Offset Piston - Calculating Max. Angular Velocity

[Mingsliced]

Homework Statement

After happily working my way through the earlier parts of this question, I'm pretty much at the end of my tether with the last two parts. Please find the diagram attached:

A) Determine the value of the angle θ (measured from vertical) when the angular velocity of link AB a maximum.

B) What is the maximum angular velocity of link AB.

Homework Equations

Vao = 1.57m/s
Vab = 1.11m/s
Vbo = 1.11m/s

Aba(r) = 6.06m/s
Aoa(r) = 49.36m/s
Aba(t) = 35.1m/s
Abo = 41.4m/s

Angular Velocity of AB = Vab/Lab
Angular Velocity of AB = 1.11/0.2
Angular Velocity of AB = 5.5 rad/s

Angular Velocity of AO = 2πN/60
Angular Velocity of AO = 2π300/60
Angular Velocity of AO = 31.42 rad/s

The Attempt at a Solution

I can't seem to find any relevant equations for finding the MAXIMUM angular velocity. Any help will be greatly appreciated, would like a nudge in the right direction so i can figure it all out. If it helps at all I've calculated the acceleration and velocities of each component.

I think, but I am not 100% sure, that maximum angular velocity occurs when the piston is at maximum/minimum displacement. Can anyone confirm this?

Cheers!

 

[Buzz Bloom]

Hi Mingsliced:

Unfortunately, when I tried to open your JGP file I got the following message:
The image . . . cannot be displayed because it contains errors.

Regards,
Buzz

 

[Mingsliced]

Apologies, I've attached a new image to this post which should hopefully work for you.

Regards,

Ming

 

[adamhere]

I think when acceleration equals zero angular velocity will be at a maximum.

 

[Mingsliced]

Thank you, I'm pretty confident I've cracked it now :)

 

[adamhere]

Wondering if anyone can add to this.
I want to derive a formula for angular acceleration so I can then work out the maximum angular velocity, but I'm not sure how to go about