How does a Harmonic Drive work? Why are they used?

  • One of the many advantages of a harmonic drive is the lack of backlash due to the unique design. However, the fact that they are lightweight and extremely compact is also important.
  • High gear reduction ratios of up to 30 times that achieved with planetary gears are possible in the same space.
  • C W Musser designed strain wave gearing back in 1957 and by 1960 he was already selling licenses so that industry giants could use his patented product.
harmonic drive assembled

Image © 2018 EngineeringClicks

The harmonic drive is a type of gear arrangement often referred to as a strain wave gear because of the way it works. It is a kind of reduction gear mechanism consisting of a minimum of three main components. These components interact in a way that allows for very high precision reduction ratios that would otherwise require much more complex and voluminous mechanisms.

As a product, the harmonic drive was invented by the American engineer Clarence Walton Musser in 1957, and it quickly conquered the industry with the countless advantages that it brought to the table. Musser identified the potential of his invention at an early stage and in 1960 began selling licenses to manufacturers so they could use his patented product. Nowadays, there are only a handful of manufacturers in the USA, Germany, and Japan who are holding the license to produce harmonic drives, doing so at their top-notch facilities and producing ultimate quality strain gears for the whole world.

harmonic drive exploded view

Image © 2018 EngineeringClicks

The workings of a harmonic drive

The rotational motion comes from an input shaft that can be a servo motor axis for example. This is connected to an element called “wave generation” which has an elliptical shape and is encircled by an elliptical ball bearing. As the shaft rotates, the edges change position, so it looks like it is generating a motion wave. This part is inserted inside a flex spline that is made out of a  torsionally stiff yet flexible material. The material takes up this wavy motion by flexing according to the rotation of the input shaft and also creates an elliptical shape. The outer edge of this flex spline features gear teeth that are suitable for transferring high loads without any problem. To transfer these loads, the flex spline is fitted inside the circular spline which is a round gear featuring internal teeth. This outer ring is rigid and its internal diameter is marginally larger than the major axis of the ellipse formed by the flex spline. This means that the circular spline does not assume the elliptical shape of the other two components, but instead, it simply meshes its inner teeth with those of the outer flex spline side, resulting in the rotation of the flex spline.

The rate of rotation is dependent on the rotation of the input shaft and the difference in the number of teeth between the flex spline and the circular spline. The flex spline has fewer teeth than the circular spline, so it can rotate at a much reduced ratio and in the opposite direction than that of the input shaft. The reduction ration is given by: (number of flex spline teeth – number of circular spline teeth) / number of flex spline teeth. So for example, if the flex spline has 100 teeth and the circular spline has 105, the reduction ratio is (100 – 105) / 100 = -0.05 which means that the flex spline ration is -5/100 (minus indicates the opposite direction of spin). The difference in the number of teeth can be changed to accommodate different reduction ratios and thus different specialized needs and requirements.


  • Achieving reduction ratios of 1/100 and up to even 1/300 by simply using such a compact light arrangement of gears cannot be matched by any other gear type.
  • The harmonic drive is the only gear arrangement that doesn’t feature any backlash or recoil effect, or at least they are negligible in practice. This is mainly thanks to the elliptical bearing fitted on the outer rim of the input shaft allowing the free rotation of the flex spline.
  • The positional accuracy of harmonic drives even at an extreme number of repetitions is extraordinary.
  • Harmonic drives can accommodate both forward and backward rotation with no need to change anything, and they retain the same positional accuracy on both spin directions.
  • The efficiency of a typical harmonic drive measured on real shaft to shaft tests by the manufacturer goes up to 90%. There are very few mechanical engineering elements that can claim such an operational efficiency level.

Uses for a harmonic drive

In short a harmonic drive can be used “in any gear reduction application where small size, low weight, zero backlash, very high precision and high reliability are required”. Examples include aerospace applications, robotics, electric vehicles, medical x-ray and stereotactic machines, milling and lathe machines, flexo-printing machines, semiconductor equipment, optical measuring machines, woodworking machines and camera head pans and tilt axes. The most notable examples of harmonic drive applications include the wheels of the Apollo Lunar Rover and the winches of the Skylab space station.

About: Bill Toulas

Passionate engineer and new technologies advocate, writing about the ways they shape our world and amplify our very existence. Believes that engineering is the art of changing this world forever, every day, little by little, and sometimes all at once.

One Response to How does a Harmonic Drive work? Why are they used?

  1. Steven Weinberg says:

    Good article, A few questions/comments:a. Correct me if I'm wrong, but I don't think the flex spline actually rotates.It basically undulates in and out, based on the motion of the wave generator, meshing one tooth on each edge of the spline with the circular spline at a time. The fact that it does not rotate, and there is a difference in number of teeth, is what causes the rotation of the circular spline.b. I don't think the lack of backlash is due to the bearing. I think it's simply a function of the large gear ratio, so the backlash is negligible. Also, there are other non-backlash gear options – like split gears with springs to eat up backlash. c. I'm curious about the torque density of harmonic drives. I don't recall if this was an issue when I have used them (it's been a long time), but since they only mesh at two teeth, I'd think it would be relatively low.

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