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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 |

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