Space Velocity Vector Model of Real-time Non-clearance Ball Precise Transmissions

Abstract

Abstract: To solve the space motion problems of ball existed in the real-time non-clearance precision ball transmissions，a modified D-H transform matrix was derived and the positions of any point on the steel balls relative to the center plate and the combined planetary plate were obtained based on differential geometry theory.A mathematical model of the relative velocity vectors of the balls relative to the center plate and the combined planetary plate was established by using the transform mechanism method and space geometric modeling method.The influences of the groove angle of the cycloid plate and numbers of ball on the velocity vector model were analyzed.The comparisons between the numerical results and the simulation results verify the reliability of the velocity vector models.

Key words: real-time non-clearance ball precision transmission, modified D-H transform matrix, space geometric modeling, relative velocity vector

摘要： 针对实时无隙钢球精密传动机构中钢球的空间运动问题，根据微分几何理论，推导出了修正D-H变换矩阵，得到了传动机构钢球上任意一点相对于中心盘和组合行星盘的位置。利用转换机构法和空间几何建模理论，建立了钢球相对于中心盘和组合行星盘的空间相对速度矢模型。分析了传动机构摆线盘槽形角和钢球数对速度矢模型的影响。仿真结果与数值模拟结果的对比分析验证了空间速度矢模型的可靠性。

关键词: 实时无隙钢球精密传动, 修正D-H变换矩阵, 空间几何建模, 相对速度矢量

CLC Number:

TH132.4

DUAN Liying1;AN Zijun1;FU Zhiqiang2. Space Velocity Vector Model of Real-time Non-clearance Ball Precise Transmissions[J]. China Mechanical Engineering.

段利英1;安子军1;付志强2. 实时无隙钢球精密传动空间速度矢模型[J]. 中国机械工程.

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