Null Points, Overhang, Arc and Effective Length for Dummies

Null Points, Overhang, Arc and Effective Length for Dummies

Postby billo » Sat Dec 29, 2018 12:13 pm

I've never gotten the Big Picture of how all these interact and why until now, especially the mechanism of null points. In answering a question on why a Mint protractor works exclusively for a single P2S (this is the dangerous part seeing as how it gets a little smokey around here now and then) I did some thinking. So here it is in a nutshell:
"You said; "But shouldn't the alignment lines be parallel to the grooves if they occur at null points? This makes the cantilever parallel to the grooves."
Yes. It's the grooves that are not parallel to each other at the two null points. As the stylus tracks past the outer null point, the stylus tracing angle (relative to the spindle) turns too far inward. As the stylus approaches the inner null point, the groove angle (relative to the pivot point) turns inward even faster (nearer record center) and catches up with the stylus tracing angle at the null. Overhang staggers the null points (a line cannot be drawn from the Spindle through both null points) to make this possible. As the effective length of the arm increases, the (tracing) arc gets shallower and shallower and the overhang is decreased, bringing the arc closer to ninety degrees to a line drawn between Pivot and Spindle - until you have no arc, no overhang and a linear tracking arm."
Sounds right to me. true? Partly true? Total B.S.? :oops:
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billo
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Re: Null Points, Overhang, Arc and Effective Length for Dumm

Postby Golear » Mon Dec 31, 2018 2:01 pm

Well.... first of all, I think we have to treat the LP, stylus and tonearm as three perfect spheres....

Too nerdy? Please see the second joke in Section (2) at http://www.math.utah.edu/~cherk/mathjokes.html. Reproduced here:


A mathematician, a physicist, an engineer went again to the races and laid their money down. Commiserating in the bar after the race, the engineer says, "I don't understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run..."

The physicist interrupted him: "...but you didn't take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning..."

"...so if you're so hot why are you broke?" asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret.

"Well," he says, "first I assumed all the horses were identical and spherical..."


Happy New Year!
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Re: Null Points, Overhang, Arc and Effective Length for Dumm

Postby billo » Mon Dec 31, 2018 4:43 pm

Ha!
My fear was "A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact (that I had missed!)" :D
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