The Fifth R

Linkages in LEGO

The leg bone is connected to the thigh bone

1 bar linkage
When a single bar is pivoted at one end, the other end will turn round in a circle. This is the basis of the familiar crank. The axle around which the free end of the crank turns is called, appropriately, the crankshaft.  There are many LEGO parts that can be used as a crank: engine crank, pulley, gear, liftarm, cam, etc.

Applications: windlass

A crank is actually a form of lever where the force is applied in a circular motion (better known as torque).
The force can be applied to turn the crankshaft as by a motor and the free end of the crank can then be made to perform work, like kicking a ball. 
Alternatively, the force can be applied to the free end of the crank and the work is done at the axle (or crankshaft) as in a windlass. 
This is also what you are doing when you crank up an engine.  But nowadays it is easier to just turn the ignition key :-)
2 bar linkage
The 2-bar link forms a hinge with the two bars opening or closing about the common pivot point. Familiar as a pair of tongs. Most commonly used as a jaw.  Actually a 2nd class lever with the fulcrum at the pivot point.  How about the jaws of T. rex?
Use as grabber
Lever for pumping the large pneumatic pump.
3 bar linkage
The 3-bar linkage is familiar as the Watts linkage.
Note that if the 3 links are closed, a triangle results which is a rigid structure. Although the closed 3-bar linkage is useless as a mechanism as the parts are immovable, it is just great for strengthening your creations. Triangular tread drive.
It has been known since ancient times that if the bars are in the ratio 3:4:5, a right angled triangle results. There are not many right angled triangles you can make with LEGO. Can you find them? Good old Pythagoras' Theorem?
4 bar linkage
This is the most important linkage category. You will find applications of the 4-bar linkage in almost if not all of the Technic models.
Inversions
 
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