# 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? Sep 25, 2017 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. Sep 25, 2017 at 11:27
• I will try to give inputs. Sep 25, 2017 at 11:29
• I think the only challenge here is to determine the centroid of a half circle. Am I right? Sep 25, 2017 at 11:32
• click this link and see what i had try: www53.zippyshare.com/v/HRgoVoQL/file.html Sep 25, 2017 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 Sep 25, 2017 at 11:48
• And please understand how the values are taken. :) Sep 25, 2017 at 11:53