过约束与局部自由度对机构关节约束反力可解性的影响

Influences of Over-constraint and Local Degree of Freedom on the Solvability of Mechanism Joint Constraint Force

利用静力学平衡方程研究了一种含局部自由度的4-SPS/CU无过约束并联机构的受力分析。写出了该机构的静力学平衡方程并得出其方程组中方程个数大于未知量的个数,采用局部转换矩阵去掉了该机构中局部自由度对应的力矩平衡方程使原来的超定方程变为静定方程。说明了对机构中局部自由度的预处理提高了静力学平衡方程的求解效率。为了系统的研究过约束和局部自由度对机构静力学平衡方程的影响,分别讨论了2阶至5阶过约束机构静力学平衡方程的可解性与机构中过约束与局部自由度的关系,制定了机构中局部自由度和过约束的判定方法。证明了机构中过约束与局部自由度对机构静力学平衡方程的可解性影响具有一般性,为机构的关节约束反力求解提供了理论基础。

The force analysis of a novel 4-SPS /CU parallel mechanism is investigated through statics vector equilibrium equations. The equilibrium equations in which the equations＇ number is greater than the unknown variables are formulated for this mechanism. It happens that the number of redundant equations is equal to the local degrees of freedom,and redundant equations are abandoned by using the local switch matrix. Such preprocessing for the local degrees of freedom can improve the efficiency of the solved statics equilibrium equations. In order to systematically research the influence of the local degrees of freedom and over-constraint on the statics equilibrium equations,the relations between the solvability of statics equilibrium equations in the two to five order overconstrained mechanism and the local degrees of freedom,over-constraint are respectively discussed. The judgment method of the local degrees of freedom and over-constraint is established. It proves that the influences of the local degrees of freedom and over-constraint on the statics equilibrium equations are universal,which provides the rationale for the solution of joint constraint forces.