  In this paper, the concept of moment and couple in mechanics is examined from
a fundamental perspective. It turns out that although representing a couple by
its moment vector is very useful in rigid body mechanics and strength of
materials, it has been very misleading in continuum mechanics. To specify the
effect of a concentrated couple in continuum mechanics, not only the couple
moment, but also the line of action of its constituent parallel opposite forces
must be specified. However, in the governing equations of equilibrium or motion
of a continuum, only moment of body couple, moment of couple-tractions, and
moment of couple-stresses appear without specifying the line of action of any
couple density forces. This results in non-uniqueness of the state of stresses
and deformation in the continuum, which has shown itself in the indeterminacy
of the couple-stress tensor. Nevertheless, the physical state of stress and
deformation in the continuum is unique and determinate. Therefore, this imposes
some restrictions on the form of body couple, couple-traction and
couple-stresses. Here, the uniqueness of interactions in the continuum is used
to establish that the continuum does not support a distribution of body couple,
and a distribution of surface twisting couple-traction with normal moment. From
this the mechanism of action of the couple-traction as a double layer of shear
force-tractions, and the skew-symmetric character of the couple-stress moment
tensor in continuum mechanics are also established.
