DYNAMICS

TRUSS SIMULATOR (DYNAMICS+STATICS+KINEMATICS)

Preview

Montage Video (2K60FPS)

Montage (Parallel) Video (2K60FPS)

Steps

Pre-Requirements

Installation: GNU/Linux and apt package manager

Compilation: GNU/Linux and gcc-14 C23 or higher

Execution: GNU/Linux and minimum 2GB memory (for 2K60FPS)

(Recommended distro: Ubuntu 24.04 or higher)

Setup

./setup.sh

Format

./format.sh

Build

./build.sh

Usage (Scripts)

./custom.sh (stdin option)

strandbeest.txt
0.0
8.0
1000000.0
60.0
1920
1080
0.0
-0.5
0.2
1.0
tmp/strandbeest

Generates a video representing the states of the structure, a video representing the forces on the structure, multiple text files representing the states of the structure in two parts (problems and solutions) from beginning to end, a swept area graph of the structure and a shell script that would be used to generate the aforementioned content.

or

./custom.sh filename=strandbeest.txt gacceleration=0.0 timef=8.0 srate=1000000.0 frate=60.0 fwidth=1920 fheight=1080 fcenterx=0.0 fcentery=-0.5 fzoom=0.2 fscale=1.0 dirname=tmp/strandbeest (args option)

or

./bridges.sh

or

./miscellaneous.sh

or

./machines.sh

or

./pendulums.sh

or

./montage.sh

Usage (Tools)

Truss Solver

cat problem.txt | ./bin/solvetruss gacceleration=float timef=float srate=float

• stdin: Truss Problem
• stdout: Truss Solution
• stderr: error and usage messages

1. gacceleration: vertical component of the gravitational acceleration of a free mass in meters per second squared (positive for downwards, negative for upwards)
2. timef: duration of the simulation in the simulation
3. srate: number of solver time steps in a second of the simulation

Truss Renderer

cat problem.txt | ./bin/rendertruss filename fsize=widthxheight "fcenter=(float float)" fzoom=float fscale=float

• stdin: Truss Problem
• stderr: error and usage messages

1. filename: renderer image output filename
2. fsize: renderer image resolution in pixels (width and height)
3. fcenter: renderer camera center in meters
4. fzoom: renderer camera zoom
5. fscale: renderer scale factor

renderer graphical design from Simple 2D Constraint Solver Demo by Ange Yaghi

Truss Force Diagram Renderer

cat problem.txt solution.txt | ./bin/forcediagram filename gacceleration=float fsize=widthxheight "fcenter=(float float)" fzoom=float fscale=float

• stdin: concatenation of Truss Problem and Truss Solution
• stderr: error and usage messages

1. filename: renderer image output filename
2. gacceleration: vertical component of the gravitational acceleration of a free mass in meters per second squared (positive for downwards, negative for upwards)
3. fsize: renderer image resolution in pixels (width and height)
4. fcenter: renderer camera center in meters
5. fzoom: renderer camera zoom
6. fscale: renderer scale factor

Truss Swept Area Renderer

cat problems/*.txt | ./bin/sweptarea filename fsize=widthxheight "fcenter=(float float)" fzoom=float fscale=float

• stdin: concatenation of many Truss Problem
• stderr: error and usage messages

1. filename: renderer image output filename
2. fsize: renderer image resolution in pixels (width and height)
3. fcenter: renderer camera center in meters
4. fzoom: renderer camera zoom
5. fscale: renderer scale factor

Truss Problem Format

(example: Strandbeest by Theo Jansen)

joints=8
mass=1.000000000e+00 position=(0.000000000e+00 0.000000000e+00) velocity=<0.000000000e+00 0.000000000e+00>
mass=1.000000000e+00 position=(1.143000000e+00 2.280000000e-01) velocity=<0.000000000e+00 0.000000000e+00>
mass=1.000000000e+00 position=(1.575000000e+00 1.380000000e-01) velocity=<0.000000000e+00 -1.000000000e+01>
mass=1.000000000e+00 position=(4.680000000e-01 1.140000000e+00) velocity=<0.000000000e+00 0.000000000e+00>
mass=1.000000000e+00 position=(2.460000000e-01 -1.149000000e+00) velocity=<0.000000000e+00 0.000000000e+00>
mass=1.000000000e+00 position=(-1.074000000e+00 5.160000000e-01) velocity=<0.000000000e+00 0.000000000e+00>
mass=1.000000000e+00 position=(-6.930000000e-01 -6.060000000e-01) velocity=<0.000000000e+00 0.000000000e+00>
mass=1.000000000e+00 position=(-2.910000000e-01 -2.505000000e+00) velocity=<0.000000000e+00 0.000000000e+00>
members=11
joint1=[2] joint2=[3] stiffness=1.000000000e+05 length0=4.412754243e-01 dampening=1.000000000e+03
joint1=[1] joint2=[4] stiffness=1.000000000e+05 length0=1.232324633e+00 dampening=1.000000000e+03
joint1=[1] joint2=[5] stiffness=1.000000000e+05 length0=1.175039148e+00 dampening=1.000000000e+03
joint1=[3] joint2=[4] stiffness=1.000000000e+05 length0=1.493135292e+00 dampening=1.000000000e+03
joint1=[3] joint2=[5] stiffness=1.000000000e+05 length0=1.850029729e+00 dampening=1.000000000e+03
joint1=[1] joint2=[6] stiffness=1.000000000e+05 length0=1.191525073e+00 dampening=1.000000000e+03
joint1=[4] joint2=[6] stiffness=1.000000000e+05 length0=1.663472272e+00 dampening=1.000000000e+03
joint1=[5] joint2=[7] stiffness=1.000000000e+05 length0=1.084698115e+00 dampening=1.000000000e+03
joint1=[6] joint2=[7] stiffness=1.000000000e+05 length0=1.184924048e+00 dampening=1.000000000e+03
joint1=[5] joint2=[8] stiffness=1.000000000e+05 length0=1.458459804e+00 dampening=1.000000000e+03
joint1=[7] joint2=[8] stiffness=1.000000000e+05 length0=1.941083460e+00 dampening=1.000000000e+03
supports=2
joint=[1] axes={xy}
joint=[2] axes={xy}
loads=0

1. Joints Count Header
   • syntax: joints=count (trailing newline)
   • number of joints in following body
2. Joints Lines Body
   • syntax: mass=float position=(float float) velocity=<float float> (trailing newline)
   • each individual joint mass in kg, position vector in meters and velocity vector in meters per second
3. Members Count Header
   • syntax: members=count (trailing newline)
   • number of members in following body
4. Members Lines Body
   • syntax: joint1=[index] joint2=[index] stiffness=float length0=float dampening=float (trailing newline)
   • each individual member joints connection indices, stiffness of spring component in Newtons per meter, resting length in meters and dampening of damper component in Newton seconds per meter
5. Supports Count Header
   • syntax: supports=count (trailing newline)
   • number of supports in following body
6. Supports Lines Body
   • syntax: joint=[index] axes={xy|x|y} (trailing newline)
   • each individual support joint connection and axes of reactions
   • if axes={xy}, support is of type pin
   • if axes={x}, support is of type vertical roller
   • if axes={y}, support is of type horizontal roller
7. Loads Count Header
   • syntax: loads=count (trailing newline)
   • number of loads in following body
8. Loads Lines Body
   • syntax: joint=[index] force=<float float> (trailing newline)
   • each individual point load joint connection and global space force vector in Newtons

Truss Solution Format

(example: Strandbeest by Theo Jansen)

joints=8
force=<0.000000000e+00 0.000000000e+00> position=(0.000000000e+00 0.000000000e+00) velocity=<0.000000000e+00 0.000000000e+00>
force=<0.000000000e+00 0.000000000e+00> position=(1.143000000e+00 2.280000000e-01) velocity=<0.000000000e+00 0.000000000e+00>
force=<-1.924897646e+03 9.597507536e+03> position=(1.574999912e+00 1.379004370e-01) velocity=<-1.853201138e-02 -9.908014981e+00>
force=<4.866518460e+03 -4.411109044e+03> position=(4.680002224e-01 1.139999799e+00) velocity=<4.677640373e-02 -4.236804246e-02>
force=<-4.894829223e+03 -4.691786492e+03> position=(2.459997765e-01 -1.149000216e+00) velocity=<-4.701461205e-02 -4.530948283e-02>
force=<2.398431816e+01 9.802039727e+00> position=(-1.074000000e+00 5.160000001e-01) velocity=<1.086096053e-04 4.421615561e-05>
force=<-1.466608796e+01 8.247068603e+00> position=(-6.930000002e-01 -6.059999999e-01) velocity=<-6.627556866e-05 3.765965475e-05>
force=<-2.072519689e+01 -5.198418530e+01> position=(-2.910000003e-01 -2.505000001e+00) velocity=<-9.373943350e-05 -2.357097579e-04>
members=11
force=2.007722245e+03 displacement=2.022962826e-05 length=4.412956539e-01 velocity=2.005699282e+00
force=-2.030252987e+01 displacement=-1.022870788e-07 length=1.232324531e+00 velocity=-2.029230117e-02
force=3.267559743e+01 displacement=1.644910510e-07 length=1.175039312e+00 velocity=3.265914833e-02
force=6.586358850e+03 displacement=6.645013175e-05 length=1.493201742e+00 velocity=6.579713837e+00
force=-6.853336830e+03 displacement=-6.901320613e-05 length=1.849960716e+00 velocity=-6.846435509e+00
force=-6.061074116e-02 displacement=-5.170974759e-11 length=1.191525073e+00 velocity=-6.060557019e-05
force=2.594808640e+01 displacement=1.303784438e-07 length=1.663472402e+00 velocity=2.593504856e-02
force=-1.701401920e+01 displacement=-8.555581577e-08 length=1.084698029e+00 velocity=-1.700546362e-02
force=-4.454160954e-02 displacement=4.953393251e-11 length=1.184924048e+00 velocity=-4.454656293e-05
force=-5.615733072e+01 displacement=-2.821528446e-07 length=1.458459522e+00 velocity=-5.612911543e-02
force=2.330313412e-01 displacement=1.117602011e-09 length=1.941083461e+00 velocity=2.329195810e-04
supports=2
reaction=<8.148812387e-01 5.075922909e+01>
reaction=<-1.965430257e+03 4.099176931e+02>

1. Joints Count Header
   • syntax: joints=count (trailing newline)
   • number of joints in following body
2. Joints Lines Body
   • syntax: force=<float float> position=(float float) velocity=<float float> (trailing newline)
   • each individual joint force vector in Newtons, modified position vector in meters and modified velocity vector in meters per second
3. Members Count Header
   • syntax: members=count (trailing newline)
   • number of members in following body
4. Members Lines Body
   • syntax: force=float displacement=float length=float velocity=float (trailing newline)
   • each individual member tension force (positive for in tension, negative for in compression) in Newtons, displacement from resting length in meters, current measured length in meters and velocity of expansion in meters per second
5. Supports Count Header
   • syntax: supports=count (trailing newline)
   • number of supports in following body
6. Supports Lines Body
   • syntax: reaction=<float float> (trailing newline)
   • each individual support reaction force vector in Newtons