tapered tap

I have in my posetion a wooden pantograph by Conti of Paris,both of the split tapered collets for holding the lead and a stylus have their tapered threaded closers missing.I have this implement for 40years and was given it by an old friend whose farther used it at the turn of the last century.I would like to make the collet closers and I am unawhere of any suppliers of tapered taps unless someone knows of one.Failing not being able to get one I will have to make one.The dimentions of the collet are 8.85mm long 6mm tapering to 4.13 the thread is 0.7 mm.My trigonemetry is not good so if someone can work out an included angle for me it would be much appreciated.Working with pencil and paper I got it to 8 degrees but I am sure I will be out.

Frank

Are you sure the female thread needs to be tapered? If you were to try an M4 nut would it start, and would it tighten up the collet as it moved up the thread?

Dave

As Dave says, the threads will be parallel and clamped to the male thread by the outside taper.

Two halves glued/soldered together (or held by other means), drill and tap the hole, separate the two halves and skim/file/grind the closing edges to allow them to tightly clamp on the male thread.

You can set the taper angle either by trig calculation or by setting the female outer onto the lathe centre line and adjusting the compound so that a dti on the taper shows no change, as the compound is wound along the taper. I would prefer the latter method, if possible.