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654
EDWARD W. KELLOGG
[J. S. M. P. E.
represent either a pulling sprocket with counter clockwise rotation or a hold-backs procket with clockwise rotation. Let us consider the case of a pulling sprocket. So long as the film is against the bottom of tooth No. 1, no other tooth being in contact with film, there will be no slipping over the cylindrical supporting surface, and the film will move at the non-slip speed, V = ir(D + t)n, in which D is the diameter of the cylindrical supporting surface, t the thickness of the film, and n the number of revolutions per second. When tooth No. 1 reaches the end of the arc of wrap and the film begins to strip from No. 1, it must slip back by the amounts by which tooth No. 2 previousy failed to touch, before No. 2 can exert any pull. After this slip-back has occurred and tooth No. 2 is in contact, the film speed
CONTffCT
FIG. 1. Sprocket and film with perfect fit.
resumes the non-slip value until No. 2 begins to strip. The film motion thus consists of a series of movements at non-slip speed, alternated with movements at lower speed during which the slip-back is taking place.
What the speed of the film is during slip-back and what fraction of the time the slipping back occupies, depends on the shape of the teeth and the manner in which the stripping takes place. The ideal stripping would be for the film at a certain point to cease following the arc and follow a tangent. Tooth roughness would cause inevitable departures from the manner of stripping just described, with consequent irregularities in the film velocity, but only by assuming that the film moves outward from the sprocket at some definite rate can