Stepper motors - stride angle?

The notation 5.625°/64 indicates that the motor has a step angle of 5.625°, and the output shaft is driven via a 64:1 gear ratio. If you look at the picture of the motor, you can see that that output shaft is offset from the center of the unit, also indicating a geared output shaft.

So, following through, the motor has 360/5.625 = 64 steps/rev, but the output shaft has 64 steps/rev * 64 gear ratio = 4096 steps/rev, or 0.088°/step

That should be plenty of precision for you!

5.625 = 360 / 64, ie, there are 64 steps per revolution.

However, the actual number of steps can be some multiple of that, depending on how you energize the windings. 2 to 4 times that number is easily achieved, and microstepping drivers can provide substantially finer interpolated resolution.

Your specification is not very clear - you seem to say both 2 degree steps, and 2 degree accuracy. Probably you want 2 degree steps with an accuracy of some fraction of that.

64 steps is relatively course - 200 step motors are widely available.

If you are looking at mechanical reduction, consider toothed timing belts and sprockets instead of gears. They are have less critical needs for mechanical alignment, and run quieter. If your system must operate in both directions without slop, the fact that timing belts suffer minimal backlash when the direction of torque is reversed makes them strongly preferable versus gears.

Two easy solutions:

• Most stepper drive IC's will support 1/2, 1/4, 1/8th or 1/16th micro-stepping, so you can divide the number by that to get much better resolution.
• Use gearing / belts