Try this book: Book about £30 with no postage to pay. This tells you all you could possibly need to know about clock wheel cutting.

There are also clock wheel drawing and calculating programs available on the web – Google will help you.

You can buy cutters (which are extremely expensive!!) or make your own – which is quite easy to do, especially after a bit of practice.  Forget pressure angles and involute curves – these do not apply to clock wheels or pinions.

Edited By Bizibilder on 22/12/2019 13:17:27

You might find this useful, Chris : **LINK**

http://www.delphelectronics.co.uk/gcode.htm

… and this of interest : https://www.csparks.com/watchmaking/CycloidalGears/index.jxl

[ be sure to follow the embedded links on that page ]

MichaelG.

Edited By Michael Gilligan on 22/12/2019 15:17:20

Inkscape can draw Involute gears and racks by following the menu Extensions->Render->Gear.

The dialogue and gear it drew is shown below:

The teeth are sized and shaped to engage with another gear of the same specification, this boiling down to the numbers entered in the dialogue.

Almost all modern gears are involute because they are smooth running, not effected by small spacing errors, and are easy to mass produce. Most gears are used to transmit power, and the involute form is said to be good for this – low wear, whilst careful shaping of the teeth reduces gear whine at speed. Typically a fast rotating power source is geared down to drive road wheels or a machine.

Clock gearing is arranged the other way round: a very slow turning drum powered by a spring or weight gears up to turn a relatively fast moving seconds or minute hand. Somewhere near the top of the gear train, an escapement connected to an accurate timer like a pendulum, allows the train to tick in timed steps, perhaps once per second. These ticks are divided down through another gear train to show HH : MM : SS. As clocks don't have power to spare its important to minimise friction. Cycloidal gears are said to be better for low friction than involutes, but it's not clear to me why. My admittedly weak understanding suggests involute gears should be best for everything.

Early clock-makers knew sod-all about involutes and cycloids! Their clocks were built by eye and experience. The experience comes from looking at worn teeth, perhaps in a local water mill, because teeth tend to grind down naturally to matching curves. Craftsman copied these curves with a file to cut new teeth, avoiding the running in stage. Later on mathematicians did a proper analysis and produced the formulae needed to shape properly matching gears from first principles.

One way of making clock gears is to carefully grind a tool to fit the profile of an existing gear. (This may be essential when repairing a very old clock.) Then, with the gear blank held in a dividing head, the tool can be spun like a fly-cutter to chop teeth one by one around the circumference. A posh dividing head isn't necessary – people use old saw blades to provide the necessary indexed steps.

Making tools to cut mathematically defined curves is more challenging. Ivan Law's Gears and Gear Cutting is a good place for practical men to start – I've found the maths in engineering textbooks very difficult. You could also grind tools to match gears drawn by Inkscape.

Most professional gears are made by hobbing, where a specially shaped cutter and blank are synchronised together. Or gear cutters can be bought to match the required DP(Imperial) or Modulus(Metric) : quite a lot of them may be needed. Ivan Law describes a method using buttons, and a more modern idea produces the curves by facing the new tool into the side of a cone drill. The only method I've used is this medieval home-made tool, which, despite it's crude appearance generates involutes that fit Meccano.

Hours of fun ahead!

Dave

Edit: Poxy Smileys!

Edited By SillyOldDuffer on 22/12/2019 15:16:27

.

… especially this one :

Finally, I would like to mention a privately published monograph by my gear-expert friend, Richard Thoen. This work explains why, in his opinion, cycloidal gearing belongs entirely in the dust-bin of history.

MichaelG.

Chris

Remember that mostly on a clock it's the wheel which drives the pinion. Which is not the most efficient situation.

Roy

Not sure I understand the first sentence. Aren't cycloids and epicycloids particular curves with mathematical definitions, whereas 'ogive' is just a general description of any pointy shape like an arch or tooth? Likewise, there are lots of different curves, pretty much anything other than a straight line. I'm sure clock teeth could be made of unscientific ogives and curves and still work, but they're unlikely to be low friction. A clock made of substandard gears would wear faster and need more power to drive it reliably. It might need so much power that pinions carve or bend.

CAD has the advantage of producing properly designed gears without any need to understand the rather difficult theory or do the necessary number crunching and drawings. Guessing is eliminated. In contrast Rule of Thumb and copying other gears is comparitively hit and miss. Why blunder about in the dark when an electric light is available?

Dave

You can use CAD to draw a profile, but forming it in metal is quite another issue!

Involute gears can be generated by a "rack form" cutter, which has straight edges, usually by hobbing. But If you want to hob "cycloidal" gears then the hob has to have a complex curved shape which just moves the problem of making a precise complex curve from the gear to the cutter.

Approximations to involute teeth can just use circles instead of the true involute – cutters for this can be made by the "two button" method. It is also possible to CNC turn the precise shape into the cutter profile, which could be done for both involute and "cycloidal" teeth.

This shows the tooth form of a "two-button" type cutter (circular approximation to involute) being formed by CNC on a form-relieving fixture in my lathe. It would be just a matter of having the right equation to make a cycloidal type cutter.

CAD is only for making gears for digital clocks.

Grinding a tool to match your existing good gear would get the job done, for this one-off repair job. Modern technology is a wonderful thing but often cruder olde-worlde methods are quicker and simpler in the home workshop.

Involute gears provide 'constant velocity ratio' in transmission, so no variations in speed transmitted which in say a car gearbox would cause vibration. They do this at the expense of the faces sliding over one another which means friction and loss of power.
Cycloidal gears are not constant velocity but that doesn't matter when it's stop start over and over anyway at each tick tock. They are closer to rolling contact, less friction and less energy loss,
Cycloids for small gears approximate to a circle, hence birdcage pinions with round rods as teeth. For large gears, wheels, the cycloid approximates to a straight line. So the tooth can be made with a flat flank and a curved top just to look better and avoid a sharp top to the tooth. If you observe such a wheel in operation the point of contact does not go past that flat section (ideally).
Pressure angel: It was mentioned above that an involute gear is 'generated' by a straight flank rack. Or the ideal rack (an infinite radius gear) to mate with an involute gear has flat flanks and they are at an angle that is called the pressure angle. This pressure angle persists in the shape as you turn the rack into a curve then a gear. When the gear is engaged with the rack the force between them, the pressure, is perpendicular to the face of the rack tooth – hence its direction relates to the pressure angle.

Final question of when would a clockmaker use CAD to form the teeth etc. Answer Never. A clockmaker would use CAD to layout the positions of wheels and pinions and general design but would never draw actual gear teeth just circles to show the position to avoid hitting pillars etc but the teeth don't need drawing just making using the normal methods. An engineer would draw such teeth because they are more interested in playing with the toy than making a clock.

You left out the word "armchair".

There are those that talk about it and those that do it.

CAD:

CAM:

CNC:

Real gears:

I thought that the involute tooth form gave primarily a rolling contact, with a little sliding. It would seem strange to use a tooth form for power transmission that has inherent losses due to friction over another tooth form.

Andrew