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How can I sense/measure the force applied, or the length, of thick rubber surgical tubing as it is pulled/stretched?
It will be consistent everywhere along the length as the thickness is the same.
Let's assume we only have 1ft to work with before it's pulled to 4ft max.
Durable, Cheap...
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If you put a stripe mark on it, the mark will move and get wider when the tube is stretched.
You can measure the tube diameter at a fixed distance from one end, it should get smaller with pull or at least my old wrist rocket tubes did.
If you attach one end to a spring and can find how much that stretches, you can know.
You can put a magnet in the tube and measure the field change at a stationary Hall sensor.
You can see if the air pressure inside the tube changes relative to outside.
You can have the pull compress a piezo and check the charge difference across the leads but that's far trickier than all the above.

Every conductor and semi-conductor I know of changes resistance when under stress (one of the many ways resistance can be changed), that's how at least some solid state scales work.

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Some great ideas thanks!  How can I measure the magic marker stripe getting wider cheaply?  How can I measure the tube diameter?  It's the same nearly everywhere.  I don't need a spring, the tube is similar enough.  I can just shove a magnet and hall sensor in the tube.  They don't need to be stationary with respect to the outside world.  How far apart would they work?  If only 5mm then they could start at only 1mm apart.  How many different values would I get when stretching 4x the length?  In other words what's the resolution of this method?  Air pressure would be cool, but more expensive?  How can a pull, compress a piezo?  Mechanically.  Do you think rubber would change it's resistance when stretched?  It is getting thinner. 

Great ideas for me to start thinking about.  More details please?
Cheap and durable.
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How about alternating black/clear stripes. You could count how many go past a sensor. They would get wider as the tube was stretched, but could still give a useful indication.
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Great idea!  But I'd like the sensor to be inside the tube.  There is no stationary point with a different frame of reference, outside of the tube.  The sensor could be outside, but there's nothing to attach it to, besides the tube itself.  There is no other object besides the tube.  Understand?  You could put your idea inside it, but what if the marks passed very slowly?  The light would change slowly.  Maybe not as much as the external lighting. 
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Ok. I didn't get the lack of a support structure. What is the internal diameter of the tubing in the unstretched state? Is it (or could it be made) wide enough to fit an ultrasonic sensor in it? Some of them are reasonably small.
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I could buy thicker tubing, there is not reasonable limit there.  Then what?
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I wondered if you could use the ultrasonic sensor inside the tubing. The far end would need to be closed, but you might get an echo back. I haven't put a lot of thought into it. Just putting ideas into the hat.
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That's a great idea!  Simple.  It wouldn't have to go 4 ft.  Just start it 2" away.  When it stretches it'll be only 8".  It may have to be in a straight line, but that's not a problem, it will be.  I wonder what the precision would be at this distance?  Will try it!  What is the smallest sensor you can find?  I can use the cheap circuit board, with a different transducer.  I have some small ones.  Wow perfect!
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This has only one sender/receiver:
http://adafruit.com/products/172?gclid=CL3U--7Ft68CFbMEQAod_EePgg

The cheap ones have 2.  Can I modify those to work with 1?
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This seems quite reasonable.

http://www.maplin.co.uk/ultrasonic-transceiver-40khz-10mm-open-aluminium-591660

I would think you could get something similar in your part of the world.
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I have plenty of those, but which circuit?  The ones from Ebay, I have, require 2.
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The spec says it can be used as a transmitter and receiver. You'll need one of the electronics experts for any more info. I'm certainly not of of those.
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Could you not use something like this:

http://adafruit.com/products/519?gclid=CMjGo5zNt68CFWcHRQoduxrShw

?
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Just as a matter of interest, what is pulling on the tubing?
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