This paper presents an algorithm using an optimization technique to outline the boundary profile of a manipulator workspace and perform quantitative evaluation of the workspace volume. The algorithm is applicable to general N-link manipulators with not only the revolute joints, but also joints of other types, such as, the prismatic and cylindrical joints. It is a partial-scanning technique which offers significant reduction on the number of scanning points to generate the workspace and the method is particularly efficient in dealing with complicated manipulator geometry. The [3 × 3] dual-number matrix method is used as the basis for analytical formulations, and consequently, computational advantage is gained. A comparative study is given with a previously used algorithm. Several specific examples involving industrial robots of various kinds are given to demonstrate the capability of the algorithm.

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