4 Bar Linkage Optimizer 

​​​​This Scratch 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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Below is an interactive Scratch simulator.  You can also run the simulator on MIT's site where you can modify the Scratch 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.
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​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.
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Evolution has also found 4-bar linkages to be useful:

4-bar linkages can also used to create robotic arms and legs.  Below is a feasibility test of a hopping robot based on a 4-bar linkage.  

A 4-Bar Linkage Optimized for Jumping

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 using an EV3 brick to program the motor to do a partial rotation, or by adding a crank and a 6th bar to the mechanism as done in the following video: