Mixed methods for complex kinematic constraints in dynamic figure animation

Advances for achieving user control of a dynamic simulation of linked figures is presented. The formulation integrates forward and inverse kinematics specification within a mixed method of forward and inverse dynamics simulation. Kinematic specifications can be imposed through kinematic constraints embedded within the dynamics framework. Kinematic constraints may be simple (functions of one degree of freedom), or complex (functions of multiple interrelated degrees of freedom). Thus, keyframed paths, closed loops, point-to-path constraints, and collisions between links and the environment can be simulated. A simultaneous solution for unknown motion and forces of constraint is performed. A Lagrange multiplier method is outlined for incorporating these general constraints into the mathematical formulation of the equations of motion. Results from three example simulations are presented and discussed.