Inverse Dynamic Problem of Two Parallel Manipulators with Identical Limbs Structures

This paper aims at obtaining the dynamic models of twoconstraint-over parallel mechanisms (PM) with 3-DOF (degree of freedom) and 4-DOF, the Tripteron and the Quadrupteron. The reasoning used in this paper is based on a judicious concept in detaching the whole mechanism into several subsystems and consecutive synergies between kinematic analysis, Lagrangian and Newtonian approaches. In this regard, the mechanisms are made equivalent to some subsystems and the equations of kinematic constraints are derived for all subsystems. Afterwards upon resorting to Lagrangian approach and blending it with the latter kinematic relations, the dynamic model of each leg in task space is obtained. The dynamic model of the end- effector is written in virtue of Newton-Euler’s approach where yields to three differential equations. Finally, the problem leads to a system of 12 equations for the Tripteron and 16 equations for the Quadrupteron, which do not need usaul simplifications in such problems. For the sake of comparison, the results are put into contrast by the one obtained with a dynamic analyzer software. The results obtained by both approaches are coherent which affirms the correctness of the proposed algorithm.