A picture from a previous repair shows the foot pedal’s innards:
The top cover pivots on small studs that lock into the front of the case. A projection on the cover passes behind the bar near the top of the picture and presses the roller forward as the cover pivots downward under foot pressure.
The bar has an absolute maximum travel of about 15 mm, although it’s impossible to measure in situ with the cover in place:
The shaft in the middle of the carbon rheostat aligns the bar and actuates the full-speed switch contacts on the far right (not shown here). The compression spring vanishing into the ceramic body pushes the bar back against the projection on the top cover and ensures the whole affair turns off with the pedal released. The brass plate connects the two carbon buttons on the ends of the disk piles, which is what controls the motor speed from low to high, with the conical spring applying pressure to the piles as the bar moves forward:
The conical spring compresses about 4 mm after the brass plate contacts the buttons and has about 2 mm of overtravel after the shaft touches the full-speed contacts.
The carbon rheostat in the crash test dummy machine’s foot pedal works better than the much-repaired one from Mary’s machine, with smoother low-speed control and slower starts.
The resistance varies from about 1 kΩ with the most gentle of button touches down to about 30 Ω just before the full-speed contacts close. That’s across 4 mm of travel, so it’s rather sensitive. Most of the range seems to produce 300 to 50 Ω, more or less, kinda-sorta.
Which explains why my repairs were unavailing: the carbon piles must produce the proper resistances as the bar travels over that short distance. Changing the pile length, as happens when the disks erode and I rebuild parts, changes the resistance.
The unloaded motor draws about 300 mA regardless of the applied voltage, which suggests that the motor really wants to see a variable resistance, not a current source. More measurements are needed…
The Smell of Molten Projects in the Morning 
Hmm, a few years ago I built a bobbin winder for Julie’s loom. Got a used motor from the sewing machine repair place, and drove it through a rheostat foot pedal purchased some years before. I’m not clear just what the carbon pile system is supposed to improve over the rheostat, but then I never did much sewing. Is the pile control that much better than the wire-wound system?
Looks like all you need is a 100W. 100V DC opamp for the motor controller. [grin]
Which, it turns out, is actually a thing: Kepco BOP-100.
Right now, the 1 A BOP-100-1M is half the price of the 2 A -2M version, a BOP-200-1M could goose the motor with 200 V, and they’re all way out of my range.
Given that I need just a voltage-controlled DC supply, there ought to be a way…
I vaguely recall various Kepcos, though Harrison/HP was pretty common at work. [grin] We had some units the size of a dorm-room fridge for burn-in. The chambers only had AC, no heaters needed…
Back the the ’70s, Crown did a DC-300 amplifier as one of the first of the overpowered stereo system components. The marketing material said it was also useable for things like shaker tables and other such. The first version was slightly less than stable with a reactive load. I had a chance to listen to one driving electrostatic speakers for several hours, and it got painful after a while. It was much happier with conventional speakers. Supposedly, the DC-300A fixed the stability problem..