A multifilar flexible rotary shaft includes a plurality of individual filaments which are not wound around each other or around a central core, a loose ensemble of filaments. The input ends of each filament are coupled to each other and the output ends of each filament are coupled to each other. Preferably all of the filaments are identical. A loose ensemble of N filaments can transmit N times the torque of a single filament, and will have N times the torsional stiffness of a single filament, while retaining the minimum radius of operation of a single filament. Since a loose ensemble of filaments does not have any appreciable contact forces among the filaments (because they are not forcibly twisted together), there is no appreciable internal friction or hysteresis. In order to appreciably eliminate all the hysteresis in such an ensemble of filaments, the filaments should be no more than loosely twisted together, if at all. The only reason for loosely twisting the wires together is to allow the ensemble to be easily handled and to insure that the individual wire filaments follow the same general curved path from one end to the other. Several practical applications of the invention are also disclosed.