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The rate of taper is 1:20 on diameter, in other words 0.600" on diameter per foot, .050" on diameter per inch. Tapers range from a Number 2 to a Number 20. The diameter of the big end in inches is always the taper size divided by 8, the small end is always the taper size divided by 10 and the length is the taper size divided by 2.
A form of taper pin that precedes these standards is the clock pin, used to accurately and repeatably register parts of a clock to one another. Clock pins do not have a standardised taper, but they generally have a more pronounced taper than the standard engineering pins. The size or gauge is defined by diameter at each end, and the length.
A syringe with a male luer lock fitting, and a needle with female luer lock fitting (purple) which screws into it. The Luer taper is a standardized system of small-scale fluid fittings used for making leak-free connections between a male-taper fitting and its mating female part on medical and laboratory instruments, including hypodermic syringe tips and needles or stopcocks and needles.
The tapered key is tapered only on the side that engages the hub. The keyway in the hub has a taper that matches that of the tapered key. Some taper keys have a gib, or tab, for easy removal during disassembly. The purpose of the taper is to secure the key itself, as well as to firmly engage the shaft to the hub without the need for a set screw.
The most popular size is 8 mm which came in several variations but all 8 mm collets are interchangeable. Lorch, a German Lathe maker, started with 6 mm collets and the first Boleys used a 6.5 mm collet. 6 mm collets will fit into a 6.5 mm lathe but it is a poor practice. Another popular size is the 10 mm collet used by Clement and Levin.
Both the tool and socket have a slight taper. The contemporary square drive screw has all but replaced the Robertson screw proper and is commonly referred to as a Robertson because it has practically identical drive dimensions and the same colour identification system, but the contemporary square drive socket has parallel sides rather than tapered.