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Would you mesh with this?

Some thoughts on cycloidal clock teeth

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Hnclad15/04/2019 03:55:58
23 forum posts
1 photos


Great CAD dwgs. Up front I'll say I know nothing about gear design or theory and my clock making knowledge is not much better. I have made 2 clocks Allan Timmins 8 day long case and Wildings Elegant Skeleton clock and at the moment I am again constructing Timmins long case clock.

Looking at Sam's charts on "pressure angles" I am surprised at how quickly that the angle of the power component is not acting directly in line the tangent of the pitch circle dia. i.e. theta is not zero! in other words there are reaction forces so that only part of the power force is actually driving the gear train, the other reaction force would be acting on the pivots, creating friction and wear. This gets worse as the tooth completes one cycle.

It is making me wonder how accurate do I have to be with my depthing since the pc will not line up for long anyway.

It was always my assumption that cycloidal gears were used because there was a rolling action keeping the contact for most of the cycle.

Help me out here, and tell me what I am doing wrong.

Thanks David,

Sam Stones15/04/2019 04:57:29
746 forum posts
296 photos

Thank you David.

This business of teeth making rolling contact has been discussed here. **LINK**

I felt the need pose the question because I couldn't accept that two contact points on the faces of gear teeth through travelling along their own vector lines could not be rolling but sliding (skidding). As was mentioned, true rolling only takes place where the PCD's converge. Unless I didn't understand the explanation.

Does this help David?

Sam smile d


Edited By Sam Stones on 15/04/2019 04:58:14

Michael Gilligan15/04/2019 08:56:50
15746 forum posts
688 photos


As an interesting diversion [and maybe of value in that it simplifies the model] you might try modelling the behaviour of a lantern pinion with your cycloidal wheel.


Bazyle15/04/2019 11:40:12
5230 forum posts
201 photos

Am I right in thinking the pressure angle graph would be flat if the gears are the same size?

Neil Wyatt15/04/2019 12:26:04
17902 forum posts
706 photos
77 articles

" That is where I should sign off. "

And perhaps start writing this up for submission to ME?


Sam Stones15/04/2019 20:20:55
746 forum posts
296 photos

A good idea Michael, I'll do that.

The large 290 tooth wheel and an 8 'leaf' (pin) lantern should provide a good comparison.

At a practical level, and since pinions with few leaves (teeth) are usually solid, I wonder if lantern pinions would be too challenging, even strong enough?

Bazyle ...

Being symmetrical, I'd say 'Yes, it has to be a flat line; appearing horizontal the way I've constructed the other pairs of 'gears''.

Sam smile d



Edited By Sam Stones on 15/04/2019 20:26:14

Sam Stones16/04/2019 02:56:07
746 forum posts
296 photos

I was totally wrong Bazyle.

Rotating meshed identical 8 leaf pinions through 45 degrees in steps of 3 degrees, the pressure angle plot is parabolic, symmetrical about the vertical centre line, and dipping from about 22 degrees to 5.5 degrees (and back again).

The trace of the line of contact wobbles slightly, tracking at an average of about 13.7 degrees.

As with previous results and following the BS 978:Part 2 design parameters, the 'wobble' results from the radius of one tooth contacting the flank of the opposing tooth for at least 50% of the trace.

Although I can't see where this could be useful, I'll prepare the results as before.

Sam smile d

Bazyle16/04/2019 11:38:24
5230 forum posts
201 photos

Thanks Sam, I'm finding this interesting though my CAD skills don't go much beyond square blocks. I was basing my thought on the way it was bending towards the smaller gear, so I surmised that as you moved progressively to the other gear being smaller it would bend that way , therefore going through a 'zero'. But of course that wasn't allowing for different gear profiles.

Rolling contact: Following link after link given so far I came to this one which has a brief mention of cycloidal form and indicates that it is achievable with true cycloids but actually making them is the problem, so everyone just approximates and lives with it.

Michael Gilligan16/04/2019 23:54:57
15746 forum posts
688 photos
Posted by Bazyle on 16/04/2019 11:38:24:

... Following link after link given so far I came to this one which has a brief mention of cycloidal form and indicates that it is achievable with true cycloids but actually making them is the problem, so everyone just approximates and lives with it.


Hopefully, you followed the links within that, and eventually reached this page: **LINK**

... which is a very fine piece of work.


Sam Stones17/04/2019 01:08:09
746 forum posts
296 photos

From your question Bazyle, here are two identical ‘gears’ in mesh.


I chose to use the 8-leaf pinions as a simple and quicker method to get the results. When I was doing the 290-tooth wheel meshing with the 8-leaf pinion, it was quite laborious ‘chasing’ a pinion tooth with a wheel tooth. There’s nothing in my CAD package that allows any sort of dynamic interaction.

This close-up shows the contact trace, a slightly wobbly blue line at an angle of about 13.7 degrees.


I have to confess that in view of the symmetry and a somewhat lazy attitude, I flipped (mirrored) a half-trace (left to right and top to bottom).

Here's the plot of the pressure angle, also featuring the mirrored data.

img_0650 - 8-8 - meshing pinions.jpg

I couldn't bring myself to reduce the depth and plot each one as I did for the 290-8 and 198-7 pairs.

Sam smile d

Sam Stones22/04/2019 03:52:05
746 forum posts
296 photos

This thread was becoming such a mesh, that I decided to deal with the lantern pinion issue (suggested earlier) under another title.

Once it's loaded, I'll leave a link on this thread.

Sam smile d

Sam Stones23/04/2019 01:01:09
746 forum posts
296 photos

Here are the links ...

Part A


Part B



Sam smile d

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