Development of Kinematic/Kinetic Performance Tools in Synthesis of Multi-DOF Mechanisms

Kinematic and kinetic performance are important issues in designing multi-degree-of-freedom mechanisms such as robotic manipulators. In the engineering design stage, it is especially important that the designer can grasp the characteristics of the mechanism. The aim of this study is to develop a means of representing the kinematic and kinetic performance of the mechanism in such a way that the performance characteristics are quantified analytically and visible graphically to the designer in their entirety at the conceptual design stage. Various performance indices are derived from the Jacobian matrix and its quadratic form. These performance indices are the local kinematic cross-coupling index (angle of intersection between column vectors of the Jacobian), the local directional mobility index (ratio of Jacobian’s eigenvalues), and the local efficiency index (product of Jacobian’s eigenvalues). Graphical images of these performance characteristics using eigen-ellipsoid and workspace trajectory contours are introduced. Critical performance points in mechanism workspace are identified and elaborated for design considerations. Based on the graphical representation of these performance characteristics, design rules for achieving different performance objectives can easily be implemented. This method is applicable to computer-aided design of a mechanism and predetermination of its kinematic and kinetic performance.