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4-Bar Linkage Optimizer 

Posted by Ben and Wade

​​​​This linkage simulator allows you to quickly check how changing the linkage's bar lengths affect the path it draws as the crank is rotated. 

The bar map below shows 5 bars, b0 thru b4, but since the angle between b2 and b4 is fixed, j1 thru j4 is considered a single bar.  Also, the frame functions as a bar of the linkage, with frame connections j0 and j3 creating bar b0.
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Chebyshev's Lambda Mechanism
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Below is an interactive simulator which is started by clicking the green flag.  You can also run the simulator on MIT's site where you can modify the code.

After changing a bar's length, click somewhere other than a slider bar and then press the space bar to see the new linkage, and use your keyboard's left/right arrows to rotate the crank.

​​A description of the algorithms, and how we used them to simulate linkages, is here.
​
​Below are some of the major categories of 4-bar linkage behavior, created by re-arranging the yellow, white, orange and red bars:

​When building a simulated linkage in LEGO, remember to use beams with one more hole than the bar's length.  For example, a bar of length 8 requires a LEGO beam with 9 holes, because when determining the length of LEGO beams, the first hole is always counted as zero.
​

​​​4-bar linkages configured to have a crank and rocker can be used to make simple, sturdy and efficient mechanical legs like this, which can be modified on our 4-Bar Walking Linkage Optimizer page.
Picture
Picture
A 4-Bar Walking Linkage with a Crank and Rocker

4-bar linkages can also serve as a starting point for making more complicated mechanisms with improved features, like Strider's paired-leg, 10-bar linkage below which we originally made by linking two 4-bar linkages:
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Evolution has also found 4-bar linkages to be useful for knee joints:

4-bar linkages can be used to create robotic arms and legs in numerous ways.  Below is a feasibility test of a hopping robot based on a 4-bar linkage.  
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A 4-Bar Linkage Optimized for Jumping
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LEGO Hopping Robot

And for a fun classroom activity for introducing 4-bar linkages, see LEGO Punchers:

These punchers can also be motorized, but this requires converting the circular motion of the motor to oscillation.  This can be done by programming a servo motor to do a partial rotation, or by adding a crank and a 6th bar to the mechanism as done in the following video:
  • 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
      • Mindstorms TrotBot, Ver 2
      • Mindstorms TrotBot
      • 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 Mechanical Spider - Climbing Mod
      • Klann's Spider, EV3 Long Legs
      • Klann High-Step Mod
      • Klann's Spider, Ver 2
      • Mindstorms Klann
      • Klann's Spider, Ver 1
      • Klann's Linkage Plans
    • Strandbeest
    • LEGO Spot Micro
    • Linkage Warm Ups >
      • Lever Paradox
      • LEGO Biters
      • LEGO Punchers (4 bar linkage warm-up)
      • LEGO Hopping Robot
    • Hiro Labo
    • Whegs (wheel-legs)
  • Customize
    • Strider Linkage Optimizer
    • Klann Linkage Optimizer
    • Strandbeest Optimizer for LEGO
    • TrotBot Optimizer
    • 4 Bar Linkage Optimizer
    • 4 Bar Walking Linkage
    • 6 Bar Walking Linkage
  • Linkage Simulation
    • Python Linkage Simulator
    • Scratch Linkage Simulator
  • Blog