An apparatus for determining a position and orientation of first and second rigid bodies in relation to each other. The apparatus includes a light source mounted to the first rigid body, an image sensor mounted to either the first or second rigid body and positioned in a field of light, a shadow mask mounted to either the first or second rigid body and arranged in the field of light, and a computation unit configured to calculate at least one angle by evaluating a shadow image which passes the shadow mask and is detected by the image sensor. The apparatus may include a mechanical constraint mounted to the first and second rigid bodies that defines a fixed distance between the first and second rigid bodies, is stationary in relation to one of the first or second rigid body, and is variably inclinable in relation to the other.