[Robot Hardware 03] - Harmonic Drive Reducers
Robot hardware from a Physical AI perspective - Harmonic Drive
Among the many types of reducers, Harmonic Drive, technically called strain-wave gearing, is widely used in cobots and precision robot arms. This post looks at its structure and operating principle, along with its advantages and limitations.
Operating Principle
Harmonic Drive differs from conventional gears because it transmits power through elastic deformation, rather than rigid-body meshing alone.
It has three main components:
- Wave generator (input): an elliptical cam combined with a thin bearing. It connects to the motor shaft, rotates, and deforms the flexspline into an ellipse.
- Flexspline (output): a thin, cup-shaped metal gear. It is elastic, deforms repeatedly, and connects to the output shaft.
- Circular spline (fixed): a rigid outer ring gear with internal teeth. It normally has two more teeth than the flexspline.
Calculating the Reduction Ratio
When the wave generator rotates, the flexspline and circular spline mesh at the ends of the ellipse’s major axis. Their relative rotation comes from the difference in tooth count.
For example:
- Flexspline: 200 teeth
- Circular spline: 202 teeth
When the input wave generator makes one revolution, the flexspline cannot advance through all 202 teeth of the circular spline. It rotates backward by the difference, 2 teeth.
The reduction ratio is therefore
\[\text{Gear Ratio}=\frac{-N_{flex}}{N_{circular}-N_{flex}} =\frac{-200}{202-200}=-100:1\]This principle makes it possible to achieve a high reduction ratio of 100:1 or more in a single stage.
Advantages
1. Compact Size and High Torque Density
Compared with a planetary gear of similar capacity, a Harmonic Drive can be smaller and lighter.
- It enables a compact joint module.
- It reduces the inertia of the robot links, which can improve the dynamics of the complete robot.
2. Zero Backlash
Because the flexspline is preloaded against the circular spline during operation, Harmonic Drive has virtually no mechanical backlash.
- High repeatability: End-effector position error can be minimized.
- It is a key reason for limiting the amplification of end-effector error caused by accumulated backlash across multiple robot joints.
Disadvantages and Limitations
1. Fatigue Life
The flexspline is made from thin sheet metal and repeatedly undergoes elliptical deformation during operation. It is structurally exposed to low-cycle fatigue, which is a major factor in the service life of the reducer.
2. Vulnerability to Shock: Ratcheting
Harmonic Drive is highly vulnerable to external shock loads. If a transient force from a collision exceeds the momentary peak-torque limit, the flexspline teeth can pass over the circular-spline teeth beyond their elastic limit. This is called ratcheting.
Permanent deformation or buckling of the gear teeth can result, requiring the reducer to be replaced.
3. Low Stiffness: Wind-up
Harmonic Drive has little backlash, but its mechanical stiffness is relatively low. The flexspline can twist like a spring under torsional load, a phenomenon known as wind-up. At high control gain, this can cause resonance and limit control bandwidth.
Compensating Design: SEA and Torque Sensors
To compensate for Harmonic Drive’s limited shock tolerance and stiffness, robot-joint designs may place a torque sensor on the output shaft to detect collisions or add an intentional elastic element in a Series Elastic Actuator (SEA) configuration. SEA will be discussed in more detail later.
Next post: [Robot Hardware 03] - Planetary Gearboxes
References
This post on Harmonic Drive was written with reference to source [2].
[1] https://www.harmonicdrive.net/_hd/content/documents/FBB_DifferentialGear.pdf
[2] https://www.cubemars.com/product/ak10-9-v2-0-kv60-robotic-actuator.html