DrD

Apparently I must write the dullest stuff found anywhere. As I write this, 290 folks have read this article, and not a single one has made a comment. I am really baffled. I had the (obviously mistaken) impression that this was significant, important information. It talks about a problem that is slightly out of the mainstream, a bit of an unusual challenge. It points to the fallibility of all people, even famous, highly successful authors. But no; not a single comment. I am baffled. DrD

117 views, and yet no comments! Does no one have any reaction to this? Do you think Rao had it right in the first place? Do you think he got it wrong, but that getting it wrong does not matter, its only an example problem? Or did you read it at all? DrD

Mechanics Corner A Journal of Applied Mechanics & Mathematics, #49 A Bad Example Most of us are inclined to trust an established textbook. We assume (1) the author knows what he is talking about, (2) the book has been carefully vetted by several editors and reviewers, and finally (3) the fact that it is well established in the market means that thousands of other readers have tacitly endorsed it as well. While these assumptions are usually true, they are no guarantee, and they can and do fail us at times. The topic of this post is one such failure. Beware!! The format of engineering textbooks is fairly uniform, consisting of alternating sections of Theory and Examples. For a student encountering the material for the first time, the Theory is often simply too much, and blows right over the head of the student. The starting student relies heavily on the Examples to comprehend, even if incompletely, what the material is about. The Theory is most useful when the material is studied a second or third time in some depth. Because many will only study the material a single time while in college, it is critically important that the Examples be correct and in no way misleading. Sadly, both of these problems exist in the book discussed here. The book in question here is Mechanical Vibrations by S.S. Rao, where both the book and the author are well known. The book was published early by Addison-Wesley; I have a 2nd edition dated 1990. It has been re-published more recently by Pearson in a 6th edition with a 2018 copyright date. The problem shown in the Figure is used in both of these, with only very minor changes. The same errors exist in both versions, indicating that in 28 years, Rao has learned nothing about this simple statics problem. I encourage all readers to examine carefully the discussion in t he attached paper. It demonstrates clearly that even the experts go badly astray at times. RaoCrane.pdf

How did you think it was supposed to work? DrD

James, your device looks more like a ratchet than a gear. Have you studied the principles of gearing? Your sketch just seems to bounce from one position to the next, whereas a gear controls the motion at all points in the tooth engagement. DrD

I don't know how difficult this problem is with FEA because I don't do FEA (I have no access to an FEA program). Let me suggest that you first try to work the simple statics problem where a load with components (Fx, Fy) is applied to the joint and then you need to compute the displacements of the joint. From this you can compute a stiffness, and you will be on your way to getting the natural frequencies. If you run into trouble you my consider my help offer in a recent post on my blog. DrD

This looks much like a class of problems I've been studying recently. There are several questions that need to be answered, I think. 1) Are both supports fixed (immovable)? 2) Do you have numerical values for all the data? (This is a very tough problem to address entirely in symbols!) 3) When you speak of "initial nodal displacement for the common node" I presume you mean an initial displacement for the connecting joint; is that correct? You have both magnitude and direction for this displacement? 4) What do you mean when you speak of "velocity of the oscilation as function of time "? Are you looking for an oscillation frequency? 5) How many degrees of freedom do you need in your model? Is bending to be included, or only axial deformation? Please fill in these gaps, and perhaps we can help you. DrD

Dear HKS, Thank you for the kind comments. I hope that I can be of help to many folks. As to working with practicing engineers in developing countries, let me say (1) I do this to a limited extent now, and (2) I would certainly consider doing more. Please go to my web site and write to me through the e-mail address given there. I'd like to hear more about what you have in mind; perhaps we can work something out. DrD

You don't specify the stroke. How far does it have to move? DrD

I'd like to invite all readers to visit my new website: Machinery-Mechanics-Professor.site I'm offering free help for engineering students through that site, so come on over and take a look. DrD

I would like to invite you to submit this question over at my new website: Machinery-Mechanics-Professor.site Hope to see you there. DrD

Today, I have a question for readers. I'd like to get everyone who is willing to answer the same question, but also tell me whether you are a practicing graduate engineer or if you currently a student. I think these two groups will answer somewhat differently, so it is important that you identify which one you fall into. The question is really simple: When you ask for help, what do you really want? Are you asking for someone to step in and solve a problem for you? Or, are you asking for a few hints so that you can move forward toward a solution yourself? Perhaps you are asking for something else altogether; if so, please tell me what you want to receive. Thanks, folks. DrD

That's pretty fuzzy. I doubt you will get a lot of takers. Maybe you could at least identify what sort of help you expect to need? DrD

My own experience left me permanently traumatized by the law. I see justice as accidental at best. When they told me to destroy work I had done that was the truth, in so far as I was able to approach the truth, I discovered that winning was all that mattered to the lawyers. Truth and justice are the lowest concern of an attorney, while winning and greed are upper most. DrD

Where did you get this force expression? Did you check the derivation? DrD