A Novel Method for Solving Assembly Constraint using Spherical Geometry and Spherical Linkage Mechanism

This paper presents a novel approach for solving angular constraints with spherical geometry to determine the orientation of a set of parts given the mating constraints. The combination of angular constraints can be divided into operable and un-operable cases which can be solved efficiently with simple spherical surface reasoning and spherical linkage mechanism respectively. Thus the rotation transformation matrix of the dependent rigid body is worked out. This method has the advantages over numerical and symbolic approaches of clear geometric solubility, geometric operability, and it can also avoid solving all the constraint equations simultaneously. The presented algorithms have been substantiated in a prototype system-INTEVUE.