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
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #41
(c) Machinery Dynamics Research, July 2017
Modeling Hysteresis
1. Introduction
What do you know about hysteresis? Many Mechanical Engineers will associate this term with the magnetization curve of a piece of magnetic material, and quickly conclude, "I don't have to worry about that!" But that would be wrong. While hysteresis does occur in magnetic systems, it happens in many other situatio
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #40
July, 2017
Two Short Math Problems
Do you ever read the ads that appear on ME Forum? I try to avoid them as much as possible, but an organization called BRILLIANT has put up some interesting math problems of late that have caught my eye. Two of them are the subject of today's post.
The first problem that I want to discuss is actually more recent than the other, but it gives us a good plac
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #39
(c) Machinery Dynamics Research, 2017
Comments on a Textbook Theory of Machines
by
R.S. Khurmi & J.K. Gupta
1 Introduction
Recently, through the wonders of the Internet, I have come across a copy of the textbook Theory of Machines by R.S. Khurmi and J.K. Gupta (S.Chand & Co., Ltd., 2005). Since theory of machines has been my primary technical interest since the early 1980s, I was interested
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #38
Machinery Dynamics Research, 2017
Rocket Homework Problem
Introduction
Most engineers find problems involving rockets to be exciting. There is something about a rocket that fires our imagination, whether we think of going to the moon or one of the planets, or simply of shooting down an incoming missile. The subject of this post involves a rocket on a mobile launcher. The rocket is i
Mechanics Corner
Where Would You Publish It?
Since long before my time, there has been a desire to have important results published where they become accessible to many others. Some of the great names, such as Newton, Euler, Bernoulli, and others, we know primarily because of what they published. Their work formed the fundamentals upon which modern engineering and science is built. Publication of research results has long been particularly important to faculty members; it is often take
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, # 37
29 April 2017
Two Balls Rolling On An Incline
A Problem Where I Learned Something New
Introduction
In previous articles, I have mentioned another web site called Physics Forums (PF) where people post problems for which they need help. In this note, I want to present to you one such problem and it solution, along with a new insight that came from another commenter at PF, one of the advi
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, #36
Base Acceleration Problem
Introduction
In a recent post (#35) I mentioned that I often participate in another forum called Physics Forums (PF). The problem that I want to discuss here is an elaboration on a problem that recently appeared at PF. I'm going to add a little bit of complexity to the problem (the problme as stated at PF was extremely simple) in order to make a particular point.
Mechanics Corner
A Journal of Applied Mechanics and Mathematics by DrD, # 35
Machinery Dynamics Research, 2017
Good News --- Bad News
Rolling Disk in a Rolling Ring
Introduction
Well, it looks like Mechanics Corner is back, at least in terms of an occasional post. It will probably be less frequent than previously, but there are just too many interesting things to talk about to remain entirely silent! The title for this post may leave you wondering wh