Unified Robotics I: Actuation

Linkages

Types of Motion

Let's now define some different types of motion. First of all we have pure translation, which is where all points on the body have identical displacements. Secondly, we can have pure rotation. In this case different points on a body will undergo different displacements. Finally, we can have complex motion which can incorporate both translation and rotation. That sounds like it can be very complicated. The good news though is that Chasles' theorem tells us that:

Any displacement of a rigid body is equivalent to the sum of a translation of any one point on that body and a rotation of the body about an axis through that point.

Here we see an example of pure translation, where all points and the body have the same displacement. We can see that the path that the link took doesn't really matter. In the end there was simply some translation in the X direction as well as the Y direction.

Figure 1 - Translation, rotation and complex motion

Here we can see the link rotating around A (which in this case is located at the origin of the coordinate system). It should be apparent that different points on the link will have different displacements. In this case we can see that point B has a displacement RB'B as a result of the rotation.

Figure 2 - Rotation

Finally, we have a case of complex motion where the link AB experiences first translation and then rotation around point A'.

Would it matter if the order of the translation and rotation operations were reversed?

  • Show Answer
    • No-it wouldn't
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