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The position function and the gear ratio function of the elliptical gear transmission can represent the geometric characteristics of the elliptical gear pair, which are independent of the change of the motion law of the driving wheel with time. The gear ratio function of the congruent elliptical gear mechanism is conjugated to a pair of congruent elliptical gears, and the angular velocity of the driven wheel is periodically changed.
When the elliptical gear is continuously driven, its pitch curve should be a closed curve. In the elliptical gear, the polar coordinate equation of the pitch curve of wheel 1 is r1=1-cos1(1), because the center distance of the elliptical gear transmission is r1 r2=2a, so r2=a(1-2cos1 2)1 -cos1(2). The lubricant agent transmission ratio function is i21=1-21-2cos1 2(3). R2 can also be expressed as r2 = 1 cos2 so the pitch curve of the elliptical gear is also a pair of congruent ellipse.
The position function of the elliptical gear can be obtained by the integral of the gear ratio function: 2=∫10i21d1=∫101-2(1 2)-2cos1d1=2arctan1 1-tan12, ie tan22=1 1-tan12(4), the moment of the driven wheel Angular velocity 2=d2dt=i21d1dt=11-21-2cos1 2(5), if 1 is a constant, then 1=0, 2max=11 1-=1a ca-c121=180°, 2min=11-1 =1a- The maximum angular velocity and the minimum angular velocity of the ca c driven wheel alternately appear. The ratio k=a ca-c2 of the driven wheel is to ensure smooth motion of the follower, and generally should take k ≤ 5. When the transmission ratio change range of the congruent elliptical gear mechanism and the phase difference between the driven wheel and the driving wheel increase as the eccentricity increases, the main driven wheel synchronously operates.