Lantern Pinion

[Alan CharlestonParticipant @alancharleston78882]

Hi All,

Another question about gears. Will a lantern pinion work with a spur gear? If so, what would be an appropriate diameter for the pins in an 11 tooth lantern gear to mesh with a 147 tooth spur gear – module 1? I assume the pins would be on a pcd of 11 mm.

Regards,

Alan C.

[Michael GilliganParticipant @michaelgilligan61133]

The lantern pinion is a special case of a Cycloidal Gear … so works beautifully with a  Cycloidal spur gear.

I will leave you to determine whether that makes the answer to your question Yes or No

MichaelG.

.

https://www.tec-science.com/mechanical-power-transmission/cycloidal-gear/lantern-pinion/

[John HaineParticipant @johnhaine32865]

Well, there’s probably a theoretical answer but I know from experience that a 1mm end mill is just too big to profile out a 1mod cycloidal gear.  So the maximum pin size would be about 0.8mm I think.

[SillyOldDufferModerator @sillyoldduffer]

Drawing the gears in CAD to see the mesh suggests the answer is yes, only just, and might not be good enough. (To save time the example is drawn with a spur gear.  Readers should imagine the 10 toothed gear’s teeth replaced with round pins.  This is only an example.)

As the number of teeth on an involute gear drops to accommodate a large ratio, the mesh first becomes inefficient and then becomes impossible.  Gears with cycloidal teeth can accommodate larger ratios than involute, hence popular in clocks.   Claimed to be more efficient too, but that’s a mixed blessing.

In the past there was bitter debate over the merits of cycloidal vs involute gears, much of it emotional rather than engineering. and often ignoring the fact that the high gear-up ratios needed in low-power clocks are a special case.    Almost every other machine gears down to transfer considerable power, and for those applications involutes are superior.  They’re also cheaper to make, robust, and less fussy about depth.

Alan’s requirement is interesting because it’s on the border!  Involute isn’t clearly unsuitable, but eyeballing the mesh doesn’t prove 10 pins will transfer enough power to drive a big involute gear. Frictional losses and slop at the interface could stall it.

Alan hasn’t told us what his application is, which makes any answer guesswork.   I assume it’s a clock with lots of gear-up friction to worry about, but maybe it’s for a less critical mechanism?   A grandfather clock powered by a heavy weight might be happy, whilst a spring powered clock would stick – not enough oomph to overcome friction.

An example from WW2 – engineers in a famous US clockmaker,  making time fuses for shells insisted the gears must be expensive cycloid types.  They were forced, weeping and wailing about ‘quality’, to build a cheaper involute version.  It worked just as well.  They were wrong, misled by their clockmaking experience into believing cycloidal gears were essential.   To be fair, time fuses are a borderline application, and the success of involutes doesn’t prove cycloidal gears are always unnecessary.  Far from it!

Dave

 

[John HaineParticipant @johnhaine32865]

Here’s another image from this website: https://hessmer.org/gears/CycloidalGearBuilder.html for cycloidal gears.

Generated for your specific parameters.  You can see that the max width of the pinion teeth must be a bit less than a third of the circumferential pitch which is 3.14 mm, so a bit less than 1 mm.

This is a useful site – you can download the profiles as dxf so they can be imported into CAM to generate g-code – I used CamBam.

[JasonBModerator @jasonb]

I don’t have a licence for Gearotic so can’t import the file but using one created in the site linked to by John above and overlaying the data from Gearotic I get  apin of 1.25mm on 11mm PCD

Take the OD and PCD from Gearotic

And draw them (orange) over the top of the DXF from Hessmer(red)

Hopefully the OP’s requirement is drive in one direction as there looks to be a lot of backlash – gaps in the Hessmer one whereas Gearotic has no noticable gaps, though Gearotic does Epicycloidal

[RobinParticipant @robin]

Stop it. Much more of this and I will wind up wasting my declining years cutting ancient tooth forms

Robin

[John HaineParticipant @johnhaine32865]

Yes, the Hessmer one is based on a BS for horological gears with recommended clearances hence the backlash.

Thinking back the reason why I couldn’t use a 1 module was that a 1mm cutter (the smallest I can comfortably use with the limited top speed of my Novamill) wouldn’t do the teeth on the solid pinions, especially the roots, hence I had to use a slightly larger module.  I didn’t think of using lantern pinions.

[Robin]

On Robin Said:

Stop it. Much more of this and I will wind up wasting my declining years cutting ancient tooth forms

Robin

Since the train I was designing was all step down my original plan was to use involute (there’s an equivalent site for involute gears), but I found that I would have needed to use an even larger module for that using 1 mm cutters.  So though cycloidal is “ancient” it was appropriate for the purpose.  Of course these “standard” shapes aren’t really cycloidal at all but just use circular and straight line approximations.

Added: Once you choose a lantern pinion you pretty well define the wheel as cycloidal.  As you can see from the pictures the mating surfaces will be normal to the pitch circle whereas with an involute the wheel tooth will be at an angle.

[Peter Cook 6Participant @petercook6]

According to Malcolm Wild’s  book (copied from W.O. Davis), the pin diameter for cycloid lantern pinions is 1.05M where the no of teeth is 10 or less, and 1.25M where no of teeth is greater than 10. So for 11 teeth Mod 1.0 Jason’s 1.25 seems to be the number.

He also stresses the lantern pinions must be the driven member.

[duncan webster 1Participant @duncanwebster1]

But I’ve never understood why. Can anyone explain?

[John HaineParticipant @johnhaine32865]

All to do with the “action being after centres”, but this is likely a myth.

[Peter Cook 6Participant @petercook6]

Ivan Law’s book on Gears & Gear Cutting goes into some detail. On p20 he states that ” It is an engineering fact that the friction that is generated during the engagement of the teeth is far greater than the friction arising during disengagement” Apparently the lantern pinion being the driven element produces a gear pair where all the contact is during disengagement, which minimises frictional losses. Particularly important in clocks where no lubrication is used on the wheels.

In situations where lubrication is present, and or frictional losses can be tolerated, I guess it doesn’t matter much.

[Alan CharlestonParticipant @alancharleston78882]

Thanks for all the replies. The pinion is required for Zeamon’s Orrerey. The 147 tooth gear is fixed to the central shaft and the pinion is driven and travels around it. It rotates the Earth and moon assembley so it appears that the moon circles the Earth every 27.3 days. It is a complication to the orrery that I’m not sure I will pursue. I don’t have a CNC mill so I can’t do the fancy engraving on the 147T gear which serves as a calendar ring. I have some 1.0mm blued steel rod so I may make an 11T lantern pinion out of interest and see if it meshes with one of the other gears.

In any event, there is no hurry. I found out this morning that I misread the settings table for my dividing head and managed to cut 3 110T gears instead of 3 106T gears. The orrery runs OK and looks fine but it’s not right so I’m going to recut them which is going to take a while.

Zeamon cut his gears using a cycloidal rather than an involute cutter because he was worried about the accumulated friction from the large number of gears. I cut them with involute cutters and even with the off spec 106T gears, the orrery operates with very little resistance being felt when turning the handle.

Zeamon’s page is here:

Building An Orrery (Part 1)

Regards,

Alan C.

[John HaineParticipant @johnhaine32865]

This document says it all really.

https://www.csparks.com/watchmaking/CycloidalGears/RichardThoen.xhtml

[John Haine]

On John Haine Said:

This document says it all really.

[…]

I would beg to differ, John

Yes, that document says a lot … but it does nothing to address the question that opened this topic.

 

MichaelG.

[JasonBModerator @jasonb]

Addressing the original question, It looks like a similar 1.25mm dia pin would work with a spur gear.

[John HaineParticipant @johnhaine32865]

Michael, I was really responding to Alan’s comment about the lack of friction in his involute gears. Not unexpected in the light of Thoen’s document.

[duncan webster 1Participant @duncanwebster1]

But as I ‘have an enquiring mind’ (otherwise known as being an awkward so and so) I’m not inclined to accept an assertion of ‘it is an engineering fact’ without explanation. Strikes me as being in the same vein as politicians saying something is obvious when it isn’t.

[duncan webster 1]

On duncan webster 1 Said:

[…] I’m not inclined to accept an assertion of ‘it is an engineering fact’ without explanation. […]

I’m with you there, Duncan !

… If this wonderful new magazine of ours is to prove its worth, then a serious analysis of this “engineering fact” [sic]  would make a good article.

… I regret that I do not feel qualified to write it 🙁

MichaelG.

 

[John HaineParticipant @johnhaine32865]

This is explained in the Thoen document.  The reason normally given is that if gear teeth engage before the line of centres the pressure between the teeth where they are in contact causes increased friction, and this is typically illustrated by pushing a screwdriver along a piece of coarse sandpaper.  As the blade catches on a bit of grit it tends to “trip” the blade and drive it into the paper, so increasing the friction.  Engaging after is like pulling the blade back when this doesn’t happen.  However this is not a very useful picture and doesn’t represent reality very well, as the unevenness in the surfaces is on a much smaller scale and in practice there isn’t significantly increased friction.  Thoen observed this by comparing thousands of similar clockwork fuse mechanisms where they worked equally well with involute gears and in many cases the tolerancing meant they wouldn’t work with cycloidal but would with involute.

Sinclair Harding make very fine clocks in West Yorkshire and at least some of their gears use involute teeth.

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