Strain wave gearing

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Strain wave gearing also known as harmonic gearing is a special type of mechanical gear system that can improve certain characteristics compared to traditional gearing systems such as helical gears or planetary gears. It was invented in 1957 by C.W. Musser while he was a research advisor at United Shoe Machinery (USM). The advantages include: no backlash, compactness and light weight, high gear ratios, reconfigurable ratios within a standard housing, good resolution and excellent 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 from 30:1 up to 320:1 is possible in the same space in which planetary gears typically only produce a 10:1 ratio). Disadvantages include a tendency for 'wind-up' (a torsional spring rate) in the low torque region. Strain wave gears are typically used in industrial motion control, machine tool, printing machine, robotics and aerospace, for gear reduction but may also be used to increase rotational speed, or for differential gearing.


The basic concept of strain wave gearing (SWG) was introduced by C.W. Musser in his 1955 patent while he was an advisor at United Shoe Machinery Corporation (USM). The electrically-driven wheels of the Apollo Lunar Rover[1] included strain wave gears. Also, the winches used on Skylab to deploy the solar panels were powered using strain wave gears. Both of these system were developed by The Harmonic Drive division of United Shoe Machinery Corp.[citation needed] The most notable manufacturers using this gear technology is the Harmonic Drive group of companies located in Japan, USA and Germany.[2]


The strain wave gearing theory is based on elastic dynamics and utilizes the flexibility of metal. The mechanism has three basic components: a wave generator, a flexspline, and a circular spline. More complex versions have a fourth component normally used to shorten the overall length or to increase the gear reduction within a smaller diameter, but still follow the same basic principles. The wave generator is made up of two separate parts: an elliptical disk called a wave generator plug and an outer ball bearing. The gear plug is inserted into the bearing, giving the bearing an elliptical shape as well. The flexspline is like a shallow cup. The sides of the spline are very thin, but the bottom is thick and rigid. This results in significant flexibility of the walls at the open end due to the thin wall, but in the closed side being quite rigid and able to be tightly secured (to a shaft, for example). Teeth are positioned radially around the outside of the open end of the flexspline. The flexspline fits tightly over the wave generator, so that when the wave generator plug is rotated, the flexspline deforms to the shape of a rotating ellipse but does not rotate with the wave generator. The circular spline is a rigid circular ring with teeth on the inside. The flexspline and wave generator are placed inside the circular spline, meshing the teeth of the flexspline and the circular spline. Because the flexspline has an elliptical shape, its teeth only actually mesh with the teeth of the circular spline in two regions on opposite sides of the flexspline, along the major axis of the ellipse. Assume that the wave generator is the input rotation. As the wave generator plug rotates, the flexspline teeth which are meshed with those of the circular spline change. The major axis of the flexspline actually rotates with wave generator, so the points where the teeth mesh revolve around the center point at the same rate as the wave generator. The key to the design of the strain wave gear is that there are fewer teeth (for example two fewer) on the flexspline than there are on the circular spline. This means that for every full rotation of the wave generator, the flexspline would be required to rotate a slight amount (two teeth, for example) backward relative to the circular spline. Thus the rotation action of the wave generator results in a much slower rotation of the flexspline in the opposite direction. For a strain wave gearing mechanism, the gearing reduction ratio can be calculated from the number of teeth on each gear:

For example, if there are 202 teeth on the circular spline and 200 on the flexspline, the reduction ratio is (200 − 202)/200 = −0.01 Thus the flexspline spins at 1/100 the speed of the wave generator plug and in the opposite direction. This allows different reduction ratios to be set without changing the mechanism's shape, increasing its weight, or adding stages. The range of possible gear ratios is limited by tooth size limits for a given configuration.

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