Subject:
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Re: Axle joiner angles
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Newsgroups:
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lugnet.robotics
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Date:
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Mon, 11 Dec 2000 06:13:54 GMT
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Original-From:
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Brian Alano <alano@*stopspam*kiva.net>
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Viewed:
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1124 times
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I suspect the crux of your answer lies in the 3-4-5 triangle. [NOT! read
on to see why this isn't true!]
The complements of 112.5 and 157.5 degrees are 67.5 and 22.5 degrees. The
sum of 67.5 and 22.5 is 90 degrees. Add add a 90 degree angle and you get
a complete right triangle. [OK. Maybe this idea has some merit. None of
the rest seems to.]
Law of sins says sin A/a = sin B/b = sin C/c, where A, B, and C are
angles of the triangle
and a, b, and c are the lengths of the sides.
We'll use C=90 degrees. Let's let c = 5 stud-lengths. What then, must the
lengths of the other sides be?
, so sin C = 1, so
1/5 = sin 22.5/a = sin 67.5/b
A little algebra yields a = 3.22 and b = 4.62.
Hmmm. not what I expected. I wanted a=3 and b=4.
Let's see, the angles for a 3-4-5 triangle are
sin A/3 = sin B/4 = 1/5
A = inverse sin of (3/5) = 36.87 degrees.
B = inverse sin of (4/5) = 53.13 degrees
C = 90
Ok, that wasn't the answer.
Anybody else?
> connect two axles at an angle.
>
> The angles Lego have chosen to supply seem incredibly
> non-useful (apart from the obvious 180 and 90 degree ones).
>
> Each part also has a number on it. Here is a table of the
> angles for each one:
>
> 1 : 0 deg (well, it takes just one axle)
> 2 : 180 deg
> 3 : 112.5 deg
> 5 : 157.5 deg
> 6 : 90 deg
>
> Since it's most unlike the Lego designers to make parts like
> these without thinking carefully about the choice of dimensions
> and such, does anyone have *any* idea why they thought that angles
> like 112.5 and 157.5 were useful whilst missing out the more obvious
> ones like 120 and 135 degrees? You get *lots* of them in RIS and RDS
> sets - so they presumably aren't like that for some cosmetic reason
> that's unique to a particular model.
>
> There must be method in their madness - but I'm damned if I can see
> what it is.
>
> ---
> Steve Baker HomeEmail: <sjbaker1@airmail.net>
___________________
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Suppose one of you has a hundred sheep and
loses one of them. Does he not leave the
ninety-nine in the open country and go
after the lost sheep until he finds it?
---Luke 15:4. The Holy Bible (NIV)
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Message has 1 Reply:
 | | Re: Axle joiner angles
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| I think these just correspond to the splines on the old connectors which they replace. I haven't checked it, but I think the splines are every 12.5 degrees. The connectors are too chunky to make accute angles, so they only do the obtuse angles: 0.0 (...) (24 years ago, 12-Dec-00, to lugnet.robotics)
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Message is in Reply To:
| | Axle joiner angles
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| I was looking at the axle joiner thingies that let you connect two axles at an angle. The angles Lego have chosen to supply seem incredibly non-useful (apart from the obvious 180 and 90 degree ones). Each part also has a number on it. Here is a (...) (24 years ago, 10-Dec-00, to lugnet.robotics)
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