# Is one accelerometer enough for detecting tilt/orientation of a rigid body?

I’m not familiar with sensor hardware, and I don’t really know how an accelerometer works. But I do know that from a mathematical point of view, you wouldn’t be able to uniquely determine the orientation of a solid object knowing only the acceleration of one of its points.

Indeed, assuming known initial conditions and acceleration function of one point, say point X, one can solve the second order ODE and get the position function for that point, but that wouldn’t determine the position of the rest of the points in the solid object, because the object could perform a rotation centered on point X, leaving it unchanged. Despite all that, I have seen several claims that modern mobile phones benefit from the inclusion of accelerometer sensor in such a way that enables them to, for example, determine the orientation of the screen. I don’t understand how an IPhone would know to what position the screen was tilted. Consider the following example where the red dot indicates the location of the accelerometer sensor.

Suppose acceleration data was processed and the motion of the sensor was determined as the red arc shown in the pictures below. How one could distinguish from the two depicted motions? Notice that the final orientation of the device is different.

Edit: Regarding some comments made, I want to clarify that by one accelerometer, I mean one that would be able to register accelerations in all 3 dimensions. That way, upon integration I would get the spacial (3D) trajectory of the point. I believe the issue I describe here holds even in such scenario.

• Note that velocity is dependent upon direction; therefore, rotations about a fixed axis are a type of acceleration too.
– BHT
Mar 7, 2015 at 0:53
• @Ethan yes I know, but the problem is that by looking only at the acceleration you can't uniquely determine the movement that caused it. Mar 7, 2015 at 1:04
• I don't see why it couldn't tell the difference. It looks to me that the force applied during the motion acts in different directions. Mar 7, 2015 at 1:31
• When manufacturers say "an accelerometer", they likely mean a tiny surface-mount package containing three accelerometers mounted at right angles to one another. Mar 7, 2015 at 3:01