A unique dimensional representation of a spherical linkage called the primary linkage is defined using supplemental transformations. This primary linkage representation has the property that the sum of its any two links is less than π. Then several theorems and lemmas concerning the assemblability, revolvability of angles and full rotatability are presented for this primary linkage representation using extensions of the spherical triangle inequalities.

Since all different supplemental dimensional representations of a spherical linkage are equivalent, the assemblability, revolvability of angles and the rotatability of links of an N-bar spherical linkage of a given dimensional representation can be determined by first determining the primary linkage representation and then using the theorems and laws provided in the paper. The rotatability criteria of spherical four-link and five-link mechanisms are very special cases of the N-bar rotatability criteria presented in the paper.

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