This paper synthesizes 4C and RCCC linkages based on the solution region methodology, that is an extension of the synthesis of spherical 4R linkages. The synthesis of spatial RCCC linkages is significantly more complicated than 4C linkages, because they are composed of an RC and a CC dyads. For the four positions problem, there are infinite solutions of the CC dyad, but there is no solution for the RC dyad theoretically. We first synthesize the spherical 4R linkages by setting up spherical 4R linkage solution region using four orientations of four given positions. So the directions of the kinematic pairs for a 4C linkage can be determined by picking a point on the spherical 4R linkage solution region. Then we use the directions of the 4C linkage and the points of four given positions to determine the spatial solution lines for 4C linkages. Next we establish a 4C linkage solution region using the solution lines. Each point on a 4C linkage solution region corresponds to a 4C linkage that visits the four positions. Different point on a spherical 4R linkage solution region corresponds to a different solution region for 4C linkages. Thus, we find the linkage solution on the solution region, which has no sliding displacement between input and fixed links through the four positions. The solution is an RCCC linkage that visits the four positions. Finally, we find all RCCC linkages on many different 4C linkage solution regions and establish the RCCC linkage solution region.

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