A mathematical optimization methodology for the optimal design of a planarrobotic manipulator

A general optimization methodology for the optimal design of robotic manipu lators is presented and illustrated by its application to a realistic and p ractical three-link revolute-joint planar manipulator. The end-effector car ries out a prescribed vertical motion for which, respectively, the average torque requirement from electrical driving motors, and the electric input e nergy to the driving motors are minimized with respect to positional and di mensional design variables. In addition to simple physical bounds placed on the variables, the maximum deliverable torques of the driving motors and t he allowable joint angles between successive links represent further constr aints on the system, The optimization is carried out via a penalty function formulation of the constrained problem to which a proven robust unconstrai ned optimization method is applied. The problem of singularities (also know n as degeneracy or lock-up), which may occur for certain choices of design variables, is successfully dealt with by means of a specially proposed proc edure in which a high artificial objective function value is computed for s uch 'lock-up trajectories'. Designs are obtained that are feasible and prac tical with reductions in the objective functions in comparison to that of a rbitrarily chosen infeasible initial designs. Copyright (C) 1999 John Wiley & Sons, Ltd.