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Contents 1. Compass & Straightedge 2. Triangle: Points & Lines 3. Economical Constructions 4. 3D Workshop 5. Wire Puzzles 6. Quadratic Functions 7. Conics and Other Curves 8. Linkages 
LinkagesA linkage in its simplest form is a system of rigid bars, or links, connected by hinged joints that allow two connected bars to rotate with respect to each other. Such linkages are used in a pantograph (a tool for copying a drawing to a desired scale), in a windshield wiper, in the piston system of an engine and so on. In 1877 Sir Alfred Kempe published an amazing theorem which, in a popularized form, can be worded as follows: there exists a plane linkage that can forge your signature with any desired precision. In fact, Kempe’s proof contained a flaw, which was corrected in 2002. A huge contribution to the theory of linkages was made by the great Russian mathematician P. L. Chebyshev. He was especially interested in the mechanisms that convert circular and rectilinear motions into each other. One of these devices and its simpler predecessors are presented in the models below. FourBar Linkage
CrankandRocker MechanismA crankandrocker mechanism is obtained from the fourbar linkage by attaching a rigid triangle to the floating link (the one in the middle). The path described by the outer vertex of this triangle heavily depends on its shape, as you can see by varying the triangle's side lengths.
Chebyshev's Lambda MechanismPafnuty Lvovich Chebyshev, the great Russian mathematician (18211894), who made a substantial contribution to numerous areas of mathematics, invented many interesting mechanisms based on the fourbar linkage. The "Lambda mechanism," called so because it resembles the Greek letter lambda, was intended to convert the rotational motion into rectilinear motion. The mechanism was later studied by Karl Hoecken and is often referred to as Hoecken's Mechanism.

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