Saturday, February 9, 2013

Centroid of a Linkage (Part I)

Point I in Figure 1 is an instantaneous centroid of the four-bar linkage. The centroid of a linkage is important in mechanical design because when the mechanism is subjected to a combined force that passes through the centroid, it will act like a rigid structure. That is, the system will not deform.
Figure 1
In a design related course, the class was asked to find both the fixed (space) centroid and the body (moving) centroid of a mechanical structure. The fixed centroid is the locus of the instantaneous centroid of the structure at different geometry configurations. The body centroid, on the other hand, is the position of the fixed centroid when viewed from the joint of the stricture (in the case of the four-bar linkage shown in Figure 1, the body centroid is viewed from points (e, f) or (g, h)).
Figure 2
The meaning of this definition will be apparent as we explore more on the subject in Part II. First, we will get familiar of the subject by an example of what the centroid locus look like when drawn in the same picture. Figure 2 is an example of the centroid calculated for the particular linkage. The body centroid (red) will move with the linkage (blue). At each given instant, one of the points of the body centroid will coincide with a point on the fixed centroid. Again, how the calculation is done will be covered in Part II.