Macchine Matematiche

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Tool drawing a hyperbola by means of an antiparallelogram

An atiparallelogram linkage is an articulated quadrilateral ABCD where the opposite sides, AB and CD, are the non-parallel sides of an isosceles trapezoid; the remaining two side, AD and BC, are the diagonals of the same trapezoid.

If the antiparallelogram is placed on a plan , one of the two shortest sides (for example AB) blocked on and side BC moved on the plan, it can easily be inferred that C and B describe two circumferences with centers in D and A respectively. When properly extended sides AB and CD cross in P.

Because P belongs to the axis of symmetry of the antiparallelogram it is PA – PB = PA – PD = AB = cost. Therefore the set of points described by P is an arc of a hyperbola with A and D as focal points.

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