绳牵引并联机构若干关键理论问题及其在风洞支撑系统中的应用研究
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摘要
课题“绳牵引并联机构若干关键理论问题及其在风洞支撑系统中的应用研究”是在总结绳牵引并联机构研究概况的基础上,在不考虑现有技术限制的条件下,对从该类型机构自身概念所引出的一些全新理论问题进行研究,并剖析风洞绳牵引并联支撑系统的关键技术及研究其设计方法,其目的在于在绳牵引并联机构的结构、工作空间、优化拉力分布、静刚度和运动学等方面做一些开拓性和奠基性的基础理论研究工作,介绍风洞绳牵引并联支撑系统的设计与控制等新技术。
首先,建立并分析作为具有完整约束的绳牵引串/并联机构系统的约束方程,并用其偏微分形式分析了机构在驱动器空间、约束空间、末端执行器空间的运动关系。基于此,将末端执行器的自由度数定义为从绳牵引并联机构基于动态静力分析的力学平衡方程推导出的结构矩阵J~T的所有列矢量正张成的空间R~n的维数n,阐明机构在所有位姿处可能存在的末端执行器自由度的组合。另一方面,本文从绳牵引并联机构与多指手抓取之间潜在的连接关系出发,研究绳牵引并联机构与等价的无摩擦点接触抓取模型在结构上的相关性与力传递的相似性,并利用这种相似性探讨力封闭抓取规划与绳牵引并联机构的末端执行器的自由度数的关系。
接着,用动平台在某一位姿处是否可控来界定可控工作空间的含义,根据动平台力螺旋的性质将可控工作空间分成力封闭工作空间、考虑重力的静力学平衡工作空间和动力学平衡工作空间3类,并系统研究每一类型的分析方法,从而得到确定力封闭工作空间及其边界的一些重要结论及定理。另外,研究CRPMs基于力传递性能系数的可控工作空间的分析方法。从绳牵引并联机构奇异类型为过运动性这一事实出发研究发现,奇异性是由于动平台的力螺旋失效(即动平台的力螺旋集合的维数降秩)造成的,
Based on a review of the state-of-the-art theory and technology about the wire-driven parallel kinematic manipulators (PKMs), disregarding further restrictions due to currently available technology, the exposition of the research subject "Research on Key Theoretical Issues of Wire-Driven Parallel Kinematic Manipulators and the Application to Wind Tunnel Support Systems" focuses on new perspectives of wire-driven PKMs inherent in the concept themselves, key techniques and design methodology of wire-driven parallel support systems in wind tunnels, so that it could give an overall theoretical research of what can be achieved at most in the aspects of structure, workspace, optimal tension distribution, static stiffness, kinematics, design methods and motion control schemes of wire-driven parallel support systems in wind tunnels.At first, the constraint equation of wire-driven manipulators with holonomic constraints is built and analyzed. And its partial differential equation is set up to analyze the mobility and controllability of the manipulators. The number of end-effector's degrees of freedoms(DOFs) is defined as the dimension n of linearity space R~n which is positively spanned by all of the column vectors of the structure matrix J~T, obtained from the force equilibrium equation transforming forces in actuator space into wrenches in end-effector space. The number of the combinations of end-effector's DOFs, which a wire-driven PKM can have evenly in all postures has been proven. On the other hand, on the connections between wire-driven PKMs and multi-finger grasp, the architecture correspondence and similarity of force transmission between a wire-driven PKM and its corresponding grasp with frictionless point contacts has been exploited, and the close relationship between force-closure grasp planning and the number of the combinations of end-effector's DOFs has been discussed.Then, the definition of Controllable Workspace(CWS) is given according to the fact whether a posture of the moving platform is controllable or not. CWS is classified
into Force-Closure Workspace(FCW, for short), Static Equilibrium Workspace under Gravity(SEWG for short) and Dynamic Equilibrium Workspace(DEW for short) according to the property of the wrenches exerting on the moving platform. The methods of determining the workspace volume of every kind of CWS are given, especially, some important conclusions and theorems are obtained to determine the workspace volume and its boundary of FCW. Also, force transmission index based workspace analysis of CRPMs is conducted. It is proposed that the singularity with over-mobility of wire-driven PKMs is due to the wrench deficiency of the moving platform because the dimension of the set of wrench decreases. And the influence of the gravity of the moving platform on the wrench deficiency is discussed. Using Planar Antipodal Grasp Theorem, a way to build up singularity-free CRPMs in 1R2T class with 2-2 type and 2R3T class with 3-3 type is proposed. Considering the fact that a wire-driven PKM with the decoupling of every rotational DOFs and the translational DOFs completely controlled is singularity-free, a way to build up singularity-free CRPMs in 1R2T class with 1-2-1 type, RRPMs in 2R3T class with 2-3-2 type is proposed. Using the theorem of 3-dimension force-closure grasp proposed by Canny, a method to build up singularity-free RRPMs in 3R3T class with 3-3-3 type is presented.Furthermore, considering the tension limits, the optimal tension distribution problem can be transformed into a nonlinear optimization problem on a convex polyhedron, which the optimal solution can be the linear interpolation of the lowest solution and the highest solution, in order to deal with the disadvantages of the optimal solutions solved by the traditional methods. To solve the discontinuity of the optimal solutions in some cases such as in a singular posture, the optimal solution can be approximately expressed by its p-norm. The programming in the environment of Matlab is developed to solve the optimal solutions.Moreover, a rat
首先,建立并分析作为具有完整约束的绳牵引串/并联机构系统的约束方程,并用其偏微分形式分析了机构在驱动器空间、约束空间、末端执行器空间的运动关系。基于此,将末端执行器的自由度数定义为从绳牵引并联机构基于动态静力分析的力学平衡方程推导出的结构矩阵J~T的所有列矢量正张成的空间R~n的维数n,阐明机构在所有位姿处可能存在的末端执行器自由度的组合。另一方面,本文从绳牵引并联机构与多指手抓取之间潜在的连接关系出发,研究绳牵引并联机构与等价的无摩擦点接触抓取模型在结构上的相关性与力传递的相似性,并利用这种相似性探讨力封闭抓取规划与绳牵引并联机构的末端执行器的自由度数的关系。
接着,用动平台在某一位姿处是否可控来界定可控工作空间的含义,根据动平台力螺旋的性质将可控工作空间分成力封闭工作空间、考虑重力的静力学平衡工作空间和动力学平衡工作空间3类,并系统研究每一类型的分析方法,从而得到确定力封闭工作空间及其边界的一些重要结论及定理。另外,研究CRPMs基于力传递性能系数的可控工作空间的分析方法。从绳牵引并联机构奇异类型为过运动性这一事实出发研究发现,奇异性是由于动平台的力螺旋失效(即动平台的力螺旋集合的维数降秩)造成的,
Based on a review of the state-of-the-art theory and technology about the wire-driven parallel kinematic manipulators (PKMs), disregarding further restrictions due to currently available technology, the exposition of the research subject "Research on Key Theoretical Issues of Wire-Driven Parallel Kinematic Manipulators and the Application to Wind Tunnel Support Systems" focuses on new perspectives of wire-driven PKMs inherent in the concept themselves, key techniques and design methodology of wire-driven parallel support systems in wind tunnels, so that it could give an overall theoretical research of what can be achieved at most in the aspects of structure, workspace, optimal tension distribution, static stiffness, kinematics, design methods and motion control schemes of wire-driven parallel support systems in wind tunnels.At first, the constraint equation of wire-driven manipulators with holonomic constraints is built and analyzed. And its partial differential equation is set up to analyze the mobility and controllability of the manipulators. The number of end-effector's degrees of freedoms(DOFs) is defined as the dimension n of linearity space R~n which is positively spanned by all of the column vectors of the structure matrix J~T, obtained from the force equilibrium equation transforming forces in actuator space into wrenches in end-effector space. The number of the combinations of end-effector's DOFs, which a wire-driven PKM can have evenly in all postures has been proven. On the other hand, on the connections between wire-driven PKMs and multi-finger grasp, the architecture correspondence and similarity of force transmission between a wire-driven PKM and its corresponding grasp with frictionless point contacts has been exploited, and the close relationship between force-closure grasp planning and the number of the combinations of end-effector's DOFs has been discussed.Then, the definition of Controllable Workspace(CWS) is given according to the fact whether a posture of the moving platform is controllable or not. CWS is classified
into Force-Closure Workspace(FCW, for short), Static Equilibrium Workspace under Gravity(SEWG for short) and Dynamic Equilibrium Workspace(DEW for short) according to the property of the wrenches exerting on the moving platform. The methods of determining the workspace volume of every kind of CWS are given, especially, some important conclusions and theorems are obtained to determine the workspace volume and its boundary of FCW. Also, force transmission index based workspace analysis of CRPMs is conducted. It is proposed that the singularity with over-mobility of wire-driven PKMs is due to the wrench deficiency of the moving platform because the dimension of the set of wrench decreases. And the influence of the gravity of the moving platform on the wrench deficiency is discussed. Using Planar Antipodal Grasp Theorem, a way to build up singularity-free CRPMs in 1R2T class with 2-2 type and 2R3T class with 3-3 type is proposed. Considering the fact that a wire-driven PKM with the decoupling of every rotational DOFs and the translational DOFs completely controlled is singularity-free, a way to build up singularity-free CRPMs in 1R2T class with 1-2-1 type, RRPMs in 2R3T class with 2-3-2 type is proposed. Using the theorem of 3-dimension force-closure grasp proposed by Canny, a method to build up singularity-free RRPMs in 3R3T class with 3-3-3 type is presented.Furthermore, considering the tension limits, the optimal tension distribution problem can be transformed into a nonlinear optimization problem on a convex polyhedron, which the optimal solution can be the linear interpolation of the lowest solution and the highest solution, in order to deal with the disadvantages of the optimal solutions solved by the traditional methods. To solve the discontinuity of the optimal solutions in some cases such as in a singular posture, the optimal solution can be approximately expressed by its p-norm. The programming in the environment of Matlab is developed to solve the optimal solutions.Moreover, a rat
引文
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