Optimal dimension of redundant manipulator using the workspace density function

The redundant manipulator has been broadly applied to various fields including industrial manufacturing, surgical manipulation and space exploration by providing high accuracy, flexibility, and efficiency. Particularly, the technology is capable of improving the assembling precision while simplifying the operation in complicated environments, and therefore of intense interest in industrial settings. For manipulator design, space occupation optimizing is a critical step and parameters of the flexible area, the shape and size of workspace have been commonly employed to evaluate the optimizing performance. In this paper, by combining the Fourier transform with the convolution theorem, we presented a workspace density function of redundant manipulator to describe the shape and size of workspace and flexibility. The workspace density function is an evaluation criterion to select the optimal geometric parameters for the manipulator. Based on the workspace density function shown in the simulation results section, the optimal design parameters were obtained. The approach presented in this paper holds the potential to improve the redundant manipulator design.