一类球坐标型混联机器人静刚度建模理论与方法研究
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摘要
本文紧密结合新型可重构5自由度混联机器人TriVariant-B的样机开发,系统研究了一类少自由度球坐标型并联构型装备的静刚度解析和半解析建模、有限元分析、性能指标评价及灵敏度分析等相关理论与方法。论文取得了如下创造性成果:
以Tricept和TriVariant系列5自由度混联机器人为例,利用摄动法提出一种构造可描述含恰约束主动/从动支链球坐标型并联机构全变形雅可比矩阵的建模方法,利用该矩阵可有效地分离出上述并联机构操作空间变形与关节空间变形在驱动和约束空间中的映射关系,进而为后续整机静刚度分析奠定了坚实的运动学基础。
利用全变形雅可比矩阵和变形叠加原理,系统研究了少自由度球坐标型并联机构静刚度解析建模方法。该方法利用静态凝聚技术和变形协调条件,有效地解决了恰约束支链弯曲刚度的精准建模问题,修正了前人所提出的结论。研究结果表明,利用全变形雅可比矩阵建立的刚度模型具有列式简洁,物理意义明确,通用性强等优点,并充分体现了速度与刚度模型在数学层面上的内在联系。
以TriVariant-B机器人为例,提出一种计及复杂机架柔性的并联构型装备整机静刚度半解析建模方法。该方法基于结构力学中的子结构综合思想,首先将整机系统分解为机构和机架两个子系统,然后建立各子系统的刚度矩阵,最后利用线性叠加原理构造整机系统的刚度模型。在机架子系统刚度建模中,提出一种采用商用有限元软件及静态凝聚技术构造机架子系统界面刚度模型的有效方法,大幅度提高了计算效率。利用这种建模方法,可在概念设计阶段实现整个工作空间中的整机刚度快速预估,进而为指导系统的详细机械设计提供了有力的工具。
借助商用有限元软件ANSYS的参数化设计语言,系统研究了并联构型装备中各种常用铰链的有限元精确建模技术。提出一种可在不同位形下快速建立整机有限元模型的建模策略与实施方法,有效地提高了计算效率。在此基础上,构造出计及复杂机架柔性的TriVariant-B混联机器人整机刚度有限元模型,并对机架及连架虎克铰等关键零部件的优化设计做了有益的探讨。
以TriVariant-B机器人为例,利用整机系统柔度矩阵的最大奇异值,提出一种可评价并联构型装备线刚度和角刚度性能的评价指标。利用该指标并借助灵敏度分析方法,系统考察了该机器人关键部件弹性对整机刚度的贡献,并揭示出机构子系统无约束主动支链中的铰链拉压刚度和恰约束支链本体扭转刚度是影响整机刚度的薄弱环节。另外,利用该指标并采用多目标遗传算法研究了该机器人机构尺度参数对整机刚度的影响,并据此提出了改进方案。
开展了TriVariant-B机器人物理样机的静刚度实验研究工作。业已证明,由本文提出的半解析模型和有限元分析所得计算结果与实验结果具有良好的一致性,进而验证了它们的有效性。
本文研究成果已成功地应用于新型火焰切割加工装备TriVariant-B机器人的结构设计和开发,同时对其它类似并联构型装备的相关研究提供了有益的借鉴。
This dissertation presents a theoretical package for stiffness modeling, analysis, performance evaluation and optimization of a class of spherical coordinate parallel kinematic machines (PKM) using analytical and semi-analytical approaches. The outcome has been employed for the development of a 5-DOF hybrid robot known as the TriVariant. The following contributions have been made.
By taking the Tricept and the TriVariant robots as examples, the overall deflection Jacobian of the parallel mechanisms having a properly constrained active/passive limb is formulated. In the overall deflection Jacobian, the topological characteristics in the actuations and constraints can be explicitly separated.
Using the overall deflection Jacobian and linear superposition, two analytical approaches for the stiffness modeling of the PKM having a properly constrained active/passive limb are proposed by simultaneously taking into account the component compliances in both actuations and constraints. In the modeling process, the precise bending compliance of the properly constrained limb is formulated with the static condensation and loop-closure compatibility conditions. The use of the overall deflection Jacobian allows the stiffness model to be formulated in a more effective and compact manner, and the underlying relationship between the velocity and the stiffness mapping functions to be revealed.
By taking the TriVariant-B robot as an example, a semi-analytical approach is developed for the stiffness modeling of the PKM having complex machine frame geometry. In this approach, the PKM is decomposed into two subsystems associated with the parallel mechanism and the machine frame by assuming one of them is rigid. The stiffness model of entire system is then achieved by linear superposition using the interface compatibility conditions. This approach enables the stiffness distributions throughout the workspace to be time-effectively examined.
By means of ANSYS parametric design language (APDL), the finite element analysis model of the TriVariant-B is formulated by taking into account the compliance of machine frame. Particular attentions are placed upon: (1) precise FEA formulation of different type of joints, and (2) the development of an effective modeling strategy for the rapid rigidity estimation associated with different configurations in order to avoid FEA model re-meshing.
On the basis of singular value decomposition, two global indices are proposed for evaluating the translational and rotational rigidities of the TriVariant-B robot. Utilizing these indices, the contributions of the component compliances in the parallel mechanism and the machine frame to the translational and rotational compliances of the system are investigated by sensitivity analysis. It has been found that the joints compliance has significant impact on the translational stiffness of system while the torsional compliance of the properly constrainted passive limb has significant impact on the rotational stiffness. These findings provide engineers with informative guidelines for the detailed mechanical design. In the end, the global rigidity performance indices of the TriVariant-B are also optimized using multiple-object genetic algorithm.
The experimental investigation is carried out on a TriVariant-B prototype machine. It shows that the experiment results have a good match with those obtained by the FEA and theoretical analysis.
The outcome of this thesis has been employed to the design of a TriVariant-B prototype machine for frame cutting and would be useful for the development of other similar parallel kinematic machines.
以Tricept和TriVariant系列5自由度混联机器人为例,利用摄动法提出一种构造可描述含恰约束主动/从动支链球坐标型并联机构全变形雅可比矩阵的建模方法,利用该矩阵可有效地分离出上述并联机构操作空间变形与关节空间变形在驱动和约束空间中的映射关系,进而为后续整机静刚度分析奠定了坚实的运动学基础。
利用全变形雅可比矩阵和变形叠加原理,系统研究了少自由度球坐标型并联机构静刚度解析建模方法。该方法利用静态凝聚技术和变形协调条件,有效地解决了恰约束支链弯曲刚度的精准建模问题,修正了前人所提出的结论。研究结果表明,利用全变形雅可比矩阵建立的刚度模型具有列式简洁,物理意义明确,通用性强等优点,并充分体现了速度与刚度模型在数学层面上的内在联系。
以TriVariant-B机器人为例,提出一种计及复杂机架柔性的并联构型装备整机静刚度半解析建模方法。该方法基于结构力学中的子结构综合思想,首先将整机系统分解为机构和机架两个子系统,然后建立各子系统的刚度矩阵,最后利用线性叠加原理构造整机系统的刚度模型。在机架子系统刚度建模中,提出一种采用商用有限元软件及静态凝聚技术构造机架子系统界面刚度模型的有效方法,大幅度提高了计算效率。利用这种建模方法,可在概念设计阶段实现整个工作空间中的整机刚度快速预估,进而为指导系统的详细机械设计提供了有力的工具。
借助商用有限元软件ANSYS的参数化设计语言,系统研究了并联构型装备中各种常用铰链的有限元精确建模技术。提出一种可在不同位形下快速建立整机有限元模型的建模策略与实施方法,有效地提高了计算效率。在此基础上,构造出计及复杂机架柔性的TriVariant-B混联机器人整机刚度有限元模型,并对机架及连架虎克铰等关键零部件的优化设计做了有益的探讨。
以TriVariant-B机器人为例,利用整机系统柔度矩阵的最大奇异值,提出一种可评价并联构型装备线刚度和角刚度性能的评价指标。利用该指标并借助灵敏度分析方法,系统考察了该机器人关键部件弹性对整机刚度的贡献,并揭示出机构子系统无约束主动支链中的铰链拉压刚度和恰约束支链本体扭转刚度是影响整机刚度的薄弱环节。另外,利用该指标并采用多目标遗传算法研究了该机器人机构尺度参数对整机刚度的影响,并据此提出了改进方案。
开展了TriVariant-B机器人物理样机的静刚度实验研究工作。业已证明,由本文提出的半解析模型和有限元分析所得计算结果与实验结果具有良好的一致性,进而验证了它们的有效性。
本文研究成果已成功地应用于新型火焰切割加工装备TriVariant-B机器人的结构设计和开发,同时对其它类似并联构型装备的相关研究提供了有益的借鉴。
This dissertation presents a theoretical package for stiffness modeling, analysis, performance evaluation and optimization of a class of spherical coordinate parallel kinematic machines (PKM) using analytical and semi-analytical approaches. The outcome has been employed for the development of a 5-DOF hybrid robot known as the TriVariant. The following contributions have been made.
By taking the Tricept and the TriVariant robots as examples, the overall deflection Jacobian of the parallel mechanisms having a properly constrained active/passive limb is formulated. In the overall deflection Jacobian, the topological characteristics in the actuations and constraints can be explicitly separated.
Using the overall deflection Jacobian and linear superposition, two analytical approaches for the stiffness modeling of the PKM having a properly constrained active/passive limb are proposed by simultaneously taking into account the component compliances in both actuations and constraints. In the modeling process, the precise bending compliance of the properly constrained limb is formulated with the static condensation and loop-closure compatibility conditions. The use of the overall deflection Jacobian allows the stiffness model to be formulated in a more effective and compact manner, and the underlying relationship between the velocity and the stiffness mapping functions to be revealed.
By taking the TriVariant-B robot as an example, a semi-analytical approach is developed for the stiffness modeling of the PKM having complex machine frame geometry. In this approach, the PKM is decomposed into two subsystems associated with the parallel mechanism and the machine frame by assuming one of them is rigid. The stiffness model of entire system is then achieved by linear superposition using the interface compatibility conditions. This approach enables the stiffness distributions throughout the workspace to be time-effectively examined.
By means of ANSYS parametric design language (APDL), the finite element analysis model of the TriVariant-B is formulated by taking into account the compliance of machine frame. Particular attentions are placed upon: (1) precise FEA formulation of different type of joints, and (2) the development of an effective modeling strategy for the rapid rigidity estimation associated with different configurations in order to avoid FEA model re-meshing.
On the basis of singular value decomposition, two global indices are proposed for evaluating the translational and rotational rigidities of the TriVariant-B robot. Utilizing these indices, the contributions of the component compliances in the parallel mechanism and the machine frame to the translational and rotational compliances of the system are investigated by sensitivity analysis. It has been found that the joints compliance has significant impact on the translational stiffness of system while the torsional compliance of the properly constrainted passive limb has significant impact on the rotational stiffness. These findings provide engineers with informative guidelines for the detailed mechanical design. In the end, the global rigidity performance indices of the TriVariant-B are also optimized using multiple-object genetic algorithm.
The experimental investigation is carried out on a TriVariant-B prototype machine. It shows that the experiment results have a good match with those obtained by the FEA and theoretical analysis.
The outcome of this thesis has been employed to the design of a TriVariant-B prototype machine for frame cutting and would be useful for the development of other similar parallel kinematic machines.
引文
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