Torque

Force pushes in a straight line. Torque turns. A torque about a pivot comes from a force applied some distance from it:

$$\tau = r \times F, \qquad |\tau| = r\,F\,\sin\theta$$

where $r$ is the distance from the pivot, $F$ is the force and $\theta$ is the angle between them. A force pushing straight through the pivot ($\theta = 0$) makes no torque at all. That’s why a long spanner turns a stiff bolt more easily: the same hand force, further from the bolt, gives more torque.

Torque is measured in newton-metres (N·m): one newton at a distance of one metre.

Torque and rotation

Torque is to rotation what force is to straight-line motion. Newton’s second law for rotation says

$$\tau = I\,\alpha$$

where $\alpha$ is the angular acceleration and $I$ is the moment of inertia. A heavy, long limb has a large $I$ and needs more torque to swing at the same rate.

In a body

Every joint in a simulated body is turned by a motor applying torque (see actuator). Gravity also applies torque: a leaning trunk pulls itself further over, with torque $m g$ times the horizontal distance of its centre of mass from the hip. The leg and hip motors must push back.

In this project

Each motor is a position servo whose torque is capped at a maximum chosen for that joint, so the simulated fighter can’t be stronger than a person.