I don't imagine you'll need all that much torque unless you've messed up with the centre bearing and rollers. It's more about getting from 1.8 degree motor steps to whatever the chosen increment is (5 degrees) in a whole number of steps. Those silly-cheap geared steppers may be worth a try though - like you say a little backlash, but probably not enough to be a problem here.
The center bearing right now is a 1/4" bolt but I may step that up to 3/8 or 1/2 or m10.
I haven't installed the bearing (it actually seats into a 3d printed part, not the wood) but I've been testing the platform with the non-rotating casters I got for this purpose and the force required to overcome inertia is more than I imagined. I got a luggage scale and will test about how much force is required to get the thing moving.
My hope is that a stepper moving slow enough with smoothly ramping acceleration will be able to get the thing moving and stop it accurately. The tic software allows you to adjust all this.
Regarding the gear, I decided to go with this design for a few reasons. The first is positional accuracy - a belt could slip even if it is unlikely in a well optimized design. The second is strain on the axle and motor mount - my thinking is the tension required to keep a belt snug is much more than that required to get a gt2 fiber reinforced belt taut. These gt2 belts have very little stretch to them.
The third is that it creates a mechanical advantage; by my calculations, with the cheapest tic driver and a 20 dollar NEMA 17 size motor I get .23 pound feet, but with the gear ratio I'm working with now I have 2 pound feet, which if I'm not mistaken is equivalent to 4 pounds at two feet, which is where I'll be measuring later. The most powerful tic board can put out 4 amps to the motor, and looking at the stepper website the most powerful 4A stepper is only 2.5 foot pounds. The mechanical advantage can be anything you want, of course - I'm assuming 25T/225T, but if I did 10T/216T I would be looking at 5lb feet. Leverage is no joke.
The most important reason to use the gear, however, is that it allows exact stepping of degree increments without microstepping. From what I've read
here, holding torque is vastly diminished when microstepping, so the approach of simply microstepping your 1.8 degrees /32 to .05625 degree increments comes with a 95% reduction in holding torque.
Part of me is tempted to design this thing just using a beefy motor, however, there is a certain appeal to the simplicity, and you don't need to spend money on a 3d printed gear, a drive gear, a belt and some kind of sliding motor mount. The python code I have written can accommodate non-whole numbers for positioning, it just rounds them to the nearest integer. So I may explore that, it would definitely be a more elegant design if it worked.
The most fun part of the build has been trying to source a homing switch. In cnc applications limit switches are normally used to sense proximity are unidirectional, in the sense that the obstruction the switch senses comes from one direction. In a rotational application, the switch might be activated by clockwise or counterclockwise movement. Ideally, a non contact switch would work. I got some big weather sealed roller limit switches but I felt they were too substantial. The best solution I've come up with is to use an
optical interrupter switch, which shines an IR LED through a gap and senses when the connection is broken. According to the datasheets for these products, the flag which blocks the LED can be quite narrow, perhaps under 1mm wide, so it can be used for this application, but it should be as far from the axis of rotation as possible.
I'm not a great mechanical designer but I am having a ton of fun designing this thing and building it out of scraps from my basement. There's something very appealing about making a device with better than .1 degree accuracy literally using trash.
Regarding angular resolution - I think for speaker measurements, my suspicion is that only at the front of the speaker and only at high frequencies is this kind of accuracy even close to desirable. The most important thing is to be able to quickly capture polars to make design easier.
