Analytical Constraints for a Workspace Design of 2R Manipulators

Abstract

In this paper an algebraic formulation is used to deduce a closed-form design algorithm for 2R manipulators. The general expression of a torus has been inverted for synthesis purposes and the algebraic nature has been preserved to deduce both solving formulas and design constraints. These constraints have been used to draw a chart of feasible region for a prescribed workspace through some given points. Once structural parameters are found, dimensional sizes of the 2R chain have been solved by inverting the expressions of definition for the structural parameters. A third order algebraic equation has been obtained and the solutions discussed, so that it turns out that a torus can be generated by two or four different 2R manipulators only. Numerical examples illustrate a design procedure and some peculiar charts of feasible regions.