Tusi-couple

As Cardanische circles the two circles are called, which by rolling a circle inside a circle with double radius through each point of the rolling circle a straight hypocycloid is generated. This relationship was first described in 1570 by the Italian humanists Gerolamo Cardano. This is to early studies of Cycloid, which were later expanded by Galileo.

Formulation of the set of Cardano

Given a circle k with center M and radius r = R is in a circle K with center Z and twice the radius 2r and touching it at point P. The circle k 'll imaged by rolling on the edge of the circle K on the circle k1 and P1 denote the contact point of k1 with K.

Then:

(i ) If the intersection of the circle k, then the arcs PP ' and PP1 same length.

( iii ) If k rolled up into its original position, then the point A moves in a straight line on the diameter and passes through each point of the diameter exactly twice.

In short form: Roll a circle inside a circle with twice the radius from, then each point of the small circle moves in a straight line on a diameter of the large circle.

Addition: Each point in the interior of the rolling disc during one revolution describes an ellipse whose center coincides with the center of the large circle. This was published in 1706 by Philippe de La Hire.

Technical Applications

Is the outer circle toothed internal and executed, the inner circle of a toothed wheel, it may be a rod that is fixed at point A and moves in parallel to the diameter, a use up and down movement of the machine. This principle was based on the invention of the printing presses of Quick König & Bauer.