Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing

Abstract

A computer amenable symbolic computing approach for the synthesis of six different link and geared mechanisms is presented. Burmester theory, complex number algebra, and loop closure equations are employed to develop governing equations for the mechanism to be synthesized. Closed-form and iterative solution techniques have been developed which permit synthesis of six-link Watt and Stephenson chains for function, path, and motion generation tasks with up to eleven precision points. Closed-form solution techniques have also been developed for the synthesis of geared five-bar, six-bar, and five-link cycloidal crack mechanisms, for synthesis tasks with up to six finitely and multiply separated precision points. The symbolic manipulation language MACSYMA is used to simplify the resulting synthesis equations and obtain closed-form solutions. A design methodology which demonstrates the feasibility and versatility of symbolic computing in computer-aided mechanisms design is outlined. A computer program which incorporates these synthesis procedures is developed. Two examples are presented to illustrate the role of symbolic computing in an automated mechanism design process.