Geared 7-Segment Display, Part 4 – Pinion Gears and First Rotation

This weekend I’ve added the pinion gears to the seven-segment display, and performed the first test rotation of the mechanism.

As previous noted, the arm gears are 6-tooth gears of module 4 (metric) – in clockmaking terms, these would be pinions. In the clockmaking world, where I’ve been doing quite a bit of research during this project, there doesn’t seem to be a hard dividing line between what’s considered a “gear” and what’s considered a “pinion,” except that gears are big and pinions are small. Fair enough. From this point forward I’ll be referring to the arm gears as arm pinions.

I printed 6 of the pinions in just over an hour, and fitted them to their axles, which are just hacked-off pieces of 1/8″ rod stock from the hardware store. With the tolerancing on the prints as it is, the pinions are a snug fit on the axles, so I’m not too concerned about slippage once I can get the whole thing turning smoothly.

Speaking of turning, here are the first (partial) rotations of the mechanism.

Right now, the biggest impediment seems to be that the frame lacks rigidity, and easy warps and slews far enough to drive the arm pinions out of mesh with the drive gears. I’m currently working on a two-part version of the frame with interlocking members that firmly affixes both halves on the frame so that they remain rigid and parallel.

I’d assumed when I started this project that the axles (arbors) would need to be made of metal rod or dowel stock, so that they were firm, perfectly round, and rigid. But this being a 3d printing project, I’m now experimenting with a fully3D printed arbor-and-arm-pinion assemblies. These have the advantage that there’s no need to manually locate the pinion on the arbor by sliding the arm pinons up and down the arbors – they’re all one piece. As a sample, I printed a C-Arm assembly in two different orientations, both vertically and horizontally:

The vertically-printed arbor and pinion came out much better – the axle on the horizontally-printed unit is limited in smoothness by the layer height of the print, while on the vertical print it’s limited by the X and Y resolution of the printer. Additionally, while there is significantly more support plastic on the vertically printed unit, it’s not touching any of the working surfaces of the pinion itself, making the post-processing and filing significantly simpler. Both seemed to rotate well in the axle holes, however; well enough that I plan to work up a full set of these and test them in the next version of the frame. That means the only non-3D printed part in the project would be the main axle, and possibly the G-Arm tubing.

Next steps are printing the stiffer frame and the pinion/arbor assemblies.

Geared 7-Segment Display, Part 3 – Drive Gear Interlocks

The heart of the seven segment display is the seven drive gears with select teeth, which share a common shaft and all rotate together. As I was developing the idea of the drive gears and conceiving of how the presence/lack of teeth could “signal” the arm gears to turn or not, I though of them as plain, 2-dimensional shapes. I had planned on spacing them out along their common shaft using 3D printed washers of a set thickness. As for aligning them at the appropriate relative rotation, I thought I might print a jig (some kind of tall internal gear) to hold all the drive gears in the right relationship. Then I would either affix the gears and washers with superglue, or drill an alignment hole through all 7 gears and insert a small alignment rod to maintain their orientation.

Here are the first three drive gears (A, B, C) with a 2mm-tall washer between each. Looking good!

But this is thinking like someone who only has access to subtraction manufacturing. Why carve out a hole and insert new material when we could print the holes and alignment rods as part of the gear themselves?

I took another pass through all the drive gears, and added two 3mm wide, 7mm long “pegs” to the front side of each one (except gear A, the front gear). I also carved out a matching “slot” in each gear to receive the pegs behind it, with 0.3mm of clearance in all dimensions. (0.3 is my standard clearance value when I want two mechanical parts to fit together with no problem at all – your experience may vary.) Additionally, I extruded the center portion of the gear an extra 3mm upward to eliminate the need for the spacing washers I’d previously planned on.

Here’s the new E gear as an example:

You can see the two protruding rectangular “pegs” on the top that fit into the D gear, and the two similar slots on the bottom that receives the pegs of the F gear.

So, here’s what all 7 interlocking gears look like on an axle:

I whipped up a couple of minimalist end-frames to hold the drive axle and the axles for the arm gears – with both front and back in place, the mechanism is starting to take shape:

These endframes are a good example of something I’ve noticed with mechanical objects and additive manufacturing – there are huge time paybacks for small investments in drafting time. I’d first conceived of these end-frames and simple, 2mm thick rectangles with 7 holes in them. Cura estimated that each of those plates would take around seven and a half hours to print. Oof! There goes the weekend. But another 15 minutes of casually cutting things away in Fusion360 and the resulting frame took about two hours and 45 minutes. That’s ten hours of printing time saved with a quarter hour of drafting, a massive return on time invested.

Next step will be to re-print the pinion arm gears with appropriate axle holes, and then test fit the gears together. Here goes nothing.

Geared 7-Segment Display – Part 2, More Gears

While time at home is scarce this week, I’ve stolen a couple moments late night to continue working on the design of the geared 7-segment display, including finishing the modelling of the 7 drive gears.

Each drive gear is based on a 30-tooth, involute gear of module 4. Each segment of 3 adjacent teeth represents a single transition of a segment (or lack there of) – if there are teeth in a segment, the associated arm gear will rotate, changing a segment from active to inactive for a given transition or vice versa.

As a side note, each gear has a even number of teeth remaining, and each segment makes an even number of transitions as the display makes a full cycle of ten digits. If a segment made an odd number of transitions, it would start the next “cycle” in a different state than on the previous cycle, causing the numbers to “look” different on each time a given number came up, which is clearly wrong. This served as a useful sanity check as I was working through each gear in turn.

Here is the mechanism in its current Fusion360 form (support plates, arms and mounts, and a drive mechanism yet to come):

 

The A, D, and G arm gears lie on the vertical axis of the mechanism. The A and G arm gears, as noted in my previous post, are currently intended to be co-axial, the shaft of the A segment being a small hollow tube which completely surrounds the shaft of the G segment. Of all the details in this mechanism, this one seems the most fiddly at the moment, since any tolerance issues are going to compound on each other.

The B, C, E, and F arm gears lie at ±50° from the vertical axis, which is just about as close to the vertical axis as they can be and still have their arms clear the axes of the A/D/G segments.

In contrast to what I said a the end of my last post, I’m thinking I’ll print each of the gears individually and then mount them on the center axle with spacer washers. The whole-gear-assembly-as-barrel has one fatal flaw: printability. That’s a lot of overhanging teeth to worry about. That said, the print-individual-gears approach means needing to worry about registering adjacent gears to each other, but that seems like a solvable problem.

Looking down the road, here’s a quick Vectorworks sketch of how close adjacent digit displays could be. It seems I could squeeze them to about 175mm (~7 inch) centers.

 

Currently, the plan is to build one digit and evaluate… but the only thing better than N mechanisms is N+1 mechanisms…

Geared 7-Segment Display – Part 1

Over the weekend, I got started on a project I’ve been musing about for a few months – making a mechanical 7-segment display, using gears to move individual segments in and out of the display area via rotation of a central shaft or belt.

The inspiration for this idea is undoubtedly Arthur Ganson’s mechanical sculpture Gary’s Yellow Chair at the MIT Museum in Cambridge, video of which periodically makes the rounds on Reddit. In it, a bicycle-chain drive six separate sprockets, each of which moves a long rod to which is connected one sixth of a chair. Each time the sprockets make a full rotation, their connected arms point toward a central point and the fragments of the chair briefly assemble into a whole (if tiny) yellow chair. Then the pieces split apart again, sent on another rotation by the action of the driving chain.

In this vein, my goal is to create a series of seven moving arms, each with a segment of a 7-segment display on it. A central shaft will drift seven attached gears, each with teeth placed and left out at specific intervals. These seven drive gears will turn seven arm gears, which in turn attach via shafts to long, thin (metal?) arms at the front of the device. The spacing of the teeth on the drive gears will ensure that each of the arm gears turns at the appropriate time to move the segments in and out of the display area. Each time the arm gear needs to move an arm in or out of the way, the drive gear will cause its paired arm gear

Here is a quick drafting of how I currently think this project will be laid out. The grey circles indicate the base circle of each gear, while the concentric circles are the pitch and addendum (i.e. maximum extent) circles.  The green segments indicate when a given physical segment is in its “displayed” position, while blue indicates where that segment will be when “not displayed”. The dotted lines around each segment indicate its travel, and are useful that none of the arms sweep through another segment’s shaft. In section, you can see that the segments are going to be situated on 3 different front-to-back planes to avoid collisions between arms and shafts. You can also see the concentric relationship between the top segment and the center segment.

It turns out, fitting 7 arm gears around what is essentially one central drive gear shaft is tricky, especially to do so in such a way that none of the arms contact each others’ shafts as they rotate. To accommodate this, I currently have the top segment operated with a hollow shaft, and the shaft for the center segment runs through this hollow shaft to protrude out the top. We’ll see how that goes.

Here is a quick sketch of the digits on a typical 7-segment display as it moves through the digits 0 through 9. The small red marks in between each digital denote which segments change between digits.

Which leads us to the following chart of which segments need to move between which digits.  Note that the horizontal axis is for “moving to this digit,” so that an X in the “7” column, for example, means that that segment needs to change when moving from a 6 to a 7.

After some preliminary work in Fusion360, I did a couple preliminary test prints, both of one of the “30-tooth” drive gears and some of the 6-tooth pinion gears.  (Since the total number of possible necessary transitions is 10, and each transition only needs to turn the arm gears ½ a rotation, the arm gears have 1/5 as many teeth as the drive gears.) You can also see one of the 2mm spacer washes I whipped up, which I think will be unnecessary (see below).

With the slight creep and elephant’s-foot that my printer makes, I think I will need to depth these a little further apart than the idealized spacing – even when the teeth are not engaged, the tips of the pinon teeth drag a bit on the drive gear. Even another .2 or .4 millimeters would help here.

It occurs to me at this point that there’s no reason for the central gears to all be separate assemblies and prints – they’re all meant to rotate in lockstep, so there’s no reason not to print them as one large barrel with protruding teeth at 7 depths. That will be a necessary future improvement. Of course, the supports, axel holes, and whatever I’m doing for that hollow shaft are also future problems to be solved.