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.     

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.     

Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator

This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equations of motion of the manipulator are derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.     

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.     

Conceptual development of an enhanced tripod mechanism for machine tool

In this paper, a spatial three degrees of freedom parallel mechanism enhanced by a passive leg is proposed. The proposed parallel mechanism can be used in several applications, e.g. motion simulator, micromanipulator and machine tools. First, the geometric model of the three degrees of freedom parallel mechanism is addressed, in which a fourth kinematic link—a passive link connecting the base center to the platform center—is introduced. This last link is used to constrain the motion of the platform to only three degrees of freedom, i.e. the degree of freedom of the mechanism depends on the passive leg. The passive leg also enhances the global stiffness of the structure and distributes the torque from machining. Second, the kinematic analysis with the consideration of link flexibility is conducted. A kinetostatic model of the three degrees of freedom parallel mechanism with a passive link is then established and analyzed using lumped-parameter model. With the proposed method, a significant effect of the link flexibility on the mechanism's precision has been demonstrated. The influence of the change of structure parameters, including material properties, on the system behavior is discussed. Compliance mapping is also illustrated. The kinetostatic model proposed in the paper can be extended for optimal design and control of parallel kinematic machines. Finally, design optimization is conducted using genetic algorithms and some design guideline is given.     

Orientationability analyses of a special class of the Stewart–Gough parallel manipulators using the unit quaternion representation

This paper addresses the orientation-singularity and orientationability analyses of a special class of the Stewart–Gough parallel manipulators whose moving and base platforms are two similar semi-symmetrical hexagons. Employing a unit quaternion to represent the orientation of the moving platform, an analytical expression representing the singularity locus of this class of parallel manipulators in a six-dimensional Cartesian space is obtained. It shows that for a given orientation, the position-singularity locus is a cubic polynomial expression in the moving platform position parameters, and for a given position, the orientation-singularity locus is an analytical expression but not a polynomial directly with respect to the mobile platform orientation parameters. Further inspection shows that for the special class of parallel manipulators, there must exist a nonsingular orientation void in the orientation space around the orientation origin for each position in the position-workspace. Therefore, a new performance index referred to as orientationability is introduced to describe the orientation capability of the special class of manipulators at a given position. A discretization algorithm is proposed for the computation of the orientationability of the special class of manipulators. Moreover, effects of the design parameters and position parameters on the orientationability are investigated in details. Based on the orientationability performance index, another novel performance index referred to as practical orientationability is presented which represents the practical orientation capability of the manipulator at a given position. The practical orientationability not only can satisfy all the kinematic demands and constraints of such class of manipulators, but also can guarantee that the manipulator is nonsingular.     

Kinematic analysis and optimal design of a novel 1T3R parallel manipulator with an articulated travelling plate

Driven by the requirements of the large-scale component assemblage for the docking platform, this paper proposes a novel one-translational-three-rotational (1T3R) parallel manipulator with an articulated travelling plate, which can provide high stiffness and good accuracy performances in the assemblage. The underlying architecture of this manipulator is briefly addressed with emphasis on the practical realization of the articulated travelling plate. On the basis of the kinematic analysis of the 1T3R parallel manipulator, its optimal design considering the force and motion transmissibility is carried out, in which the generalized virtual power transmissibility of this manipulator is defined. This paper aims at laying a solid theoretical and technical foundation for the prototype design and manufacture of the 1T3R parallel manipulator.     

Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry

This paper presents an optimal design of a parallel manipulator aiming to perform pick-and-place operations at high speed and high acceleration. After reviewing existing architectures of high-speed and high-acceleration parallel manipulators, a new design of a 4-DOF parallel manipulator is presented, with an articulated traveling plate, which is free of internal singularities and is able to achieve high performances. The kinematic and simplified, but realistic, dynamic models are derived and validated on a manipulator prototype. Experimental tests show that this design is able to perform beyond the high targets, i.e., it reaches a speed of 5.5 m/s and an acceleration of 165 m/s². The experimental prototype was further optimized on the basis of kinematic and dynamic criteria. Once the motors, gear ratio, and several link lengths are determined, a modified design of the articulated traveling plate is proposed in order to reach a better dynamic equilibrium among the four legs of the manipulator. The obtained design is the basis of a commercial product offering the shortest cycle times among all robots available in today's market.     

仿人机器人轻型高刚性手臂设计及运动学分析

重点研究了7自由度轻型高刚性作业型仿人机器人手臂的机构设计和运动学分析方法.首先使用动力学仿真、有限元分析与实验测试相结合的方法,设计了仿人机器人手臂,该机械臂结构紧凑、质量轻、刚度高.同时,提出结合查询数据库和逆运动学计算去模仿人类手臂姿态,从而获得逆运动学最优解的方法.该方法不仅解决了冗余自由度带来的逆运动学多解问...     

Position and stiffness analysis of a new asymmetric 2PRR–PPR parallel CNC machine

In this paper, structural stiffness analysis of a new 3-axis asymmetric planar parallel manipulator, a 2 P RR–P P R structural kinematic chain, is investigated. The manipulator is proposed as a tool holder for a 5-axis hybrid computer numerical control (CNC) machine. First, the structure of the robot is introduced and inverse kinematics solution is presented. Secondly, stiffness matrix of the robot is determined using a continuous method based on Castigliano’s theorem and calculation of strain energy of the robot components. This method removes the need for commonly used simplifying assumptions and, therefore, results in good accuracy. For this purpose, force and strain energy for each segment of the robot are analyzed. Finally, to verify the analytical results, commercial FEM software is used to simulate the physical structure of the manipulator. A numerical example is presented which confirms the correctness of the analytical formulations.     

Intelligent spherical joints based tri-actuated spatial parallel manipulator for precision applications

This paper contributes to the design of a new table top size tri-actuated spatial parallel manipulator. The manipulator configuration is considered for its ability to provide a maximum achievable workspace freedom. A minimum of three legs with all the spherical joints is selected to make three SPS (Spherical-prismatic-spherical) kinematic chain configuration. The complexity of building a minimum constraint manipulator lies in the fact that it cannot stand on its own on three ball joints. To transform this into a workable mechanism, spherical joints are designed with internal stiffness and braking system such that the manipulator can withstand even external loads. A detailed design analysis is conducted for the customized ball joint with different inside actuation mechanisms. Manipulator working in the workspace is found smooth under a pre-loaded condition whereas magnetic actuation locks the joints at the destination point, thereby achieving both capabilities. The manipulator overall stiffness is then evaluated to make its use in micro‑meso scale applications.     

Geometrical conditions for the design of partial or full isotropic hexapods

This paper presents a methodology for the design of PKMs (parallel kinematic machines) with defined isotropy and stiffness. Partial isotropy or full isotropy can be achieved by suitable design choices. The former is useful for five axis applications, while the latter for six axis manipulators. The paper summarizes the concept of full and partial isotropy, and for a wide class of hexapods defines in analytical form the conditions to achieve it exactly. These conditions can be used to design isotropic parallel manipulators. The methodology requires that the six legs have to be divided into two groups (terns). The legs belonging to one tern are mutually identical and are positioned with radial symmetry with respect to the TCP (tool center point). The paper shows that the manipulator structure can be defined in term of 13 design parameters, the value of six of them are chosen in order to achieve the required isotropy and stiffness properties, while the remaining seven parameters can be used to optimize the structure. The design criterion here presented assures that stiffness isotropy, force, and velocity isotropy are all achieved contemporarily. This methodology can be practically applied to a large family of hexapods. © 2005 Wiley Periodicals, Inc.     

旋翼飞行机械臂建模及动态重心补偿控制

旋翼飞行机械臂是将多关节机械臂固连在旋翼飞行平台上而组成的一种面向主动任务操作的特殊系统,其飞行平台和机械臂之间存在强耦合特性.本文针对机械臂的规划运动对飞行平台的干扰问题,建立了系统运动学和动力学模型,并通过动态计算系统重心位置坐标,设计出基于backstepping的动态重心补偿控制方法,针对补偿项测量噪声问题设计了二阶低通滤波器,并使用Lyapunov稳定性理论证明了系统的稳定性.仿真和实验均验证了在相同的参数条件下,具有动态重心补偿项的控制算法比没有重心补偿项的控制算法在轨迹跟踪和姿态稳定方面具有明显优势.     

Dynamic modeling and redundant force optimization of a 2-DOF parallel kinematic machine with kinematic redundancy

High precision is still one of the challenges when parallel kinematic machines are applied to advanced equipment. In this paper, a novel planar 2-DOF parallel kinematic machine with kinematic redundancy is proposed and a method for redundant force optimization is presented to improve the precision of the machine. The inverse kinematics is derived, and the dynamic model is modeled with the Newton–Euler method. The deformations of the kinematic chains are calculated and their relationship with kinematic error of the machine is established. Then the size and direction of the redundant force acting on the platform are optimized to minimize the position error of the machine. The dynamic performance of the kinematically redundant machine is simulated and compared with its two corresponding counterparts, one is redundantly actuated and the other is non-redundant. The proposed kinematically redundant machine possesses the highest position precision during the motion process and is applied to develop a precision planar mobile platform as an application example. The method is general and suitable for the dynamic modeling and redundant force optimization of other redundant parallel kinematic machines.     

Design-by-Optimization and Control of Redundantly Actuated Parallel Kinematics Sliding Star

The paper deals with the design and control of an example of redundantly actuated parallel kinematic structure that can be a machine tool. The principle of redundant actuation brings parallel kinematic structures which do not have singular positions in workspace and which has increased dynamic, stiffness and accuracy properties. There is proposed a parallel kinematic structure called Sliding Star that has promising dynamic and stiffness properties. The conceptual design-by-optimization of this structure is briefly described. The redundantly actuated parallel kinematics have control problem due to mutual fighting of redundant drives. There is described the solution of this problem. Based on the investigated redundantly actuated parallel kinematics there has been built a laboratory prototype. The experimental results from the control of this prototype are briefly presented.     

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.     

Supervised learning based on the self-organizing maps for forward kinematic modeling of Stewart platform

In this study, we propose an alternative technique for solving the forward kinematic problem of parallel manipulator which is designed based on generalized Stewart platform. The focus of this work is to predict a pose vector of a moving plate from a given set of six leg lengths. Since the data of parallel kinematics are usually available in the form of nonlinear dynamic system, several methods of system identification have been proposed in order to construct the forward kinematic model and approximate the pose vectors. Although these methods based on a multilayer perceptron (MLP) neural network provide acceptable results, MLP training suffers from convergence to local optima. Thus, we propose to use an alternative supervised learning algorithm called vector-quantized temporal associative memory (VQTAM) instead of MLP-based methods. VQTAM relying on self-organizing map architecture is used to build the mapping from the input space to the output space such that the training/testing datasets are generated from inverse kinematic model. The solutions from standard VQTAM are improved by an autoregressive (AR) model and locally linear embedding (LLE). The experimental results indicate that VQTAM with AR/LLE gives the outputs with nearly 100% prediction accuracy in the case of smooth data, while VQTAM + LLE provides the most accurate prediction on noisy data. Therefore, VQTAM + LLE is a very robust estimation method and can practically be used for solving the forward kinematic problem.

     

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.