Dynamic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator

Abstract

In this paper the dynamic analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of next-generation giant radio telescopes. In this structure it is proposed to use two parallel redundant manipulators at the macro and micro level, both actuated by cables. In this paper, the governing dynamic equation of motion of such a structure is derived using the Newton–Euler formulation. Next, the dynamic equations of the system are used in the open-loop inverse dynamics simulations, as well as closed-loop forward dynamics simulations. In the open-loop dynamic simulations it is observed that the inertial forces of the limbs contribute only 10% of the dynamic forces required to generate a typical trajectory and, moreover, the total dynamic forces contribute only 10% of the experimentally measured disturbance forces. Furthermore, in the closed-loop simulations using decentralized PD controllers at the macro and micro levels, it is shown that the macro–micro structure results in a 10 times more accurate positioning than that in the first stage of the macro–micro structure. This convincing result promotes the use of the macro–micro structure for LAR application.