Kinematics and Statics of the Gough-Stewart Platform

Abstract

This paper presents an algorithm for the kinematics and statics analysis of a Gough–Stewart platform. Through defining the velocity screw, the relative angular and linear velocities of a single rigid body can be expressed as a single vector. The velocity screw equations of various mechanisms are deduced in detail, the forward and inverse kinematics of a parallel mechanism can be solved through the velocity screw equation. Similarly, the definition of the force screw allows all constraint forces and torques of a single rigid body to be expressed using a single vector, and the static screw equation can be used to solve the forward and inverse statics of a parallel mechanism in one coordinate system. The advantage of this approach is that kinematics and statics modeling are unified in screw coordinates because the kinematic parameters in screw form can be directly employed in statics modeling. The results of the kinematics and statics analysis of the Gough-Stewart platform validate this method. This algorithm is easy to compute and program with high efficiency, and it can also be applied to any other spatial, complex multi-rigid-body systems.