Contact Analysis of Spatial Fixed-Axes Pairs Using Configuration Spaces

We present the first configuration space computation algorithm for pairs of rigid parts that move along fixed spatial 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 parametric boundary representation using planes, cylinders, and spheres. Our strategy is to exploit the specialized part geometry and the two-dimensional structure of the configuration space to: (1) derive low-degree algebraic contact equations in the two part motion parameters, which can readily be solved to obtain contact curves, and (2) to use a practical planar configuration space construction algorithm. We demonstrate a preliminary implementation on three representative pairs, none of which is covered by other contact analysis algorithms. We show how the program is used in answering design questions.