面向约束及其误差的少自由度并联机构分析与构型综合
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摘要
少自由度并联机构由支链内以及支链间运动副轴线的严格几何约束关系限制动平台非期望运动自由度,获得预期的少自由度运动特性。由于误差的不可避免性,运动副轴线间严格的几何约束条件通常难以得到精确满足,从而对机构的工作性能可能产生一系列不良影响。
针对此问题,本论文首先应用螺旋理论及集合论原理,系统分析少自由度并联机构的力约束系统及其过约束特性,从而确定机构在动平台不可动自由度空间中的静定与超静定性质。在机构过约束分析基础上,从结构力学理论出发,应用拆开连架副方法,通过误差建模,定量分析运动副轴线间几何约束误差在少自由度并联机构中的传递与耦合规律,揭示了过约束结构对几何约束误差的敏感性及其对机构性能影响的机理。针对过约束少自由度并联机构对几何约束误差敏感的固有特点,为改善机构对此类误差的自适应性和提高机构的动力学性能,对无过约束构型设计方法进行了系统研究。本论文的主要工作如下:
①以螺旋理论和集合论为数学工具,系统总结并深入研究了运动副、串联开链机构、单回路机构的自由度和约束系统的分析方法。在此基础上,按支链并联和回路耦合两种结构组成观点,系统分析了少自由度并联机构的约束系统和过约束特性,得出了少自由度并联机构基于支链约束的构型条件及构型特征,和基于基本回路的过约束特征。提出了一种表示少自由度并联机构约束特征的符号方法,并给出一种机构总过约束数计算、过约束回路识别以及分析过约束在回路中的分布与协调的系统方法。提出了全回路过约束、多回路过约束以及单回路过约束的概念。为按约束特征及过约束特性进行并联机构构型设计与分析奠定了理论基础。
②应用运动螺旋的指数映射描述刚体运动和坐标变换,进行了串联开链机构几何约束误差建模方法的研究。将误差看成虚拟运动副运动的结果,应用螺旋理论分析运动副轴线位姿误差的螺旋表示,从而建立了串联开链机构含误差螺旋的运动学指数积模型。并将工具坐标系的位置和姿态误差看成虚拟移动副和虚拟转动副运动的结果,给出了相应运动螺旋参数的计算公式。在Matlab环境下开发了一套通用的螺旋计算软件包,对两种典型的串联开链机构进行了误差仿真分析,并使用Adams进行了对比仿真,验证了该建模方法的正确性和有效性。该误差建模方法具有良好的几何直观性,便于从整体上描述机构的误差,为按拆开连架副法分析运动副轴线几何约束误差对少自由度并联机构的影响提供了有效的方法与工具。
③在过约束分析基础上,采用拆开连架副法,通过基于螺旋理论的误差建模,系统分析了运动副轴线几何约束误差对少自由度并联机构的不良影响。提出了基于矩阵力法的误差影响分析方法和步骤,并以计算过约束回路强制装配力、机构运动副中的附加载荷、连杆弹性变形、动平台寄生运动和机构的应变能波动等一系列定量指标,评估过约束并联机构对运动副轴线间几何约束误差的敏感性。通过对一种过约束并联机构的分析与仿真,揭示了过约束回路对运动副轴线间几何约束误差的敏感性及其对机构性能影响的机理。同时分析了运动副轴线几何约束误差对一种完全解耦并联机构的影响。研究结果为少自由度并联机构的构型分析、构型优选以及评估其实用性提供了一种新的思路和方法。
④针对过约束少自由度并联机构对运动副轴线间几何约束误差敏感的固有缺点,提出采用无过约束构型来消除此类不良影响的主动设计方法。提出了少自由度并联机构无过约束构型设计的支链力约束条件和支链间力约束几何方位配置条件。基于直接约束设计的理念,归纳总结出了一种根据支链约束要求设计具体支链结构,并按支链间约束配置几何条件并联装配,综合无过约束少自由度并联机构的系统方法和一般步骤。详细讨论了只提供一个力约束以及只提供一个力偶约束的两类支链的结构设计,并简要讨论了几种含多个约束的支链设计问题。应用按约束要求设计的支链结构,利用与静平台以及与动平台直接连接的运动副轴线确定支链间约束的几何关系,根据相关的约束配置要求,综合出了一类新的完全对称结构的平面3自由度、球面3自由度以及空间3移动并联机构无过约束构型。并对无过约束构型和过约束构型进行了对比分析。为少自由度并联机构的创新设计及消除运动副轴线几何约束误差对过约束构型的不良影响提供了一种新的思路和解决途径。
以上研究工作,解释了少自由度并联机构支链约束以及回路过约束的作用和耦合特点,揭示了过约束构型对运动副轴线间几何约束误差的敏感性及其对机构性能影响的机理,为过约束少自由度并联机构的分析提供了一种新的观点。无过约束构型设计方法为少自由度并联机构的构型综合提供了一种新的思路和创新方法,并为消除过约束的影响和提高机构的实用性提供了一条新的途径。本文的研究成果,对丰富和拓展少自由度并联机构的分析理论与方法,开拓无过约束构型的创新设计及应用领域,具有重要的理论意义和工程实用价值。
Lower-mobility parallel mechanisms rely on strictly geometrical constraints of axis of pairs in and between limbs to obtain the reduced number of DOF. In practice however these constraints will never been perfectly fulfilled due to the inevitability of errors, and hence produce series bad effects and problems.
In this paper,the constraint system and overconstraint characteristics of lower mobility parallel mechanisms were analysed systematically based on screw theory and set theory.And then the statically determinate and statically indeterminate nature of the mechanisms in the reduced DOF space were obtained.Using structural mechanics theory,effects of geometrical constraints errors on lower-mobility parallel mechanisms were studied via virtual open kinematic chain method.The results revealed the sensitivity with respect to geometrical conditions of overconstrainted mobility,and provided an insight into the effects of constraint errors and overconstraints on parallel mechanisms.Due to the inherent shortcomings of overconstraint mechanisms,the design method of non-overconstrained structure were presented systematically in order to improve the self-adaptive and dynamic performance.
The main work and achievement of this paper is as follows:
①Using screw theory and set theory as mathematical tools,the DOF and constraint system of pairs,open kinematic chains,single loop mechanisms,were systematically summarized and in-depth studied.The constraint and overconstraint characteristics of lower-mobility parallel mechanisms were studied via the union of limb constraints and the coupling of loop overconstraint.A symbol method to describe the constraint mode were built.The quantity relationship of overconstraints between basic loops and whole mechanism had been obtained.A system approach for overconstraint quatity calculation,overconstrained loop identification,overconstraint distribution in loop,have been established.The concepts of all-loop overconstraint,multi loop overconstraint, and single-loop overconstraint ,have been provided.This builds a concrete basis for analysis and design of lower-mobility parallel mechanisms.
②Based upon the exponential matrix and exponential products of modern screw theory for the rigid body transformation,the pose error of kinematic pair axis were treated as the result of equivalent screw motion,and an error model of open kinematic chain was built by using the products of exponentials formula.Meanwhile,the position and orientation errors of tool tip were represented as virtual prismatic and revolute pair’s screw motion respectivly,and its calculation formula is presented.A software package for screw calculation was developed under Matlab enviroment.Using this package,the error simulation of two typical open kinematic mechanisms were performed via Matlab programming.Furthermore,Adams’s simulation were used in verifying the established model.The results indicate that the simulation method is effective and correct,the modeling process is simple and intuitive.
③Based on overconstraint analysis, and using the virtual open kinematic chain mehod of loop,the effects of geometric constraint erros of pairs’axis on lower-mobiliy parallel mechanism, were studied.Using matrix force method,the internal force and deformations of links were caculated,and parasitic motions of moving platform were analysised.Moreover,the strain energy fluctuations were investigated.Simulation results provide an insight into the effects of constraint errors and overconstraints on parallel mechanisms.
④Based upon wrench system and set theory, the structural conditions of non-overconstrained lower-mobility parallel mechanisms and its synthesis method were proposed.The detailed synthesis procedure of 3-DOF parallel mechanisms were discussed and a series novel symmetrical structures had been found.Finally, the difference between overconstrained and non-overconstrained structure was compared. This provides a new point of view and approach for the structural synthesis of lower-mobility parallel robots and a new way to eliminate the sensitivity of overconstraint with respect to geometrical erros of the kinematic pairs.
The above research results provided an insight into the principal of interaction between limb constraint,and overconstraint coupling in different loops.Furthermore it revealed the sensitivity with respect to the geometrical conditions of overconstrained lower-mobility parallel mechanisms and its impact on the performance of the mechanism.This provided a new idea for mechanism analysis.The systematic design procedure of non-overconstrained structure provided a comprehensive new way and innovative approaches to eliminate the effects of overconstraint and geometrical conditions erros.The achievement of this paper enriched the analysis theory and methods of lower-mobility parallel mechanisms.It also given a new way and opened up a new field for the applications of non-overconstrained mechanisms.The results have important theoretical and practical engineering value.
针对此问题,本论文首先应用螺旋理论及集合论原理,系统分析少自由度并联机构的力约束系统及其过约束特性,从而确定机构在动平台不可动自由度空间中的静定与超静定性质。在机构过约束分析基础上,从结构力学理论出发,应用拆开连架副方法,通过误差建模,定量分析运动副轴线间几何约束误差在少自由度并联机构中的传递与耦合规律,揭示了过约束结构对几何约束误差的敏感性及其对机构性能影响的机理。针对过约束少自由度并联机构对几何约束误差敏感的固有特点,为改善机构对此类误差的自适应性和提高机构的动力学性能,对无过约束构型设计方法进行了系统研究。本论文的主要工作如下:
①以螺旋理论和集合论为数学工具,系统总结并深入研究了运动副、串联开链机构、单回路机构的自由度和约束系统的分析方法。在此基础上,按支链并联和回路耦合两种结构组成观点,系统分析了少自由度并联机构的约束系统和过约束特性,得出了少自由度并联机构基于支链约束的构型条件及构型特征,和基于基本回路的过约束特征。提出了一种表示少自由度并联机构约束特征的符号方法,并给出一种机构总过约束数计算、过约束回路识别以及分析过约束在回路中的分布与协调的系统方法。提出了全回路过约束、多回路过约束以及单回路过约束的概念。为按约束特征及过约束特性进行并联机构构型设计与分析奠定了理论基础。
②应用运动螺旋的指数映射描述刚体运动和坐标变换,进行了串联开链机构几何约束误差建模方法的研究。将误差看成虚拟运动副运动的结果,应用螺旋理论分析运动副轴线位姿误差的螺旋表示,从而建立了串联开链机构含误差螺旋的运动学指数积模型。并将工具坐标系的位置和姿态误差看成虚拟移动副和虚拟转动副运动的结果,给出了相应运动螺旋参数的计算公式。在Matlab环境下开发了一套通用的螺旋计算软件包,对两种典型的串联开链机构进行了误差仿真分析,并使用Adams进行了对比仿真,验证了该建模方法的正确性和有效性。该误差建模方法具有良好的几何直观性,便于从整体上描述机构的误差,为按拆开连架副法分析运动副轴线几何约束误差对少自由度并联机构的影响提供了有效的方法与工具。
③在过约束分析基础上,采用拆开连架副法,通过基于螺旋理论的误差建模,系统分析了运动副轴线几何约束误差对少自由度并联机构的不良影响。提出了基于矩阵力法的误差影响分析方法和步骤,并以计算过约束回路强制装配力、机构运动副中的附加载荷、连杆弹性变形、动平台寄生运动和机构的应变能波动等一系列定量指标,评估过约束并联机构对运动副轴线间几何约束误差的敏感性。通过对一种过约束并联机构的分析与仿真,揭示了过约束回路对运动副轴线间几何约束误差的敏感性及其对机构性能影响的机理。同时分析了运动副轴线几何约束误差对一种完全解耦并联机构的影响。研究结果为少自由度并联机构的构型分析、构型优选以及评估其实用性提供了一种新的思路和方法。
④针对过约束少自由度并联机构对运动副轴线间几何约束误差敏感的固有缺点,提出采用无过约束构型来消除此类不良影响的主动设计方法。提出了少自由度并联机构无过约束构型设计的支链力约束条件和支链间力约束几何方位配置条件。基于直接约束设计的理念,归纳总结出了一种根据支链约束要求设计具体支链结构,并按支链间约束配置几何条件并联装配,综合无过约束少自由度并联机构的系统方法和一般步骤。详细讨论了只提供一个力约束以及只提供一个力偶约束的两类支链的结构设计,并简要讨论了几种含多个约束的支链设计问题。应用按约束要求设计的支链结构,利用与静平台以及与动平台直接连接的运动副轴线确定支链间约束的几何关系,根据相关的约束配置要求,综合出了一类新的完全对称结构的平面3自由度、球面3自由度以及空间3移动并联机构无过约束构型。并对无过约束构型和过约束构型进行了对比分析。为少自由度并联机构的创新设计及消除运动副轴线几何约束误差对过约束构型的不良影响提供了一种新的思路和解决途径。
以上研究工作,解释了少自由度并联机构支链约束以及回路过约束的作用和耦合特点,揭示了过约束构型对运动副轴线间几何约束误差的敏感性及其对机构性能影响的机理,为过约束少自由度并联机构的分析提供了一种新的观点。无过约束构型设计方法为少自由度并联机构的构型综合提供了一种新的思路和创新方法,并为消除过约束的影响和提高机构的实用性提供了一条新的途径。本文的研究成果,对丰富和拓展少自由度并联机构的分析理论与方法,开拓无过约束构型的创新设计及应用领域,具有重要的理论意义和工程实用价值。
Lower-mobility parallel mechanisms rely on strictly geometrical constraints of axis of pairs in and between limbs to obtain the reduced number of DOF. In practice however these constraints will never been perfectly fulfilled due to the inevitability of errors, and hence produce series bad effects and problems.
In this paper,the constraint system and overconstraint characteristics of lower mobility parallel mechanisms were analysed systematically based on screw theory and set theory.And then the statically determinate and statically indeterminate nature of the mechanisms in the reduced DOF space were obtained.Using structural mechanics theory,effects of geometrical constraints errors on lower-mobility parallel mechanisms were studied via virtual open kinematic chain method.The results revealed the sensitivity with respect to geometrical conditions of overconstrainted mobility,and provided an insight into the effects of constraint errors and overconstraints on parallel mechanisms.Due to the inherent shortcomings of overconstraint mechanisms,the design method of non-overconstrained structure were presented systematically in order to improve the self-adaptive and dynamic performance.
The main work and achievement of this paper is as follows:
①Using screw theory and set theory as mathematical tools,the DOF and constraint system of pairs,open kinematic chains,single loop mechanisms,were systematically summarized and in-depth studied.The constraint and overconstraint characteristics of lower-mobility parallel mechanisms were studied via the union of limb constraints and the coupling of loop overconstraint.A symbol method to describe the constraint mode were built.The quantity relationship of overconstraints between basic loops and whole mechanism had been obtained.A system approach for overconstraint quatity calculation,overconstrained loop identification,overconstraint distribution in loop,have been established.The concepts of all-loop overconstraint,multi loop overconstraint, and single-loop overconstraint ,have been provided.This builds a concrete basis for analysis and design of lower-mobility parallel mechanisms.
②Based upon the exponential matrix and exponential products of modern screw theory for the rigid body transformation,the pose error of kinematic pair axis were treated as the result of equivalent screw motion,and an error model of open kinematic chain was built by using the products of exponentials formula.Meanwhile,the position and orientation errors of tool tip were represented as virtual prismatic and revolute pair’s screw motion respectivly,and its calculation formula is presented.A software package for screw calculation was developed under Matlab enviroment.Using this package,the error simulation of two typical open kinematic mechanisms were performed via Matlab programming.Furthermore,Adams’s simulation were used in verifying the established model.The results indicate that the simulation method is effective and correct,the modeling process is simple and intuitive.
③Based on overconstraint analysis, and using the virtual open kinematic chain mehod of loop,the effects of geometric constraint erros of pairs’axis on lower-mobiliy parallel mechanism, were studied.Using matrix force method,the internal force and deformations of links were caculated,and parasitic motions of moving platform were analysised.Moreover,the strain energy fluctuations were investigated.Simulation results provide an insight into the effects of constraint errors and overconstraints on parallel mechanisms.
④Based upon wrench system and set theory, the structural conditions of non-overconstrained lower-mobility parallel mechanisms and its synthesis method were proposed.The detailed synthesis procedure of 3-DOF parallel mechanisms were discussed and a series novel symmetrical structures had been found.Finally, the difference between overconstrained and non-overconstrained structure was compared. This provides a new point of view and approach for the structural synthesis of lower-mobility parallel robots and a new way to eliminate the sensitivity of overconstraint with respect to geometrical erros of the kinematic pairs.
The above research results provided an insight into the principal of interaction between limb constraint,and overconstraint coupling in different loops.Furthermore it revealed the sensitivity with respect to the geometrical conditions of overconstrained lower-mobility parallel mechanisms and its impact on the performance of the mechanism.This provided a new idea for mechanism analysis.The systematic design procedure of non-overconstrained structure provided a comprehensive new way and innovative approaches to eliminate the effects of overconstraint and geometrical conditions erros.The achievement of this paper enriched the analysis theory and methods of lower-mobility parallel mechanisms.It also given a new way and opened up a new field for the applications of non-overconstrained mechanisms.The results have important theoretical and practical engineering value.
引文
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