Analysis of kinematics/statics and workspace of a 2(SP+SPR+SPU) serial–parallel manipulator

The kinematics/statics and workspace of a 2(SP+SPR+SPU) serial–parallel manipulator are studied systematically. First, a 2(SP+SPR+SPU) manipulator including an upper and a lower SP+SPR+SPU parallel manipulators is constructed, and the inverse/forward displacements, velocity, acceleration and statics of the lower/upper parallel manipulators are studied, respectively. Second, the kinematics and statics of the lower/upper manipulators are combined and the displacement, velocity, acceleration, statics, and workspace of a 2(SP+SPR+SPU) manipulator are analyzed systematically. Third, the analytic solutions’ examples are given and verified by the simulation mechanism. This manipulator has some potential applications for the robot’s arm, leg, and twist, the serial–parallel machine tools, the sensor, the surgical manipulator, the tunnel borer, the barbette of warship, and the satellite surveillance platform.     

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.     

A New Approach to the Architecture Optimization of a General 3-PUU Translational Parallel Manipulator

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The manipulator workspace is generated by a numerical searching method with the physical constraints taken into consideration. Simulation results illustrate clearly the necessity to introduce a mixed performance index using space utility ratio for architectural optimization of the manipulator, and the optimization procedure is carried out with the goal of reaching a compromise between the two indices. The analytical results are helpful in designing a general 3-PUU TPM, and the proposed design methodology can also be applied to architectural optimization for other types of parallel manipulators.     

On the position analysis of a new spherical parallel robot with orientation applications

In this paper, we propose a new spherical parallel robot for celestial orientation, and rehabilitation applications (TV satellite dish, tracking systems, solar panels, cameras, telescopes, table of the machine tools, ankle, shoulder, wrist and etc.). The proposed robot can completely rotate about an axis. After describing the robot and its inverse position analysis, using the genetic algorithm, the dimensional optimization to maximize the workspace of the robot is performed. The workspace analysis shows that the proposed robot has a relatively large workspace. Also, singularity analysis represents that the manipulator is a singularity-free workspace. It is a great advantage of the proposed robot. Next, an optimal approach is proposed for solving the direct position problem of the robot. According to the geometry of the robot, two coupled trigonometric equations are obtained through using a special form of Rodrigues' rotation formula. Next, the two coupled equations are transformed to a 8-degrees polynomial using the Sylvester's Dialytic elimination method. Finally, a numerical example for the robot with an asymmetric structure is given with eight real solutions. Therefore, the polynomial being minimal and the proposed approach is optimal. This greatly decreases computational time, which is necessary for dynamics, control and simulation.     

并联机器人工作空间的研究

本文对并联机器人的工作空间进行了研究.算法上采用输入转化的方法.使优化过程大为简化.在此基础上.对并联机器人工作空间的各截面进行了分析.并详细讨论了结构尺寸与工作空间的关系.得出扩大工作空间的几种途径.这对设计和应用并联机器人都有实际意义.     

Kinematics analysis of a hybrid manipulator for computer controlled ultra-precision freeform polishing

As one of the final processing steps of precision machining, polishing process is a very key decision for surface quality. This paper presents a novel hybrid manipulator for computer controlled ultra-precision (CCUP) freeform polishing. The hybrid manipulator is composed of a three degree-of-freedom (DOF) parallel module, a two DOF serial module and a turntable providing a redundant DOF. The parallel module gives the workpiece three translations without rotations. The serial module holds the polishing tool and gives it no translations on the polishing contact area due to its particular mechanical design. A detailed kinematics model is established for analyzing the kinematics of the parallel module and the serial module, respectively. For the parallel module, the inverse kinematics, the forward kinematics, the Jacobian matrix, the workspace and the dexterity distribution are analyzed systematically. Workspaces are also investigated for varying structural parameters. For the serial module, the inverse kinematics, the forward kinematics, the workspace and the precession motion analysis are carried out. An example of saddle surface finishing with this manipulator is given and the movement of actuators with respect to this shape is analyzed theoretically. These analysis results illustrate that the proposed hybrid manipulator is a very suitable machine structure for CCUP freeform polishing.     

线驱动模块化七自由度机器人轨迹跟踪控制

阐述了一种线驱动与常规串联驱动相结合的混合设计方法．这种设计方法融合了线驱动并联机构和模块化串联机构的优点，而且混合驱动机器人的工作空间大于完全线驱动机器人的工作空间．文章首先介绍了混合驱动机器人的机构设计，也就是机器人的肩关节采用模块化串联结构，而肘、腕关节采用线驱动结构．然后利用几何分析的方法来解机器人前向运动学问题．在分析驱动线长与关节角之间变换关系的基础上，分别利用速度法和关节角增量法来计算机器人逆向运动学解．最后，使用VC++实现混合驱动机器人对直线运动轨迹进行跟踪的仿真，从而证明了文章所描述的设计方法的正确性．     

Singularity analysis and detection of 6-UCU parallel manipulator

6-UCU kind Gough–Stewart platform (GSP) has been used extensively in practice. The singularity of GSP has been studied by many scholars, but their works mainly focused on finding the methods to divide the cases of singularity or searching the solutions with Jacobian matrices. On the other hand, this paper studies the singularities of 6-UCU parallel manipulator caused by not only the active joints but also passive universal joints. Two types of singularity are derived based on a degree of freedom method by using screw theory. Singularity detection is essential to certify the absence of singularity within a prescribed workspace or a reachable workspace for a practical use of the 6-UCU parallel manipulator. Algorithms are proposed by using evolutionary strategy to detect the singularity in the desired or reachable workspace of the 6-UCU parallel manipulator. Case studies are presented to demonstrate the effectiveness of the proposed singularity detection methods.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

Kinematic analysis of a 3-PRS parallel manipulator

Although the current 3-PRS parallel manipulators have different methods on the arrangement of actuators, they may be considered as the same kind of mechanism since they can be treated with the same kinematic algorithm. A 3-PRS parallel manipulator with adjustable layout angle of actuators has been proposed in this paper. The key issues of how the kinematic characteristics in terms of workspace and dexterity vary with differences in the arrangement of actuators are investigated in detail. The mobility of the manipulator is analyzed by resorting to reciprocal screw theory. Then the inverse, forward, and velocity kinematics problems are solved, which can be applied to a 3-PRS parallel manipulator regardless of the arrangement of actuators. The reachable workspace features and dexterity characteristics including kinematic manipulability and global dexterity index are derived by the changing of layout angle of actuators. Simulation results illustrate that different tasks should be taken into consideration when the layout angles of actuators of a 3-PRS parallel manipulator are designed.     

Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment

The paper deals with the workspace and dynamic performance evaluation of the PRR–PRR parallel manipulator in spray-painting equipment. Functional workspace of planar fully parallel robots is often limited because of interference among their mechanical components. The proposed 3-DOF planar parallel manipulator with two kinematic chains connecting the moving platform to the base can reduce interference while still maintaining 3 DOFs. Based on the kinematics, four working modes are analyzed and singularity is studied. The workspace is investigated and the inverse dynamics is formulated using the virtual work principle. The dynamic performance evaluation indices are designed on the basis of maximum and minimum magnitude of acceleration vector of the moving platform produced by a unit actuated force. The index not only can evaluate the accelerating performance of a manipulator, but also can reflect the isotropy of accelerating performance. Workspace and dynamic performances of the four working modes are compared and the optimal working mode for the painting of a large object with conical surface is determined.     

Workspace Determination of General 6-d.o.f. Cable Manipulators

This paper addresses workspace determination of general 6-d.o.f. cable-driven parallel manipulators with more than seven cables. The workspace under study is called force-closure workspace, which is defined as the set of end-effector poses satisfying the force-closure condition. Having force-closure in a specific end-effector pose means that any external wrench applied to the end-effector can be balanced through a set of non-negative cable forces under any motion condition of the end-effector. In other words, the inverse dynamics problem of the manipulator always has a feasible solution at any pose in the force-closure workspace. The workspace can be determined by the Jacobian matrix and, thus, it is consistent with the usual definition of workspace in the robotics literature. A systematic method of determining whether or not a given end-effector pose is in the workspace is proposed. Based on this method, the shape, boundary, dimensions and volume of the workspace of a 6-d.o.f., eight-cable manipulator are discussed.     

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．     

Optimizing the kinematic chains for a spatial parallel manipulator via searching the desired dexterous workspace

This paper exploits a new algorithm to optimize the length of the legs of a spatial parallel manipulator for the purpose of obtaining a desired dexterous workspace rather than the whole reachable workspace. With the analysis of the degree of freedom (DoF) of a manipulator, we can select the least number of variables to depict the kinematic constraints of each leg of a manipulator. The optimum parameters can be obtained by searching the extreme values of the objective functions with the given adroit workspace. Example is utilized to demonstrate the significant advantages of this method in the dexterous workspace synthesis. In applications, this method can be widely used to synthesize, optimize and create all kinds of new spatial parallel manipulator with a desired dexterous workspace.     

Architecture Selection and Singularity Analysis of a Three-Degree-of-Freedom Planar Parallel Manipulator

A three degree-of-freedom planar parallel manipulator, intended for high-speed, high-precision wire-bonding and electronic-component placement tasks, has been developed in our laboratory. In this paper, the work related to the kinematic manipulator-architecture selection is presented. The reachable workspace and effective base area metrics of the parallel manipulator were utilized for selecting the best possible architecture amongst six potential configurations. Constant platform-orientation regions, within the reachable workspace of the selected manipulator, were identified based on the manipulator task requirements. Simulation results for the workspace analyses (reachable workspace, effective base areas, and constant-orientation regions) are presented in this paper. Once the optimal-workspace architecture was selected, both workspace-boundary and internal singularities were further investigated in order to have a clear view of the set of uncontrollable poses of the manipulator. Singularity analyses examples are also included herein.     

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.     

一类平转耦合并联机构运动学性能的评价方法

三自由度平转耦合并联机构已在航空大型结构件加工中得到应用,但因这类机构的Jacobian矩阵量纲不统一,故难于用其代数特征评价机构的运动学性能.本文基于螺旋理论构造出3-PRS并联机构速度映射模型,采用虚功原理定义了两种可描述机构链内和链间瞬时功率传递特性的无量纲运动学性能评价指标,并通过算例说明其有效性.研究成果对指导这类并联机构的运动学优化设计具有重要的参考价值.     

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.     

Dynamic formulation and performance evaluation of the redundant parallel manipulator

The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.