Gears and Horology
I've been fascinated with clocks for YEARS... One of the first clues that you might be someday be an engineer is if you take apart a geared alarm clock as a kid. Of course, these days, alarm clocks seldom have gears!
In high school, I attempted making a wooden clock, based on an article that appeard in an old Fine Woodworking (?) magazine. That attempt was not successful.
Now that I have a 3D printer, the task of printing gears and possibly even making a geared clock seemed to be a possibility.
See this web page for a PDF explaining a lot of the math behind clocks and especially escapements:
https://www.abbeyclock.com/EscMechanics.pdf
See this web page for instructions on how to use the gear script in Fusion 360:
https://productdesignonline.com/fusion-360-tutorials/create-custom-3d-printable-gears-in-fusion-360/
Notes from that page:
MINIMUM - Put at LEAST 13 teeth on the gear.
First Gear Experiment 10/20/23
The first experiment was simply to see if I could print gears and a base that would work together. Using the Fusion 360 script, I laid out a 16T and a 32T gear, then measured the distance needed to place the pins, and designed a simple plate to hold the assembly.
I used the Python spur gear script. The C++ version didn't seem to load or run. ??
Example used a module of 2. That seemed to work well for the 16T and 32T gears.
I used the recommended .15mm backlash from the web page. Worked fine.
Used recommended .9mm Root Fillet Radius for 32 tooth gear. This was dropped in half for the 16T gear.
I printed the gears with a thickness of 2 mm, and hole size of 7mm (for a 1/4-20 bolt). This was sufficient for a proof of concept, but may want to be thicker for a working mechanism with multiple gears?? Or maybe this is ok to keep weight down? Web page suggested 5mm thickness.
With a 2mm thickness for all three parts, it still took over 3 hours to print the base and 2 gears.
Using the above web page, I was able to print a 16T and 32T gear and base that worked on the 3D printer.
The gears were printed in PLA.
Second Gear Experiment (10/29/23)
The second experiment is significantly more agressive than the first, which was simply to test the viability of printing gears on a 3D printer. The objective of the second experiment is to create something closer to a clock. The device will use a stepper motor to power it, instead of an escapement. The point of the second effort will be to design a gear train that will provide timing for a clock, and demonstrate that the gears can be arranged successfully.
Here's a web page that provides details on driving a stepper motor with an Arduino:
https://www.makerguides.com/a4988-stepper-motor-driver-arduino-tutorial/
Here's an inexpensive stepper kit:
$14, gives 5 motors and 5 drivers. Runs on 5V (though separate supply for motor may be needed!).
Unfortunately, these are SMALL motors - probably not much torque. They are geared, which will help the torque, but slows down the motor. 64:1 reduction? They mention 10RPM... Unknown what the max speed is.
The above kit also has NO HEATSINKS - so they may not run long continuously. Finding DIP chip heat sinks could be a challenge??
I decided to order the larger, stronger Nema 17 stepper motor, and the driver for it that can be controlled with an Arduino:
Stepper: https://www.amazon.com/dp/B07LF898KN?ref=ppx_yo2ov_dt_b_product_details&th=1
The stepper is rated for 1.5A, 2.3ohm coil resistance, 12-24V, with 63oz-in of torque.
The stepper driver is: https://www.amazon.com/dp/B07G15Z31B?psc=1&ref=ppx_yo2ov_dt_b_product_details, based on the A4988 stepper driver chip. Hopefully these will be sufficient to drive the stepper under continuous usage (though at least at a very slow speed of 1 RPM.
The stepper motor will be operated at the speed of the "second hand" of the clock, then two successive 60:1 gear reductions will provide minutes, and hours. Of course, it's cheating to use the Arduino to time the stepper to operate at 60 RPM, but the point of this experiment is the gear reduction, not the timing of the clock. The Arduino could just as simply be connected to an LED display to achieve a digital clock - but the gear train will look "cooler". <grin>
A significant detail missing from this experiment will be making any effort to have clock hands with a common axis. This clock will borrow the concept from "Making Wooden Gear Clocks" (from the editors of "Scroll Saw Woodworking and Crafts". The clock on the cover of that books has fixed hands, with the gears behind the hands rotating to indicate the respective seconds, minutes, and hours. This arrangement allows for excusing the arrangement of the gears to not overlap at the hands, tremendously simplifying the gear reduction and placement design process.
As simple as the project is - there are still a number of factors to be taken into consideration:
The gear train must have two sets of 60:1 reductions.
With each reduction, if the first gear turns clockwise, the next gear will turn counter-clockwise. Therefore an even number of reductions is required to result in the motor, the minute gear, and the hour gear all turning clockwise.
The ordering of the reduction must progress from smallest reduction to largest reduction to keep the pins moving further outside, so that the pins and gears don't interfere.
The following gear reduction stages were selected:
Motor - spinning at 1 RPM
2 : 1
2.5 : 1
3 : 1
4 : 1 This will produce the "minute" wheel.
2 : 1
2.5 : 1
3 : 1
4 : 1 This will produce the "hour" wheel.
The gears used will be:
16T gear with hub to mount to motor with set screw
32T 16T
40T 16T
48T 16T
64T 24T This gear will indicate minutes
48T 24T
60T 24T
72T 24T
96T Single gear will indicate hours.
Each gear has it's own pin. The pins are arranged in a clockwise order around the base place.
The "pitch diameter" is a construction line or imaginary diameter about equidistant between the peak and valley of the teeth. This diamater is used to calculate where one gear will interact with the next. The pitch diameter results from the module (selected to be "2" for these gears), and the number of teeth. In this case, with the gears designed in metric, and using the Fusion 360 script - it conveniently works out that the pitch diameter is 2mm * number of teeth.
Ideally, the spacing of the gears should defined as half the sum of the larger and smaller pitch diameters of the two gears. To allow a bit of buffer, I added an extra 1mm of space to the sum of the pitch diameters.
The gears were printed with a hole diameter of 4.4mm (to fit an 8-32 screw to be used as the "pin"). The gears were all printed at 5mm thick (so total of 10mm for a combination gear). The gear layout in Fusion 360 places the gears at the "origin" of the design. For reductions, the larger gear was created first, then the smaller gear (both with thicknesses of 5mm), and then the small gear was raised 5mm on the z-axis. No additional spacing was provided. The base plate was printed at 5mm thick, with a 2mm inset for the stepper motor. The base is approximately 245mm tall (9.65"), and 190mm wide (7.5"). Making large rectangular cutouts in the plate cut the printing time from 13 hours down to approximately 9 hours. No cutouts were made in the gears.
The project design was completed in metric (with the exception of English threaded screws for the pins) to keep the math simpler.
Experiement 3 (11/11/23)
The third experiment will simply try modifications of much of the work done in Experiment 2. This design will use the same stepper motor and controller board. It would be nice to add an additional LED or two on the Arduino board. Code modifications will be made to attempt to tune the motor to 1 RPM, and hopefully also smooth out the steps a little.
The base plate layout has been redesigned to provide clearance for all the clock pins. The gears have all been designed with a 4.4 mm hole (which ends up being smaller when printed). The root fill radius was set to .45 mm for most of the teeth sets, whether 16 teeth or 40, 48, etc., instead of the .9 mm radius for larger gear sizes. The additional gear buffer clearance between gears pitch diameters was reduced from 1mm to .5mm. The gear holes are all 4.4mm, reduced from the 4.75mm holes used for some of the first gears in Experiment 2.
Experiment 3 was limited to just 4 sets of gears to get to the minute hand. The second 60:1 ratio to give the hour hand was omitted.
The base plate was simplified as much as reasonable to reduce print time, which was substantially improved by limiting the number of gears to be mounted. The thickness of the motor area was reduced from 5mm to 4mm. The thickness for most of the rest of the plate was reduced to 2mm, and significant cutouts were made to reduce printing time. The estimated print time of the base plate from the slicer was 5-6 hours.
The gear reduction of the entire train is a single 60:1 set. The reduction sequence is (as with experiment 2) 2:1, 2.5:1, 3:1, and finally 4:1. The following gears are to be supported:
Motor gear: 16T
32T_16T_4.4
40T_16T_4.4
48T_16T_4.4
64T_16T_4.4
Two additional holes were provided in the template to allow playing with different gear orders.