4-dimensional version of the 6 simple machine.

[andykhang]

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?

[Eebster the Great]

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

[cyanyoshi]

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]

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)

[cyanyoshi]

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]

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."

[Eebster the Great]

Maybe something like a kinematic pair?

[jewish_scientist]

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

[Eebster the Great]

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.