Dynamics analysis for a novel 6-DoF parallel manipulator I with three planar limbs

A novel 6-DoF parallel manipulator I with three planar limbs is proposed and its dynamics is analyzed systematically. First, its characteristics and DoF are analyzed and calculated. Second, the formulae for solving kinematics of the moving platform and the planar limbs are derived. Third, the formulae for solving the inertial wrench applied on the planar limbs and the moving platform are derived, and dynamics formula is derived for solving dynamic active forces applied onto the planar limbs. Fourth, a singularity of the proposed parallel manipulator is determined and analyzed. Fifth, an analytic example is given for solving the kinetostatics and dynamics of the proposed parallel manipulator, and the solved results are analyzed and verified by the simulation mechanism. Finally, a workspace is constructed and analyzed by comparing with an existing 6-DoF parallel manipulator.     

Topology design and kinematic optimization of cyclical 5-DoF parallel manipulator with proper constrained limb

This paper proposes topology design and kinematic optimization of cyclical 5-degree-of-freedom (DoF) parallel manipulator with proper constrained limb. Firstly, a type of cyclical 5-DoF parallel manipulators with proper constrained limb is proposed by analyzing DoF of the proper constrained limb within workspace. Exampled by a cyclical 5-DoF parallel manipulator with the topology 4-UPS&1-RPS, its motion mapping model is formulated. By taking the reciprocal product of a wrench on a twist as the generalized virtual power, the local and global kinematic performance indices are provided. Then, on the basis of the actuated and constrained singularity analysis of the 4-UPS&1-RPS parallel manipulator within the position and pose workspace, the topology design of the manipulator without singularity is carried out, and its reachable and prescribed workspaces are obtained. Finally, by maximizing the global kinematic performance index and subjecting to a set of appropriate constraint conditions, the kinematic optimal design of the 4-UPS&1-RPS parallel manipulator is carried out utilizing the genetic algorithm of MATLAB optimization toolbox.     

Dimensional optimization of 6-DOF 3-CCC type asymmetric parallel manipulator

In this paper, dimensional optimization of a six-degrees-of-freedom (DOF) 3-CCC (C: cylindrical joint) type asymmetric parallel manipulator (APM) is performed by using particle swarm optimization (PSO). The 3-CCC APM constructed by defining three angle and three distance constraints between base and moving platforms is a member of 3D3A generalized Stewart–Gough platform (GSP) type parallel manipulators. The dimensional optimization purposes to find the optimum limb lengths, lengths of line segments on the base and moving platforms, attachment points of the line segments on the base platform, the orientation angles of the moving platform, and position of the end-effector in the reachable workspace in order to maximize the translational and orientational dexterous workspaces of the 3-CCC APM, separately. The dexterous workspaces are obtained by applying condition number and minimum singular values of the Jacobian matrix. The optimization results are compared with the traditional GSP manipulator for illustrating the kinematic performance of 3-CCC APM. Optimizations show that 3-CCC APM have superior dexterous workspace characteristics than the traditional GSP manipulator.     

基于LPV 方法的Stewart 平台关节空间分散控制

为了提高Stewart 平台关节空间分散控制系统的性能,提出一种基于线性变参数(Linear Parameter Varying,LPV) 方法的控制策略．首先建立了平台关节空间动力学模型;通过分析平台惯性矩阵,指出单支路 子系统等效负载变化以及子系统间的耦合干扰是分散控制需要处理的主要问题．然后将平台惯性矩阵分解为 一个对角阵与一个耦合阵之和,子系统间耦合作用视为对单支路的干扰,从而得到每个子系统的动力学方程． 最后针对子系统等效负载随着上平台运动而在较大范围内变化的特点,引入LPV 控制方法,使控制器参数能 够适应子系统负载变化,减少了保守性．仿真结果表明了所提方法的有效性．     

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.     

Performance investigations on optimum mechanical design aspects of planar parallel manipulators

This paper presents a comparative analysis of three degrees of freedom planar parallel robotic manipulators (x, y and θ_z motion platforms) namely 2PRP-PPR, 2PRR-PPR, 3PPR (Hybrid), 3PRP (Hephaist) and 3PPR U-base in terms of optimal kinematic design performance, static structural stiffness and dynamic performance (energy and power consumption). Kinematic and dynamic performance analyses of these platforms have been done using multibody dynamics software (namely ADAMS/View). Static stiffness of the above-mentioned manipulators have been analysed, compared using the conventional joint space Jacobian stiffness matrix method, and this method has been verified through a standard finite-element software (namely NASTRAN) as well. The size of the fixed base or aspect ratio (width/height) can be varied for various working conditions to understand its design parameters and optimal design aspects which are depending on the fixed base structure. Different aspect ratios (fixed base size) are considered for the comparative analyses of isotropy, manipulability and stiffness for the above-mentioned planar parallel manipulators. From the numerical simulation results, it is observed that the 2PRP-PPR manipulator is associated with a few favourable optimum design aspects such as singularity-free workspace, better manipulability, isotropy, higher stiffness and better dynamic performance in terms of power and energy requirement as compared to other planar parallel manipulators.     

A new method for actuating parallel manipulators

This paper presents a new technique of actuating a parallel platform manipulator using shape memory alloy (SMA). This is a type of smart materials that can attain a high strength-to-weight ratio, which makes them ideal for miniature application. The work is mainly to develop a new SMA actuator and then incorporating the actuator in building the parallel manipulator prototype. The SMA used in this study is a commercial NiTi wire. The SMA wire provides an actuating force that produces a large bending and end displacement. A 3-UPU (universal–prismatic–universal) parallel manipulator using linear SMA actuators was developed. The manipulator consists of a fixed platform, a moving platform and three SMA actuators. The manipulator workspace was specified based on the restrictions due to actuator strokes and joint angle limits. System identification techniques were used to model both heating and cooling processes. An ON/OFF control was performed and the results showed closeness in simulation and experimental results. This study showed that shape memory alloy actuated beam can successfully be used to provide linear displacement. The built prototype indicates the feasibility of using SMA actuators in parallel manipulators.     

Optimal design of a 3-PUPU parallel robot with compliant hinges for micromanipulation in a cubic workspace

In recent years, nanotechnology has been developing rapidly due to its potential applications in various fields that new materials and products are produced. In this paper, a novel macro/micro 3-DOF parallel platform is proposed for micro positioning applications. The kinematics model of the dual parallel mechanism system is established by the stiffness model with individual wide-range flexure hinge and the vector-loop equation. The inverse solutions and parasitic rotations of the moving platform are obtained and analyzed, which are based on a parallel mechanism with real parameters. The reachable and usable workspace of the macro motion and micro motion of the mechanism are plotted and analyzed. Finally, based on the analysis of parasitic rotations and usable workspace of micro motion, an optimization for the parallel manipulator is presented. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for the dual parallel mechanism in order to achieve the features of both larger workspace and higher motion precision.     

Parametric design optimization of 2-DOF R–R planar manipulator—A design of experiment approach

This work illustrates simulation approach for optimizing the parametric design and performance of a 2-DOF R–R planar manipulator. Using dynamic and kinematic models of a manipulator different performance measures for the manipulator are obtained for different combination of parameters with effect of noise incorporated to imitate the real time performance of the manipulator. A novel approach has been proposed to model, the otherwise difficult to model, noise effects. The data generated during simulation for various parameter combinations are utilized to analyze the statistical significance of kinematic and dynamic parameters on performance of manipulator using ANOVA technique. The parameter combinations, which give optimum performance measures obtained for different points in workspace, are compared and reported.     

基于AutoCAD平台的六自由度并联机器人

本文研究基于AutoCAD平台的六自由度并联机器人在姿态给定情况下工作空间(即位置工作空 间)的几何确定方法,该方法以机器人的运动学反解为基础,得出Stewart并联机器人和6-R TS并联机器人位置工作空间的边界方程,从而得出Stewart并联机器人的位置工作空 间是6个球体的交集,6-RTS并联机器人在姿态给定时其工作空间是6个相同的规则曲面体 的交集．基于AutoCAD平台,其交集以及交集的容积可以很容易的得出,该方法是确定六自 由度并联机器人工作空间的一种简单、有效方法．     

A 6-DOF adaptive parallel manipulator with large tilting capacity

In this paper, a novel 6 degrees of freedom (DOFs) adaptive parallel manipulator with large tilting capacity is presented. The manipulator consists of four identical peripheral limbs and one center limb connecting the base and the moving platform. Due to the special architecture, the doubly actuated center limb of the manipulator could have infinite inverse solutions. In every configuration of the end-effector, the manipulator can adapt its center limb to the position and orientation with best dexterity. An optimization equation for obtaining the optimized dexterity of the manipulator is introduced to solve this nonholonomic problem, which also makes the manipulator capable of large tilting capacity. Targeting for the application of five-face machining, the detailed kinematic analysis of the manipulator is developed, which includes the closed-form solutions of inverse position problems, the singularity, dexterity, workspace and tilting capability. The analysis developed in this paper shows that the proposed manipulator has large tilting capacity and thus a suitable candidate for five-face machining.     

Inverse Dynamic Model and a Control Application of a Novel 6-DOF Hybrid Kinematics Manipulator

Kinematics with six degrees of freedom can be of several types. This paper describes the inverse dynamic model of a novel hybrid kinematics manipulator. The so-called Epizactor consists of two planar disk systems that together move a connecting element in 6 DOF. To do so each of the disk systems has a linkage point equipped with a homokinetic joint. Each disk system can be described as a serial 3-link planar manipulator with unlimited angles of rotation. To compensate singularities, a kinematic redundancy is introduced via a fourth link. The kinematic concept leads to several technical advantages for compact 6-DOF-manipulators when compared to established parallel kinematics: The ratio of workspace volume and installation space is beneficial, the number of kinematic elements is smaller, and rotating drives are used exclusively. For a singularity-robust control-approach, the inverse dynamic model is derived using the iterative Newton–Euler-method. Feasibility is shown by the application of the model to an example where excessive actuator velocities and torques are avoided.     

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.     

Design and kinetostatic analysis of a new parallel manipulator

This paper proposes an innovative design for a parallel manipulator that can be applied to a machine tool. The proposed parallel manipulator has three degrees of freedom (DOFs), including the rotations of a moving platform about the x and y axes and a translation of this platform along the z-axis. A passive link is introduced into this new parallel manipulator in order to increase the stiffness of the system and eliminate any unexpected motion. Both direct and inverse kinematic problems are investigated, and a dynamic model using a Newton–Euler approach is implemented. The global system stiffness of the proposed parallel manipulator, which considers the compliance of links and joints, is formulated and the kinetostatic analysis is conducted. Finally, a case study is presented to demonstrate the applications of the kinematic and dynamic models and to verify the concept of the new design.     

Optimum design of the 5R symmetrical parallel manipulator with a surrounded and good-condition workspace

This paper concerns the optimum design issue of the 5R symmetrical parallel manipulator with a surrounded workspace. Generally, such a manipulator has a very large workspace. With different working modes, a manipulator will have different singular loci and workspaces. In this paper, the singularity and the usable workspace without singularity inside will be determined for the manipulator with a specified mode. The usable workspace can be used to define the global conditioning index (GCI). In order to obtain the optimum design of the manipulator, a non-dimensional design space is established. Because each of the non-dimensional manipulators in the established design space can represent the performances of all of its possible similarity manipulators, the design space is a very useful tool for guaranteeing a global comparative result. Within the design space, the singularity, usable workspace and control accuracy (evaluated using the GCI) are studied and the corresponding atlases are constructed. Based on the atlases, one can synthesize link lengths of the manipulator studied with respect to specified criteria. One example will be given to show how to use the atlases. In particular, an example will be presented of reaching the optimum dimensional result with respect to a desired practical workspace based on the optimum non-dimensional result identified from the atlases. For the reason that using the atlases presented in this paper a designer can obtain the optimum result with respect to any specification, the optimum design method proposed in this paper may be accepted by others.     

Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator

In this study, the effects of joint clearance on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator are investigated. The parallel manipulator is modeled by multi-body system dynamics. The contact effect in revolute joints with clearance is established by using a continuous analysis approach that is combined with a contact force model considering hysteretic damping. The evaluation of the contact force is based on Hertzian contact theory that accounts for the geometrical and material properties of the contacting bodies. Furthermore, the incorporation of the friction effect in clearance joints is performed using a modified Coulomb friction model. By numerical simulation, variations of the clearance joint's eccentric trajectory, the joint reaction force, the input torque, the acceleration, and trajectory of the end-effector are used to illustrate the dynamic behavior of the mechanism when multiple clearance revolute joints are considered. The results indicate that the clearance joints present two obvious separation leaps in a complete pick-and-place working cycle of the parallel manipulator, following a collision. The impact induces system vibration and thus reduces the dynamic stability of the system. The joint clearances affect the amplitudes of the joint reaction force, the input torque, and the end-effector's acceleration, additionally the joint clearances degrade the kinematic and dynamic accuracy of the manipulator's end-effector. Finally, this study proposes related approaches to decrease the effect of joint clearances on the system's dynamic properties for such parallel manipulator and prevent “separation-leap-impact” events in clearance joints.     

Kinematics,dynamics and dimensional synthesis of a novel 2-DoF translational manipulator

In the past few years, parallel manipulators have become increasingly popular in industry, especially, in the field of machine tools. In this paper, a novel 2-degree-of-freedom (DoF) parallel manipulator, which has two translational DoFs, is proposed. It is characterized by the fact that the output of the manipulator is two planar DoFs of a rigid body, while its orientation remains constant. The inverse and forward kinematics can be described in closed form. The velocity equation, singularity, and workspace of the manipulator are presented. In addition the inverse dynamics problem of the device is investigated employing the Lagrange multipliers approach. The dimensional synthesis based on the workspace and conditioning indices is presented. The proposed manipulator can be applied to the field of machine tools or used as the mobile base for a spatial manipulator. The results of the paper are very useful for the design and application of the new manipulator.     

Randomized Optimal Design of Parallel Manipulators

This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework. Observing that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality. The effectiveness of a workspace is characterized by the dexterity of the mechanism over every point in the workspace. Other performance indices, such as manipulability and stiffness, provide alternatives of dexterity characterization of workspace effectiveness. An optimal design problem, including constraints on actuated/passive joint limits and link interference, is then formulated to find the manipulator geometry that maximizes the effective regular workspace. This problem is a constrained nonlinear optimization problem without explicitly analytical expression. Traditional gradient based approaches may have difficulty in searching the global optimum. The controlled random search technique, as reported robust and reliable, is used to obtain an numerical solution. The design procedure is demonstrated through examples of a Delta robot and a Gough-Stewart platform.     

基于张拉整体结构的连续型弯曲机械臂设计与研究

为实现对目标物体的缠绕捕获，利用张拉整体结构质量轻、变形大等特点，提出一种基于张拉整体结构的连续型机械臂的设计．本文首先设计连续型机械臂的结构，建立其力学模型．通过准静态和动态分析，对不同驱动形式下的连续型机械臂运动进行仿真，并在实验平台上验证所建力学模型的准确性，最后分析了其工作空间及奇异位姿．实验结果表明本文设计的连续型机械臂可以实现弯曲缠绕变形，满足对不同大小物体进行缠绕捕获的需求．     

五轴并联机床的尺度综合

基于逆向思维提出了一种满足工作空间要求的五轴并联机床的尺度综合方法．首先用极坐标来描述并联机床的姿态空间；然后基于工作空间的要求得到运动平台上铰链点与固定平台上铰链点的距离极值表达式；最后考虑到杆件的力传递性能，得到一组性能较优的参数．该方法对类似的并联机构的尺度综合具有较高的参考价值．