Contact analysis of spatial fixed-axes pairs using configuration spaces

We present the first configuration space computation al- gorithm for pairs of rigid parts that move along fixed spa- tial axes. The motivation is contact analysis for mechanical design of spatial systems and of planar systems with axis misalignment. The part geometry is specified in a paramet- ric boundary representation using planes, cylinders, and spheres. Our strategy is to exploit the specialized part ge- ometry and the two-dimensional structure of the configura- tion space to: (1) derive low-degree algebraic contact equa- tions in the two part motion parameters, which can readily be solved to obtain contact curves, and (2) to use a practi- cal planar configuration space construction algorithm. We demonstrate a preliminary implementation on three repre- sentative pairs, none of which is covered by other contact analysis algorithms. We show how the program is used in answering design questions.