The paper begins with introducing the 5-dimensional (5D) double Schoenflies-motion (X-X motion) set employing the group product of two 4D X-motion subgroups of displacements. Two families of primitive X-X motion generators are briefly outlined. Then, the geometric constraints for homokinetic transmission via Lie-group-algebraic properties of the displacement set are established. After that, using the described mechanical generators of X-X motion as the basic building cell, we geometrically generate two major families of homokinetic shaft-coupling mechanisms characterized by a subchain with a mechanical generator of 5D X-X motion set of displacement. The obtained constant-velocity shaft couplings (CVSC) are isoconstrained linkages with two parallel shaft axes, which will be less sensitive to manufacture errors. In addition, by means of the reordering method for displacement group compositions, more CVSC mechanisms can be further obtained. The simple or special findings stemming from the proposed general architectures are presented for the potential applications too.

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