Dynamic modeling and base inertial parameters determination of a 2-DOF spherical parallel mechanism

Abstract

This paper deals with the dynamic modeling and base inertial parameter determination of a general 5R 2-degree-of-freedom spherical parallel manipulator. By using a new geometric approach, inverse and forward kinematic problem are transformed to the problem of determining the intersection of two cones with common vertex. Compared to other proposed methods, this approach yields more compact and closed-form solutions. The instantaneous kinematic and acceleration problem is solved via employing the screw theory. The dynamic model is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. In order to verify the proposed methods and equations, a case study is performed, in which an orthogonal 2-DOF spherical parallel manipulator, named TezGoz, is considered. Performed simulations and comparisons with a SimMechanics model show the correctness of the derived equations. Furthermore, a reduced dynamic model is obtained by determining the base inertial parameters. To do so, first the dynamic model is rewritten in a linear matrix form with respect to the inertial parameters of the mechanism, then parameters are grouped to obtain a set of independent base parameters, reducing the number of inertial parameters from 40 to 19. As a result, while maintaining the accuracy, the computational time is reduced to 63% of that of the original dynamic model. Finally, to calibrate the dynamic model, an experimental dynamic identification is performed.