基于伪刚体模型和雅克比矩阵的柔顺机构拓扑优化方法

发布时间：2018-03-10 08:52

本文选题：柔顺机构　切入点：柔顺并联机构　出处：《华南理工大学》2016年博士论文　论文类型：学位论文

【摘要】：系统化的概念设计是现代机构学的发展趋势之一,未来的机构概念设计将不再停留于机构功能的实现,而是同时实现机构的功能和较高的性能,因此,发展相关的概念设计理论和方法具有深远意义。本文朝着此发展方向,深入研究了柔顺机构的概念设计理论和方法,针对简单铰链型柔顺机构和多自由度柔顺并联机构,提出了两种考虑性能的概念设计方法。主要开展了如下研究:(1)重点讨论了柔顺机构现有的两大主流概念设计方法。刚体替代法不能创造拓扑和优选拓扑,拓扑优化方法虽能针对具体问题优选拓扑,但其设计对象局限于简单的分布式柔顺机构,因此,本文提出将拓扑优化拓展到刚体替代法的设计范围(上述两类柔顺机构)。(2)针对简单铰链型柔顺机构,提出了基于伪刚体模型的拓扑优化方法。该方法以伪刚体机构代替柔顺机构的拓扑,将拓扑优化问题描述为伪刚体机构的拓扑优化,然后将最优的伪刚体机构转化为柔顺机构。该方法通过采用全新的拓扑表达方案和拓扑分析方法,将拓扑优化拓展到了铰链型柔顺机构,为简单铰链型柔顺机构提供了一种考虑拓扑性能的概念设计方法。(3)针对多自由度柔顺并联机构,提出了基于雅克比矩阵的拓扑优化方法。该方法的核心在于将雅克比矩阵引进了拓扑优化领域,可以统一而简洁的形式表达机构动平台上所有自由度的运动,摆脱了传统拓扑优化方法通过预设多个具体输出位移实现多输出的方式,实现了多自由度柔顺机构拓扑优化。雅克比矩阵同时包含了机构自由度和运动正解的信息,对其优化既能综合出期望的自由度数以实现机构的功能,又能提高运动传递能力以实现较优的机构性能。(4)为实现多自由度柔顺并联机构拓扑优化,采用了多个子设计域并联在动平台和机架之间,用于综合柔顺并联机构的运动支链。通过建立运动支链子设计域和机构整体运动特性之间的映射关系,将多自由度柔顺并联机构拓扑优化问题描述为:使用一定材料在多个子设计域内综合出运动支链拓扑,使得柔顺并联机构具有期望的自由度数,同时拥有较优的运动性能。采用多设计域具有利于降低计算成本和添加边界条件等优势。(5)通过基于雅克比矩阵的拓扑优化方法,实现了平面两自由度和三自由度柔顺并联机构拓扑优化设计,并在空间柔顺并联机构拓扑优化上进行了探索性的尝试,优化结果和样机实验结果分别验证了所提方法的有效性和所设计机构的运动能力。所设计的柔顺并联机构属于分布式柔顺机构,为柔顺并联机构补充了结构类型的拓扑。本文将拓扑优化思想拓展到了简单铰链型柔顺机构和柔顺并联机构的概念设计中,为这两类机构提供了考虑性能的概念设计方法,丰富了拓扑优化的理论和方法,并拓展了其应用范围。
[Abstract]:Systematic conceptual design is one of the development trends of modern mechanism. In the future, the conceptual design of mechanism will not stop at the realization of mechanism function, but realize the function and higher performance of mechanism at the same time. The theory and method of conceptual design related to development are of profound significance. In this paper, the conceptual design theory and method of compliant mechanism are studied in depth, aiming at simple hinged compliant mechanism and multi-degree-of-freedom compliant parallel mechanism. In this paper, two conceptual design methods considering performance are put forward. The main research is as follows: 1) the two main conceptual design methods of compliant mechanism are discussed. Rigid body substitution method can not create topology and select topology. Although topology optimization method can select topology according to specific problems, its design object is limited to simple distributed compliant mechanism, so, In this paper, we propose to extend topology optimization to the design scope of rigid body substitution method (two types of compliance mechanisms mentioned above) for simple hinged compliant mechanisms. A topology optimization method based on pseudo-rigid-body model is proposed, in which the pseudo-rigid-body mechanism is used instead of the compliant mechanism topology, and the topology optimization problem is described as the topological optimization of the pseudo-rigid mechanism. Then the optimal pseudo rigid body mechanism is transformed into a compliant mechanism. By adopting a new topology representation scheme and topological analysis method, the topology optimization is extended to a hinged compliant mechanism. This paper provides a conceptual design method for simple hinged compliant mechanism considering topological performance. A topology optimization method based on Jacobian matrix is proposed. The core of this method is to introduce Jacobian matrix into the field of topology optimization, which can express the motion of all degrees of freedom on the mechanism platform in a unified and concise form. This paper gets rid of the traditional topology optimization method and realizes the topology optimization of multi-degree-of-freedom compliant mechanism by presetting several specific output displacements. The Jacobian matrix includes the information of both the degree of freedom and the forward solution of the mechanism. The optimization can not only synthesize the desired number of degrees of freedom to realize the function of the mechanism, but also improve the ability of motion transfer to achieve the better performance of the mechanism. Several sub-design domains are used in parallel between the moving platform and the frame to synthesize the kinematic branching chain of the compliant parallel mechanism. The mapping relationship between the design domain of the kinematic branch chain and the whole kinematic characteristic of the mechanism is established. The topology optimization problem of multi-degree-of-freedom compliant parallel mechanism is described as: using certain materials to synthesize the kinematic branch topology in several sub-design domains, so that the compliant parallel mechanism has the desired number of degrees of freedom. At the same time, it has better kinematic performance. Using multi-design domain has the advantages of reducing computation cost and adding boundary conditions, etc.) the topology optimization method based on Jacobian matrix is proposed. The topology optimization design of planar two-degree-of-freedom and three-degree-of-freedom compliant parallel mechanism is realized, and an exploratory attempt is made on the topology optimization of spatial compliant parallel mechanism. The results of optimization and prototype experiments verify the effectiveness of the proposed method and the kinematic capability of the designed mechanism. The designed compliant parallel mechanism belongs to the distributed compliant mechanism. In this paper, the idea of topology optimization is extended to the conceptual design of simple hinge compliant mechanism and compliant parallel mechanism. It enriches the theory and method of topology optimization and extends its application scope.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH112

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