Moment arm

A muscle turns a joint the way a hand turns a spanner: the further its pull acts from the axis, the more torque it gets from the same force,

$$\tau = r(q)\, F$$

where $r$ is the moment arm. For a muscle on a real path over the bones, $r$ changes with the joint angle $q$: as a joint bends, the tendon’s line moves closer to or further from the axis. It also equals how fast the muscle’s length changes as the joint turns, $r = -\partial \ell / \partial q$, which is how simulators compute it.

A muscle crossing two joints, like the hamstrings over the hip and the knee, has a moment arm at each and makes torque at both.

In this project

The stage 1 muscles in Muscles instead of motors act on a joint with a fixed moment arm. The stage 2 leg muscles come from MyoSuite, on their paths, and their moment arms were checked against MyoSuite’s own model at every joint each one crosses: within 2.2 cm everywhere, most within 1 cm. At the stance’s rear hip, turned out 45°, the hip abductors lose half their moment arm, leaving about 120 N m of abduction, in MyoSuite’s own models too.