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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 plane p, one of the two shortest sides (for example AB) blocked and side AD moved on the plane, it can easily be inferred that C and D describe two circumferences with centers in A and B respectively. Sides AD and BC cross in P.
Because P belongs to the axis of symmetry of the antiparallelogram it is PA + PB = PA + PD = AD = cost. Therefore the set of points described by P is an ellipse with A and B as focal points.
