To understand this unit we'll start with the accelerometer. When thinking about accelerometers it is often useful to image a box in shape of a cube with a ball inside it. You may imagine something else like a cookie or a donut , but I'll imagine a ball:
If we take this box in a place with no gravitation fields or for that matter with no other fields that might affect the ball's position – the ball will simply float in the middle of the box. You can imagine the box is in outer-space far-far away from any cosmic bodies, or if such a place is hard to find imagine at least a space craft orbiting around the planet where everything is in weightless state . From the picture above you can see that we assign to each axis a pair of walls (we removed the wall Y+ so we can look inside the box). Imagine that each wall is pressure sensitive. If we move suddenly the box to the left (we accelerate it with acceleration 1g = 9.8m/s^2), the ball will hit the wall X-. We then measure the pressure force that the ball applies to the wall and output a value of -1g on the X axis.
Please note that the accelerometer will actually detect a force that is directed in the opposite direction from the acceleration vector. This force is often called Inertial Force or Fictitious Force . One thing you should learn from this is that an accelerometer measures acceleration indirectly through a force that is applied to one of it's walls (according to our model, it might be a spring or something else in real life accelerometers). This force can be caused by the acceleration , but as we'll see in the next example it is not always caused by acceleration.
If we take our model and put it on Earth the ball will fall on the Z- wall and will apply a force of 1g on the bottom wall, as shown in the picture below:
In this case the box isn't moving but we still get a reading of -1g on the Z axis. The pressure that the ball has applied on the wall was caused by a gravitation force. In theory it could be a different type of force – for example, if you imagine that our ball is metallic, placing a magnet next to the box could move the ball so it hits another wall. This was said just to prove that in essence accelerometer measures force not acceleration. It just happens that acceleration causes an inertial force that is captured by the force detection mechanism of the accelerometer.
While this model is not exactly how a MEMS sensor is constructed it is often useful in solving accelerometer related problems. There are actually similar sensors that have metallic balls inside, they are called tilt switches, however they are more primitive and usually they can only tell if the device is inclined within some range or not, not the extent of inclination.
So far we have analyzed the accelerometer output on a single axis and this is all you'll get with a single axis accelerometers. The real value of triaxial accelerometers comes from the fact that they can detect inertial forces on all three axes. Let's go back to our box model, and let's rotate the box 45 degrees to the right. The ball will touch 2 walls now: Z- and X- as shown in the picture below:
This is direct copy and paste from Starlino
http://www.starlino.com/imu_guide.html
since there is no better way to explain this part I just copy and paste it from this website, but I personally don't like the rest of their explanations in this topic.
Just there is something about last picture that I would like to explain as you may noticed:
square root of 0.5g is approximately 0.71g. So the resultant acceleration is:
SQRT{ (0.71g) ^ 2 + (0.71g) ^ 2 }
which is equal to:
SQRT { 0.5g + 0.5g }
which is equal to:
1g
So we can see that when gravity is applied at 45 degree the resultant will remains at the same value because it is caused by same gravity.
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