Optimization of linkages for generalized rigid-body guidance synthesis based on finite element models

This paper presents a method for the generalized rigid-body guidance dimensional synthesis of planar linkages. The error function is based on the elastic energy stored in a finite element model of the linkage, built with rod-type elements, when it is forced to fulfil the synthesis data. The best linkage dimensions are the ones that give the minimum energy. The nonlinear deformed equilibrium position is solved in every synthesis position to evaluate the error. To do this, a second-order method has been developed that guarantees the convergence with low computational cost. The possibility of constraints in the lengths of some rods is included in the method through the use of Lagrange multipliers. The minimization of the synthesis error function is also tackled with two different second-order methods; the best results are obtained with the use of both, each of them in different instants of the iterative process. There are several dimensional synthesis problems, but the main objective of this paper is the one that deals with the coordination of the relative positions of several elements. This kind of synthesis has interest for instance in the design of robotic hands, grippers and surgical instruments. The method presented here is also suitable for the other simpler kinds of kinematic syntheses: trajectory, function generation, rigid-body guidance, and combined synthesis, and therefore it may be considered as a general purpose one.