A speedometer is a device for measuring and presenting to an operator the speed of a wheeled vehicle, such as an automobile. A sample point is selected, typically at the final output (the tailshaft) of the transmission, where a flexible rotating cable is driven. The other end of this cable is connected to the speedometer, which is a specially calibrated tachometer. The responsiveness of this tachometer and its calibrated numbering must take into consideration the gear reduction from the tailshaft to the flexible cable, the final drive ratio in the differential unit, and the diameter of the driven tires. The mechanism within the speedometer head will usually also drive one or more wheeled numeric counters called odometers.
Automobile speedometers are often calibrated to display a higher than true reading, in order to guarantee that the driver does not exceed a legal speed limit due to an inaccuracy. A major reason for inaccuracy is tire diameter, which varies with inflation pressure.
Speedometers may also be electronic. Some rotation sensor delivers a pulse with each rotation. A computer is used to convert the interval between pulses to a digital display. A count of the pulses is also accumulated to use in calculating an odometer reading of the distance traveled.
A GPS system may also be used as a speedometer. This is usually more accurate as car speedometers as GPS systems are not calibrated to display a higher reading. Another advantage of using a GPS as speedometer is that it is easy to install and only depends on a somewhat clear view of the sky and a power supply. However it takes up to a minute before it has "tracked" all the satellites and only updates the reading every second or two. Bad signal will lead to it being inaccurate.
As for the spedometer, what may have happened when they were changing the oil they may have accidentally frayed or loosened the cord that connects it to the motor itself, causing it to fall out.
If it was frayed or snapped, you're looking at having to replace the cord itself (be sure to get it new, I got a used one for my car that looked decent, but turns out it was worn down a bit so every time I drive it looks like my speedometer's having a seizure).
The sensor alone was the reason the spedometer wasn't working AND it is also why the car was shifting like crap.
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