Dynamical simulation of assemblies of planar, 1 DOF parts with changing contacts using configuration spaces

We present an algorithm for dynamical simulation of rigid-body mechanical systems with changing contact topologies based on configuration spaces. The algorithm advances the state of the art in contact analysis, which is the main bottleneck in dynamical simulation. The task is to identify the touching parts and to compute the ensuing contact forces. Our algorithm computes the configuration spaces of all pairs of parts and uses them as contact models. It overcomes the limitations of mechanical systems simulators, which require precomputed contact models, and of general-body simulators, which perform contact analysis on the part models at every time step. Neither approach is practical for mechanisms with multiple contacts and complex contact geometry, such as clock escapements, chain gears, and part feeders. We describe a configuration space simulator for assemblies of planar parts with one degree of freedom apiece and demonstrate it on two mechanisms with many complex contacts.