少自由度并联机构真实运动特性分析
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摘要
少自由度并联机构由于本身的特点在实际中有很广泛的应用。特别是具有完全相同的分支,结构对称具有各向同性的少自由度并联机构更具有应用潜力。但由于少自由度并联机构本身的特点,其对于装配和加工具有很高的要求,多年来具有相同分支的少自由度并联机构的装配误差问题没有得到很好的解决,突出表现在到目前为止还没有人对少自由度并联机构约束误差进行研究,缺乏全面的约束误差分析理论,致使少自由度并联机构真实运动特性分析成为目前国际学术界的一个难点。本文主要研究对称少自由度并联机构的误差问题,旨在建立全面有效的误差分析理论,分析少自由度并联机构动平台的真实运动特性。主要研究内容包括以下几个方面:
引入螺旋理论,分析了公共约束,在此基础上概括了普遍适用于少自由度并联机构自由度计算公式;给出了具有相同分支的少自由度并联机构的分支以及机构的输出矩阵以及并联机构可能存在的寄生运动,并对寄生运动进行了优化。
根据约束螺旋在空间不同几何条件下的线性相关性对约束螺旋系进行分类,并通过反螺旋定理获取每种约束螺旋系所约束的运动。给出了机器人正常装配时,运动副轴线之间的几何关系,动平台实现预定运动各分支必须满足的几何条件。
少自由度并联机器人机构之间的特殊性质,造成其对于装配、安装等因素比较敏感。当机器人各分支由于加工、安装或装配的原因造成各分支内部和分支之间存在误差时,动平台的运动能力将发生变化。装配误差分为两种形式:不平行和不相交。研究了存在这两种误差的情况下,机构的各运动副轴线与动平台之间的关系,存在误差时机构的动平台产生的寄生运动形式,以及机器人的雅可比矩阵的变化。在上面分析的基础上,形成了一套较完整的对于少自由度并联机构的约束误差进行分析的理论体系。
给出了具有相同分支的少自由度机构运动副存在的间隙,分析了这些间隙对应约束方程的表达形式。利用螺旋分析了并联机构动平台的运动能力与运动副间隙之间的关系。给出了最大间隙的表达形式。
本文利用螺旋理论分析了机构存在误差时,机构各分支对于动平台提供的约束螺旋的主螺旋的表达形式。分别建立了机构驱动关节和非驱动关节存在误差时,具有相同分支的少自由度并联机构动平台的运动学表达形式。
The symmetrical lower-mobility parallel mechanism,which characterizes identical limbs,symmetrical arrangement and isotropy,has great potentials in practical application.Particularly the symmetrical lower-mobility parallel mechanism,which characterizes identical limbs,symmetrical arrangement and isotropy,has great potentials in practical application.However,the parallel manipulator is sensitive to assembling and manufacturing due to characteristic of lower DOF parallel manipulator.The problem of constraint error of lower-mobility parallel mechanisms has not been well solved over many years.A universal and effective theory of error has not been established and consequently there is a difficulty to know the actual kinematic performance for lower DOF parallel manipulator.This paper focuses on constraint error of symmetrical lower-mobility parallel mechanisms and aims to establish a universal and effective theory and to analyze actual movement for lower DOF parallel manipulators.The main contributions are as follows:
The concept and geometrical condition of common constraint is obtained using screw theory.Then the criterions of common constraint is proposed.A mobility criterion based on constraint analysis is proposed.The sublimb for the symmetrical lower-mobility parallel mechanism which characterizes identical limbs is analysed.Given the output maxtric and parasitic motion of parallel manipulator.
Given a system of wrenches of constraint,the corresponding reciprocal basis screws are determined.Then,the joint screws of a limb are obtained by a linear combination of these basis screws.The condition which the parallel manipulator can moves according to anticipated aim is offered.
From perspective of structure synthesis,certain special geometric constraints, such asjoint axes intersecting at one point or perpendicular to each other,are necessary in realizing the end-effector motion of kinematically parallel manipulators along individual motion axes.Those errors that violate the geometric constraint requirements are termed "constraint errors".The constraint errors usually are more troublesome than other manipulator errors because the motion characteristics of the manipulator may no longer exist and the kinematic models will be rendered useless due to these constraint errors.Therefore,identification and prevention of these constraint errors in initial design and manufacturing stage are of great significance.In this article,three basic types of constraint errors are identified,and an approach to evaluate the effects of constraint errors on characteristics of parallel manipulators is proposed.The parasitic motion and Jacobian matrix of lower DOF parallel manipulator is offered in the paper.A total theory for constraint error of lower DOF parallel manipulator is developed according to the principles discussed.
This paper presents a method based on screw theory for the analysis of positioning accuracy in parallel manipulators with joint clearances.A general method is introduced, and a new analytical procedure is formulated which allows to determine analytically a sub-optimal estimation of the worst case condition for positioning accuracy.Moreover this procedure can determine exactly the worst-case angular accuracy in translating fully-parallel manipulators under the influence of joint clearances.
The paper proposes a unified analytical methodology to identify the principal screws sysrems.The accuracy synthesis model has been formulated by means of the D-H theory.Based on the principle that primary errors exert the same effects on the driven and the concept—influence factors of the pose errors,two methods for pose error synthesis of parallel manipulators have been presented.
引入螺旋理论,分析了公共约束,在此基础上概括了普遍适用于少自由度并联机构自由度计算公式;给出了具有相同分支的少自由度并联机构的分支以及机构的输出矩阵以及并联机构可能存在的寄生运动,并对寄生运动进行了优化。
根据约束螺旋在空间不同几何条件下的线性相关性对约束螺旋系进行分类,并通过反螺旋定理获取每种约束螺旋系所约束的运动。给出了机器人正常装配时,运动副轴线之间的几何关系,动平台实现预定运动各分支必须满足的几何条件。
少自由度并联机器人机构之间的特殊性质,造成其对于装配、安装等因素比较敏感。当机器人各分支由于加工、安装或装配的原因造成各分支内部和分支之间存在误差时,动平台的运动能力将发生变化。装配误差分为两种形式:不平行和不相交。研究了存在这两种误差的情况下,机构的各运动副轴线与动平台之间的关系,存在误差时机构的动平台产生的寄生运动形式,以及机器人的雅可比矩阵的变化。在上面分析的基础上,形成了一套较完整的对于少自由度并联机构的约束误差进行分析的理论体系。
给出了具有相同分支的少自由度机构运动副存在的间隙,分析了这些间隙对应约束方程的表达形式。利用螺旋分析了并联机构动平台的运动能力与运动副间隙之间的关系。给出了最大间隙的表达形式。
本文利用螺旋理论分析了机构存在误差时,机构各分支对于动平台提供的约束螺旋的主螺旋的表达形式。分别建立了机构驱动关节和非驱动关节存在误差时,具有相同分支的少自由度并联机构动平台的运动学表达形式。
The symmetrical lower-mobility parallel mechanism,which characterizes identical limbs,symmetrical arrangement and isotropy,has great potentials in practical application.Particularly the symmetrical lower-mobility parallel mechanism,which characterizes identical limbs,symmetrical arrangement and isotropy,has great potentials in practical application.However,the parallel manipulator is sensitive to assembling and manufacturing due to characteristic of lower DOF parallel manipulator.The problem of constraint error of lower-mobility parallel mechanisms has not been well solved over many years.A universal and effective theory of error has not been established and consequently there is a difficulty to know the actual kinematic performance for lower DOF parallel manipulator.This paper focuses on constraint error of symmetrical lower-mobility parallel mechanisms and aims to establish a universal and effective theory and to analyze actual movement for lower DOF parallel manipulators.The main contributions are as follows:
The concept and geometrical condition of common constraint is obtained using screw theory.Then the criterions of common constraint is proposed.A mobility criterion based on constraint analysis is proposed.The sublimb for the symmetrical lower-mobility parallel mechanism which characterizes identical limbs is analysed.Given the output maxtric and parasitic motion of parallel manipulator.
Given a system of wrenches of constraint,the corresponding reciprocal basis screws are determined.Then,the joint screws of a limb are obtained by a linear combination of these basis screws.The condition which the parallel manipulator can moves according to anticipated aim is offered.
From perspective of structure synthesis,certain special geometric constraints, such asjoint axes intersecting at one point or perpendicular to each other,are necessary in realizing the end-effector motion of kinematically parallel manipulators along individual motion axes.Those errors that violate the geometric constraint requirements are termed "constraint errors".The constraint errors usually are more troublesome than other manipulator errors because the motion characteristics of the manipulator may no longer exist and the kinematic models will be rendered useless due to these constraint errors.Therefore,identification and prevention of these constraint errors in initial design and manufacturing stage are of great significance.In this article,three basic types of constraint errors are identified,and an approach to evaluate the effects of constraint errors on characteristics of parallel manipulators is proposed.The parasitic motion and Jacobian matrix of lower DOF parallel manipulator is offered in the paper.A total theory for constraint error of lower DOF parallel manipulator is developed according to the principles discussed.
This paper presents a method based on screw theory for the analysis of positioning accuracy in parallel manipulators with joint clearances.A general method is introduced, and a new analytical procedure is formulated which allows to determine analytically a sub-optimal estimation of the worst case condition for positioning accuracy.Moreover this procedure can determine exactly the worst-case angular accuracy in translating fully-parallel manipulators under the influence of joint clearances.
The paper proposes a unified analytical methodology to identify the principal screws sysrems.The accuracy synthesis model has been formulated by means of the D-H theory.Based on the principle that primary errors exert the same effects on the driven and the concept—influence factors of the pose errors,two methods for pose error synthesis of parallel manipulators have been presented.
引文
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