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I would like to measure two points and tangents of a curve and transfer that information to a computer. Here is a picture of what I would like to measure:

The blade in the plane

Points (x1,y1), (x2,y2)

Tangents T1, T2 (or an approximation of the tangents)

A. Doe
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    I don't see how this is related to electrical engineering. –  Aug 06 '18 at 14:44
  • There was a related question (here:https://electronics.stackexchange.com/questions/42358/ideas-to-measure-2d-position-of-an-object-constrained-to-x-y-plane?rq=1), so I thought it belonged to this Q&A network. – A. Doe Aug 06 '18 at 14:48
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    Yes, but at least a begin was made to solve the problem with some suggestions. At the moment your question is 'please give me a solution'. Also AFAIK it is a known mechanical problem which has standard mathematical solution which requires a computer program. Nothing electrical whatsoever. – Oldfart Aug 06 '18 at 15:06
  • I know how to draw it/compute the curve mathematically given the input tangents and points. The problem is how to measure the tangents and points with a sensor of some sort. I am not asking for a solution, I am asking if it is do-able or not. – A. Doe Aug 06 '18 at 15:14
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    If you attached something to each end of the blade that measured positions and angles relative to a fixed frame you would have your numbers for your spline calculation. But the devil is in the details... – Spehro Pefhany Aug 06 '18 at 15:21
  • This is absolutely possible, but the bulk of the challenge might be on the software end. Motion capture is becoming pretty common in a lot of technology, and has been used by others in hobby projects. You need to be able to transfer 2 3d locations and 2 3d vectors to a computer, and presumably the computer needs to know the "length" of the "blade". Microsoft Kinect captures orders of magnitude more data and you could even use it to measure a blade in real time. Just one example. There are many other types of position sensors. – K H Aug 06 '18 at 22:22
  • I'll give you one hint since this is a homework problem, the function of the points and the tangent of the blade are related through their derivative, I hope you know how to find the slope of a line – Voltage Spike Aug 07 '18 at 02:16
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    I'm voting to close this question as off-topic because homework needs an attempt at a solution – Voltage Spike Aug 07 '18 at 02:17
  • It wasn't a homework problem (I am a mathematician, doing research on these types of curves). I apologize if the problem doesn't fit into the electronics StackExchange community. – A. Doe Aug 14 '18 at 09:04
  • @A.Doe Solve an system of equations with the main equation being a second order polynomial parabola, that also satisfies the two points. The last equations that will need to be satisfied are the two differential equations that define the slope of the parabola on the ends – Voltage Spike Aug 14 '18 at 15:27

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Very possible, and I think not that hard. With a few changes. 1. Hands are 3 dimensional and can point each end not in two directions but in 3-space. 2. Though it is easy to compute if you know the 3D coordinates of each end, you need to know the distance between the two ends of the blade.

Therefore I suggest these simplifications for simplicity and cost:

Recompute your script to use relative coordinates of only: the distance between the blade ends, the angle of T1 up from 0 pointing to hand 2, and the angle of T2 up from 0 pointing to T1.

Build a physical skeleton consisting of a metal ruler with a rotating potentiometer at each end (10k linear). The two pot knobs each hold an end of the blade, and restrict them to rotating in the same plane. The user adjusts the thing with his hands, first reading the distance between the ends. That gets entered into the Arduino program. The program reads the each pot to get the angles T1 and T2. Your script spits out the shape on a screen or little display.

Here's an all mechanical solution. Get two of the those metal T-square rulers that have a built in adjustable protractor. Unscrew the knobs and put both smaller protractor arms on the same long arm. Mount a blade end on each knob. You then physically adjust each angle and blade end, visually seeing the tangents since they are pieces and reading off the protractor angles.

Enter the two tangent angles and the distance between them, and if you calculated right, voila! Your script prints they shape of the reality you created!

Mitch Bogart
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