Degrees of freedom (question based on an interview I attended)

[k.udhay]

TL;DR Summary

This question is based on an interview I attended. I coudn't answer the question convincingly to myself. So seeking some help here.

I was asked by an interviewer the number of degrees of freedom (in both translation and rotational senses) this part has with respect to each axis. Indeed I can share what I think of here, but I want to start it fresh and correct.
If you were the interviewee, what would have been your answer and the rational associated?

Thanks in advance!
Edit: Added this --> (in both translation and rotational senses)

 

[hutchphd]

My answer would be that you have not specified the problem. The number of relevant degrees of freedom depends upon the question being asked of this object. For instance it contains ~N_Avagadro atoms but those degrees of freedom can be replaced by a suitable average.
So you need to consider the minimum number of variables required to specify the system. It would be easier and better for you to tell us your solution first.

 

[k.udhay]

My answer would be that you have not specified the problem. The number of relevant degrees of freedom depends upon the question being asked of this object. For instance it contains ~N_Avagadro atoms but those degrees of freedom can be replaced by a suitable average.
So you need to consider the minimum number of variables required to specify the system. It would be easier and better for you to tell us your solution first.

Thanks for your answer. It is a mehcanical problem and hence I would not get into the atomic level.
My answer (I think) was this:

X	CCW	1​
	CW	1​	Until the gap in the groove is closed
	+	1​	Acc. to stiffness of leaf spring
	-	1​	Acc. to stiffness of leaf spring
Y	CCW	1​	Acc. to stiffness of leaf spring
	CW	1​	Acc. to stiffness of leaf spring
	+	0​
	-	0​
Z	CCW	0​
	CW	0​
	+	0​
	-

 

[jack action]

I'd go with six DOF.

Translation:

• X (leaf spring)
• Y (groove)
• Z (leaf spring)

Rotation:

• X (groove)
• Y (leaf spring)
• Z (leaf spring; twisting)

 

[jrmichler]

Here's how I would attack this problem. My assumption is that the interviewer is more interested in how I attack problems than whether I can come up with (the)(a) correct answer during the interview. That being the case, I would expect that the interviewer wants to hear my thought process more than (s)he wants to hear my conclusions. So this is what I would be saying, somewhat paraphrased:

"The assembly consists of a top block, a leaf spring, and a bottom block with features."

"The leaf spring is flexible in the X direction, but is rigid in the Y direction."

"Similarly, the bottom block is flexible about the X axis, and rigid in the other axes."

"The top block is rigidly fastened to the machine, so has zero DOF."

"The bottom surface of the bottom block is rigidly connected to the machine, so has zero DOF. The fact that it is fastened to a vibrating member does not affect the DOF."

"The slot machined in the bottom piece would allow the bottom piece to flex. However, such flexing is prevented by the leaf spring. Zero DOF for flexing about the X axis."

"The leaf spring allows the bottom block to move in the X direction, but the bottom block is fastened to the machine. Zero DOF for the bottom block in the X-direction."

"I see one DOF - the middle of the leaf spring can be moved in the X direction. Even though it cannot be moved very far, it is one DOF."

"Conclusion - one DOF."

 

[hutchphd]

As part of the process, I would first ask what it means that the bottom member can "vibrate" (does that mean move freely or only in a particular fashion). This is a terrible test question but not a bad interview question.
I agree the important part of the answer is to

1. Define the unfettered system
2. Apply the constraints

Is there a way change the question so it would also overtly require reliance on symmetry ?

 

[Vanadium 50]

but not a bad interview question.

I agree.

A good response would include questions from you - like "is motion of the lea spring only a DOF, or is it treated as internal, like atomic motion?" The answer they are looking for is not a number, its whether you can ask good clarifying questions.