Analysis of Constraint Configurations in Mechanical Assembly via Screw Theory

Abstract

The essential function of a mechanical assembly is the removal of degrees of freedom (DOF) to enable the transfer of load between two bodies. Assembly constraint features serve to provide this DOF removal, so their locations and orientations greatly affect the quality of an assembly as measured by its ability to resist relative motion between the parts. This paper addresses attachment-level design in which design decisions are made to establish the types, locations, and orientations of assembly features. The analysis methodology in this paper models assembly features such as point, pin, line, and plane constraints with equivalent first, second, and third order wrench systems. The set of relative motions to be evaluated is generated by composing from among these constraints a five-system pivot wrench combination to which a freedom screw motion is reciprocal. The effectiveness of each constraint to resist these motions is calculated as the ratio of the reaction forces at each resisting constraint to the input wrench magnitude. Based on these resistance values, multiple rating metrics are calculated to rate the overall assembly’s performance in resisting the motion. This work represents the first tool available to analyze a constraint configuration’s effectiveness to resist motion with a quantitative metric. Case studies are presented to demonstrate the utility of the analysis tool.