Screws reciprocal to five lines appear in the inverse Jacobian and statics equations of many serial and parallel robots. By closely examining the geometry of systems of five lines, a set of geometric procedures for computing reciprocal screws is derived. The methodology is based on the fact that one screw in a cylindroid reciprocal to four lines is reciprocal to a fifth independent line. The constructions are easy to implement and provide geometric insight into reciprocal screws and singularities.

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