基于微分几何理论的机构研究方法

Research method of mechanism based on differential geometry

基于机构工作空间积分函数求偏导数的方法,通过工作空间积分函数并分别定义串联、并联、串并联机构的积分域来求解机构的工作空间体积,并得到了机构一元、二元、三元输入函数奇异的死点、极值点的判断条件;通过对其求二阶偏导数来定义判断机构各输入变量之间的耦合度Gk,由耦合度Gk是否为0即可判断机构各输入变量之间是否具有解耦特性;基于工作空间函数与输入变量的关系,以及输入变量与时间的关系,定义了3个新的衡量机构运动特性的指标:定位精度影响因子、动态响应影响因子、灵敏度影响因子,并给出其计算过程和物理意义,为机构运动特性的研究拓展了途径。

Based on the method for partial derivative of workingspace integral function of the mechanism,by using the working space integral function and defining the integral field of serial mechanism,parallel mechanism and serial-parallel mechanism respectively to solve the working space volume of the mechanism,judgment conditions of dead point and limit point of the singularity with unary,binary and ternary input functions obtained.The coupling degree of each input variable of mechanism was defined by the second time partial derivative of working space function.Whether there is decoupling property between input variables or not can be judged depending whether the coupling degree is equal to zero or not.Based on the relationship between working space function and input variables,as well as relationship between input variables and time,three new indices to weigh the kinematical properties of mechanism was defined： orientation accuracy influence factor,dynamic response influence factor and sensitivity influence factor.Its physical meaning and computation process was also presented,widening the way to research the kinematical properties of mechanism.