WOLFRAM|DEMONSTRATIONS PROJECT

Kinematics of Planar Elastic Chains

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number of links
4
control type
2D slider
two 1D sliders
force on initial link
torque on first link
0
total mass of chain
0
This Demonstration shows an
n
-link planar kinematic chain with a fixed base in which each joint is a linearly elastic torsional spring. The shape of this chain in static equilibrium can be represented as the solution of a discrete-time optimal control problem, with boundary conditions that vary with the position and orientation of the last link. McCarthy and Bretl proved that the set of all solutions to this problem is a smooth manifold that can be parameterized by a single chart. We have added gravitational force to this model.