Mechanical Engineering

# Mechanics Corner

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A Journal of Applied Mechanics and Mathematics by DrD

## A-10

This is another incredible aircraft, essentially a plane built around a cannon. DrD

## SR-71

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

## Wheel Climbing A Step

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 55     © December, 2020                                                        Wheel Climbing A Step Introduction     The problem that follows was brought to my attention by a student at a great European university. It was a part of a much bigger problem with which the student was engaged, but this is quite enough to hold our interest. The results are differential equations of motion which could

## Mine Hoist Problem, Hint #3

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

## Mine Hoist Problem, Hint #2

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

## Hint for Mine Hoist Problem, #54

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!!

## Mine Hoist Problem, #54

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 54     © 25 August, 2020                                                          Mine Hoist Problem Introduction     As we saw in the previous problem (A Hoisting Problem for Engineers, #53), hoisting problems can be fun. This has gotten me to thinking about some other hoist related problems, and here I present three variations on a new problem. The problem is much the same in all three cases, with

## A Hoisting Problem for Engineers, #53

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

## Suddenly Lifted Bar - Revised

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

## Suddenly Lifted Bar

Mechanics Corner     A Journal of Applied Mechanics and Mathematics by DrD, # 51     © 4 July, 2020   Suddenly Lifted Bar Introduction     In the Forum section, under the Machine Dynamics and Design Considerations heading, Mr. Negar Rahbar has posted a topic, Bending Moment. It is a problem he found in an older textbook (one that I might have studied back in my college days, although in this case, I did not), a book titled Theory and Problems of Machine Design by Allen

## 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

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

## 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

## 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

## 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

## 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

## 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

## 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

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

## 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   ***********************************************************************************************************

## #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

## #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

## 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

## #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

## 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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