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Mechanics Corner

A blog by DrD

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A Journal of Applied Mechanics and Mathematics by DrD

Entries in this blog

 

Why You Shouuld NOT Use the D'Alembert's Principle

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
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A Bad Example #49

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
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New Help Site

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
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When You Ask for Help ....

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
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What Would You Like to Know?

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
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Correction To Mass On Multiple Spring Supports

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
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Mass On Multiple Spring Supports

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
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What Makes A Ship Move?

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
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Calculus Challenge Comments

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
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A Calculus Challenge

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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#44 Mouse Trap / Pendulum Dynamics Challenge

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
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#43 Four-Bar / Toggle Linkage Mechanism

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
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Triple Rocker

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
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#42 Gear Pair Problem

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 42     © Machinery Dynamics Research, 2017 Gear Pair Problem      Introduction     In this post, I want to discuss a seemingly simple problem currently being discussed at Physics Forums (PF). The original question, posed by someone, perhaps a student but perhaps not, is quoted below:       So, we have a pinion and a gear. I give an input torque Tp in the clockwise direction. Th
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Modeling Hysteresis

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
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Two Short Math Problems

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
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Comments on a Textbook - Khurmi & Gupta

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
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Rocket Homework Problem

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
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Where Would You Publish It?

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
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Two Balls Rolling On An Incline

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
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Base Acceleration Problem -- #36

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.
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Good News -- Bad News -- Rolling Disk in a Rolling Ring

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
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Last Post -- Time to Hang It Up

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD     © Machinery Dynamics Research, 2017 Last Post Time to Hang It Up     This will be the final post of Mechanics Corner here on Mechanical Engineering Forums. It has run almost exactly two years, and there have been ups and downs along the way. In this final post, I want to reflect a bit on my original goals for the blog, and also on what has actually happened. When our host first proposed to me t
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A Problem in Statics & Dynamics, #34

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 34     © Machinery Dynamics Research, 2015 A Problem in Statics & Dynamics           Introduction         A problem was recently posted on this Forum, requesting help, that has led me to consider a somewhat more general problem for this post. The scope of this post will include the original problem, although not by the method required there, but will also go beyond to a more general geometry.
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Advanced Polynomial Curve Fitting

Mechanics Corner     A Journal of Applied Mechanics & Mathematics by DrD, #33     © Machinery Dynamics Research, 2016 Advanced Polynomial Curve Fitting     The use of polynomials to fit engineering data is a common engineering practice. In school, we learn that "A data set consisting of n data points ((x_{i},y_{i}), i=1,2,3,…n) can be exactly fitted with a polynomial of degree n-1. Thus three data points can be fitted exactly with a quadratic expression, four data points ca
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