Absolute angle determination

A device for measuring an absolute angle of an axle, the device comprising:

• a first rotatable member having a first radius (S) and a first perimeter,
• a second rotatable member having a second radius (T) and a second perimeter,
• a first number (P) of detectable elements provided on the first rotatable member adjacent to a first perimeter thereof,
• a second number (Q) of detectable elements provided on the second rotatable member adjacent to a second perimeter thereof,
• a first sensor is mounted on the first rotatable member and configured for detecting rotation of the first number of detectable elements, and a second sensor is mounted on the second rotatable member and configured for detecting rotation of the second number of detectable elements,
• wherein the first radius (S) is equal to a first integer (M), which is greater than zero, times a factor (a),
• wherein the second radius (T) is equal to a second integer (N), which is greater than zero, times said factor (a),
• wherein the first radius and the second radius are in a same units of measurement,
• wherein the second rotatable member is coupled with the first rotatable member such that a rotation of the first rotatable member over a first angle (α) causes the second rotatable member to rotate over a second angle (β) equal to the first angle (α) times the ratio (M/N) of the first radius and the second radius, and
• wherein the product of the first number (P) and the second integer (N), and the product of the second number (Q) and the first integer (M), are co-prime;
• the device further comprising a processor configured to:
• obtain parameter values (M, N, P, Q);
• calculate Bézout numbers (C, D) using the parameter values;
• obtain measured angles (γ,θ);
• multiply each measured angle (γ,θ) with a respective Bézout number (C, D);
• add resulting products;
• output a resulting sum;
• scaling the resulting sum;
• and outputting the scaled sum as the absolute angle of the axle.