A comprehensive algorithm and criterion for the rotatability and branch identification of RCRCR spatial mechanisms with zero offset at the revolute joint between the cylindrical joints are presented. The results are believed the first successfully attempt which resolves the mobility and branch identification problems of non-bimodal spatial mechanisms.

In this article, the concept of virtual linkage is proposed. A simple RCRCR mechanism is regarded as a spherical 5R linkage with one cylindroid surface constraint formed by a virtual bimodal linkage. The treatment on the rotatability of virtual bimodal linkages is identical to that of the planar and spatial bimodal linkages. Thus, from the rotatability point of view, simple RCRCR mechanisms and Stephenson six-bar linkages can be grouped together. They have the similar rotatability and branch features. The results include the classification and mobility criterion, and an algorithm for branch identification, which are equally effective for any linkage inversion, any type of linkage synthesis problem, and any number of precision positions.

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