十字轴式万向联轴器运动学再研究

Re-study on kinematics of cross joint type universal coupling

根据十字轴式万向联轴器的三维模型建立了其空间几何模型,运用向量法推导出了该联轴器的运动学方程。对该联轴器做了运动学仿真,得出十字轴式万向联轴器的一个完整的运动周期内包含着两个运动状态完全相同的半周期;在其任何一个半周期内输出轴角速度关于转角为90°处呈轴对称关系,角加速度关于转角为90°处呈中心对称关系;随着输入、输出轴间夹角的增大,输出轴运动状态曲线偏离输入轴的程度越大,但在输入轴运动状态曲线的两侧周期性波动。分析对比了不同输入、输出轴夹角状态下联轴器转动的角度、角速度以及角加速度的理论值与仿真值,验证了结论的正确性与运动学模型的准确性。

The spatial geometry model is established based on the three-dimensional model of the cross-shaft universal coupling. The kinematics equation of the coupling is derived by using the vector method. The kinematics simulation of the coupling shows that a complete motion cycle of the cross-shaft universal coupling contains two half cycles with the same motion state;the angular velocity of the output shaft is output in any one half cycle. Regarding the axis-symmetric relationship at a rotation angle of 90°, the angular acceleration has a central symmetry relationship with respect to a rotation angle of 90°;as the angle between the input and output axes increases, the degree of deviation of the output shaft motion state curve from the input axis is greater. However, the periodic fluctuations on both sides of the input axis motion state curve are concluded. The theoretical values and simulation values of the angle, angular velocity and angular acceleration of the coupling rotation under different input and output shaft angles are analyzed and compared, and the correctness of the conclusion and the accuracy of the kinematic model are verified.