Optimum synthesis of motion generating four-bar mechanisms using alternate error functions

This paper addresses the problem of optimum synthesis of motion generating four-bar mechanisms using evolutionary methods. Formulation of objective functions based on three different error functions is presented, which ensures that the synthesized mechanism is a crank-rocker, and is free from branch and order defects. One of the three error functions is an obvious choice, whereas the other two error functions are newly formulated making use of the basic theory of planar motion of a rigid body and motion generating four-bar mechanisms. The method of differential evolution is used to carry out the optimization for the three objective functions. Results for three problems are presented, all of which fall in the category of motion generation without prescribed timing. Results obtained using the three error functions are compared with regard to accuracy and computational time, on the basis of which conclusions are drawn regarding their relative performance.