The Machine Gun

dulum, the relationship between the displacement of the bob and time, involves an integral of a special type known as an "elliptic integral" which can be evaluated by the use of infinite series or by means of special tables. However, the equation derived above for the toggle linkage brccch mechanism is further complicated by the fact that F is an empirical function of time and any attempt to obtain a solution by direct methods would involve extremely intricate manipulations. Probably the best method of attack would be to assign suitable values to Mi, M2, r, and L and then (using a curve expressing the variation of F with time) to evaluate the integrals involved in the solution by one of the standard methods for numerical approximation. Because of the form of the differential equation and the fact that F varies with time, even this approach will be very laborious and much too tedious to demonstrate in this publication. Accordingly, the time-travel and time-velocity curves will not be developed here.

The general form of the time-travel and time-velocity curves for the complete cycle of a retarded blowback gun employing a toggle linkage (fig. 1-48) will closely resemble the form of the curves for a delayed blowback gun.

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