一类平面两自由度并联机构的性能分析与优选研究
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摘要
少自由度并联机构,特别是2、3自由度的新型并联机构是并联以及混联机器人机构创新和性能评价的基础和重点,有着重要的应用前景和开发价值。最近十年以来,提出了大量的2、3自由度的并联机构,然而实际在用的并联机构的数目却非常少,阻碍其广泛应用的原因主要有两方面：(1)并联机构的比较和优选困难。机构类型的多样性,使得适合于特定操作任务的最佳的机构方案难以选择；(2)机构参数的优化设计困难。机构的性能指标依赖于其拓扑类型、驱动布局和设计参数,难以进行全局优化设计。本文首先构建了一类2自由度平面并联机构(PPKM),然后提出一个系统的方法来研究它们的优选问题,目的是为规定的操作任务选择一个最合适的机构方案。主要工作如下：
首先,完整地构建一类含PRR分支的PPKM,并给出每个机构唯一的和明确的描述。主要包括三个方面的工作：(1)分析了六种不同分支的五杆机构,从中选择分支为PRR、以固定在静平台上的P关节作为驱动关节的PPKM作为研究对象；(2)以两自由矢量的独立方向数为依据,分析了该类PPKM的三种驱动布局,并采用与坐标系无关的结构参数描述每种布局；(3)提出统一的方法描述该类PPKM,每个机构都可以根据其驱动布局类型和结构参数给以唯一描述,在此基础上建立了机构统一的运动学方程、雅可比矩阵以及各向同性条件,并编制了对应的运动分析软件,以避免单个机构的分析和大量的符号运算。
其次,对三种典型驱动副布局的PPKM的性能进行了研究,主要包括三方面内容：(1)根据机构几何约束,采用归一化原理建立了三种机构的设计空间模型；(2)系统地分析了三种机构的理论工作空间、奇异轨迹以及灵活工作空间与机构杆件尺寸参数以及与机构控制模式之间的关系,讨论了其在机构尺寸设计空间内的分布规律,为优选控制模式提供依据；(3)分析了三种机构的全局条件数、全局速度指标、全局刚度指标以及空间利用率指标与机构杆件尺寸参数之间的关系,并绘制了相应的性能图谱。提出了一种新的空间利用率指标,以机构最大规则形状灵活工作空间与整个机构占地面积之比作为空间利用率,更具实用价值。同时,在机构工作空间求解过程中,简化了传统的边界搜索法,提出了一组高效的、只在边界附近搜索验证的算法来确定PPKM可达的、灵活的工作空间及其边界,以及包含在它们内部的最大规则形状的灵活工作空间。
再次,提出一种优选方法,从三种PPKM中为规定的操作任务选择一种最合适的机构方案。优选标准考虑了每个PPKM的全局条件指标、全局速度指标、全局刚度指标和空间利用率指标。优选工作分两个层次进行：(1)对三种布局PPKM进行优化设计,确定了三个运动学参数优化的PPKM,使每个PPKM都能产生一个规则灵活工作空间尽可能接近所给定的操作任务；(2)考虑不同的优选标准,确定一种最合适的机构方案。
最后,利用优选的机构进行了5自由度混联高速喷涂机器人的设计。首先,根据操作任务进行了并联机构的尺寸综合；然后,分析了并联机构部分的局部性能,利用Langrane方程建立了机构动力学模型,在Solidworks软件中建立虚拟样机并进行运动轨迹规划和受力仿真；研制单喷枪、三喷枪协同喷涂二款五轴混联高速喷涂机器人,并比较了这二种结构的性能优劣。
Lower-mobility parallel mechanism, especially the novel parallel mechanism with 2,3 degrees of freedom is the foundation and focus of the innovation and performance evaluation of parallel and hybrid robot mechanisms, and has important potential applications and the development value. In the recent ten years, the large number of 2,3 degrees of freedom parallel mechanism were proposed, however the actual number of parallel mechanism is very poor in the actual application. The reasons of hindering their wide application have two main aspects:(1) difficult to select a suitable mechanism. Since the variety of mechanism type, the comparison of different mechanisms for a given operation task is difficult. (2) Parameter optimization of the mechanism is difficult. The performance index of the parallel mechanism depend on its topological type, the actuated layout and design parameters, so it is difficult to globally optimize in the design. In this dissertation, a class of 2-DOF planar parallel mechanism (PPKM) is constructed, and then a unified method is put forward to solve the problem of their optimization for a specified operating task. The main work is as follows:
Firstly, a class of PPKM with PRR branches is built. Mainly jobs include three aspects:(1) Five-bar mechanisms with six different branches are analyzed. The PPKM with PRR branches is chosen for study, which is actuated by P joint fixed on the static platform; (2) According to the number of absolute directions of the two-vector-system, the actuated layout problem of a class of PPKM is analyzed. The coordinate-free description of each kind of actuated layout is given; (3) A unified kinematics model to describe a class of PPKM is proposed, so each mechanism in the family is depicted by means of the type of actuated layout, and the structure parameter. Based on the unified model, the kinematic problems, the Jacobian matrix and isotropic are analyzed. Additional, the kinematics analysis software is designed to avoid analyzing singular mechanism and the vast symbolic computation.
Secondly, the performance of three typical actuated layout of PPKM is analyzed, mainly including three aspects:(1) First, according to the geometric constraints condition, the design space models of the three institutions are derived using the normalization principle; (2) The relationship between theoretical workspace, singular trajectory, and dexterous workspace with structural parameters is studied and the distributing regulation in mechanism design space is discussed; (3) The global condition number, the global velocity index, the global stiffness index, and the space utilized rate index of three kinds of PPKM with traditional actuated layout are calculated. The design space is adopted to study the relationship between the full performances and size of mechanisms and to draw the performance diagram. A novel space utilized rate index is defined as the ratio of maximal regular dexterous workspace to the covering area of the whole mechanism, which is more practical. The algorithm of traditional boundary searching is simplified and an efficient numerical algorithm is proposed to determine the reachable workspaces, the dexterous workspaces and the maximal regular dexterous workspaces and their boundaries.
Thirdly, for a prescribed operation task, an optimal mechanism is found from three different PPKM. The global velocity index, the global velocity index, the global stiffness index, and the space utilized rate index are considered as optimal criterion. And the optimization is earried out at two levels:(1) Parameters of three different PPKM is optimal designed to produce a regular dexterous workspace close to the prescribed operating space; (2) The optimal mechanism is determined considering the different optimization criteria.
Finally, a 5-DOF hybrid high-speed spraying robot is designed and the optimal mechanism is adopted as its main parallel mechanism. The kinematics and dynamic analysis are done, and the mobile trajectory is investigated and simulated with Solidworks software. Meanwhile, both 5-axis hybrid robots with single airbrush and with mult-airbrush for spray painting are developed respectively according to the design method. Furthermore, the performance for the two spray robots with different structures is compared.
首先,完整地构建一类含PRR分支的PPKM,并给出每个机构唯一的和明确的描述。主要包括三个方面的工作：(1)分析了六种不同分支的五杆机构,从中选择分支为PRR、以固定在静平台上的P关节作为驱动关节的PPKM作为研究对象；(2)以两自由矢量的独立方向数为依据,分析了该类PPKM的三种驱动布局,并采用与坐标系无关的结构参数描述每种布局；(3)提出统一的方法描述该类PPKM,每个机构都可以根据其驱动布局类型和结构参数给以唯一描述,在此基础上建立了机构统一的运动学方程、雅可比矩阵以及各向同性条件,并编制了对应的运动分析软件,以避免单个机构的分析和大量的符号运算。
其次,对三种典型驱动副布局的PPKM的性能进行了研究,主要包括三方面内容：(1)根据机构几何约束,采用归一化原理建立了三种机构的设计空间模型；(2)系统地分析了三种机构的理论工作空间、奇异轨迹以及灵活工作空间与机构杆件尺寸参数以及与机构控制模式之间的关系,讨论了其在机构尺寸设计空间内的分布规律,为优选控制模式提供依据；(3)分析了三种机构的全局条件数、全局速度指标、全局刚度指标以及空间利用率指标与机构杆件尺寸参数之间的关系,并绘制了相应的性能图谱。提出了一种新的空间利用率指标,以机构最大规则形状灵活工作空间与整个机构占地面积之比作为空间利用率,更具实用价值。同时,在机构工作空间求解过程中,简化了传统的边界搜索法,提出了一组高效的、只在边界附近搜索验证的算法来确定PPKM可达的、灵活的工作空间及其边界,以及包含在它们内部的最大规则形状的灵活工作空间。
再次,提出一种优选方法,从三种PPKM中为规定的操作任务选择一种最合适的机构方案。优选标准考虑了每个PPKM的全局条件指标、全局速度指标、全局刚度指标和空间利用率指标。优选工作分两个层次进行：(1)对三种布局PPKM进行优化设计,确定了三个运动学参数优化的PPKM,使每个PPKM都能产生一个规则灵活工作空间尽可能接近所给定的操作任务；(2)考虑不同的优选标准,确定一种最合适的机构方案。
最后,利用优选的机构进行了5自由度混联高速喷涂机器人的设计。首先,根据操作任务进行了并联机构的尺寸综合；然后,分析了并联机构部分的局部性能,利用Langrane方程建立了机构动力学模型,在Solidworks软件中建立虚拟样机并进行运动轨迹规划和受力仿真；研制单喷枪、三喷枪协同喷涂二款五轴混联高速喷涂机器人,并比较了这二种结构的性能优劣。
Lower-mobility parallel mechanism, especially the novel parallel mechanism with 2,3 degrees of freedom is the foundation and focus of the innovation and performance evaluation of parallel and hybrid robot mechanisms, and has important potential applications and the development value. In the recent ten years, the large number of 2,3 degrees of freedom parallel mechanism were proposed, however the actual number of parallel mechanism is very poor in the actual application. The reasons of hindering their wide application have two main aspects:(1) difficult to select a suitable mechanism. Since the variety of mechanism type, the comparison of different mechanisms for a given operation task is difficult. (2) Parameter optimization of the mechanism is difficult. The performance index of the parallel mechanism depend on its topological type, the actuated layout and design parameters, so it is difficult to globally optimize in the design. In this dissertation, a class of 2-DOF planar parallel mechanism (PPKM) is constructed, and then a unified method is put forward to solve the problem of their optimization for a specified operating task. The main work is as follows:
Firstly, a class of PPKM with PRR branches is built. Mainly jobs include three aspects:(1) Five-bar mechanisms with six different branches are analyzed. The PPKM with PRR branches is chosen for study, which is actuated by P joint fixed on the static platform; (2) According to the number of absolute directions of the two-vector-system, the actuated layout problem of a class of PPKM is analyzed. The coordinate-free description of each kind of actuated layout is given; (3) A unified kinematics model to describe a class of PPKM is proposed, so each mechanism in the family is depicted by means of the type of actuated layout, and the structure parameter. Based on the unified model, the kinematic problems, the Jacobian matrix and isotropic are analyzed. Additional, the kinematics analysis software is designed to avoid analyzing singular mechanism and the vast symbolic computation.
Secondly, the performance of three typical actuated layout of PPKM is analyzed, mainly including three aspects:(1) First, according to the geometric constraints condition, the design space models of the three institutions are derived using the normalization principle; (2) The relationship between theoretical workspace, singular trajectory, and dexterous workspace with structural parameters is studied and the distributing regulation in mechanism design space is discussed; (3) The global condition number, the global velocity index, the global stiffness index, and the space utilized rate index of three kinds of PPKM with traditional actuated layout are calculated. The design space is adopted to study the relationship between the full performances and size of mechanisms and to draw the performance diagram. A novel space utilized rate index is defined as the ratio of maximal regular dexterous workspace to the covering area of the whole mechanism, which is more practical. The algorithm of traditional boundary searching is simplified and an efficient numerical algorithm is proposed to determine the reachable workspaces, the dexterous workspaces and the maximal regular dexterous workspaces and their boundaries.
Thirdly, for a prescribed operation task, an optimal mechanism is found from three different PPKM. The global velocity index, the global velocity index, the global stiffness index, and the space utilized rate index are considered as optimal criterion. And the optimization is earried out at two levels:(1) Parameters of three different PPKM is optimal designed to produce a regular dexterous workspace close to the prescribed operating space; (2) The optimal mechanism is determined considering the different optimization criteria.
Finally, a 5-DOF hybrid high-speed spraying robot is designed and the optimal mechanism is adopted as its main parallel mechanism. The kinematics and dynamic analysis are done, and the mobile trajectory is investigated and simulated with Solidworks software. Meanwhile, both 5-axis hybrid robots with single airbrush and with mult-airbrush for spray painting are developed respectively according to the design method. Furthermore, the performance for the two spray robots with different structures is compared.
引文
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