DrD

Mechanics Corner A Journal of Applied Mechanics and Mathematics, by Dr.D, #56 Planetary Gear Challenge Solution Introduction If you have read the comments following the original Challenge posting, you are aware that Mr. Sundaram Ramchandrand has posted work that answers part of the questions asked. I agree with his numerical results, but I remain unconvinced by his analysis. He is to be congratulated on his good results here. Please see the PDF attachment for my full solution. SolutionPost.pdf

An argument that begins with the words, "I guess ..." is not very persuasive! As an engineer, aren't you supposed to be able to justify your work, to prove your result? I've written lots of engineering reports that were required to convince the customer that our product was soundly engineered and adequate for their application. I would not dare to begin with "I guess ..." I've also reviewed lots of engineering reports written by others to either accept or reject their results. I doubt that I would ever accept a report that includes the phrase "I guess..." As to the central point, what you have stated as "the essential relationships in terms of angular velocities still hold, irrespective of the shape of the arm / carrier," I don't see any justification for that at all. I would like to be convinced. DrD

It appears to me that, in all the discussion and examples given by your reference, the velocity vectors at the contact points are exactly parallel to each other. In the Challenge problem, this is most certainly not true. How can you assure that the results taken from your reference apply to the Challenge problem when the geometry is significantly different? DrD

I found a copy of the textbook you are using, at least I think that it is the same. Just to be sure we are on the same page (literally), you are speaking of eq(10.4) on p,.318 and Example 10.2 on p. 319; is that correct? DrD

I do not have this textbook; I have it's "ancestor," the first edition, before Pennock joined the other authors and Shigley was listed as the first author. I will have to see if I can locate a copy of the 3rd edition. Can you copy the relevant pages and send them to me via a PM, perhaps? (Just as an aside, there is an error in the authors as you have them listed. The name you show as Dicker should actually be Uicker, and he is (or was?) on the faculty of the University of Wisconsin-Madison. This error pops up ever where, and does not seem to have ever been corrected.) You are correct about the energy calculation being more involved. However, it would not be much of a difficulty if you had worked through the development of the necessary kinematics as opposed to simply following a textbook example. DrD

(1) Regarding your equation (wR-wPC) /(wS - wPC) = (-Ns / N1) * (N2 / N3) * (-N4 / Nr) you say that you simply applied a formula given in standard textbooks on mechanism. You do not say what standard textbooks, nor do you show a derivation. I could certainly show you a number of "standard textbooks on mechanisms" that do not include this, so I still think your equation requires justification. The best justification would, of course, be to simply show how it is derived. Note the wording of the first question: "... develop the mathematical relation ..." This implies more than simply grabbing an equation from a book. (2) Regarding the second question, you did obtain results for this item. (3) Regarding the third question, you did obtain results for this item. (4) Regarding the fourth question, there does not appear to be any attempt to obtain an answer. Why is this? DrD

Thank you for this response. I'm very pleased to see someone make an attempt. To begin, you said, (wR-wPC) /(wS - wPC) = (-Ns / N1) * (N2 / N3) * (-N4 / Nr) Why would we believe that the ratio of differences on the left is equal to the triple product of ratios on the right? This is not obvious, and I think it requires justification. As it stands, it is simply pulled out of the blue. DrD

I will look forward to hearing from all of you regarding your solutions to the challenge problem. DrD

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #55 Planetary Gear Challenge Introduction Back in the mid-1990s, I worked as the "in-house consultant" for a small aerospace manufacturing firm in the Chicago suburbs (500 employees). The general rule was simply that any engineer in the company could bring me any problem, and I would try to give them a solution. It was one of the happiest jobs I've ever had because I was constantly being given new problems to work on. Some of the problems were simple, the sort that could be solved in 20 minutes with pencil and paper. Others took many days and lots of computer work, but I had a free hand and I really enjoyed it. For the figure and the remainder of this challenge, please see the PDF file. I am unable to save the figure in a format that will allow me to upload it here. -- DrD Planetary Gear Challenge.pdf

This is not the sort of question Mechanical Engineers typically look at. We focus on macroscopic phenomena, not sub-atomic questions. DrD

If Mr. Reid wants to work with you, you better take him up on it. I suggest that all others are going to ask for a drawing as that is the standard way for engineers to communicate. Who knows? It might even clarify your own thinking. DrD

I'm glad you are getting something useful from these posts. Alban, I have to say that I do no know enough about Kane's method to have a useful opinion. Sorry about that! DrD

Without knowing the shaft dimensions, support geometry, shaft material, etc., there is very little that any reader can say other than to guess at your problem. It would help a lot if you would post proper drawing for the shaft and the entire system. DrD

This question is best addressed experimentally. Use the system you have built, but drive it with a dead weight rather than the stepper motor. Determine both (1) the load required to initiate the flow, and (2) the load required to sustain the flow. With that data, you should be in a good position to complete your design. DrD

R depends upon the shape of the body. Since you have drawn it, I presume that you know the shape. For every point, there is an R, and the moment with respect to O is simply the sum of the R x F contributions. DrD