The input-output displacement equation is expressed as a degree eight polynomial in the half-tangent of the output angular displacement. A procedure for determining uniquely all the linkage variables verifies the closures and in addition explains the physical significance of the closures of equivalent five-link R5 spherical mechanisms. The equation can be used to generate input-output functions of spatial five-link RCCRR and RCRCR mechanisms. The results are illustrated by numerical examples.

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