# Ideas to measure 2D position of an object constrained to X-Y plane

I am working on a project, and an aspect has come up where I would like to measure (track continuously) the X and Y position of an object across a 2D plane. The object is moved by a person, with the object's movement constrained to the 2D plane (so no Z-axis displacement).

Constraints:

• I would like measured position resolution of 1 mm, ideally 0.5 mm or better.
• The space over which the object moves is 30 cm X 30 cm.
• Whatever method of measurement I use shouldn't significantly constrict the movement of the object.
• Also, please just assume that the plane on which the object moves is air, and NOT an actual solid surface (for project-specific reasons that are hard to verbalize).
• The good news is: The object is completely OK to be modified as necessary (LED on top, or string attachments, or anything else).

What might be a method to get that kind of resolution?

I am considering various approaches, but I don't know if any of them will fulfill the resolution requirement. Since there aren't many constraints on my existing system, I am OK with even a complex / bulky implementation, just as long as it's precise enough.

Here are a couple of my ideas so far:

(1) Infrared-based range sensors (only need two actually)

(2) Two long calipers/micrometers connected from the object to the sides

(3) Two strings, each connected from the object to a freely bending strain gage leaf on the side

• Strangely, it's not letting me insert images. One moment please... Sep 28, 2012 at 18:52
• You could build a theremin! Sep 28, 2012 at 18:56
• @Nick: According to my quick Wikipedia-reading, the theremin works by using the hand as one plate of a capacitor (as part of an LC circuitt). Would this work over a 30cm range (I've never played a theremin), and would this allow 0.5mm resolution? Sep 28, 2012 at 19:12
• The 30cm range would not be a problem. I would be pretty surprised if you could get 0.5mm resolution though. I'm sure it can be done with some good filtering and signal processing... but I wouldn't be the one to ask about that. Hence my suggestion is a comment, not an answer. Sep 28, 2012 at 19:18
• Place a potentiometer at one corner and attach a rotating arm on it. Then at the end of this arm again place another potentiometer with another arm. The end of the second arm is moved to the various positions, then the potentiometers are proportional to the angle they make. With a bit of math you can calculate the exact position. Sep 28, 2012 at 19:18

Idea 4: This will give you the best accuracy. You will need the following:

• 2x Precision linear slides.
• 2x Precision linear encoders.

Attach a linear encoder to each linear slide. Arrange the two slides 90º apart, and attach the object to the sliders using the linkages. Linear encoders like this are used for precision measurement applications. Using this method you could easily achieve 0.01mm resolution, and 0.1mm accuracy, and will probably do much better than that.

• Haha, this is turning out to be the most comprehensive answer (and a one-man contribution at that ;) for a position tracking question ever! Sep 28, 2012 at 21:22
• This is a bit similar, albeit better resolution than my stated possibility of two calipers (which I know are cheap). Any thoughts on how expensive such linear encoders run? Sep 28, 2012 at 21:24
• You can pick up linear encoders on eBay for less than £200. Linear bearings can also be expensive, but your application would be able to get away with cheaper cylindrical ones. Sep 28, 2012 at 21:33
• Noted. In fact, cost isn't too much of a factor, since this is just a one-off project. However, I am concerned whether this particular method might impede the movement somewhat, or are the encoders not very high-friction or heavy? (I just edited the question to state that the object should be allowed to be moved somewhat freely) Sep 28, 2012 at 21:42
• The encoders are non-contact. The only friction will come from the linear bearings, which will be very low friction indeed. If you want zero friction, then use air bearings. Sep 28, 2012 at 22:26

Idea 3: Use a camera. I don't know what constraints you have on your object, but if you can add a tiny LED, then tracking with a camera can be a doddle.

Jennifer here is sporting a range of red LED trackers. Perfect for bedazzling and confusing your friends.

Synchronise the LED to flash in time with the camera's frame rate, so that you get one image with the LED on, and one with the LED off. Subtract the images, and locating the LED within the image is trivial.

Alternatively, add an IR filter to the camea, IR LEDs around the lens, and stock a retro-reflective marker on the object. This should show up much brighter than the object or surroundings.

Alex is modelling some fetching retro-reflective tape which his mum made him wear on his bag.

• I've updated the question to state that the object is indeed open to modification/attachments. Sep 28, 2012 at 21:20
• I like the image subtraction with blinking LED idea. For clarity, could you add to the Answer a comment about the resolution achievable? I made a comment in the Comments section above, stating a 300X300 pixel image would suffice (theoretically) for resolving with 1 mm precision. But the fact that an LED is not a point-source could cut down on the resolution a bit. Sep 28, 2012 at 21:27

Idea 1: Use two String Potentiometers.

Arrange them about 90º apart and 1m from the square so that the object moves around, you can measure the distance between the object and the pot. The you can use some trigonometry to calculate the exact position. I have seen this done and it works well. Can you get the accuracy? You should do the following:

• Arrange the pots in such a way as to make use of about 80% of their range.
• Buffer the signals from the pots with op-amp followers (Good quality precision opamps).
• Use a good quality 12-bit ADC, with a properly laid out PCB.
• Make the system mechanically sound and rigid.
• Make sure the strings emerge from a small hole.

This way, you might expect to achieve an ADC range of about 3000 steps. This gives you about 0.1mm resolution. Now, to get the accuracy. You'll need to calibrate the system carefully. Accurately measure the position of the object in several locations, and correlate those readings with the measurements. This could easily give you 1mm accuracy.

• Wow, I didn't know these exact things existed, great idea! Based on a first couple of Google searches, these have fantastic resolution (well, limited just by the ADC, I suppose). Don't know how repeatable it will be (over many retractions over lifetime), but could be calibrated. Now, to find one with at least 30cm full-scale range. Sep 28, 2012 at 20:44
• @Inga - They are designed for precision measurement applications, so I expect they will be pretty repeatable. You could always do a check every now and then. Maybe you could have some fixed sockets you could attach your object to. Sep 28, 2012 at 20:46
• Noted. This is hard to beat in simplicity and directness; I'm going to test this out. And as far as the 30cm full-scale range, even if the particular string-pot had a shorter range, I could always attach further string of known length to it, to attain the 30cm span. Sep 28, 2012 at 20:54

Idea 2: Use an Ascension Sensor. These give you 6 degrees of freedom (X,Y,Z, roll, pitch, yaw) which is much more than what you need, and can be a little bit expensive, but it's a working off-the-shelf solution.

The system consists of a stationary transmitter, and a moving receiver. The system can tell you the position and orientation of the receiver relative to the transmitter.

The accuracy is specified at 1.4mm, but you could probably improve that with careful calibration.

Idea 5: Digital pen and address dot paper.

You can get these amazing pens which can record everything you write an draw. The pens contain a tiny camera which looks at the paper while you write. However, it doesn't actually look at the ink you've laid down, instead it looks at a pattern of tiny dots on the paper. (You need to buy this special paper, or you can print it).

One of these would easily be able to meet your specification.

I did a project on this, and the sextant method works fine, especially in short range, but it has its blind spot, below a certain distance, it will not work. Plus, if you have more sources of illumination, it will be erroneous. The accuracy of the measurement is a function of the quality of the camera used and the separation between the camera and the source of illumination.

Hope that helps!

what you are describing is essentially a digitizing table or tablet.

When I worked for a photogrammetry OEM our digitizing tables were about a meter square and were then (and possibly now) used by cartographers, etc. They consisted of a glass table with thin copper wires attached to the back of the table in a grid formation; and a pointing device (crosshairs) which contained an electromagnetic coil.

Logic circuits would send electrical impulses down the copper wires in the X and Y axes; these impulses would be picked up by the coil and processed by digital counters to calculate the exact X-Y position of the pointing device down to hundredths of an inch.

If for some reason you couldn't use a pointing device within your project you could try attaching a pantograph.