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628 ARTHUR J. HOLMAN [J. S. M. p. K.
universal joint supporting a cage on which is mounted the concave member, and the inner universal joint supporting a central shaft on which is mounted the convex member. The machine includes mechanism for oscillating the cage about the center of the outer universal joint and oscillating the central shaft about the center of the inner universal joint in a plane at right angles to that in which the cage oscillates. The operating gear train is arranged to provide a slight difference in the frequency of oscillation of the cage as compared with the oscillation of the central shaft. The concentric sleeves are arranged to rotate either in opposite directions 'or at slightly different rates in the same direction, but the drive for these sleeves operates very slowly in order that the resultant relative rotation of lens blank and lap about their respective axes may be a minimum. The foregoing is sufficient to illustrate that the relative movements of lens blank and lap are produced primarily by each member oscillating in a plane at right angles to the other and at slightly different frequencies, the pattern of the path of any element on the surface of the lens blank over the surface of the lap being further modified by the slow relative rotation of lens blank and lap.
The slight difference in frequencies of the oscillating members causes a constantly changing phase angle which is most effective in varying the relative movements of lens blank and lap. Assuming that the adjustable cranks have been set to give equal amplitudes of oscillation to the lens blank and the lap, and the machine has been operated till both reach a maximum at the same instant, then the path of the center of the lens blank across the lap will lie in one plane (neglecting for the moment the relatively slow rotation of lens blank and lap) and this plane will make an angle of 45 degrees with the planes of oscillation. As the device continues to operate, the oscillating members become more and more out of phase and, when the phase angle becomes 90 degrees, the path of the center of the lens blank across the lap is a circle. When the phase angle is 180 degrees the path lies in a plane again but this plane makes an angle of 90 degrees with the "in phase" plane mentioned above. When the phase angle becomes 270 degrees the path is again a circle but this circle is generated in the reverse direction. At 360 degrees the path returns to the initial "in phase" plane.
The impression created by observing the device in operation is about as follows. At the "in phase" period there is a relatively long resultant stroke along a straight line at 45 degrees to the planes of