Kinematic Synthesis of Hexapods with Specified Orientation Capability and Well-Conditioned Dexterity

This paper systematically investigates issues relevant to the kinematic synthesis of hexapod-based machine tools. Based on a full understanding of the geometrical characteristics of workspace boundary, the concept of a prescribed workspace having a given orientation capability is defined. Two performance measures are presented—the local dexterity and workspace radius ratio. The closed-form solution to these measures is formulated by means of singular value decomposition and differential geometry. The influences of the fundamental design parameters on the performance indices are discussed, resulting in an optimal design having no strut interference. An example of application to the kinematic design of a prototype hexapod is given to illustrate the effectiveness of this approach.