Optimization-based mechanism synthesis

A quasi-Newton optimization method is employed for the synthesis of Grashof mechanisms. The synthesis routine uses transformation sets that map from an unconstrained search variable space to a constrained design variable space. The transformation sets ensure that Grashof criteria are satisfied and that all mechanism parameters satisfy specified upper and lower constraints. A previously developed four-bar transformation set along with newly developed five-bar and Stephenson III six-bar transformation sets are presented to illustrate the methodology.

The synthesis routine incorporates three convergence criteria: (i) objective function value change, (ii) mechanism parameter value change, and (iii) task satisfaction. These convergence criteria prevent the optimization routine from returning undesirable minima and also allow the optimization routine to attempt a pseudo global search.

Numerous examples demonstrate the effectiveness of the quasi-Newton optimization technique, along with appropriate parameter transformations and objective function components, for the synthesis of practical four-bar, five-bar, and Stephenson III six-bar mechanisms.