Chapter 22 · Bring up real robot hardware through bounded, evidence-led gates

Today in the field story

One problem, then the next

The shortlist reaches the paper engineering desk. You separate continuous and peak torque, speed, duty cycle, encoder resolution, supply voltage, continuous and peak current, energy, heat, connectors, cabling, protection assumptions, and margin. The starter rejects a missing peak-current value because the rest of the table cannot repair that absence. These calculations expose questions for manufacturers and qualified reviewers; they do not select wire, protection, or permission to energize a real assembly.

Why now: Power and actuator assumptions must be visible before interfaces or motion are trusted.
Ignore today: Do not size live wiring, bypass protection guidance, or perform load tests.
Unlocks next: A bounded budget with every assumption, unit, source, and missing value named.

Understand

Build the physical picture first

An actuator is an operating point inside coupled mechanical, electrical, thermal, sensing, and protection envelopes, never one impressive torque or wattage number.

Start at the load and work backward through the mechanism. For a rotary joint, list every payload and link mass with its distance from the axis, add gravitational torque for the worst required orientation, add torque for requested angular acceleration and reflected inertia, then account for friction, external process force, transmission efficiency, and a justified design margin. A mobile drive similarly needs wheel force for rolling resistance, grade, acceleration, and disturbance, then wheel torque from radius. A static estimate is an early bound, not a dynamic model or safety limit.

Torque and speed must be feasible at the same time. A gearbox multiplies motor torque approximately by ratio and efficiency while increasing motor speed relative to joint speed; it also introduces backlash, compliance, friction, reflected inertia, and rated input or output limits. Compare continuous and short-duration requirements with the manufacturer's torque-speed curve, thermal condition, winding, controller, supply voltage, gearbox, brake, and duty cycle. Stall torque is normally a boundary where speed is zero and heating is severe, not a continuous design point.

Build the energy path as carefully as the force path. Estimate continuous, transient, startup, inrush, braking, and regenerative behavior for each branch; include controllers, compute, sensors, fans, brakes, and conversion losses. Check supply, battery, distribution, conductor, connector, switch, fuse or breaker, grounding or bonding, and thermal ratings using the applicable engineering rules and manufacturer data. A fuse protects against defined faults; it does not increase supply capacity or excuse undersized wiring. Never probe an unknown energized system as a learner exercise.

Close the loop with sensing and limits. Encoder resolution, accuracy, update rate, latency, multi-turn behavior, mounting, index or absolute reference, and power-loss behavior affect whether the controller can observe the intended motion. Define hard mechanical stops, drive limits, controller limits, calibrated software limits, current and temperature monitoring, and fault response as separate layers. Software limits should stay inside verified physical limits, but none becomes safety-rated merely because it is conservative or tested in a simulator.

Words you need

Name each idea precisely

Continuous operating point: A torque-speed-current-temperature condition the actuator and drive can sustain for the declared duty and cooling without exceeding ratings.
Physical example:
A shoulder joint holds and cycles at 4 N·m output and 0.4 rad/s for minutes, so that point must fit the continuous curve rather than a short peak label.
Peak operating point: A bounded higher-load condition allowed only for the documented magnitude, duration, repetition, temperature, and drive configuration.
Physical example:
A 0.3-second acceleration may need 9 N·m, but repeating it every second can violate the motor or gearbox thermal duty even when one pulse succeeds.
Torque-speed curve: The documented relationship showing which combinations of actuator torque and rotational speed are available under stated electrical and thermal conditions.
Physical example:
A motor that provides high torque near zero speed may provide far less at the shaft speed needed after the chosen gear ratio.
Regenerative energy: Energy returned toward the drive or DC bus when a driven mass decelerates or an external load drives the motor.
Physical example:
Lowering a gravity-loaded arm can raise the bus voltage unless the approved drive and energy-handling design absorb or return that energy.
Encoder resolution: The smallest count increment represented by the encoder, distinct from absolute accuracy, noise, backlash, and final tool precision.
Physical example:
An encoder with 8,192 counts per revolution represents about 0.000767 rad per count before transmission and mechanism errors.

Math, one line at a time

Work through today’s relationship

Prerequisite rescue · optionalZero-power electricity bridge: voltage, current, resistance, and power

Before buying, wiring, or energizing hardware, use paper calculations and manufacturer documentation to detect impossible loads, overheated conductors, and incompatible supplies.

V = IR: voltage equals current multiplied by resistanceUnit: volts (V)
P = VI: electrical powerUnit: watts (W)
I: charge flow through one declared pathUnit: amperes (A)

On paper, a documented 12 Ω test load across 24 V would draw I = V/R = 24/12 = 2 A.
Its electrical power would be P = VI = 24×2 = 48 W, so an ordinary low-power resistor would be unsuitable even though the arithmetic is simple.
Stop at the calculation: do not assemble or energize the circuit. Verify ratings, protection, isolation, polarity, grounding, wiring, thermal limits, and a supervised low-voltage commissioning plan with qualified guidance.

Programmer analogy

Types and range checks catch bad values in software; electrical ratings are physical contracts whose violation can create heat, fire, shock, or loss of braking.

On paper, what current would an ideal 10 Ω load draw from 5 V?

I = V/R = 5/10 = 0.5 A; this calculation is not permission to build or energize a circuit.

Payload-only static torque is

\tau=mgr=(2\ \mathrm{kg})(9.81\ \mathrm{m/s^2})(0.30\ \mathrm{m})\approx5.89\ \mathrm{N\,m}.

Link mass, dynamics, losses, and margin must be added separately.

Create a reviewable shoulder-axis sizing budget

A hypothetical unpowered arm has a 2.0 kg payload at 0.30 m and a 1.0 kg link center of mass at 0.15 m. Required joint acceleration contributes a modeled 1.20 N·m, friction contributes 0.40 N·m, transmission efficiency is estimated at 0.80, and a preliminary 1.25 design factor is being reviewed.

Calculate payload gravity torque as 2.0 × 9.81 × 0.30 = 5.886 N·m and link gravity torque as 1.0 × 9.81 × 0.15 = 1.472 N·m; retain the locations and worst required orientation beside the numbers.
Add the modeled joint-side terms before losses: 5.886 + 1.472 + 1.20 + 0.40 = 8.958 N·m. Label omitted cable forces, tool inertia, disturbances, and model uncertainty rather than hiding them in arithmetic.
Account for the stated transmission efficiency at this operating condition: 8.958 / 0.80 = 11.198 N·m required at the transmission input expressed in the chosen joint-side convention; verify the manufacturer's efficiency direction and curve before reuse.
Apply the review factor only after explaining what uncertainty it covers: 11.198 × 1.25 = 13.998 N·m. Do not call 14.0 N·m safe, continuous, or motor-shaft torque until ratio, speed, duty, gearbox rating, thermal model, and risk controls are checked.
Choose a hypothetical ratio and required joint speed, convert both torque and speed to the motor side using the same convention and efficiency, then plot continuous and peak points on the exact motor-drive-voltage torque-speed curves.
Build the electrical table for nominal, simultaneous peak, startup, braking, and fault states; include auxiliary loads and losses, then compare supply, energy storage, distribution, conductor, connector, protection, and thermal ratings without energizing anything.
Add encoder scale, accuracy, latency, temperature and current thresholds, mechanical stops, drive limits, software limits, and every unresolved assumption to the same review, then issue feasible for detailed design, revise, or insufficient evidence.

Result

The preliminary joint demand is about 8.96 N·m before transmission losses and about 14.0 N·m after the stated efficiency and review factor, but the record explicitly prevents that scalar from being mistaken for a selected motor or safe operating point.

What this proves

Sizing is complete only when one documented mechanism, actuator, drive, supply, feedback, thermal, protection, and duty configuration contains every required operating point with justified margin.

Physical examples

Where this appears in real life

Horizontal shoulder joint

A 2.0 kg payload sits 0.30 m from a shoulder axis while a 1.0 kg link has its center of mass 0.15 m from the axis; the joint also accelerates and contains a gearbox.

Look for:

Sum every gravity moment, add inertia, acceleration, friction, and external loads, then translate the joint torque-speed point through the actual ratio and efficiency before reading the motor curve.

Two-wheel supply branch

Two motor drives each draw 3 A continuously and can draw 8 A briefly from a 24 V bus; compute and sensors draw another 1 A.

Look for:

Continuous demand is 7 A or 168 W, while the named simultaneous transient is 17 A or 408 W; duration, wiring, connector, supply, protection, battery, heat, and regenerative behavior still need separate checks.

Hands-on exercise

Make the idea observable

Use a paper arm or rover diagram, a spreadsheet, and one publicly available motor or drive curve. Keep every device disconnected and use hypothetical or documented values only.

Mark each mass, center of mass, joint or wheel radius, required speed, acceleration, duty, slope or external force, and the source or assumption for each value.
Calculate static and dynamic joint or wheel loads separately, list omitted effects, and keep joint-side and motor-side units in different columns.
Add a transmission row for ratio, efficiency, backlash, rated torque, speed, brake, and thermal limits; reject any row whose convention cannot be traced.
Plot continuous and peak operating points on an official curve for the exact voltage, winding, drive, and cooling condition, or write not comparable if those conditions are missing.
Make continuous, peak, startup, and braking electrical budgets including auxiliaries, then mark which supply, battery, cable, connector, switch, protection, and heat data remain unknown.
Add encoder and physical-limit evidence, challenge one plausible single-point failure, and have a second learner audit every conversion from load to motor and motor to electrical source.

Observe

A scalar torque or wattage recommendation usually breaks when speed, duty, transmission, temperature, braking, feedback, and the full current path are placed on the same sheet.

Done when

Every number has a unit, side of transmission, operating condition, source, and uncertainty; continuous and peak cases are distinct; no stall or nominal-power number is presented as a selected safe design.

Build today

Bring up a LeRobot-supported arm or mobile robot with calibration, limits, teleoperation, and emergency stop.

Evidence to save

DONE when “Actuator sizing, motors, encoders, power, and physical limits” runs from one documented command and the nominal plus boundary outputs are attached.

Common mistakes

Catch the wrong mental model

Wrong

Selecting a motor because its stall torque exceeds the calculated static load.

Better

Compare simultaneous torque and speed against continuous and peak curves with voltage, controller, duty, cooling, gearbox, losses, temperature, and transient duration.

Wrong

Adding an arbitrary safety factor before listing omitted loads and uncertainty.

Better

Model known gravity, inertia, acceleration, friction, external force, transmission, and duty terms first, then state exactly which residual uncertainties each margin addresses.

Wrong

Sizing the supply from average current while ignoring simultaneous peaks, braking, auxiliaries, and the distribution path.

Better

Budget named operating states end to end and check source, storage, conversion, conductors, connectors, protection, heat, inrush, and regenerative handling under approved rules.

Job connection

How this becomes employable evidence

Review actuator, drive, encoder, supply, and software-limit budgets with mechanical and electrical owners, convert physical ratings into versioned runtime constraints and diagnostics, and reject bring-up when the real operating curve or energy path is incomplete.

Relevant target roles

Robotics Application / ROS 2 Integration Engineer
Robotics Software Engineer — ROS 2 / AMR
Robotics Deployment, Integration & Validation Engineer

Chapter 22 interview drill

Interview questions: Actuator sizing, motors, encoders, power, and physical limits

Practise a 60–90 second answer: define the idea, connect it to a physical robot, state assumptions, frames, and units when relevant, then finish with the failure signal or evidence you would inspect.

Primary interview scenario

Size a shoulder actuator for a gravity-loaded arm. Show the load-to-motor and motor-to-supply calculations, continuous versus peak checks, encoder and limit strategy, unknowns, and why stall torque or P = VI alone cannot approve the design.

Answer shape: clarify the situation → trace the physical and software path → test the most likely boundaries → name the evidence that would confirm the result.

Technical follow-up questions

Q1Why must torque and speed be checked as one operating point?

Model interview answer

An actuator's available torque changes with speed, voltage, drive, and temperature; a separate maximum-torque and maximum-speed claim may never be achievable simultaneously.

Q2What does `P = V × I` establish in a power budget?

Model interview answer

It converts a declared voltage-current operating point to electrical power, but does not establish torque, efficiency, thermal capacity, transient behavior, protection, wiring, braking, or safety.

Q3Why is encoder resolution not the same as joint or tool accuracy?

Model interview answer

Resolution counts representable increments, while calibration, mounting, noise, latency, gearbox backlash, compliance, structural error, and kinematics affect measured joint and tool accuracy.