基于几何代数的四面体机构自由度分析

Mobility Analysis of Tetrahedral Mechanisms Based on Geometric Algebra

针对四面体机构的多环耦合复杂结构导致的现有自由度计算方法对其进行自由度分析时不能有效地判断耦合部分的约束情况,课题组提出了一种基于几何代数的四面体机构自由度分析方法。先将整个机构进行拓扑等效,寻找机构的最短分支;通过修正分支运动空间的方式,将与分支耦合的闭环带来的约束体现在分支的运动空间中;最后通过对所有修正后的分支运动空间求交,得到输出构件的自由度解析式。结合具体算例可知:课题组提出的方法无需借助逻辑判断,可直接得到机构输出构件的自由度性质,解析式中的变量能给之后的驱动分布提供了选择方案。基于几何代数的四面体机构自由度分析方法具有一定的工程意义。

Due to the complex structure of multi-loop coupling in tetrahedral mechanisms,existing methods for calculating degrees of freedom couldnot effectively determine the constraints of the coupling part when conducting free analysis,a degree of freedom analysis method for tetrahedral mechanisms based on geometric algebra was proposed.Firstly,the topological equivalence on the entire mechanism was performed to find the shortest branch of the mechanism.By modifying the twist space of the branch,the constraints brought by the closed-loop coupling with the branch in the twist space of the branch were reflected.Finally,by intersecting all modified twist spaces,the analytical expression for the degrees of freedom of the output component was obtained.Based on specific examples,it can be seen that the proposed method does not require logical judgment and can directly obtain the degree of freedom properties of the output components of the mechanism.The variables in the analytical formula also provide a selection scheme for the subsequent drive distribution which has some engineering significance.