Abstract: The error-included kinematic geometry principles for rotational accuracy measurements and evaluations of revolute pairs are presented for the first time, which are represented by the kinematic geometry models and the basic closed-loop vector equations formed by three basic elements, including the error motion of the rotor, the geometric elements tested and the measuring parameters of the sensors. The completeness conditions for measuring rotational accuracy are derived according to the error-included kinematic geometry principles. The integrality of the measured kinematic parameters of the rotational error motion is discussed based on the existence of solutions of the basic equations, whose evolution forms are tied to the measuring methods and used to clarify the kinematic and geometric meanings of the measured data and their accuracy indexes. The invariants theorem of rotational error motion are given by considering the kinematic geometry properties of the error motion; the minimal spherical image curve and the minimal striction curve of the rotational error motion are obtained, which separates the rotational error motion of the rotor into angular error motion and translational error motion. The relationships between the current accuracy indexes and the invariants, such as the angular error and the translational error, are set up; these help to develop a new invariants method for rotational accuracy evaluation, which can avoid the influences of different geometric elements tested. It provides a theoretical basis for measuring and evaluating rotational accuracy of revolute pairs.

Key words: kinematic geometry, revolute pairs, rotational accuracy, error motion, invariants