Spatial Contact Analysis of Fixed-Axes Pairs Using Configoration 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 slrategy is to exploit the specialized part ge-ometry and the two-dimensional slruclUre of Ihe config-uration space to obtain a practical algorithm. The main technical contribution is oue derivation oflow-<legree alge-braic contact equations in the two pan motion parameters. which can readily be solved to obtain contact curves. We demonstrate a preliminary implementation on three repre-sentative pairs, none of which is covered by prior contacL analysis algorithms. We show how the program is used to answer design questions.