A Comprehensive Inverse Dynamics Problem of a Stewart Platform by Means of Lagrangian Formulation

Abstract

In this paper, using the Lagrange’s method a comprehensive inverse dynamics problem of a 6-3 UPS Stewart platform is investigated. First, the inverse kinematics problem is solved and the Jacobian matrix is derived. Next, the full inverse dynamics problem of the robot, taking into account the mass of links and inertia, is investigated and its governing equations are derived. The correctness of the dynamics equations are verified in two ways, first, using the results of the virtual work method and second using the results of a commercial multi-body dynamics software. Because the dynamic calculation is time consuming, two simplifying assumptions are considered. First, the link is assumed to have a zero mass and next it is assumed as a point mass. Studying the former assumption is rather straightforward. However, more complex equations are needed and derived in the present paper for the latter assumption. Required actuator forces for the two assumptions are compared with the case where the mass and link inertial is fully considered. It is shown that the first simplifying assumption significantly affects the accuracy of the required joint torques.