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Mechanisms – Bellcrank

A basic bellcrank is shown in Figure 1. Bellcranks are the most common component in mechanical linkages. Bellcranks are simple devices that are used to change the direction of movement. In Figure 1, the input and output direction of movement differ by 90 degrees. Bellcranks can also create mechanical advantage when L1 ≠ L2.



Figure 1 Bellcrank Geometry


Referring to Figure 1, the kinematic relationship for a bellcrank is (assuming small angular displacements)

    (1)

    (2)

where the terms are defined in Figure 1. The basic force (or torque) relationship is

    (3)

    (4)

Thus when L1 = L2, there is no gain through the bellcrank. If L1 > L2, then F2 > F1, so the gain is greater than 1. If L1 < L2, the gain is less than one. Equations (2) and (4) assume the angle between the bellcrank arms are 90 degrees. When the input/output arms are not 90 degrees, the forces will act an angle. This angle needs to be taken into account. For example, consider the bellcrank shown in Figure 2.



Figure 2 Bellcrank with Angles ≠ 90°

The force equations for the bellcrank in Figure 2 are

    (5)

Assuming no frictional losses,

    (6)

This leads to the relationship

    (7)

From equation (7), the force relationship equation for the bellcrank shown in Figure 2 is

    (8)

The relationship between input and output motion for the bellcrank shown in Figure 3 is the same as equation (2).

Bellcranks come in many different designs, shape and sizes. An example of manufactured bellcrank is shown in Figure 3.



Figure 3 Actual Bellcrank Picture