Local synthesis establishes a relationship between the relative motion and the local geometry properties of gear and pinion surfaces at one single (mean) point. Theoretically, local synthesis design of spiral bevel and hypoid gears cannot ensure the contact performance along the entire contact point path (CPP) resulting in uncontrolled contact ellipses with different sizes and unavoidable transmission errors (TEs). Based on local synthesis, tooth contact analysis (TCA) and third-order contact analysis provide supplementary methods for improvement but still cannot directly control the entire CPP. A global synthesis approach is proposed to directly design the entire CPP by which it is possible to design each instantaneous contact ellipse (ICE) for load capacity and to achieve any function of TEs. A detailed implementation based on a free-form five-axis machine is presented in which the machine settings are obtained by definite relative position and motion between the tool and the workpiece at every instant. An example and the results obtained from the authors’ implementation are also provided for illustration and validation and show better control of contact ellipses and remarkable reduction of TEs to near zero.

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