A METHOD FOR THE RAPID SOLUTION OF THE DISPLACEMENT OF THE KINEMATICS LINKAGE

Abstract

In this paper the techniques are presented which allow one to solve rapidly the displacement equation of the kinematic linkage. Especially the following two techniques make a significant contribution to the development of the method. (1) The new method of formulation of the problem saves one from the cumbersome manipulation of the equations, which is usually required to translate the statement about a given linkage into an analytical one. (2) A set of displacement equations is solved by the Newton-Raphson method, which is remarkable in convergence speed but is apt to be affected by the choice of the starting value. Owing to the closer estimation by the parabolic extrapolation through the last three solutions for the preceding three input crank angles, the convergence rate is about twice that of the usually chosen starting value of the solution corresponding to the preceding input crank angle.