DrD

You can find a lot about this and many other mechanisms in the newly released textbook Mechanics of Machines, 2nd ed. Please download a copy and encourage your friends to do the same; it is offered without charge to everyone. DrD MoM2DraftMar2019r1-compressed.pdf

I did not see any mention of negative torques, and without them, there will be nothing to slow the system down. What are your load torques? DrD

Hetal, Please publish your results here so that we may all benefit from them. DrD

There are two types of flexibility readily evident with a belt drive, and to a lesser degree with a chain drive. They are 1) Lateral flexibility that allows the pulleys to be slightly out of plane with each others. 2) longitudinal flexibility that allows the belt to stretch and shrink under load variation. For a polymer or rubber like material, the existence of both forms of flexibility is readily evident; the material is stretchy. For a steel chain, the material is also "stretchy" although to a much reduced degree. We tend to think of chain links as rigid, but in fact, they are merely stiff. They deform under load, just like any other material. In addition for the chain, there are small clearances around the pins that opens and close, allowing for both types of flexibility. All in all, it is simply a matter of degree. The belt material is far more compliant, while the chain material is more stiff. But neither is truly rigid. DrD

And Carrie Underwood has what to do with "economical joints?" DrD

Is it really necessary to ask such a question? Consider what would happen if the heat were not dissipated, and you'll quickly come to the answer.+

Can this question really be answered in general, that is, without specifying the machine element? For some, strength is a major consideration, while for others corrosion resistance it the main determinant. The list goes on and on. This question has no answer.

Whatever in the world is an "economical joint"? In American slang, a "joint" is sometimes a bar or restaurant, so an "economical joint" might be one where the prices are modest. In other American slang usage, a "joint" refers to a marijuana cigarette, so presumably an "economical joint" might be inexpensive marijuana. Just what in the world did the Administrator have in mind for an "economical joint"?+

Mechanics Corner A Journal of Applied Mechanics and Mathematics by DrD, #46 Comments on A Calculus Challenge I would like to thank all those who took part in the Challenge. My solutions and comments are attached. 46 CalcChallengeComments.pdf

I'll get to you William. Please be patient. I have a few other things going on right now. DrD

Dear Mucugia, The challenge is now closed, and I will not be reviewing additional work any longer. Thanks for the effort. DrD

Dear Mucugia, Two problems: (1) It looks like you may have left out a page. You sent Page 1 and Page 3, but what about Page 2? (2) Neither of the pages that you sent are complete. The PDF does not show the final result on either page. You might do better to copy these pages over , writing a bit smaller so t hat the scan will capture the whole page. DrD

Dear Amin, Well, I have both the 2nd and 5th editions of Roark, so I am unable to tell whether the book is correct (or if you read the book correctly). That's the problem with using a reference source (although Roark is widely recognized). I'm amused that you said, "When they ask "how do you gget formula?" the answer will be "here is the formula in the book." Does that really convince you? Are you more convinced by something in a book, or be a carefully worked out derivation that you can follow for yourself? I'll take the derivation every time!! It is certainly true that handbooks have their uses. The problem is, they also have their limitations. If there are assumptions made in the derivation, looking the formula up in a book may not tell you about those assumptions. I'm sorry that you evidently find the area moment of inertia expressions just too tedious to be worth your time. For those who want to find out if they really can use calculus, this remains a very useful exercise. DrD Dear HKS, You promised results after the New Year. Just which New Year did you have in mind? DrD

Thanks for the information, Jarek. I do not like MS Word, and would never use it given any choice in the matter. But, I know many others like it, so this is useful. DrD

Dear Jarek, Thanks for the comment on Mathtype. I have heard of it, but know little about it. I use LaTeX for all of my work, but I like the way your work looks very much. DrD