Harmonic Drive, Cycloidal (RV) or Planetary: Which Gear Reducer Belongs in Which Robot Joint

A robot joint’s motor spins fast but produces little torque. The reducer slows that rotation and multiplies the torque so the joint can move a load. Humanoids and collaborative robots mostly use three kinds — strain wave (Harmonic Drive), cycloidal (RV) and planetary — and because they work on different principles, each is good at different things. This article confirms the principles from manufacturer material, shows how to compute ratios, and suggests which reducer to evaluate first for each joint.

Five criteria for comparing reducers

1. Ratio and size — how much reduction you get in a given envelope
2. Backlash and lost motion — play when direction reverses, which directly limits positioning accuracy
3. Shock load — how well it survives momentary torque from falls or landings
4. Stiffness — torsional deflection under load
5. Backdrivability and efficiency — whether the joint yields when pushed from the output side, and how much power is lost

Strain wave gearing: a big ratio from a two-tooth difference

According to Harmonic Drive’s technology page, a strain wave gear has three parts:

• Wave generator — a thin ball bearing on an elliptical hub; the input, attached to the motor shaft.
• Flexspline — a thin alloy-steel cup with external teeth; the output.
• Circular spline — a rigid ring with internal teeth, fixed to the housing.

The circular spline has two more teeth than the flexspline. Each full turn of the wave generator moves the flexspline two teeth in the opposite direction, so the ratio equals the flexspline tooth count divided by two. Because teeth stay engaged along the ellipse’s major axis, the manufacturer claims zero backlash, and it notes that size and weight do not change with the reduction ratio.

The Wikipedia summary gives a typical range of 30:1 to 320:1 in a space where planetary gearing usually reaches about 10:1. The disadvantage it lists is wind-up — a torsional spring rate — in the low-torque region.

Cycloidal (RV) reducers: two stages built for shock and stiffness

Nabtesco describes its RV reducers as a patented two-stage cycloidal design offering large torque, high ratios, significant shock-load capability and high precision. Its RV-N series page lists backlash and lost motion both below 1 arc-minute and highlights a highly rigid component configuration.

Because many pins and discs engage at once and share the load, cycloidal designs lean toward high shock tolerance and high torsional stiffness. The cost is more parts and more weight, so they tend to sit in joints with room and mass to spare.

Planetary gears: the efficiency and backdrivability option

A planetary set has a central sun gear, planet gears around it, a carrier connecting the planets, and an outer ring gear. Wikipedia gives the ratio with the ring fixed, the sun as input and the carrier as output as:

where $N_r$ is the ring tooth count and $N_s$ the sun tooth count. With $N_s = 24$ and $N_r = 72$, the ratio is 4:1 (our worked example). The same source notes that load is shared among the planets, so more planets mean more load capacity and torque density, and that efficiency loss is typically about 3% per stage.

Low single-stage ratios plus high efficiency mean force applied at the output travels back to the motor — good backdrivability. That is why legs that must absorb landings softly often pair a strong motor with a low-ratio planetary stage.

The three side by side

Computing ratios yourself

def harmonic_ratio(flexspline_teeth):
    # circular spline has two more teeth: output moves two teeth per input turn
    return flexspline_teeth / 2

def planetary_ratio(sun_teeth, ring_teeth):
    # ring fixed, sun input, carrier output
    return 1 + ring_teeth / sun_teeth

print(harmonic_ratio(200))           # 100.0 -> 100:1
print(planetary_ratio(24, 72))       # 4.0   -> 4:1
print(planetary_ratio(24, 72) ** 2)  # 16.0  -> 16:1 with two stages in series

A flexspline with 200 teeth gives 100:1 in a single stage. Reaching the same ratio with planetary gears takes several stages in series, and each stage adds its own efficiency loss and play.

Reading a reducer datasheet without getting misled

Reducer catalogs list several torque figures, and mixing them up is the most common sizing error. Most manufacturers separate a rated torque for continuous operation, a higher limit for repeated peaks such as acceleration and deceleration, and a momentary limit for rare events such as an emergency stop or collision. A walking robot’s landing impact should be checked against the momentary figure, while the torque needed to hold a pose all day should sit below the rated one.

Precision figures need the same care. Backlash describes the dead zone when direction reverses; lost motion and hysteresis describe how the output shifts under a small load in each direction. Two catalogs can report very different numbers for similar hardware simply because one measures at a few percent of rated torque and the other at a higher load. Before comparing candidates, write down the test load behind every figure and ask the supplier when it is missing.

Which reducer to evaluate first, joint by joint

1. Wrist and elbow — tight space and high positioning accuracy. Start with strain wave gearing.
2. Hip and knee (high shock loads) — compare landing and fall scenarios against momentary allowable torque, and evaluate cycloidal designs.
3. Leg joints that need backdrivability — if the motor has enough torque, evaluate a low-ratio planetary stage.

Once the shortlist is set, compare datasheets under matching conditions: backlash, lost motion and torsional stiffness all depend on the percentage of rated torque at which they were measured. Comparing complete actuators — motor plus reducer — is covered in Rotary vs linear actuators, and the drive choices in shipping humanoids in Humanoid platforms compared.

One last practical note: the reducer is usually the part of the actuator that wears first. Ask suppliers for rated life under your duty cycle, not just peak specifications, and plan for replacement access in the joint design.