Comparative Analysis of Stiffness in Redundant Co-axial Spherical Parallel Manipulator Using Matrix Structural Analysis and VJM Method

Abstract

Several studies have addressed stifness analysis through diferent available methods including fnite element analysis (FEA) and the virtual joint method (VJM) among others. However, matrix structural analysis (MSA) has not been used, although previous research has shown that it provides reliable results. Therefore, this paper focuses on the kineto-static analysis of a three-degree-of-freedom symmetrical parallel kinematic manipulator (PKM) with curved links, known as a spherical parallel manipulator (SPM). First, kinematic modeling is introduced through the inverse kinematic problem and the Jacobian matrix; then a detailed study of the stifness modeling is established. Secondly, the force–defection relationship is studied in the form of a numerical calculation and a graphical representation. Moreover, the kinematic redundancy is derived. Through MATLAB simulations, the defection of the joints in both parts, translation, and rotation, is graphically represented using a numerical calculation method. Comparatively, SPM is purposefully compared to VJM in order to determine the efciency of the proposed method. Interestingly, kinematic redundancy leads to better SPM performance, in which adding extra links (legs) to the robot strengthens the SPM structure and yields less joint defection. It is worth noting that the MSA technique successfully deals with complex structures such as closed-loop chains, which is clearly apparent in the simplicity of its mathematical model toward the considered robot.