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Ball-and-disk integrator
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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 is a system of two gears with an infinitely 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.
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.
The basic concept of the ball-and-disk integrator was first described by James Thomson, brother of William Thomson, 1st Baron Kelvin. William used the concept to build the Harmonic Analyser in 1886. This system was used to calculate the coefficients of a Fourier series representing inputs dialled in as the positions of the balls. The inputs were set to measured tide heights from any port being studied. The output was then fed into a similar machine, the Harmonic Synthesiser, which spun several wheels to represent the phase of the contribution from the sun and moon. A wire running along the top of the wheels took the maximum value, which represented the tide in the port at a given time. Thomson mentioned the possibility of using the same system as a way to solve differential equations, but realized that the output torque from the integrator was too low to drive the required downstream systems of pointers.
A number of several systems followed, notably those of Leonardo Torres Quevedo, a Spanish physicist who built analog machines for solving real and complex roots of polynomials; and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to the mathematical understanding of the Gibbs phenomenon of overshoot in Fourier representation near discontinuities.
By the turn of the 20th century, naval ships were starting to mount guns with over-the-horizon range. At these sorts of distances, spotters in the towers could not accurately estimate range by eye, leading to the introduction of ever more complex range finding systems. Additionally, the gunners could no longer directly spot the fall of their own shot, relying on the spotters to do this and relay this information to them. At the same time the speed of the ships was increasing, consistently breaking the 20 knot barrier en masse around the time of the introduction of the Dreadnought in 1906. Centralized fire control followed in order to manage the information flow and calculations, but calculating the firing proved to be very complex and error prone.
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Ball-and-disk integrator AI simulator
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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 is a system of two gears with an infinitely 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.
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.
The basic concept of the ball-and-disk integrator was first described by James Thomson, brother of William Thomson, 1st Baron Kelvin. William used the concept to build the Harmonic Analyser in 1886. This system was used to calculate the coefficients of a Fourier series representing inputs dialled in as the positions of the balls. The inputs were set to measured tide heights from any port being studied. The output was then fed into a similar machine, the Harmonic Synthesiser, which spun several wheels to represent the phase of the contribution from the sun and moon. A wire running along the top of the wheels took the maximum value, which represented the tide in the port at a given time. Thomson mentioned the possibility of using the same system as a way to solve differential equations, but realized that the output torque from the integrator was too low to drive the required downstream systems of pointers.
A number of several systems followed, notably those of Leonardo Torres Quevedo, a Spanish physicist who built analog machines for solving real and complex roots of polynomials; and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to the mathematical understanding of the Gibbs phenomenon of overshoot in Fourier representation near discontinuities.
By the turn of the 20th century, naval ships were starting to mount guns with over-the-horizon range. At these sorts of distances, spotters in the towers could not accurately estimate range by eye, leading to the introduction of ever more complex range finding systems. Additionally, the gunners could no longer directly spot the fall of their own shot, relying on the spotters to do this and relay this information to them. At the same time the speed of the ships was increasing, consistently breaking the 20 knot barrier en masse around the time of the introduction of the Dreadnought in 1906. Centralized fire control followed in order to manage the information flow and calculations, but calculating the firing proved to be very complex and error prone.
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