Sizing joint torque for a legged robot

You can estimate the torque each joint needs with a few numbers and a sketch of the worst-case pose. Here is the method, with an example.

1. Find the worst static pose

Torque is force times the horizontal distance from the joint to the line of that force. For a leg, the force is the share of body weight on that foot and the distance is the horizontal offset between the foot and the joint. The knee is usually the worst case, in a deep crouch.

2. Worked example

  • A 12 kg quadruped trotting has two feet on the ground, so each stance leg carries about 6 kg.
  • Force on the foot: 6 kg × 9.81 m/s² ≈ 59 N.
  • In a crouch, the foot sits 0.15 m ahead of the knee horizontally.
  • Static knee torque ≈ 59 N × 0.15 m ≈ 8.8 N·m.

3. Add the dynamics

Running, jumping and landing push ground forces well above body weight. A factor of two to three over the static figure is a common starting point for trotting; jumping and landing need more. In the example, 2.5 × 8.8 ≈ 22 N·m peak.

4. Peak versus rated

  • Peak torque should cover the dynamic figure: here, a joint with at least 22 N·m peak.
  • Rated torque should cover what the joint holds for long periods, such as standing: here, at least 9 N·m, plus margin for heat.
  • Check speed as well: a swinging leg may need several hundred rpm at the joint, which favours quasi-direct-drive joints.

5. Weight changes the answer

Heavier joints raise the robot’s mass, which raises the torque needed. Compare torque density (N·m per kg) and iterate once or twice. For full-size humanoids, hip and knee joints often need 100 N·m or more; small robots can use compact joints under 500 g.

This is a first estimate. Confirm it in simulation or with a prototype before ordering a full set.