A comprehensive study of modal characteristics of a cylindrical manipulator with both link and joint flexibility

A thorough understanding of modal characteristics of vibrating manipulators is essential for improved dynamic positioning accuracy. Presented in this work is an extensive investigation of a cylindrical manipulator, consisting of a revolute and a prismatic joint. In general, for high-speed, flexible manipulators, modal properties depend mainly upon the following factors: (1) physical dimensions and material properties of components (such as arms and joints), which remain unchanged for a chosen manipulator; (2) a manipulator's position (or orientation) as a result of joint actuations; (3) the rigid-elastic coupling effect; and (4) the centrifugal stiffening effect due to the influence of internal axial force on the lateral stiffness. This work is intended to study the effects of each of the above factors on modal characteristics of the manipulator, and gives insight into the susceptibility of the modal parameters to each factor. In addition, joint flexibility has substantial influence on modal properties of a robotic system, depending on the relative importance of joint torsional stiffness to the stiffness of other members, such as the bending stiffness of arms. In the situation where the manipulator moves at a high speed, both rigid-elastic coupling and centrifugal stiffening effects can become important.     

含有柔性铰链并联机器人的刚度分析及刚度优化配置

以一类含有柔性铰链的并联机器人为研究对象，在位置分析的基础上，导出摄动位移间映射关系，为其建立了刚度分析模型。此外，还探讨了有关刚度性能指标的问题，最后以该性能指标为目标函数对其进行了刚度优化配置。     

3/6-SPS 并联机构刚度和弹性变形的解析法分析

针对并联机构中机构的刚度和弹性变形随外载荷变化的问题,以3/6-SPS 并联机构为例,采用解析法求解分析其总刚度矩阵和弹性变形。首先,分析该并联机构受力位置并确定驱动力及其姿态;然后,分析该机构的驱动约束分支的弹性变形,导出驱动约束分支的伴随矩阵;最后求解出该并联机构的总刚度矩阵和弹性变形。得到结论：当建立3/6-SPS 并联机构的总刚度矩阵和求解弹性变形时,必须理清刚度和位姿、广义六维力之间的关系。     

双锻造操作机大车行走系统控制方法探析

双锻造操作机配合压机联动完成大型高精长轴类锻件的锻造,可以有效提高锻造效率,提升锻件品质。针对双操作机夹持锻件同步行走控制难题,以燕山大学的两台20 kN锻造操作机为研究对象,综合考虑了吊挂系统、大车行走机械和液压系统的特点,搭建了双锻造操作机大车行走系统的数学模型。在此基础上,仿真研究了独立反馈位置同步控制方法、位置速度复合独立反馈同步控制方法和位置速度复合状态差值校正同步控制方法对双操作机大车行走系统控制特性的影响。仿真结果表明,对于动力性能差异较大的两台重载机械手,基于位置速度复合状态差值校正同步控制方法的控制效果最为理想,同时设定操作机A和操作机B的给定位移200 mm、加速度1000 mm/s2时,双操作机大车行走系统的动作响应时间为105 s,同步位置误差为［-0.28 mm,0.02 mm］。研究结果可为双锻造操作机控制提供技术支撑和理论指导,对于提升锻造产品质量和实现锻造生产线的智能控制具有重要意义。     

2RPU/UPR+RP五自由度混联机器人静刚度分析

为快速建立基于三自由度并联机构2RPU/UPR构造出的五自由度混联机器人的解析刚度模型,首先对混联机器人的结构进行了描述;然后基于串联和并联结构独立求解思想,建立了混联机器人的位置反解模型;再对混联机器人的结构进行简化处理,分别求解并联部分与串联部分两子系统的静刚度模型,从构造系统的力旋量系和弹性变形协调条件入手,简单且快速地建立了混联机器人的整体刚度模型;最后构造混联机器人的等效三维模型,运用有限元和MATLAB软件,对典型位姿下混联机器人受外力/力矩产生的微位移进行仿真验证,并给出了整机静刚度在任务空间中随位形变化分布图。通过仿真与理论计算的对比分析,验证了该混联机器人理论刚度模型的正确性。     

并联机器人机构静刚度研究现状与展望

静刚度是并联机器人机构的一项重要性能评价指标,是并联机器人研究的热点领域之一。从有限元分析、静刚度解析模型、静刚度分析和静刚度设计等4个领域对并联机器人机构的静刚度研究现状进行了总结回顾,并对其未来发展趋势进行了分析。     

电动车复合材料电池盒轻量化设计方法

为了减小电动汽车车体的质量，分析了电动汽车电池盒的承载特点，基于刚度等效的设计方法，采用复合材料替代金属材料。应用复合材料的叠层结构力学理论对电池盒体进行叠层结构构建，建立了力学方程和优化方程，确定了复合材料电池盒的结构参数。为了验证轻量化效果，运用理论解析和有限元数值分析相结合的方法，对比了金属材料和复合材料的刚度和形变，研究结果表明：采用复合材料利用刚度等效设计法是对电动汽车零部件进行轻量化设计的有效途径，也可为汽车板型零件承载结构的轻量化设计提供借鉴。     

Composite beam–columns with interlayer slip—Approximate analysis

An approximate second order analysis procedure for composite beam–columns with interlayer slip subjected to transverse loading and axial compressive loads is developed. The magnification factors to be applied to the first order solutions in order to estimate the deflections and internal forces obtained by the second order analysis approach are presented. The method of applying magnification factors to internal axial forces is discussed. The approximate second order analysis procedure is developed for the four Euler cases with various transverse load conditions. The procedure is applied to and the accuracy is illustrated for simply supported partially beam–columns of steel and concrete, and timber and concrete with different bending stiffness and interlayer slip properties. The deflections and internal forces obtained by the approximate method compared extremely well, except for slip forces in case of very flexible shear connectors, with those obtained by the more rigorous second order analysis approach for different composite action (partial interaction) parameters (shear connector stiffness values). The study also shows that the magnification factor associated with the deflections can be utilized to estimate also the internal actions, except shear forces in case of very flexible shear connectors, in the second order case with minimal error for simply supported beam–columns. Thus, for members with shear connector stiffness of structural significance the proposed approximate method can be used in general for simply supported beam–columns. For other boundary and loading conditions, the approximate method needs to be re-evaluated. The approach of using one magnification factor greatly simplifies the analysis task for those components.     

Enhanced stiffness modeling of manipulators with passive joints

The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the influence of external and internal loadings on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for computing the Cartesian stiffness and stability criteria for configurations of the kinematic chains. Within the developed technique, the manipulator elements are presented as pseudo-rigid bodies separated by multidimensional virtual springs and perfect passive joints. Simulation examples are presented that deal with parallel manipulators of the Ortholide family and demonstrate the ability of the developed methodology to describe non-linear behavior of the manipulator structure such as a sudden change of the elastic instability properties (buckling).     

Type design for heavy-payload forging manipulators

Heavy-payload forging manipulators are mainly characterized by large load output and large capacitive-load input.The relationship between outputs and inputs,which will greatly influence the control and...     

Generalized Jacobian analysis of lower mobility manipulators

Exploring screw theory through the formalities of linear algebra, this paper presents a general approach for Jacobian analysis of lower mobility manipulators. Given the definitions of twist/wrench spaces and their subspaces of the end-effector, the underlying relationships amongst these subspaces are identified using the virtual work principle. Using the orthogonal and dual properties of these subspaces and variational representations to account for the permitted and restricted instantaneous motions of the end-effector, a rigorous general and systematic procedure for the formulation of a generalized Jacobian is proposed. The merit of the generalized Jacobian is that it allows the first order kinematic and static modeling (velocity, accuracy, force and stiffness) to be integrated into a unified mathematical framework, so standardizing the modeling procedure and improving the efficiency of design and analysis. The generalized Jacobians for the three well-known parallel manipulators are derived as examples to illustrate the generality and effectiveness of this approach.     

求解3-RPS并联机构刚度的新方法

对于少自由度机构来说,由于结构约束的存在,机构中出现了约束反力,约束反力会在机构中产生变形,影响整个机构的精度,在机构分析中必须加以考虑。基于此,以传统的3-RPS并联机构为例,给出考虑约束反力产生变形的刚度模型的建立方法。首先,用观察法分析该机构中存在的约束反力。其次,建立该机构的6×6形式雅可比矩阵,并运用虚功原理建立该机构的静力学模型。最后,分析机构在驱动力和约束力共同作用下产生的弹性变形。在约束反力产生的变形方向上虚设P副,将3-RPS机构的变形和刚度分析转化为一个等效的无约束反力的6自由度并联机构3-RPPS的变形和刚度分析。这种方法给少自由度机构的研究提供了一些新观点。     

A method of compliance control of redundant manipulators

A compliance control method of redundant manipulators is presented. This method is based on the new stiffness model, which allows to modulate accarate joint stiffness of realizing the end effector stiffness to be varied with task requirements. A control model is developed and implemented by the proposed method in a three degree of freedom planar redundant manipulator. Also its effectiveness is validated.     

Stability problem formulation of structurally compliant robot manipulators during contact task execution: A singular perturbation approach

Aspects of modelling, stability and control of robotic manipulators with structurally compliant links and joints during contact with a stiff work environment are presented in this paper. System models of n joint robotic manipulators are cast into multiple time-scale formulations. Several different models are developed, based on the relative differences in magnitude of the scaling parameters associated with the manipulator link, joint and environment stiffnesses. These stiffnesses, if greatly different, lead to a four time-scale system with virtually no interaction between these subsystems. In these models, as various subsystem stiffness coefficients become approximately equal, strong interaction among the subsystems is seen. Utilizing the theory of singularly perturbed dynamic systems, aspects of overall system stability are touched on, and possible use of a high speed stabilizing control is considered. It is seen from the analysis presented, that depending on the relative structural stiffness of the link, joint and work environment, is is not always possible to apply a corrective control for certain structural compliance effects. An example serves to illustrate some of the concepts discussed in the paper.

It is noted that this paper does not provide general stability conclusions, but rather forms a framework for stability investigation.     

复合节流式静压气体轴承静态特性分析

为进一步提升静压气体轴承的静态性能,以普通孔式节流为基础,配合表面周向和径向槽节流,提出复合节流式静压气体轴承,以充分发挥2种节流方式的优点,使静压气体轴承具有更好的承载能力和刚度。利用Fluent计算轴承内流场参数并分析流场特性,比较复合节流式与普通孔式节流静压气体轴承的承载能力和刚度,并研究孔式参数和表面槽参数对复合节流式静压气体轴承静态特性的影响。结果表明：在一定气膜厚度范围内,复合节流式静压气体轴承对于提升承载力、增强刚度有着显著的效果;复合式节流因为有表面槽二次节流的存在,均压效果更好。增加节流孔数、节流孔直径、节流孔分布圆半径,以及在气膜厚度较小时增加表面槽长、槽宽、槽深,均有利于增加轴承承载力;在气膜厚度较小时,增加节流孔数、减小节流孔直径,以及增加表面槽长和槽宽、降低槽深,均有利于增加轴承刚度。     

基于三组测量绳结构的软体机械臂运动检测

针对气动软体机械臂运动形状检测问题,设计了一种基于拉线编码器的三组测量绳结构的运动学参数检测装置。依据分段常曲率法,构建了气动模块化软体机械臂的运动检测模型,基于机械臂柔性材料的特点,在建模过程中引入刚度法,使检测模型能准确反映从机械臂驱动气压到形状变化以及运动学参数的映射关系。提出了一种可模块化组装的气动软体机械臂,用于验证检测装置与模型的精度,所提出的机械臂在构型上由硅胶基体、运动气囊和连接板组成,能实现机械臂的模块化组装。通过对所构建的运动检测模型进行推导与仿真,得到了模型的相对误差。最后,通过试验验证了运动检测建模的精度和机械臂驱动、构型以及运动的特征。研究结果表明：相比于传统的视觉追踪方法,所设计的基于三组测量绳结构的检测装置能实现对软体机械臂运动形状的高精度检测。     

Analysis for a planar 3 degree-of-freedom parallel mechanism with actively adjustable stiffness characteristics

A planar three degree-of-freedom parallel manipulator has been extensively studied as the fundamental example of general parallel manipulators. It is proven from previous work (Kim, et. al., 1996) that when three identical joint compliances are attached to the three base joints of the mechanism in its symmetric configurations, this mechanism possesses a completely decoupled compliance characteristic at the object space, which is the important operational requirement for an RCC device. In this work, we are concerned with the adjustability of the output compliance matrix of this mechanism, by employing redundancy on either joint compliances or on actuators. Two approaches are suggested to achieve this purpose. In the first approach, the stiffness modulation is achieved through purely redundant passive springs or decoupled feedback stiffness gains. In the second approach, stiffness modulation is achieved through antagonistic actuation of the system actuators. General stiffness models are derived for both cases. Based on these stiffness models, stiffness modulation algorithms are formulated. The capability of actively adjustable stiffness will be very effective in several robotic applications.     

A simplified analysis method for composite beams with interlayer slip

A simplified static procedure is proposed for analysing and designing composite beams with interlayer slip. The method is parallel to the Eurocode 5 method, but it is general in nature and can be applied to arbitrary boundary and loading conditions. In contrast with Eurocode 5, a general and correct way of choosing the effective beam length of the problem is given by the present procedure, which is that the effective beam length equals the buckling length that is found in the corresponding column buckling problem. The procedure predicts the deflections and internal actions and stresses, in principle by replacing the fully composite bending stiffness (EI_∞) with the effective (partially) composite bending stiffness (EI_eff) in the expressions for these quantities in the corresponding fully composite beam. This effective bending stiffness depends on two non-dimensional parameters: the composite action parameter (shear connection stiffness) and the relative bending stiffness parameter. The method is applied to a number of simple practical cases and the results obtained have been compared with the exact values. The applicability of the simplified analysis procedure was found to be very good, except for interlayer shear stresses. The error in the Eurocode 5 procedure, as compared with the method proposed in this paper, can in some cases be up to almost 30% depending on the boundary conditions.     

基于共形几何代数的两种6自由度串并混联机构位置逆解分析

基于共形几何代数（Conformal geometric algebra,CGA）基本理论,解决了（3-PRS）+（3-SPR）和（3-RPS）+（3-SPS+UP）两种典型串并混联机构的位置逆解问题。首先根据机构的几何结构特征选择合适的未知参数,基于共形几何代数的基本运算建立了与该参数相关的机构中间平台某一顶点的数学表达式;然后根据该顶点坐标表达式和机构中存在的几何和尺寸约束,构造若干相关的平面或球面几何体,并对其进行外积求交运算得出中间平台其他两个顶点坐标的共形几何表达式;最后结合得到的顶点坐标与共形几何代数中的矢量内积运算,推导出只含有一个未知参数的多项式方程,由此得到机构的全部位置反解。该方法具有计算简明、高效、几何直观性强的特点,避免了传统方法求解串并混联机构位置逆解时冗长复杂的计算过程,为此类机构位置逆解的研究提供了参考。     

Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles

The parallel spindle heads with high rotational capability are demanded in the area of multi-axis machine tools and 3D printers. This paper focuses on designing a class of 2R1T (R: Rotation; T: Translation) parallel spindle heads and the corresponding collaborative 5-axis manipulators with 2-dimension (2D) large rotational angles. In order to construct 2D rotational degrees of freedom (DOFs), a platform with 2D revolute joints is proposed first. Based on the constraint screw theory, the feasible limbs that can be connected in the platform are synthesized. In order to provide constant rotational axis for the platform, a class of redundant limbs are designed. A class of redundant 2R1T parallel spindle heads is obtained by connecting the redundant limbs with the platform and the redundant characteristics are verified by the modified Grübler-Kutzbach criterion. The corresponding 5-axis collaborative manipulators are presented by constructing a 2-DOF series translational bottom moving platform. The inverse kinematics and the orientation workspace as well as the decoupling characteristics of this type of 2R1T parallel spindle heads are analyzed. The results show that these manipulators have large 2D rotational angles than the traditional A3/Z3 heads and can be potentially used in the application of multi-axis machine tools and the 3D printers.