Synthesis of spherical 4R mechanism for path generation using Differential Evolution

The problem of path generation for the spherical 4R mechanism is solved using the Differential Evolution (DE) algorithm. Formulas for the spherical geodesics are employed in order to obtain the parametric equation for the generated trajectory. Direct optimization of the objective function gives the solution to the path generation task without prescribed timing. Therefore, there is no need to separate this task into two stages to perform the optimization. Moreover, the order defect problem can be solved without difficulty by means of manipulations of the individuals in the DE algorithm. Two examples of optimum synthesis showing the simplicity and effectiveness of this approach are included.