Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots

The workspace of hexapod robots is a key performance parameter which has attracted the attention of numerous researchers during the past decades. The selection of the hexapod parameters for a desired workspace generally employs the use of numerical methods. This paper presents a general methodology for solving the closed-form constant orientation workspace of radially symmetric hexapod robots. The closed-form solution facilitates hexapod robot design and minimizes numerical efforts with on-line determination of stability and workspace utilization. The methodology can be used for robots with nonsymmetric and nonidentical kinematic chains. In this paper, the methodology is used to derive the closed-form equations of the boundary of the constant-orientation workspace of axially symmetric hexapod robots. Several applications are provided to demonstrate the capability of the presented closed-form solution in design and optimization. An approach for workspace-based design optimization is presented using the provided analytical solution by applying an iterative optimization algorithm to the find optimized structural parameters and an optimized workspace.