What Are the Angular Velocity and Acceleration in This Mechanism?

[jdawg]

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 w_CB and α_CD

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 :(

 

[OldYat47]

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.

 

[jdawg]

Why would I use an integral on this problem? I don't have any functions to integrate?

 

[SteamKing]

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.

 

[jdawg]

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.

 

[SteamKing]

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.

 

[OldYat47]

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.

 

[jdawg]

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?