Computer-aided mechanism design: a symbolic-computing approach

A computer-amenable symbolic-numerical computing blend for solving precision position-type function-, path- and motion-generation problems for six link and geared mechanisms is presented. Burmester theory, complex-number algebra and loop-closure equations are used to develop the synthesis equations for the mechanism to be designed. Closed-form and iterative solution techniques are presented which permit a synthesis of the 6-link Watt and Stephenson-II and Stephenson-III mechanisms for function-, path- and motion-generation tasks with up to 11 precision points. Closed-form solution techniques are also presented for synthetizing geared 5-bar, 6-bar and 5-link cycloidal crank mechanisms for up to six finitely and multiply separated precision points. The symbolic-manipulation language macsyma is used to carry out algebraic manipulations to help simplify the synthesis equations. A 2-step computer-aided mechanism-design procedure which combines symbolic and numerical computing is presented. The feasibility and versatility of this approach in an automated mechanism-design process is demonstrated using three example problems.