可实现空间取放作业的4自由度并联机器人机构综合

本论文旨在解决非过约束4自由度并联机构综合这一机构学难题。本文在总结已有的4自由度并联机器人综合结果的基础上,结合运动子群的概念和螺旋理论的方法,技术性地解决了约束数目和支链数目之间存在的矛盾。利用解析的手段给出了一套全新的非过约束对称4自由度并联机构设计方法。定义了一系列便于综合该机构的概念,分析了该类机构必须具有的拓扑结构,得出两种类型的该类并联机构。给出了满足设计条件的运动副组成情况及空间装配条件,最后给出了典型机构的设计范例。     

Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant-a novel 5-DOF reconfigurable hybrid robot

This paper deals with the conceptual design and dimensional synthesis of a 3-DOF parallel mechanism module which forms the main body of a newly invented 5-DOF reconfigurable hybrid robot named "TriVariant." The TriVariant is a modified version of the Tricept robot, achieved by integrating one of the three active limbs into the passive limb. The idea leading to the innovation of the module is systematically addressed. Its kinematic performance is optimized by minimizing a global and comprehensive conditioning index subject to a set of appropriate mechanical constraints. It is concluded that the proposed hybrid system is more cost-effective and has a competitive kinematic performance in comparison with the well-known Tricept robot.     

Forward and inverse kinematics of a 5-DOF hybrid robot for composite material machining

Hybrid robots consist of both serial and parallel mechanisms, which have advantages in stiffness and workspace compared with serial/parallel robots when machining composite material. However, the forward and inverse kinematics of hybrid robots generally do not have analytic solutions. This paper deals with the analytic forward and inverse kinematics solutions of a 5-degree-of-freedom (DOF) hybrid robot which consists with a 3-DOF 2UPU/SP parallel mechanism (PM) and a 2-DOF rotating head. In the forward kinematic problem, a method is proposed to transfer the high order kinematic equation to a 4th-order polynomial based on the Sylvester's dialytic elimination, and the analytic solutions can be further obtained by Ferrari's method. In the inverse problem, the redundant Euler angles expressed by four rotations are firstly proposed for decoupling different motions, then, the closed-form solution of inverse kinematics can be found. Finally, a simulation trajectory is given, and the result shows that the accuracy of the solutions’ calculation reaches femtometer grade and the efficiency reaches microsecond grade; furthermore, an experiment is performed on the prototype to validate the effectiveness of the proposed forward and inverse kinematics.     

Dynamic and stable reconfiguration of self-reconfigurable planar parallel robots

This paper discusses dynamic and stable reconfigurations of self-reconfigurable planar parallel robots that can be done by coupling and decoupling of two underactuated robots on a horizontal plane. The limbs of the parallel robots are 2R open kinematic chains with their second joints unactuated. Two types of self-reconfigurable parallel robots are considered. One is formed by two limbs, and the other is by a limb and an underactuated robot consisting of two limbs and a platform. Uncertainty singularities enable them to self-reconfigure without additional actuators at their coupling mechanism. In this paper, we propose dynamic contact motion control to move them from an initial contact configuration to an uncertainty singular configuration while maintaining their contact. This paper also considers dynamic stability at their uncertainty singularities as equilibrium and shows that there exist geometrically stable configurations without feedback control, which are useful for decoupling. Experiments with real robots are carried out to verify the effectiveness of the dynamic contact motion control and stability analysis.     

Determination of unstable singularities in parallel robots with N arms

Parallel mechanisms frequently possess an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging, and in the past, has been tackled by exhaustive numerical searches of the mechanism workspace using an accurate analytical model of the mechanism kinematics. This paper considers the singularity-determination problem from a geometric perspective for n-legged spatial parallel mechanisms. By using the constraints on the passive joint velocities, a necessary condition for an unstable singularity is derived.     

Kinematic calibration of a 2-DOF translational parallel manipulator

Two types of kinematic calibration method for a 2-DOF (degrees of freedom) translational parallel manipulator are proposed using different error models. A calibration experiment is performed on both methods using an Absolute Laser Tracker and the results are compared. Two error models of the 2-DOF translational parallel manipulator are established using differential method and linear perturbation method, respectively. The two error models are solved using both the least squares method and linear equations. The results for the two different calibration methods show that the error model based on differential method is more effective in improving the accuracy of the 2-DOF translational parallel manipulator. Overall, the absolute position error of the 2-DOF translational parallel manipulator is significantly reduced to 0.13?mm from 0.93?mm after kinematic calibration.     

基于螺旋理论的新型三自由度移动并联机器人奇异性分析

采用螺旋理论及线性几何学方法对具有3支链5关节（P-4R）的三自由度纯移动并联机器人的奇异性进行了分析和总结．研究了该并联机器人的结构奇异性以及主动关节（驱动关节）的配置的奇异性,并采用线性几何学图解形式直观地给出其处于奇异时的形位,为进一步研究其动力学、运动学性质奠定了基础．     

Kinematic analysis and error modeling of TAU parallel robot

The TAU robot presents a new configuration of parallel robots with three degrees of freedom. This robotic configuration is well adapted to perform with a high precision and high stiffness within a large working range compared with a serial robot. It has the advantages of both parallel robots and serial robots. In this paper, the kinematic modeling and error modeling are established with all errors considered using Jacobian matrix method for the robot. Meanwhile, a very effective Jacobian approximation method is introduced to calculate the forward kinematic problem instead of Newton–Raphson method. It denotes that a closed form solution can be obtained instead of a numerical solution. A full size Jacobian matrix is used in carrying out error analysis, error budget, and model parameter estimation and identification. Simulation results indicate that both Jacobian matrix and Jacobian approximation method are correct and with a level of accuracy of micron meters. ADAMS's simulation results are used in verifying the established models.     

Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis

In cable-driven parallel manipulators (CPMs), cables can perform only under tension, and therefore, redundant actuation, which can be provided by redundant limbs, is needed to maintain the cable tensions. By optimizing the distribution of the forces in the cables and the redundant limbs, the average size of actuators can be reduced resulting in lower cost. Optimizing the force distribution in CPMs requires consideration for the inequality constraints imposed on the cable forces as a result of the unilateral driving property of the cables. In this study, a projection method is presented to calculate optimum solutions for the actuators force distribution in CPMs. Two solutions are presented: 1) a minimum-norm solution that minimizes the 2-norm of all forces in the cables and redundant limbs and 2) a solution that minimizes the 2-norm of the forces in the cables only. The optimization problem is formulated as a projection on an intersection of convex sets and the Dykstra's projection method is used to obtain the solutions. This method is successfully applied to a 3-DOF CPM.     

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.     

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.     

Performance Analysis and Comparison of Planar 3-DOF Parallel Manipulators with One and Two Additional Branches

This paper constructs a symmetrical 3-DOF parallel manipulator with one and two additional branches, respectively. The conditioning, stiffness, velocity and payload indices are developed to compare the performance of the two parallel manipulators, one with one additional branch, and the other with two additional branches. The optimum performance region with desirable performance is investigated. The simulations show that the redundant manipulator with one additional branch has a larger optimum performance region with the given conditioning, velocity, payload and stiffness performance. The results are not only important for designers to design the 3-DOF parallel manipulator, but also helpful for researchers to determine how many additional branches are added to develop a redundant parallel manipulator.     

A 6-DOF reconfigurable hybrid parallel manipulator

This paper presents a case study on a reconfigurable hybrid parallel robot dubbed ReSl-Bot. It addresses the realm of reconfigurable 6-DOF parallel mechanisms, for sustainable manufacturing. It also features a self-reconfigurable architecture. A systematic analysis involving kinematics, constant orientation workspace, singularity and stiffness is developed in detail. Interesting features are discussed, revealing some unique characteristics of the studied architecture. A multi-objective optimization procedure is also carried out with weighted stiffness, dexterity and workspace volume as the performance indices.     

Local rolling and tilting capability analysis of fully parallel linear actuated platform-type manipulators

Two problems associated with the local rotatability of two types of fully parallel linearly actuated platform manipulators are investigated in this paper. The first problem is to find the physically allowable region that the movable platform can be freely rolled about any given direction at any specified position. The second problem is to evaluate the maximum angle that the movable platform can be tilted about any given position and orientation. The kinematic constraints involved in these problems are the stroke limitation of the linear actuators, the motion constraints of the passive spherical and universal joints, and the interference condition between the supporting limbs. A unified and computationally efficient approach for solving these problems which takes into account all of the kinematic constraints is developed.     

Stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates

This paper investigates the stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates. The stiffness model and natural frequency are derived, and then the stiffness and natural frequency of the manipulators are compared. The simulations show that the stiffness and natural frequency of the parallel manipulator with one or two additional legs are higher than those of the manipulator without additional leg. The stiffness performance and natural frequency of the manipulator with one additional leg can only be improved little by adding the second additional leg. It is better to develop this parallel manipulator by adding only one additional leg to construct a symmetrical architecture.     

Optimal design of a 2-DOF parallel manipulator with actuation redundancy considering kinematics and natural frequency

In this paper, a planar 2-DOF parallel manipulator with actuation redundancy is proposed and the optimal design considering kinematics and natural frequency is presented. The stiffness matrix and mass matrix are derived, and the structural dynamics is modeled. The natural frequency is obtained on the basis of dynamic model. Based on the kinematic performance, the range for link length is given. Then, considering the natural frequency, the geometry is optimized. The natural frequency is simulated and compared with the corresponding non-redundant parallel manipulator. The designed redundant parallel manipulator has desired kinematic performance and natural frequency and is incorporated into a 4-DOF hybrid machine tool.     

Closed-form forward kinematics solutions of a 4-DOF parallel robot

It is well known that the forward kinematics of parallel robots is a very difficult problem. Closed-form forward kinematics solutions have been reported only to a few special classes of parallel robots. This paper presents closed-form forward kinematics solutions of a 4-DOF parallel robot H4. A 16th order polynomial in a single variable is derived to solve the forward kinematics of the H4. The 16 roots of the polynomial lead to at most 16 different forward kinematics solutions. A numerical verification is also presented.     

Finite-time Stable Robust Sliding Mode Dynamic Control for Parallel Robots

To address the tracking control problem for n-DOF parallel robots in presence of the lumped disturbance, including modeling errors, friction and external disturbance, a finite-time stable robust sliding mode dynamic control (FRSMDC) for parallel robots is explored. From the implementation condition of the FRSMDC for parallel robots, the limitation on the change rate of the lumped disturbance is relaxed for easy realization. From the results of the FRSMDC for parallel robots, the finite-time stability of the sliding variable is proved and the settling time is derived; the switching gain required is only larger than the upper bound of the disturbance estimation error, instead of the upper bound of the disturbance, due to the feed-forward compensation to the lumped disturbance via a disturbance observer. Consequently, the system robustness is improved and the chattering of FRSMDC is alleviated. The finite-time stability of the closed-loop system is confirmed with Lyapunov theory. Besides, the application of the proposed method is extended to a general multi-input multi-output nonlinear system with the relative degree m by analogy. Finally, the case of the dynamic control of a 6-DOF parallel robot for automobile electro-coating conveying is studied for simulation and experiment, so as to attest the validity of the FRSMDC for parallel robots.

     

Optimal control of manipulators with any number of passive joints

This article discusses the problem of controlling robot manipulators with passive joints, when the number of passive joints is larger than the number of active joints. Assuming that brakes and position sensors are available at each passive joint, we investigate the following issues: (1) what is a sufficient condition for controllability of the passive joints via dynamic coupling with the active joints and how can we quantify the controllability at a given configuration; (2) what is the optimal control and locking sequence of the passive joints; and (3) how can we control both passive and active joints to an equilibrium point in joint space. We propose an optimal control method and demonstrate its validity with both simulation and experimental results. The work presented here is significant because it provides a better understanding and a guideline for utilizing manipulators with passive joints for energy efficiency and fault-tolerant design in applications such as space robotics, hyperredundant robots, and sport mechanics. © 1998 John Wiley & Sons, Inc. 15: 115–129, 1998     

Analytical Inverse Kinematics Solver for Anthropomorphic 7-DOF Redundant Manipulators with Human-Like Configuration Constraints

It is a common belief that service robots shall move in a human-like manner to enable natural and convenient interaction with a human user or collaborator. In particular, this applies to anthropomorphic 7-DOF redundant robot manipulators that have a shoulder-elbow-wrist configuration. On the kinematic level, human-like movement then can be realized by means of selecting a redundancy resolution for the inverse kinematics (IK), which realizes human-like movement through respective nullspace preferences. In this paper, key positions are introduced and defined as Cartesian positions of the manipulator’s elbow and wrist joints. The key positions are used as constraints on the inverse kinematics in addition to orientation constraints at the end-effector, such that the inverse kinematics can be calculated through an efficient analytical scheme and realizes human-like configurations. To obtain suitable key positions, a correspondence method named wrist-elbow-in-line is derived to map key positions of human demonstrations to the real robot for obtaining a valid analytical inverse kinematics solution. A human demonstration tracking experiment is conducted to evaluate the end-effector accuracy and human-likeness of the generated motion for a 7-DOF Kuka-LWR arm. The results are compared to a similar correspondance method that emphasizes only the wrist postion and show that the subtle differences between the two different correspondence methods may lead to significant performance differences. Furthermore, the wrist-elbow-in-line method is validated as more stable in practical application and extended for obstacle avoidance.