Velocity of a piston in a piston-shaft mechanism

AI Thread Summary
The discussion revolves around calculating the velocity of a piston in a piston-shaft mechanism, given specific parameters like angular speed and angles. The initial calculations led to an unrealistic velocity result, prompting participants to question the approach and the role of angular velocity in the solution. There is confusion about the influence of the wheel's rotation on the piston's movement, with suggestions that additional mechanical constraints may be necessary for clarity. Participants emphasize the importance of considering the wheel's angular speed in the calculations. The conversation highlights the complexities of the problem and the need for accurate diagrammatic representation to aid understanding.
afaiyaz
hr3nr5

Homework Statement


In the figure, a piston P is connected to a cylinder. The piston is connected to a rotating wheel with two shafts AB and BC. The shaft AB is connected on the periphery of the wheel. The wheel is rotating with angular speed ω= 100 rad s-1. At the moment A,C and the center of the wheel is collinear and θ=30° and dθ/dt = 500 rad s-1 , what is the velocity of the piston? (AB = 1.5m, BC = 1m)

Homework Equations


a2 = b2+c2-2abcosθ
Basic Trigonometry
Implicit DIfferentiation
dx/dt = dx/dθ × dθ/dt

The Attempt at a Solution


Since the linking rods are rigid, they must maintain their length throughout.
ebo1jQ

From the diagram, I assumed a pathway of shaft AB (denoted by y) and used it to find x, which I presumed is the horizontal motion of shaft BC. The rate of change of x with respect to time is, therefore, the velocity of the piston.

My working is as follows:
tan 60 = 1.5/y
∴y=√3/2 m.
Using sine rule,
sin C = y × (sin 120/1)
∴ C = 48.6°
sin (11.4) / x = sin (120) / 1
∴ x=0.228

Using cosine rule,
y2+x2+xy = 1
(2y × dy/dt) + (2x × dx/dt) + (x × dy/dt) + (y × dx/dt) = 0
∴ dx/dt = (- (2y+x) × dy/dt) / (2y+x)

dy/dt = 500 × 1.5 = 750 m/s
Plugging in values of y,x and dy/dt, I get -1111.9≈-1112 m/s.

I feel like this answers very unrealistic as it is more than 3.5 times the speed of sound. Could anyone point out where the mistake is? Could there be a completely different approach to the problem?
 
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You forgot to upload the figure.
 
as.jpg
 
the original figure
as2.jpg
 
Why didn't you consider ##\omega## in your solution?
 
This is either a trick question or it was set by an academic with no knowledge of mechanisms .

There is no sensible answer .
 
Do I have to? @arpon bro
If so, how do I use it in the solution?
 
What do you mean by 'no sensible answer'? @Nidum
Could you please clarify?
 
afaiyaz said:
Do I have to? @arpon bro
If so, how do I use it in the solution?
If ##\frac{d\theta}{dt} = 0## and ##\omega## is nonzero, will the piston move? What do you think?
Drawing diagrams may help.
 
  • #10
I think it should because, even if \frac{dθ}{dt}=0, the wheel is still rotating so there's ω.There may be no angualr velocity of the shaft AB along centre A, but there is the ω of the wheel. And if that's the case, I think ω has to be considered for calculating piston's velocity, although I'm not sure how to use it.
 
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  • #11
afaiyaz said:
What do you mean by 'no sensible answer'? @Nidum
Could you please clarify?
Because you could keep the position of C fixed and the wheel could still rotate. B will just move back and forth in an arc centred on C.
To make sense of the question there needs to beanother mechanical constraint.
 
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