On the Theory of the Progressive Universal Winding

The rigorous theory previously developed by the author for the ordinary or stationary universal winding is extended to the progressive universal winding; in particular, an exact formula for calculating the gear ratio to be employed in winding a progressive universal coil is deduced, and, by neglecting certain terms therein, formulas representing various degrees of approximation of the same are derived and shown to be equivalent of those previously given by the author, by Joyner and Landon, and by Hershey. The theory of the spiral ridges and close-packed layers of progressive universal coils is developed, and formulas giving the slope of the spiral ridge and the dimensions of the close-packed layers are deduced. The principles underlying the selection of the optimum number of crossovers per turn are discussed, and an example of the application of the formulas to the design of a progressive universal coil is given.