DrD

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

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

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

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

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?

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

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

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

Henry, your comparison of authors between rabbits and moles is very funny! Thank you. DrD

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

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

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?

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.

Thanks, Henry. Nice to know that at least some one is actually reading. DrD

I was able to answer my own question. The result is posted at the Mechanics Corner, so please read it there. DrD