROLLING THE GLOBAL FORM By using multiple global aggregations it would be possible to possible to construct a wall comprised of preinformed clusters that could react to various stimuli such as light or motion. These inputs can then be interpreted and used to adjust the length of “C� thus morphing the wall from a solid wall to one that has openings.
Figure 9.1
Open (Figure 9.1) Closed (Figure 9.2)
Figure 9.2
Alexander Yu
Arch 490.1
ADJUSTMENT “C”
Photo Cell Tube
However, this method is slow, requires human input, and the panels cannot all change simultaneously.
A possible solution is to use arduino and stepper motors to control the length of “C”
Alexander Yu
Arch 490.1
Threaded Rod
Coupler
Motor Control
Stepper Shield
This led to the idea that the aggregation can be controlled by an electrical mechanism because it can be automated such that human input is not required so it is possible for the mechanism to work even when humans are not present.
Nut
Micro Controller
ARDUINO
Initially, it was proposed to use sets of interchangeable panels that had different values of “C” in order to manipulate the global form.
Stepper
Based on the amount of light hitting the photo cell, arduino and the motor shield can control the number of revolutions the motor turns, thus allowing the system to control “C” in a finite way.
C
MATERIALS
Adjustable Side Length Arduino Motor Shield Stepper Motor Coupler Threaded Rod
Front and Back Plate Thin Sheet Metal (Aluminum) Fiberglass Wood
Material
Quantity
Cost
Material
Quantity
Cost
Aluminum .05
(2) 4x8
$230
Arduino
1
$30
Fiberglass 8 oz
(2) 4x8
$172
Motor Shield
5
$100
Wood
(2) 4x8
$80
Stepper Motor
9
$126
Coupler
9
$45
Threaded Rod
9
$27
Total Alexander Yu
Arch 490.1
$328