 # Finding a distance of a point.

Hello,

I need your help with the following:

Imagine a rod rotating about a point, its location is unknown. My objective is to find where that point is. If I place two gyroscopic/accelerometer sensors (mpu6050), one at each end, and read the centripetal acceleration. Using the following formula Ac=W^2/R, I can find the distance between the sensor and the instant center of rotation.

1-is this feasible? Are the results a accurate? 2-Is raw data reliable enough to do this calculation or should I use some kind of filter? 3-Now imagine I am holding the rod and i'm moving it sideways, would it mess with the results? I've low programming skills but its not my first time playing around with this sensors on arduino.

Not very clear on what you are looking for. A distance requires two points. So one is the axis of rotation, I think I get that. But where's the other end of this distance?

I'm sorry if I wasn't clear enough, my English is not so good.. :-[ The other point is where the sensor is placed. The objective is to mesure the angle, angular velocity and angular acceleration about its axis. The problem is that i cant put the sensor close do the rod axis due to physical space.

I think your formula, Ac=W^2/R, is wrong but you haven't defined what each of the symbols means. From Wikipedia: A = R * W^2 Where A is the radial acceleration towards the centre of rotation. R is the radius, the distance of the point from the centre of rotation. W is the angular velocity in radians/sec. To find R we have: R = A/W^2 which means that you have to measure two quantities. 'A' will require an accelerometer. There's more than one way to measure 'W' but I'll leave that as an exercise for the OP. The accuracy, of course, depends upon the accuracy of the measurements of 'A' and 'W'.

Now imagine I am holding the rod and i'm moving it sideways

If the rod is still rotating but the whole system is also moving/moved in a straight line without acceleration, it won't affect the calculation of R. And BTW, the formula above is only valid for a constant rate of rotation - i.e. no angular acceleration.

Pete

That's right. The OP has got the expressions wrong. The radial acceleration (aka centripetal acceleration) is (V^2)/R, or (W^2).R, where 'W' is omega....angular velocity. V is tangential velocity (ie. tangential speed ....at right angles to the radial line). And V = R.W