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.

The torque and neuron post records every motor’s torque as a percentage of its maximum (the hip’s strongest 220 N·m, the elbow’s 90, the toes’ 30) and lights the joints by it. In almost every punch the hips work hardest (the jab: 56 % and 54 % on average over the second after the press); in the knees and kicks, the ankles and toes (up to 82 %).