Gravity-Based Kinetostatic Modeling of Parallel Manipulators Using Screw Theory

Abstract

The pose accuracy of parallel manipulators (PMs) is a key index to measure their performance. Establishing the gravity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement. In this paper, a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs. First, the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches. Second, the gravity model of the mechanism is established based on the screw theory and the principle of virtual work. Finally, the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained, and the influences of the external load, platform gravity, and rod gravity on the stiffness of the mechanism are decoupled. The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method. This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.