A further study on kane's equations approach of robots dynamics

This paper presents the further work and improvement about a new dynamics algorithm of robots --- Kane's equations algorithm of robots based on the paper's author's previous work. The improved algorithm is obtained using Kane's equations and Newton-Euler formulations. The algorithm is given in recurrence form and can be easily realized on computers. It is suited not only for robots with all rotatory joints but also for robots with some prismatic joints. Formulations of the algorithm keep the recurrence characteristics of the Newton-Euler formulations, but possess stronger physical significance. Unlike the conventional algorithms. such as the Lagrange and Newton-Euler algorithm etc., the algorithm can conveniently solve the problem of dynamics of robots containing closed chains without cutting the closed chains open. The paper introduces the method suited for dealing with robots with closed chains in detail. In addition, this paper makes a comparision between the algorithm and conventional algorithms from the number of multiplications and additions, and it is shown that for open chain linkage robots the amount of computation of the algorithm is only a little more than that of Newton-Euler's, but much less than that of all others. For robots with closed chains, the computation amount of the algotithm is less than that of all conventional algorithms.