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几类空间并联机器人的奇异研究
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摘要
并联机器人有着串联机器人所不具有的优点,在应用上与串联机器人呈互补的态势。应用的需要促进并联机器人理论研究的深入。奇异位形的研究是并联机器人理论研究中的一个重要组成部分。本文对并联机器人奇异位形产生的根源、存在的规律性、线性丛性质等进行了全面系统的研究。
    在分析有关文献并研究并联机器人的奇异特征的基础上,本文首先综合性地给出机器人奇异的概念,分别阐述了串联机器人和并联机器人奇异的不同,然后对奇异提出新的分类方法,分别从奇异对机构的运动状态的影响、奇异形成的原因、线性丛性质、奇异位形的研究方法等几方面进行了系统的分类,这对深入认识奇异以及对并联机器人的奇异研究有理论价值。
    空间少自由度并联机器人机构是所有并联结构中运动规律最复杂的。在少自由度家族中,3-RPS 并联机器人机构是应用研究最广泛的一种。本文首次得到了它的最一般奇异判别式、姿态奇异分布和三维空间位置奇异分布。分析了奇异分布的几何特点,而且发现了本机器人机构可能出现的所有共十种奇异位形,系统地讨论了它们的线性丛性质和奇异运动规律,给出了奇异的线几何理论依据。另外还进行了本机器人六个输出参数的解耦性研究,给出了输出参数之间的简洁的解耦关系式。 四和五自由度并联机器人机构,特别是对称四自由度和五自由度并联机器人机构也是少自由度并联机器人家族中不可缺少的机构。这里首次建立了两种新型对称
    四自由度和一种新型对称五自由度并联机器人机构的奇异方程。提出了奇异的几何条件,给出了奇异的数值算例,而且研究了奇异的自由度变化规律和奇异的运动性质,剖析了分支奇异对并联机器人的影响。首次给出了以上三种并联机器人机构的约束条件、位置正解方程、位置逆解方程以及正解和逆解的数值算例,并进行了自由度和运动性质的分析,确定了其合理的输入方案以及最优输入方案。为其工作空间研究奠定基础。这对它们的进一步的奇异研究和推广应用很有意义。 六自由度并联机器人机构是应用最普遍的,其中 6/6-Stewart 和 3/6-Stewart 并联
    机器人机构是最典型的并联机器人机构。对于 3/6-Stewart 并联机器人机构,这里首次得到其奇异点在β 斜平面上的双曲线分布规律,而且得到 3/6-Stewart 并联机器人机构在三维空间中的奇异判别式和双曲抛物面分布规律。作为算例,还给出了某些
Compared with a series manipulator, a parallel manipulator is with some advantages. Parallel manipulators can fill the area which series manipulators are not applicable. The needs of the application accelerate the theoretical research of parallel manipulators. The study of the singularity is important in the theoretical research of parallel manipulators. With the complete analysis of the developments of the application and the research of parallel manipulators, especially the progresses of the singularity research of parallel manipulators international and at home, a thorough and systemic study about the root and principle of singularity and the behavior of the mechanical and movement of the parallel manipulator in singularity is gone along in this paper.
    Depending on the investigation of the singular characteristics of parallel manipu- lators and analyzing some references about the singularity, this paper expatiates the dis- tinctness of singularity in parallel and series manipulator based on the definition of singu- larity of manipulator. The force Jacobian matrix of lower-mobility parallel manipulator is established. Furthermore, several new methods to class the singularity, such as the method based on the causes of singularity, motion stations at singularity, linear-complex charac- teristics, and method to research singularity, are presented. This is significant to the singu- larity research.
    The analysis of the kinematics characteristics for spatial lower-DOF parallel manipu- lators is the most complicated in the theoretical study of parallel manipulators. In the fa- mily of the lower-DOF parallel manipulators, the 3-RPS parallel manipulator is a focus in the applications and researches. In this paper, the symplectics of the six output variables is studied firstly, then the singularity regularity of the 3-RPS parallel manipulator is presen- ted firstly and then the general singularity discriminant is obtained. The distributing chart of position singularity and the distributing chart of pose singularity are gained. The cha- racteristics of all the ten positions and orientations in the singularity are analyzed tho- roughly and the attestations to the singularity based on the line geometry are presented. 4-dof and 5-dof parallel manipulator, particularly symmetrical 4-dof and 5-dof para-
    llel manipulator is indispensabe in the family of lower-DOF parallel manipulators. The restricting conditions, the solutions of the forward and inverse position kinematics of two 4-dof and one 5-dof parallel manipulator are established firstly. Three expressions to dis- tinguish singularity of the three parallel manipulators are built. This is groundwork to the popular applications and the singularity study of the three parallel manipulators. 6-dof parallel manipulator is applied universally. The 6/6 and 3/6-Stewart are ty- pical among the 6-dof parallel manipulators. About 3/6-Stewart parallel manipulator, the singularity regularity in the β inclined plane is found by the geometrical condition of singularity firstly. The singularity locus is a hyperbola in the β inclined plane. Its asym- ptote and real axis and image axis are ascertained. Then with the kinematics method and the singularity transform method, the discriminants of singularity in the three dimensional space is received. By way of the corresponding numerical examples, the singularity dis- tributing in the three-dimensional space and the singularity analyzing of the 3/6-Stewart parallel manipulator at some poses are worked out. Moreover, the relation of inverse to each other of velocity Jacobian and the force Jacobian matrix of 6-dof Stewart parallel manipulator is proved. Finally, the correctness of the singularity principle and analysis is validated with tests.
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