In inertial motion tracking of kinematic chains, inertial measurement units (IMUs) are attached to each segment in order to track their motion in three-dimensional space. Determining the relations between the functional axes of a joint and the local coordinate system of the attached sensor is a crucial requirement. For the case of hinge joints, methods have been proposed that exploit kinematic constraints to automatically identify the local hinge joint axis coordinates from the raw data of almost arbitrary motions. However, to current date, it remains unclear which joint motions are sufficiently rich for the joint axis to become identifiable. We consider a commonly used gyroscope-based kinematic constraint and present a novel accelerometer-based kinematic constraint. We study conditions of identifiability by analyzing the nonlinear constraint equations and present practical conditions for the minimum excitation that is required. Among other results, we prove that planar motions and subsequent motions of both ends of the joint are sufficient as long as the joint axis does not remain perfectly horizontal. Theoretical results are validated in experimental studies of a human upper limb wearing an exoskeleton. Despite the typical IMU-related measurement inaccuracies and although the human elbow joint is only an approximate hinge joint, the cost function defined by the kinematic constraints exhibits a distinct global minimum at the true joint axis coordinates if the motion fulfills the proposed requirements.