大洋采矿补偿平台串并联机构的运动学研究
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摘要
大洋采矿系统的船舶在海浪等的作用下产生的运动中,升沉、纵摇、横摇(本文定义为广义升沉运动)对大洋采矿系统的影响比较严重,应当进行补偿,使位于采矿平台上的扬矿管相对惯性系具有静止的位姿。
针对国外大洋采矿系统的采矿平台的不足,考虑到并联机构具有刚性高、响应快的特点,本文提出使用串并联机构作为广义升沉补偿系统的驱动平台。该串并联机构由两个3-UPU并联机构串联而成。底座固连在采矿船甲板上,静平台上安装扬矿管系统。由底座和中间平台构成的纯移动式并联机构用于补偿升沉和由于横摇和纵摇产生的扬矿管的偏移,由静平台和中间平台构成的纯转动式并联机构用于补偿由于横摇和纵摇产生的扬矿管的倾斜。
本文针对构成大洋采矿补偿平台的串并联机构的运动学特性进行分析和应用仿真,为该串并联混合补偿机构的设计和控制提供一定的理论基础。研究内容主要包括位置、速度和加速度、机构的奇异性、工作空间等运动学分析,及机构的刚度的分析计算。单位四元数在坐标变换中具有简捷高效的特点。四元数变换和矢量代数是本文中并联机构分析的理论工具。
对移动型3-UPU并联机构的正解分析表明,当给定三个连杆的长度时,它具有两组封闭形式的正解。转动型3-UPU并联机构,在一般情形下,由于非线性导致其不具有封闭形式的解析解;在特殊几何条件下,给出了其封闭形式的正解。在机构的几何位形已知的前提下,建立了两种并联机构的速度和加速度的表示形式以及相应的Jacobian矩阵。
通过判断机构Jacobian矩阵的奇异性,可以判断并联机构的奇异性。论文提出了两种并联机构奇异构形的判别准则。
论文采用规么化方法分析了两种并联机构的工作空间。分析表明,移动型并联机构上下平台外接圆的半径差、连杆最小长度以及通用副的转动角度限制对工作空间的形状和体积均有不同程度的影响,而反映机构灵活性的平均条件数只受到上下平台外接圆的半
径差的影响,并且存在一个最优值。
针对转动型并联机构,提出了一种新的直观的工作空间描述方法,方位工作空间使用动平台的可达法线矢量的集合和绕每个可达法线矢量转动的角度来描述;并建立了不相容构形的准确判别准则,进行了该机构的工作空间计算和分析。
由机构Jacobian矩阵,论文分析了两种并联机构的刚度矩阵及其特点。结果表明,移动型并联机构的最大刚度有比较集中的方向和一致的大小,转动型并联机构的刚度矩阵的主轴方向分布比较分散。
根据大洋采矿系统的补偿要求和两种并联机构的运动学分析结论,本文确定了作为广义升沉补偿平台的串并联机构的规格尺寸,并且进行了3D运动仿真。仿真结果表明,本文所提出的串并联机构作为大洋采矿补偿平台是运动可行的。
The mining ship’s motions, including heave, pitch and roll which are defined as generalized heave in this dissertation and are main motions influencing the mining system, should be compensated to keep mining platform where the hoisting system located on and load suspended, having a stable pose with respect to the inertial frame.
Considering shortcomings of existing heave compensation methods and gimballed platform of mining systems in developed countries and advantages of higher overall stiffness, low inertial, and higher operating speeds of parallel mechanisms (PM), a hybrid serial-parallel mechanism used to be compensating platform is proposed in this dissertation. A translational 3-UPU PM composed of base fixed on the deck of mining ship and middle platform is used to compensate heave and conduit center shifts due to pitch and roll, and another rotational 3-UPU PM connected with the translational PM serially is used to counteract conduit inclination due to pitch and roll.
The kinematical analysis and 3D simulation are worked out for the hybrid serial-parallel mechanisms used to be as the compensating platform in deep ocean mining. Forward position analysis, velocities, accelerations, singularities of mechanism, workspace and stiffness matrices are all involved in the researches of this dissertation. The unit quaternion transformation and vector algebra are applied to be analysis tools.
There are two sets of closed-form direct solutions of the translational PM. For the rotational PM, although there is no closed-form direct solution generally due to its non-linearity, closed-form direct solutions can be solved on special geometric conditions. Based on known geometrical configurations of two kinds of PM, mappings of velocities, accelerations of the end-effector to its geometrical configurations are constructed, and the Jacobian matrices are derived out.
Based on identifying singularity of the Jacobian matrix, the singular configuration of PM
can be identified. The criteria are given out to identify singular configurations of the translational and rotational PM.
A normalized method is applied to search workspace of two kinds of PM. The workspace analysis of the translational PM shows that the workspace volume is affected by all geometric and non-geometric constraints, while the average condition number is affected only by the circumcircle radius difference of the fixed base and the moving platform and there exists an optimal value of average condition number.
In workspace analysis of the rotational PM, a straightforward and non-degenerate definition of orientation workspace is presented with a set of reachable unit normal vectors of moving platform and rotation angles around each normal vector. A simple criteri to identify non-compatible configurations is build up and used in determining the orientation workspace of rotational 3-UPU mechanisms.
According to Jacobian matrices and results of workspace analysis, stiffness matrices of two PMs are analyzed. Comparing to the rotational PM, directions and magnitudes of the maximum stiffness of the translational PM are focused in a small range.
Applying above-mentioned results of kinematical analysis of the two PMs and accordance with requirements of the compensating platform in deep ocean mining system, an optimal parameter design of the hybrid serial-parallel mechanism is carried out. A 3D simulation of compensating the generalized heave by the hybrid serial-parallel mechanism is worked out successfully. It is proved that the actively compensating platform based on hybrid serial-parallel mechanism is of kinematic feasibility for deep ocean mining.
针对国外大洋采矿系统的采矿平台的不足,考虑到并联机构具有刚性高、响应快的特点,本文提出使用串并联机构作为广义升沉补偿系统的驱动平台。该串并联机构由两个3-UPU并联机构串联而成。底座固连在采矿船甲板上,静平台上安装扬矿管系统。由底座和中间平台构成的纯移动式并联机构用于补偿升沉和由于横摇和纵摇产生的扬矿管的偏移,由静平台和中间平台构成的纯转动式并联机构用于补偿由于横摇和纵摇产生的扬矿管的倾斜。
本文针对构成大洋采矿补偿平台的串并联机构的运动学特性进行分析和应用仿真,为该串并联混合补偿机构的设计和控制提供一定的理论基础。研究内容主要包括位置、速度和加速度、机构的奇异性、工作空间等运动学分析,及机构的刚度的分析计算。单位四元数在坐标变换中具有简捷高效的特点。四元数变换和矢量代数是本文中并联机构分析的理论工具。
对移动型3-UPU并联机构的正解分析表明,当给定三个连杆的长度时,它具有两组封闭形式的正解。转动型3-UPU并联机构,在一般情形下,由于非线性导致其不具有封闭形式的解析解;在特殊几何条件下,给出了其封闭形式的正解。在机构的几何位形已知的前提下,建立了两种并联机构的速度和加速度的表示形式以及相应的Jacobian矩阵。
通过判断机构Jacobian矩阵的奇异性,可以判断并联机构的奇异性。论文提出了两种并联机构奇异构形的判别准则。
论文采用规么化方法分析了两种并联机构的工作空间。分析表明,移动型并联机构上下平台外接圆的半径差、连杆最小长度以及通用副的转动角度限制对工作空间的形状和体积均有不同程度的影响,而反映机构灵活性的平均条件数只受到上下平台外接圆的半
径差的影响,并且存在一个最优值。
针对转动型并联机构,提出了一种新的直观的工作空间描述方法,方位工作空间使用动平台的可达法线矢量的集合和绕每个可达法线矢量转动的角度来描述;并建立了不相容构形的准确判别准则,进行了该机构的工作空间计算和分析。
由机构Jacobian矩阵,论文分析了两种并联机构的刚度矩阵及其特点。结果表明,移动型并联机构的最大刚度有比较集中的方向和一致的大小,转动型并联机构的刚度矩阵的主轴方向分布比较分散。
根据大洋采矿系统的补偿要求和两种并联机构的运动学分析结论,本文确定了作为广义升沉补偿平台的串并联机构的规格尺寸,并且进行了3D运动仿真。仿真结果表明,本文所提出的串并联机构作为大洋采矿补偿平台是运动可行的。
The mining ship’s motions, including heave, pitch and roll which are defined as generalized heave in this dissertation and are main motions influencing the mining system, should be compensated to keep mining platform where the hoisting system located on and load suspended, having a stable pose with respect to the inertial frame.
Considering shortcomings of existing heave compensation methods and gimballed platform of mining systems in developed countries and advantages of higher overall stiffness, low inertial, and higher operating speeds of parallel mechanisms (PM), a hybrid serial-parallel mechanism used to be compensating platform is proposed in this dissertation. A translational 3-UPU PM composed of base fixed on the deck of mining ship and middle platform is used to compensate heave and conduit center shifts due to pitch and roll, and another rotational 3-UPU PM connected with the translational PM serially is used to counteract conduit inclination due to pitch and roll.
The kinematical analysis and 3D simulation are worked out for the hybrid serial-parallel mechanisms used to be as the compensating platform in deep ocean mining. Forward position analysis, velocities, accelerations, singularities of mechanism, workspace and stiffness matrices are all involved in the researches of this dissertation. The unit quaternion transformation and vector algebra are applied to be analysis tools.
There are two sets of closed-form direct solutions of the translational PM. For the rotational PM, although there is no closed-form direct solution generally due to its non-linearity, closed-form direct solutions can be solved on special geometric conditions. Based on known geometrical configurations of two kinds of PM, mappings of velocities, accelerations of the end-effector to its geometrical configurations are constructed, and the Jacobian matrices are derived out.
Based on identifying singularity of the Jacobian matrix, the singular configuration of PM
can be identified. The criteria are given out to identify singular configurations of the translational and rotational PM.
A normalized method is applied to search workspace of two kinds of PM. The workspace analysis of the translational PM shows that the workspace volume is affected by all geometric and non-geometric constraints, while the average condition number is affected only by the circumcircle radius difference of the fixed base and the moving platform and there exists an optimal value of average condition number.
In workspace analysis of the rotational PM, a straightforward and non-degenerate definition of orientation workspace is presented with a set of reachable unit normal vectors of moving platform and rotation angles around each normal vector. A simple criteri to identify non-compatible configurations is build up and used in determining the orientation workspace of rotational 3-UPU mechanisms.
According to Jacobian matrices and results of workspace analysis, stiffness matrices of two PMs are analyzed. Comparing to the rotational PM, directions and magnitudes of the maximum stiffness of the translational PM are focused in a small range.
Applying above-mentioned results of kinematical analysis of the two PMs and accordance with requirements of the compensating platform in deep ocean mining system, an optimal parameter design of the hybrid serial-parallel mechanism is carried out. A 3D simulation of compensating the generalized heave by the hybrid serial-parallel mechanism is worked out successfully. It is proved that the actively compensating platform based on hybrid serial-parallel mechanism is of kinematic feasibility for deep ocean mining.
引文
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