机器人串联弹性关节驱动器的刚度控制方法

机器人关节的柔顺性在人机协作过程中具有重要作用，然而固定的关节柔性无法满足动态变化的人机协作需求，因此对机器人的关节驱动器提出了具有刚度调节能力的要求.本文采用阿基米德螺旋线平面涡卷弹簧作为机器人关节的柔性元件，并提出一种可用于具有固定刚度的串联弹性驱动器的刚度控制方法.根据关节刚度的定义，将测量得到的弹簧输出端角度用于计算弹簧的输入端转角，使得机器人关节驱动器的等效刚度可以被调整到所期望的大小.该方法以电机位置控制为内环，关节刚度控制为外环，简化了控制器设计，并实现了解耦控制.对所设计的刚度控制器进行了分析.最后在自主设计的单自由度薄型串联弹性驱动器实验平台上进行了刚度调节实验，包括刚度的双向阶跃、零刚度和正弦变化的刚度，实验结果表明关节等效刚度能准确跟踪期望值，验证了该方法的有效性.     

Minimal realizations of spatial stiffnesses with parallel or serial mechanisms having concurrent axes

This article presents a new method for the synthesis of an arbitrary spatial elastic behavior with an elastic mechanism. The mechanisms considered are parallel and serial mechanisms with concurrent axes. We show that any full‐rank spatial stiffness matrix can be realized using a parallel mechanism with all spring axes intersecting at a unique point. It is shown that this intersection point must be the center of stiffness. We also show that any full‐rank spatial compliance matrix can be realized using a serial mechanism with all joint axes intersecting at a unique point. This point is shown to be the center of compliance. Synthesis procedures for mechanisms with these properties are provided. The realizations are shown to be minimal in the sense that both the number of screw components and the total number of components are minimum. © 2001 John Wiley & Sons, Inc.     

Post-buckling of cylindrically orthotropic circular plates on elastic foundation with edges elastically restrained against rotation

The post-buckling behaviour of cylindrically orthotropic circular plates is investigated through a finite element formulation, with the plates resting on an elastic foundation and their edges are elastically restrained against rotation. Results are presented in the form of linear buckling load parameters and empirical formulae for radial load ratios for various values of spring stiffness, foundation stiffness and orthotropy parameter.     

Stiffness modeling of a soft finger

This paper presents the design and stiffness modeling of a new 3 DOF soft finger mechanism using a spring as a backbone. The mechanism consists of a spring and 3 cylinders, which behave like joints. To control each joint, wires of different length are penetrated into the cylinders which have small holes in their cross-sectional areas, and each joint can be controlled by pulling each wire. Also, the stiffness modeling is conducted to measure the softness of the finger mechanism as well as to estimate the actuator size. First, the forward kinematics is solved by using the geometry of mechanism, and length of wires and Jacobian are obtained. In order to evaluate the efficiency of the proposed mechanism, the position control, the flexibility and safety, and the stiffness model are verified through experimental work.     

Dynamic analysis and determination of the joint characteristics of parallel-drive robot manipulators

This article presents a theoretical and experimental study on structural dynamic response and determination of the joint characteristics of a five degree-of-freedom industrial robot manipulator with a parallel-drive mechanism. The joints were modeled as a linear spring in parallel with a viscous damper while the link members were assumed to be rigid in this study. The dynamic equations of motion of the robot manipulator were derived using the principle of virtual work. Based on these equations, the complex structural characteristics of the manipulator were simplified by carefully arranging the manipulator in proper arm configurations to avoid coupling effects among joints. Hence, the joint stiffness and damping ratio of each joint were determined experimentally. Meanwhile, the dynamic responses of the robot manipulator were also investigated. Good correlation between computer simulations and experimental results was achieved. From the experimental study, an additional troublesome flexural mode of about 10 Hz that tends to dominate the whole dynamic response and influence the positioning accuracy of the manipulator was found due to the weakness of the structural member at the base rotation joint, which was not modeled in the dynamic equations. The results of this study will be useful in providing a basis for improving the design of mechanical components and the articulating members of industrial robot manipulators.     

Optimal elastic coupling in form of one mechanical spring to improve energy efficiency of walking bipedal robots

This paper presents a method to optimize the energy efficiency of walking bipedal robots by more than 80 % in a speed range from 0.3 to 2.3 m/s using elastic couplings—mechanical springs with movement speed independent parameters. The considered planar robot consists of a trunk, two two-segmented legs, two actuators in the hip joints, two actuators in the knee joints and an elastic coupling between the shanks. It is modeled as underactuated system to make use of its natural dynamics and feedback controlled via input–output linearization. A numerical optimization of the joint angle trajectories as well as the elastic couplings is performed to minimize the average energy expenditure over the whole speed range. The elastic couplings increase the swing leg motion’s natural frequency thus making smaller steps more efficient which reduce the impact loss at the touchdown of the swing leg. The process of energy turnover is investigated in detail for the robot with and without elastic coupling between the shanks. Furthermore, the influences of the elastic couplings’ topology and of joint friction are analyzed. It is shown that the optimization of the robot’s motion and elastic coupling towards energy efficiency leads to a slightly slower convergence rate of the controller, yet no loss of stability, but a lower sensitivity with respect to disturbances. The optimal elastic coupling discovered via numerical optimization is a linear torsion spring with transmissions between the shanks. A design proposal for this elastic coupling—which does not affect the robot’s trunk and parallel shank motion and can be used to enhance an existing robot—is given for planar as well as spatial robots.     

Mechanical Design and Analysis of the Novel 6-DOF Variable Stiffness Robot Arm Based on Antagonistic Driven Joints

This paper proposes four types of conceptual models of the 6-DOF variable stiffness robot arms based on the antagonistic driven joints (ADJs). For convenience of control, the equivalent quadratic torsion spring (EQTS) is selected as the elastic element of the ADJ. The relationship between the output stiffness and the angular displacement of the EQTS is fairly linear. The elastic actuating torque of the ADJ is related to the initial amount of deformation of the EQTS and the angular deflection of the ADJ. The output stiffness of the ADJ is a linear function of the initial amount of deformation of the EQTS. The convenience control of the torque and stiffness of the ADJ will be beneficial to reduce the complexity of the control strategy, and this feature is beneficial for real-time control. In the mechanical solutions, nine types of conceptual models of the EQTSs are presented, and nine types of conceptual models of the ADJs are demonstrated. The cam parameters and the spring parameters of the EQTSs are given. The cam profiles and the pressure angles of the cam-roller mechanisms are illustrated. The elastic actuating torque and output stiffness of the EQTSs and the ADJs are shown. The structure features and actuation characteristics of the EQTSs and the ADJs are compared and analyzed. Since the actuation requirements of the joints of the robot arm differ significantly, four types of conceptual models of the 6-DOF robot arms are assembled based on the different ADJs.     

Cubical Mass-Spring Model design based on a tensile deformation test and nonlinear material model

Mass-Spring Models (MSMs) are used to simulate the mechanical behavior of deformable bodies such as soft tissues in medical applications. Although they are fast to compute, they lack accuracy and their design remains still a great challenge. The major difficulties in building realistic MSMs lie on the spring stiffness estimation and the topology identification. In this work, the mechanical behavior of MSMs under tensile loads is analyzed before studying the spring stiffness estimation. In particular, the performed qualitative and quantitative analysis of the behavior of cubical MSMs shows that they have a nonlinear response similar to hyperelastic material models. According to this behavior, a new method for spring stiffness estimation valid for linear and nonlinear material models is proposed. This method adjusts the stress-strain and compressibility curves to a given reference behavior. The accuracy of the MSMs designed with this method is tested taking as reference some soft-tissue simulations based on nonlinear Finite Element Method (FEM). The obtained results show that MSMs can be designed to realistically model the behavior of hyperelastic materials such as soft tissues and can become an interesting alternative to other approaches such as nonlinear FEM.     

MACCEPA 2.0: compliant actuator used for energy efficient hopping robot Chobino1D

The MACCEPA (Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator) is an electric actuator of which the compliance and equilibrium position are fully independently controllable and both are set by two dedicated servomotor. In this paper an improvement of the actuator is proposed where the torque-angle curve and consequently the stiffness-angle curve can be modified by choosing an appropriate shape of a profile disk, which replaces the lever arm of the original design. The actuator has a large joint angle, torque and stiffness range and these properties can be made beneficial for safe human robot interaction and the construction of energy efficient walking, hopping and running robots. The benefit of the ability to store and release energy is shown by the 1DOF hopping robot Chobino1D. The achieved hopping height is much higher compared to a configuration in which the same motor is used without a series elastic element. The stiffness of the actuator increases with deflection, more closely resembling the properties shown by elastic tissue in humans.     

Application of genetic algorithm in crack detection of beam-like structures using a new cracked Euler–Bernoulli beam element

In this paper, a crack identification approach is presented for detecting crack depth and location in beam-like structures. For this purpose, a new beam element with a single transverse edge crack, in arbitrary position of beam element with any depth, is developed. The crack is not physically modeled within the element, but its effect on the local flexibility of the element is considered by the modification of the element stiffness as a function of crack's depth and position. The development is based on a simplified model, where each crack is substituted by a corresponding linear rotational spring, connecting two adjacent elastic parts. The localized spring may be represented based on linear fracture mechanics theory. The components of the stiffness matrix for the cracked element are derived using the conjugate beam concept and Betti's theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain accurate natural frequencies of beam-like structures knowing the cracks’ characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results as well as available experimental measurements. Moreover, by knowing the natural frequencies, an inverse problem is established in which the cracks location and depth are identified. In the inverse approach, an optimization problem based on the new beam element and genetic algorithms (GAs) is solved to search the solution. The proposed approach is verified through various examples on cracked beams with different damage scenarios. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam.     

A numerical approach to define the rotational stiffness of a prefabricated connection and experimental study

A numerical approach is proposed to define the elastic rotational stiffness of a typical joint on the top beam of a prefabricated reinforced concrete gable frame structure. The 12 degrees of freedom triangular plane stress finite element is used to examine the connection region. Using this joint rotational stiffness value, realistic results are obtained in the frame analysis. The experimental verification is performed by means of the photoelastic method. Following the proposed method, an effective joint length with reduced moment of inertia is defined and using this concept the frame solution is simply achieved, including the existence of joint.     

Dynamics and control of a MEMS angle measuring gyroscope

This paper presents an algorithm for controlling vibratory MEMS gyroscopes so that they can directly measure the rotation angle without integration of the angular rate, thus eliminating the accumulation of numerical integration errors incurred in obtaining the angle from the angular rate. The proposed control algorithm consists of a weighted energy control and a mode tuning control. The weighed energy control compensates unequal damping terms and keeps the amplitude of oscillation constant in an inertial frame by maintaining the prescribed total energy. The mode tuning control continuously tunes mismatches in spring stiffness in order to maintain a straight line of oscillation for the proof mass. The simulation results demonstrate the feasibility of the control algorithm and the viability of the concept of using a vibratory gyroscope to directly measure rotation angle.     

Elastic analysis of frames considering panel zones deformations

Structural analysis of frames is generally based on centreline-to-centreline geometry. However in many structures, member dimensions might be quite large and have a significant effect on frame lateral stiffness. Rigid offsets extending from the joint centrelines to the faces of the members are used to model the rigid rotation kinematic of finite joint area. This approach can underestimate drifts of structures since it neglects elastic deformations of the joint regions. In this paper, a joint element is used to consider the rigid kinematic motion, elastic shear, and bending deformations of beam-column panel zone regions. Parametric analyses have been carried out on the seismic response of a ten-storey steel frame to determine the impact of panel zone deformations on the structure's elastic response. It is shown that kinematic effects and panel zone shear deformations are best modelled using rigid zone reduction factors to define rigid offset effective lengths. On the other hand, the consideration of panel zone bending deformations resulted in drifts values that were significantly larger than the usual rigid point joint assumption.     

Numerical Solution Framework of Kinematics for a Tendon-Driven Manipulator Equipped with Cylindrical Elastic Elements

To date, many hardware devices to control joint stiffness have been proposed for tendon-driven manipulators. However, the earlier devices presented some problems such as complex structures, increase of friction, increase of inertia, etc. To overcome these problems, we propose the cylindrical elastic element (CEE) to vary the joint stiffness by changing the internal force among wires. By inserting the CEEs into routes of wires, the joint stiffness of a tendon-driven manipulator can be changed depending on the internal force. However, it is difficult to obtain the kinematics because of the complexity of a CEE's deformation. Since a finite element method usually requires much time to calculate, the establishment of a simple CEE model is very important to solve the kinematics. This paper presents a numerical framework to approximately solve the kinematics of a one-link manipulator equipped with two CEEs. First, we propose some approximate models of a CEE and evaluate them. Using the most useful model, we then demonstrate a numerical solving method of the forward kinematics. Next, expanding this solving method, we also provide the inverse kinematics. The precision of the proposed methods is discussed through comparison of experimental results with numerical results.     

Development of a linear vibration motor with fast response time for mobile phones

This research investigated the magnetic and mechanical characteristics of a linear actuator by using structural and magnetic finite element analyses as well as experimental verification. The response time to reach the steady state of vibration was investigated through the equivalent mass–spring–damper system of the linear actuator. The response time can be reduced by increasing the magnetic force or by decreasing the mass. In the case of decreasing the mass, the spring constant should also be decreased in order to maintain the same natural frequency. However, reduction of both the mass and stiffness decreases the vibration magnitude because it is proportional to the spring constant. The results show that the ideal method to reduce response time without decreasing vibration magnitude is to increase magnetic force. Finally, this research proposes a novel design of a linear actuator with a large magnetic force to reduce the response time.     

Large deflection analysis of plates and shells by discrete energy method

The discrete energy method—a special form of finite difference energy approach—is presented as a suitable alternative to the finite element method for the large deflection elastic analysis of plates and shallow shells of constant thickness. Strain displacement relations are derived for the calculation of various linear and nonlinear element stiffness matrices for two types of elements into which the structure is discretized for considering separately energy due to extension and bending and energy due to shear and twisting. Large deflection analyses of plates with various edge and loading conditions and of a shallow cylindrical shell are carried out using the proposed method and the results compared with finite element solutions. The computational efforts required are also indicated.     

空间机器人双臂捕获卫星操作的事件采样输出反馈神经网络避撞柔顺控制

讨论漂浮基空间机器人双臂捕获非合作卫星过程避免关节冲击破坏的避撞柔顺控制问题,提出在机械臂与关节电机之间加入一种旋转型串联弹性执行器(rotatory series elastic actuator,RSEA)作为柔顺缓冲机构,其作用在于:1)捕获碰撞过程,通过其内置弹簧的拉伸或压缩吸收捕获操作过程中被捕获卫星对空间机器人关节产生的冲击能量;2)捕获完成后的镇定过程,利用设计与之配合的避撞柔顺控制策略保证关节冲击力矩限制在安全范围.利用第二类拉格朗日方程推导得到捕获操作前含柔顺机构双臂空间机器人系统及目标卫星的各分体系统动力学模型;基于系统动量守恒关系、系统运动几何关系及牛顿第三定律,得到捕获操作后双臂空间机器人与被捕获卫星混合体系统综合动力学方程;针对捕获操作后受碰撞影响而产生不稳定运动的混合体系统,提出一种基于事件采样输出反馈的RBF神经网络避撞柔顺控制方案.上述方案与柔顺机构相结合不仅能有效吸收被捕获卫星的冲击能量,还能在冲击能量过大时应时开、关双臂空间机器人关节电机,以防止关节电机发生过载和破坏.通过李雅普诺夫稳定性理论证明系统的全局稳定性,并通过仿真结果验证所提避撞柔顺控制方案的有效性.     

A novel variable stiffness scotch yoke series elastic actuator for enhanced functional stiffness

This paper presents a new design and modeling of a novel variable stiffness scotch yoke series elastic actuator (VSY-SEA) mechanism that can achieve variable stiffness values with a linear relationship between torque and displacement. The main goal of this study was to design the yoke’s shape in the scotch yoke mechanism for a system with the desired stiffness. The word “variable” in VSY-SEA does not simply mean that the system has different random stiffness, but rather that the system has the stiffness of the functional form desired by the designer. Yoke shapes in the scotch-yoke mechanism were designed by calculating the relationship between external torque and rotation angle of VSY-SEA, and the simulations were performed using CAD models with various yoke designs. A prototype of the model was built and the calculations were verified through experiments.

     

Stiffness Design of Springs for a Screw Drive In-Pipe Robot to Pass through Curved Pipes and Vertical Straight Pipes

Various in-pipe robots used for inspection have been developed as a preventive measure against leakage. To expand the use of these robots in small pipelines, high environmental adaptability via a simple structure must be achieved. One solution, using the screw drive mechanism, has been focused on because it requires only one motor. However, the screw drive mechanism cannot achieve complex motion because of its 1-d.o.f. Therefore, existing screw drive in-pipe robots cannot pass through curved pipes with a small curvature radius. To overcome this problem, the kinematic analysis of the screw drive mechanism has been conducted on the basis of the basic principle of helical motion in curved pipes. From the analysis, the relationship among the spring stiffness, motor torque, robot length and static friction on the inner pipe wall is established for the design of stiffness of the supporting springs. The optimal spring stiffness is, thus, derived for the robot to pass through the curved pipe and to climb up in the vertical pipe. The experimental test has been used to verify the validity of the design.     

Stability of columns subjected to a uniformly distributed load with one end elastically restrained to move axially

The stability behaviour of columns, subjected to a uniformly distributed axial load and with one end elastically restrained to move axially, is studied in this paper. The elastic axial restraint is represented by means of an axial spring. The finite element formulation, including prebuckling load analysis and stability analysis, is briefly described. Numerical results in terms of stability parameter for various values of axial spring stiffness parameter for four types of boundary conditions are obtained. Stability mode shapes for three specific values of axial spring stiffness parameter are given.