Mechanism and Machine Theory Vol, 18, No. 6, pp. 431~,38, 1983 0094~114)(/83 $3.00 + .00 Printed in Great Britain. Pergamon Press Ltd. COMPUTER-AIDED DESIGN OF MANIPULATION ROBOTS VIA MULTI-PARAMETER OPTIMIZATION'[" V. POTKONJAK Electrical Engineering Faculty, Beograd, Yugoslavia and M. VUKOBRATOVI(~ Mihailo Pupin Institute, Beograd, Yugoslavia (Receivedfor publication 11 April 1983) Abstract--In the paper are presented the basic ideas of computer-aided design of manipulation robots based on adopted optimizational criteria and on set constraints of strengths, as well as on actuator capabilities. Using complete models of manipulator dynamics, a simulation programme was derived, giving at its output the optimal design parameters of manipulator. An algorithm was formed, optimizing simultaneously two of the several significant manipulator parameters. In one case these a~ two diameters of circular cross-section segments, in another, one is a diameter and the other the reducing ratio of the DCmotor type actuator. 1. INTRODUCTION Computer-oriented methods for the construction of mathematical models of active mechanisms[l-8] and appropriate algorithms for the simulation of manipu- lator dynamics have made possible wider application of computers to the design of industrial manipu- lators. The calculation of all required dynamic char- acteristics for different manipulator configurations and different manipulation tasks has been made possible by simply changing the input data for an algorithm. This has, in turn, enabled the choice of such configuration and parameters of a manipulator which are optimal for a particular purpose. Such procedures become even more useful if com- bined with a certain criterion to give a so-called dynamic method for the evaluation and choice of industrial manipulators. The basic ideas of this method are presented in[7-9]. 2. ALGORITHM FOR THE SIMULATION OF MANIPULATOR DYNAMICS We now describe the algorithm for the simulation of manipulator dynamics. It should he stressed that the algorithm operates automatically, i.e. that a program package has been prepared for an arbitrary manipulator configuration. It follows that the configuration and the manipulation task represent input data. In practical applications the manipulation task is given by time functions of some "external coordi- nates". For instance, the manipulation task can be given by motion laws of the manipulator tip and by the change in orientation of the last segment. Since the methods for the setting of models use the generalized coordinates, the simulation algorithm has to perform the transfer from the external to the generalized (internal) coordinates. Let a manipulator with 6 degrees of freedom (d.o.f.) be considered. 6 d.o.f, are needed to attain the wanted tip velocity v and the wanted angular velocity to of the last segment. The trajectories, the orientation and the velocities profiles (tip velocity and last seg- ment angular velocity) are prescribed via the initial position, the tip acceleration law w(t) and the last segment angular acceleration ~(r). Let the time interval of the movement be divided into k subintervals At, and the initial state (the 6-dimensional vector of the generalized coordinates q and the generalized velocity vector q) be prescribed. Using the recurrent formulae for the center of gravity accelerations of mechanism segments and for the angular acceleration of segments, we can derive a procedure for calculating the matrices fl, 0, F, ~b[3, 4] such that w =f~ +0;E = F~/+ q~ (1) or Ew]:E ] o+E:] where w and E are 3 x 1 matrices corresponding to the vectors w and ~. The procedure calculates matrices for one time-instant t* when the state (q, q) is known. Let the designations be introduced Now, the generalized accelerations are obtained from (2) ii = B-'(x ° - A). (3) fThis work has been supported by the Mathematical With known values of q, q, q at some time instant, Institute in Beograd, Yugoslavia. the driving forces and torques in the joints, needed 431