具有串并混联形式与变自由度特性的空间多环机构的拓扑设计方法
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摘要
空间多环机构主要包含了并联与混联的各种布局形式,而对于混联非拓展树网状结构与变自由度的设计,仍然没有具体的设计方法可利用。因此,为了实现空间多环复杂机构的系统化结构设计和变自由度运动分析,本文提出了一种全新的具有串并混联形式与变自由度特性空间多环机构的拓扑设计方法。
本研究从全新的数理逻辑学角度对空间机构进行了二进制12位数组矩阵的表示,同时运用逻辑命题推理,提出3阶逻辑的6值非经典逻辑矩阵表示空间的拓扑运动、关系及坐标选取,建立机构的组合逻辑库,并将其公理化用于拓扑结构的设计当中。由此可将运动与约束关系进行逻辑矩阵的结构运算定义,从而可对机构做数据结构的逻辑运算与推理,实现拓扑结构的逻辑设计算法。
在拓扑结构的设计中,提出支链与平台连接形式的拓扑布局矩阵,其拓扑布局的形式可利用杆组映射和分形的方法得到,并建立拓扑布局对于空间几何体的映射组合规律,包含单末端输出的闭型与多末端输出的开型拓扑布局。进而针对末端输出与支链运动关系的分析,提出了拓扑布局结构的空间多环逻辑拆分方法(SMD),并由此结果建立了支链运动位移子集的结构配置卡(CCDS),从而可解决非拓展树网状拓扑结构的设计,并系统化方法于应用当中。对于多环的运动约束结构,考虑其多环变自由度特性,可建立运动的拓扑结构库,并分析变自由度的原理,从而得到混联结构变自由度的系统设计方法。
论文研究的最后由实例说明了逻辑拓扑结构设计方法的应用,设计了各种全新的空间多环机构,其中特别设计了一种全新双轴变自由度混联操作器KHPM-Ⅰ对其进行了运动学特性的分析,并建立此样机原型用于实际运动输出的操作测试当中。
本论文提出的设计方法有助于空间多环机构的复杂拓扑结构设计,同时数理逻辑的表示与算法有利于实现拓扑结构设计的自动化。
The spatial multi-loop mechanisms can be categorized into parallel and hybrid forms. However, as far as the design of hybrid non-spanning tree netted forms and variable mobility are concerned, there are no any developed method are available. Thus, to realize the systematic design of spatial hybrid mechanisms and kinematotropic analysis of mobility, this research presents a novel topological design method of spatial mutli-loop mechanisms with serial-parallel hybrid forms and kinematotropic properties.
This research adopts12bits of binary string matrices to represent the spatial mechanisms based on mathematical logic method. Meanwhile, the three orders of six values non-classical logical matrices are developed to represent spatial topological motions, relations and determination of reference frames. The combinatorial logical sets are built and axiomatized for the design of topological structures. Thus, the motions and constraint relations can be defined in the structural operation of logical matrices, and the logical operation and reasoning can be developed in the design of topological structures.
To realize the design of topological structures, the matrices of topological arrangements are presented in the connected forms of subchains and platforms. The topological arrangements can be generated by the linkage group mapping and fractal methods. The mapping relationships between the topological arrangement and geometry are developed which include the closed type and opened type of topological arrangements with single and multiple ending output manipulators respectively. Furthermore, the logical method of Spatial Multi-loop Detachment (SMD) is presented for the topological arrangements to analyze the relationships between the ending output motions and motions of subchains. Meanwhile, the Configuration Card of Displacement subsets of Subchains (CCDS) is developed for the structural configuration of subchains according to the results of SMD. The design of topological structure with non-spanning tree netted forms can be solved to build the novel systematic method of topological structural design. As far as the kinematotropic properties of multi-loop structures are concerned, the principles of kinematotropic mechanisms and topological structural sets are developed to design the spatial multi-loop mechanisms with kinematotropic properties.
At last, various novel spatial multi-loop mechanisms are built as examples to illustrate the applications of the presented method. A novel kinematotropic hybrid parallel manipulator in dual axes KHPM-Ⅰ is built in particular, and the kinematic properties are analyzed. Meanwhile, the corresponding prototype is manufactured and applied into the testing of the practical output motions.
On the one hand, the presented method is helpful to the topological structural design of the complicate spatial multi-loop mechanisms, and on the other is that the mathematical logical representation and operations of structures are programmable, and it is somewhat to realize the automatic design of spatial multi-loop mechanisms easily.
本研究从全新的数理逻辑学角度对空间机构进行了二进制12位数组矩阵的表示,同时运用逻辑命题推理,提出3阶逻辑的6值非经典逻辑矩阵表示空间的拓扑运动、关系及坐标选取,建立机构的组合逻辑库,并将其公理化用于拓扑结构的设计当中。由此可将运动与约束关系进行逻辑矩阵的结构运算定义,从而可对机构做数据结构的逻辑运算与推理,实现拓扑结构的逻辑设计算法。
在拓扑结构的设计中,提出支链与平台连接形式的拓扑布局矩阵,其拓扑布局的形式可利用杆组映射和分形的方法得到,并建立拓扑布局对于空间几何体的映射组合规律,包含单末端输出的闭型与多末端输出的开型拓扑布局。进而针对末端输出与支链运动关系的分析,提出了拓扑布局结构的空间多环逻辑拆分方法(SMD),并由此结果建立了支链运动位移子集的结构配置卡(CCDS),从而可解决非拓展树网状拓扑结构的设计,并系统化方法于应用当中。对于多环的运动约束结构,考虑其多环变自由度特性,可建立运动的拓扑结构库,并分析变自由度的原理,从而得到混联结构变自由度的系统设计方法。
论文研究的最后由实例说明了逻辑拓扑结构设计方法的应用,设计了各种全新的空间多环机构,其中特别设计了一种全新双轴变自由度混联操作器KHPM-Ⅰ对其进行了运动学特性的分析,并建立此样机原型用于实际运动输出的操作测试当中。
本论文提出的设计方法有助于空间多环机构的复杂拓扑结构设计,同时数理逻辑的表示与算法有利于实现拓扑结构设计的自动化。
The spatial multi-loop mechanisms can be categorized into parallel and hybrid forms. However, as far as the design of hybrid non-spanning tree netted forms and variable mobility are concerned, there are no any developed method are available. Thus, to realize the systematic design of spatial hybrid mechanisms and kinematotropic analysis of mobility, this research presents a novel topological design method of spatial mutli-loop mechanisms with serial-parallel hybrid forms and kinematotropic properties.
This research adopts12bits of binary string matrices to represent the spatial mechanisms based on mathematical logic method. Meanwhile, the three orders of six values non-classical logical matrices are developed to represent spatial topological motions, relations and determination of reference frames. The combinatorial logical sets are built and axiomatized for the design of topological structures. Thus, the motions and constraint relations can be defined in the structural operation of logical matrices, and the logical operation and reasoning can be developed in the design of topological structures.
To realize the design of topological structures, the matrices of topological arrangements are presented in the connected forms of subchains and platforms. The topological arrangements can be generated by the linkage group mapping and fractal methods. The mapping relationships between the topological arrangement and geometry are developed which include the closed type and opened type of topological arrangements with single and multiple ending output manipulators respectively. Furthermore, the logical method of Spatial Multi-loop Detachment (SMD) is presented for the topological arrangements to analyze the relationships between the ending output motions and motions of subchains. Meanwhile, the Configuration Card of Displacement subsets of Subchains (CCDS) is developed for the structural configuration of subchains according to the results of SMD. The design of topological structure with non-spanning tree netted forms can be solved to build the novel systematic method of topological structural design. As far as the kinematotropic properties of multi-loop structures are concerned, the principles of kinematotropic mechanisms and topological structural sets are developed to design the spatial multi-loop mechanisms with kinematotropic properties.
At last, various novel spatial multi-loop mechanisms are built as examples to illustrate the applications of the presented method. A novel kinematotropic hybrid parallel manipulator in dual axes KHPM-Ⅰ is built in particular, and the kinematic properties are analyzed. Meanwhile, the corresponding prototype is manufactured and applied into the testing of the practical output motions.
On the one hand, the presented method is helpful to the topological structural design of the complicate spatial multi-loop mechanisms, and on the other is that the mathematical logical representation and operations of structures are programmable, and it is somewhat to realize the automatic design of spatial multi-loop mechanisms easily.
引文
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