Cobots are a class of robots that use infinitely variable transmissions to develop high fidelity programmable constraint surfaces. Cobots consume very little electrical power even when resisting high forces, and their transmissions are highly power efficient across a broad range of transmission ratios. We have recently introduced the Cobotic Hand Controller, a haptic display that illustrates the high dynamic range and low-power consumption achievable by cobots. In this paper, we present models of the rotational-to-linear rolling contact transmissions utilized in the Cobotic Hand Controller. We compare their efficiency to fixed-ratio gear trains. We also compare the overall power efficiency of the cobotic architecture to the power efficiency of a conventional electromechanical actuation scheme, for both constant and dynamic power flows. The cobotic architecture is shown to be more efficient at frequencies and power levels characteristic of voluntary human motions.