I always appreciate a good discussion.
Ohm's Law works at all frequencies. It's not different for AC. RMS semantics can muddy the waters but do not fundamentally change anything.
You are, of course, correct. My 3dof model is based on the assumption that the nerves don't have infinite bandwidth. By ohms law, there are two degrees of freedom at any infinitely small point in time. I think the nerves send signals based on the average voltage/current over a short amount of time (wild guess: 10ms). I also don't think it matters whether the current flows in or outward, so expressing the strength of the waveform in rms sounds like a reasonable choice.
It's not surprising you're confused by the initial diagrams, because I didn't understood this at that time. The way I used negative voltages was bogus. I was under the impression that I could do everything without entering the time domain, not true.
I have not considered induction/capacitance. I don't think it is relevant at this point in the development process. Somewhere in the future I would like to exchange the sine wave for an arbitrary waveform, then these concepts might become relevant. In another thread, someone mentioned the term energy saving curve, you mentioned 444/555/666/777, the coyote uses a square waveform at high intensity with low duty cycle, I believe all of these are exploiting the same mechanisms.
Correct, until you connect the two channels in tri-phase. Then, the amplifier absolutely regulates the difference between A+ and B+, indirectly, through the fact that A- and B- are locked at the same potential. If I understand correctly, your entire approach is for tri-phase. Maybe you're saying the same thing in different words.
Yes that was my point -- with three phase, the mathematics are clear because the neutral is regulated. With four separate pads, the mathematics become more murky... I suspect 4 pads (with 2 driven channels) still has the same number of degrees of freedom as 3 pads with a shared common, and the same unit circle math is still appropriate for driving 4 pads. But this is just my intuition, I didn't do any math to confirm this.
Is this due to what I am pointing out? I do not understand your model enough to say. Or maybe most of the confusion lies in the rms semantics. Any talk of current canceling out at the common without regard to phase implies not rms.
I believe the issue is what edger477 pointed out. If I use a star resistor network instead of a delta resistor network, it becomes obvious why the observed behavior happens. Specifically:
If the two waveforms are 180° out of phase, the bottom resistor has an rms of zero. This is what happens at FileFlax bottom position.
I worked out the math on paper to see if there was a relation with the calibration parameters, but this turned out to be a dead end. The math works, but there is no obvious relation with the calibration parameters.
I make no attempt at calculating body resistance. The phase diagram is based on the vrms between the three pads. What's the current? I don't know and I don't think there is a general solution. My solution is to give the user lots of knobs to adjust the current based on the position.
SIMPLER OPTIONS
These options are indeed simpler, but have some limitations...
Why not just open Audacity and compute (L+R)/2 into one track, put that on the head, and turn the volume dial on your box for direct control? Put (L-R)/2 on the other track and connect it wherever you want, also with its own volume knob. Then you don't need to generate a new e-stim file for every recalibration (moving/changing electrodes).
If the two channels are far apart and no current flows between, this does indeed fix the problem but you also severely limited the number of different sensations that can be felt in the cock. If the channels are close together, it will act like a three phase setup.
You can even tri-phase with (L+R,L-R)/2. Again, put (L+R) on the head for its own volume control, and put Common somewhere less sensitive (the butt! is great). (L-R) goes anywhere that makes a nice push/pull with the head. Super simple, no more head overload!
This approach works, but:
It does so by chopping off some parts of the unit circle. Whether these sensations are important, I don't know.
It transforms the input in a nonlinear way. If the author intended to stim the three pads in a particular order, or hit the peak of the stroke at a particular time, those timings are changed.
There is only one calibration parameter. This might be sufficient, it might not.
Even if this did solve the strong head stim problem without any drawbacks, I still think my approach has several advantages that make it worth exploring.
I made this diagram to show the relative strength (rms) of the three channels (left, right, center) for my transformation, conditional on the script position (alpha, beta). This might be useful for understanding my choice of coordinate system and the degrees of freedom. If the right point of the triangle is head, then right is max head stim (fileflax top position), left is max ball stim (fileflax bottom position), up/down moves the sensation between the bottom and top of the shaft. The third degree of freedom (magnitude) is not shown.
Feel free to ask more questions.