Closed-form dynamic formulation of spherical parallel manipulators by Gibbs-Appell method

Spherical Parallel Robot (SPR) is a complex but widely used type of manipulators that performs only rotational motion. Dynamic analysis of SPR has a vital role in mechanical design, model-based controller, identification and fault detection of such robots. Complexity of SPR kinematic structure makes traditional dynamic modeling methods such as Newton-Euler, virtual work and Lagrange formulations a prohibitive task. In this paper a new procedure for deriving closed form dynamics of general SPR using Gibbs-Appell method is presented. The proposed method does not require any recursive computation or symbolic manipulation and dynamic matrices of the robot is directly derived in an explicit form. By using the proposed method, closed form dynamic formulation of a general 3DOF SPR, known as agile wrist, is obtained and it is verified for an arbitrary trajectory. The unique feature of the method presented in this paper, makes it promising to be used for other parallel manipulators.