differential

differential, in the automobile, a set of gears used on the driving (usually rear) axle. The two wheels on the driving axle must be interconnected in order to receive their energy from the same source, the driving shaft; at the same time they must be free to revolve at different speeds when necessary (e.g., when rounding a curve, the outer wheel travels farther and thus must revolve faster than the inner wheel in order to prevent skidding). These two requirements are met by the differential gearing. Furthermore, through it the rotating motion of the driving shaft is transmitted to the axle and the wheels. The axle is in two halves; to each half is attached a wheel at one end and, at the inner end, a gear (see gear). The end of the driving shaft is also equipped with a gear. By an ingenious arrangement of these and other gears, together constituting the differential, a difference in speed of the two wheels is compensated for without a loss of tractive force. A disadvantage of the conventional differential is that when one wheel is on a dry and the other on a slippery surface, the differential causes the wheel on the slippery surface to revolve at double speed while the other wheel remains stationary. This hazard can be avoided by use of a limited slip differential, which feeds power to one wheel when the other wheel starts to slip and thus keeps the automobile moving.

Bibliography

See R. T. Hinkle, Kinematics of Machines (2d ed. 1960).

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differential

In calculus, an expression based on the derivative of a function, useful for approximating certain values of the function. The differential of an independent variable x, written Δx, is an infinitesimal change in its value. The corresponding differential of its dependent variable y is given by Δy = f(x + Δx) − f(x). Because the derivative of the function f(x), f′(x), is equal to the ratio ^Δy⁄_Δy as Δx approaches zero (see limit), for small values of Δx, Δy ≅ f′(x)Δx. This formula often enables a quick and fairly accurate approximation to be made for what otherwise would be a tedious calculation.