Kinematic design of a six-DOF parallel-kinematics Machine with decoupled-motion architecture

The design of a new six-degree-of-freedom (6-DOF) parallel-kinematics machine (PKM) has been proposed. Different from the conventional Stewart-Gough platform which has six extensible legs, the new PKM employs three identical RPRS legs to support the moving platform. Since all joint axes, excluding the three spherical joints at the leg ends, are parallel to each other and perpendicular to the base plane, this 6-DOF PKM presents a promising platform structure with decoupled-motion architecture (DMA) such that translation in a horizontal plane and rotation about a vertical axis are driven by the three active revolute joints, while translation in the vertical direction and rotation about horizontal axes are driven by the three active prismatic joints. As a result, this 6-DOF 3RPRS PKM with DMA has simple kinematics, large cylindrical reachable workspace, and high stiffness in the vertical direction. These features make it appropriate for light machining and heavy parts assembly tasks. Because of the DMA, a projection technique is employed for its kinematics analysis. By projecting the manipulator onto horizontal directions and vertical planes, the kinematics issues such as the displacement, singularity, and workspace analysis are significantly simplified.     

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 Analysis of a Novel 3D Decoupled Manipulator Based on Compliant Pantograph for Micromanipulation

A novel 3D compliant manipulator for micromanipulation is introduced based on pantograph linkage. The proposed manipulator provides decoupled 3DOF translational motions. The key design feature is the use of parallelograms, which maintain the orientation of the end-effector fixed. The proposed manipulator provides advantages over its counterparts in the literature. It has significantly higher workspace to size ratio if its pantograph acts as a magnification device. On the other hand, it has higher resolution if its pantograph acts as a miniaturizing device. This provides great flexibility in the design process to account for the limited variety of the micro-actuators and the large variety of the micro-scale tasks in terms of workspace and resolution. Thus, the proposed system possesses the characteristics of gearing (speed up or speed down). A suitable choice of flexure hinges and material is done. The position and velocity kinematic analysis are carried out. Analytical expressions are derived for singularity-free-workspace boundaries in terms of physical constraints of the flexure joints. Dexterity analysis is performed to evaluate the design performance. A synthesis methodology of the proposed manipulator is developed. A finite element analysis is carried out and a prototype is manufactured to validate the conceptual design. Simulation and experimental results have successfully demonstrated the linearity and consistency between input and output displacements with acceptable parasitic motions. Moreover, the manipulability of the proposed manipulator is found to be configuration independent. Also, the manipulator could have isotropic performance over its workspace for certain actuator setup.     

Kinematics,Singularity Study and Optimization of an Innovative Spherical Parallel Manipulator with Large Workspace

A novel design for three degree of freedom (DoF) mechanical arm, i.e. a 3-PUS/S Spherical Parallel Manipulator (SPM) with three rotational motions is proposed in this article. In addition, its kinematic equations, singularity and design optimization are studied according to its application. The proposed parallel robot that has three legs with three prismatic joints can rotate about Z-axis unlimitedly. Therefore, the manipulator has large workspace and good flexibility, hence being attractive to study. To complete the kinematic analysis of the manipulator, three stages are considered as follows. At the first, the kinematics of the SPM is explained to obtain the positions, velocities, and accelerations. Furthermore, the Jacobian and Hessian matrices of the 3-PUS/S Parallel Manipulator are derived. The results are verified by the use of CAD and Adams software. Next, the Jacobian matrix obtained from the kinematic equations is utilized to study the different types of singularities. Finally, the optimum dimensions of the manipulator based on kinematic and singularity features are studied by Genetic Algorithm (GA), and the Global Condition Index (GCI) is maximized. The results help the designers to achieve an ideal geometry for the parallel manipulator with good workspace and minimum singularity.     

Tri-pyramid Robot: Design and kinematic analysis of a 3-DOF translational parallel manipulator

3-DOF translational parallel manipulators have been developed in many different forms, but they still have respective disadvantages in different applications. To overcome their disadvantages, the structure and constraint design of a 3-DOF translational parallel manipulator is presented and named the Tri-pyramid Robot. In the constraint design of the presented manipulator, a conical displacement subset is defined based on displacement group theory. A triangular pyramidal constraint is presented and applied in the constraint designs between the manipulator?s subchains. The structural properties including the decoupled motions, overconstraint elimination, singularity free workspace, fixed actuators and isotropic configuration are analyzed and compared to existing structures. The Tri-pyramid Robot is constrained and realized by a minimal number of 1-DOF joints. The kinematic position solutions, workspace with variation of structural parameters, Jacobian matrix, isotropic and dexterity analysis are performed and evaluated in the numerical simulations.     

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.     

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.     

Forward displacement analysis and uncertainty configurations of parallel manipulators with a redundant branch

The effect of adding a redundant branch in terms of reduction of the number of assembly modes and elimination of potential uncertainty configuration types is investigated for a class of parallel manipulators. Considered is a broad class that includes all three-branch manipulators where each branch is comprised of a serial arrangement of three main-arm joints supporting a common payload platform through a passive spherical branch end joint-group. The addition of a redundant branch effectively yields a four-branch manipulator class. Considered in particular is a 3–4 form of the manipulator where two branch ends meet at one point on the mobile platform. Symmetric main-arm joint sensing and actuation (two sensed/acutated main-arm joints per branch) is utilized. Synthetic geometry is used to study the number of assembly configurations of the resulting 3–4 four-branch parallel manipulators. It is presented that the number of assembly modes of three-branch parallel manipulators with passive spherical branch end joints can be reduced by utilizing a redundant branch. It is shown that there exist up to eight and up to four assembly modes when all unsensed joints are revolute and when all unsensed joints are prismatic, respectively. Combinations of unsensed prismatic and revolute joints are also investigated. It is determined that there are up to eight and up to four assembly modes when the unsensed main-arm joint of one of the concurrent branches is prismatic and when the unsensed joints of both concurrent branches are prismatic joints, respectively. Resolving the potential assembly modes require only the consideration of, at highest, second-order single-variable polynomials. In addition, kinematic design considerations allowing reduction of feasible assembly modes are discussed. The investigation of potential uncertainty configuration types is based on examining degeneracies of the screw systems formed by wrenches associated with the forces that the actuated-joints can apply. All linear dependency cases that could potentially cause uncertainties for the class of four-branch manipulators are identified. It is shown that while significantly reducing potential uncertainty configuration types, the addition of a redundant branch number cannot eliminate all potential dependency (uncertainty) cases completely. For the remaining potential uncertainty configuration types, the characteristics of the corresponding unconstrained instantaneous degrees of freedom are discussed. © 1996 John Wiley & Sons, Inc.     

Stewart并联机器人力敏感性分析及实验验证

研究了Stewart并联机器人的人机交互安全性问题．首先建立机器人的静力学方程,提取关节力敏感度和关节力敏感方向指标,度量关节力对操作力的感知敏感性．采用解析法和数值法结合的方法求算关节全局力敏感度．接着分析关节力敏感度在笛卡儿工作空间和位姿工作空间中的分布,以及构型参数对关节全局和局部力敏感度的影响．然后通过限制工作空间和调节末端执行器在工作过程中的位姿,在设计阶段合理选取构型参数,改善关节力敏感度的方法提高人机交互安全性．最后通过实验测试证明了,关节力敏感度能有效度量关节对交互力的敏感性,末端执行器的位置和姿态能直接改变关节力敏感度．     

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.     

Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling

This paper deals with the performance analysis of a 3-degree-of-freedom (3-DOF) planar parallel manipulator with actuation redundancy. Closed-form solutions are developed for both the inverse and direct kinematics about the redundant parallel manipulator. In performance analysis phase, the dexterity is analyzed, three kinds of singularities are investigated, and the stiffness is estimated. Compared with the corresponding non-redundant parallel manipulator with the redundant link removed, the redundantly actuated one has better dexterity, litter singular configurations and higher stiffness. The redundantly actuated parallel manipulator was applied to the design of a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.     

Dexterous Workspace Optimization of a Tricept Parallel Manipulator

The growing interest in the use of parallel manipulators in machining applications requires clear determination of the workspace and dexterity. In this paper, the workspace optimization of a Tricept parallel manipulator under joint constraints is performed. This parallel manipulator has complex degrees of freedom and, therefore, leads to dimensionally inhomogeneous Jacobian matrices. Here, we divide the Jacobian entries by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. By multiplying the associated entries of the twist array to the same length, we made this array homogeneous as well. The workspace of the manipulator is parameterized using several design parameters and is optimized using a genetic algorithm. For the workspace of the manipulator, local conditioning indices and minimum singular values are calculated. For the optimal design, it is shown that by introducing the local conditioning indices and minimum singular values, the quality of the parallel manipulator is improved at the cost of workspace reduction.     

Dynamics and Coupling Actuation of Elastic Underactuated Manipulators

This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton‐Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three‐link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc.     

Collision-avoidance for redundant robots through control of the self-motion of the manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.     

CAT4 (Cable Actuated Truss—4 Degrees of Freedom): A Novel 4 DOF Cable Actuated Parallel Manipulator

The CAT4 (Cable Actuated Truss—4 degrees of freedom) robot is a novel, passively jointed, parallel robot utilizing six control cables for actuation. The architecture has been under development at the Queen's University Robotics Laboratory. The robot utilizes a passive jointed linkage with 18 revolute joints to constrain the end effector motion and provide the desired structural stability, restricting the end effector to 3 translational degrees of freedom (DOF) and 1 DOF for end effector pitch. This central mechanism together with winched cable actuation gives a number of important benefits for applications where the advantages of a parallel robot are required in conjunction with light weight. Six electric motor driven winches control the length of the cable actuators that extend from the top frame to points on the end effector raft and jointed linkage to create a stiff, but lightweight, actuated robot. Simulation work on the robot is presented giving the kinematics, including a computational estimate of the workspace for a specific configuration. Results of computational simulation of the motion of the manipulator and a discussion of the advantages and potential difficulties are also presented. © 2002 Wiley Periodicals, Inc.     

Obstacle Modelling Oriented to Safe Motion Planning and Control for Planar Rigid Robot Manipulators

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly challenging when obstacles are present in the manipulator workspace. In this paper a n-joint planar robot manipulator is considered and it is assumed that obstacles located in its workspace can be approximated in a conservative way with circles. The goal is to represent the obstacles in the robot configuration space. The representation allows to obtain an efficient and accurate trajectory planning and tracking. A simple but effective path planning strategy is proposed in the paper. Since path planning depends on tracking accuracy, in this paper an adequate tracking accuracy is guaranteed by means of a suitably designed Second Order Sliding Mode Controller (SOSMC). The proposed approach guarantees a collision-free motion of the manipulator in its workspace in spite of the presence of obstacles, as confirmed by experimental results.     

An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory

This paper analyzes the mobility and stiffness of a three-prismatic-revolute-cylindrical (3-PRC) translational parallel manipulator (TPM). Firstly, the original 3-PRC TPM is converted into a non-overconstrained manipulator since there exist some practical problems for the overconstrained mechanism. By resorting to the screw theory, it is demonstrated that the conversion brings no influences to the mobility and kinematics of the manipulator. Secondly, the stiffness matrix is derived intuitively via an alternative approach based upon screw theory with the consideration of actuations and constraints, and the compliances subject to both actuators and legs are taken into account to establish the stiffness model. Furthermore, the stiffness performance of the manipulator is evaluated by utilizing the extremum stiffness values over the usable workspace, and the influences of design parameters on stiffness properties are presented, which will be helpful for the architecture design of the TPM.     

Equivolumetric partition of solid spheres with applications to orientation workspace analysis of robot manipulators

Orientation workspace analysis is a critical issue in the design of robot manipulators, especially the spherical manipulators. However, there is a lack of effective methods for such analysis, because the orientation workspace of a robot manipulator is normally a subset of SO(3) (the special orthogonal group) with a complex boundary. Numerical approaches appear more practical in actual implementations. For numerical analysis, a finite partition of the orientation workspace in its parametric domain is necessary. It has been realized that the exponential coordinates parameterization is more appropriate for finite partition. With such a parameterization, the rigid body rotation group, i.e., SO(3), can be mapped to a solid sphere D/sup 3/ of radius /spl pi/ with antipodal points identified. A novel partition scheme is proposed to geometrically divide the parametric domain, i.e., the solid sphere D/sup 3/ of radius /spl pi/, into finite elements with equal volume. Subsequently, the volume of SO(3) can be numerically computed as a weighted volume sum of the equivolumetric elements, in which the weightages are the element-associated integration measures. In this way, we can simplify the partition scheme and also reduce the computation efforts, as the elements in the same partition layer (along the radial direction) have the same integration measure. The effectiveness of the partition scheme is demonstrated through analysis of the orientation workspace of a three-degree-of-freedom spherical parallel manipulator. Numerical convergence on various orientation workspace measures, such as the workspace volume and the global condition index, are obtained based on this partition scheme.     

基于Metropolis遗传算法的并联机器人结构优化设计

以六自由度Stewart并联机器人的灵巧度为目标函数,以设计空间、每条支腿的最大最小长度之比和虎克铰、球铰的极限摆角为约束条件建立了结构优化模型．将模拟退火算法中的Metropolis准则引入到实值编码遗传算法的选择操作中,产生了Metropolis遗传算法,采用该算法进行了并联机器人结构优化问题的求解．通过与采用标准遗传算法得出的结果比较,证实了Metropolis遗传算法在并联机器人结构优化设计中的有效性和优越性．     

Dynamic analysis and control of a stewart platform manipulator

The Stewart platform is a six-axis parallel robot manipulator with a force-to-weight ratio and positioning accuracy far exceeding that of a conventional serial-link arm. Its stiffness and accuracy approach that of a machine tool yet its workspace dexterity approaches that of a conventional manipulator. In this article, we study the dynamic equations of the Stewart platform manipulator. Our derivation is closed to that of Nguyen and Pooran because the dynamics are not explicitly given but are in a step-by-step algorithm. However, we give some insight into the structure and properties of these equations: We obtain compact expressions of some coefficients. These expressions should be interesting from a control point of view. A stiffness control scheme is designed for milling application. Some path-planning notions are discussed that take into account singularity positions and the required task. The objective is to make the milling station into a semiautonomous robotic tool needing some operator interaction but having some intelligence of its own. It should interface naturally with part delivery and other higher-level tasks.