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CONSIDERATION IN SPROCKETS DESIGN 165
The film path, in general, is fixed by the design of film shoe, stripper, roller, or other means, and in some cases may be determined wholly or in part by the film tension and stiffness. In order to simplify the analysis and the shoe construction, the film path, AP, is taken to be the arc of a circle (or a straight line) tangent to the base circle at P. The sprocket-base circle is a convenient reference circle and may not exist on the actual finished sprocket if other means of film support are provided.
The film may remain in contact with the base circle any arbitrary distance, say, PC, and then disengage from the teeth along any suitable path similar to or different from AP. The special case of PC = 0, as well as the general case, will be treated later in the paper.
In general, only one sprocket-tooth will touch the film at any given time except at the transition instant when two teeth will touch.
SPROCKET TOOTH
FIG. 1. Sketch of film and sprocket. FLUTTER
The aim of the designer is to produce a sprocket that will move the film along as steadily as possible. Unsteady movement will produce density variations in the case of picture printers or "flutter" in the case of sound apparatus. For purposes of this paper, flutter will be considered as a measure of the unsteadiness and will be defined as the ratio between the unsteady film velocity component and the steady velocity component. If the film speed is 1 per cent higher than the average at a given instant, the flutter is 1 per cent at that instant. The flutter frequency will be that of the sprocket teeth, 24 cycles per second for 16-mm film and 96 cycles per second for 35-mm film. As a rough basis of comparison, the time average of the instantaneous flutter may be considered but is not to be taken as a measure of the subjective effect.
The determination of flutter is facilitated if we consider only velocities relative to the base circle of the sprocket, which is assumed to rotate at constant velocity. For this reason we will consider that