# Free-Body Diagram

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To fully understand the safety of a machine, all forces that act on the links need to be examined. It is widely accepted that the best way to track these forces is to construct a free body diagram. A free-body diagram is a picture of the isolated part, as if it were floating freely. The part appears to be floating because all the supports and contacts with other parts have been removed. All these supports and contacts are then replaced with forces that represent the action of the support. Thus, a free-body diagram of a part shows all the forces acting on the part.

## Drawing a Free-Body Diagram

Figure 1 illustrates a free-body diagram of an isolated link. Notice that this part is designated as link 3. It is essential that all forces are shown on the free-body diagram. A convenient notation is to label the forces consistent with the link number that is being acted upon and the link number that is driving the action. Thus, a force designated as F34 is a force on link 3 from the contact of link 4.

Figure 1:Free-body diagram

Because forces are vectors, determination of a force requires knowledge of the magnitude and direction of that force. If the direction of a force is known, it should be indicated on the free-body diagram. This is the case for F34 in figure 1. When the direction of a force is not known, it is common to draw two orthogonal components of the unknown force. These two components represent the two items that need to be determined for full understanding of the force. Notice that this is the case for F32 in figure 1.

The following steps can help us in systematically drawing a free-body diagram:

1. Isolate the components that must be studied.
2. Draw the component as if it were floating freely in space by removing all visible supports and physical contact that it has with other objects.
3. Replace the supports or physical contacts, with the appropriate force and moments, which have the same effect as the supports.

## Characterizing Contact Forces

Establishing the supporting forces takes some care. As a general rule, if the nature of the contact prevents motion in a certain direction, there must be a supporting force in that direction.

Figure 2: Reaction forces

The types of reactions can be classified into three groups corresponding to the type of physical contacts.

a. Direction of Reaction is Known: Components in this group (figure 2a) include rollers, sliders, pins in slots, and cables. Each of these supports can prevent motion in only one direction. Reactions in this group involve only one unknown, namely the magnitude of the reaction force.

b. Direction of Reaction is Unknown: Components in this group (figure 2b) include frictionless pins, hinges, and sliders on rough surfaces. Each of these supports can prevent translation in both planar directions. Reactions in this group involve two unknowns, usually shown as the x- and y-components of the reaction force.

c. Reaction Prohibits Rotation: Components in this group (figure 2c) include fixed supports and pin joints at an actuator (motor or engine). Each of these supports can prevent translation in both planar directions and free rotation. Reactions in this group involve three unknowns, usually shown as the x- and y-components of the reaction force and a reaction moment.