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03:01
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Q: Is there an electronic version of this mechanical system?

CyberstratorI'm asking this question in this way because I don't know any other way to explain what I'm trying to do. Imagine you have 2 gears, gear A and gear B, gear B is 3 times larger then gear A. So, if gear A rotates one full turn, gear B rotates 1/3 of a turn. gear A is the input and gear B is the out...

Is this a thought experiment or are you actually trying to make something? If the latter, you should really just say what it is you're trying to make.
Possibly what you are looking for is a phase locked loop with gain?
"no pulses or wave forms or the likes." An output switching between 3 states is, by definition, a waveform consisting of pulses.
"can it be made in an electronic version" - Yes. Any more questions?
I agree. This is a common phase resolver with a user transfer function for resolution with a counter ratio of 3.
03:01
So, in short, are you asking how to make a circuit that counts directly in ternary? If so, you may wish to edit your question to put that right up at the top, perhaps with an expression of the action in more normal notation (i.e., it looks like you want to count 00, 01, 02, 10, 11, etc., or the equivalent). As it stands now it's hard to pick out the actual question from the exposition.
I've updated the question with more clarity, I hope?!
You are repurposing + and - as numbers which makes interpretation difficult. + and - are unary operators, Then using 0,1,2 also allows -1,-2.
balance ternary uses -1, 0, +1 or minus one, zero and positive one. I just used the minus, zero and positive to represent them.
"I'm looking for to just use straight DC voltage only, no pulses or wave forms": I agree with the phase nature of the problem which implies a periodic waveform. You won't be able to do this with dc. Its phase is always 0 degrees.
thats why I was just looking at it as different voltages instead of some waveform or signal or something, just 3volt, 6 volt and 9 volt.
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forwards or backwards the sequence is the same ? If -1, 0, +1, -1, 0, +1… is forward, what is +1, 0, -1, +1, 0, -1…? The latter is not the same, but the reverse of the former.
yes, your right. that's the beauty, instead of trying to move from -1 to 0 then to +1 then back through 0 to get to the -1 you can just roll over from +1 to -1 which is exactly what the number system does as it counts up or down. everyone is trying to make a three state switch that has 3 position that is limited in how far it can move like left to right, a gear that rotates just rotates back around, stepping through one direction clockwise or counter, you can count as ternary does.
Hm. Transfer some charge to an initially uncharged capacitor: a voltage results. Transfer more of "the same charge", have break through in any component with a suitable characteristic: little charge/small voltage results. Not quite, but what if that breakdown was through an inductor? Ho hum.
another way of looking at is if your on +1 how would you get to -1, just move back or forward one step and you never had to pass through zero
Wait, there is something "electronic" quite like positions of gears: phases of related sine waves. You can keep shifting them in the same direction on and on.
Using dc voltage steps requires energy = dqdv. Stepping directly back from 9V to 3V requires triple the energy. Phase shifts do not require nearly the energy input to accomplish. Sinewaves are direcly related to a rotating machine and so are better suited.
03:01
but the question then become how would you know if your at the 1/3 or the 2/3 or 3/3 position, plus how complex would that circuit need to be to make that phase transitions? a single wire on one end as the input and the other end as the output can easily go from 3v to 6v to 9v but you would have to input 3v then 6v then 9v. but to have a 3 volt input ONLY that would step the input +3 volts or -3 volts that would roll the output over again to 3v from 9v, 3,6,9,3,6,9,3,6,9 - forwards or backwards 9,6,3,9,6,3,9,6,3
ok if sine waves are better then how would that be implemented then? I would need two sine waves put together to create AND/OR gates. what kind of circuitry can do that and how complex would it be?
As hinted by greybeard and RussellH, sine waves can be used in that way. Specifically, two must be used, one as phase reference, the other for signal representation. Which is just such a representation as Hoagie mentioned: resolvers use AC angles (phasors) to correspond to mechanical angles. Doing arithmetic on such a representation is nontrivial and an exercise for the reader, but examples include switching in an all-pass (phase shift) network, which will "overflow" naturally as desired, without using digital values (the angle is continuous).
but the issue I see with resolvers is that they still have to pass through zero to get to the other side because their using the center point as the point of revolution. a sine wave will still come out as going from positive, zero negative, zero then back to positive. you still have to pass through zero. it would look like this if 6 is zero and 3 is negative and 9 is positive = 3,6,9,6,3,6,9,6,3,6,9,6,3 which is not a rotation around the number like this from the outer edge = 3,6,9,3,6,9,3,6,9,3,6,9

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