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industry · Mar – Aug 2026

A six-axis force sensor for robot joints

An inductive sensor that measures three forces and three torques for robotic interaction.

Exploded schematic of the six-axis force sensor: anchoring plate, coil boards, compliant aluminium structure, alignment pins, sensor cover and load connector.
Sixteen coils detect deflection of the compliant structure. Each sensing beam has one planar coil above, one below and two vertical coils beside it. Apply a force or torque to see how the coil gaps and six output signals change. Shapes are simplified and deflections exaggerated.

Summary view

Project details

  1. Fx Fy Fz Mx My Mz

    Force and torque sensing

    A robot needs force and torque measurements to control contact with its surroundings. A six-axis sensor measures three force components and three torque components. Most designs bond strain gauges to a compliant structure, but gauges drift with temperature and are delicate to assemble in volume.

  2. load coil boards compliant part gap-dependent coil signal

    Inductive measurement of deformation

    This design uses coils on two circular boards to measure deformation of a compliant aluminium part. The company defined the sensing principle and product direction. I led the project and carried out almost all of the development, from mechanical design and electronics to acquisition and calibration, with advice from the team.

  3. stiffness deflection Pareto front 782 evaluations schematic optimisation plot

    Optimising stiffness and sensitivity

    782 FEM evaluations

    The structure must deform enough to resolve small forces while remaining sufficiently stiff for a robot joint. I parameterised its geometry and ran a global optimisation with 782 FEM evaluations. The result is a Pareto front rather than a single answer, which makes the trade-off between stiffness and sensitivity visible before choosing the geometry.

  4. load 25 N·m 202 MPa nominal, 10⁶ cycles 187 MPa peak corrected envelope met not met

    Fatigue assessment

    The final geometry reaches 187 MPa under a 25 N·m load, below the aluminium’s nominal one-million-cycle strength of 202 MPa. Applying the corrected fatigue envelope’s knock-down factors lowers the allowable stress below every evaluated load case. So the design meets the nominal limit, but not the corrected one.

  5. reference sensor residual error non-linearity zero drift hysteresis

    Calibration and sources of error

    I calibrated the sensor against a reference wrench using seven recordings. I separated the residual error into non-linearity, zero drift after warm-up and hysteresis during unloading, and assessed cross-axis coupling. Splitting the error this way shows which term to work on next, instead of hiding everything in one accuracy figure.

  6. Prototype demonstration

    0.36 %FS accuracy · 9.1 bits effective resolution

    The demonstration shows the measured force and torque traces responding as the handle is pushed and twisted, with a cube visualising the motion. Calibration against the reference wrench gave 0.36 %FS accuracy, 9.1 bits of effective resolution and 0.13 % cross-axis coupling. In a next version, I would start from the corrected fatigue allowable.

Pushing and twisting the prototype’s handle changes the live force and torque traces. The cube on screen follows the applied load.

My contribution

I led the sensor project and carried out almost all of the mechanical design, FEM optimisation, readout electronics, acquisition and calibration. The rest of the team provided advice throughout.