CONSTRAINED OPTIMIZATION OF MULTI-DEGREE-OF-FREEDOM MECHANISMS FOR NEAR-TIME-OPTIMAL MOTIONS

This paper presents a method to design multi-degree-of-freedom mechani sms for near-time optimal motions. The design objective is to select s ystem parameters, such as link lengths and actuator sizes, that will m inimize the optimal motion time of the mechanism along a given path. T he exact time-optimization problem is approximated by a simpler proced ure that maximizes the acceleration near the end points. Representing the directions of maximum acceleration with the acceleration lines, an d the reachability constraints as explicit functions of the design par ameters, we transform the constrained optimization to a simpler curve- fitting procedure. This problem is formulated analytically, permitting the use of efficient gradient-based optimizations instead of the zero order optimization that is otherwise required. It is shown that with the appropriate choice of variables, the reachability constraints for planar mechanisms are linear in the design parameters. Consequently, t he reachability of the entire path can be guaranteed by satisfying the reachability of only two extreme points along the path. This greatly simplifies the optimization problem since it reduces the dimensionalit y of the constraints and it permits the use of efficient projection me thods. Examples for optimizing the dimensions of a five-bar planar mec hanism demonstrate close correlation between the approximate and the e xact solutions and better computational efficiency of the constrained optimization over previous penalty-based methods.