This paper rigorously presents a new theory called compensated conjugation for gear transmission error balance. The proposed theory is a systematic study based on conjugation equation and transmission function. The basic idea is that conjugation is essentially impaired by loading condition but can be compensated by modifying transmission function. In contrast to the traditional method which is mainly applicable for planar involute gears, the new idea generally applies for all conjugation types based on the same concept of transmission. Multiple Concepts of conjugation and transmission are rigorously modeled and defined by screw theory. A theorem about the continuity of motion and conjugate geometries is presented and proved in order for desirable modification. The proposed theory is consistent with the standard manufacturing process for tooth modification. Tooth geometries and cutter geometries can be obtained after the theoretical transmission error function is designed. For the most important application — planar involute gear design, a practically convenient method with a direct rack-cutter modification is proposed and rigorously analyzed by kinematics and differential geometry. Examples show the effectiveness of the methodology.

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