Digital Function Slide Rule

Grind x and display f(x) of it, analoguely

This device merges elements from traditional slide-rules, and digital calipers, resulting in a digital slide rule, in which is embedded a numeric display that returns a number based on the amount of 'slide' measured by the sliding runner component of the rule.

To use, two parameters are set via (say) bluetooth from a coupled app or website. The domain of a function is scaled, allowing one to set the min and max values of x to span the full length of the ruler, while the content of the function f(x) is also assigned to the ruler's processor.

The result is a nicely analog, physical method for computing a function, with values returned in real-time.

Some buttons (or perhaps some kind of jog-dial) might
serve to switch between favourite preloaded, or user-
defined functions.

-- zen_tom,
Apr 08 2016

Digital Calipers

Some examples of digital calipers. [zen_tom, Apr 08 2016]

Slide Rule

Example of a slide-rule. [zen_tom, Apr 08 2016]

Function Explorer

A website allowing a user to enter a function f(a) and then shows what happens as you slide the value of a up and down. The slide-rule does the same thing, only digitally (i.e. it shows you the numbers) and physically (i.e. you keep it in your pocket) [zen_tom, Apr 08 2016]

Some high-precision prior art

[MaxwellBuchanan, Apr 08 2016]

I think this idea is missing the essence of what a slide rule was/is used for

Though a common slide rule is a trivial kind of logarithm table – just find x on its “D” scale and, on no slide required, find the matching Log10(x) on its “L” scale – its real utility is for binary functions like f(a,b)=a*b, better known just as multiplication. So you wouldn’t want the digital readout to show something based on the position of the sliding strip, but on the position of sliding “cursor” optionally used to point between the b value on the strip’s C scale to the a*b value on the fixed strip’s D scale.

Still gets my bun, as you can’t have too many weird mathic knickknacks.

-- CraigD,
Apr 08 2016

Ahem. <link>

-- MaxwellBuchanan,
Apr 08 2016

[CraigD] I see your point - and you're right, I was rather dumbing-down/glossing over the whole cursor part - however, it's not a huge leap to consider the description above as being a simplified one where the cursor (or eye, for non cursor-rules) is constantly at the 1 position, and the rule slid around for setting the x-value, reading off the associated f(x) from the readout.

Consider setting a function f(x) as set by the chosen function, and position of the slide, and then setting a new function g(a,b) where a=f(x), and b=is the cursor position to give the result g(f(x),y). Having a pair of interacting functions ought to allow some fairly nifty results.

The really expensive option would include powered maxima, zeroes, and minima functions, whereby, given the functions given, and the ranges set for slide and cursor, and choosing one, or the other or none as being fixed in place, the ruler moves both slide and ruler towards various solutions of the provided functions.

// Ahem //

Your <Ahem> is duly acknowledged and is being chiselled into the national <Ahem> archival tablet as we speak.

I guess, it's a natural progression from using one of those multi-keyed digital scientific calculators to wishing you didn't have to press quite so many buttons.

-- zen_tom,
Apr 11 2016

I've been thinking of it the other way: A traditional slide-
rule, but with points like calipers, for direct entry of
measurements into the math.

I'd love to measure the width of an object, slide the cursor over, measure the length of the object, and directly read the calculated area from one of the scales under the cursor, for instance.

I'm sure many more operations would be possible, but simply having a sliding zero cursor on a mechanical caliper would cover addition and subtraction. Including a log scale and some marks at values like Pi just seems natural.

In machining, calculating the SFM speed for a cutter is a
frequent task. If the instrument could measure the
diameter of the part being turned on a lathe (or in the
case of a mill, the diameter of the cutter itself), and
directly read out the circumference, that saves a step in
the calculation. If the slide rule could be used to multiply
by RPM and read out in SFM directly (or better yet, set as
desired SFM and divide to get the required RPM), it would
save tons of multi-step lookup tables.

-- Myself,
Nov 11 2017

random,
halfbakery