Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators

摘要

Optimization is an important step in the design and development of a planar parallel manipulator. For optimization processes, workspace analysis is a crucial and preliminary objective. Generally, the workspace analysis for such manipulators is carried out using a non-dimensional approach. For planar parallel manipulators of two degrees of freedom (2-DOF), a non-dimensional workspace analysis is very advantageous. However, it becomes very difficult in the case of 3-DOF and higher DOF manipulators because of the complex shape of the workspace. In this study, the workspace shape is classified as a function of the geometric parameters, and the closed-form area expressions are derived for a constant orientation workspace of a three revolute-revolute-revolute (3-RRR) planar manipulator. The approach is also shown to be feasible for different orientations of a mobile platform. An optimization procedure for the design of planar 3-RRR manipulators is proposed for a prescribed workspace area. It is observed that the closed-form area expression for all the possible shapes of the workspace provides a larger solution space, which is further optimized considering singularity, mass of the manipulator, and a force transmission index.