What Are the Angular Velocity and Acceleration in This Mechanism?

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Discussion Overview

The discussion revolves around determining the angular velocity and acceleration in a mechanical system involving a rotating link and a slider. Participants explore methods for calculating these quantities, including the use of integrals and derivatives, while addressing specific challenges encountered in the problem-solving process.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that the angular velocity of link AD is known to be ωAD = 4 rad/s and seeks to find wCB and αCD.
  • Another participant suggests generating position equations for the slider and using integrals to find instantaneous velocity and acceleration, indicating that these values can help calculate angular quantities.
  • Some participants express confusion about the use of integrals, questioning their relevance in the absence of developed functions.
  • A participant clarifies that the term "integral" was mistakenly used and meant "derivative" for finding velocity or acceleration.
  • One participant mentions feeling uncertain about their understanding of the technique and worries about potential exam penalties for not following the taught method.
  • Another participant empathizes with the challenges of solving such problems, especially while unwell, and reflects on frequent mistakes in calculating acceleration.

Areas of Agreement / Disagreement

Participants exhibit uncertainty regarding the appropriate methods for solving the problem, with some advocating for the use of integrals while others express confusion about their application. There is no consensus on the best approach to take.

Contextual Notes

Participants have not fully developed the necessary functions for integration, leading to confusion about the mathematical techniques required for the problem. The discussion highlights the dependence on specific teaching methods and individual understanding of the concepts involved.

Who May Find This Useful

This discussion may be useful for students studying mechanical systems, particularly those grappling with angular motion, derivatives, and integrals in the context of kinematics.

jdawg
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Homework Statement


Block D of the mechanism is confined to move within the slot of member CB . Link AD is rotating at a constant rate of ωAD = 4 rad/s measured counterclockwise. Suppose that a = 350 mm , b = 200 mm.

Find wCB and αCD

Homework Equations

The Attempt at a Solution


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I hope its ok that I just scanned my work and uploaded it, I thought it would be easier to read from my paper than trying to organize it on here. I know my angular velocity is correct, but I can't seem to find the angular acceleration for CD :(
 

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First generate the x and y position equation of the slider itself (so far, simple). The first integral with respect to time will give instantaneous velocity, the second integral will give instantaneous acceleration of the slider pin (which is always equidistant to the sides of the slot). These integrals should be available on the web or in a good mechanical technician's handbook if you don't feel like doing the integration. Knowing those instantaneous values for the 60 degree position shown you can calculate the instantaneous angular velocity and angular acceleration of the slotted arm (translate the x and y values to values perpendicular to the slotted arm).

Hope that helps.
 
Why would I use an integral on this problem? I don't have any functions to integrate?
 
jdawg said:
Why would I use an integral on this problem? I don't have any functions to integrate?
You mean, you haven't developed them yet.
 
Ohhh... I don't think I was taught that technique. I might loose points on the exam if I don't do it the way I was taught.
 
jdawg said:
Ohhh... I don't think I was taught that technique. I might loose points on the exam if I don't do it the way I was taught.
OldYat47 got confused. Where he says "integral", he means "derivative" to find velocity or acceleration.
 
Yes, I reversed the terms. I'm fighting a bad flu and am not thinking too clearly. The approach I presented is a simple way to find the solution. If you are being taught a particular method you are correct, you'd better stick with that. I'm just not up to working through the math.
 
Yeah, these problems are tedious. I would definitely not feel like working one if I was sick, I hope you get better soon!

I just can't figure out what I'm doing wrong. I mess up on finding the acceleration at least 90% of the time. I feel like I'm following the procedure exactly. Am I just making some dumb algebra mistake? Or maybe not assigning the correct direction to some position vectors or something?
 

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