Abstract: This invention comprises a general redundant spherical linkage capable of producing a hemisphere or greater of singularity-free, relative motion of two arms which intersect at a fixed point. All points of all links of the invention move on spheres that are concentric about this fixed point of intersection of the two arms. In a general way, the invention can be considered as a sphere which is divided by a central link that supports two pairs of scissoring and intersecting axes of rotation for four semicircular links that are 180.degree. arcs. The semicircular links maintain a constant angle at their point of overlap and support radial arms having axes which pass through the center of the sphere. Each pair of pivoted links controls the spherical motion of one arm within one hemisphere. By simultaneously controlling all four pivoted links, arbitrary relative motion of the two arms can be achieved.