# For the machine element shown, locate the X, Y and Z coordinate of the center of gravity

QUESTION:

My working: I had divided the body into 5 common shapes which are shown here:

now that I'm solving for x bar, y bar, and z bar I find it difficult in finding the x, y and z directions.

see my table of working here:

• I cannot understand your table. :( Do you know the center of gravity of a circle? – Jem Eripol Sep 25 '17 at 11:18
• first column is the volume calculation of the shape, the second column is the x bar or x direction of the shape, same as y and third is the x direction multiply by volume and sames as for y. the element had been divided into five common shapes, two rectangular, two half cylinders and one cylinder. – Surdz Sep 25 '17 at 11:27
• I will try to give inputs. – Jem Eripol Sep 25 '17 at 11:29
• I think the only challenge here is to determine the centroid of a half circle. Am I right? – Jem Eripol Sep 25 '17 at 11:32
• click this link and see what i had try: www53.zippyshare.com/v/HRgoVoQL/file.html – Surdz Sep 25 '17 at 11:45

Try this one. (Note: I don't know how to do tables in this site but please tabulate the data on your own.)

Areas are:

1. $0.75(4)(7)$
2. $\frac{\pi(2^2)}{2}(0.75)$
3. $-\pi(1.25^2)(0.75)$
4. $1(4)(2)$
5. $-\frac{\pi(1.25^2)}{2}(1)$

Note: Negative areas as holes that need to be subtracted from the system.

X-Centroids are:

1. $2$
2. $2$
3. $2$
4. $0.5$
5. $0.5$

Y-Centroids are:

1. $-0.75/2$
2. $-0.75/2$
3. $-0.75/2$
4. $2/2=1$
5. $2-\frac{4(1.25)}{3(\pi)}$

Z-centroids are:

1. $7/2$
2. $7+\frac{4(1.25)}{3(\pi)}$
3. $7$
4. $2$
5. $2$

You can then apply Varignon's Theorem to get the centroid.

• I just edited. I made a mistake looking at the location of the x-axis. Y-centroids for areas 1,2, and 3 should be negative – Jem Eripol Sep 25 '17 at 11:48
• And please understand how the values are taken. :) – Jem Eripol Sep 25 '17 at 11:53