3 point radius gage

[Nimitz]

Has anyone ever heard of/built such a thing? Something similar to using a depth mic and calculating the radius from the drop and chord length, useful for odd radii that you won't find on a fixed gage (a bit of plate with a 1/4" or whatever radius cut in it).

I've been thinking (okay, I've filled half a notebook with plans & suppliers) about building one myself, and I think I could pull it off. I was thinking of using a hacked up digital caliper as a depth mic and two bars for the angle (with a linear taper pot as an angle sensor). Feed both into a microcontroller with ADC pins (maybe hijack the caliper's output to its LCD) and it should be possible to spit out a meaningful answer.

The question of accuracy bothers me, though. Pots aren't exactly precision angle sensors. I know a 16 bit microcontroller would allow me to make some pretty large lookup tables for sin/cos values, settling that issue of accuracy. But taking voltage through a pot, an ADC, and then depending on it for fairly accurate results doesn't fill me with confidence.

Anyone have comments or suggestions? Or, heck, point me to a similar retail product and settle this right off?

Jason
Jacksonville, FL

 

[NickE]

How about a very fine digital encoder.

Seems to me you could "hi-jack" the SPC signal off of the caliper, then use the digital signal coming off of the encoder for angle.

http://www.rotaryencoders.com/products/rotary-encoders.shtml?source=google

And instead of Hacking a caliper, just use a digtal depth gauge, you can also pull SPC off of it too.

Nick
I love materials science!

 

[byrdj]

Some thoughs and comments;

I don't see what the angle has to do with calculations. The "cord" can be set to a standard (and measured with calier), then the drop be the measured variable for calculating the diameters.

If the concept of two hinged bars to set cord at thier opening is key to your need, could they be made standard increaments, like notched teeth. once set, the cord could be verified with calipers to be entered as fixed value into calc and then drop from input caliper will display calculated radius.

What diameter range are you thinking of. I use this calc to quickly get diameters of objects (3 to 30 feet)too big to wrap (circumference/pi) or center obstructed. I've also made a bridge (plate with ends supported) to set the cord and depth mic for drop to get cam radius in the range of 3 to 6 inches

 

[griffengm]

Nimitz,
We built something like what you describe to verify the radius of a form on the corner of a panel. Sorry that I do not have pictures but will do the best I can to describe it.
The closest commericial mechanism (maybe where I got the idea) is a radius dresser for grinding wheels. The dressing point is held at some distance from a centerline and rotated around the line to generate a radius.
Our device had a swing arm that could move through a bit more than 90 degrees. A dial gauge was mounted on the end of the arm with the anvil pointed toward the centerline. Several angles were marked on the plate so that we took readings in consistent locations, usually at 90's, 45 and 22.5's.
After taking a series of readings, we could then plot them in most any CAD program and produce a visual as well as numeric illustration of the form.

Griffy

 

[byrdj]

 

[Nimitz]

NickeE, I like the idea of a digital encoder for the angle sensor; I hadn't before seen any that were realistically (for this project) priced. I'm looking at this as a one-off solution to awkward radius measurements, and I have to compete with the simplicity/economy of just grabbing a depth mic and doing the math.

I'm hoping I can get away with relatively cheap digital calipers for this; dropping $400 for an instrument I'll never use for anything else doesn't make sense. Even so, the cheap ones seem to have the same basic specs as the expensive ones (similar resolution, accuracy). Does anyone know any compelling reason to only use expensive digital calipers?

byrdj, I hadn't considered setting up the angle bars for increments. I was looking at mounting a gear on the ends (making the angle measurement fairly painless) and had come up with the focal length as a function of angle.

However it incremented, it would have to be relatively solid in both directions. It wouldn't work so well if the bars kept opening/closing on you while you tried to get a decent depth measurement.

The gage would be used on things like arc segments, or filleted corners on a part. The upper range would become an issue of accuracy rather than mechanical limitation. When the curve is so large that the drop falls to within the accuracy of the calipers, I'd say that's past the limit. The lower range would be limited to how close together the angle bars can be placed; a 1/4" radius will not work if the bars are 3/4" apart.

I'm hoping to be able to measure from 1/2" diameter through at least several feet. I'll have to crunch the numbers and find out where the caliper accuracy overcomes (or becomes a significant portion of) the depth measurement.

The main equation I came up with goes like so:

R = 1/2(L + d - L*sin[a] - [L*cos{a}]^2/[L + d + L*sin{a}])

R is the radius, L is from the angle bar tip to vertex (which is a function of angle and gear radius), d is the depth measurement from its neutral position, and a is half of the angle between the angle bars.

It doesn't look like the radius goes to infinity (as it should) when d goes to zero, so I'm not sure what's wrong with it.

 

[byrdj]

The simplier equation I used with the bridge and depth mic was
radius=(drop^2+chord^2/4)/2*drop

As far as calipers, I have a ~$100 starrett and a $10 grab box, both are only good to 0.001", however the repeatablity and thus accuracy is many times better with the smooth operating starrett verses el cheapo. (both are dial verneer type)
While a a verneer depth mic should let you get 0.001/10", I can't do much better than 0.001/2.

 

[MarkUMSU]

I think this is an interesting discussion, but maybe another option is to find friend who has a CMM...?

 

[Nimitz]

MarkUMSU, actually I have been pushing for a digitizing probe for our CNC machine. As I understand it, that would let our CNC fake being a CMM fairly effectively. If I can get that through, then this little project of mine is superfluous.