Application of screw theory to constraint analysis of assemblies of rigid parts

Abstract

Screw theory is used to provide mathematical models of assembly features, allowing the determination of positioning constraints imposed on one part in an assembly by another part based on the geometry of the features that join them. Seventeen feature types have been modeled. A user of this theory is able to combine members of this set to join two parts and then determine whether or not the defined feature set over-, under-, or fully-constrains the location and orientation of the part. The ability to calculate the state of constraint of parts in an assembly is useful in supporting quantitative design of properly constrained assemblies in CAD systems. Locational overconstraint of parts can lead to assemblability problems or require deformation of parts in order to complete assembly. The theory has been implemented in a computer program that is integrated with others to form an assembly analysis tool suite.