Here are some simple applets demonstrating algorithms for linked rigid bodies.
Note that you must have Java 1.6 installed for some of these to work.
A simple IK demo
IK stands for inverse kinematics. Forward kinematics stands for the function that maps joint angles to positions on the articulated object. Inverse kinematics maps positions to joint angles. For this simple system, you can use an analytic solver to invert the dynamics. Note that there is not a unique inverse, even in this simple case. More complicated systems require numerical iterative solvers.
Double-click to start or stop a physical simulation of the double pendulum. You can
position the double-pendulum as in the ik applet. Gravity and damping
eventually bring the system to rest in the stable equilibrium point. The
equations of motion for this system can easily be derived using
Euler-Lagrange mechanics (least action principle).
Now the movement of the double pendulum is controlled using inverse
dynamics, or computed torques, to stabilize around the unstable
equilibrium point. A precise model of the system dynamics is used to
drive the system to that point in a spring-like fashion. You can grab the
double pendulum during simulation and watch it react to perturbations.
Marco da Silva
Last modified: Tue Aug 19 14:05:02 EDT 2008