杆系机构的可动性和运动分岔分析

考察了杆系机构的可动性和运动分叉点的判别准则,建立了杆系机构的精确运动控制方程.杆系的可动性在数学上被抽象为满足运动连续性前提下的控制方程非零解的存在性判别,从理论上说明了平衡矩阵准则中的机构位移模态数大于零仅是杆系可动性判别的必要条件,但并不充分.基于对协调方程的高阶项分析表明,如果一阶机构变形的残余伸长量与自应力模态构成的向量空间正交,则可动性条件必然满足.证明了线性协调矩阵的零奇异值与机构位移模态的等效关系,解释了其可作为运动分岔点跟踪的理论原因.阐明了机构分岔路径的性质还必须根据高阶协调条件来判定.

Movability and kinematic bifurcation analysis for pin-bar mechanisms

Criteria for determining the movability and kinematic bifurcation points of pin-bar mechanisms were investigated. The exact kinematic governing equation of the pin-bar mechanisms was established. The movability of pin-bar assemblies was induced mathematically to judge the existence of nonzero root of the  governing equation for continuous displacement. The number of inextensional deformation modes is greater than zero, resulted from the equilibrium matrix rule, was theoretically clarified to be only the necessary condition for the movability of pin-bar assemblies, but insufficient to determine. By analyzing the higher-order terms of compatibility equation, it was found that the assembly is unconditionally movable if the residual elongations caused by the first-order inextensional deformation are orthogonal to the vector space consisting of the self-stress modes. The zero singular value of linear compatibility matrix was proved to form an equivalent relationship with the corresponding inextensional deformation mode, and reflect its numeric usability in tracing kinematic bifurcation points. The higher-order compatibility analysis was expounded to be necessary for further investigating the characteristics of bifurcation points and computing consequent kinematic paths．