This paper describes a design methodology for a three degree-of-freedom, linkage-based constant-velocity coupling. This coupling resembles the Clemens coupling patented in 1872 and has evolved from the authors' previous research in parallel mechanisms. This coupling contains only revolute joints and is therefore likely to be more durable and less prone to manufacturing errors than conventional higher-pair couplings. The kinematic configuration, based on the symmetric double octahedral Variable Geometry Truss mechanism (figure 2), has many inherent traits that make it ideal for application to industrial uses. Its parallel design of simple links and revolute joints provide it with high strength, rigidity, and light-weight characteristics. It has a link-joint construction that allows its geometry to be varied for specific applications, such as producing high angular deflection between the input and output shafts. In fact this coupling has the unique capability of producing solid joint angles greater than 180 degrees. Further, the physical construction of the coupling greatly improves heat transfer, making it less susceptible to thermal failures that limit the speed and range of motion of some existing couplings.