Power couple

Couple of forces: It generates the torque a · F

Torque to turn a screw : As a force couple (3rd case) it does not cause any transverse force on the screw head

Couple of forces or couple of forces is a term from technical mechanics and was introduced by Louis Poinsot (1777-1859) in 1803.

The couple exists

from two equal forces ,
which are parallel to each other , but
act in two opposite directions .

A couple of forces acting on a rigid (non-deformable) body can not move its center of mass because the resulting force is zero. Couples of forces can only rotate the body around its center of mass. The effect of a couple of forces on a rigid body thus corresponds to the effect of a “ moment of a single force”, also referred to as a “moment of force” or (especially in physics) as torque . (A single force can, however, also shift the center of mass.)

The amount of the moment caused by the couple of forces is the product of the amount of one of the forces and the perpendicular distance between the forces: ${\ displaystyle F}$ ${\ displaystyle a}$

{\ displaystyle M = a \ cdot F}

. The sign results from the direction of rotation : In general, clockwise torques are evaluated positively, counterclockwise torques negatively.

If only one couple acts on a body, it is in equilibrium . If both forces of the force couple are on the same line, it is also in equilibrium of moments .

The pair of forces is useful for the arithmetical treatment of the general system of forces (the lines of action of the forces do not intersect at a common point) on the rigid body. The forces can be combined into a single force and a force couple.

Special features compared to individual workers

Resultant:

In the mechanics of rigid bodies, several individual forces can be replaced by their resulting force. (The effect changes with deformable bodies). "Effect" means a change in the state of motion, that is to say acceleration or deceleration. The internal forces also change in a rigid body. The amount, direction and point of application of the resultant depend on the amount, direction and point of application of the individual forces.
Pairs of forces cannot be replaced by a resulting individual force. Instead, they are replaced with a resulting moment. The resultant of a pair of forces is always zero.

Shift and point of attack:

In the mechanics of rigid bodies, a single force or the resultant of several individual forces may be shifted along its line of action without changing the effect on the rigid body. If a single force is displaced perpendicular to its line of action, an additional moment of displacement (also called moment of displacement or displacement moment) must be introduced if the effect on the body is to remain the same.
A pair of forces, on the other hand, can be moved freely in the plane in which it acts without changing the effect on the rigid body.

Rotation:

Individual forces must not be rotated without changing the effect on the rigid body.
Forces pairs can be rotated through any angle as long as they stay in the same plane and the distance between the forces does not change.

Moments:

The moment of a pair of forces with the amount of the forces F and distance a corresponds in terms of amount to the moment of a single force F with lever arm a: M = a · F. The moments caused by pairs of forces and individual forces can be added (taking into account the sign).
In the mechanics of rigid bodies, a pair of forces can be replaced by a corresponding moment; not a single force.
The moment of a couple of forces is independent of its point of attack. The moment of a single force, on the other hand, depends on the reference point.
If all moments (of pairs of forces and individual forces) are in equilibrium with respect to any reference point, they are also in equilibrium with respect to any other reference point.

Balance:

A force system that only consists of a single force fulfills the equilibrium of moments , but not the equilibrium of forces .
A force system that consists of only one force couple, conversely, fulfills the balance of forces, but not the balance of moments.

Web links

Wikisource: MKL1888: Couple of forces - Sources and full texts

literature

Böge and Böge: Technical Mechanics , 31st edition, p. 4.
Dankert and Dankert: Technische Mechanik , 7th edition, pp. 19–23.
Mahnken: Technische Mechanik - Statik , 2012, pp. 97–101.

Individual evidence

↑ Karl-Eugen Kurrer: The couple of forces . In: History of structural engineering. In search of balance . 2nd, greatly expanded edition. Ernst & Sohn, Berlin 2016, ISBN 978-3-433-03134-6 , pp. 31 u. Pp. 1021-1022 .
^ Alfred Recknagel : Physics - Mechanics. Verlag Technik, Berlin, 1955, p. 176.
^ Alfred Recknagel: Physik - Mechanik , Verlag Technik, Berlin, 1955, p. 180
↑ Gross et al .: Technical Mechanics - Statics , 11th edition, p. 50.
↑ Gross et al .: Technical Mechanics - Statics , 11th edition, p. 52.
↑ Dankert, Dankert: Technische Mechanik , Springer, 7th edition, 2013, p. 24.
↑ Mahnken: Technische Mechanik - Statik , 2012, p. 97.

[1] Karl-Eugen Kurrer: The couple of forces . In: History of structural engineering. In search of balance . 2nd, greatly expanded edition. Ernst & Sohn, Berlin 2016, ISBN 978-3-433-03134-6 , pp. 31 u. Pp. 1021-1022 .

[2] Alfred Recknagel : Physics - Mechanics. Verlag Technik, Berlin, 1955, p. 176.

[3] Alfred Recknagel: Physik - Mechanik , Verlag Technik, Berlin, 1955, p. 180

[4] Gross et al .: Technical Mechanics - Statics , 11th edition, p. 50.

[5] Gross et al .: Technical Mechanics - Statics , 11th edition, p. 52.

[6] Dankert, Dankert: Technische Mechanik , Springer, 7th edition, 2013, p. 24.

[7] Mahnken: Technische Mechanik - Statik , 2012, p. 97.