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Yesterday, I had an Engineering Mechanics exam which involved a Piston and a Crankshaft engineering dynamics problem, which I was a bit stumped about. I sought clarification from the teaching staff but they were not exactly in front of the exam paper when I spoke to them on the phone, so I am unsure if they understood my question properly.

Whilst I've already submitted my exam paper, I was wondering if someone could clarify whether this question is correctly set up, as I suspect they have mixed the definition of crankshaft/connecting rod incorrectly.

I think I was the only student sitting the paper (resit exam), but to avoid anyone else gleaning in on the exam paper, I've slightly modified the question's values here but kept the question consistent with the way it was written by the lecturer.


The question is as follows:

Consider the piston and crank mechanism at the time instant shown below. The Crank $BC$ of length 30 mm is rotating at angular velocity $\dotθ=0.25s^{-1}$. The piston $C$ is free to move along the vertical housing. Determine the velocity $V_C$ of the piston when $θ=30°$.

Piston and crankshaft diagram


Now, I'm not looking for an answer to this question as I know how to do it (using instantaneous centre method), but what I am really asking is clarification as to whether the above question is even physically possible?

From the various example problems I've attempted, the piston $C$ is attached to a connecting rod (say $BC$), which is connected with the crankshaft (say $AB$) at point $B$. However, in the above question, they have defined the crankshaft to be $BC$ that is directly attached to the piston, rotating (I assume from point $B$) with no connecting rod. Is this possible? Also, what is the point of $AB$ then?


I'd appreciate some clarification on this question, as I suspect the question is incorrectly written and subsequently would affect my chance of passing the already difficult exam. Many thanks for taking the time to look at my question.

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  • $\begingroup$ @PhilSweet couldn’t we use law of sines to find angle at A using length BC. After we find that angle we can find angle at B by subtracting angle A and angle C (θ = 30°) from 180°, and then finally we can find length AC? $\endgroup$
    – AVelj
    Apr 9, 2022 at 14:18
  • $\begingroup$ Yes, I was wrong about that. $\endgroup$
    – Phil Sweet
    Apr 9, 2022 at 14:50
  • $\begingroup$ @PhilSweet that’s ok. But I’m still unsure about having a crankshaft directly connected to the piston. Usually there’s a connecting rod in between, which doesn’t appear to be the case with this question. It seems like it’s rotating around point B when typical set ups would have it rotating around point A, right? $\endgroup$
    – AVelj
    Apr 9, 2022 at 15:12
  • $\begingroup$ Are you asking whether AB is going to rotate about A like an engine crankshaft would? $\endgroup$
    – NMech
    Apr 11, 2022 at 12:15
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    $\begingroup$ I can't really comment on the appeal thing (to be honest I don't think you would get much luck). This mechanism may not be required to rotate fully about B. And the information that is provided is sufficient to calculate the velocity in a limited range. (Having said that, If I was taking the exam I would have asked during the exam to clarify certain thing e.g. if the position of C is level with A, of whether it is grounded). $\endgroup$
    – NMech
    Apr 11, 2022 at 12:50

1 Answer 1

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I don't think there is a problem.

As C moves up and down the shape of triangle ABC will change and therefore θ will change too.

You do seem to be missing one more measurement though. You haven't got AC or any of the angles to allow you to work it out.

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  • $\begingroup$ Thank you for your input, I’ll have a discussion with the lecturer regarding the lack of knowns (angles/lengths). But realistically should a crankshaft be attached directly to a piston? I thought there would always be a connecting rod in between them? $\endgroup$
    – AVelj
    Apr 9, 2022 at 13:54
  • $\begingroup$ I think BC is the connecting rod. $\endgroup$
    – Transistor
    Apr 9, 2022 at 14:01
  • $\begingroup$ I agree with you, but the question says that the crankshaft is BC, so that’s why I was puzzled so much. It doesn’t rotate around point B but rather point A right? I’ll have to speak to the lecturer to clarify this. $\endgroup$
    – AVelj
    Apr 9, 2022 at 14:05
  • $\begingroup$ Also, couldn’t we use sine law to find AC, by first finding the angle at A to find the angle at B and finally the length AC? We have length AB and BC and the angle at C (θ = 30°) so that should be enough right? $\endgroup$
    – AVelj
    Apr 9, 2022 at 14:14
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    $\begingroup$ That might work: $ \frac {sinA}{30} = \frac {sin \theta}{50} $. Now you've only one unknown. $\endgroup$
    – Transistor
    Apr 9, 2022 at 15:09

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