An optimal design of 3R manipulators taking into account regular workspace boundary

摘要

Abstract. The workspace of a manipulator robot is considered of great interest from theoretical and practical viewpoint, being a basic tool for kinematic evaluation and dimensional design. The accurate calculation of workspace and its boundary is of great importance because of its influence on the manipulator design, the manipulator position in the work environment and its dexterity. The presence of voids and singularities adds great difficulty in the algebraic formulation of a correct mathematical model for the calculus of the workspace volume. In this paper an optimization problem is formulated with the objective of determining the optimal geometric parameters of the manipulator, considering the case where the envelope of the workspace is regular. Since a fundamental feature of a manipulator is recognized as a workspace capability, the manipulator design can be expressed as a function of this workspace. The objective of the optimization problem is the maximization of the workspace volume. The main constraint is the regular form. Additional constraints are included to obtain manipulator dimensions within practical values, and to specify limits at the workspace. In the optimization procedure, the optimal design is achieved by means of sequential minimization techniques. A numerical example is presented to validate the proposal methodology.