Robot Drive Motor Sizing Calculator

The straight-line force balance is derived here from Newton's second law. RobotShop motivates the sizing workflow; the University of Florida EML2322L handout, pp. 1–2, supplies a worked force/torque example. We resolve rolling resistance against the slope-normal load, rather than the handout's small-angle approximation.

With $n_d$ identical drive paths, $r$ the loaded radius, $G=\omega_m/\omega_w$, and $J_o$ the driven-wheel/output inertia per path:

The motor model adapts Zhou, Bai and Hansen (2011), drivetrain model equation (3.4) in the attached thesis, source page 49 (printed p. 34):

$J_i$ combines rotor and gear inertia referred to the input shaft. Enter this inertia in kg·cm²; an explicit conversion to kg·m² is applied before calculating torque. The default 0.5 kg·cm² equals 0.00005 kg·m². The sizing factor multiplies the entire peak torque and steady motor torque; it does not increase actual forces or energy. Continuous torque is $S F_cr/(n_d\eta_gG)$; this is steady uphill torque, not a thermal duty-cycle RMS value. Specify gearbox output torque $S T_o$ separately.

For fixed inertia and efficiency, peak shaft torque has the form $S(A/G+BG)$, with $A=T_o/\eta_g$ and $B=J_i\alpha_w$. Differentiation gives $G_0=\sqrt{A/B}$. The recommendation clamps it to $1\leq G\leq\min(1000,n_{limit}/n_w)$. If $B=0$, use the upper bound. No ratio is feasible if the bound is below 1. This is our single-drive analytical adaptation, not Zhou's discrete multi-joint, minimum-mass optimisation.

Traction requires $F_p\leq\mu f_dN$. The chart compares actual ground-contact torque against this limit, without the sizing factor or driven-wheel spin-up torque. Candidate checks compare both shaft torques and speed at the entered operating point.

Actual peak shaft power is $n_d T_m\omega_m$. Battery power divides shaft power by motor/controller efficiency and adds auxiliaries. Cruise power uses $F_cv/(\eta_g\eta_e)$. Average mission power is moving fraction times selected drive power, plus auxiliaries. Multiply by mission hours to get Wh; divide by usable battery fraction for nameplate Wh, then by nominal battery voltage for nameplate Ah. Loaded terminal voltage is used separately for running current, $I=P_{battery}/V_{loaded}$; voltage sag must not change the Wh-to-nameplate-Ah conversion. For example, Victron specifies 5120 Wh at nominal 51.2 V as 100 Ah. Peak-envelope energy holds end-of-acceleration power during all moving time; cruise-only energy excludes starts.

• Forward, straight uphill motion on firm ground; slope 0–60 degrees, travel speed 0.001–10 m/s, reduction 1–1000. Total mass includes every component and payload.
• All drive paths have the same radius, ratio and load share. Input inertia is per motor shaft; output inertia is the driven wheels and output parts per path. Free caster rotational inertia and swivel drag are omitted; use measured resistance or extra design allowance when material.
• Rolling resistance and tyre grip are independent, user-supplied coefficients. Driven-wheel normal-load fraction is supplied for the slope; no load-transfer or stability model is used.
• Efficiencies are constant estimates for uphill motoring. Torque factor applies to sizing results only. The default inertia and motor-check values are illustrative engineering inputs, not catalogue specifications.
• Available loaded speed is a usable limit at the needed torque and voltage. Candidate torques must be read from the same operating-speed region; changing ratio requires a new curve check. Short-time torque must be available for the stated acceleration duration.
• Battery energy is a planning estimate. Nominal voltage is the battery's nameplate voltage; loaded voltage is its representative terminal voltage under drive load. Drive power is zero while stopped, auxiliary power continues, and there is no braking recovery or holding current. Standard gravity is 9.80665 m/s².

Use for preliminary wheeled drive sizing and data-sheet comparison. The ratio recommendation minimises peak shaft torque only, for fixed inertias and efficiency; it does not minimise mass, cost, heat or battery energy. Choose a real gearbox ratio nearby, update its efficiency/inertia and rerun.

Continuous sizing torque covers steady uphill cruise. Repeated accelerations require a separate RMS-current/torque and thermal assessment. Candidate checks cover the entered operating point, not full motor approval. Check gearbox continuous/peak ratings, peak duration, motor curve, supply sag and controller limits independently.

No skid-steer scrub, obstacles, caster swivel, soft soil, aerodynamic drag, mechanical resonance, downhill motion, braking, tipping or load transfer is modelled. Results beyond the traction limit describe an infeasible request; larger motors cannot cure insufficient grip. A recommended ratio is unavailable when even a 1:1 drive exceeds the entered loaded motor speed.

Peak running battery current is not startup/stall current or motor phase current. At standstill, the power/efficiency approximation cannot predict copper loss or holding demand. Cruise-only energy excludes acceleration energy; the peak envelope is deliberately conservative for time-varying acceleration and assumes the entered efficiencies and slope. Validate rolling resistance, grip, temperatures and current on the real robot.