The lengths of the links comply with the conditions: A͞B=A͞C=D͞P=D͞Q=a and A͞D=B͞P=C͞Q=b. Figure ABPD is a crossed-crank linkage and figure ADQC is a parallel-crank linkage. Links 1 and 2 turn about fixed axis A which is the centre of inversion transformation. Links 3 and 4 are connected by turning pairs B and C to link 2 and by turning pairs P and Q to links 5 and 6. Links 5 and 6 are connected by turning pairs D to each other and to link 1. For any configuration of the mechanism, points A, P and Q lie on a single straight line. When point P or Q travels along any arbitrary curve, the other point describes a curve which is the inversion of the first curve. Hence, the mechanism accomplishes inversion transformations of the form A͞P×A͞Q=b²-a² =const.
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