Rechnergestützte optimierung der antriebs- und gestellkraftgrössen ebener koppelgetriebe—Teil II

Abstract

In the first part of this paper the mathematical model for a new technique for the computer-aided optimization of the input torque and the inertia forces and moments in planar linkages has been described. The nonlinear optimization problem consists of an objective function f(X), a vector of design variables X, and constraints g j(X) 0. The objective function contains the forces and moments. Objectives are the minimization of the maximal deviation of a prescribed function (20) or the minimization of the sum of the squares of deviations from a prescribed function (21). The vector of design variables may contain the masses, inertia moments, and centers of mass of the moving links. Constraints may be placed on upper and lower bounds of variables. A computer program based on this new technique is a part of the programmed system KOGEOP. The first example presented is a six-bar linkage; the problem is to balance the input torque and the forces on the frame. The nonlinear optimization methods used (the Gauss-Seidel method, the Powell method, and a stochastic method with normal distribution) are compared in a second example, a four-bar linkage.