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BASE OF THE SLIDER-CRANK MECHANISM
Self-invented name. |
Let OP = a be the crank and PQ = b be the
connecting rod:
Polar equation: . Cartesian parametrization: (). Cartesian equation: . Sextic of genus 1. |
Given an articulated mechanism (OPQ), O
being fixed and Q being bound to move on a straight line D
passing through O (here Ox), the curve (G)
that we are studying is the locus of the points of the line (OP)
whose projection on D is Q.
Therefore, it is the base of
the movement of the plane for which P is a fixed point and (PQ)
a fixed line. This movement is called the slider-crank
mechanism, (hence the name of this curve). The rolling curve of the movement
(in yellow on the figure on the right) is Jerabek's
curve.
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The curve has two bounded components when the crank is
longer than the connecting rod (a > b), and two components
with asymptotes when a < b; when a = b, it is a circle.
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© Robert FERRÉOL 2017