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

Question

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

Answer 1

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

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

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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!

Answer 7

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.