GENERAL FORMULATION OF AN EFFICIENT RECURSIVE ALGORITHM BASED ON CANONICAL MOMENTA FOR FORWARD DYNAMICS OF CLOSED-LOOP MULTIBODY SYSTEMS

摘要

In previous work, a method for establishing the equations of motion of open-loop multibody mechanisms was introduced. The proposed forward dynamics formulation resulted in a Hamilto-nian set of 2n first order ODE's in the generalized coordinates q and the canonical momenta p. These Hamiltonian equations were derived from a recursive Newton-Euler formulation. It was shown how an O(n) formulation could be obtained in the case of a serial structure with general joints. The amount of required arithmetical operations was considerably less than comparable acceleration based formulations. In this paper, a further step is taken: the method is extended to constrained multibody systems. Using the principle of virtual power, it is possible to obtain a recursive Hamiltonian formulation for closed-loop mechanisms as well, enabling the combination of the low amount of arithmetical operations and a better evolution of the constraints violation errors, when compared with acceleration based methods.