Optimal synthesis of robot manipulators based on global kinematic parameters

The local nature of inertial, nonlinear, and coupling character-istics of manipulators is an impediment to their optimal design. In this article, a method to represent and measure the global and posture-independent measures of inertia, coupling, and nonlinear forces is presented. A new concept, referred to as the global inertia ellipsoid, which represents the global iner-tial characteristics of a manipulator, is introduced. The global inertia ellipsoid is obtained by considering a weighted distri-bution of the end-effector position over the workspace of the manipulator. Based on this concept, four global parameters, representing the global nonlinear, coupling, and inertial char-acteristics of the manipulator, are obtained. The number of global parameters does not change with the degrees of freedom or the complexity of the manipulator structure. A probabilistic or deterministic description of payload range can be included while designing the manipulator. Criteria for the optimal de-sign of manipulators are presented in the form of an objective function of the global parameters. The method is illustrated by the design of a 2R manipulator, a 2R manipulator with given payload range, and a 3R manipulator. The extension of the concept of the global inertia ellipsoid to task placement and task planning is discussed. 1