The lengths of the links comply with the conditions: A͞B=A͞C, B͞P=B͞Q and C͞P=C͞Q. Figure PBQC is a rhomboid 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 to link 2 and by turning pairs Q and P to links 6 and 5. Links 6 and 5 are connected by turning pairs C to link 1. For any configuration of the mechanism, points A, P and Q lie on straight line Aa. 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 A͞PxA͞Q=A͞B²-B͞P²=A͞C²-C͞P²=const. The mechanism is equivalent to either of two link-gear mechanisms, consisting of links 1, 5, 6, 7 and 8, or of links 2, 3, 4, 7 and 8, where links 7 and 8 are sliders moving along guiding link Aa which turns about axis A. The mechanism accomplishes rectilinear translation of straight line BC which is perpendicular to straight line APQ.
$1374$LG,GI$