Answers.Body: <p>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.</p>
  
  <p>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).</p>
  
  <p>That reason is that it forms a <a href="http://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean triangle</a>, 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.</p>
  
  <p>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 <a href="http://peeron.com/inv/parts/6629">longer one</a> 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.</p>
  
  <p>LEGO uses that to connect beams 4 studs apart in a very solid way, for example in <a href="http://www.brickset.com/detail/?set=8435-1">8435 - 4WD</a> (the blue beam behind the front wheel) or in the more recent <a href="http://www.brickset.com/detail/?Set=8053-1">8053 - Mobile Crane</a> (left of the linear actuator)</p>
  
  <p>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.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2013-02-19T15:34:53.693Z
Answers.Text: 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.
Answers.UserDisplayName: Clinton Blackmore
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2013-02-19T15:42:00.530Z
Answers.Text: 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.
Answers.UserDisplayName: Joubarc
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2013-02-19T16:58:50.327Z
Answers.Text: Ah.  It must've been the #5 ones I was working with.  Thanks again : )
Answers.UserDisplayName: Clinton Blackmore
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2013-02-19T07:59:27.127Z
Answers.LastActivityDate: 2013-02-19T07:59:27.127Z
Answers.UserDisplayName: Joubarc
Body: <p>LEGO makes Technic Angle Connectors, like these:</p>
  
  <p><img src="https://i.sstatic.net/3aE0L.png" alt="Technic Angle Connector #1">
  <img src="https://i.sstatic.net/lEK6L.png" alt="Technic Angle Connector #2">
  <img src="https://i.sstatic.net/oHVvn.png" alt="Technic Angle Connector #3">
  <img src="https://i.sstatic.net/3l5nG.png" alt="Technic Angle Connector #4">
  <img src="https://i.sstatic.net/hc7QC.png" alt="Technic Angle Connector #5">
  <img src="https://i.sstatic.net/AqKHA.png" alt="Technic Angle Connector #6"></p>
  
  <p>(<a href="http://static.robotclub.ab.ca/pages/nxt/InventoryComparison/nxt_1_vs_2_vs_edu.html#AngleConnectors" rel="noreferrer">Here are names and part numbers</a>).</p>
  
  <p>They also make angular liftarms, like these:</p>
  
  <p><img src="https://i.sstatic.net/zFve6.png" alt="Technic Beam 4x4 liftarm bent"> (part <a href="http://peeron.com/inv/parts/32348" rel="noreferrer">32348</a>).</p>
  
  <p>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?!) </p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-02-25T16:09:25.923Z
Comments.Text: I came here because I was looking for pieces with a given angle to aid in a construction of mine. I also found [this site](http://neilwebber.com/notes/2015/07/25/lego-technic-triangle-geometry/) very helpful, since it gives examples of how to form 30 & 60 degree angles, in addition to a [script](http://neilwebber.com/files/legotriangles) which allows you to ask for any angle you'd like. Hope this helps someone else, too.
Comments.UserDisplayName: Frank Bryce
Tags: <technic><piece-information>
Title: What are the angles used in angle connectors and liftarms?
UserDisplayName: Clinton Blackmore
ThreadText: # What are the angles used in angle connectors and liftarms?
  
  (Asked by: username_0 on 2013-02-19)
  
  LEGO makes Technic Angle Connectors, like these:
  
  ![Technic Angle Connector #1](https://i.sstatic.net/3aE0L.png)
  ![Technic Angle Connector #2](https://i.sstatic.net/lEK6L.png)
  ![Technic Angle Connector #3](https://i.sstatic.net/oHVvn.png)
  ![Technic Angle Connector #4](https://i.sstatic.net/3l5nG.png)
  ![Technic Angle Connector #5](https://i.sstatic.net/hc7QC.png)
  ![Technic Angle Connector #6](https://i.sstatic.net/AqKHA.png)
  
  ([Here are names and part numbers](http://static.robotclub.ab.ca/pages/nxt/InventoryComparison/nxt_1_vs_2_vs_edu.html#AngleConnectors)).
  
  They also make angular liftarms, like these:
  
  ![Technic Beam 4x4 liftarm bent](https://i.sstatic.net/zFve6.png) (part [32348](http://peeron.com/inv/parts/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?!)
  
  **Tags:** technic, piece-information
  
  > **Comments:**
  > **username_1**: I came here because I was looking for pieces with a given angle to aid in a construction of mine. I also found [this site](http://neilwebber.com/notes/2015/07/25/lego-technic-triangle-geometry/) very helpful, since it gives examples of how to form 30 & 60 degree angles, in addition to a [script](http://neilwebber.com/files/legotriangles) which allows you to ask for any angle you'd like. Hope this helps someone else, too.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2013-02-19. Score: 22 | Accepted answer
  
  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](http://en.wikipedia.org/wiki/Pythagorean_triple), 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](http://peeron.com/inv/parts/6629) 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](http://www.brickset.com/detail/?set=8435-1) (the blue beam behind the front wheel) or in the more recent [8053 - Mobile Crane](http://www.brickset.com/detail/?Set=8053-1) (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.
  
  > **Comments:**
  > **username_0**: 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.  
  > **username_2**: 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.  
  > **username_0**: Ah.  It must've been the #5 ones I was working with.  Thanks again : )  
  
  ---
  
  