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Measuring pitch diameter of clock wheel

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Chris TickTock10/10/2020 17:54:18
622 forum posts
46 photos

Hi Guys,

Measuring the pitch diameter from a cycloidal clock wheel exactly can be an issue. My technique is to measure from the bottom of a tooth on one side of the wheel to the top on the other. Finding the exact point the addendum starts is not easy. My technique makes the assumption the pitch circle is exactly half way from tooth tip to bottom.

Am I doing this right though or can anyone suggest a better method.

Regards

Chris

DC31k10/10/2020 19:49:22
686 forum posts
2 photos

Let me start by saying I know nothing about cycloidal gears.

However, I have some familiarity with involute gears. In the involute system, pitch diameter is never measured directly. It is a number that is derived from other measurements of the gear (you measure the outside diameter of the gear and count the number of teeth - the pitch diameter falls out of manipulating these two numbers).

If you are measuring from the bottom of the tooth space, you have a good chance of being incorrect as the dedendum may incorporate clearance.

This page seems to me, a complete beginner on cycloidal gears, as good a reference as any and contains a number of subsequent references:

https://www.csparks.com/watchmaking/CycloidalGears/index.jxl

Neil Wyatt11/10/2020 13:08:23
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19033 forum posts
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Strictly, you need to find the point on the tooth whose tangent is radial - i.e. the transition between the internal and external cycloid.

Without details of the cutter this is not easy to determine and is affected by exactly how the cutter was set up.

It matters because of the geometry meaning the gear works ideally when the two meshing gears have coincident pitch circles or lantern pinions have the centres of their pins on the PCD.

The ubiquity of tools for setting the mesh of clock gears (depthing tools) and their absence in the world of involute gears is testament to the challenge of meshing clock gears accurately and the contrasting tolerance of involute gears of centre distance errors.

I would guess your method might slightly underestimate the PCD due to clearance (as explained by another poster) but should get you close enough to use a depthing tool to place the pivot correctly.

Neil

Chris TickTock11/10/2020 14:24:32
622 forum posts
46 photos
Posted by Neil Wyatt on 11/10/2020 13:08:23:

Strictly, you need to find the point on the tooth whose tangent is radial - i.e. the transition between the internal and external cycloid.

Without details of the cutter this is not easy to determine and is affected by exactly how the cutter was set up.

It matters because of the geometry meaning the gear works ideally when the two meshing gears have coincident pitch circles or lantern pinions have the centres of their pins on the PCD.

The ubiquity of tools for setting the mesh of clock gears (depthing tools) and their absence in the world of involute gears is testament to the challenge of meshing clock gears accurately and the contrasting tolerance of involute gears of centre distance errors.

I would guess your method might slightly underestimate the PCD due to clearance (as explained by another poster) but should get you close enough to use a depthing tool to place the pivot correctly.

Neil

Neil, yes your thinking is mine to. At the moment I am only measuring to get an idea of module size used where on a clock. In this circumstance it doesn't matter. You introduce 'the depthing tool', which reminds me to get to know more about it....thanks for that.

Chris

Howard Lewis12/10/2020 14:50:01
6113 forum posts
14 photos

Totally ignorant of gears used in clocks, but would suggest that reading Ivan Law's "Gears and Gear Cutting" (No 17 in the Workshop Practice Series ) may prove useful.

Having seen the word "Module", normally this would be applied to gears with Metric dimensions, so that the Tooth Count and the Module determine the O D of the gear, in mm, in the same way that Tooth Count and DP do for Imperial sized gears

I realise that clock makers may march to a different drum when it comes to gears; so am prepared to be told that i am wrong.

Howard

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