球面2-DOF并联机构的理论分析与实验研究
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摘要
球面2-DOF并联机构具有沿球面移动的两个自由度，可以应用于球面上点的定位设备，具有重要的应用前景。球面5R并联机构是其中结构最简单的一种，但研究表明，其工作空间内存在较多的奇异，承载能力和刚度也有限。为此本课题组提出在球面5R并联机构的基础上增加一个相同的运动支链，得到球面2-DOF冗余驱动并联机构，以改善上述性能。本课题以此球面非冗余与冗余并联机构为研究对象，对机构的静力学、静刚度、轨迹规划、误差、标定、样机研制、控制系统开发与实验研究等几个方面进行了系统深入的研究，主要研究内容如下：
本文基于D-H参数，建立了包含球面2-DOF并联机构所有结构参数的约束方程，求解了机构的实际位置解，建立了机构的运动学模型。
采用传统的拆杆法建立了球面2-DOF并联机构静力学平衡方程，运用小变形叠加原理建立了机构的变形协调补充方程，对于冗余驱动机构，再补充驱动力矩优化方程，求解了球面2-DOF并联机构的静力学全解。在此基础上，建立了机构输出轴角位移和球心点线位移与外载荷之间的关系，得到了球面2-DOF并联机构的静刚度矩阵。并通过数值算例，对比分析了非冗余与冗余机构的静刚度。
利用加速度为连续分段函数和组合正弦函数两种轨迹规划方法，在笛卡尔空间对球面2-DOF并联机构进行了运动学轨迹规划。并借助拉格朗日逆向动力学模型，采用力优化方法建立了冗余驱动机构驱动关节力矩数学模型。
基于环路增量法，建立了球面2-DOF并联机构位置和姿态误差模型，分析了机构位置和姿态误差与各原始误差源之间的关系，并进行了灵敏度分析，同时研究了机构平稳运行的条件，提出了抑制末端位姿误差的加工装配工艺设计方法，为样机的研制、标定奠定了基础。在误差分析的基础上，建立了球面2-DOF并联机构位置和姿态运动学标定简化模型，解决了标定模型参数辨识问题；综合运用三坐标测量机和三维绘图软件，测量了末端执行器的实际位姿；通过标定实验，验证标定方法的有效性。
设计加工了球面2-DOF并联机构样机，开发了其控制系统，采用“PC机+PMAC运动控制卡”的主从分布式结构体系。针对冗余驱动机构，提出了冗余支链采用位置判断与动力学差分预测控制相结合的力矩控制和其余支链采用位置控制的力/位置混合初步控制策略，实现了样机的协调运动。最后进行了非冗余与冗余机构样机的轨迹跟踪实验研究。
Spherical2-DOF parallel manipulator has two degrees of freedom moving alongspherical surface, which can be applied to the locating equipment of point on thespherical surface, and it has an important application prospect. Spherical5R parallelmanipulator possesses the simplest structure, but researches show that there are lots ofsingular curve in its workspace, and its bearing capacity and stiffness are also limited. Soour thesis group proposes spherical2-DOF parallel manipulator with redundant actuationwhich is obtained by increasing an identical kinematic chain on the basis of spherical5Rparallel manipulator to overcome the above problems. This paper studies the statics, staticstiffness, trajectory planning, error, calibration, prototype manufacture, development ofcontrol system and experimental researches of non-redundant and redundant spherical2-DOF parallel manipulator in depth, and the main work is as follows:
Constraint equations including all structural parameters of spherical2-DOF parallelmanipulators are established on the basis of D-H parameter of the manipulators, theactual position solution of the manipulators are obtained, and the kinematics models ofthe manipulators are also established.
The static equilibrium equations of spherical2-DOF parallel manipulators areestablished via the traditional dismantle-bar method, the deformation equations ofcompatibility are established by utilizing the micro-deformation and superpositionprinciple, the static full-solutions of spherical2-DOF parallel manipulators are obtainedby adding input torque optimization equation to redundant actuation manipulators. Basedon the result of static analysis, the relationship between the outer loads and the angulardisplacement of output axis and linear displacement of spherical center point isestablished, that is to say, the static stiffness matrices of spherical2-DOF parallelmanipulators are obtained. Through numerical example, the comparative analysis ofstatic stiffness of non-redundant and redundant parallel manipulator is carried on.
Kinematics track of spherical2-DOF parallel manipulators is planned by two kindsof trajectory planning methods that acceleration are continuous segmental function and combined sine function in Cartesian space. With the help of Lagrange inverse dynamicsmodel, the joint torque model of redundant actuation manipulator is established throughforce optimization method.
The position and posture error models of spherical2–DOF parallel manipulators areestablished based on the loop increment method, the relationships between the positionand posture error and each original error sources are analyzed, and the sensitivity is alsoanalyzed. At the same time, the conditions that the manipulator can move smoothly arestudied, the processing and assembly process design method of restraining pose error isproposed, which lay the foundation for processing and calibration of the prototype. Onthe basis of error analysis, the simplified model of position and posture kinematicscalibration is established, which simplifies the calculation of parameter identification anderror compensation; and the end-effectors’ actual position of the manipulator is measuredby using three coordinate measuring machine and3d drawing software; at last thevalidity of the method of calibration is verified through the calibration experiment.
The prototype of spherical2-DOF parallel manipulators are designed and processed,and its control system adopting master-slave distributed structure system based on “PC+PMAC motion control card” is developed. For spherical2-DOF parallel manipulator withredundant actuation, the hybrid control of force/position that redundant chain usingtorque control in combination with position judgment and kinetic differential predictivecontrol and other chains using position control is proposed, and the coordinated motionof prototype is realized. Finally, the trajectory tracking experiments of non-redundant andredundant spherical parallel manipulators are carried on.
本文基于D-H参数，建立了包含球面2-DOF并联机构所有结构参数的约束方程，求解了机构的实际位置解，建立了机构的运动学模型。
采用传统的拆杆法建立了球面2-DOF并联机构静力学平衡方程，运用小变形叠加原理建立了机构的变形协调补充方程，对于冗余驱动机构，再补充驱动力矩优化方程，求解了球面2-DOF并联机构的静力学全解。在此基础上，建立了机构输出轴角位移和球心点线位移与外载荷之间的关系，得到了球面2-DOF并联机构的静刚度矩阵。并通过数值算例，对比分析了非冗余与冗余机构的静刚度。
利用加速度为连续分段函数和组合正弦函数两种轨迹规划方法，在笛卡尔空间对球面2-DOF并联机构进行了运动学轨迹规划。并借助拉格朗日逆向动力学模型，采用力优化方法建立了冗余驱动机构驱动关节力矩数学模型。
基于环路增量法，建立了球面2-DOF并联机构位置和姿态误差模型，分析了机构位置和姿态误差与各原始误差源之间的关系，并进行了灵敏度分析，同时研究了机构平稳运行的条件，提出了抑制末端位姿误差的加工装配工艺设计方法，为样机的研制、标定奠定了基础。在误差分析的基础上，建立了球面2-DOF并联机构位置和姿态运动学标定简化模型，解决了标定模型参数辨识问题；综合运用三坐标测量机和三维绘图软件，测量了末端执行器的实际位姿；通过标定实验，验证标定方法的有效性。
设计加工了球面2-DOF并联机构样机，开发了其控制系统，采用“PC机+PMAC运动控制卡”的主从分布式结构体系。针对冗余驱动机构，提出了冗余支链采用位置判断与动力学差分预测控制相结合的力矩控制和其余支链采用位置控制的力/位置混合初步控制策略，实现了样机的协调运动。最后进行了非冗余与冗余机构样机的轨迹跟踪实验研究。
Spherical2-DOF parallel manipulator has two degrees of freedom moving alongspherical surface, which can be applied to the locating equipment of point on thespherical surface, and it has an important application prospect. Spherical5R parallelmanipulator possesses the simplest structure, but researches show that there are lots ofsingular curve in its workspace, and its bearing capacity and stiffness are also limited. Soour thesis group proposes spherical2-DOF parallel manipulator with redundant actuationwhich is obtained by increasing an identical kinematic chain on the basis of spherical5Rparallel manipulator to overcome the above problems. This paper studies the statics, staticstiffness, trajectory planning, error, calibration, prototype manufacture, development ofcontrol system and experimental researches of non-redundant and redundant spherical2-DOF parallel manipulator in depth, and the main work is as follows:
Constraint equations including all structural parameters of spherical2-DOF parallelmanipulators are established on the basis of D-H parameter of the manipulators, theactual position solution of the manipulators are obtained, and the kinematics models ofthe manipulators are also established.
The static equilibrium equations of spherical2-DOF parallel manipulators areestablished via the traditional dismantle-bar method, the deformation equations ofcompatibility are established by utilizing the micro-deformation and superpositionprinciple, the static full-solutions of spherical2-DOF parallel manipulators are obtainedby adding input torque optimization equation to redundant actuation manipulators. Basedon the result of static analysis, the relationship between the outer loads and the angulardisplacement of output axis and linear displacement of spherical center point isestablished, that is to say, the static stiffness matrices of spherical2-DOF parallelmanipulators are obtained. Through numerical example, the comparative analysis ofstatic stiffness of non-redundant and redundant parallel manipulator is carried on.
Kinematics track of spherical2-DOF parallel manipulators is planned by two kindsof trajectory planning methods that acceleration are continuous segmental function and combined sine function in Cartesian space. With the help of Lagrange inverse dynamicsmodel, the joint torque model of redundant actuation manipulator is established throughforce optimization method.
The position and posture error models of spherical2–DOF parallel manipulators areestablished based on the loop increment method, the relationships between the positionand posture error and each original error sources are analyzed, and the sensitivity is alsoanalyzed. At the same time, the conditions that the manipulator can move smoothly arestudied, the processing and assembly process design method of restraining pose error isproposed, which lay the foundation for processing and calibration of the prototype. Onthe basis of error analysis, the simplified model of position and posture kinematicscalibration is established, which simplifies the calculation of parameter identification anderror compensation; and the end-effectors’ actual position of the manipulator is measuredby using three coordinate measuring machine and3d drawing software; at last thevalidity of the method of calibration is verified through the calibration experiment.
The prototype of spherical2-DOF parallel manipulators are designed and processed,and its control system adopting master-slave distributed structure system based on “PC+PMAC motion control card” is developed. For spherical2-DOF parallel manipulator withredundant actuation, the hybrid control of force/position that redundant chain usingtorque control in combination with position judgment and kinetic differential predictivecontrol and other chains using position control is proposed, and the coordinated motionof prototype is realized. Finally, the trajectory tracking experiments of non-redundant andredundant spherical parallel manipulators are carried on.
引文
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