In 2-D, the reaction force of the roller support can be represented by one force perpendicular to the surface. It prohibits translation towards the surface. It also permits translation in any direction parallel to the surface. The roller permits rotation about any axis. It can, however, exert a force perpendicular to the surface on which it rests. It cannot exert a couple about any axis, nor can it exert a force parallel to the surface on which the roller support rests. The roller support is similar to a pin support but mounted on wheels. In 2-D, the reaction force of a pin can be broken down into two component forces parallel to the x and y axes. Thus, the pin support exerts forces in any direction, but it cannot exert a moment about the axis of the pin. The pin prevents translation but permits rotation. With a pin support, a bracket and an object are connected by means of a smooth pin passing through the object and connected to the bracket. They are the pin support, the roller support, and the fixed support. To better understand the relationship between support conventions and support reactions, detailed explanation of three of the more commonly used support conventions are presented below. The table to the left shows common 2-D support conventions. Supports can be broken down into two categories: 2-D supports and 3-D supports. Then the support exerts a couple, or moment, in the direction of the rotation.
In general, if a support prevents translation in a given direction, then the support exerts a force in that direction. These forces and moments are reacting to external loads that are applied to the rigid body. The forces and moments exerted on a rigid body by its supports are called reactions. An actual support may be a close approximation of a model. Supports that are commonly found in statics can be represented by stylized models called support conventions. Before the equilibrium of rigid bodies can be investigated, the supports that hold them in place, or hold them to other objects, must be first analyzed.
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