Enhancing the originality of the Stewart platform through its kinematic analyses

Abstract

In this study, an approach to solve the kinematics of the Stewart platform is introduced with the purpose to enhance its originality. Contrary to the Gough platform, the forward displacement analysis of the Stewart platform is based on closure equations that allow to obtain nearly closed-form solutions. These equations lead to decoupled functions which are solved by means of the well-known Sylvester's dialytic method of elimination. The input–output equations of velocity and acceleration as well as the singularities of the robot are obtained systematically by resorting to reciprocal-screw theory. Numerical examples are provided in order to demonstrate the application of the proposed method. Furthermore, the numerical results obtained via screw theory are successfully compared with simulations generated with the aid of commercially available software. Finally, the contribution may be useful to recognize that the flight simulator proposed by Stewart almost five decades ago and the tire testing machine attributed to Gough are in reality robot manipulators with quite different characteristics.