Dexterous Workspace Shape and Size Optimization of Tricept Parallel Manipulator

This work intends to deal with the optimal kinematic synthesis problem of Tricept parallel manipulator. Observing that cuboid workspaces are desirable for most machines, we use the concept of effective inscribed cuboid workspace, which reflects requirements on the workspace shape, volume and quality, simultaneously. The effectiveness of a workspace is characterized by the dexterity of the manipulator all over its workspace. Tricept has a complex degree of freedom, i.e. both rotational and translational DoF, therefore its performance indices depend on the singular values of the dimensional in-homogeneous Jacobian. Here, we divide the Jacobian entries by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. By multiplying the associated entries of the twist array to the same length, we made this array homogeneous as well. This implies some sort of tradeoff between position and orientation components of the twist array. An optimal design problem, including constraints on actuated and passive joint limits, is then formulated. This problem is a constrained nonlinear optimization problem. Therefore, Genetic Algorithm toolbox of Matlab is adopted to solve the problem.