Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index

This paper presents a hybrid method for the optimum kinematic design of two-degree-of-freedom (2-DOF) parallel manipulators with mirror symmetrical geometry. By taking advantage of both local and global approaches, the proposed method can be implemented in two steps. In the first step, the optimal architecture, in terms of isotropy and the behavior of the direct Jacobian matrix, is achieved, resulting in a set of closed-form parametric relationships that enable the number of design variables to be reduced. In the second step, the workspace bounded by the specified conditioning index is generated, which allows only one design parameter to be determined by optimizing a comprehensive index in a rectangular workspace. The kinematic optimization of a revolute-jointed 2-DOF parallel robot has been taken as an example to illustrate the effectiveness of this approach.