what is the function of an angle pin in a lathe?
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“Angle pin” is not a term I’m familiar with, but a couple of possibilities come to mind.
Small tapered pins are sometimes used to hold parts together. For example they might be used to hold hand wheels onto shafts. The taper in the hole and on the pin does a couple of things. First, it allows for a little variation in the size of the hole when the parts are manufactured. If the hole is a little bigger, the pin just goes in further. Second, it makes assembly and disassembly a little easier than a tight fitting straight pin (a dowel pin). The taper pin usually only needs a few taps to put in or take out, a straight dowel pin needs to be driven the full length of the hole.
A tapered hole is common in the tailstock to hold a “center”, a drill, or other tool. With just the right angle to the taper (usually a Morse taper), friction will grip the tool without having to tighten anything (like a chuck requires). Yet, when you want to remove the tool, it comes out fairly easily as well.
If neither of these is what you are referring to, maybe you could describe the part you are interested in a bit more.
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