Backdrivability is one of the most misunderstood specifications in joint actuator design. Catalog numbers rarely explain what's being measured, under what conditions, or how the gear ratio and control architecture interact with the mechanical baseline. This post works through the problem honestly: why harmonic drives are naturally non-backdrivable, what the design levers are for improving that, and where the control layer can and cannot compensate for mechanical limitations.
Why Harmonic Drives Are Inherently Non-Backdrivable
A harmonic drive achieves its high gear ratio — typically 50:1 to 160:1 in compact joint packages — through the elastic deflection of a thin-walled flex-spline meshing against a rigid circular spline. This mechanism produces extraordinary torque density in a compact package, sub-arcminute positional accuracy, and zero backlash. It also produces high friction.
The friction arises from two sources. First, the contact geometry between the flex-spline teeth and the circular spline involves a large contact area under high Hertzian stress — the elastic compliance that eliminates backlash also creates high normal forces at the tooth interfaces. Second, the wave generator bearing that deforms the flex-spline generates substantial rolling-element friction, particularly at low speeds where the Stribeck curve is in the boundary lubrication regime.
For a typical compact harmonic drive at 100:1 ratio, the no-load backdrive friction at the output is in the range of 1.5–4 Nm. For comparison, the static friction of human wrist flexion (the force a human can oppose with their wrist before motion initiates) is roughly 2–5 Nm. A joint that requires more than human-level force to backdrive is not safe in unguarded human-robot interaction without active power.
Planetary gearboxes present a different friction profile. The distributed load across multiple planets produces better bearing efficiency than a harmonic drive at equivalent gear ratios, and the gear mesh losses are lower per stage. A two-stage planetary at 100:1 has measurably better backdrivability than a harmonic drive at the same ratio — but it has backlash. For position-critical manipulation, backlash is unacceptable. For legged locomotion where ground contact impacts must be absorbed through the gearbox, high backdrivability is more critical than zero backlash, and planetary gearboxes are sometimes the correct choice despite their backlash.
Mechanical Design Levers for Improved Backdrivability
The first lever is gear ratio selection. The backdrive friction at the output scales approximately with the gear ratio — a 50:1 harmonic drive will backdrive at roughly half the output force of a 100:1 unit with identical mechanics, because the motor-side friction is amplified less. The trade-off is obvious: lower gear ratio means higher motor speed for the same output velocity, or lower output torque for the same motor torque. For humanoid joint applications, the sweet spot for backdrivability versus torque density appears to be in the 80:1 to 120:1 range — enough gear ratio to keep motor size compact, not so much that backdrive friction becomes unmanageable.
The second lever is lubrication choice. Harmonic drive manufacturers specify grease viscosity ranges for their units, and operating at the lower end of the viscosity specification significantly reduces Stribeck friction in the low-speed regime without meaningfully affecting high-speed efficiency. The TK-120 uses a synthetic grease with kinematic viscosity of 32 cSt at 40°C — towards the low end for this flex-spline diameter. The consequence is a maintenance interval: grease migration under cyclic loading means re-lubrication is required roughly every 1,500–2,000 operating hours.
The third lever is flex-spline wall thickness. A thinner flex-spline deflects under lower force, which reduces the tooth contact stress at the mesh interface. Thinner flex-splines also reduce the wave generator bearing load. The trade-off is fatigue life — thinner walls mean lower cycles-to-failure. This is an actuator design decision, not a user-tunable parameter, but it explains why different harmonic drive sizes have meaningfully different backdrivability characteristics even at equivalent gear ratios.
We're not saying you can engineer a harmonic drive actuator to be as backdrivable as a direct-drive motor. That's not the physics. What you can do is push the harmonic drive down to a regime where active control compensation can bring the total backdrive force within human-interaction-safe limits.
Active Friction Compensation in the FOC Layer
Once the mechanical baseline is set, the control layer takes over. The goal of active friction compensation is to cancel the joint friction torque as observed from the output, making the effective impedance at the output much lower than the mechanical backdrive would suggest.
There are two main approaches to friction compensation in the current controller: model-based (Coulomb + viscous friction model) and disturbance observer-based. The model-based approach uses a pre-identified friction model with static Coulomb friction τ_c and viscous coefficient b:
// Model-based friction feed-forward compensation
// Applied additively to the impedance control torque command
float sign_velocity = (dθ > 0.0f) ? 1.0f : ((dθ < 0.0f) ? -1.0f : 0.0f);
// TK-120 identified parameters (100:1 harmonic drive, 25°C)
float tau_coulomb = 0.48f; // [Nm] static friction at output
float b_viscous = 0.012f; // [Nm·s/rad] viscous coefficient
float dθ_deadband_rad = 0.003f; // [rad/s] velocity deadband
float tau_friction_ff = tau_coulomb * sign_velocity
+ b_viscous * dθ;
// Zero feed-forward in the deadband to avoid dither
if (fabsf(dθ) < dθ_deadband_rad) tau_friction_ff = 0.0f;
τ_cmd += tau_friction_ff;The velocity deadband is essential. Near-zero velocity, the sign of dθ is dominated by encoder noise. Without a deadband, the Coulomb term chatters at high frequency, which shows up as acoustic noise and micro-oscillations in the joint. The deadband introduces a small velocity-dead zone in the transparency, but the alternative — chatter-induced wear and audible noise — is worse.
Disturbance Observer for Non-Parametric Friction
Model-based friction compensation works well when the friction is stationary — same temperature, same lubrication state, same load history. In practice, harmonic drive friction varies with temperature by 30–50% over the operating range, and it changes with load because the tooth contact geometry shifts under high torque. A fixed friction model built at 25°C and no-load will under-compensate at peak torque and at elevated temperature.
A disturbance observer (DOB) addresses this by estimating total joint disturbance — friction plus any unmodeled dynamics — from measured torque and velocity without requiring a parametric friction model. The DOB operates by comparing the actual joint response to what a nominal plant model predicts. The difference is attributed to disturbance and subtracted from the torque command.
The bandwidth of the DOB filter determines how fast disturbances can be rejected. A wide-bandwidth DOB (200–400 Hz cutoff) can track friction variations in real time but amplifies high-frequency encoder noise. A narrow-bandwidth DOB (20–50 Hz) is more noise-tolerant but cannot reject rapidly varying friction, such as during stick-slip transitions when the joint reverses direction.
For the TK-120, we run the DOB at 80 Hz cutoff — empirically determined as the crossover where noise amplification begins to exceed disturbance rejection benefit. This provides effective friction compensation for velocities above approximately 15 RPM output. Below that, the model-based Coulomb term carries most of the compensation load.
Quantifying Backdrivability: Transparency Ratio in Practice
Backdrivability is often expressed as the external force required to move the joint at a specified constant velocity — typically 5–10 rpm — divided by the output torque at rated speed. Lower is better. A transparency ratio (where 1.0 = ideal zero-impedance) is a cleaner metric: it's the ratio of ideal joint compliance to actual joint compliance as measured at the output.
For the TK-120 at operating temperature with friction compensation active:
| Mode | Backdrive force at 5 RPM output | Notes |
|---|---|---|
| Unpowered mechanical | 4.8 Nm | Room temp, no-load |
| Powered, no compensation | 5.6 Nm | Motor stiction adds ~0.8 Nm reflected |
| Model-based compensation only | 1.4 Nm | 25°C, no-load identification |
| Model + DOB at 80 Hz | 0.7 Nm | Steady thermal state |
The 0.7 Nm figure at the output is within human wrist-force range — a person can easily back-drive the joint in gravity-compensation mode. This is the threshold we consider necessary for human-safe physical interaction. The same figure rises to approximately 1.1 Nm at 60°C steady-state — friction compensation partly compensates for the temperature-dependent friction increase, but not fully, because the DOB bandwidth limits its tracking speed.
Regen Braking and Its Effect on Perceived Backdrivability
One backdrivability degradation mechanism that rarely appears in spec sheets is regenerative braking. When the joint is back-driven while the motor is in generating mode — for example, a gravity-loaded arm joint being lowered under control — the motor generates back-EMF that must be absorbed by the bus. If the bus is not actively sinking the regenerated energy, bus voltage rises.
Elevated bus voltage increases the effective motor back-EMF resistance to backdrive motion. The motor appears stiffer than its winding resistance alone would predict. In impedance-controlled gravity compensation mode, this shows up as the joint feeling heavier than the gravity model expects — exactly the sensation of increased backdrive friction, even though the mechanical friction hasn't changed.
The TK firmware includes a dynamic braking resistor (DBR) activation threshold: if bus voltage rises above 26.5 V during regeneration on a 24 V nominal bus, the DBR MOSFET activates and shunts excess energy as heat. This keeps bus voltage controlled and prevents perceived backdrive stiffening during gravity-loaded lowering operations. The DBR resistor is sized at 10 W continuous — adequate for slow lowering of typical humanoid arm masses, but not for rapid deceleration of a heavy loaded platform where a proper regenerative power supply is needed.
Active backdrivability is a system-level design problem, not a motor specification problem. The gearbox mechanics, lubrication, friction compensation bandwidth, bus voltage management, and control architecture all interact. Getting to sub-1 Nm backdrive force on a 100:1 harmonic drive requires attention to all of them simultaneously.