Optimal Splines for Rigid Motion Systems: Benchmarking and Extensions

Abstract

This paper illustrates the power and versatility of the convex programming framework for optimal spline synthesis that was developed in a companion paper (Demeulenaere, Pipeleers, De Caigny, Swevers, De Schutter, and Vandenberghe, 2009, “Optimal Spines for Rigid Motion Systems: A Convex Programming Framework”, ASME J. Mech. Des., 131, p. 101005.). Two case studies concerning rigid motion systems illustrate the ability of the framework to improve upon recent (2005) literature results: (i) a numerical optimization study concerning kinematic optimization of uniform quintic splines for cam systems and (ii) an analytical study concerning time optimal quartic splines for motion systems driven by servomotors and subject to kinematic constraints. In a third study, the versatility of the framework is illustrated by generating time optimal and time-energy optimal motions for a rigid servomotor driven system under torque constraints. Based on these three case studies, the convex programming framework of the companion paper is extended with the following generic aspects: (i) a bisection to generate time optimal motions, (ii) a direct expression of the upper and lower bounds on motor torque, and (iii) a convex quadratic energy objective function for servomotor driven systems.