Geometry Question

[metrologist]

In machining and toolmaking, a very flat surface plate is used as a reference for measurement. Often a "height" gauge is used, which has a dial indicator mounted to a base. (video at end of post for reference).

We have a roundish cylinder that we slide on the surface plate and under the height gauge to determine it's diameter. We repeat this measurement around its circumference and obtain the same reading at every point. We cannot say that the cylinder is round because there are shapes such as a Reuleaux triangle that foils our measurement technique. A smart machinist might suggest you need to set the cylinder into a vee block, so that there are three points of contact, two on the vees and one on the dial indicator.

Is there a shape that will similarly foil the that measurement technique, and what would that shape be?

This question was born from a debate about whether a 90 degree or 60 degree included angle vee block yields a more accurate reading of "out of roundness."

[rob77]

and that's why roundness is checked against the centre of the object by rotating the object on it's axis (e.g. in a lathe) and checking with a dial indicator.

[Terry Bites]

A messge from the old country.

https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwip286K88P4AhVUSsAKHVCLBXEQFnoECA4QAQ&url=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F326597023_Measuring_the_roundness_deviation_in_the_Vblock_measurement_method%2Ffulltext%2F5b58a6be458515c4b244b888%2FMeasuring-the-roundness-deviation-in-the-Vblock-measurement-method.pdf&usg=AOvVaw1CK5N3x2KnzZKTYQQDS5Dv

I love this, "Studies have shown that non-asymmetrical measurement schemes are more universal."
So I you dont want an error, avoid balancing your rod on balls of differing sizes.

[metrologist]

Sometimes there are no centers.

Glorious nugget of knowledge. It does indeed answer the V-block debate. I still wonder if a shape exists that would evade out of roundness using this method.