Definitions

# Couple (mechanics)

A Couple is a system of forces with a resultant moment but no resultant force. Another term for a couple is a pure moment. Its effect is to create rotation without translation. The simplest couple consists of two equal and opposite forces whose lines of action do not coincide. The forces have a turning effect or moment called a torque about an axis which is normal to the plane of the forces. The SI unit for the torque of the couple is newton metre.

If the two forces are F and -F, then the magnitude of the torque is calculated by:

$tau = F times d ,$
where
$tau$ is the torque
F is the magnitude of one of the forces
d is the perpendicular distance between the forces

Suppose that the two forces are a distance, d, apart with position vectors measured from an arbitrary reference point O. Then $tau$ is given by:

$tau = F times r_0 + -F times r_1 = F times \left(r_0 - r_1\right) = Fd hat\left\{e\right\}$

This shows that regardless of the reference point, the magnitude of the torque is always equal to Fd, with the direction of the torque given by the unit vector $hat\left\{e\right\}$, which is perpendicular to the plane containing the two forces. In other words, the moment vector is a "free vector". In systems with more than two forces, then the resultant net couple can be computed from the algebraic sum of the components of the individual couples. Couples are very important in mechanical engineering and the physical sciences. A few examples are:

• The forces exerted by your hand on a screw-driver
• The forces exerted by the tip of a screw-driver on the head of a screw
• Drag forces acting on a spinning propeller
• Forces on an electric dipole in a uniform electric field.