Page:The Kinematics of Machinery.djvu/91

 fore lie in that line or its prolongation. Assume, provisionally, that is the instantaneous centre, and suppose the line c d to be fixed, so that both a and b may revolve as they did at first, then the two centroids, both moving, roll upon one another in 0, and have therefore at that point the

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same peripheral velocities. Their angular velocities will have to each other the ratio d: cO. But by hypothesis this ratio is constant, there- fore also d and c themselves must be constant; and the centroids become circles described about c and d with radii which are in inverse