There is a website called THE GREAT BRITISH WATCH COMPANY by Colin Andrews. Colin completed both the BHI and WOSTEP courses and is now a professional watch repair technician. His website covers many of the challenges he faced getting through these schools and his employment situation after graduating. The part that is of interest for this topic is his discussion of what he went through learning how to turn watch pivots with a graver and T-rest. All of his articles are very informative but the article on making watch pivots is of particular interest for this discussion.
As different people have different backgrounds, budgets, skill ranges, and different ways of attacking a machining problems, the really important issue is having control over the process and producing a correct part.
Using a cross slide requires requires more equipment but an understanding of how to adjust, and in some cases repair, the cross slide mechanisms is really needed to get the desired result. The cutters used in a cross slide can be more critical and complex because they are mounted in a fixed position and will not cut properly if the relief and cutter angles are incorrect. This requires additional skills and equipment. Once everything is properly adjusted and set up this process can produce extremely precise and repeatable results.
Using a graver requires less equipment to adjust but requires more hand manipulation during the metal removal process. Since the graver angles are adjusted during the cutting process the angles on the cutting tool itself are less critical. The approach to removing metal is very different as you are physically moving a cutting tool a distance that can not really be seen. This is why a shaft is first cut to a taper and the part to be fitted is moved up the taper during the cutting process. If the process was more controllable you would simply turn the shaft to the correct cylindrical diameter and press on the balance wheel.
Removing metal with a graver was around centuries before cross slides were invented. Products were made by hand fitting on part into another part. The system worked but problems arose such as slow production and a lack of interchangeability. During the American Civil War Eli Whitney came up with the concept of interchangeable parts for the manufacture of rifles.
The cross slide allowed the application of mathematical concepts such as the Cartesian Coordinate System, Trigonometry and Analytic Geometry to be directly applied to the manufacturing process.
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