I was thinking about differential gears having discovered them in Lego Technic recently and been impressed by there working.

 

Using only simple cogs that turn along the conventional axis. Shafts that are cylindrical, connect the gears together, don't move around except rotation along their usual axis, the usual three input\output differential gears and rigid parts that hold things in place what sort of logic could one construct?

 

When two gears are connected the 2nd turns at the same speed as the first but in the other direction, like a multiplication by -1. A trivial setup with differential gears allows two inputs and one output where the speed of the output is the average of the input speeds. Thus we could imagine doing mathamatics with such systems.

 

Below are examples that should be possible with the design constraints described above. ✔s show ones that I have confirmed work.

i or i1, i2, i3 etc... represents inputs.

o or o1, o2, o3 etc... represents outputs.

n or n1, n2, n3 etc... represents constants, in a programming languege you might think of thease as literals, they would usually be defined here as for example the number of teeth on a cog.

 

✔ o = i

✔ o1, o2, o3 etc... = i

✔ o = i * -1

✔ o = i * n

✔ o = average(i1, i2) = (i1 + i2) * 0.5, this uses a differential gear

✔ o = i1 + i2 = average(i1, i2) * 2

✔ o = i1 - i2 = i1 + (i2 * -1)

 

The following use speed 0 as false and 1 as true

o = not(i) = ((i - 0.5) * -1) + 0.5

✔ o = i1 uxor i2 = i1 - i2

o = i1 uxnor i2 = not(i1 uxor i2)

etc...

 

uxor (uneven xor) truth table:

i1  i2  o
0   0   0
1   0   1
0   1   -1 - uneven
1   1   1

 

Conditions such as the 'if' used in programming requires for example the a logic gate 'implies'. I don't know how this could be done.

 

There couldn't at this point be flow controll, recursion, storing of state etc... or could there?

 

If the ouptut to a differential was optionally scaled and then connected to it's input then the mechanism locks up. Why this occurs is more apparent when it is built.

Edited February 12, 201114 yr by alan2here

You are considering ideas associated with analogue computers. Have a look at

http://en.wikipedia.org/wiki/Analog_computer

Thanks. Although it didn't answer many of my questions.

Edited January 20, 201114 yr by alan2here

Can't really add much more. Analogue computing doesn't get much of a look in these days. If interested looking up Babbage's difference engine and perhaps an early application might provide you with some ideas.

http://en.wikipedia.org/wiki/Difference_engine

 

http://en.wikipedia.org/wiki/Analog_computer#Mechanical_analog_computer_mechanisms

 

On second link go to section "Mechanical analogue computer mechanisms". Then click on link "World War 11 mechanical fire control computer mechanisms". Then click on "section 2 op1140-2 . pdf" and you will get some information regarding use of mechanical differential gearing.

Edited January 9, 201114 yr by TonyMcC