This paper presents an analytical investigation of manipulator workspace. The first part presents the derivation of a set of recursive equations in terms of motion and design parameters representing the workspace. These formulas are basic for the determination of the characteristics as well as the shape of workspace. The remainder of the paper concerns the investigation of the existence of hole and void in workspace. A set of criteria is formulated. Algorithms for implementing these criteria are developed. Manipulators with both unlimited and limited revolute joints are studied in this investigation.

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