My second Python Project is an application that allows the 2D Kinematics simulation of simple rod and ball joint frameworks. As an example the movement of a Strandbeest leg is simulated. The app is an ideal introduction to Python in mechanical engineering as it covers two key aspects: Visualization and Numerics.

A Model consists of:

• a set of nodes. Each node has a unique name and a current position (x,y)
• a set edges (or rods), specified by the name of the two edges it connects
• a set of boundary constraints that constrain the movement of the nodes

Each node introduces two degrees of freedom to the model (x and y). A rod enforces a constant distance between two edges. Each rod constrains one degree of freedom. The boundary constraints constrain the movement of a node. The NodeMoveBC constrains the speed of a node alongside a direction vector. The velocity orthogonal to the direction is not constrained. Each NodeMoveBC there constrains one degree of freedom. The RotationBC constrains a node to move in a circular motion around a pivot point. It constraings two degrees of freedom. If there is as many (rendundancy free) constraints as there are degrees of freedom, the system is terminate and can be simulated.

Nodes are added via the addNode() method, edges via addEdge(). Boundary constraints are added directly to the bcs list.

import Strandbeest

leg = Strandbeest.Model()
leg.addNode('p0',   0.,             0.)
leg.addNode('p1', -35.0353991829,  19.5071987762)
leg.addNode('p2',  17.7855809088,  37.4956412365)
leg.addNode('p3',  50.7538954493,  -0.0954512769988)
leg.addNode('p4',  2.77183874468, -39.2021288959)
leg.addNode('p5', -17.0054756067, -84.0335669394)
leg.addNode('p6', -28.0419102143, -19.2671627536)
leg.addEdge('p0','p1')
leg.addEdge('p0','p2')
leg.addEdge('p0','p4')
leg.addEdge('p1','p2')
leg.addEdge('p1','p6')
leg.addEdge('p2','p3')
leg.addEdge('p3','p4')
leg.addEdge('p4','p5')
leg.addEdge('p4','p6')
leg.addEdge('p5','p6')
leg.bcs += [
  Strandbeest.NodeMoveBC(leg,'p0',(1,0),0),
  Strandbeest.NodeMoveBC(leg,'p0',(0,1),0),
  Strandbeest.RotationBC(leg,'p3',(38,7.8),-1)
]

The Model::increment() method advances the simulation by the specified time step dt. The node positions change accordingly. The Runge Kutta Method (RK4) is used to numerically integrate the node movements. Generally speaking, the simulation precision increases with smaller time steps.

The Strandbeest.Widget allows the visualization and inspection of the Model's simulation results. Once a Model submitted to the Widget it must not be modified. The Widget is handled like a regular PyQt4 QWidget, with the difference of taking a Model as constructor argument:

from PyQt4.QtGui import QApplication
import sys
import Strandbeest

app = QApplication(sys.argv)
wdgt = Strandbeest.Widget(model)
wdgt.setGeometry(200,200,800,600)
wdgt.show()
sys.exit( app.exec_() )

The Start/Stop button on the upper left hand of the window allows to start and stop the animation. The slider changes the animation speed. Moving the mouse over the nodes displays the name of the nodes. A secondary mouse button click on a node opens a context menu that allows to display a movement curve for the node and allows to display the nodes values in a separate diagram.