This paper classifies and evaluates the solutions to the four orientation synthesis of spherical 4R linkages. Burmester’s result that a one-parameter set of planar RR dyads exists that guide a body through the four planar positions has an analogous form for spherical RR dyads given four orientations. The theory provides a two dimensional set of spherical 4R linkages that can be assembled in each of the four chosen orientations. A map of linkage types is obtained by classifying each spherical mechanism at the vertices of a finite grid on this set; Erdman titles this a “Map of Solutions” for the planar case. Each mechanism is then checked for input drivability, that is, whether or not the input link can drive the coupler smoothly through all four positions. The result is a map of the spherical 4R mechanisms that the designer can use to find practical solutions to the spherical synthesis problems.

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