Measure Angle with an accelerometer 3axis in dynamics

[Roux Terence]

Hello,

I would like to measure the angle that I made with my accelerometer 3D. I have only this to measure it. I tried many fonctions but I didn't find something good.

Is it possible to measure angle in dynamics with an accelerometer ?

[Ton van den Bogert]

Re: Measure Angle with an accelerometer 3axis in dynamics

If the accelerations of the device are small, relative to gravity (1 g), you can measure the sensor orientation relative to gravity. This uses the accelerometer as an inclinometer or tilt sensor. This will give you two of the three 3D orientation angles. The analysis involves solving the two angles from the static equilibrium equation.

Since you say "in dynamics", I suspect that your accelerations are too large to be neglected. If you or anyone else is interested in the static case, I can go into more detail.

If accelerations can't be neglected, you can still determine orientation but this requires more complicated mathematics, and an inertial measurement unit (IMU) which combines the accelerometer with an angular velocity sensor, and sometimes a magnetic field sensor (if rotation in the horizontal plane must be measured).

--

Ton van den Bogert

[Roux Terence]

Re: Measure Angle with an accelerometer 3axis in dynamics

Hello,

Thank you for your answer. But that's the point, I can't use an IMU for measuring angles. I tried with formua like Angle = X/ (sqrt(Y^2 + Z^2). But it gave me only angles between -10° and 10°, but I had angle on video near to 45° so that's not so good.

Do you have any idea ?

[Josh Baxter]

Re: Measure Angle with an accelerometer 3axis in dynamics

My first guess is that you are actually measuring the accelerations values rather than degrees - where 1 g (which is what the answer should always be if your device isn't accelerating) is 9.81 m/s/s which is really close to the number 10. asin(channel / 9.81) * 180 / pi = angulation of the device... I think. This is all assuming that your sensor is at rest.

[Tim Wrigley]

Re: Measure Angle with an accelerometer 3axis in dynamics

Almost all of the major accelerometer manufacturers provide application notes on calculating tilt angles. Most describe the 3 possible approaches (1-, 2- and 3-axis). As Ton mentions, these solutions will only work under (pseudo) static conditions. Google the following ...

AN3182 Tilt measurement using a low-g 3-axis accelerometer
AN 005 Tilt-Sensing with Kionix MEMS Accelerometers
AN3461 Tilt Sensing Using Linear Accelerometers
AN3461 Tilt Sensing Using a Three-Axis Accelerometer
AN 1057 Using an Accelerometer for Inclination Sensing
AN3107 Measuring Tilt with Low-g Accelerometers

Tim Wrigley
University of Melbourne

[Ton van den Bogert]

Re: Measure Angle with an accelerometer 3axis in dynamics

That is exactly the correct formula, except it requires an inverse tan operation on the right hand side. But that can't explain your error. When the angle is 10 degrees or less, tan(x) is close to x (in radians).

Josh mentions acceleration units and g, but this formula does not need it. Units cancel out, and g is not needed, it will work equally well on the moon.

The error must come from acceleration being too large. To explain an error of 35 degrees, the acceleration must be a significant fraction of g, maybe 30-50%. Do you know if that is the case?

Also make sure that the accelerometer outputs 1 g vertical when at rest, and is not "zeroed" to compensate for the gravity effect. That is sometimes done when an accelerometer is used to measure acceleration (instead of tilt). Tilt calculation would go wrong if that is done.

Ton

[Roux Terence]

Re: Measure Angle with an accelerometer 3axis in dynamics

Thank you all for your answer firstable.

I tried to measure the angle but the acceleration is maybe to high and that's why I found an error (near to 35° or 40°). I don't know if the acceleration must be significant fraction of g. I have to see in the datasheet. But can you explain me the fraction of g what is it ?

Thank you

[Ton van den Bogert]

Re: Measure Angle with an accelerometer 3axis in dynamics

Let's say you have a horizontal acceleration a, and no vertical acceleration and no tilt. The accelerometer signals (ax,ay,az) will be (a,0,g) if the z axis of the accelerometer is vertical.

The formula for static tilt measurement will give you: theta = atan(a/g). The actual tilt is zero, so this is exactly the error in your tilt measurement. If a is 0.7 g, you get an error of about 35 degrees.

Vertical acceleration will also cause error, but not as much and not when the actual tilt is zero.

Maybe a good way to check the acceleration is to take the (calibrated) accelerometer signal and check if sqrt(ax^2 + ay^2 + az^2) is close to 1 g.

Ton