Harmonic drives are gear reduction devices used to couple motors with linear axes. The basic principle used is a “Strain Wave Gearing” mechanism. It is an input/output gearing mechanism. Claimed characteristics include: no backlash, compactness and light weight, high gear ratio, ratio reconfigurable within a standard housing, good resolution and repeatability when repositioning inertial loads, high torque capability, and coaxial input and output shafts. High gear reduction ratios are possible in a small volume (a ratio of 100:1 is possible in the same space in which planetary gears typically only produce a 10:1 ratio).
Below is an animated illustration of how they work (whoever invented that is very brilliant!):