Based on the numerical calculation results, the tooth profile in the transverse plane is produced and the teeth of the whole gear model are formed to build the complete 3D gear model. The center of the rounded corner at the tip traces out a trochoid and then, the rounded tip will envelope another curve defining the root fillet. Figure 3 shows the generating hob tool and the trochoidal root fillet in an arbitrary position during a cycle of contact in a transverse plane for a gear with the number of teeth 20 (without under- cut), module of 3 mm and pressure angle of 20 ̊. Equation (9) can be used to calculate the Cartesian coordinates of the envelope of trochoidal root fillets for four different cutter tip radius having 0.0, 0.25, 0.4 and 0.5 times the module.
