# Angular relationship of fixed shaft eccentric gear train

The unequal model solution of a pair of fixed shaft eccentric gears is extended to the fixed shaft gear train. Taking the three-stage eccentric gear transmission around the driving center wheel 1 shown in Fig. 1 as an example, the rotation angle relationship of the fixed shaft eccentric gear train is calculated.

All eccentric gears in the gear train are installed in the same phase, the axial distance a is 34.3 mm, and the eccentricity is ε For 0.104 3, the driving center wheel 1 rotates clockwise. According to the bisection model, the calculation formula of the 2nd and 3rd stage eccentric gear transmission on the forward side is:

According to the solution of the unequal division model, at the initial position, the midpoint of the reference tooth top of the central wheel 1 is located on the x-axis, the installation angles of the forward side eccentric gears 2, 3 and 4 are – 0.367 °, 0.651 ° and – 0.911 ° respectively, and the initial installation angles of the reverse side gears 2 ‘, 3’ and 4 ‘are – 0.435 °, 0.970 ° and – 1.628 ° respectively. The mating teeth of the eccentric gears at all levels form meshing, As shown in figures 1a and 1b. Taking the meshing state of eccentric gears at all levels in the initial position as the reference position, when the center wheel 1 rotates clockwise at any angle, the mating teeth of eccentric gears at all levels form meshing again. Figures 1c and 1D show the meshing state of eccentric gears when the center wheel rotates clockwise by 60 °.

Angle of eccentric gears 3 and 4 on the positive side φ 3 and φ 4 can be expressed as:

For the bisection model, the phase difference between the rotation angle of each stage eccentric gear on the reverse side and that of each stage eccentric gear on the forward side is 180 °, and the rotation angles of 2 ‘, 3’ and 4 ‘of the eccentric gear on the reverse side can be obtained φ~’ 2、 φ~’ 3 and φ~’ 4, there are:

According to the formula, under the unequal division model, the transmission angle relationship of all levels of eccentric gears on the positive and negative sides is shown in Figure 2, and the angle error curve is shown in Figure 3.

Under the bisection model, when the driving wheel angle is 180 °, the driven wheel angle is also equal to 180 °. However, it can be seen from Figure 2 that there are positive or negative angle errors of eccentric gears at all levels when the angle of the central wheel is 180 °, the angles of the driving wheel and the driven wheel are not equal, and the angle error of multi-stage eccentric gear transmission is amplified step by step. It can be seen from Fig. 3 that when the rotation angle of the central wheel exceeds a certain position after 180 °, the rotation angle curve of the eccentric gear on the forward side and the rotation angle curve of the gear on the reverse side produce an intersection, the corresponding rotation angles of the central wheel are different, and the rotation angle relationship of the eccentric gear at the same level on the forward and reverse sides is not symmetrical to the intersection. The initial state of each stage eccentric gear on the reverse side is not the state of the eccentric gear on the forward side after the center wheel rotates 180 °.

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