Tendon tension sensing: Bowden friction, sensor location and calibration

01 / ENGINEERING DECISION

Choose which tension you need to observe.

A tendon tension load cell for robotics observes force at its own location. Between that location and the contact point, sheath friction, pulleys, compliant tendons and joints can change the relationship to the desired force. A good sensor reading is not automatically a measurement of fingertip contact force.

Start with a free-body sketch of the controlled structure. Decide whether the variable is proximal cable tension, distal tendon tension, joint torque or contact force. Converting among them needs the relevant routing, moment arms and other forces; moving a sensor does not remove that modeling requirement.

Supporting scope: Wagner & Emmanouil (2018): tendon-sheath transmission ↗ · Zhou et al. (2024): tension sensor array for cable-driven robots ↗

02 / ENGINEERING DECISION

Use the capstan model only within its assumptions.

For a simple sliding-friction screen, define a proximal pulling tension T_in, positive total wrap angle theta in radians and an assumed effective friction coefficient mu. A corresponding distal estimate is T_out = T_in × exp(−mu × theta). This gives a direction-specific estimate under the model assumptions.

Wagner and Emmanouil analyze tendon-sheath transmission with explicit assumptions. The equation does not establish a constant friction coefficient for an actual moving hand. At rest or reversal, friction can support a range of tensions; a single exponential equality does not describe that history. Compliance, acceleration and changing routing add further limitations.

Supporting scope: Wagner & Emmanouil (2018): tendon-sheath transmission ↗ · Single tendon-sheath system with time-varying parameters (2025) ↗

03 / ENGINEERING DECISION

Worked example: a good proximal reading can miss distal loss.

Assume mu = 0.10 and T_in = 20 N for an idealized sliding case. The values below are calculated, not measured. At a total angle of pi radians, the estimate is 14.61 N distally even while the proximal sensor reads 20 N. A controller that needs distal tension cannot treat those values as equivalent.

These are sensitivity checks for an assumed coefficient. Do not enter mu = 0.10 as an identified material property or extrapolate this table through a direction reversal. Compare it with measured local references for the intended routing.

Supporting scope: Wagner & Emmanouil (2018): tendon-sheath transmission ↗

04 / ENGINEERING DECISION

Select range from pretension, useful increment and assembly load.

A tendon can have a substantial baseline tension while the desired control increment is small. The useful signal is the increment on top of that baseline, not the entire nominal range. Include cable forces and fixture mass when testing the smallest observable change.

Do not solve an assembly overload problem only by increasing capacity. A larger range may reduce the force signal per volt; a protected attachment procedure or an appropriate mechanical stop may be the more relevant change. The proposed sensor’s actual range, noise and directional overload evidence govern the choice.

Supporting scope: Zhou et al. (2024): tension sensor array for cable-driven robots ↗

05 / ENGINEERING DECISION

Build a validation matrix, not one fitted curve.

Use a local force reference at the quantity you intend to infer, and record its calibration scope and uncertainty. Compare at multiple sheath shapes and both motion directions, with held loads and the intended speed range. Keep fitting data separate from validation data.

The sensor-array research by Zhou and colleagues reports different loading and unloading behavior in a tendon-sheath setup. It motivates testing direction history; its measured coefficients and results do not characterize a different hand or MT-ILC sensor.

Supporting scope: Zhou et al. (2024): tension sensor array for cable-driven robots ↗ · Single tendon-sheath system with time-varying parameters (2025) ↗

06 / ENGINEERING DECISION

Worked example: check an increment in electrical units.

Assume a hypothetical 50 N sensor produces 2 mV/V at rated force and uses 5 V excitation. Its nominal full-range change is 10 mV, or 200 microvolts per newton. A 0.20 N increment produces 40 microvolts under a linear approximation. If the complete chain has 4 microvolts RMS noise in the stated measurement bandwidth, its input-referred force noise is 0.02 N RMS.

That is not an accuracy or pass/fail claim. Calibration uncertainty, friction, attachment loading and zero drift remain separate. Record the bandwidth and observation interval with the noise number; an ADC bit count alone cannot substantiate the result.

Supporting scope: NI-DAQmx: Bridge Sensor Scaling ↗

07 / ENGINEERING DECISION

Preserve independent measurements and useful timing.

Independent tendons need independently recoverable measurements. A multiplexed converter can provide separate values without simultaneous sampling or electrical isolation. Request per-channel sample rate, scan order, timing skew, timestamps, filtering, latency and dropout behavior, rather than only the converter’s aggregate rate.

For illustration, 16 channels × 1,000 samples/s × 3 bytes/sample require 48,000 bytes/s of sample payload before headers, timestamps and transport overhead. This arithmetic does not establish a board’s usable throughput or a controller update rate.

1. Calibrate the channel with its actual sensor and cable association.
2. Align reference and sensor timestamps before comparing moving trajectories.
3. Test channel skew with a shared time-varying input appropriate to the hardware.
4. Test missing samples, saturation and stale-data handling before closing the loop.

Supporting scope: NI-DAQmx: Bridge Sensor Scaling ↗

08 / ENGINEERING DECISION

Request the sensor and acquisition chain as one defined system.

Send the measurement location, pretension and peak load, minimum increment, attachment sketch and available envelope. Include channel count, per-channel rate, acceptable latency and the controller interface. Ask for model-specific noise, calibration, overload and cable evidence.

The existing tendon/actuator application page covers the broader system request; this guide supplies a transmission-model and validation method. Neither page establishes clinical suitability or a validated robot safety function.