4.1 THE BASIC RELATIONSHIPS

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À  p

One form of velocity is translation. In proper terms it is the first derivative of position,

A second form of velocity is rotational. This is in terms of orientation angle,

When we deal with 3D rotation and velocity we must consider the effects of the entire body. If we consider two points (P and Q) on a single rigid body, then we can write the two following relationships,

Consider that the apparent position equation from before can be extended to apparent velocity,

Consider the example shown below, from Shigley and Uicker, 1995,

While we have considered apparent velocity in translation before we may also consider apparent angular velocity.

Consider that in most cases seen so far the joints are of the pin type, and therefore are fixed points on each member.

If we have a rolling contact we will have the following conditions, (Note: even though the rollers are round below, they could be other shapes)