几类少自由度冗余驱动并联机构综合及优选研究
发布时间：2018-07-13 17:09
【摘要】：并联机构由于相对串联机构具有更高的精度、刚度和承载能力等优点,特别是少自由度并联机构,在诸多领域具有广泛的应用前景。然而并联机构也具有工作空间小且存在奇异等缺点,限制了其应用。采用冗余驱动的并联机构可减少或消除一些常规并联机构无法避免的缺点,同时又不减弱原并联机构的优点。但现有的冗余驱动并联机构的研究更多是对单个机构的研究,还缺乏对冗余并联机构新构型的系统综合。因此,本文以少自由度冗余驱动并联机构为研究对像,研究了该类型机构的综合方法,并优选了部分新机型。提出了一种基于克莱因映射理论的线矢相关性判断方法,将射影几何理论引入到并联机构的奇异研究理论分析中,得出力线矢与力偶任意组合时发生线性相关性通用计算公式及线矢空间的几何关系,得到了可用于判断任意力线矢与力偶组合的线性相关性的方法。利用该方法对几类少自由度并联机构的内部奇异进行分析,该方法为并联机器人奇异理论研究提供了理论依据,也是机构优选的理论依据。利用螺旋理论,提出一种冗余驱动并联机构机型构造的新方法。对冗余驱动并联机构的冗余驱动支链的类型进行综合,并对支链安装位置、安装支链条数进行了理论分析。综合出3R、2T1R、3R1T、2R2T、3R2T和3T2R六类支链型冗余驱动并联机构的新机型,该新机型能够有效降低并联机构在运行过程中出现的非预期运动,例如可以有效的规避奇异位形,还可以提高并联机构的驱动力、刚度及灵巧度等性能指标。综合出一类基于无约束支链的冗余驱动并联机构,9种少自由度类型全部包括在内。通过不同支链的约束组合及添加数量不同的无约束支链,构造出了大量的冗余驱动并联机构,如3-UPU/SPS,4-SPS/RZPZUXY,3-RPUR/SPS等冗余驱动并联机构,这些机构可以完全避免内部奇异。利用构造完整的雅可比满秩矩阵综合机构的方法,可以计算出驱动螺旋以任意角度输入时,灵巧度、刚度的最小奇异值的力矩阵与力矩矩阵的通用计算公式。根据该方法可得到灵巧度与刚度性能最优的冗余驱动支链组合,为冗余驱动并联机构性能优选提供了理论依据。通过Ansys对综合的冗余驱动支链并联机构进行仿真,并运用Matlab对冗余驱动支链的力矩阵与力矩矩阵的条件数进行了求解,找到添加不同支链时并联机构的灵巧性的大小关系。通过理论与仿真研究,本文综合出若干灵巧度与刚度最优的冗余驱动并联机构新机型。
[Abstract]:The parallel mechanism has many advantages, such as higher precision, stiffness and bearing capacity than the series mechanism, especially the small degree of freedom parallel mechanism, so it has a wide application prospect in many fields. However, the parallel mechanism also has the disadvantages of small workspace and singularity, which limits its application. The redundant parallel mechanism can reduce or eliminate some disadvantages that can not be avoided by the conventional parallel mechanism, and at the same time, it can not weaken the advantages of the original parallel mechanism. However, the existing researches on redundant parallel mechanism are more about single mechanism and lack of system synthesis for the new configuration of redundant parallel mechanism. Therefore, in this paper, the synthesis method of this type of mechanism is studied, and some new models are selected. A linear vector correlation judgment method based on Klein mapping theory is proposed. The projective geometry theory is introduced into the singularity analysis of parallel mechanism. The general formula of linear correlation and the geometric relation of linear vector space are obtained when the combination of force line vector and couple is arbitrary, and the method can be used to judge the linear correlation of arbitrary force line vector and couple combination. This method is used to analyze the internal singularity of several kinds of parallel mechanisms with less degrees of freedom. This method provides a theoretical basis for the study of singularity theory of parallel manipulators and is also the theoretical basis for mechanism optimization. Based on spiral theory, a new method for the construction of redundant parallel mechanism is presented. This paper synthesizes the type of redundant driving branch chain of redundant drive parallel mechanism, and analyzes theoretically the position and number of branch chain. This paper synthesizes the new models of 3RN2T1R1R2R1Tn2R2T and 3T2R six kinds of redundant drive parallel mechanism. The new model can effectively reduce the unexpected movement of the parallel mechanism during operation, for example, it can avoid singularity effectively. It can also improve the driving force, stiffness and dexterity of parallel mechanism. A class of redundant drive parallel mechanisms based on unconstrained branching chains is synthesized. All of the nine types of less degrees of freedom are included. A large number of redundant parallel driven parallel mechanisms, such as 3-UPUP / SPSU 4-SPS / RZPZUXY / 3-RPURP / SPS, are constructed through constraint combinations of different branching chains and adding different numbers of unconstrained branched chains. These mechanisms can completely avoid internal singularity. By using the method of constructing a complete Jacobian full rank matrix synthesis mechanism, a general formula for calculating the force matrix and moment matrix of the minimum singular value of dexterity and stiffness when the driving screw is input at any angle can be calculated. According to this method, the optimal combination of dexterity and stiffness can be obtained, which provides a theoretical basis for the performance optimization of redundant drive parallel mechanism. The parallel mechanism is simulated by Ansys, and the condition number of force matrix and torque matrix of redundant drive branch chain is solved by using Matlab. The dexterity relationship of parallel mechanism is found when different branch chains are added. Through theoretical and simulation research, several new redundant drive parallel mechanism models with optimal dexterity and stiffness are synthesized in this paper.
【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH112
本文编号：2120127
[Abstract]:The parallel mechanism has many advantages, such as higher precision, stiffness and bearing capacity than the series mechanism, especially the small degree of freedom parallel mechanism, so it has a wide application prospect in many fields. However, the parallel mechanism also has the disadvantages of small workspace and singularity, which limits its application. The redundant parallel mechanism can reduce or eliminate some disadvantages that can not be avoided by the conventional parallel mechanism, and at the same time, it can not weaken the advantages of the original parallel mechanism. However, the existing researches on redundant parallel mechanism are more about single mechanism and lack of system synthesis for the new configuration of redundant parallel mechanism. Therefore, in this paper, the synthesis method of this type of mechanism is studied, and some new models are selected. A linear vector correlation judgment method based on Klein mapping theory is proposed. The projective geometry theory is introduced into the singularity analysis of parallel mechanism. The general formula of linear correlation and the geometric relation of linear vector space are obtained when the combination of force line vector and couple is arbitrary, and the method can be used to judge the linear correlation of arbitrary force line vector and couple combination. This method is used to analyze the internal singularity of several kinds of parallel mechanisms with less degrees of freedom. This method provides a theoretical basis for the study of singularity theory of parallel manipulators and is also the theoretical basis for mechanism optimization. Based on spiral theory, a new method for the construction of redundant parallel mechanism is presented. This paper synthesizes the type of redundant driving branch chain of redundant drive parallel mechanism, and analyzes theoretically the position and number of branch chain. This paper synthesizes the new models of 3RN2T1R1R2R1Tn2R2T and 3T2R six kinds of redundant drive parallel mechanism. The new model can effectively reduce the unexpected movement of the parallel mechanism during operation, for example, it can avoid singularity effectively. It can also improve the driving force, stiffness and dexterity of parallel mechanism. A class of redundant drive parallel mechanisms based on unconstrained branching chains is synthesized. All of the nine types of less degrees of freedom are included. A large number of redundant parallel driven parallel mechanisms, such as 3-UPUP / SPSU 4-SPS / RZPZUXY / 3-RPURP / SPS, are constructed through constraint combinations of different branching chains and adding different numbers of unconstrained branched chains. These mechanisms can completely avoid internal singularity. By using the method of constructing a complete Jacobian full rank matrix synthesis mechanism, a general formula for calculating the force matrix and moment matrix of the minimum singular value of dexterity and stiffness when the driving screw is input at any angle can be calculated. According to this method, the optimal combination of dexterity and stiffness can be obtained, which provides a theoretical basis for the performance optimization of redundant drive parallel mechanism. The parallel mechanism is simulated by Ansys, and the condition number of force matrix and torque matrix of redundant drive branch chain is solved by using Matlab. The dexterity relationship of parallel mechanism is found when different branch chains are added. Through theoretical and simulation research, several new redundant drive parallel mechanism models with optimal dexterity and stiffness are synthesized in this paper.
【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH112
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