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Power, torque & gearing

The drivetrain problem: choose a motor, gear ratio, and wheel diameter so the robot reaches a useful top speed and can still move when an opponent is pushing back.

A brushed or brushless DC motor is characterized by:

  • Kv (rpm per volt, no load). Free speed ≈ Kv × V_batt.
  • Stall torque at a given voltage — torque at zero rpm, drawing stall current.
  • Kt (torque constant, N·m/A) = 9.549 / Kv. Torque ≈ Kt × (I − I_0).

Torque and speed trade linearly between no-load and stall.1

wheel rpm = motor rpm / gear_ratio
wheel torque = motor torque × gear_ratio × drivetrain_efficiency
robot speed = wheel rpm × π × wheel_diameter / 60
tractive force = wheel torque / wheel_radius (per driven wheel)

Spur/planetary gearboxes: assume 85–90% efficiency per stage. Belt: ~95%.1

Parameter Typical range Notes
Top speed 3–6 m/s (10–20 ft/s) Faster is hard to drive in a small box
Gear ratio 20:1 – 60:1 From a ~1000–3000 Kv motor on 2–3S
Wheel diameter 30–50 mm Larger clears debris, raises the robot
Drive motor power 30–80 W each 2 or 4 driven wheels

The design must survive being pushed at full throttle against a wall (a “pushing match”) without the motors overheating or the ESC cutting out.

  1. Compute tractive force at the wheels from wheel torque.
  2. Compute the traction limit — see Traction & pushing force. The lower of the two is your real pushing force.
  3. If tractive force ≫ traction limit, you are geared too aggressively: the wheels just spin. Gear taller (lower ratio) or add weight/grip.
  4. If tractive force ≪ traction limit, the motor stalls before the tires break loose — it will overheat in a pushing match. Gear shorter (higher ratio).

A balanced beetle drive can push roughly 0.7–1.2× its own weight before the tires slip. Team Run Amok’s drivetrain calculator automates this check and the gear-ratio selection.2

Peak drive current ≈ n_motors × stall_current × duty. Full-throttle direction changes approach stall current briefly. Size wiring, ESCs, and battery C-rating for that peak, not the average.

  1. Meggiolaro, M. A. RioBotz Combat Robot Tutorial, v2.0, PUC-Rio, 2009 (CC BY-NC-ND) — ch. on motors and drivetrain design. ↩ ↩2

  2. Team Run Amok — the Tentacle Torque & Amp-Hour Calculator and the “Ask Aaron” drivetrain design archives. ↩