Chapter 2 Review of Forces and Moments - Brown University

Three rules that help to establish the direction of frictionless
contact forces are:
(1) When one of the two contacting surfaces is flat, the
force must act perpendicular to the flat surface;
(2) When two solids contact along sharp edges, the
contact force must be perpendicular to both edges.
(3) When two curved surfaces contact, the reaction force
acts along a line joining the centers of curvature of the
two objects.
Forces acting at rough (infinite friction) nonconformal contacts
A rough nonconformal contact behaves somewhat like a pinned
joint. There can be no relative motion of the contacting surfaces,
therefore there must be three components of reaction force acting on
both contacting solids. Unlike a pin joint, however, the contact can
only sustain a repulsive normal force. This means that the
components of force shown in the picture must satisfy N
A
≥ 0 . If
the normal force is zero (eg when the two surfaces are about to
separate), the tangential forces T
1
= T
2
= 0 as well.
A
A
The contacting solids can rotate freely relative to one another. Therefore there must be no moment acting
on the contacting solids at the point of contact.
Usually the forces acting at a rough contact are represented by components acting perpendicular and
parallel to the contacting surfaces, as shown in the picture above. If you do this, it’s easy to enforce the
N
A
≥ 0 constraint. But if it’s more convenient, you can treat the contact just like a pin joint, and express
the reaction forces in any arbitrary basis, as shown in the picture below.
There’s a minor disadvantage to doing this – it’s not easy to check whether the normal force between the
surface is repulsive. You can do it using vectors – for the picture shown the normal force is repulsive if
(1/ 2) (1)
R ⋅n
≥ 0
A
A