4R spatial and 5R parallel manipulators that can reach maximum number of isotropic positions

Methods for developing manipulators to reach maximum number of isotropic positions are presented in this paper. The spatial 4R manipulators are directly obtained from 3R planar manipulators, and the 2-DOF 5R planar parallel manipulators are developed from four-bar mechanisms. In addition, a general method is proposed for developing other types of manipulators. Criteria for determining the number of solutions of nth degree polynomials are presented to facilitate the searching process.