Bet you've come accross the terms involute and cycloidal in your search on how to design clock gears?
Wonder what the terms mean, and what do they have to do with building your clock?
There is a wealth of information out there on gears.
Not all of it applies to gears for clocks.
It's not my intention to repeat info about gears that you can find in textbooks,
The Machinery's Handbook
or from searches on the web.
What I'd like to do is try and explain how to make the best wooden gear profiles for your clock.
Filter out some of the nonsense and geeky stuff about gears if you will.
Friction is our biggest enemy.
A gear profile optimized for wooden clocks will go a long way towards reducing friction and building a truly satisfying project.
There will always be some sliding between the gear teeth regardless of how the teeth are designed. However there are ways to minimize this friction in the gear train.
Some Theory- The fundamental law of gearing.
Kinematics and Dynamics of Machines.
by George H. Martin
The Fundamental law of gearing:
The common normal to the contacting surfaces, intersects the line of centers at all
There are many different tooth profiles
that satisfy the fundamental law of gearing shown above.
Involute and Cycloidal profiles are just two.
Gear profiles that do not satisfy this law will not have a constant angular velocity ratio.
In other words the driving pinion could travel at a constant rpm but the driven wheel would speed up and slow down instead of rotating smoothly.
This would cause all kinds of problems.
Lantern Gears are also used sometimes in clocks.
These are simple gears sometimes found on toys.
The pinion could be round pegs and the wheel gear posicle sticks.
This gear pair certainly would not pass the fundamental laws of gearing.
Involute tooth formThe most common type of gear form is the involute.
Gears with this shape are what you are most likely to find in industrial machines.
Imagine unwinding a spool of thread.
The arc at the end of the thread forms an involute curve.
Involute gears are economical to make because the cutters used to make the gears are straight.
Another advantage is that the center distance between the gears can be changed and the gears will still transmit a constant velocity.
Involute gears in Action
This shows a pair of full fitting involute gears.
Gears found in machines or purchased from a catalogue would have tooth form like this.
Cycloidal Tooth form
Cycloidal tooth forms are used primarily in clocks for a number of reasons.
Two generating circles roll on the pitch circle to trace the cycloidal tooth profile.
The outside circle traces the "face" of the gear tooth.
The inside circle traces the "flank" of the gear tooth.
Clock gears have a further refinement.
Radial lines are drawn from the center of the gear tangent to the flank.
The flank area is then removed along these lines to reduce friction.
Full Cycloidal-Flank still present
Animation shows a full cycloidal tooth profile with no modification to the flank.
This full profile is commonly found on bicycle sprockets.
The difference is that one of the gears is replaced by a chain.
The reduced friction and wear of the cycloidal form is ideal for a sprocket.
Look close and you will see that there is still a great deal of sliding and friction between this gear set.
Cycloial Gears-Modified Flank
This cycloidal gear set has the flanks removed.
See how the gears do not engage until the pitch circles nearly come in contact.
The length of time the gears are touching is reduced too.
Also see that the only one pair of teeth is engaged at a time.
As one tooth starts to drive, the previous driver looses contact.
The teeth are narrower and easier to make.
Backlash is not a problem for clocks because the gears always turn in one direction.
This tooth form isn't what you'd like to see in your car but is ideal for slow moving,light load gears for clocks.
Compare Involute to Cycloidal tooth form
So what does it all mean?
The animation shows two gears laid on top of each other. One involute. The other cycloidal.
There is very little difference between the two.
It's probably not worth getting too worked up about trying to get the perfect tooth form.
Clocks just don't run as fast or have the same loads as machinery.
Just be careful and try to get your gears to match the downloadable templates as close as you can.
Sandpaper is bound to raise its head sooner or later, making the differences between ideal tooth forms a debate better left to PHD's.
My clock has been running continuously for 7 years with no visible signs of parts wearing out. Pretty sure the eventual tooth shape is far from ideal even though I started out with the best intentions.
I'm sure that you will have as much success.
Just when you thought you'd seen it all get ready to check out a uniquely modified gear profile that is ideal for the scroll saw worker.