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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



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.




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DrD, any idea what kind of apparatus that using this mechanism?


Side note: (you could consider not related to this blog)

Back in college, I have a professor who is really imaginative and often create problems that unlikely to exist in real life.

He taught mechanics of materials back then, and since it was a compulsory subject, everyone gets it.

His exams would often feel like a massacre because the questions were often very different from the textbook or outside of common logic.

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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?

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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.


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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.



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