4-dimensional version of the 6 simple machine.

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andykhang
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4-dimensional version of the 6 simple machine.

Postby andykhang » Sat Jan 27, 2018 4:13 am UTC

Just read about it slightly make me wonder: How many simple machine is needed to do all thing in a 4 dimensional space, or alternatively, just how many way is there to applied force in 4 dimension? I know that it's 0 for 0th, 1 for 1th and 3 for 2th if I'm correct?

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Eebster the Great
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Re: 4-dimensional version of the 6 simple machine.

Postby Eebster the Great » Sat Jan 27, 2018 5:37 am UTC

I'm not sure there is any technical definition of "simple machine;" it's kind of a classical idea.

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cyanyoshi
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Re: 4-dimensional version of the 6 simple machine.

Postby cyanyoshi » Sat Jan 27, 2018 5:49 am UTC

F=ma is still intact no matter if you're in 1D, 2D, or 3D, so the main thing that changes when going to higher dimensions is more involved rotational dynamics. Torque is best understood as a bivector rather than as a (pseudo)vector, and angular velocity would have n(n-1)/2 degrees of freedom for n-dimensional space. I can't really say for sure how this would affect the engineering principles of how to get some of this stuff to work (like, would an axle need to be a plane instead of a rod shape?), but Newtonian mechanics should still work just as well in case you want to analyze stuff.

andykhang
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Re: 4-dimensional version of the 6 simple machine.

Postby andykhang » Sat Jan 27, 2018 12:09 pm UTC

So, again, if you boil it down, you only need how many machine to have it all? (In term of movement of force, I mean)

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cyanyoshi
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Re: 4-dimensional version of the 6 simple machine.

Postby cyanyoshi » Sat Jan 27, 2018 4:27 pm UTC

What is or isn't a simple machine is pretty arbitrary. When you get down to it, most are just rigid bodies of varying shapes and friction coeffecients used for different purposes. The one exception is a pulley, which is basically a wheel and axle plus a flexible rope. Why not consider a rope to be a simple machine?

jewish_scientist
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Re: 4-dimensional version of the 6 simple machine.

Postby jewish_scientist » Mon Jan 29, 2018 3:25 am UTC

I would define a simple machine somewhere along the lines of, "All mechanical processes are the result of one or more simple machines acting in conjunction."

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Eebster the Great
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Re: 4-dimensional version of the 6 simple machine.

Postby Eebster the Great » Mon Jan 29, 2018 7:30 pm UTC

Maybe something like a kinematic pair?

jewish_scientist
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Re: 4-dimensional version of the 6 simple machine.

Postby jewish_scientist » Tue Jan 30, 2018 6:55 pm UTC

It seems to me that kinematic pairs are a way to connect two simple machines in order to form a complex machine.

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Eebster the Great
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Re: 4-dimensional version of the 6 simple machine.

Postby Eebster the Great » Wed Jan 31, 2018 5:14 am UTC

But that's not correct. Simple machines do nothing on their own; they need to be linked to some other object. A wedge does nothing without a floor and something to lift. If you slide a wedge along the floor underneath a load, lifting that load, then you have mechanical advantage. Here, it is the linkage between the wedge, the floor, and the load that is actually important. On the other hand, if you fix the wedge to the floor and push the load up its slope, the wedge suddenly becomes an inclined plane. The only difference between these two simple machines is the linkage. Kinematic pairs are actually more fundamental than simple machines.

I think this becomes even more apparent when you consider the pulley or wheel-and-axle, which I always thought were somewhat silly simple machines.


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