Synthesis of Mechanisms using Time-Varying Dimensions

Many methods of performing mechanism synthesis rely on an attempt to redefine the dimensions of the system in such a way that a deviation from the desired behavior is minimized by the use of optimization methods. During the optimization process the optimizer may, however, suggest values of the dimensions, or design variables, that lead to infeasible designs, i.e. dimensions for which the mechanism cannot be assembled in one or more positions.

With the method proposed her, this problem is overcome by allowing the dimensions to vary during the motion of the system and subsequently minimizing the deviation of each variable dimension over a cycle. That is, for each time step the dimensions are allowed to change in order to obtain assembly as well as a desired kinematic behavior.

This will lead to a variation of each dimension during a cycle of the mechanism, and this variation is the objective that is sought minimized. The minimization problem is solved using the optimality criterion.