Hello,(adsbygoogle = window.adsbygoogle || []).push({});

Background:

We have a machine with two rotational axes (b,c) attached to each other. By design the B axis is rotating about the Y-axis and the c-axis is attached on top of the b axis.

Ideally the axes are orthogonal but in practice they are not. However we can measure the directions of the axes. Hence we have the axes of rotations described as two vectors.

The target is to align an arbitrary vector that is attached to the c-axis of rotation to a vector that is described in the global coordinates by changing the rotation angle of the b and c axis. We can construct the full rotation matrix but how do we find the angles b and c that aligns the vectors. From CAD we can see that there are multiple solutions.0

16

We can find numerous examples on how to get one angle and one axis of rotation from a rotation matrix. We can also find a lot of examples on how to split the transform into three Euler angles.

We know that the problem is possible to solve numerically but is there a closed form solution?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Find rotation to align two vectors by rotation about two arbitrary axes

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**