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并联机构的运动类型(或运动模式)指的是机构末端执行器可实现的刚体运动的集合,它是所有支链运动类型的交集.作为非瞬时自由度并联机构一个主要运动学特性,运动类型在局部具有刚体变换群(或特殊欧氏群)的子流形(或特别地具有Lie子群)结构.基于这个子流形性质和子流形簇的概念,我们定义了运动类型以及并联机构的等价关系和偏序关系:如果两个运动类型在SE(3)单位元的某一开邻域内一致,那么我们称这两个运动类型等价;如果其中一个运动类型在SE(3)单位元的某一开邻域内为另外一个的子流形,那么我们称这两个运动类型之间具有序关系,并由此定义了并联机构的一种偏序关系,研究了运动类型和并联机构的等价与偏序关系,并给出了其在并联机构综合、自由度分析和非过约束构型等方面的应用.
The kinematic type (or kinematic mode) of a parallel mechanism refers to a set of rigid body motions achievable by the end effector of the mechanism, which is the intersection of all types of branched motions.As one of the major kinematic characteristics of a parallel mechanism of non-momentary degrees of freedom, the type of motion Submanifolds (or particularly Lie subgroups) with local rigid transformation groups (or special Euclidean groups) locally. Based on this submanifold property and the concept of submanifold clusters, we define the type of motion and the number of parallel mechanisms Equivalent relation and partial order relation: If two motion types are consistent in a certain open neighborhood of SE (3) unit cells, then we call these two motion types equivalent; if one of the motion types is in SE (3) units We call the order relationship between the two types of motion, and thus define a partial order relationship between the parallel mechanism, the type of movement and the parallel mechanism The relationship between equivalence and partial order is also given and its application in synthesis of parallel mechanism, analysis of degrees of freedom and non-overconstrained configurations are given.