The closest thing I've been able to find so far is a servo motor from a company in the US:
www.midwestmotion.com. With 1000 count per rev encoder attached they quoted me something like $300US, which is a bit out of my range while I'm still experimenting. And it needs a 24V PSU, which I don't have.
But put that aside a minute and presume that I'm using a DC motor. For position feedback I was thinking about a single turn pot on the axle at the opposite side of the wheel from the motor. I guess I need a pretty good pot with a mechanical range of about 350 degrees, and a linear accuracy of 0.14%, then using that to generate a 10-bit digital position reading... is that all unrealistic? I just don't know much about encoders and position feedback. I know roughly what they are, but I don't know how to go about finding what I need. Sorry if I haven't done a good job of explaining this. I guess I wasn't realistic in imagining that it would be fairly inexpensive to get the kind of pot I would need. Wow, that last sentence could really be taken out of context!
I think part of my challenge is that I have a very specific idea of what I want to accomplish, but I'm still learning a lot about how to get there. I'm coming from an intense music background, much more than engineering. After reading the comments about newbie posts on this forum, I guess more members like to get a lot of info out of newcomers rather than vague questions, so here it is...
I'm trying to build the right arm of a trombone robot. The hardest part of building any automated musical instrument is keeping in mind that mechanical noise must be kept to a minimum. The next hardest part is copying motion that humans have had hundreds of years to develop. There's some video on the internet out there from some engineering students at Hosei University who made a trombone robot, but their strategy for the right arm was all wrong.
To keep the weight of the non-trombone parts to a minimum, my design is for a large wheel (or spool, if that helps you visualize this better) with a slightly larger circumference than the operational length of the trombone slide. Lines attached to the handle of the slide will pull the slide in opposing directions. The motion of these lines is redirected and attached to the spool so that as one line wraps, the other unravels. This keeps enough tension in the lines to keep them in place on the mechanism, and also readily available for instantaneous motion transfer from the wheel/spool in either direction. I hope that makes sense, but if not I'll draw you a picture.
I've calculated conservatively for the weight of the slide, its friction, the weight of the wheel/lines/etc, and the force required to move it from top speed in one direction to top speed in the other. The answer is about a 1.4Nm torque requirement. This takes into account that the slide has to be able to move 60cm in a tenth of a second. And it, ideally, has to be able to stop within a millimetre anywhere along that 60cm (okay, I'd be happy with 2mm). This is what it'd take to build the equivalent of a professional trombonist's right arm - I'm well aware that my first prototype might fall short of that goal, but I'd like to get as close to it as I'm able on the first try. Hence asking as many questions as I can before I get started building the thing.