3.6 DISPLACEMENT, TRANSLATION AND ROTATION

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À  p

As a mechanism is moved, points on the mechanism will also move through space. The problem is that they will continue to be the same points, but we need to indicate the difference in position (displacement) for calculation purposes.

We will indicate position using the traditional delta symbol,

We can also consider relative positions between points on rigid bodies,

Translation of a rigid body indicates that all points are traveling in the same direction at the same velocity. In this case the displacements of both points will be equal for pure translation.

Rotation occurs when the displacements of two points on a body are not equal. If one of the displacements is zero, then it is the center of rotation.

Apparent displacement considers that the coordinate axes are also moving. In this case the displacement and apparent position notations are combined.

Consider the example below and find the motion of the point B using complex polar notation, and then matrices.