Kinematic Analysis of Spatial Fixed-Axes Pairs Using Configuration Spaces

We present a kinematic analysis program for spatial higher pairs whose parts rotate around or translate along fixed spalial axes. The part geometry is specified in a parametric boundary representation consisting of planar, cylindrical. and spherical patches bounded by line segments and circular arcs. The program consis[S of two pans: contact curve computation and configuration space computation. We perform kinematic analysis by the configuration space, which needs contact curves as an input. The configuration space computation follows the method that we developed for planar pairs. In Ihis paper, we analyze each type of contact by hand to obtain low-degree equations that are readily solvable in closed-fonn or numerically. The results are stored in a table that is parameterized by the part geometry and motion type. The program obtains contact equations for all pairs of part features from the table, solves them to obtain contact curves, and composes the curves to obtain the configuration space. The computations take a few seconds on a workstation. We demonstrate the program on design scenarios involving spatial systems and planar systems with axis misalignment.