MUJOCO · DEVICE PHYSICS

Sizing a Joint Actuator

Size a compliant joint's holding stiffness so it supports a leg segment at a target crouch, the balance a real series-elastic actuator must strike.

01Challenge

The knee joint's stiffness is too low, so the leg sags well past the design crouch. Raise the stiffness until the joint settles at exactly -0.12 m, where the holding force balances the weight. Real MuJoCo statics decide the verdict.

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02Model

Before a humanoid can think, it has to hold itself up. Every joint carries a load, and the actuator behind it (often a series-elastic one, a motor through a spring) has to produce a holding force that balances gravity at the pose you want. The physics is one line: stiffness times deflection equals mass times g. Set the stiffness too low and the joint collapses under the body; too high and it is stiff, heavy, and unsafe near people. You are picking the number where the body sits exactly where you designed it to.

03Guided practice

1. The rule. At rest, stiffness * deflection = m * g. Here m = 0.6 kg, target deflection = 0.12 m. 2. Solve. stiffness = m*g/deflection = 0.6 * 9.81 / 0.12 ≈ 49 N/m. 3. Edit. Change stiffness="25" to about 49 in the knee joint. 4. Read the verdict. It must settle AT -0.12 m and stop moving (velocity near zero).

04Feedback

PASS WHEN PASS when the joint settles (velocity ~0) at -0.12 m: the holding force balances the leg's weight there. Real MuJoCo statics on the device.

If your run fails, check:

Still sagging below -0.12 m: the stiffness is too low. Raise it toward m*g/0.12 ≈ 49 N/m.
Now it holds above -0.12 m: stiffness slightly too high. Bring it back down toward 49.
Reaches -0.12 m but keeps oscillating: that is the damping's job; here the target stiffness settles within the time.

05Retrieve & space

What single equation sets a joint's holding stiffness at rest? (stiffness * deflection = m*g).
Why is a stiffer joint not simply better on a humanoid? (weight, energy, and safety near people).
What is a series-elastic actuator, and why put a spring between the motor and the joint? (compliance: force sensing and shock tolerance).

06Mastery & project

Size an actuator against gravity in real physics: the first design decision of any embodied robot.

The body-design habit the whole course builds on: pick the physical parameter that makes the robot sit where you intend.

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MUJOCO · DEVICE PHYSICS

Sizing a Joint Actuator

Edit the MJCF and run real MuJoCo. Size the joint stiffness so the leg settles at the design crouch.

You read

the body's mass, the spring and gravity forces, and its deflection each step

You change

the mass, stiffness, and damping you set on the device

Fixed

the MuJoCo solver, the device, and the settle check