基于螺旋理论的机构自由度自动分析-《集美大学学报（自然科学版）》

文章信息/Info

Author(s):: WANG Chengzhi; (School of Marine Equipment and Mechanical Engineering,Jimei University,Xiamen 361021,China)

Keywords:: screw theory; mechanisms mobility; mobility analysis; passive degrees of freedom; symbolic variables

摘要:: 为了实现机构自由度快速自动分析，将字符、符号等自动转变为字符变量的方法和便于局部自由度分析的参数输入原则，并由此分析自动构建运动螺旋集及相应约束螺旋集的算法；然后提出局部自由度、公共约束、冗余约束及整个机构自由度的自动分析算法；最后得出机构中存在局部自由度的充要条件。用该程序自动分析了61个各类机构的自由度，计算结果完全正确，且计算效率高，可输入含任意字母与数字组合的字符变量、简单运算符和三角函数的表达式，可用于自动分析计算平面、空间、单环及多环机构的自由度。

Abstract:: The rapid and automatic mobility analysis of a mechanism is of great significance to the innovative design of the mechanism.In the mobility analysis based on screw theory,arbitrary character variables,digital variables and their combination are often used to describe the axis vectors and coordinates of kinematic pairs,hence,the method of automatically transforming characters and symbols into character variables and the parameter inputting principles for conveniently analyzing passive degrees of freedom are studied firstly,and based on these the algorithms for constructing the kinematic pair screw sets and the corresponding constraint screw systems are analyzed.Then the algorithms for calculating the passive degree of freedom,common constraint,redundant constraint,and the whole mobility in the mechanism are proposed.The necessary and sufficient conditions for the existence of passive degrees of freedom in the mechanism are obtained.The program presented in this paper was used to automatically analyze the mobility of 61 various kinds of mechanisms,and the results are completely correct.Examples show that the program is simple and efficient,and can be input the expressions containing the symbolic variables with combinations of letters and digits,simple operators,and trigonometric functions.It can be utilized to automatically analyze and calculate the mobility of planar or spatial,single-loop or multi-loop mechanisms.