An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form

In this paper, the stiffness of a 3-PSP spatial parallel manipulator is investigated. Unlike traditional stiffness analysis, the moving platform is assumed to be flexible. Two analytical methods are used in finding the robot stiffness. In the first method, robot is modeled as lumped system and principle of virtual work is used. In the second method, the robot is modeled as a distributed system and strain energy of robot main components as well as Castigliano's theorem are used. Force analysis is also presented and reaction forces at the joints as well as internal forces/moments are obtained. For each of the main robot components, a matrix called Wrench Compliant Module Jacobian, WCMJ, is introduced. These matrices will allow mapping the applied external wrench on the moving platform to corresponding reaction forces for the corresponding compliant module. All analysis is presented using invariant form. To evaluate accuracy of the two methods, finite element analysis is used. Finally, using the distributed method, maximum and minimum eigenvalues of the stiffness matrix are obtained and values of kinematic stiffness index are presented. (C) 2011 Elsevier Ltd. All rights reserved.