Kinematic Synthesis of Nonspherical Orientation Manipulators: Maximization of Dexterous Regular Workspace by Multiple Response Optimization

Abstract

Kinematic synthesis of a parallel manipulator refers to the systematic determination of the optimum geometry that maximizes a set of kinematic performance characteristics. Essentially, this is an optimization problem where the objective function is composed of certain kinematic performance metrics that encapsulate specific requirements. Additional constraints (e.g., choice of an actuator) limit the parameter space and thus force kinematic synthesis to find a local optimum that is consistent with all design requirements. The volume and the dexterity of the workspace characterize the kinematic performance of an orientation manipulator requiring a small form factor. In this paper, the optimum geometries of two orientation manipulators differing in limb configurations (i.e., kinematic architecture) are synthesized through the application of the efficient and statistically robust response surface methodology (RSM). To this end, a gradient-based iterative technique is employed to estimate the objective function by solving the direct kinematics of each manipulator. The optimization procedure presented in this paper begins with an arbitrarily chosen initial parameter space. A hybrid approach consisting of a space-filling and an IV-optimal (integrated variance) experiment design is employed in order to reduce the initial search space and to find appropriate regression models that adequately fit the objective function. Subsequently, the empirical models thus determined are employed to find an optimum parameter set that maximizes the objective function. This solution approach efficiently identifies the optimal manipulators for both architectures that can accommodate a prospective linear actuator capable of delivering high dynamic performance.