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I'm trying to determine the gear radius using a ruler by $cm$ but I just don't know what to measure:

1- the length from gear center point to the end of the gear tooth ?

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Or

2- the length from gear center point to the start of the gear tooth ?

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2 Answers 2

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You have to measure the radius to the point of contact between the teeth. Now this point of contact might move as both teeth roll over each other, and the effective radius of the gear corresponds to the angularly-averaged distance between the axis of the gear and the contact point at the teeth.

If you need a quick and dirty estimate for the average radial distance to the contact point, I would suggest to take the average of the two radii you listed.

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  • $\begingroup$ I am no expert about gears. But I would think this means that the torque transmission is variable, dpending on which of the two gears is using the tip of a tooth (or can there be more than one working at a time). If you are doing computation to determine the size for a minimum torque transmission to be achieved, you might want to chose the top for one gear and the bottom for the other. I suspect gear design is a very specialised topic. Another point is to check how much of a difference it makes. $\endgroup$
    – babou
    Commented Jul 20, 2013 at 18:52
  • $\begingroup$ @Babou -- torque transmission would still be constant provided the interlocked gears increase their effective radii with the same factor. And yes, gear design is a very specialized topic. $\endgroup$
    – Johannes
    Commented Jul 20, 2013 at 19:57
  • $\begingroup$ @babou Gears for applications like power transmissions are designed with helical teeth so that the average the Johannes proposes is spacial and there is no time variance of the effective gear ratio. This is a very well studied field and undergraduate mechanical engineers spend quite some time on it (the course is often called "design" or something similar). $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jul 21, 2013 at 2:44
  • $\begingroup$ @dmckee and Johannes - I just did what I should have done first: look at the web. In wikipedia, The design they give (for involute gears) is preserving constant angular velocity ratio. The next sentence mentions torque variation (actually visible on the animation), but is very unclear. Helical gears seem significantly more complex and less intuitive. I guess there must be also an issue of velocity difference at the contact point that causes slipping and wear. $\endgroup$
    – babou
    Commented Jul 21, 2013 at 10:18
  • $\begingroup$ @babou Involutes are the profile of the teeth in cross-section; they minimize wear because there is never any motion at the point of contact. You run them helixcaly around the cylinder of the gear to arrange both less noise (they engage and disengage smoothly) and no torque variation. It is hard to write about but if you play with a pair of gears built this way you'll get it. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jul 21, 2013 at 13:26
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you will have to measure the radius by the second method as in first case the tooth are only for hooking with another gear the do not provide any help in rotating the system

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