• Content count

  • Joined

  • Last visited

  • Days Won


Everything posted by DrD

  1. 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 shown below in Figure 1. I want to spend a few minutes discussing this mouse trap, to be certain that all readers understand how it works, before moving on to the main part of the post. MouseTrapPendulumDynamics-1.pdf
  2. Be sure to check out the new post at Mechanics Corner. It poses a challenge problem for each of you to work on. Do you really know kinematics of machines? Find out!! Try the simple problem posted over at Mechanics Corner now. DrD
  3. #43 Four-Bar / Toggle Linkage Mechanism

    Wow, Henry!! I freely admit to being older than dirt, but these books are old even for me! You are correct; they are very interesting. Sadly, many of the figures don't really tell enough to make clear how the things work. But some do, and that makes for fun browsing. Thanks, DrD
  4. 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 implies only a single degree of freedom. Neither of these statements is true. In this note, I want to discuss a counter example, a mechanism called the four-bar / toggle linkage; it is shown in Figure 1. TogglePress.pdf
  5. #43 Four-Bar / Toggle Linkage Mechanism

    Been "speed reading" again, Henry? That is indeed an interesting image you posted. If I recall correctly, this is a variable compression ratio engine mechanism. It is particularly interesting that you post it here. It is another variant on the four-bar/toggle linkage idea. The crank, the link, and the radius bar form a four-bar linage. The connecting rod drives the crank through the link, essentially a slider-crank of a strange sort. This is a type of engine called an L-head engine, referring to the idea that the combustion chamber and the dead volume near the valves form an L-shape. It is interesting that one valve is in the block while the other is directly opposite in the head. I wonder how well that works? In a two-stroke cycle, you would risk pulling most of the mixture right through from inlet to outlet without burning at all! Most likely it is for a four-stroke cycle. DrD
  6. #43 Four-Bar / Toggle Linkage Mechanism

    Henry, did you read the blog post? Let me quote: If a tool of some sort is attached to the orange block, it is repeatedly brought down to bear against the work piece located below. This may be a punch to make a hole, a die to form a shape, a welding contact to make a spot weld, our countless other operations that require only momentary contact between the tool and the work. And again: Notice the shape of the solid curve. It is rather ‡at-topped, with something like a dwell in the down position. This would be useful for a situation where extended contact time between the tool and the work is required, such as in a spot welding operation. It would not be preferred in a punching operation where the best operation is to complete the punch and withdraw the tool quickly. The shape of the curve can be modified to some extent by adjusting the link lengths. Doesn't that suggest some applications?
  7. 4 Bar Linkage Problem

    Dear Nerd, Please post your work, both solutions and the final results from each. I think a lot of folks would find it very interesting. My intentions, from the equations I gave you was simply to use Newton-Raphson to get the final numbers. DrD
  8. 4 Bar Linkage Problem

    Crossed4Bar.pdf Dear Nerd, I have assembled the equations you want, at least as well as I understand your problem. Please let me know if this answers your question or not. DrD
  9. Comments on a Textbook - Khurmi & Gupta

    Henry, your comparison of authors between rabbits and moles is very funny! Thank you. DrD
  10. 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 to see what would be in this book, particularly in view of the many favorable comments posted in regard to it. Many people seem to think that this is a most excellent book, and I’m always interested to see what brings forth comments of that sort. As I looked through the Table of Contents, I saw that one of the last chapters was given to the topic of Torsional Vibrations (Ch. 24). Since the area of torsional vibrations has been a topic of intense personal interest for 40+ years, I was naturally drawn to this chapter. The comments that follow are based on what I found in that chapter; I have not reviewed the remainder of the book at all. In my comments below, I will refer to the authors, Khurmi and Gupta, simply as K&G to avoid writing their names out repeatedly. One of the things I think is necessary in a textbook is that it should be directed toward teaching students to solve real problems, not simply textbook examples. Certainly, textbook examples should be simple so that they can be easily understood, but they should also be as general as possible. Where they involve special, limiting assumptions that may likely not be true in actual practice, this should be made clear. Failure to do that marks an author as one who has never actually done engineering in the real world. If the assumptions are not made clear, there is a tendency for students to later want to simply apply directly the results from the textbook problem, not realizing that they may not apply at all. So, what did I find? Comments on Textbook - Khurmi.pdf
  11. A Question for Readers

    Many of you have asked me various questions, so now it is my turn. Let me lay a bit of background first, and then the questions. I have had some conversations recently with JAG (one of the other writers here at ME Forums) regarding the choice of software for 3D modeling and analysis. JAG has made some excellent suggestions, specifically a cloud based program called Onshape. Unfortunately, for reasons that are unclear, my computer cannot run Onshape; I have worked with their help people for several hours, all to no avail. JAG recommends this in part because there is a "free version for the hobbyist" and a relatively inexpensive "full version for the professional." That is pretty attractive, but since I can't run it, I'm stuck. I gather that virtually all engineering colleges these days are teaching some sort of 3D modeling and analysis software, but that raises a few questions in my mind. 1. If your college teaches brandX 3D software, what will you do when you go to work for a small company that cannot afford anything more than 2D drafting (simple CAD), with no analysis capability at all? How will you do your job then? You probably have your own pocket calculator, but will you have your own copy of ANSYS or Pro-E? 2. What software does your school teach (every students should have an answer to this question, so I expect lots of replies on this one!)? 3. If you have used software extensively for analysis of engineering problems (beam deflections, stress analysis, fluid flow, heat transfer, etc), are you confident that you will be able to work all of those problems if there is no such software available to you on the job? I might add, as sort of a postscript, most of you know that I am older than dirt (I just had another birthday, so the situation is even worse!), so I tend to look at things from an elderly perspective. One of my great fears as a working engineer was "What will happen when I'm ask to do something that I don't know how to do?" It happened more than once, and it usually resulted in a flurry of intense research to come up to speed on whatever topic was involved. I could usually do that because I have a pretty good library, and I knew how to use a university library as well. But in terms of software, I was always concerned that I had no FEA program, so how could I do problems that others were doing by FEA? I have come up with some interesting work-arounds, including writing my own FEA for some problems, but I never wanted to be dependent on software that I could not afford to own. So, back to my questions about: How are you going to buy your own copy of ANSYS? DrD
  12. 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 of a four-bar linkage where no link is able to rotate around a full circle. My request has not generated any answers, but fortunately, I stumbled onto one. Since the definition of a rocker is a link that cannot rotate completely, it is evident that the linkage shown is in fact a Triple Rocker. None of the links is able to move through a complete revolution. If we try to rotate the input (left) link further down, it cannot happen without stretching the combination of the coupler and the output (right) links. When the input link (left side) gets to the top, again its motion is stopped by the need to stretch the coupler and output link. Thus, a figure I drew as an illustration for something else turns out to be a Triple Rocker, the item I was looking to find. In connection with four-bar linkages, some readers will have heard of Grashof's theorem. Let s = length of shortest link L = length of the longest link p, q = lengths of the two intermediate links Grashof's theorem says that a necessary and sufficient condition for at least one link to be a crank (able to rotate entirely around), it is necessary that s + L < p + q This inequality is not satisfied for the four-bar that I drew by chance, so Grashof's theorem says that none of the links can be a crank. That is precisely the condition required for a Triple Rocker (a ground link plus three moving but not fully rotating links). So, there you have it. That is an example of a Triple Rocker, and we now have the criteria for identifying such as a four-bar linkage that does not satisfy Grashof's Theorem.
  13. 4 Bar Linkage Problem

    The vector loop equations do not care what parameter you choose to assign. Just write them as I've indicated, and then put the knowns on one side of the equation and the unknowns on the other side. It is really simple. I'm not sure what you mean by a "passive joint." This is not terminology that I use. I presume you wish to use the motor rotation angle as the independent variable. This will be measured between two moving links, but that should not matter. If the motor rotation is denoted as q and the angle of one of the moving links is A, you may very well find yourself looking at some terms involving sin (A+q) or cos (q-A), but everything should still work in the same way. If you need more help, send the drawings to me in a private message and I'll look further at the problem. DrD
  14. 4 Bar Linkage Problem

    If you will go over to the Mechanics Corner blog, I think you will find the information you need in post #3, early in the series. I don't think I ever posted on a four-bar linkage per se, but the methods described there will fit for any planar linkage. The only thing special about the four-bar is that the equations can be rather difficult to solve, and a numerical solution is usually preferred. Please read through the early posts at the Mechanics Corner, and let me know if you need further help. DrD
  15. The statement quoted above seems to indicate that the motor is running all the time. But later, you say So, does the conveyor motor run all the time, or only when a load is placed on the conveyor?
  16. Triple Rocker

    Henry, as I look more at your project, it does not appear to be a Triple Rocker at all. Instead, it is a Crank-Rocker. You show the left side link making a full circle, and that is by definition a Crank, not a rocker. When you mentioned that it was designed to shake flour, that is what got me to thinking more about it. I wondered, "how is it powered?" If with an electric motor, then a crank input would be much more suitable than a rocker input.
  17. Triple Rocker

    Thanks, Henry. Nice to know that at least some one is actually reading. DrD
  18. In terms of four-bar linkages, most of them obey Grashof's Law, but evidently a few do not. Those that do not are called "non-Grashofian" or "triple rockers." I have a difficult time visualizing a triple rocker. The name implies that no link can turn a full revolution. Can any of you point me to an example, a problem discussion, or any other information regarding a Triple Rocker linkage? DrD
  19. Triple Rocker

    I was able to answer my own question. The result is posted at the Mechanics Corner, so please read it there. DrD
  20. Dear Ms. Chakraborty, Your posts so often seem like sales advertising. They describe new products, mostly in terms of benefits to the user, but tell us little of engineering interest about the product. Are you principally interested in selling thing? It seems to me that an appropriate post on this item would describe what engineering design innovations enable it to function. How do they package this capability in a suitable compact form? Please let us look more at engineering and less a promotional features. DrD
  21. Pulley and belt system

    If a value is assigned for "x" then a value can be computed for "y", but there is no unique combination that works "best." Simply choose a value for x roughly midway between the two pulleys and then mount the idler in such a way that it can move to maintain the belt tension. The idler needs to be able to move vertically, so there are basically two options: 1) mount the idler on a block that sliders in a vertical channel as a guide, or 2) mount the idler on a swinging arm that is pivoted to one side or the other, such that the arc of idler motion is largely vertical. With either of these two options, you can then push the idler down on the belt (a) by gravity (put a significant weight on the idler), or (b) preload a spring to press the idler down on the belt. For an assigned value of "x", the calculation of the exact value of "y" is rather lengthy and basically pointless since as the belt stretches, "y" will have to change. DrD
  22. weighing machine

    The original question posed was this: "what does a weighing machine measure our weight or mass?" To measure anything simply means to compare an unknown to a standard of the same type. Thus to measure a length of string, you compare the unknown length to the length of a ruler and discover that it goes, for example, 5 and 1/4 times. Thus the unknown is 5.25*(ruler length). OK, I'm sure everybody knows that part. To compare to items, they must be of the same type. Thus you can compare one length to another length, but you cannot compare a length to a time interval. You can compare one force with another, but you cannot compare a force with a displacement. One way to look at this question is to ask a second question: Do we have any means to compare one mass with another? Mass"what does a weighing machine measure our weight or mass?" is the quantity of matter, the amount of "stuff" in the material. That "stuff" includes electrons, protons, and neutrons, each of which contribute a little bit of "stuff." The obvious answer is no, we cannot compare masses. We cannot count the number of protons, the number of neutrons, and the number of electrons in on body to compare with those in another body. When we talk about weighing something, we are determining its weight, which is a force. It is important that we keep in mind that weight is a force, the force of gravity on the body. As I mentioned in the earlier comment on this topic, there are basically two types of scales, the common term for a weighing machine. There is the beam balance type, where a known weight is moved along a beam in order to balance the beam and create an equilibrium situation. There is also the spring scale in which an elastic member is deformed, and the amount of deformation is an indication of the weight applied. When we weigh something, we are comparing forces and the torques developed by those forces. We say the forces are equal when we have established an equilibrium condition, and we can do this because this requires that the sum of forces be zero. In the beam type balance, we put an unknown weight in the pan, and then adjust the known weight so that the upward force through the mechanism is equal to the weight; this is the required equilibrium condition. All of this is a matter of comparing forces. In the spring type scale (including the modern electronic read-out strain gage based scales), we are deforming a spring in order to support the weight of the test object. The measure of that deformation (a displacement) is taken as the measure of the weight. This is true wither the displacement is many millimeters (as in the common fish scale) or only a few thousandths of a millimeter as in a strain gage scale. To go one step further, consider the following thought experiment. Imagine a scale (or either type) under a low shed roof. Now, put an empty balloon on the scale and weigh it. It will weigh very little, even if it is a rather large balloon. Next step, begin to inflate the balloon. For a while, as the balloon swells, you will only see a tiny increase in weight due to the weight of the air enclosed, but keep going. Eventually, the balloon will begin to bear against the shed roof, so that with increased air pressure, the balloon pushes up against the roof and down against the weight pan. After contacting the shed roof, the addition of even a small amount of air to the balloon will show a marked increase in indicated weight. Does this mean that the last little bit of air you added was much heavier than that previously pumped in? No, the last bit was just like the first part. It means that your scale is no longer indicating weight (gravitational attraction), but is showing the effect of the pressure loading from the internal pressure of the balloon. Add a little bit more air, and you will see a significant increase in indicated weight, but again, this is not truly weight but the force of air pressure. Even at this advanced stage in the process, the actual mass of the balloon and the air contained are very small, but the indicated weight is quite large. This is because it is no longer showing weight, but the force of the applied air pressure. The point of the thought experiment is to show that it is downward force that is read by the scale, not mass sitting in the pan. The answer to the original question is, "the scale measures weight (a force), not mass." DrD
  23. weighing machine

    For starters, we might consider just what sort of "weighing machine" you have in mind. There are basically two types: 1) the beam balance, where the position of a sliding block is adjusted to the point where the moments on the beam are in equilibrium; 2) the force cell (usually a strain gage device) that is actually a spring scale with a very stiff spring. Either of these can be calibrated in either force or mass units, but they operate on different principles (or do they?), so do they measure the same quantity? DrD
  24. #42 Gear Pair Problem

    As I write this, there are 1539 views, and yet, no one is moved to make even a single comment. What does it take to motivate you folks to participate? Not even a single "Wow," just nothing. DrD
  25. #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. Therefore, the pinion will rotate with ωp angular velocity in clockwise and the gear ωg in counter-clockwise. There is a load TL against the gear motion. The bearing friction both in pinion and gear are considered by means of linearly-viscous damping coefficients cp and cg for pinion and gear, respectively. The friction between the gear mesh is neglected at this point. The moments of inertia of the pinion and the gear are Ip and Ig, respectively. Moreover, the radii of the pinion and the gear are rp and rg, respectively. My question is what the output torque To is because I want to find the efficiency of this gear pair. I have tried four options for To and simulated them in MATLAB, but I have not found the correct results yet. Followings are the explanation of each option I tried for To. The sketch in Figure 1 and the two paragraphs following are exactly as posted by the original questioner. There follows on PF a long sequence of responses and more questions, but he still seems no closer to understanding what is going on. Let us see what we can do to help him. Before someone thinks badly of me for not helping him, let me say that I did give several hints, but the rules of PF forbid me to actually post an analysis. I have been severely scolded in the past for doing just that. 42 Gear Pair Problem.pdf