基于单开链单元的并联机器人机构学理论研究
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摘要
本文基于并联机构的支路单开链及序单开链两种结构组成原理,以单开链单元描述机构的拓扑结构,对并联机构的结构学、运动学、动力学理论进行了深入、系统的研究。揭示了并联机构拓扑结构与其运动学、动力学之间的内在联系,试图并初步实现了并联机器人机构学理论的系统化,为并联机构的创新设计提供了坚实的理论基础。
首先,给出了支路单开链的约束度定义及计算公式,揭示了约束度与机构过约束性之间的定量关系。得出了完全对称的四、五自由度并联机构必为过约束机构的结论。提出了基于支路单开链单元的型综合方法。给出了3-6自由度无过约束并联机构所有可能的型综合方案。按对称性、机构耦合度、控制解耦性等拓扑结构特征对综合方案进行了分类。综合出了若干并联机构的新构型,其中包括一类含串联输入支路的并联机构。
然后,基于序单开链结构组成原理,给出了并联机构正运动学分析一种新的数值方法——序单开链法。按有序单开链单元之间的约束关系建立了与机构拓扑结构相统一的机构位置、速度、加速度分析数学模型。无需技巧性降维即可得到维数最少,且恰等于机构耦合度的运动学方程。揭示了并联机构拓扑结构与运动学之间的内在联系。分析实例结果证明了方法的系统性及有效性,并表明具有分析过程简明,且物理意义明晰等优点。
其次,基于序单开链结构组成原理,提出了并联机构逆动力学分析的序单开链法。按机构序单开链结构分解路线的逆序,应用牛顿-欧拉方程建立了动力学分析模型,该模型揭示了拓扑结构与动力学之间的内在联系。并与机构运动学分析模型相统一。该方法具有普遍的适用性,且可获得维数恰等于机构耦合度的最低维数的动力学方程。
最后,用牛顿-欧拉法首次给出了并联机构逆动力学分析的一般方法。该方法数学模型推导过程比较简单,适用于具有不同结构的简单支路单开链并联机构,其数学模型含6维线性方程组,较序单开链法得出的方程维数高。
Based on the principle of the composing of sub-chain single-opened-chain and ordered single-opened-chain, this dissertation presents a profound and systematic research on parallel mechanism. By using the single-opened-chain unit to describe the topological structure of the mechanism, the dissertation reveals the essential relationship between topological structure and kinematics and dynamics of parallel mechanisms. The research intends to achieve the systematization of parallel manipulators theory and to provide a solid theoretic foundation for parallel mechanism innovation.
Firstly, the definition and calculation formula for constraint degree of sub-chain single-opened-chain are presented to reveal the quantitative relationship between constraint degree and over-constraint of the mechanism, which indicates that a totally symmetrical mechanism with four or five degrees of freedom must be a over-constraint mechanism. And a topological structure synthesis method based on sub-chain single-opened-chain is proposed to demonstrate all possible topological structure types for a parallel mechanism with 3-6 degrees of freedom without over-constraint. These types are classified with topological characteristics such as symmetry, coupling degree, decoupling control of the mechanism. Some new topological structures of parallel mechanism are synthesized, of which includes a sub-chain with serial inputs.
Then, a new numerical method named ordered single-opened-chain method for directed kinematics of parallel mechanism is presented based on the principle of composing of ordered single-opened-chain. Mathematical models for mechanism displacement, velocity and acceleration analysis are built on the base of constraint relationships between ordered single-opened-chain units, which are coherent with the mechanism topological structure. This method needs no skill in dimension reduction to obtain kinematics equations with least dimension that equals to the coupling degrees of the mechanism. The method reveals the essential relationship between the topological structure and kinematics of a parallel mechanism. The analysis results
首先,给出了支路单开链的约束度定义及计算公式,揭示了约束度与机构过约束性之间的定量关系。得出了完全对称的四、五自由度并联机构必为过约束机构的结论。提出了基于支路单开链单元的型综合方法。给出了3-6自由度无过约束并联机构所有可能的型综合方案。按对称性、机构耦合度、控制解耦性等拓扑结构特征对综合方案进行了分类。综合出了若干并联机构的新构型,其中包括一类含串联输入支路的并联机构。
然后,基于序单开链结构组成原理,给出了并联机构正运动学分析一种新的数值方法——序单开链法。按有序单开链单元之间的约束关系建立了与机构拓扑结构相统一的机构位置、速度、加速度分析数学模型。无需技巧性降维即可得到维数最少,且恰等于机构耦合度的运动学方程。揭示了并联机构拓扑结构与运动学之间的内在联系。分析实例结果证明了方法的系统性及有效性,并表明具有分析过程简明,且物理意义明晰等优点。
其次,基于序单开链结构组成原理,提出了并联机构逆动力学分析的序单开链法。按机构序单开链结构分解路线的逆序,应用牛顿-欧拉方程建立了动力学分析模型,该模型揭示了拓扑结构与动力学之间的内在联系。并与机构运动学分析模型相统一。该方法具有普遍的适用性,且可获得维数恰等于机构耦合度的最低维数的动力学方程。
最后,用牛顿-欧拉法首次给出了并联机构逆动力学分析的一般方法。该方法数学模型推导过程比较简单,适用于具有不同结构的简单支路单开链并联机构,其数学模型含6维线性方程组,较序单开链法得出的方程维数高。
Based on the principle of the composing of sub-chain single-opened-chain and ordered single-opened-chain, this dissertation presents a profound and systematic research on parallel mechanism. By using the single-opened-chain unit to describe the topological structure of the mechanism, the dissertation reveals the essential relationship between topological structure and kinematics and dynamics of parallel mechanisms. The research intends to achieve the systematization of parallel manipulators theory and to provide a solid theoretic foundation for parallel mechanism innovation.
Firstly, the definition and calculation formula for constraint degree of sub-chain single-opened-chain are presented to reveal the quantitative relationship between constraint degree and over-constraint of the mechanism, which indicates that a totally symmetrical mechanism with four or five degrees of freedom must be a over-constraint mechanism. And a topological structure synthesis method based on sub-chain single-opened-chain is proposed to demonstrate all possible topological structure types for a parallel mechanism with 3-6 degrees of freedom without over-constraint. These types are classified with topological characteristics such as symmetry, coupling degree, decoupling control of the mechanism. Some new topological structures of parallel mechanism are synthesized, of which includes a sub-chain with serial inputs.
Then, a new numerical method named ordered single-opened-chain method for directed kinematics of parallel mechanism is presented based on the principle of composing of ordered single-opened-chain. Mathematical models for mechanism displacement, velocity and acceleration analysis are built on the base of constraint relationships between ordered single-opened-chain units, which are coherent with the mechanism topological structure. This method needs no skill in dimension reduction to obtain kinematics equations with least dimension that equals to the coupling degrees of the mechanism. The method reveals the essential relationship between the topological structure and kinematics of a parallel mechanism. The analysis results
引文
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