[Robot Hardware 03] - Harmonic Drives
Robot hardware from a Physical AI perspective - Harmonic Drive reducers
Among reducer types, Harmonic Drives, technically known as strain wave gears, are widely used in collaborative robots and precision robot arms. This note looks at their structure, operating principle, strengths, and limitations.
Operating Principle
A Harmonic Drive is different from ordinary rigid gear trains because it transfers power through elastic deformation.
It has three main components:
- Wave Generator (Input): An elliptical cam combined with a thin bearing. It is connected to the motor shaft and deforms the flexspline into an elliptical shape as it rotates.
- Flexspline (Output): A thin cup-shaped metal gear. Because it is elastic, it repeatedly deforms during operation and is connected to the output side.
- Circular Spline (Fixed): A stiff outer ring gear with internal teeth. It usually has two more teeth than the flexspline.
Gear Ratio
As the wave generator rotates, the long axis of the ellipse pushes the flexspline into mesh with the circular spline. The difference in tooth count produces relative motion.
For example:
- Flexspline: 200 teeth
- Circular Spline: 202 teeth
When the wave generator makes one full revolution, the flexspline cannot advance through all 202 teeth of the circular spline. Instead, it moves backward by the tooth difference, which is 2 teeth.
The gear ratio becomes:
\[\text{Gear Ratio} = \frac{-N_{flex}}{N_{circular} - N_{flex}} = \frac{-200}{202 - 200} = -100:1\]This mechanism can produce reduction ratios above 100:1 in a single stage.
Advantages
1. Compact Size and High Torque Density
Compared with a planetary gearbox of similar capacity, a Harmonic Drive can be smaller and lighter.
- Smaller joint modules
- Lower robot link inertia
Both of these can improve the overall dynamics of the robot.
2. Zero Backlash
The flexspline is preloaded against the circular spline, so mechanical backlash is almost eliminated.
- High repeatability: End-effector position error can be reduced.
- In multi-jointed robots, removing backlash at each joint is important because small joint errors accumulate at the end effector.
Limitations
1. Fatigue Life
The flexspline is a thin metal shell that repeatedly deforms during operation. Structurally, it experiences low-cycle fatigue, and that fatigue often determines the reducer’s lifetime.
2. Shock Vulnerability and Ratcheting
Harmonic Drives are vulnerable to external shock loads. If a collision or impact exceeds the momentary peak torque, the flexspline teeth can ride over the circular spline teeth. This is called ratcheting.
Once ratcheting occurs, teeth can permanently deform or buckle, and the reducer may need to be replaced.
3. Low Torsional Stiffness and Wind-Up
Although there is almost no backlash, the mechanical stiffness is relatively low. Under torsional load, the flexspline behaves like a spring and twists. This wind-up can excite resonance under high-gain control and can limit control bandwidth.
Compensation: SEA and Torque Sensors
To compensate for the low shock tolerance and stiffness of Harmonic Drives, robot joint designs sometimes add a torque sensor at the output side or intentionally introduce compliance through a Series Elastic Actuator (SEA). I will discuss SEA in more detail later.
Next reference note: [Robot Hardware 03] - Planetary Gearboxes
References
This note on Harmonic Drives was written with reference to [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