## Artobolevsky's Ellipsograph

This is a basic linkage illustrating several elements entering into link mechanisms. First the four bar mechanism itself, called [crossed-crank linkage], consisting of four segments making an isosceles trapezium together with its diagonals. At their intersection point is added a double guiding element consisting of two sliders, connected together by a turning pair E. |BE|+|EA| = |BD| = |BC| is constant and equal to the radius of the [Director] circle of the ellipse. The tangent to the ellipse at E is the axis of symmetry of the crossed-crank. This gives also the method to build such a moving crank: Draw first the fixed length segment AB and the radius BD to the moving point D. Then define the axis of symmetry which coincides with the medial line of segment AD. Finally reflect ABD on this axis.

The shape of the ellipse is controlled by moving points A and C. |BC| defines the radius of the director circle. |AB| is the focal distance. The construction is taken from Artobolevsky's book [Mechanisms in modern engineering design, Mir 1976 vol. II, p. 93].