If you want something that looks exactly like the original part there are several ways of going about it. Using a single point screw cutting tool wont achieve this as the general idea is that the bar is turned to a size under the normal thread dia that removes the need for the rad on the crest of the top of just about every imperial thread form. As it's a pointed tool it needs to cut deeper than the correct form as well. You should be able to find calculations for this about on the web. The information needed is available when the full details of the thread are given, crest and root rads etc..
I've ignored that you mentioned the word cap so if it is the above needs reversing.
If you have a feeling it's a cycle thread it's probably a brass thread, whit form rather than 60 degrees. Brass is usually reckoned to be 26 tpi but I have a feeling 32 is used as well. At all diameters. The idea is not to weaken tube wall too much as say using 10 tpi which might be more sensible at some diameter. Thread gauges should come in whit and unified as then it's possible to see what the thread angle that is being copied is. Often now they only come in metric and unified so if the flank angle looks to be wrong using the unified guages it's assumed to be a 55 degree whit form.
Screw cutting with a chaser isn't really any different to cutting with a single pointed tool other than when the end of the thread has been cut the chaser has to be wound out of contact otherwise it will mess up the thread. A single point tool can be left in contact as it will just turn a groove at the end of the thread. In that case screw cutting just has to be disengaged. With a chaser the tool has to be wound out of contact and screw cutting disengaged at the "same time"- very slightly later. Not that difficult to do with the lathe running slowly providing that there is a bit of space available at the end of the thread for the tool to run on a bit. A typical chaser may need modifying on an off hand grinder. Some may have a bit of a lead in. That needs grinding off slowly without over heating the chaser and wrecking it's temper. If it is a cap it wouldn't be a bad idea to cut a recess at the end of the thread to provide some space for either type of tool to run into. Sometimes when a single point tool is being used the noises change when the tool enters the recess. Some fit a long travel DTI to the lathe bed for tricky jobs and use that to gauge when the end of the thread is reached.
Not often mentioned but for internal threads and a single point tool there is another technique. Run the lathe backwards with the tool upside down or even cutting on the opposite face to the one usually cut. This way the tool runs out of the work rather than in. Problems – screw on chucks might unscrew and normally screw cutting is engaged some distance from the work so that when the actual cut starts all play has been removed. Might work out with a decent sized recess. With a chaser too if it can fit into the recess. It would be best to only have a few teeth on it, only 2 are needed really for machine chasing.
Once upon a time many threads were cut by hand with chasers. They can also be used to correct single point cut threads to the correct form or correct the pitch slightly when some one has an imperial lathe and wants metric. Chasers self correct as they cut which is why hand chasers have so many teeth on them. The modern machine chaser is in the form of a disposable carbide tip. Advice from a now rather old clock restorer is to make up a handle around 18in long for fully cutting threads with them from scratch. What I found is that it's best to lightly score the work with the chaser stationary 1st and the use this as a guide to feeding the chaser along by hand. Higher speeds for finer threads seems to work best as it's easier to match the required feed speed.
My boxford came with it's hand turning rest – make me think it must have been a model engineer that initially bought it.
John
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