Subject:
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Re: Mechanical pneumatic piston
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Newsgroups:
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lugnet.robotics
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Date:
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Sun, 12 Oct 2003 09:49:13 GMT
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Viewed:
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2486 times
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I have given this question some thought in the past and I came up with a theory.
First of all some gear geometry background.
Lego gears have 8 teeth per Lego unit (aka stud) of pitch diameter, the
effective diameter to where the gears mesh. Using that fact we can determine
the circular pitch of the teeth by calculating the pitch-circle circumference.
Lets look at an 8 tooth gear as an example. Since the diameter is 1 Lego unit,
the circumference is pi Lego units. Therefore 8/pi is the circular pitch, the
distance from tooth to tooth along the circumference. 8/pi is about 2.54648.
Now lets look at the 1x4 gear rack. Using the pitch we calculated, the gear
rack should have 2.54648 x 4 = 10.186 number of teeth on it. Obviously we know
that is not true. In order to make the gear rack have a whole number of teeth,
the Lego designers fudged the pitch to 2.5 so that it became exactly 10 teeth.
And we never even noticed.
When Lego designed the worm gear, they had to deal with the pitch in basically
the same way. The long tooth on the worm gear makes 5 complete rotations along
its axis. By dividing 5 by our calculated pitch, we get 1.96349. That would be
the ideal length of the worm gear given the five rotations of the tooth.
So why did LEGO fudge the teeth spacing on the gear rack and not on the worm
gear? I don't know for sure but I suspect that the designers realized that the
gear rack piece would often be used in a series and therefore had to be
normalized to a whole number of teeth. Similarly, they figured the worm gear
would not need to be used in a series the same way. I suppose it is also
possible that they determined that the worm gear worked better if its pitch
matched exactly the pitch of the spur gears.
Anyway, I predict that if someone had enough worm gears, it would take 14 worm
gears before you could squeeze in an extra half bushing and not cause any
binding. 14 x 1.96349 = 27.48886. I don't have enough worm gears to verify
this.
Gus Jansson
Seattle, WA
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Message has 1 Reply:
 | | Re: Mechanical pneumatic piston
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| (...) Very nice analysis! All seems perfectly logical to me! (...) The other problem is not having an axle long enough to put them on. So I connected them together with axles butting each other about halfway through each worm gear. And with 14 worm (...) (21 years ago, 12-Oct-03, to lugnet.robotics)
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Message is in Reply To:
| | Re: Mechanical pneumatic piston
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| Restating for clarity, (I hope) I think the issue is the + shaped central hole. If you mounted these worm gears on an axle which requires them to be mounted at 0 (180), 45, 90, and 135, then of course you can't turn the gears anywhich way to line up (...) (21 years ago, 11-Oct-03, to lugnet.robotics)
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