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LEGO makes Technic Angle Connectors, like these:

Technic Angle Connector #1 Technic Angle Connector #2 Technic Angle Connector #3 Technic Angle Connector #4 Technic Angle Connector #5 Technic Angle Connector #6

(Here are names and part numbers).

They also make angular liftarms, like these:

Technic Beam 4x4 liftarm bent (part 32348).

That last part has an angle of 53.5 degrees. What are the angles of the angle connectors, and why were these angles chosen? (I'd understand angles like 45, 60, and 72 degrees, but 53.5?!)

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1 Answer 1

up vote 14 down vote accepted

The regular connector have simple angles which are multiples of 22.5°. #4 is 45°, #3 is 22.5° and #5 is 67.5°. That's pretty boring stuff, but there you go.

The 53.5 angle isn't as bizarre as you would think and there's a very good reason for it (and less boring to me, but YMMV).

That reason is that it forms a Pythagorean triangle, and specifically the best known 3:4:5 one, meaning these liftarms can be used together with regular right-angle frames to make sturdy constructions.

The one you chose isn't the best example as the beam doesn't extend to the full hypotenuse (the connection points need to be 5 studs apart), but the longer one is perfect for that. If the small side is attached to a beam, the cross at the end of the long side will be perfectly aligned on a beam that would be 4 studs higher.

LEGO uses that to connect beams 4 studs apart in a very solid way, for example in 8435 - 4WD (the blue beam behind the front wheel) or in the more recent 8053 - Mobile Crane (left of the linear actuator)

And for the record, the angle in degrees is weirder that just 53.5°; it's actually 53.130102...°, or the invert cosine of 3/5. So if you thought Pythagoras and trigonometry wouldn't come and annoy you in your play, you're oh so wrong.

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Aha! I knew there was a reason for the angle on the lift arm. Thank you. I did try connecting a number of angle bricks (of the same type) together with axles to see if I could make a complete circle, and it didn't work. I'll have to try again; maybe my axles are bent. –  Clinton Blackmore Feb 19 '13 at 15:34
    
Try shorter axles :-) - that said, it works fine with #3 (16 sides) #4 (8) and #6 (simple square, obviously), but it won't work with the #5 one. And #2 might take a loooooong time, but there at least bendy axles will actually help. –  Joubarc Feb 19 '13 at 15:42
    
Ah. It must've been the #5 ones I was working with. Thanks again : ) –  Clinton Blackmore Feb 19 '13 at 16:58

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