Pseudo-rigid-body model for corrugated cantilever beam used in compliant mechanisms

Common compliant joints generally have limited range of motion, reduced fatigue life and high stress concentration. To overcome these shortcomings, periodically corrugated cantilever beam is applied to design compliant joints. Basic corrugated beam unit is modeled by using pseudo-rigid-body method. The trajectory and deformation behavior of periodically corrugated cantilever beam are estimated by the transformation of coordinate and superposition of the deformation of corrugated beam units. Finite element analysis（FEA） is carried out on corrugated cantilever beam to estimate the accuracy of the pseudo-rigid-body model. Results show that the kinetostatic behaviors obtained by this method, which has a relative error less than 6%, has good applicability and corrugated cantilever beam has the characteristics of a large range of motion and high mechanical strength. The corrugated cantilever beam is then applied to design a flexible rotational joint to obtain a larger angle output. The paper proposes a pseudo-rigid-body model for corrugated cantilever beam and designed a flexible rotational joint with large angle output.     

Compliant thin-walled joint based on zygoptera nonlinear geometry

This paper introduces a Compliant thin-walled joint (CTWJ) that expands the group of existing compliant joints. The CTWJ design is based on the nonlinear geometry of the zygoptera animal. With a thin-walled structure, the CTWJ allows a considerably large range of motion in the x-and-y axes. In addition, the thin-walled structure is then filled by polydimethylsiloxane material to reinforce the stiffness of the CTWJ. First, design of experiment methodology is used for the sensitive analysis of the width and the thickness to the strain of joint. The range of motion, the strain, the buckling behavior, and the first natural frequency of CTWJ are investigated via finite element analysis and experiments. The behavior of the CTWJ is subsequently compared with the conventional compliant joints to realize the efficient performance of the CTWJ. The results revealed that the CTWJ has a range of motion and strain energy larger than those of traditional compliant joints. Finally, an example of vibration isolator is modeled by using the CTWJ as planar spring. It is believed that the CTWJ has a great potential for the development of compliant mechanisms in terms of large range of motions in mutliple axes.

     

Compound joints: Behavior and benefits of flexure arrays

Because compliant mechanisms achieve their motion through deflection of flexible members, they have a limited range of motion and finite stiffness. Many common flexure geometries also suffer from a non-stationary center of rotation. These properties can be obstacles to their adoption in applications that require large displacements, low stiffness, or stationary centers of rotation. This work presents the concept of compound flexures: by assembling arrays of flexures, we can increase range of motion, decrease stiffness, and reduce center shift. We first develop the theory behind some of the basic behavior of compound joints. Then finite element analysis is used to explore other aspects of compound joint behavior such as off-axis stiffness and quantifying the center shift for two flexure types when used in compound joints of various configurations. It is shown in an example that range of motion can be doubled with no appreciable loss in off-axis stiffness, while the desired stiffness κ_θz remains unchanged. A method is presented to achieve zero center shift for a specified rotational displacement. Compound joints are shown to exhibit greater ranges of motion, higher off-axis stiffness, and reduced center shift compared to traditional joints.     

绳索驱动式变刚度关节柔顺控制与力补偿方法研究

机器人柔顺运动有助于提高机器人交互运动时的安全性与稳定性,越来越受到人们的重视。针对一种绳索驱动式具有主被动柔顺性的柔性机器人关节,提出一种适用于绳索驱动式变刚度关节的刚度与位置解耦控制方式,实现了关节位置控制的同时,又实现了关节柔顺性的统一。利用雅可比矩阵和模型间静力学关系,得到关节刚度模型,并通过优化方法对变刚度装置的力学模型和刚度模型构成的非线性方程组求解,实现变刚度关节刚度与位置的非线性解耦。在解耦控制基础上提出一种力矩观测方法,实现了关节力矩补偿,增强了关节位置控制能力;建立了绳索驱动式变刚度关节样机和控制系统,并通过仿真和实验分析的方式验证了所提柔顺控制方式的可行性和有效性。     

基于伪刚体模型法的全柔性机构位置分析

柔性机构是一种依靠构件元素的弹性变形传输所希望运动的机构。具有集中柔度的全柔性机构是其中的一种类型，其特征是机构中传统形式的铰链全部被柔性铰链所代替。对它的研究，近年来也已成为一个热点。为探索这类全柔性机构的运动学问题，首先建立起柔性铰链变形刚度模型。在此基础上，提出了一种扩展的伪刚体模型法，很好地解决了机构的位置正、反解问题。     

Lamina Emergent Torsional (LET) Joint

Part of the challenge in designing compliant mechanisms is finding suitable joints that provide the needed motion and force–deflection characteristics. The Lamina Emergent Torsional (LET) Joint is presented as a compliant joint suited for applications where large angular rotation is desired, but high off-axis stiffness is not as critical. The joint is introduced and the equations necessary for determining the force–deflection characteristics are presented. Since the LET Joint can be fabricated from a single planar layer, it is well suited for macro and micro applications. Illustrative examples are provided with devices fabricated from materials as diverse as steel, polypropylene, and polycrystalline silicon.     

A compliant end-effector for microscribing

A new end-effector was designed and built for microscribing processes using principles of compliant mechanisms. Initial testing of a chemomechanical microscribing process showed that low forces produce lines that are significantly smoother, more uniform, and exhibit less material chipping. From the testing it is apparent that there is a need for a specialized precision end-effector that (1) is passively controlled, (2) has low axial stiffness, and (3) has high lateral stiffness. To meet these needs a three segment folded-beam compliant mechanism was chosen. This design is passively controlled, has a high axial/lateral stiffness ratio, is ideal for clean sensitive applications, and can be designed for a range of low forces. The axial stiffness of the end-effector was modeled using both the compliant mechanism pseudo-rigid body model and linear-elastic beam theory. The lateral stiffness was modeled using FEA techniques. Ratios of lateral stiffness to axial stiffness were found to be nearly 1000:1. A fatigue analysis was also performed and it was determined that the mechanism could reach approximately 1 billion cycles before failure. The compliant end-effector design is a significant improvement over existing scribing alternatives and can produce smooth and uniform scribed lines that exhibit less material chipping.     

滚动接触柔性连续体机器人的设计与运动能力分析

针对航空原位检修领域对机器人在复杂、狭小空间的作业需求,基于滚动接触原理设计了一种新型的柔性连续体机器人,解决了连续体机器人轴向刚度需求与运动柔顺性之间的矛盾。对连续体机器人单元柔性关节和整体系统进行了详细分析,根据机器人的冗余自由度特点设计了主动运动与被动运动两种运动策略。对机器人单元关节的力学仿真结果表明,该柔性关节转动刚度适宜,轴向刚度较大。机器人长600 mm,最大弯曲角度大于360°,最小弯曲半径40 mm;实验结果表明该机器人运动柔顺,具备良好的环境自适应能力。     

一种旋转型机器人柔性关节设计与分析

通过对人类膝关节柔性产生机理研究,仿照动物关节肌肉-肌腱组织设计出一种适用于电机驱动的旋转型柔性关节。通过研究对比旋转型SEA（series elastic actuator）与直线型SEA机构特点,提出一种由8个压缩弹簧协同组成的柔性输出机构,并建立柔性输出机构刚度模型,确立了弹性元件参数与柔性关节等效刚度的数学关系。在此基础上,对柔性关节整体进行紧凑化设计,电机、减速器、柔性输出机构集中安装于关节部位,使柔性关节模块化、通用性强。通过对该柔性关节软件仿真及关节样机测试,验证了关节抗冲击能力和柔性输出能力可以满足柔性关节型机器人对柔性关节的应用需求。     

基于多刚体离散元模型的柔顺机构动力分析新方法

柔顺机构是部分或者全部由其构件的预期弹性变形来传递运动和力,这使得构件的弹性变形一般都较大。它的分析一般属于几何非线性问题。基于弹性体的多刚体离散元模型,研究了柔顺段和柔顺机构的多刚体离散元建模方法,推导了柔顺机构系统的一般控制方程,该方程可以解决柔顺机构的特征频率和几何非线性变形问题。并给出了算例,计算结果表明多刚体离散元方法能较好解决柔顺机构的几何非线性静力学和动力学分析。     

A novel flexure beam module with low stiffness loss in compliant mechanisms

Flexure mechanisms provide guided motion via elastic deformation of thin beams. Due to the employment of compliant elements, these mechanisms cannot sufficiently maintain acceptable constraint stiffness level in the entire range of motion. The stiffness deterioration afflicts the performance of flexure mechanisms in terms of motion range, accuracy and constraint characteristics. This paper presents a novel flexure beam module with improved constraint behavior in beam-based flexure mechanisms. The proposed module alleviates the problem of stiffness loss in large displacements and provides a better motion performance. The mathematical model governing the static behavior of the module is developed using the principle of virtual work. The geometric nonlinearity associated with large midplane stretching is taken into account. Closed-form solutions are derived for load-displacement relationships, providing a powerful design tool for the novel flexure. Also a nonlinear expression is obtained for the strain energy of the flexure in terms of end displacements. The functionality of the presented module is exploited in a multi-beam parallelogram mechanism. The constraint behavior of the parallelogram is analytically quantified and considerable improvements in stiffnesses and error motions are observed. The analytical results provided in this paper are verified via finite element simulations. The proposed novel module can be used as the building block of more complex flexures to improve their stiffness characteristics, diminish their error motions and widen their stability region.     

Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the crosssection(i.e., the thickness and the width). After reviewing the available equations, two thickness-to-width ratio Independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design Insights are obtained. These equations, together with the previous work on symmetric equations for calculating torsional compliance, provide a convenient and effective way for designing and optimizing torsional beams in compliant mechanisms.     

具有零刚度特性的微动平台优化设计

针对传统常力机构存在的运动副间隙、装配误差和摩擦磨损等问题,设计了一种基于柔顺机构的常力微动平台。平台利用直梁正刚度和双稳态梁屈曲行为产生负刚度来实现其零刚度特性。平台由对称的直梁、双稳态梁和刚性连接块组成,直梁和双稳态梁通过连接块并联连接。采用伪刚体法和椭圆积分法相结合的建模方法,建立反映常力平台力学性能的理论模型。通过与有限元分析结果进行比较,分析结果显示所建立的模型能准确反映常力平台的力学性能。基于所建立的力学模型,提出一种提高平台常力运动范围和承载能力的优化设计方法。制作样机对该平台力学性能进行实验测试,实验结果表明,平台能在输出位移范围为[0.6~1.7]mm内能够保持约48N常力,证明了常力平台设计思路的可行性、所建模型的准确性和优化方法的有效性。     

Dynamic optimization of robot arm based on flexible multi-body model

This paper examines the effect mechanism of torsional stiffness on flexible joints and the dynamic optimization of a six Degree-of-freedom industrial robot arm. The design optimization of the robot arm is investigated based on the rotor-torsional spring model and finite element method. The flexible multi-body dynamic model of the robot arm are established by considering the flexible characteristics of arms and joints, and the natural frequencies of a robot arm are calculated to obtain the torsional stiffness of the flexible joints. Natural frequency results gradually increased with joint stiffness improvement. Using the established dynamic model, the topology optimization on the robot arm is carried out by regarding lightweight as design goal and total displacement as constraints. The tare-load ratio and dynamic performance of the optimized robot arm are significantly enhanced compared with the original design model. This research can provide the theoretical basis for the dynamic optimization and upgrade of lightweight robot arm.     

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.     

Design of compliant straight-line mechanisms using flexural joints

Straight-line compliant mechanisms are important building blocks to design a linear-motion stage, which is very useful in precision applications. However, only a few configurations of straight-line compliant mechanisms are applicable. To construct more kinds of them, an approach to design large-displacement straight-line flexural mechanisms with rotational flexural joints is proposed, which is based on a viewpoint that the straight-line motion is regarded as a compromise of rigid and compliant parasitic motion of a rotational flexural joint. An analytical design method based on the Taylor series expansion is proposed to quickly obtain an approximate solution. To illustrate and verify the proposed method, two kinds of flexural joints, cross-axis hinge and leaf-type isosceles-trapezoidal flexural（LITF） pivot are used to reconstruct straight-line flexural mechanisms. Their performances are obtained by analytic and FEA method respectively. The comparisons of the results show the accuracy of the approach. Both examples show that the proposed approach can convert a large-deflection flexural joint into approximate straight-line mechanism with a high linearity that is higher than 5 000 within 5 man displacement. This can lead to a new way to design, analyze or optimize straight-line flexure mechanisms.     

Integrating mechanism synthesis and topological optimization technique for stiffness-oriented design of a three degrees-of-freedom flexure-based parallel mechanism

This paper introduces a new design approach to synthesize multiple degrees-of-freedom (DOF) flexure-based parallel mechanism (FPM). Termed as an integrated design approach, it is a systematic design methodology, which integrates both classical mechanism synthesis and modern topology optimization technique, to deliver an optimized multi-DOF FPM. This design approach is separated into two levels. At sub-chain level, a novel topology optimization technique, which uses the classical linkage mechanisms as DNA seeds, is used to synthesize the compliant joints or limbs. At configuration level, the optimal compliant joints are used to form the parallel limbs of the multi-DOF FPM and another stage of optimization was conducted to determine the optimal space distribution between these compliant joints so as to generate a multi-DOF FPM with optimized stiffness characteristic. In this paper, the design of a 3-DOF planar motion FPM was used to demonstrate the effectiveness and accuracy of this proposed design approach.     

空间机器人捕获航天器操作的避撞柔顺无源神经网络H∞控制

研究了空间机器人在轨捕获非合作航天器过程避免关节受冲击破坏的避撞柔顺控制问题。为此在关节电机与机械臂之间配置了一种柔顺机构--旋转型串联弹性执行器(RSEA),可通过其内置弹簧的变形来吸收捕获过程目标航天器对空间机器人关节产生的冲击能量;结合所设计的开、关机控制策略可保证关节冲击力矩受限在安全范围内。首先利用拉格朗日方法及牛顿-欧拉法分别获得了捕获前空间机器人及目标航天器的分体系统动力学模型;之后,结合冲量定理、系统运动几何关系及力的传递规律,建立了捕获后两者形成混合体系统的动力学模型,并计算了碰撞过程的冲击力矩;最后,基于无源性理论提出了一种神经网络鲁棒H∞避撞柔顺控制策略以实现失稳混合体的镇定控制。数值仿真结果表明,配置柔顺空间机器人在捕获碰撞阶段最大可减小61.9%的关节冲击力矩,最小也可减小47.8%;而在镇定运动阶段,各关节冲击力矩均受限在安全范围内,实现了对关节有效地保护。     

Complete dynamic modeling and approximate state space equations of the flexible link manipulator

This work treats the problem of dynamic modeling and state space approximation for robotic manipulators with flexibility. Case studies are planar manipulators with a single flexible link together with clamped-free ends and tip mass conditions. In this paper, complete dynamic modeling of the flexible beam without premature linearization in the formulation of the dynamics equations is developed, whereby this model is capable of reproducing nonlinear dynamic effects, such as the beam stiffening due to the centrifugal and the Coriolis forces induced by rotation of the joints, giving it the capability to predict reliable dynamic behavior. On the other hand, in order to show the joint flexibility effects on the model dynamic behaviors, manipulator with structural and joint flexibility is considered. Thus, a reliable model for flexible beam is then presented. The model is founded on two basic assumptions: inextensibility of the neutral fiber and moderate rotations of the cross sections in order to account for the foreshortening of the beam due to bending. To achieve flexible manipulator control, the standard form of state space equations for a flexible manipulator system (flexible link and actuator) is very important. In this study, finite difference method for discretization of the dynamic equations is used and the state space equations of the flexible link with tip mass considering complete dynamic of the system are obtained. Simulation results indicated substantial improvements on dynamic behavior and it is shown that the joint flexibility has a considerable effect on the dynamic behavior of rotating flexible arm that should not be simply neglected. The effects of tip mass is proved to be increasing the elastic deformations?? amplitudes and increasing stability.     

A new type of spherical flexure joint based on tetrahedron elements

In this paper we present two new designs of spherical flexure joints, which are the compliant equivalent of a traditional ball-and-socket joint. The designs are formed by tetrahedron-shaped elements, each composed of three blade flexures with a trapezoidal shape, that are connected in series without intermediate bodies. This is new with respect to the designs currently found in literature and helps to increase the range of motion. We also present two planar (x-y-${\theta }_z$) flexure joint designs which were derived as special versions of the spherical designs. In these designs the tetrahedron elements have degenerated to a triangular prisms. For detailed investigation we developed equivalent representations of the tetrahedron and triangular prism elements and proved that three of the four constraint stiffness terms depend solely on the properties of the main blade flexure. Furthermore, we derived equations for these stiffness terms which are compared to finite-element simulations, showing a good correspondence for the prism element with a Normalized Mean Absolute Error (NMAE) of 1.9%. For the tetrahedron element, the equations showed to only capture the qualitative behaviour with a NMAE of 34.9%. Also, we derived an equation for the optimal width of the prism element regarding rotational stiffness.