Journal of the Society of Motion Picture and Television Engineers (1950-1954)

slip back uniformly with respect to the base of the sprocket as it stripped off the teeth. By this means, films of minimum and of maximum shrinkage would be driven without flutter. For intermediate values of shrinkage, the film would be driven for part of each pitch length of travel at the speed of unshrunk film, and for the remainder of the pitch length at the speed of film of maximum shrinkage. If the sprocket were designed for a shrinkage range of 1%, the peak variation in velocity would be 1.0% for all intermediate values of shrinkage. The rms deviation in velocity, commonly referred to as "flutter," would depend on shrinkage, because this determines the relative time the film is driven at each of the two speeds. For a shrinkage of 0.5%, the times would be equal, and the rms deviation would equal the peak deviation of 0.5%. The Mechau proposal is shown in Fig. 1. The film is driven by a waferlike sprocket and is supported by rotatable disks on either side of the sprocket. The disks are slightly larger in diameter than the base diameter of the sprocket and are eccentrically mounted relative to the sprocket. This provides a continuously increasing effective sprocket radius as the film passes through its engagement with the sprocket. The presumption is that the effective sprocket pitch depends on the effective radius. Film of any shrinkage is automatically driven in that region where the effective sprocket pitch most nearly matches the film pitch. Since no mention was made of the manner of determining the optimum tooth profile, the Mechau specification was incomplete until a geometrical analysis was published by Chandler. His analysis follows these lines : Referring to Fig. 1 , assume that the film is ted onto the sprocket at the point where the supporting disks are tangent to the base of the sprocket. The perforation will then describe an epicycloid curve relative to the sprocket base as it moves along the surface of the supporting member and away from the center of the sprocket. This epicycloid curve would be the correct tooth profile to drive unshrunk film. The sprocket and film would be in perfect mesh, i.e., each tooth would bear against each perforation. However, if the pitch of the film were either slightly shorter or slightly longer than that of the sprocket, then either the last tooth or the first tooth engaged with the film would be the only one which did any driving, and the film motion would be nonuniform. To achieve the variable-pitch sprocket, it is necessary to modify the epicycloid curve, as shown in Fig. 2. When this is done, it can be seen that the effective pitch of the sprocket, i.e., the distance between teeth along the film line, will continually decrease as the film passes from the tangent point to the point of disengagement along the supporting drum or "stripper." The result is that any film whose shrinkage is within the range for which the sprocket is designed is automatically driven in that region where the effective sprocket pitch matches the film pitch. Several of these variable-pitch sprockets have been tried, particularly in 16mm contact and optical printers. While all of these sprockets handled the shrinkage range for which they were designed, picture steadiness and sound flutter were not as good as was believed possible, on the basis of the known precision of the film and of the mechanical parts involved. It can readily be seen that accurate longitudinal registration of a film by means of a sprocket tooth which presents an inclined face to the edge of the perforation, depends on accurate control of the distance of the driven edge of the perforation from the center of the sprocket. For example, if the driven edge of the perforation were drawn down into the slot between the two supporting disks on either side of the sprocket because of friction of the film on the 530 December 1951 Journal of the SMPTE Vol. 57