Motion analysis of a tripod parallel mechanism

A tripod parallel mechanism consists of three links of fixed length and a rigid platform, and these are connected by revolute joints. The platform can achieve sixdegrees-of-freedom (6-DOF) motion by the coordinated movement of the bottom ends of the three links on a horizontal plane. This mechanism has advantages over the more common six extendible parallel manipulators. It has a much larger work space and a simple structure. In this article, we show that the vector analysis for this tripod parallel mechanism and the derivation of the positions of the three bottom ends of the links in an arbitrary attitude of platform can be found by inverse kinematics and the conditions of geometrical constraint. Then, by a numerical simulation, the trajectories of the bottom ends of the three links are shown.     

Solution of forward kinematics in Stewart platform using six rotary sensors on joints of three legs

A novel method is proposed for real-time solution of direct kinematics problem of Stewart platform (SP) using six measurements on three legs’ joints consisting of the rotations of three legs in two directions. After the application of the method on a laboratory sample SP, it is observed that the method is preferable to the conventional method that uses the length measurements of all six legs, in the grounds of industrial applicability. It is due to simpler implementation, less expense, easier maintenance, and stress-free assembly. The algorithms of both forward and inverse kinematics are fully derived based on geometric relationships between the platform states and the measurement data. The sensitivity to the measurement errors is analyzed theoretically and is applied through a computer simulation to several configurations of the sample SP which are uniformly distributed in the workspace. The variances of measurement errors for those configurations are compared between the conventional and proposed methods and it is observed that: the proposed method operates more accurate in position measurement especially in lateral movements. Additionally, the proposed method is not too sensitive to direction of movement and geometry of the SP.     

Kinematic analysis of the 3-CUP parallel mechanism

This paper investigates the kinematics of a parallel mechanism that is composed of three identical CUP legs evenly distributed on the fixed base. The platform of the mechanism has three degrees-of-freedom, namely: two rotations and one translation along the axis perpendicular to the base. The paper obtains closed form solutions for the inverse and forward kinematics problems. Furthermore, the Jacobian matrix is determined in order to solve the instantaneous kinematics analysis. It is used for the identification of the singular configurations of the mechanism, which are investigated by applying screw theory. The parasitic motions of the platform are determined by means of a workspace analysis. This paper uses several simulations and numerical examples to prove the accuracy of the analytical results.     

Kinematic design of a 6-DOF parallel manipulator with decoupled translation and rotation

A new three-limb, six-degree-of-freedom (DOF) parallel manipulator (PM), termed a selectively actuated PM (SA-PM), is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion, depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture completely decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. Singularity analysis shows that the SA-PM is an isotropic translation PM when all the actuators are in linear mode. Because of the decoupled motion structure, a decomposition method is applied for both the displacement analysis and dimension optimization. With the index of maximal workspace satisfying given global conditioning requirements, the geometrical parameters are optimized. As a result, the translational workspace is a cube, and the orientation workspace is nearly unlimited.     

Stiffness analysis of hexaslide machine tools

This paper presents stiffness analysis of hexaslides, a class of parallel manipulators with six constant length legs, the base joints of which move along six distinct rail-axes. In the design of hexaslides for machine tool applications, stiffness as well as its variation within the workspace is important. The stiffness of any parallel kinematic machine and, thus, the accuracy depends on the pose of the tool platform. A stiffness model of a generic hexaslide is developed here considering the flexibilities in both the actuator and the legs of the hexaslide. The methodology adopted is based on the concept of the determination of stiffness of a group of serially connected linear springs. Based on the proposed model, the average stiffness and its variation along and about the Cartesian coordinate axes offered by three typical hexaslides, having the same foot print size, are estimated and compared. Other typical performance indices, i.e. workspace volume, workspace volume index (ratio of workspace volume to machine size), global dexterity index and global stiffness index, are also compared.     

飞行模拟器的结构设计与仿真研究

飞行模拟器具有真实飞行训练无法比拟的优势,其结构设计是优化飞机设计,改善飞行性能的关键问题,故飞行模拟器的建模与仿真研究工作是飞行器设计的难点。通过与液压缸驱动的六自由度飞行模拟器对比分析,以3-RPS机构为基础,以在UG环境下建立的电动缸驱动的三自由度飞行模拟器运动平台模型为研究对象,在ADAMS/View模块下,对其添加约束和驱动后,进行了运动学特性仿真。对于给定的运动学特性曲线,运用ADAMS/Post Processor模块,对测量结果进行后处理,得到各种飞行姿态下的运动学曲线。仿真实验结果验证了该设计可实现升降、横滚、俯仰三种姿态的运动,且符合民航飞行模拟器的技术指标要求。上述分析过程为飞行模拟器的设计提供了一套有效的研究方法。     

Inverse Kinematics and Workspace Analysis of a 3 DOF Flexible Parallel Humanoid Neck Robot

To mimic the human neck’s three degree-of-freedom (DOF) rotation motion, we present a novel bio-inspired cable driven parallel robot with a flexible spine. Although there exists many parallel robotic platform that can mimic the human neck motion, most of them have only two DOF, with the yaw motion being actuated separately. The presented flexible parallel humanoid neck robot employs a column compression spring as the main body of cervical vertebra and four cables as neck muscles to connect the base and moving platform. The pitch and roll movements of moving platform are realized by the two dimensional lateral bending motion of the flexible spring, and a bearing located at the top of the compression spring and embedded in the moving platform is used to achieve the yaw motion of the moving platform. By combing the force and torque balance equations with the lateral bending statics of the spring, inverse kinematics and optimizing the cable placements to minimize the actuating cable force are investigated. Moreover, the translational workspace corresponding to pitch and roll movements and rotational workspace corresponding to yaw movement are analyzed with positive cable tension constraint. Extensive simulations were performed and demonstrated the feasibility and effectiveness of the proposed inverse kinematics and workspace analysis of the novel 3 DOF flexible parallel humanoid neck robot.     

基于MATLAB的某型机器人运动学可视化仿真平台实现

针对六自由度机器人关节运动强耦合难分析的问题,开发了可视化机器人仿真、平台.该平台以KLD 600型六自由度教学机器人为研究对象,利用MATLAB集成仿真环境,分别实现了机器人正逆运动学计算、机器人点动和联动操作的动画田演示等功能,且所有功能以图形用户界面的形式进行调用.该仿真、平台可作为机器人教学和科研的仿真工具.     

Dynamics of the spherical 3- \mathit{U\underline{P}S/}S parallel mechanism with prismatic actuators

Recursive relations in kinematics and dynamics of the symmetric spherical 3- parallel mechanism having three prismatic actuators are established in this paper. Controlled by three forces, the parallel manipulator is a 3-DOF mechanical system with three parallel legs connecting to the moving platform. Knowing the position and the rotation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity, and acceleration of each manipulator’s link. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work, but it has been verified using the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input forces and powers are obtained.     

Inverse dynamics of the 3-PRR planar parallel robot

Recursive modelling for the kinematics and dynamics of the known 3-PRR planar parallel robot is established in this paper. Three identical planar legs connecting to the moving platform are located in a vertical plane. Knowing the motion of the platform, we develop first the inverse kinematics and determine the positions, velocities and accelerations of the robot. Further, the principle of virtual work is used in the inverse dynamics problem. Several matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two different actuation schemes: prismatic actuators and revolute actuators. For the same evolution of the moving platform in the vertical plane, the power distribution upon the three actuators depends on the actuating configuration, but the total power absorbed by the set of three actuators is the same, at any instant, for both driving systems. The study of the dynamics of the parallel mechanisms is done mainly to solve successfully the control of the motion of such robotic systems.     

New Architecture of a Hybrid Two-Fingered Micro–Nano Manipulator Hand: Optimization and Design

This paper presents the synthesis and design optimization of a compact and yet economical hybrid two-fingered micro–nano manipulator hand. The proposed manipulator hand consists of two series modules, i.e., an upper and lower modules. Each of them consists of a parallel kinematics chain with a glass pipette (1 mm diameter and 3–10 cm length) tapered to a very sharp end as an end-effector. It is driven by three piezo-electric actuated prismatic joints in each of the three legs of the parallel kinematics chain. Each leg of the kinematics chain has the prismatic–revolute–spherical joint structure. As the length of the glass pipette end-effector is decreased, the resolution and accuracy of the micro–nano manipulator hand is increased. For long lengths of the glass pipette end-effector, this manipulator works as a micro manipulator and for short lengths it works as a nano manipulator. A novel closed-form solution for the problem of inverse kinematics is obtained. Based on this solution, a simulation program has been developed to optimally choose the design parameters of each module so that the manipulator will have a maximum workspace volume. A computer-aided design model based on optimal parameters is built and investigated to check its workspace volume. Experimental work has been carried out for the purpose of calibration. Also, the system hardware setup of the hybrid two-fingered micro–nano manipulator hand and its practical Jacobian inverse matrices are presented.     

Design and Control of 6-DOF Mechanism for Twin-Frame Mobile Robot

A new lightweight six-legged robot that uses a simple mechanism and can move and work with high efficiency has been developed. This robot consists of two leg-bases with three legs each, and walks by moving each leg-base alternately. These leg-bases are connected to each other with a 6 degrees of freedom (DOF) mechanism. While designing this robot, the output force, velocity, and workspace of various connection mechanisms were compared, and the results showed that good performance could be achieved with a serial/parallel hybrid mechanism. The serial/parallel hybrid mechanism consists of three 6-DOF serially linked arms positioned with radial symmetry about the center of each leg-base; each leg-base is composed of two active and four passive joints. Walking experiments with this robot confirmed that this mechanism has satisfactory performance not only as a walking robot, but also as an active walking platform. Furthermore, in this robot, the entire leg-drive mechanism acts as a 6-axis force sensor, and individual sensors at the feet are not necessary. The forces and moments can be calculated from the changes in the joint angles. Experiments conducted verified that smooth contact with the ground by the swing-leg and successful switching from swing to support leg can be achieved using this force control and force measurement method.     

耦合型3自由度并联稳定平台机构及其运动特征

基于舰船摇荡运动的耦合特征,采用耦合型3-SRR/SRU 3自由度并联机构作为舰载稳定平台机构,实现了稳定平台三轴驱动、动平台五轴联动补偿的目标．运用螺旋理论分析了机构的自由度和运动特征, 并讨论了输入关节选取的合理性|采用坐标等效运动的方法,建立机构耦合运动约束方程,得到了位置解及工作空间．本文将耦合型3-SRR/SRU 3自由度并联机构用于舰载稳定平台五轴联动补偿,拓展了少自由度并联机构的应用领域．     

Indirect disturbance compensation control of a planar parallel (2-PRP and 1-PPR) robotic manipulator

This study addresses the dynamic modelling and indirect disturbance compensation control of planar parallel robotic motion platform with three degrees of freedom (3-DOF) in the presence of parameter uncertainties and external disturbances. The proposed planar parallel motion platform is a singularity free manipulator and has three manipulator legs located on the same plane linked with a moving platform. Of the three aforementioned manipulator legs, two legs have a prismatic–revolute–prismatic (PRP) joint configuration each with only one prismatic joint deliberated to be active, and the other leg consists of prismatic–revolute–prismatic (PPR) joint configuration with one active prismatic joint. The closed form kinematic solution (both forward and reverse kinematics) for the platform has been obtained in completion. In addition, the dynamic model for the platform has been communicated using the energy based Euler–Lagrangian formulation method. The proposed controller is based on a computer torque control with disturbance compensation integrated with it. Disturbance vectors comprising disturbances due to parameter variations, payload variations, frictional effects and other additional effects have been estimated using an extended Kalman filter (EKF). The EKF proposed for this specific platform uses only position and orientation measurements for estimation and noise mitigation. Simulations with a characteristic trajectory are presented and the results have been paralleled with traditional controllers such as the proportional integral derivative (PID) controller and computed torque controller (CTC). The results demonstrate satisfactory tracking performance for the proposed controller in the presence of parameter uncertainties and external disturbances.     

面向非完全姿态约束问题的旋转矩阵群中的垂线理论

在很多机器人领域,有很多给定任务要求并不需要3维空间的完整姿态约束,而是只限定了目标姿态某一轴的方向．这类问题称为非完全姿态约束问题．针对该问题,定义了旋转矩阵群中测地线的垂足和垂线,并给出了其解析表达式．基于垂线理论,提出了沿垂线规划的点到点轨迹生成算法．最后通过仿真实验求解操作臂的轨迹规划问题,仿真以6自由度的PUMA 560为平台,并依次固定第6关节、第4关节得到5自由度和4自由度的操作臂．提出的算法不仅适用于具有功能冗余的6自由度操作臂,也可应用于不具有冗余特性的5自由度和4自由度操作臂．实验结果验证了提出的理论和算法在解决非完全姿态约束问题上的通用性．同时,该算法还能避免参数表示方法中的奇异性问题．     

Kinematics of a Family of Translational Parallel Mechanisms with Three 4‐DOF Legs and Rotary Actuators

This paper focuses on the kinematics of a family of translational parallel mechanisms equipped with three 4‐DOF legs and rotary actuators. The direct and the inverse position problems are solved in analytical form, the velocity analysis is carried out, the workspace is determined and the loci of both kinematic singularities and isotropic configurations are derived. Furthermore, the problem of singularity avoidance by means of actuator redundancy is addressed and some solutions are proposed. Two special architectures are finally considered as case studies: in the first, the three actuation axes are mutually orthogonal; in the second, two actuation axes are parallel to each other and the third is perpendicular to them. The comparison of the two architectures on the basis of kinematic considerations allows for the selection of the second one as a preferable solution. © 2003 Wiley Periodicals, Inc.     

Analysis and optimization of the 5-RPUR parallel manipulator

Many industrial applications need less than 6 degrees of freedom (DOF) to manipulate. On one hand, the parallel manipulators (PMs) with lower DOF have some advantages such as low manufacturing and control cost. On the other hand, they have more complicated kinematics. Among PMs with lower DOF, the 5-DOF PMs have particularly many industrial applications. Within the group of 5-DOF PMs, the three translational and two rotational (3T2R) type has more industrial applications than three rotational and two translational type. In this paper, we analyze and optimize the 5-RPUR PM which is a 3T2R type. The kinematic analysis is studied using the screw theory. The boundary and volume of the workspace is obtained using a geometrical method. In addition, singularity analysis is studied. Particle swarm optimization is utilized to optimize the workspace and the accuracy simultaneously, and achieve a roughly homogeneous accuracy index over the workspace. The boundary of the optimized workspace is depicted and we show that the optimized workspace is singularity free. The accuracy index of the manipulator is calculated and depicted in several cross-sections of the workspace.     

Determination of the orientation workspace of parallel manipulators

An important step during the design of a parallel manipulators is the determination of its workspace. For a 6-d.o.f. parallel manipulator workspace limitations are due to the bounded range of their linear actuators, mechanical limits on their passive joints and links interference. The computation of the workspace of a parallel manipulator is far more complex than for a serial link manipulator as its translation ability is dependent upon the orientation of the end-effector.We present in this paper an algorithm enabling to compute the possible rotation of the end-effector around a fixed point. This algorithm enables to take into account all the constraints limiting the workspace. Various examples are presented.     

Intra-articular kinematics of the upper limb joints: a six degrees of freedom study of coupled motions

In sport, leisure and certain occupational activities, joint lesions of the upper limb are very common. To understand their aetiology in order to prevent and treat these pathologies on a scientific basis, a comprehensive knowledge of the involved stress and kinematics is imperative. For many years intra-articular joint kinematics have been described hypothetically in terms of the convex-concave principle. This principle, however, has not been validated. The in vitro research on the acromioclavicular, glenohumeral and elbow joints was performed using an electromagnetic tracking device (Flock of Birds). By recalculating the positions of the trackers to an embedded coordinate system on the joint surface, the intra-articular joint movements can be analysed. Therefore, the bony configurations and articular surface features were registered with a 3D drawing stylus (Microscribe). Thirteen acromioclavicular joints, six glenohumeral joints and seven elbows were studied. The coupled intra-articular movements were analysed using the Euler angles and finite helical axis approaches. The results of the acromioclavicular joint analysis indicate that during movements in the scapular plane a superior rotation of the clavicle was coupled with an inferior translation and vice versa, whilst during movements in the plane perpendicular to the scapular plane the anterior rotation was coupled with an anterior translation and vice versa. In the glenohumeral joint, the abduction-elevation was coupled with an external rotation. In the humero-ulnar joint, the extension was coupled with an external rotation and varus movement. This intra-articular behaviour was in contradiction to currently accepted convex-concave concepts in arthrokinematics and manual therapy. The results may have major implications for manual therapy and orthopaedic medical practice.