Abstract
The optimum design of a 3-CPS parallel-kinematics machine (PKM), dubbed the SDelta Robot, is investigated in this paper based on a dexterity index. The six-dof PKM described here bears a simple three-limb structure with all its motors mounted on the base, thereby avoiding limb-interference while offering a low inertial load, which makes it quite suitable for high-speed operations. In this paper we find the inverse of the robot forward-kinematics Jacobian matrix symbolically, to be used in singularity analysis, design for isotropy and optimal control; in fact, the inverse derived here applies to all PKMs whose six active-wrench axes intersect pairwise. The inverse of a 6 × 6 matrix is usually difficult to derive or evaluate in symbolic form. We find the symbolic inverse of a Jacobian matrix that is applicable to the large class of PKMs mentioned above, which, to the authors’ knowledge, is an original contribution. Next, we formulate an optimization problem of the robot, based on its condition number, for maximum dexterity. Drawing from the optimization results, we offer some guidelines on choosing the optimum design parameters. It is shown that the SDelta can achieve a local minimum condition number close to unity.
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