revolute invariance?

[3DDave]

pmarc mentioned:

Per that chart, a cylindrical feature primary and a planar feature secondary will resolve in so called revolute invariance class which will be associated with a datum axis and a datum point lying on that axis (the point will be located at the intersection of the primary axis E and the secondary plane D) - similar to the scenario of a conical feature defined as primary datum feature.

The only reference that is tangentially connected seems to be in Geometric invariant theory, but that has to do with transformations as in

Invariant theory is concerned with a group action of a group G on an algebraic variety (or a scheme) X. Classical invariant theory addresses the situation when X = V is a vector space and G is either a finite group, or one of the classical Lie groups that acts linearly on V. This action induces a linear action of G on the space of polynomial functions R(V) on V by the formula ...

per

https://en.wikipedia.org/wiki/Geometric_invariant_theory

Is there some source of information about how "revolute invariance" came to be included in a discussion of Y14.5.1?

 

[pmarc]

https://www.iso.org/standard/40358.html

 

[3DDave]

Too bad I'm not spending CHF 208 to find out that ISO has no explanation of where they made up the term.

One would think accepted mathematics would be the basis for a mathematical explanation and not drawing improperly or just plain fabrication.

Even so, Google has no one using that term in public.

Edit: found this paper

https://www.researchgate.net/public...cation/link/5b8fdc92a6fdcc1ddd103445/download

Seems like they like to use the same basis theory I found before and with as much distance from the audience of engineers and inspectors as possible. However, they use them as ways to classify surfaces, not to derive datums.

ISO GPS standards define seven invariance classes shown in
Table 1 [1]. For geometrical product specifications, the
boundary of a nominal solid should be partitioned into surface
patches, each of which belongs to one of the seven invariance
classes. These seven classes are derived from a science-based
classification of continuous symmetry groups of surfaces in
three-dimensions (3D) [2]. The use of group theory for
advancing the study of geometry dates back to the pioneering
works of Sophus Lie, Felid Kline, and Henri Poincaré

Any hints on a simple, 5th grader level, explanation of Lie would be a help, because that is the ideal target for taking time from a busy machinist to explain it.

 

[pmarc]

And I thought you had realized long time ago that none of the standards we have been debating on (and you've been complaining about) so passionately in this forum for years is targeted at busy machinists ;-)