一种新的平面机构自由度通用计算公式  

A New Universal Formula of Degree of Freedom for Planar Mechanism

作　　者：韩青[1,2] 李天成[2,3] 

机构地区：[1]红河学院工学院,云南红河661100 [2]西北工业大学机电学院,陕西西安710072 [3]Salamanca大学科学学院,西班牙萨拉曼卡37008

出　　处：《机械传动》2015年第3期153-157,共5页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51075337);云南省教育厅资助项目(2014Y459);西北工业大学优秀博士论文基金(YBJL 201407)

摘　　要：传统平面机构自由度计算公式缺乏考虑公共约束、虚约束和局部自由度,难以通用于平面机构自由度计算,且机构增减构件后需重新求解。基于构件对于机构输入和输出运动关系的实效性影响,建立一种新型平面机构自由度通用计算公式。研究了虚约束、公共约束、局部自由度与机构自由度代数关系,定义平面机构有效构件、有效环路、广义高副概念等作为公式变量。新公式不需考虑低副和复合铰链,可以直接套用各类平面机构,克服了传统公式存在的不足。同时,新公式基于机构有效闭环划分,明确机构的基本组成单元——构件对其自由度影响,能够有效解决平面机构变形后自由度计算问题,避免重复查算。实例对比说明了新公式的简便性和正确性,且可以应用于传统公式失效或不易求解的平面机构。Without taking into account of redundant constraints,common constraints and isolated degree of freedom（DOF）,the traditional DOF calculation formulas are inefficient in calculating the DOF of planar mechanism in certain complicated cases.In addition,recalculating is needed when the configuration of mechanisms is changed.To solve these problems,a novel universal formula of DOF for planar mechanisms is presented based on the effectiveness impact of the components on the relation of input and output motion of mechanism.The algebraic relationship between redundant constraints,common constraints,partial DOF and the DOF of mechanism is studied respectively.The valid components,valid loops and higher pairs are defined as formula variables.The new formula does not need to calculate compound hinges and lower pairs and overcomes the invalidity of traditional formulas,which can be used directly for all kinds of planar mechanisms.In addition,by defining valid loops of mechanisms,the new formula emphasizes the impact of components,the basic unit of mechanisms,on the DOF of mechanism,which can avoid recalculating when the configuration of mechanisms is slightly changed.Contrast examples are presented to show the simplicity and validity of the new formula,which can be applied to ad-hoc planar mechanisms that couldn＇t be solved by traditional formulas.

关 键 词：自由度计算 平面机构 虚约束 公共约束 局部自由度 

分 类 号：TH112[机械工程—机械设计及理论]