Pericyclic Gears

Pericyclic gears offer the possibility of obtaining high ratios for 3D printed gear boxes for use in DIY telescope drives, at least for the smaller models, say, up to 12 inch apertures.  There are working examples that make me want to try one.

That center, yellow, gear 'wobbles' or 'nutates' and only engages a few of the stator teeth (left most gear) at a time and does the same with the output gear (right most gear).  But there are different numbers of teeth between each of the interacting surfaces.  As such, the nutating gear cannot fit exactly into the fixed stator gear, so must rotate slightly to fit the few teeth it engages.  On the other side of the nutating gear, the number of teeth are again different which means the output gear must move a slight amount to fit the few teeth it engages.  The overall gear ratio from input to output is given by a strange looking formula  where n1 is the number of teeth on the first gear, n2 on the second, etc.

I am interested to use NEMA 17 stepper motors to drive ALT/AZ (or RA/DEC) axes on a small telescope.  They are inexpensive and easy to control but they need torque amplification and resolution enhancement that gear boxes can provide.

Consider they usually come in 200 step/rev models.  That is 1.8 deg per step - too coarse for telescope pointing and tracking.  They can be controlled to at least 16 microsteps per step (32/step is possible, too).  At 16 microsteps we are down to 6.75 arcmin per step - pretty good for pointing small telescopes with wide fovs but a bit coarse for tracking, plus we could use some torque amplification.

Consider a 50:1 gear ratio.  With microstepping we can get 9  arcsec/step which is excellent for pointing and requires one step every 0.6 seconds for tracking.

On the other hand we would like to slew much faster.  To get, say, 8 deg/sec slew (about what a C-14 does, the 32-in is at 4 deg/sec), we need an input speed of about 10 rpm from the NEMA motor at the 50:1 ratio.

The NEMA 17 motors are capable of 50 N-cm of torque.  At 50:1 (minus inefficiencies) we can hope to get about ~25 N-m which should be sufficient to move small telescopes on roller bearings.