The nutating disc meter is is probably the most widely used flowmeter in the world. It is claimed that more than half the water meters installed in domestic premises in the US and Europe are of this type. Used for 150 years, the illustration below shows its ancestry very clearly - it is essentially a Dakeyne Disc Engine. That is not surprising - at least one specialist website attributes the design of the meter to Edward and James Dakeyne in 1830 - the same year they patented the disc engine! It is more likely to have been developed by Farey and Donkin who laid claim to a fluid measurement meter in their disc engine patent granted in 1850. By 1859, perhaps amongst others,they were being manufactured by the Buffalo Meter Company of Buffalo, New York.
A positive displacement meter that is relatively cheap to mass produce, it is a robust design requiring virtually no maintenance. Whilst because of leakage past the disc it is not 100% accurate, that is more than compensated for by its reliabilty - a major concern for utility companies who want to install a "fit and forget" meter in your house.
And why is it nutating? To quote Wikpedia "Nutation is a slight irregular motion (etymologically a "nodding") in the axis of rotation of a largely axially symmetric object, such as a gyroscope or a planet". Whilst the Dakeyne engine was never called a nutating engine, there is at least one reference in mid nineteenth century literature to a disc engine "nutating".