[Robot Hardware 03] - Cycloidal Reducers
Robot hardware from a Physical AI perspective - cycloidal reducers
This post examines the cycloidal drive, which has recently attracted renewed attention in legged robots and small actuators because of its excellent shock tolerance and high torque density.
A cycloidal drive achieves reduction and torque amplification using an eccentric input and the resulting cycloidal path. The reduction ratio is determined by the cycloid tooth geometry. The mechanism can produce high torque in a very compact package and, above all, has strong structural resistance to shock.
Operating Principle and Reduction Ratio
The operating principle consists of three main mechanisms:
- Eccentric input: An eccentric bearing is attached to the input shaft connected to the motor. As the shaft rotates, it creates motion offset from the center axis.
- Cycloidal motion: The cycloid disk mounted on the eccentric bearing meshes with the outer ring pins of the housing and rocks and rotates along a cycloidal path.
- Output extraction: Pins on the output shaft pass through holes in the disk and transmit only the disk’s slow rotational motion to the output shaft.
Reduction Ratio for Different Fixed Elements
The reduction ratio and rotation direction change depending on which element is fixed. Let the number of housing pins be $N$ and the number of cycloid-disk lobes be $N-1$.
-
Outer ring fixed / disk output:
When the input shaft makes one revolution, the disk rotates by one tooth or lobe in the opposite direction to the input shaft.
Gear Ratio = $(N-1)/1$
Cycloidal Drive — Fixed Ring (short) -
Disk fixed / outer ring output:
When the input shaft makes one revolution, the housing rotates by one pin in the same direction as the input shaft.
Gear Ratio = $N/1$
Cycloidal Drive — Fixed Shaft (short)
2. Contact-Mechanism Design: Rolling vs. Sliding Contact
Unlike conventional gears that transmit power through friction between gear teeth, a cycloidal drive is fully determined by kinematic constraints. Depending on the design objective, both rolling contact and sliding contact can be used.
Rolling Contact
Bearings or cylindrical rollers are added at the housing-pin or output-pin positions to minimize friction.
- Characteristic: Friction loss is extremely low, so transmission efficiency is high and heat generation is low.
- Limitation: Miniaturization is difficult. Increasing the reduction ratio requires more rollers, which increases the part count and the overall reducer weight rapidly.
Sliding Contact
Without separate rollers, the shape of the cycloid disk itself contacts the housing or output pins and slides against them.
- Characteristic: Omitting the rollers makes the structure very simple and enables extreme miniaturization and weight reduction.
- Limitation: Sliding friction is large, so power-transmission efficiency drops substantially and wear becomes a concern.
In an actual actuator design, the heavily loaded central eccentric-shaft region often uses bearings to implement rolling contact, while sliding contact is used between the disk and housing on the outside of the reducer, where the relative linear speed is lower.
To reduce the high friction and wear of sliding contact, the cycloid disk may be machined from a low-friction engineering plastic such as Delrin (POM) or nylon instead of metal.
3. Advantages
1. High Torque Density
Like Harmonic Drive, a cycloidal drive can produce high torque in a very small volume, enabling compact joint packaging.
2. High Shock Tolerance
Where a spur gear carries torque through only one or two teeth, a cycloidal drive structurally distributes load across approximately 30–50% of its teeth at the same time.
This distributes external shock load and reduces the chance of gear failure, making the mechanism well suited to repeated impacts such as foot strikes in legged robots or collisions in manipulation robots.
3. High Reduction Ratio in a Single Stage
A single-stage structure can achieve a high reduction ratio of 50:1 to 100:1 or more, reducing the volume and complexity associated with multi-stage reducers.
4. Disadvantages and Design Considerations
1. Machining Difficulty
The part count may look small, but the machining requirements are demanding. The precise cycloidal curve must be produced without error, so high-precision CNC machining is essential, and assembly also requires considerable skill.
2. Tolerance Sensitivity
Tolerance and assembly errors directly degrade overall performance. If the tolerance is too tight, jamming can make the mechanism impossible to drive. If it is too loose, backlash reduces position accuracy.
3. Profile Modification
Eccentricity is a key variable that determines the curvature and kinematic constraint of the cycloid profile. If the theoretical cycloidal curve is machined exactly, assembly tolerance and thermal expansion can easily cause interference. The curve therefore needs a profile-modification step, such as shrinking or offsetting it slightly. This greatly increases design complexity.
4. Mass Imbalance and Vibration
Because the center of mass of the eccentrically moving disk continuously shifts, high-speed rotation can cause severe vibration. To cancel it, two cycloid disks with a 180-degree phase difference are commonly stacked as a dual-disk design, adding weight and volume.
Next post: [Robot Hardware 04] - Actuators (3): QDD Actuators
References
[1] https://mevirtuoso.com/become-a-member-cycloidal/
[2] https://www.youtube.com/watch?v=KX9Mx8ghtio
[3] https://www.youtube.com/watch?v=yBckAoqNQx4