ball-and-disk integrator

 The ball-and-disk integrator is a key component of many advanced mechanical computers

Through simple mechanical means, it performs continual integration of the value of an input. Typical uses were the measurement of area or volume of material in industrial settings, range-keeping systems on ships, and tachometric bombsights

The addition of the torque amplifier by Vannevar Bush led to the differential analysers of the 1930s and 1940s

The basic mechanism consists of two inputs and one output. 

The first input is a spinning disk, generally electrically driven, and using some sort of governor to ensure that it turns at a fixed rate. The second input is a movable carriage that holds a bearing against the input disk, along its radius. 

The bearing transfers motion from the disk to an output shaft. The axis of the output shaft is oriented parallel to the rails of the carriage. 

As the carriage slides, the bearing remains in contact with both the disk & the output, allowing one to drive the other.

The spin rate of the output shaft is governed by the displacement of the carriage; this is the "integration." When the bearing is positioned at the center of the disk, no net motion is imparted; the output shaft remains stationary. As the carriage moves the bearing away from the center and towards the edge of the disk, the bearing, and thus the output shaft, begins to rotate faster and faster. Effectively, this a system of two gears with a continuously variable gear ratio; when the bearing is nearer to the center of the disk, the ratio is low (or zero), and when the bearing is nearer to the edge, it is high.[1]

The output shaft can rotate either "forward" or "backward," depending on the direction of the bearing's displacement; this is a useful property for an integrator.

Consider an example system that measures the total amount of water flowing through a sluice: A float is attached to the input carriage so the bearing moves up and down with the level of the water. As the water level rises, the bearing is pushed farther from the center of the input disk, increasing the output's rotation rate. By counting the total number of turns of the output shaft (for example, with an odometer-type device), and multiplying by the cross-sectional area of the sluice, the total amount of water flowing past the meter can be determined..

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