General plane motion relative motion analysis

Описание: Relative Motion Analysis
In a previous article I discussed absolute motion analysis. In order to use absolute motion analysis you have to be able to solve the problem with one point of reference. However, there could be cases where you will need more than one frame of reference to solve the problem. If this is the case than you would need to use relative motion analysis.

Position
When you are using relative motion analysis you will need to have at least two frames of reference. Let’s use the image below as an example. The first frame of motion is the x, y coordinate system is based off the absolute position of points A and B in respect to the fixed position O. Furthermore, you will need to determine a base point. In this case the base point will be point A. The base point will normally have a known motion where an additional coordinate system x’, y’ will translate in respect to the fixed x,y coordinate system. The base point, however, will not rotate with the rest of the body.
rB=rA+rB/A
A real life example of where relative motion analysis can be applied is a four bar linkage. A four bar linkage typically consists of a crank link, a rocker link, a coupling link, and a ground link. The crank and the rocker will be connected to two different pinned points that are fixed to the ground link which has no motion. Due to this fact the crank’s and rocker’s motion will be rotation about a fixed axis. The coupling link however will have a complex translation motion that is dependent on the length of the rocker and the crank. Below is an example of a simple four bar linkage.