Kinetostatic modelling of a 3-PRR planar compliant parallel manipulator with flexure pivots

Flexure pivots are widely used in long stroke complaint parallel manipulators (CPMs) for their large deformation capacity. However the parasitic motion caused by the flexure pivots cannot be neglected as the rotation angle gets large, which will finally affect the absolute positioning accuracy of the manipulators. In this paper, a modelling approach to calculate the nonlinear kinetostatics of a long stroke planar CPM with flexure pivots is proposed, in which the parasitic motion of the flexure joints are taken into account. The displacement constraint equations and the static equilibrium equations of the CPM are established under the deformed configuration. Finite element analysis (FEA) shows the accuracy and efficiency of the nonlinear kinematic model (NLKM) for both the inverse and forward kinematic analysis. Moreover, the prediction accuracy of the CPM’s kinematic behavior has been improved more than 20 times by employing the NLKM compared with the conventional kinematic model (CKM).     

A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules

This paper presents normalized, nonlinear and analytical models of spatial compliant parallel modules—multi-beam modules with a large range of motion. The models address the non-linearity of load-equilibrium equations, applied in the deformed configuration, under small deflection hypothesis. First, spatial nonlinear load-displacement equations of the tip of a beam, conditions of geometry compatibility and load-equilibrium conditions for a spatial three-beam module are derived. The nonlinear and analytical load-displacement equations for the three-beam module are then solved using three methods: approximate analytical method, improved analytical method and numerical method. The nonlinear-analytical solutions, linear solutions and large-deflection FEA solutions are further analyzed and compared. FEA verifies that the accuracy of the proposed nonlinear-analytical model is acceptable. Moreover, a class of multi-beam modules with four or more beams is proposed, and their general nonlinear load-displacement equations are obtained based on the approximate load-displacement equations of the three-beam module. The proposed multi-beam modules and their nonlinear models have potential applications in the compliant mechanism design. Especially, the multi-beam modules can be regarded as building blocks of novel compliant parallel mechanisms.     

三支链六自由度并联柔性铰微动机器人的研究

提出了一种过程中采用的新型三支链六自由度并联微动机器人结构。采用两端分别带有柔性球铰和柔性旋转铰的支杆以简化结构,整体加工包含三个二自由度单元的基平台来有效减小装配误差,并用压电陶瓷驱动弹性平板获得高分辨率高精度。根据运动影响系数理论对其运动学进行分析,求出了其平动台、支杆和柔性铰链的速度表达式。考虑柔性铰链的弹性变形,基于虚功原理建立了其刚度模型。 分析了此类并联微动机器人的设计目标和柔性铰链设计原则,采用模块化精密定位控制器设计了控制系统。实验结果表明,所设计的微动机器人可达到纳米级精度, 简化了六支链六自由度并联微动机器人的复杂结构,减小了装配误差。     

Nonlinear modeling of compliant mechanisms incorporating circular flexure hinges with finite beam elements

Modeling of compliant mechanisms incorporating flexure hinges is mainly focused on linear methods. However, geometrically nonlinear effects cannot be ignored generally. This work shows that nonlinear behavior plays an important role in the deformation and stress analysis, which consequently impacts the design of compliant mechanisms. In this study a nonlinear higher order finite beam element based modeling approach is presented strongly reducing the computation time of nonlinear models. Planar deformation and mechanical stress of a single circular flexure hinge under a wide range of loads is modeled and computed with the proposed approach. A comparison with a 3D-nonlinear finite element model shows very good agreement and validates the beam model. It is shown that the linear and nonlinear deformation behavior of a single flexure hinge deviate marginally so that linear modeling approaches are sufficient. Furthermore a planar displacement amplification mechanism incorporating circular flexure hinges is studied by means of the same method highlighting the distinct deviation of the behavior of the geometrically nonlinear model from its linear prediction. In conclusion the nonlinear behavior at the system level can not longer be neglected. Finally, a study shows that different designs of the displacement amplification mechanism are achieved when linear or nonlinear modeling approaches are applied.     

空间曲线切口式柔性铰的设计

为了满足精密仪器连接部件的柔度和强度需求,以切口曲线为二次曲面和圆柱面的相贯线的柔性铰为例,研究了一类空间曲线切口式柔性铰的设计方法。推导了此类柔性铰转动柔度的一般设计计算公式,分析了设计参数对柔度特性的影响,在此基础上提出了此类柔性铰的设计方法。依据提出的方法设计了空间曲线切口式柔性铰,并利用有限元分析方法对设计实例进行了柔度和强度校核,同时建立了模态实验系统识别其柔度。结果表明,两种柔度校核结果与设计计算公式结果吻合较好,最大误差不超过5%,验证了设计方法的有效性,为此类柔性铰应用于精密仪器的工程设计提供了参考。此外,文中给出的有限元建模分析方法以及试验测试方法也可用于相同类型的精密构件的力学特性研究与分析。     

Spatial force-based non-prismatic beam element for static and dynamic analyses of circular flexure hinges in compliant mechanisms

This paper presents a spatial force-based non-prismatic beam element modeling approach for circular flexure hinges, which is capable of accurate and efficient modeling of both static and dynamic characteristics of flexure-based compliant mechanisms. The spatial force-based non-prismatic beam element is an improvement and extension of the existing beam elements by considering shear and torsional effects of circular flexure hinge. The new consistent mass matrix formulation was derived using the Unit Load method. A parallel-guided compliant mechanism was taken as an example to validate the efficiency and accuracy of the proposed approach through static and modal analyses with fewer non-prismatic beam elements, and the results are well agreed with ANSYS simulation results with massive 3D solid or 2D shell elements. The developed approach is also available to model arbitrarily shaped flexure hinges in compliant mechanisms.     

Synthesis of multiple degrees-of-freedom spatial-motion compliant parallel mechanisms with desired stiffness and dynamics characteristics

This paper presents a new design method to synthesize multiple degrees-of-freedom (DOF) spatial-motion compliant parallel mechanisms (CPMs). Termed as the beam-based structural optimization approach, a novel curved-and-twisted (C-T) beam configuration is used as the basic design module to optimize the design parameters of the CPMs so as to achieve the targeted stiffness and dynamic characteristics. To derive well-defined fitness (objective) functions for the optimization algorithm, a new analytical approach is introduced to normalize the differences in the units, e.g., N/m or N m/rad, etc., for every component within the stiffness matrix. To evaluate the effectiveness of this design method, it was used to synthesize a 3-DOF spatial-motion (θ_x − θ_y − Z) CPM that delivers an optimized stiffness characteristics with a desired natural frequency of 100 Hz. A working prototype was developed and the experimental investigations show that the synthesized 3-DOF CPM can achieved a large workspace of 8°×8°×5.5 mm, high stiffness ratios, i.e., >200 for non-actuating over actuating stiffness, and a measured natural frequency of 84.4 Hz.     

空间弹性并联机器人KED建模

本文首次用有限元方法建立了一种空间６自由度并联机器人的弹性动力学模型,文中根据并联机器人的结构特点,设其平台为刚性体,各条腿为弹性体,再根据平台与腿部的运动协调方程推导出它的ＫＥＤ方程,已知机器人的刚体运动规律,由此方程可以求出其平台以及腿部各关节的弹性运动规律,最后给出了数值例。     

Accurate low DOF modeling of a planar compliant mechanism with flexure hinges: the equivalent beam methodology

A methodology for accurate and efficient finite elements method (FEM) simulations of planar compliant mechanisms with flexure hinges is presented. First, using symmetry/antisymmetry boundary conditions and 3D elements, one-eighth of a single hinge is simulated to determine its true stress/stiffness characteristics. A set of fictitious beams is derived, which have the identical characteristics. This set is used in conjunction with other beams that model relatively stiff links to generate an equivalent model of an entire mechanism consisting of the beam elements only. The model has a low number of degrees-of-freedom (DOF) and appears to be more accurate than any 2D FEM models, even those with very large number of DOF. The methodology has been developed specifically for the right circular flexure hinge; however, it can be applied to all types of revolute flexure hinges.     

一种二自由度并联机构设计及空间误差建模

设计了一种应用于大构件装配的二自由度并联平台机构,该机构可以实现平移运动、旋转运动及平移和旋转的复合运动,承载力大,运动平稳。为使所设计的平台具有高的定位精度,以多体系统理论为基础,根据并联平台实际情况,推导出并联平台的空间误差模型,为进一步研究并联平台的误差补偿方法和相应的仿真分析奠定了基础。     

新型三自由度并联机构工作空间分析

随着并联机构技术的发展,少自由度并联机构由于具有结构相对简单,控制容易等优点,逐步成为机构学领域新的研究热点,在工业领域有着广阔的应用前景。针对并联机构工作空间较小的特点,对一种新型三自由度并联机构进行研究。该机构的工作空间对称分布于定平台的两侧。在分析其结构特点的基础上,推导出其位置反解方程。根据约束条件,采用数值方法绘制出工作空间的三维立体图和Z截面上的边界图。并定量分析了机构设计参数对工作空间大小的影响。     

空间机械臂模拟系统的设计与实现

针对某科技馆的一个科普展品,设计了一种空间机械臂模拟系统。首先对空间机械臂各部分的结构和传动机构进行了设计,利用D—H坐标法建立了机械臂的运动学模型,并进行了其运动学正、反解的求解。然后,构建了空间机械臂的伺服控制系统,开发了上位工控机和底层运动控制器的控制软件。最后,使用Quest3D虚拟现实软件制作了VR机械臂。机械臂模拟系统的工作情况表明,该系统可以满足科普展品的要求。     

Motion capability analysis of a quadruped robot as a parallel manipulator

This paper presents the forward and inverse displacement analysis of a quadruped robot MANA as a parallel manipulator in quadruple stance phase, which is used to obtain the workspace and control the motion of the body. The robot MANA designed on the basis of the structure of quadruped mammal is able to not only walk and turn in the uneven terrain, but also accomplish various manipulating tasks as a parallel manipulator in quadruple stance phase. The latter will be the focus of this paper, however. For this purpose, the leg kinematics is primarily analyzed, which lays the foundation on the gait planning in terms of locomotion and body kinematics analysis as a parallel manipulator. When all four feet of the robot contact on the ground, by assuming there is no slipping at the feet, each contacting point is treated as a passive spherical joint and the kinematic model of parallel manipulator is established. The method for choosing six non-redundant actuated joints for the parallel manipulator from all twelve optional joints is elaborated. The inverse and forward displacement analysis of the parallel manipulator is carried out using the method of coordinate transformation. Finally, based on the inverse and forward kinematic model, two issues on obtaining the reachable workspace of parallel manipulator and planning the motion of the body are implemented and verified by ADAMS simulation.     

Geometric approach for kinematic analysis of a class of 2-DOF rotational parallel manipulators

Euler angles are commonly used as the orientation representation of most two degrees of freedom (2-DOF) rotational parallel mechanisms (RPMs),as a result,the coupling of two angle parameters leads to c...     

Reciprocal screw theory based singularity analysis of a novel 3-DOF parallel manipulator

Singularity analysis is an essential issue for the development and application of parallel manipulators.Most of the existing researches focus on the singularity of parallel manipulators are carried out based on the study of Jacobian matrices.A 3-DOF parallel manipulator with symmetrical structure is presented.The novel parallel manipulator employs only revolute joints and consists of four closed-loop subchains connecting to both base and platform via revolute joints.The closed-loop subchain in each chain-leg is a spherical 6R linkage.The motion characteristics of the output link in the spherical 6R linkage with symmetrical structure are analyzed based on the interrelationships between screw systems.The constraints that are exerted on the platform by each chain-leg are investigated applying the concept of generalized kinematic pair in terms of equivalent screw system.Considering the geometric characteristics of the parallel manipulator,the singularity criteria of the parallel manipulator corresponding to different configurations are revealed based on the dependency of screw system and line geometry.The existing conditions of certain configuration that a singularity must occur are determined.This paper presents a new way of singularity analysis based on disposition of constraint forces on the geometrically identified constraint plane and the proposed approach is capable of avoiding the complexity in solving the Jacobian matrices.     

并联机器人的工作空间研究现状

随着并联机器人成为机器人研究的主要研究热点,并联机构学理论的研究正经历着蓬勃发展,并联机器人的运动学、动力学及性能分析等方面的理论不断得到丰富.本文掌握的大量的有关性能分析中的工作空间的文献,对工作空间这一分支的研究现状做了深入分析.     

Manufacturing error analysis of compliant 3-DOF microrobot

In the fields of micro/nanopositioning application, error analysis is an effective way to enhance the precision of micromanipulators. Manufacturing imperfections, which are inevitable, are the most important factors influencing the accuracy. Therefore, various manufacturing imperfections were studied by taking a planar 3 degrees of freedom (3-DOF) flexure hinge-based microrobot as a case. By formulating static stiffness of the robot, mapping between manufacturing imperfections and end-effector positioning accuracy was obtained. Using the theoretical calculation and finite element method (FEM), effects of various machining imperfection types on end-effector positioning accuracy were evaluated. The results showed that errors of the radium of the hinges and angular differences of the centerline of the hinges were dominant factors resulting in output errors. Conclusions drawn from the experiments can be used to instruct the design of compliant parallel mechanisms by distributing various manufacturing differences of configurable parameters to guarantee precision in the positioning of the end-effector within the required range; they may also be helpful while calibrating this kind of manipulator. __________ Translated from Journal of Beijing University of Aeronautics and Astronautics, 2005, 31(7) (in Chinese)     

On the workspace of spatial parallel manipulator with multi-translational degrees of freedom

This paper presents a new simple but effective algebra-geometry methodology to investigate the workspace of spatial parallel manipulators based on the analysis of its degree of freedom (DoF). Through coordinate transformation, we depict the geometric relationships with a set of parameter equations, which should be widely adapted to address the workspace of spatial parallel manipulators with multi-translational DoF. We also point out that the workspace of certain spatial parallel manipulators can be large enough rather than very small for applications. This revised version was published online March 2005 with corrections to Figure 5.     

具有两个双轴柔性铰链的快速反射镜设计

为了改善快速反射镜(FSM)对车载运动平台振动、冲击环境的适应性,设计了一款具有中心和四周两个双轴柔性铰链支撑结构的FSM。在明确车载跟瞄发射系统应用需求的基础上,分别对FSM的平面反射镜、驱动元件、测角元件和柔性铰链进行了详细设计和选择。采用两两差分的方法对四通道电涡流传感器的测量噪声进行抑制,有效保证了FSM的测量精度。采用有限元分析的方法对中心和四周柔性铰链的模态和刚度进行分析与优化设计,有利保证了FSM控制带宽的提高。完成FSM的精密加工、装调后,对系统的指向精度、控制带宽和阶跃响应时间进行了实验测试分析。结果表明,所设计FSM的指向精度优于1″,闭环控制带宽大于200 Hz,阶跃响应时间约为10 ms,满足车载平台系统的应用需求。