Force Couples

A couple is formed from two force vectors $F$ that are equal in magnitude, opposite in sense, and acting along parallel lines of action on a body.

The magnitude of the couple is calculated as follows:

M = F (d_{0} + d) - F d_{0} = F d

where $d$ is the distance between forces. In three dimensions, the cross product is used:
$\vec{M} = \hat{r_{B A}} \times \vec{F}$
where $\hat{r_{B A}}$ is the position vector between two points which lie on the lines of action of the forces.