Figure P15.52 represents an ingenious gear train for obtaining a tremendous reduc-tion

Chapter 15, Problem 15.52

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Figure P15.52 represents an ingenious gear train for obtaining a tremendous reduction ratio in a small space. It is similar to Figure P15.49 except that the arm is the driver and the diameters of the two suns and the diameters of the two planets (which are made together as a single piece) are very nearly the same. First, notice that if these pairs of gears had exactly the same diameters, the output velocity would be zero. If we make the pitch of S1 and P1 just slightly greater than the pitch of S2 and P2, the center distances will be the same for the numbers of teeth shown. Determine the magnitude and sign of the gear train speed ratio.