A Yu

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

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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

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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