According to the defect of traditional method of determining instantaneous contact regions for conjugate surfaces, a numerical approach to the determination is proposed. A local coordinate system is built by using the surface unit tangent and unit normal at the contact point. Considering that the gap forming the boundary of instantaneous contact region in the direction of the common normal vectors is given, a system of nonlinear equations is built to fred the instantaneous contact boundary in local coordinate system, a modified Powell's hybrid algorithm of finite-difference approximation to the Jacobian used to solve the system. The new method simplifies the task of determining instantaneous contact regions without calculating curvature and relative curvature. The validity of the proposed approach is verified by an example of hypoid gears.
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