A request for a bit of tolerance regarding tolerances.
It is entirely appropriate to round figures when manufacturing. In fact it is a requirement of manufacturing that there are tolerances and that they are practicable to achieve and measure, and appropriate for the requirements of the item being made.
There are suitable tolerances for all the different parts of an arm or turntable, to the nearest millimeter, tenth of a mm, or less. These depend on the function of the part and the type of fit needed. These will be specified on the drawings, and no point in making things more accurately than necessary, as it simply adds to the cost, and there is no benefit. This applies also to the geometry.
Perhaps it is because stylus and groove are so small that it is easy to get sucked into unnecessarily precise numbers when discussing arm geometry. It is one thing to illustrate the scale of the stylus/groove interface with descriptions of the equivalent sizes of cantilever and arm if the groove was big enough to stand in (cantilever 600metres long, arm pivot 23km away, a 0.5mm error in alignment becomes 50 metres, etc, etc). But this is just for laughs. While you can see the details of the groove, using a microscope it is a pointless task thinking about how you can work to equivalent tolerances when setting up.
No alignment protractor manufacturers will say how accurately their protractor can be used to set up a cartridge. They will tell you how accurately the lines are etched, the material cut, or whatever, but not what level of accuracy can be obtained when using it. The difficulty is how to establish this. From what little information I have found, I would imagine that getting closer than +/- 0.2mm in overhang and +/- 0.5 degrees in offset angle is extremely rare. To see what this means, take for example, the Odyssey.
The nominal effective length is 230mm, overhang 17.2mm and cartridge offset angle 23.5 degrees. Leaving aside for a moment the fact that effective length and overhang are nominal, (the effective length and cartridge offset, like the SME, varying with each cartridge, and the spindle to pivot distance adjusted appropriately, thus varying overhang), it may be that the offset angle should be specified as 23.46 degrees and that the overhang 17.16 mm. However, even an arm with a fixed mounting distance accurate to within 0.04mm would not suffer from having an offset angle 0.04 of a degree away from the stated 23.46, ie 23.5, because, unless the cartridge is integral with the arm, the variation caused by clearances between screws and mounting hole are at very best +/- 0.5 degrees. So the cartridge would have to be dowelled in place so that it could be located precisely, never mind the fact that its generator and cantilever would need super tight tolerances. Apart from that, you would most likely be unable to see that error, so how would you know it was there?
The nominal effective length is 230mm, overhang 17.2mm and cartridge offset angle 23.5 degrees. Leaving aside for a moment the fact that effective length and overhang are nominal, (the effective length and cartridge offset, like the SME, varying with each cartridge, and the spindle to pivot distance adjusted appropriately, thus varying overhang), it may be that the offset angle should be specified as 23.46 degrees and that the overhang 17.16 mm. However, even an arm with a fixed mounting distance accurate to within 0.04mm would not suffer from having an offset angle 0.04 of a degree away from the stated 23.46, ie 23.5, because, unless the cartridge is integral with the arm, the variation caused by clearances between screws and mounting hole are at very best +/- 0.5 degrees. So the cartridge would have to be dowelled in place so that it could be located precisely, never mind the fact that its generator and cantilever would need super tight tolerances. Apart from that, you would most likely be unable to see that error, so how would you know it was there?
And that, in turn, depends on how accurately arm boards and plinths are manufactured. Are they within these kind of tolerances? Unlikely, as boards will be mounted with screws which need some sort of clearance (unless the board is dowelled in place). Then there is expansion and contraction.
If you need convincing, buy a cheap digital caliper. Apart from its usefulness in measuring items and setting mounting distances when used with a rod of known size, it shows exactly how tiny 0.01mm is, and how difficult it is to set up to those tolerances. It is also illustrative to look at the Vinyl Engine calculators and see what tiny differences these numbers make. The differences are not visible on the graphs, only the numbers show that there is any difference at all. If, instead of a single thin line on the graphs there was a line the width of which was related to the likely errors in set up, the differences in most alignments would be obliterated, and would illustrate the advantage of being careful with set up, but not being too hung up on a specific alignment.
