Measure

Joint torque budget

You might say: load table, moment budget, torque sizing

A joint torque budget lists every force that one axis must resist or create at each important configuration. It includes downstream links, servos, gearboxes, brackets, cables, tool and payload, not only the payload at the tip.

What it does

It turns gesture, reach and mass measurements into a torque and power requirement that can be compared with an actuator's applicable torque-speed and thermal data.

Ask

At the worst pose, what are each mass, centre of mass, perpendicular lever arm, acceleration, friction assumption, supply voltage, current and duty cycle?

Typical

Start with a free-body sketch for each joint and its unit axis a_j at each pose. For gravity, the signed scalar torque about that axis is τg,j(q) = a_j · Σ_i ((r_i − r_j) × m_i g), where r_i is each mass centre, r_j is the joint position, and g is the gravity-acceleration vector; include the end effector, payload, downstream actuators and links. In a planar arm with a horizontal joint axis, the signed gravity torque is Σ_i m_i g ℓ_i with signed horizontal lever arms ℓ_i, and its magnitude is |Σ_i m_i g ℓ_i|; opposite-sign terms reduce the net magnitude, while a vertical yaw axis gets zero gravity torque. At static hold, the commanded motor torque must oppose the applied gravity and external torque, with sign set by the chosen axis. A force at angle θ uses |τ| = rF sin θ = r⊥F only in the chosen axis/plane, so an arm's length alone is not enough. For an end-effector wrench F expressed in the frame used by J, use the Jacobian-transpose map τ_F = J(q)ᵀF; if F is a disturbance applied to the robot, the holding motor command has the opposite sign. Add acceleration/inertia, friction and transmission losses only when they are modelled or measured and record the assumptions. For each candidate actuator record the manufacturer's stall/maximum figure, rated or continuous figure or torque-speed curve, voltage, current, speed, mass, output spline/horn, thermal limits and bus or PWM interface. Do not treat stall torque as continuous capacity. Measure a restrained joint with a known perpendicular force or load cell and log angle, supply V, current I, input P = V I, temperature, duration and supply sag; stop on unexpected motion, pinch, smoke, odour or rapid heating.

Trouble

The shoulder passes a payload-only calculation but stalls after the elbow servo is installed; torque changes sharply with pose; the quoted stall number has no duty-cycle meaning; current spikes collapse the supply; temperature rises while holding; or the physical joint flexes before the actuator reaches its quoted limit.

Connections

• See also: Workspace and payload
• See also: Robot dynamics
• See also: Actuators
• See also: Electric motor
• See also: Motor driver
• See also: Safety
• See also: Risk assessment

Sources

1. OpenStax, University Physics Volume 1, §10.6 Torque, §10.6, TorqueThe SI unit of torque is newtons times meters, usually written as N·m.
2. OpenStax, University Physics Volume 1, §10.6 Torque, §10.6, TorqueThe first point implies that the farther the force is applied from the axis of rotation, the greater the angular acceleration; the second implies that the effectiveness depends on the angle at which the force is applied.
3. Manoel Carlos Ramon, Intel Galileo and Intel Galileo Gen 2, Chapter 11, pp. 509–577, torque sizing discussionThe formula that defines torque can be expressed as follows: T = F × L
4. Manoel Carlos Ramon, Intel Galileo and Intel Galileo Gen 2, Chapter 11, pp. 509–577, several actuatorseach servo will have a different torque due to its location along the arm.
5. Kevin M. Lynch and Frank C. Park, Modern Robotics §5.2 Statics of Open Chains, §5.2, Statics of Open ChainsTo resist a wrench minus F applied to the end-effector at a configuration theta, the joint torques and forces tau must be J of theta transposed times F.
6. Kevin M. Lynch and Frank C. Park, Modern Robotics §5.2 Statics of Open Chains, §5.2, Statics of Open ChainsThis result holds no matter what frame the Jacobian and wrench are expressed in.
7. ROBOTIS, XL430-W250-T technical manual and safety warnings, Torque specification noteThe given Stall torque rating for a servo is different from it’s continuous output rating, and may also differ from it’s expected real world performance.
8. Jan, Pololu Servo Control Interface in Detail, Power and current observationsmultiple servos can quickly become a very demanding load for a power supply.

Unverified: The measurement recipe and the choice of any design margin, test duration or current limit are procedural advice; no universal safe-force, safety-factor or continuous-torque value is asserted here.

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