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Frame Triangles and the Power of Pythagoras

3/5/2017

4 Comments

 
​​I rushed my Klann Ver 2 build and didn't build the outer frames in an optimal way:
Picture
The only thing keeping this frame's corners at right angles are the two 3x5 L-shaped LEGO parts.  If this frame were put under a lot of force, like would happen at a larger scale, the corners would be subjected to torque that could easily cause the rectangle to collapse. To avoid this diagonals need to be added, which will convert the rectangles into triangles and lock the corner's angles.
​
The challenge with walkers in LEGO is we often need diagonals for rectangles that define the linkage's parameters.  In other words, these diagonals often need to be the hypotenuses of right triangles.   As you can see below, my Klann's upper support rods are 7 holes above the motor's axle, and the lower support rods are 2 holes below the motor's axle.  Neither of these lengths work with a 3-4-5 or 6-8-10 right triangle with LEGO parts for hypotenuses. What can we do using the integer lengths of LEGO's beams?  
Picture
NOTE:  When determining the length of LEGO beams the first hole is always counted as 0!  If you don't measure LEGO beam lengths in this way you won't be able to use the Pythagorean theorem to calculate which beams to use as hypotenuses.
​

Fortunately, with LEGO we don't have to be at precise integer numbers, and we can use hypotenuses that are "close enough". 
​
1.  Hypotenuses for rectangles of height 7. 
Plugging in a 90 degree angle with a side length of 7, plus a few other whole number sides into the Pythagorean theorem yields this near integer number triangle:
Picture
​I used this triangle for Klann's inner frame where two 9 hole beams create hypotenuses of length 8:
Picture
I also used this.triangle for TrotBot's frame:
Picture
Picture
Triangles convert bending forces to tension and compression, which even plastic LEGO parts can handle well
Picture
Strider's Outer Frame's Triangle


​2. Hypotenuses for rectangles of height 9. 
We can also connect the top and bottom beams of Klann's frame with a hypotenuse:

Picture

Plugging a 90 degree angle with a side length of 9, plus a few other whole number sides into the Pythagorean theorem yields another near integer number triangle:
Picture
So, 13 hole LEGO beams can be used to lock Klann's outer frames into triangles, like this:
Picture
​​
Here are a few other useful triangles for LEGO frames:
Picture
Picture
Picture

​​Also, the below 5-3 bent beam can be used as a hypotenuse.
Picture
​


​The length of the part is 7.212:  
Picture
​​

​Which allows us to create this right triangle: 
Picture
You can create more triangles by lengthening a side of the above parts by attaching a LEGO beam to it.

​As shown in the image to the right, Strider Ver 2's frame height is not a whole number, but is 9.165.   Below shows some LEGO beam lengths for creating frames of a few different heights.
Picture
Picture
LEGO beam lengths for creating frames of varying heights
4 Comments
saran
2/13/2018 08:30:49 am

so in the mindstorm klaan they showed only the body
then I searched every where about how to build the legs

Reply
Ben
2/13/2018 03:27:31 pm

You can find the instructions on how to build the legs here:
https://www.diywalkers.com/klanns-spider-ver-2.html

Reply
Diamabolo
12/8/2021 09:01:31 am

Very good informations
For a Moc I want to build a
isosceles triangle with 90 degrees. This might not possible?

Reply
Wade
12/19/2021 10:46:35 am

You can get close with a 12 X 12 X 16.97

Reply

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  • Home
  • Walker ABC's
  • Build Instructions
    • TrotBot Builds >
      • TrotBot Linkage Plans
      • TrotBot's Legs Simplified
      • Quadruped TrotBot
      • Hexapod TrotBot
      • TrotBot
      • TrotBot, Ver 3
      • Mindstorms TrotBot, Ver 3
      • Wooden TrotBots by Automata Korea Design
      • 3D Printed TrotBot by Scott Anderson
      • Large-Scale TrotBot
    • Strider Builds >
      • Strider Linkage Plans
      • Strider Ver 3's Legs
      • Strider Ver 3's Frame
      • Mindstorms Strider Ver 3 Mod
      • Strider
      • Strider's Legs Simplified (ver 2's)
      • RC Strider
    • Mechanical Spider >
      • Klann's Linkage Plans
      • Klann Mechanical Spider - Climbing Mod
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      • Klann High-Step Mod
      • Klann's Spider, Ver 2
      • Mindstorms Klann
    • Strandbeest
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    • Linkage Warm Ups >
      • Lever Paradox
      • LEGO Biters
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      • LEGO Hopping Robot
    • Hiro Labo
    • Whegs (wheel-legs)
  • Customize
    • 4 Bar Linkage Optimizer
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    • Klann Linkage Optimizer
    • Strandbeest Optimizer for LEGO
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  • Linkage Simulation
    • Python Linkage Simulator
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  • Blog