Hybrid (Symbolic-Numerical) Optimization in Mechanism Design for the Elimination of Redundant Constraints

Abstract

Hybrid optimization, a new approach to design optimization employing both symbolic reasoning and algorithmic analysis, has been applied to the design of kinematic pairs in mechanisms. This hybrid design methodology provides a three-step systematic approach for (1) combining the degrees-of-freedom found in simple, lower kinematic pairs to obtain more complex but robust higher pairs, (2) judging inappropriately assigned joints for the elimination of redundant kinematic constraints and harmful mobilities, and (3) assisting nonexpert designers in applying nonlinear programming algorithms for detailed numerical design optimization of kinematic pairs. An example taken from the design of a spatial mechanism, specifically a universal joint, is presented and serves to demonstrate the utility of this procedure for detailed hybrid design optimization of kinematic pairs in mechanisms.