Kinematic analysis of spatial fixed-axis higher pairs using configuration spaces

We present a kinematic analysis algorithm for spatial higher pairs whose parts rotate around or translate along fixed spatial axes. The part geometry is specified in a parametric boundary representation consisting of planar, cylindrical, and spherical patches bounded by line and circle segments. Kinematic analysis is performed by configuration space construction following the method that we developed for planar pairs. The configuration space of a pair is a complete encoding of its kinematics, including contact constraints, contact changes, and part motions. The algorithm constructs contact curves for all pairs of part features, computes the induced configuration space partition, and identifies the free space components. Spatial contact analysis is far harder than planar analysis because there are 72 types of contact versus 8. We have developed a systematic analysis technique and have used it to derive low-degree equations for all cases, which are readily solvable in closed form or numerically. We demonstrate the implemented algorithm on three design scenarios involving spatial pairs and planar pairs with axis misalignment.