Serpentine Belt Analysis Homework: Length & Motion Equations Explained

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Discussion Overview

The discussion revolves around a homework problem related to the analysis of a serpentine belt system, specifically focusing on deriving the length of the belt between pulleys and the equations of motion associated with the system. The scope includes mathematical reasoning and technical explanations related to mechanical systems.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • The first participant outlines the problem, indicating a need to prove the length of the belt while considering negative radii for backwrapped pulleys and to derive motion equations.
  • The first participant expresses difficulty in deriving the length equation, mentioning various attempts including expanding formulas and manipulating triangle dimensions.
  • The first participant believes they have the correct motion equation but is uncertain about validating the compression of a spring in their diagram.
  • The second participant notes they have resolved the motion equations but remain confused about the length of the belt, questioning their approach to defining the length.
  • The second participant suggests that drawing a triangle between the centers of the circles could provide the length of the belt.
  • A third participant recommends making a sketch of the belt and its sheaves for clarity, indicating that they do not understand the variables used by the first participant.
  • The fourth participant announces that they have resolved all issues related to the problem two days after their initial post and requests to close the thread.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and resolution regarding the motion equations, while there remains uncertainty and disagreement about the length of the belt and the correct approach to derive it.

Contextual Notes

Some participants mention confusion over definitions and the need for visual aids, indicating potential limitations in understanding the problem without additional context or diagrams.

chriskay301
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Homework Statement



Here is what the belt system looks like.
kcmip1.jpg


The first part of the problem is to prove that the length of the belt between pulleys is
ay1ppk.jpg
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.
2rc37d2.jpg


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)

r8im4i.jpg


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.

1q08kp.jpg


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

THIS POST CAN BE CLOSED.
 

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