Sizing AMR Drive Motors: From Wheel Force to Gear Ratio

Asking how many watts a drive motor needs is an incomplete starting point. The same mechanical power can occur at different combinations of torque and speed. A robot that moves unloaded on a level floor may still fail to accelerate uphill with its intended payload.

For a two-wheel differential-drive AMR, begin with the force and speed required at the wheels. Then translate those requirements to the motor shaft through the transmission. This article develops an initial calculation, not a complete vehicle design or a motor recommendation.

Define the operating case before calculating

Total mass includes the chassis, wheels, battery, equipment, and payload. Use the effective rolling radius under load. State whether the required speed, acceleration, and slope must occur together. Also specify the slope convention: 5 degrees is about an 8.75% grade, not a 5% grade.

Here, Crr is a dimensionless rolling-resistance coefficient relating resistance to normal load. It is not the coefficient used to assess available tire traction. Some rolling-resistance definitions use a quantity with units of length; those values cannot be inserted into this model without conversion.

Oriental Motor's AGV sizing tool asks for considerably more than payload, including wheel and vehicle mass, slope, rolling resistance, efficiency, and motion timing. These are useful prompts for an input sheet, even when doing the calculations independently. Official AGV sizing tool

Calculate wheel force and speed

For a simplified uphill, straight-line case with no slip:

F = m * a + m * g * sin(theta) + Crr * m * g * cos(theta)
Tw = F * r / 2
nw = 60 * v / (2 * pi * r)

F is total required traction force in newtons. Mass m is in kilograms, acceleration a is along the slope, g is 9.81 m/s², theta is the slope angle, r is wheel radius in metres, and v is vehicle speed in metres per second. Tw is torque per driven wheel in N·m; nw is wheel speed in revolutions per minute.

Dividing by two assumes symmetric drives sharing the traction demand equally. Passive support wheels contribute mass and rolling resistance but do not thereby share the commanded drive torque. Available traction still depends on the normal load on the driven wheels. Torque at the shaft cannot overcome insufficient tire-floor grip.

Turning, uneven wheel loads, and an offset centre of mass can invalidate equal sharing. Treat them as additional operating cases, not as small details automatically covered by this equation.

Work through an explicitly hypothetical case

All inputs below are assumptions for explaining the method. They are not measurements and include no design margin.

The case deliberately combines acceleration with the uphill slope. Efficiency here is mechanical efficiency between the motor shaft and wheel, excluding electrical losses in the motor and drive.

Acceleration force = 300 * 0.40 = 120.00 N
Slope force = 300 * 9.81 * sin(5 degrees) = 256.50 N
Rolling resistance = 0.020 * 300 * 9.81 * cos(5 degrees) = 58.64 N
Total traction force = 435.14 N
Torque per driven wheel = 435.14 * 0.10 / 2 = 21.76 N·m
Wheel speed at the target vehicle speed = 114.59 rpm

Define i as motor speed divided by wheel speed. In the driving direction, motor speed is nm = i * nw and motor torque is Tm = Tw / (i * eta). The resulting demand per motor is approximately 2,292 rpm and 1.28 N·m at the end of the assumed acceleration. Both quantities must be available together. Oriental Motor gearhead relationships

Acceleration from rest to the target speed takes three seconds. At constant speed on the same slope, the calculated demand falls to about 0.93 N·m per motor. On a level floor at constant speed, it is about 0.17 N·m under the same assumed efficiency. Holding efficiency constant here only isolates the other variables; it does not establish actual efficiency at light load.

An operating demand is not a motor rating

The 1.28 N·m result is a demand from the simplified model. It is not an instruction to buy a motor rated at exactly that value. Build a complete cycle containing acceleration, travel, deceleration, turns, and stops, then assess peak capability and thermal loading separately.

For piecewise-constant torque, an RMS calculation can help screen applicable motor systems:

Trms = sqrt[(T1² * t1 + T2² * t2 + ...) / total_cycle_time]

Use torque values referred to the same shaft. Include holding intervals if the motor is energized to hold a load. Check permitted peak duration and repetition, speed-dependent capability, mounting, ambient temperature, and cooling. RMS torque alone does not establish acceptable winding temperature across every speed and installation. Oriental Motor: acceleration and RMS torque

Definitions of rated, nominal, and continuous torque must come from the relevant data sheet. Maxon's foundational motor guide distinguishes continuous operation from short-duration operating regions. Its 2014 edition is cited for these concepts, not for current product specifications. Maxon motor fundamentals

Check what the simple model leaves out

The example omits rotating inertia, caster swivel effects, turning resistance, impacts, and surface transitions. Those omissions can matter. Wu and colleagues' research on differential-drive robots with a caster develops a multibody model and compares models with and without caster dynamics. It supports treating caster effects as a modelling question; it does not supply a universal correction factor for the vehicle in this example. Wu et al., 2018

Increasing the reduction ratio lowers the required motor torque but raises motor speed for the same vehicle speed. Check motor torque-speed capability, drive current, actual bus voltage, gearhead input speed, continuous and intermittent output torque, and shaft-bearing loads together. A wheel mounted directly on an output shaft also introduces a load-position question.

Gearhead efficiency is not necessarily constant across load. Maxon's terminology document explicitly qualifies efficiency and intermittent ratings. Use the selected unit's operating conditions rather than a generic efficiency or an arbitrary safety factor. Maxon gearhead terminology

Finally, distinguish load holding from repeated dynamic braking. Some motor-mounted brakes are intended primarily for holding; the suitability of a brake for repeated stopping must be checked in its own documentation. Stopping behavior and protective functions require a separate vehicle-level assessment.

Make the supplier request reviewable

Provide a table of simultaneous speed and torque demands, the duration and repetition of each segment, bus-voltage limits, cooling conditions, gearhead loads, and unresolved assumptions. Add measured floor and wheel data when available. Ask the supplier to identify which limits govern each operating point.

That turns a vague request for a powerful motor into a set of conditions that can be checked. The next step is a representative test programme, including turning, thermal behavior, and abnormal stops, rather than treating a successful level-floor run as acceptance.

Evidence and limits

Sources were reviewed on November 4, 2026. The equations and example are engineering calculations under stated assumptions; the article does not report physical tests, a validated duty cycle, or a complete selection. No universal margin, motor model, braking guarantee, or vehicle safety conclusion is implied.