Method for rolling compensation with wheel-mounted sensors

A method for identifying an axis of rotation for a vehicle wheel using a wheel-mounted alignment sensor configured to acquire at least toe angle measurements, camber angle measurements, and wheel rotational position measurements, comprising:

• mounting the alignment sensor to the wheel;
• acquiring toe angle and camber angle measurements at the wheel-mounted alignments sensor for a first measured rotational position of the wheel;
• rolling the wheel through an arc of rotation to a second measured rotational position;
• acquiring toe angle and camber angle measurements at the wheel-mounted alignments sensor for the second measured rotational position of the wheel;
• establishing a rotational matrix for each of said first and second measured rotational positions of the wheel;
• determining a mathematical similarity between each of said rotational matrices by developing a third rotational matrix [Rot,XYZ]1,2 by multiplying the first rotational matrix with the inverse of the second rotational matrix;
• and
• decomposing said third rotational matrix to identify matrices of eigenvalues and eigenvectors associated with an identifiable wheel axis of rotation.

A method for identifying an axis of rotation for a vehicle wheel using a wheel-mounted alignment sensor configured to acquire at least toe angle measurements, camber angle measurements, and wheel rotational position measurements, comprising:

• mounting the alignment sensor to the wheel;
• acquiring toe angle and camber angle measurements at the wheel-mounted alignments sensor for a first measured rotational position of the wheel;
• rolling the wheel through an arc of rotation to a second measured rotational position;
• acquiring toe angle and camber angle measurements at the wheel-mounted alignments sensor for the second measured rotational position of the wheel;
• establishing a rotational matrix for each of said first and second measured rotational positions of the wheel;
• determining a mathematical similarity between each of said rotational matrices using a third rotational matrix [Rot,XYZ]1,2 constructed by multiplying the first rotational matrix with the inverse of the second rotational matrix;
• and
• decomposing said third rotational matrix to identify matrices associated with an identifiable wheel axis of rotation.