具有多模式球面4R机构结构参数研究  

Structural Parameters of Spherical 4R Mechanism with Multiple Modes

作　　者：刘伟[1,2] 刘宏昭[1] 胡旭宇[1] LIU Wei;LIU Hongzhao;HU Xuyu(Faculty of Mechanical and Precision Instrument Engineering,Xi'an University of Technology,Xi'an 710048,China;School of Electrical and Mechanical Engineering,Xi'an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048 [2]西安工程大学机电工程学院,西安710048

出　　处：《农业机械学报》2022年第3期440-448,共9页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家自然科学基金项目(51275404)。

摘　　要：基于代数几何理论,结合双变量代数方程可因式分解的判定条件,对球面4R机构运动学方程进行研究,提出一种确定具有多模式球面4R机构结构参数的分析方法。可得5类具有约束奇异位形的球面4R机构,其中多模式球面4R机构可分为4类:具有定轴线和变轴线2种转动运动模式,具有2种变轴线转动运动模式,具有1种变轴线和2种定轴线3种转动运动模式,具有4种定轴线转动运动模式,总共4大类多模式机构。对球面4R机构连杆在约束奇异位形下的瞬时转动轴线进行计算,可得球面4R机构处于约束奇异位形时,其连杆的瞬时转动轴线均不重合,瞬时转动轴线均为2条。具有约束奇异位形且只具有一种运动模式的球面4R机构处于约束奇异位形时,虽然其运动可能产生分岔,但其运动模式不一定发生改变。运动分岔机构与多模式机构不能等同。使用该方法对球面4R机构的运动模式进行分析,研究多模式单环单自由度机构结构参数对其运动模式的影响,对拓展多模式机构构型具有一定的理论价值。Based on the theory of algebraic geometry,the kinematic equation of spherical 4R mechanism was studied in combination with the judging condition of factorization of bivariate algebraic equation,and an analytical method for determining the structural parameters of spherical 4R mechanism with multi-mode was proposed.Five kinds of spherical 4R mechanisms with constrained singular configurations were found,among which the multi-mode spherical 4R mechanisms can be divided into four types:two rotational motion modes with fixed axis and variable axis,two rotational motion modes with variable axis,one rotational motion mode with variable axis and two rotational motion modes with fixed axis,and four rotational motion modes with fixed axis.The instantaneous rotation axes of spherical 4R linkage in constrained singular configuration were calculated.When the spherical 4R mechanism was in the constrained singular configuration,the instantaneous rotation axes of its connecting rod were not coincident.There were two instantaneous rotation axes of spherical 4R linkage in constrained singular configuration.When the spherical 4R mechanism with constrained singular configuration and only one motion mode was in constrained singular configuration,its motion mode did not necessarily change,although its motion may bifurcate.Bifurcation mechanism and multi-mode mechanism were not equal.Using this method,the motion modes of spherical 4R mechanism were analyzed comprehensively,which had certain theoretical value for studying the influence of structural parameters of multi-mode single loop single degree of freedom mechanism on its motion modes and expanding the type of multi-mode mechanism.

关 键 词：运动模式 准素分解 球面4R机构 变轴线转动 

分 类 号：TH112[机械工程—机械设计及理论]