Second-order methods for the optimum synthesis of multibody systems

The present paper takes a general approach to the dimensional synthesis of mechanisms via second-order optimization techniques. The error function is the same for any type of kinematic synthesis and is independent of the kinematic configuration of the mechanism. Mechanisms are modelled by means of rod-type finite elements, while the solution of syntheses is based on the judicious choice of constraints. The optimization parameters are the lengths of the rods making up the model. Two procedures are developed for minimizing the error function, each of second-order. The first is based on using a precise estimate of the first and second derivatives of the error function, while the second involves a rougher estimate based on the assumption that the rods are uncoupled. By combining the two procedures in the iterative process, and by adopting a variable convergence tolerance, one can synthesize mechanisms even when the initial dimensions are very different from those of an acceptable solution.