Math Gear Clock: Time Told by Geometry

简介

A standard quartz clock movement drives the yellow minute arm directly from its minuteshaft. A visible two-stage cycloidal gear train (12T:36T, then 15T:60T = exactly 12:1)reduces that motion down to a large 60-tooth hour wheel carrying the blue hour arm. Botharms sweep clockwise, tracing spiral curves across a Ø180 mm face packed with skeletonizeddecorative gears, ringed by engraved numerals, on a sculpted Art-Nouveau pedestal.Why this arrangement matters: the movement only ever sees its normal load plus lightreduction-train friction. Designs that gear UP from the hour output multiply torque demand~12x and stall quartz motors. This one is horologically correct.The gears are true clockmaker's cycloidal profiles — epicycloidal faces on the wheels,radial flanks with rounded leaf tips on the pinions — which tolerate FDM printing and lowtooth counts far better than involute gears (a 12T involute pinion undercuts badly; a 12Tcycloidal pinion is happy).PRINT THE COUPON FIRSTPart 09 is a fit-test coupon (~25 g, under an hour) that tests every critical interfacebefore you commit ~180 g to the clock: 608ZZ bearing pocket, M8 bore, both movement shaftbores, the arm key joint, movement pocket width, the hour-wheel journal (with a loose testring), M3 pilots, decorative peg fit, and a 100.0 mm calibration bar for printer scale.Nine pass/fail checks with fixes are in README_09_FIT_TEST.md. If all nine pass with yourprofile, the clock will assemble.WHAT'S IN THE FILES22 printable parts…