Force and Torque Sensing — Robotics Tutorials

Strain Gauges: Measuring Deformation as Electrical Resistance

Strain gauges are the fundamental transducer technology underlying most force and torque sensors in robotics. A strain gauge is a thin metallic (or semiconductor) foil whose electrical resistance changes when it is mechanically deformed. When a force is applied to a structure, the structure deforms (strains), and the bonded strain gauge stretches or compresses, changing its resistance.

The gauge factor (GF) quantifies this relationship: GF = (ΔR/R) / ε, where ε is the mechanical strain (dimensionless, = ΔL/L). Metal foil gauges have GF ≈ 2; semiconductor gauges have GF ≈ 50–150 but are more sensitive to temperature.

To measure small resistance changes (typically 0.001–0.1 Ω from a nominal 120–350 Ω gauge), the gauges are arranged in a Wheatstone bridge circuit. A bridge with four active gauges (two in tension, two in compression, arranged in opposite arms) cancels temperature effects and doubles output sensitivity. The differential voltage output is amplified by an instrumentation amplifier and sampled by an ADC.

Modern force sensors achieve sub-millinewton force resolution and operate at sampling rates of 1–4 kHz, making them suitable for real-time force control in robotic manipulation.

Strain Gauge and Wheatstone Bridge Equations

The mechanical strain, gauge factor, and bridge output relate as follows:

ε = ΔL / L

GF = (ΔR / R) / ε

V_out = (V_in / 4) × GF × ε  [full bridge, one active gauge]

V_out = V_in × GF × ε  [full bridge, four active gauges]

For a stainless steel beam of Young's modulus E = 200 GPa under stress σ:

ε = σ / E

F = σ × A  (A = cross-sectional area)

So:  V_out = (V_in × GF × F) / (4 × E × A)  [single active gauge]

A typical sensor with V_in = 10 V, GF = 2, E = 200 GPa, A = 1 cm², loaded with F = 100 N produces ε = 5×10⁻⁶, and V_out ≈ 25 µV — requiring high-gain, low-noise amplification.

6-Axis Force/Torque Sensors for Robot Wrists

A 6-axis force/torque (F/T) sensor measures all six components of wrench simultaneously: three forces (Fx, Fy, Fz) and three moments (Mx, My, Mz). These sensors are typically mounted at the robot wrist, between the robot flange and the tool or gripper.

The mechanical structure contains multiple strain gauge bridges arranged so that each bridge is primarily sensitive to one load component. A calibration matrix (6×6) maps the raw bridge voltages to the six wrench components, accounting for cross-coupling between axes. This calibration matrix is determined during manufacturing using precision reference loads.

Key specifications of commercial 6-axis F/T sensors:

Measurement range: Forces 50–6000 N; Torques 2–500 Nm (varies with model)
Resolution: Typically 1/1000 to 1/4000 of full scale
Cross-talk: Less than 1–3% full scale (how much force on one axis affects readings on others)
Communication: Analog voltage, RS485, EtherCAT, or USB at 1–7 kHz sampling rates

Leading manufacturers include ATI Industrial Automation (Mini45, Gamma, Omega series), Kistler, Robotiq, and Sunrise Instruments. Many collaborative robots (Universal Robots, KUKA iiwa) integrate proprietary joint torque sensors instead of or in addition to wrist F/T sensors.

Wrist F/T Sensors vs. Joint Torque Sensors

Wrist-Mounted F/T Sensor

Measures all 6 components of wrench at tool-object interface
Direct measurement of contact forces and moments
High accuracy at point of contact — ideal for assembly and polishing
Adds mass and volume at the wrist — affects robot payload
Cannot detect collisions along the arm links, only at the tool
Examples: ATI Gamma, Robotiq FT 300, Kistler 9119AA
Typical cost: $3,000 – $20,000

Joint Torque Sensor (Series Elastic Actuator)

Strain gauges or deflection measurement in each joint actuator
Measures torque at each joint — full-arm collision detection
Enables whole-arm impedance and force control
Integrated into the robot structure — no added wrist mass
Reading is joint torque — must compute end-effector forces via Jacobian
Examples: KUKA iiwa, Franka Emika Panda, ABB YuMi
Typically included in cobot design; not easily retrofitted

Commercial 6-Axis F/T Sensor Specifications

Manufacturer / Model	Force Range (N)	Torque Range (Nm)	Resolution (N / Nm)	Application
ATI Mini45	±145 / ±145 / ±290	±5 / ±5 / ±5	0.06 N / 0.003 Nm	Small robot assembly, research
ATI Gamma SI-130-10	±130 / ±130 / ±400	±10 / ±10 / ±10	0.05 N / 0.001 Nm	Robot wrist, general manipulation
ATI Omega 160	±2500 / ±2500 / ±5000	±200 / ±200 / ±200	0.5 N / 0.05 Nm	Heavy industrial robots
Robotiq FT 300-S	±300 / ±300 / ±300	±30 / ±30 / ±30	0.1 N / 0.01 Nm	Collaborative robots (UR series)
Kistler 9119AA2	±5000 / ±5000 / ±5000	±300 / ±300 / ±300	0.2 N / 0.01 Nm	Machining, testing, assembly
Sunrise M3714C	±70 / ±70 / ±200	±3 / ±3 / ±6	0.04 N / 0.001 Nm	Medical robots, teleoperation

Force Control Applications in Robotics

Force sensing unlocks a class of tasks impossible with pure position control:

Assembly and insertion: Peg-in-hole, connector mating, and bearing insertion require compliant motion. The robot detects contact forces and adjusts position to reduce jamming — an approach called compliance control or force-guided assembly.

Surface finishing (polishing/deburring): The robot must maintain a constant normal force against a workpiece surface regardless of surface geometry variations. A force controller maintains F_normal = F_desired while the position controller traces the nominal path.

Human-robot collaboration safety: Collaborative robots (cobots) use F/T sensing or joint torque sensing to detect unexpected contact with humans. ISO/TS 15066 defines power-and-force-limiting (PFL) thresholds; the robot must stop within milliseconds of detecting forces exceeding these limits.

Medical and surgical robots: Force feedback is critical for needle insertion, tissue manipulation, and bone cutting, where exceeding safe force limits can cause injury. The surgeon receives haptic feedback through the control interface.

Key terms

Strain gauge: A sensor whose electrical resistance changes in proportion to mechanical strain (deformation); the primary transducer in most force/torque sensors.
Wheatstone bridge: A circuit configuration of four resistors used to measure small resistance changes with high accuracy; arranging strain gauges in a bridge cancels temperature drift and improves sensitivity.
Gauge factor (GF): A dimensionless parameter characterizing the sensitivity of a strain gauge: GF = (ΔR/R) / ε, where ε is mechanical strain. Metal foil gauges have GF ≈ 2.
6-axis F/T sensor: A transducer that simultaneously measures all six components of a wrench (Fx, Fy, Fz, Mx, My, Mz) at a point; typically mounted at the robot wrist.
Compliance: The tendency of a mechanical system to deflect under applied force; compliant mechanisms or control strategies allow a robot to yield appropriately to contact forces.
Impedance control: A robot control strategy that regulates the dynamic relationship between end-effector position and contact force, modeling the robot as a mass-spring-damper system.
Admittance control: A control strategy that takes force input and produces motion output, complementary to impedance control; commonly used when the robot has a stiff position controller.
Series elastic actuator (SEA): An actuator design with an elastic element (spring) in series between the motor and the load; spring deflection is measured to estimate output torque, providing compliance and accurate force control.
Force control: A control paradigm in which the robot regulates applied force (rather than position) as the primary controlled variable; essential for contact tasks such as assembly and polishing.
Cross-talk: The unwanted influence of force or torque on one axis of a multi-axis sensor on the readings of other axes; typically less than 1–3% of full scale in well-designed F/T sensors.

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