Serpentine Belt Analysis Homework: Length & Motion Equations Explained

[chriskay301]

Homework Statement

Here is what the belt system looks like.

The first part of the problem is to prove that the length of the belt between pulleys is

assuming a negative radius for the backwrapped pulleys (idler and tensioner).

The second part is to derive the equations for motion, which are given so we can use them to check out answers.

Homework Equations

Listed above in pictures.

The Attempt at a Solution

So here are my attempts at both the length equation and the first motion equation (which will be the same concept for the first few)

For this length equation I've tried so many different things and I can't seem to get anything to work out. The picture I've posted is my last attempt that I've tried by just expanding out the formula and seeing if I can see where it is coming from. I've also tried subtracting/adding the radius when making the triangle, etc.

For the motion equation I know I have the correct equation. But I have that one spring written in compression to achieve it (the circles in the diagram). I'm not sure how I can validate that I know that spring is in compression, or if I just did the solution incorrectly. Any help would be appreciated..thanks!

 

[chriskay301]

Okay..so I figured out all of the motion equations. I'm still stuck on the length of the belt however. I've tried numerous approaches.. I am not sure if I'm defining the length wrong, or just not thinking about it properly. Or maybe over thinking it. But just drawing a triangle from center of circle A to the center of circle B would give you length of the belt wouldn't it?

 

[SteamKing]

Maybe you should make a sketch of the belt and show the sheaves which the belt drives. You know what xA, xB, rA, rB, etc. mean, but we do not.

 

[chriskay301]

I actually figured out all of this 2 days after I posted it.

THIS POST CAN BE CLOSED.