Last time, I wrote about the design considerations for a clock adapted from William Strutt's epicyclic gear clock. Now it is time to complete the design by adding the frame and the driving/timing mechanism. There is one small change I made to the design documented in the previous post. The planet gear is mounted on a carrier pivoted on the minute arbor. This works better if you add a counterweight opposite the planet gear. A US quarter seems to be about right.
A few pictures and video of the completed design first, and then I'll fill in a few details.
The frame for Strutt's original design (illustrated here) is rather ornate and a little too fancy for my tastes. I like the frame seen on a GrabCAD version and used this as the starting point for my own. The overall frame has to be taller than will fit on the print bed. In previous designs, I've looked for a point where I can split the frame and then joined the pieces with glue and pins. For my design, I decided to print it so that the very top part attaches with a couple of screws. This also allowed me to defer the decision about the drive and timing mechanism. Depending on what I decided, I could print the top pieces with different dimensions.
Drive and Timing
Most of the remaining design decisions concerned the drive and timing mechanism, that is how to get power into the clock and how to make it run at the right rate. The original clock used a spring, but I was not sure the plastic design would hold up to the stresses from it. Another option was to drive it with a weight attached to the minute arbor. The works OK for a wall mounted clock, but is not suitable for a desk clock. I toyed with using a stepper motor, but again did not like this. In the end I settled on the same drive as my two previous clocks: an electromagnetic pendulum. As before, the pendulum rotates a cam, causing pawls to engage with a toothed wheel. I'll call it an escape wheel, though this might not be an accurate use of terminology. The escape wheel then drives the ring gear via a pinion.
There are several design considerations. The number of teeth on the pinion and escape wheel must be chosen to drive the ring gear at the right rate; details of the calculations are in the previous post. The period of the escape wheel then determines the length of the pendulum, which must be less than the height of the frame at the pivot point of the cam. Finally, the teeth on the escape wheel must be large enough for the pawl to engage with it reliably. I considered reusing the exact escape wheel dimensions from one of the previous designs, but the escape wheel looks large and out of proportion. A smaller escape wheel is possible, but it must then have fewer teeth so that they are a reasonable size. After some playing around I decided on an escape wheel about 80mm in diameter with 40 teeth, with an 8 tooth pinion. This is about the smallest size of pinion that I was willing to trust. I used a trick I learned from Steve Peterson for the pinion. As only one face comes into contact with the ring gear, you can fatten up the teeth and make them stronger by displacing the trailing face.
With the gears I chose before, the ring must rotate once every 754.49 seconds, and the escape wheel then rotates each 8/168*754.49 = 35.928 seconds. Each complete swing on the pendulum advances it by one tooth, so the time per swing of the pendulum is 35.928/40 = 0.8982 seconds. An ideal pendulum for this period would then be almost exactly 200mm long, which fits well with the size of the frame.
Cam and pawl dimensions
I'll come back to the pendulum design in a moment, but first there is the question of how to design the cam and pawls given the escape wheel. A reason for wanting to reuse the previous designs is that I knew they worked. Unlike designs for standard escapements (such as the Graham escapement), I couldn't find any guidelines for working out the geometry. To solve this, I set up a sketch in Fusion 360 to try to make sure it would all work. Here is an annotated version: