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

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

I've seen this plane close enough to touch it. It is the most frightening machine you can imagine.
DrD
SR-71 Blackbird: The Cold War's ultimate spy plane
(Image credit: Lockheed Martin)
By Stephen Dowling1st July 2013
Colonel Rich Graham spent 15 years as a Blackbird pilot and wing commander. He told BBC

Mechanics Corner
A Journal of Mechanics & Mathematics by DrD, #54C
Mine Hoist Problem, Hint #3
Introduction
The original Mine Hoist Problem was posted 23 August, and it is not 10 October, over 6 weeks later. Thus far, I have not received any attempts at a solution. In this third (and probably last) hint, I want to explore some new ideas and also re-work much of the second hint in vector form. It will be

Mechanics Corner
A Journal of Mechanics & Mathematics by Dr.D, #54 B
Mine Hoist Problem, Hint #2
Introduction
The original Mine Hoist Problem was posted 25 August 2020, and the first Hint was given on 8 September. We are now almost one month into this problem, and thus far no one has sent me even so much as a question other than Tim Dennison's request for a video. I'm not quite sure how to understand this. I see

It appears that only a very few folks are even attempting these problems, but it also appears that no one has sent me a solution. For that reason, a small hint seems to be in order.
Hint: Turn the picture upside down. For most of us, it is conceptually easier to think about the problem if the X-axis goes to the right and the Y-axis is upward. Of course, if you do this, you must recall that gravity then acts up, not down.
Don't be shy; give it a try!!

Mechanics Corner, #53
A Journal of Applied Mechanics and Mathematics by DrD
A Hoisting Problem for Engineers
A Learning Experience in Machine Design
There is a document available on the Internet at several locations with the title 2.003 Problem Archive by MIT Professor David Trumper, Last Updated April 19, 2005. It is a collection of engineering problems, some

The previous post on this topic was certainly acceptable for engineering purposes, but there was one small oversight in the model. Many would actually prefer that oversight because it makes the algebra quite a bit less complex. Even so, it is not quite correct, so this revised post is offered to correct the oversight.
There are also a few additional comments that may be of interest, and a final question for the readers to consider.
DrD
LiftedBar_Revised.pdf

Mechanics Corner #50
A Journal of Applied Mechanics and Mathematics by DrD
Why You Should NOT Use the D'Alembert's Principle
I think it is safe to say that every engineering student studies both Statics and Dynamics. We are told that Statics is easier than Dynamics, which is often true but not so in all cases. When we get to Dynamics, many teachers, particularly physics teachers, will urge the use of something called D'Alembert's Principle. The

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

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

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 f

What Would You Like to Know?
If you could ask me any question you want, what would you like to know that you think I might know? I certainly do not know everything, but through the years I have accumulated a certan amount of knowledge that I'd like to pass on to you. Therefore, I ask, what would you like to know?
Many readers are still in college, and no doubt they would like to know what is going to be on the next exam. I'm sorry, but I have no way to know that. What I might be able

Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #48-B
Correction To
Mass On Multiple Spring Supports
Correction
The previous post, #48 titled Mass on Multiple Spring Supports had several typographical errors. Strangely, they are all in the brief introductory example regarding the loads on the four legs

Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #48
Mass On Multiple Spring Supports
Introduction
One of the classic problems of elementary mechanics is to determine the load on each leg of a four-legged table. The table top is assumed to be a uniform rectangle, the legs are of equal length, the center of mass is the centroid of the table top, and the floor is level. What is the load in ea

Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #47
What Makes a Ship Move?
One of the problems that often confronts engineers is the description of large, interconnected systems. Engineers tend to specialize, so that one is very knowledgeable on gears, another knows bearings, a third knows pumps, but none of them are comfortable with the whole system. In the automotive context, this is often exp

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

Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #45
(c) DrD, 2018
It has been quite a while since I last posted anything here, but an interesting problem has come to mind that I wanted to share with you. If you really know calculus, this should be straight forward; if you don't know calculus, don't even try!
MEForumChallenge.pdf
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Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, # 44
Machinery Dynamics Research, 2017
Mouse Trap / Pendulum Dynamics Challenge - Part I
Introduction
Mice are a problem all over the world, and as a result, I'm sure that there are mouse traps of various sorts found everywhere. It would be utterly amazing if this were not true! In the USA, there is a very common type of mouse trap that I have seen used all my life, the sort of system

Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #43
(c) Machinery Dynamics Research, 2017
Four-Bar / Toggle Linkage Mechanism
Introduction
I believe that it would be correct to say that all of the single degree of freedom mechanisms that I have discussed on ME Forums have involved only a single loop. This might lead a reader to conclude that a single degree of freedom implies only a single loop, and vice versa, that a single loop imp

Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD
July 31, 2017
Triple Rocker
Over at the Kinematics of Machines club, I recently ask if anyone could show me an example of a four-bar linkage that would be classed as a triple rocker. In the terminology of four-bar linkages, a link is classed as either a crank or a rocker:
Crank - can rotate in a complete circle
Rocker - cannot rotate in a complete circle]
Thus my question was for an example