How to rotate coordinate frame (transform point or vector coordinates) using angles from 2-axis inclination sensor if both X and Y angles are non-zero?

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    $\begingroup$ What format is the inclinometer output? Euler angles or Tait–Bryan angles? And which axis comes first? And for only 2 axes, if both axes are not 90 degrees, does it even matter? I would need these questions answered before attempting your 3(!) questions on this topic. If you don't know the answer, perhaps this would be a good separate question. $\endgroup$
    – Ben
    May 18, 2020 at 19:21
  • $\begingroup$ The inclinometer is GEMAC IS2TK090-C-RL (2 axis XY, 90 degrees). Docs don't mention neither angle types, nor which axis comes first. As I understand it, those angles indicate simultaneous rotation with respect to XY plane. What I can't get is what projection of a gravitational vector on X/Y axis means: is it the angle 0) between inertial & inclined Z axis or 1) XY plane and respective X'/Y' axis. $\endgroup$ May 19, 2020 at 5:01

1 Answer 1


The output angle of an inclinometer is generally the angle between the axes of the sensor frame and the horizontal plane instead of the Euler angles. You can refer to the following article about how to use these two angles to get the rotation matrix:

Integrated calibration of a 3D attitude sensor in large-scale metrology

It is worth noting that the inclinometer cannot obtain a complete rotation matrix, and may need to cooperate with other sensors


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