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Fast forward kinematics algorithm for real-time and high-precision control of the 3-RPS parallel mechanism

Yue WANG, Jingjun YU, Xu PEI

《机械工程前沿（英文）》 2018年第13卷第3期页码 368-375 doi: 10.1007/s11465-018-0519-5

摘要：

A new forward kinematics algorithm for the mechanism of 3-RPS (R: Revolute; P: Prismatic; S: Spherical) parallel manipulators is proposed in this study. This algorithm is primarily based on the special geometric conditions of the 3-RPS parallel mechanism, and it eliminates the errors produced by parasitic motions to improve and ensure accuracy. Specifically, the errors can be less than 10^-6 . In this method, only the group of solutions that is consistent with the actual situation of the platform is obtained rapidly. This algorithm substantially improves calculation efficiency because the selected initial values are reasonable, and all the formulas in the calculation are analytical. This novel forward kinematics algorithm is well suited for real-time and high-precision control of the 3-RPS parallel mechanism.

关键词： 3-RPS parallel mechanism forward kinematics numerical algorithm parasitic motion

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含参数初值整定和自适应鲁棒方法的3-RPS气动并联平台位姿控制 Article

Guo-liang TAO,Ce SHANG,De-yuan MENG,Chao-chao ZHOU

《信息与电子工程前沿（英文）》 2017年第18卷第3期页码 303-316 doi: 10.1631/FITEE.1500353

摘要：本文讨论了关于气缸驱动的3-RPS并联平台的一种控制方法。研究对象使用气动比例方向阀控制各驱动气缸，并建立了系统的运动学和动力学模型，采用基于反步法和在线参数辨识的自适应鲁棒控制器作为主要控制方式。

关键词：参数初值整定；自适应鲁棒控制；并联机构；气缸

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Self-motions of 3-RPS manipulators

Josef SCHADLBAUER, Manfred L. HUSTY, Stéphane CARO, Philippe WENGERY

《机械工程前沿（英文）》 2013年第8卷第1期页码 62-69 doi: 10.1007/s11465-013-0366-3

摘要：

Recently a complete kinematic description of the 3-RPS parallel manipulator was obtained using algebraic constraint equations. It turned out that the workspace splits into two components describing two kinematically different operation modes. In this paper the algebraic description is used to give a complete analysis of all possible self-motions of this manipulator in both operation modes. Furthermore it is shown that a transition from one operation mode into the other in a self-motion is possible.

关键词： 3-RPS-manipulator singularity self-motion

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A rolling 3-UPU parallel mechanism

Zhihuai MIAO, Yan’an YAO, Xianwen KONG

《机械工程前沿（英文）》 2013年第8卷第4期页码 340-349 doi: 10.1007/s11465-013-0282-6

摘要：

A novel rolling mechanism is proposed based on a 3-UPU parallel mechanism in this paper. The rolling mechanism is composed of two platforms connected by three UPU (universal-prismatic-universal) serial-chain type limbs. The degree-of-freedom of the mechanism is analyzed using screw theory. Gait analysis and stability analysis are presented in detail. Four rolling modes of the mechanism are discussed and simulated. The feasibility of the rolling mechanism is verified by means of a physical prototype. Finally, its terrain adaptability is enhanced through planning the rolling gaits.

关键词： parallel mechanism rolling mechanism screw theory

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Parasitic rotation evaluation and avoidance of 3-UPU parallel mechanism

Haibo QU, Yuefa FANG, Sheng GUO

《机械工程前沿（英文）》 2012年第7卷第2期页码 210-218 doi: 10.1007/s11465-012-0317-4

摘要：

Based on the prototype of 3-UPU (universal-prismatic-universal joint) parallel mechanism proposed by Tsai [ ], the parasitic rotation evaluation is performed and calculated the bound of instability of SNU Seoul National University 3-UPU parallel mechanism. Through analysis of the terminal constraint system of the 3-UPU parallel mechanism, the equation about the parasitic rotation and limited clearance is presented. Then the norm of possible parasitic rotation is employed to evaluate the mechanism stability with limited clearance. The higher this number the worst is the pose, the lower it is the best it is. And the contour atlas of parasitic rotation is obtained, which can be used for further analysis and design. With the practice experiment result of SUN 3-UPU parallel mechanism, we find it’s bound of instability, which indicates there will appear the parasitic rotation when the number exceeds the bound. Finally, the method for avoidance of possible parasitic motions is presented by adding redundantly actuated limbs.

关键词： parallel mechanism 3-UPU (universal-prismatic-universal joint) parasitic motions limited clearance redundantly actuated limbs

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A comprehensive analysis of a 3-P (Pa) S spatial parallel manipulator

Yuzhe LIU,Liping WANG,Jun WU,Jinsong WANG

《机械工程前沿（英文）》 2015年第10卷第1期页码 7-19 doi: 10.1007/s11465-015-0324-3

摘要：

In this paper, a novel 3-degree of freedom (3-DOF) spatial parallel kinematic machine (PKM) is analyzed. The manipulator owns three main motions (two rotations and one translation) and three concomitant motions (one rotation and two translations). At first, the structure of this spatial PKM is simplified according to the characteristic of each limb. Secondly, the kinematics model of this spatial PKM is set up. In addition, the relationship between the main motions and concomitant motions is studied. The workspaces respectively based on the outputs and inputs are derived and analyzed. Furthermore, the velocity model is put forward. Two indexes based on the velocity model are employed to investigate the performance of this spatial PKM. At last, the output error model can be obtained and simulated. The comprehensive kinematics analysis in this paper is greatly useful for the future applications of this spatial PKM.

关键词： parallel mechanism concomitant motions kinematics workspaces error model

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Optimal design of a linkage–cam mechanism-based redundantly actuated parallel manipulator

《机械工程前沿（英文）》 2021年第16卷第3期页码 451-467 doi: 10.1007/s11465-021-0634-6

摘要： A redundantly actuated parallel manipulator (RAPM) with mixed translational and rotational degrees of freedom (DOFs) is challenged for its dimensionally homogeneous Jacobian modeling and optimal design of architecture. In this paper, a means to achieve redundant actuation by adding kinematic constraints is introduced, which reduces the DOFs of the end-effector (EE). A generic dimensionally homogeneous Jacobian is developed for this type of RAPMs, which maps the generalized velocities of three points on the EE to the joint velocities. A new optimization algorithm derived from this dimensionally homogeneous Jacobian is proposed for the optimal design of this type of RAPMs. As an example, this paper presents a spatial RAPM involving linkages and cam mechanisms. This RAPM has 4 DOFs and 6 translational actuations. The linkage lengths and the position of the universal joints of the RAPM are optimized based on the dimensionally homogeneous Jacobian.

关键词： redundant actuation parallel manipulator linkage–cam mechanism Jacobian optimal design

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Design and analysis of the gripper mechanism based on generalized parallel mechanisms with configurable

《机械工程前沿（英文）》 2021年第16卷第4期页码 765-781 doi: 10.1007/s11465-021-0655-1

摘要： Generalized parallel mechanisms with a configurable moving platform have become popular in the research field of parallel mechanism. This type of gripper mechanism can be applied to grasp large or heavy objects in different environments that are dangerous and complex for humans. This study proposes a family of novel (5 + 1) degrees of freedom (three translations and two rotations plus an additional grasping motion) gripper mechanisms based on the generalized parallel mechanisms with a configurable moving platform. First, the configurable moving platform, which is a closed loop, is designed for grasping manipulation. The hybrid topological arrangement is determined to improve the stiffness of the manipulator and realize high load-to-weight ratios. A sufficient rule based on Lie group theory is proposed to synthesize the mechanism. The hybrid limb structure is also enumerated. A family of novel gripper mechanisms can be assembled through the hybrid limbs by satisfying the rule. Two examples of the gripper mechanisms with and without parallelogram pairs are shown in this study. A kinematic analysis of the example mechanism is presented. The workspace shows that the mechanism possesses high rotational capability. In addition, a stiffness analysis is performed.

关键词： generalized parallel mechanism configurable moving platform gripper mechanism type synthesis kinematic analysis

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Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

null

《机械工程前沿（英文）》 2014年第9卷第2期页码 120-129 doi: 10.1007/s11465-014-0300-3

摘要：

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kinematic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z- axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. Error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.

关键词： translational Parallel Kinematic Machine error modeling global error transformation index

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A feasibility study on the design and walking operation of a biped locomotor via dynamic simulation

null

《机械工程前沿（英文）》 2016年第11卷第2期页码 144-158 doi: 10.1007/s11465-016-0391-0

摘要：

A feasibility study on the mechanical design and walking operation of a Cassino biped locomotor is presented in this paper. The biped locomotor consists of two identical 3 degrees-of-freedom tripod leg mechanisms with a parallel manipulator architecture. Planning of the biped walking gait is performed by coordinating the motions of the two leg mechanisms and waist. A three-dimensional model is elaborated in SolidWorks^® environment in order to characterize a feasible mechanical design. Dynamic simulation is carried out in MSC.ADAMS^® environment with the aims of characterizing and evaluating the dynamic walking performance of the proposed design. Simulation results show that the proposed biped locomotor with proper input motions of linear actuators performs practical and feasible walking on flat surfaces with limited actuation and reaction forces between its feet and the ground. A preliminary prototype of the biped locomotor is built for the purpose of evaluating the operation performance of the biped walking gait of the proposed locomotor.

关键词： feasibility study biped locomotor biped walking mechanical design dynamic simulation tripod leg mechanism 3-UPU parallel manipulator

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Variable identification and automatic tuning of the main module of a servo system of parallel mechanism

YANG Zhiyong, XU Meng, HUANG Tian, NI Yanbing

《机械工程前沿（英文）》 2007年第2卷第1期页码 82-88 doi: 10.1007/s11465-007-0014-x

摘要： The variables of the main module of a servo system for miniature reconfigurable parallel mechanism were identified and automatically tuned. With the reverse solution module of the translation, the module with the exerted translation joint was obtained, which included the location, velocity and acceleration of the parallelogram carriage-branch. The rigid dynamic reverse model was set as the virtual work principle. To identify the variables of the servo system, the triangle-shaped input signal with variable frequency was adopted to overcome the disadvantages of the pseudo-random number sequence, i.e., making the change of the vibration amplitude of the motor dramatically, easily impact the servo motor and make the velocity loop open and so on. Moreover, all the variables including the rotary inertia of the servo system were identified by the additive mass. The overshoot and rise time were the optimum goals, the limited changing load with the attitude was considered, and the range of the controller variables in the servo system was identified. The results of the experiments prove that the method is accurate.

关键词： acceleration reconfigurable parallel additive sequence parallel mechanism

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Design, analysis, and neural control of a bionic parallel mechanism

《机械工程前沿（英文）》 2021年第16卷第3期页码 468-486 doi: 10.1007/s11465-021-0640-8

摘要： Although the torso plays an important role in the movement coordination and versatile locomotion of mammals, the structural design and neuromechanical control of a bionic torso have not been fully addressed. In this paper, a parallel mechanism is designed as a bionic torso to improve the agility, coordination, and diversity of robot locomotion. The mechanism consists of 6-degree of freedom actuated parallel joints and can perfectly simulate the bending and stretching of an animal’s torso during walking and running. The overall spatial motion performance of the parallel mechanism is improved by optimizing the structural parameters. Based on this structure, the rhythmic motion of the parallel mechanism is obtained by supporting state analysis. The neural control of the parallel mechanism is realized by constructing a neuromechanical network, which merges the rhythmic signals of the legs and generates the locomotion of the bionic parallel mechanism for different motion patterns. Experimental results show that the complete integrated system can be controlled in real time to achieve proper limb–torso coordination. This coordination enables several different motions with effectiveness and good performance.

关键词： neural control behavior network rhythm motion pattern

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Singularity loci of an orthogonal spherical two-degree-of-freedom parallel mechanism

Jialun YANG, Feng GAO,

《机械工程前沿（英文）》 2009年第4卷第4期页码 379-385 doi: 10.1007/s11465-009-0075-0

摘要： Singularity analysis plays an important role in the design of robots, especially for parallel robots. In this paper, the direct and inverse kinematics of an orthogonal spherical two-degree-of-freedom parallel mechanism is proposed based on the modified Euler angles. All the singular poses of the mechanism are achieved through the direct kinematic analysis. Self-motions, which are different from the general spherical 5 parallel mechanisms, are also discussed. Singularity loci in the joint space and Cartesian space are plotted according to the Jacobin of the mechanism. Result shows that the singularity loci at the joint space are two circles and one line, whereas at the Cartesian space are a circle.

关键词： 2-DOF orthogonal spherical parallel mechanism singularity loci self-motions

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Design and analysis of partially decoupled translational parallel mechanisms with single-loop structures

《机械工程前沿（英文）》 2022年第17卷第3期 doi: 10.1007/s11465-022-0695-1

摘要： This study presents a family of novel translational parallel mechanisms (TPMs) with single-loop topological structures. The proposed mechanism consists of only revolute and prismatic joints. The novel TPMs are simpler in structure and have fewer joints and components than the well-known Delta Robot. Four types of 2-degree of freedom driving systems are applied to different limb structures to avoid the moving actuator that causes the problem of increased moving mass. Four sample TPMs are constructed using the synthesized limbs, and one of them is investigated in terms of kinematic performance. First, a position analysis is performed and validated through numerical simulation to reveal the characteristics of partially decoupled motion, which improves the controllability of TPM. Second, singular configurations are identified, and the resulting singularity curve is obtained. Lastly, the workspace of TPM is analyzed, and the relationship between the singular configurations and the reachable workspace is explored. The workspace of the 3-CRR (C denotes the cylindrical joint and R denotes the revolute joint) translational mechanism is also presented to prove that the proposed TPM has a fairly large workspace.

关键词： translational parallel mechanism single loop multiple driving system workspace analysis singularity

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Stiffness of a 3-degree of freedom translational parallel kinematic machine

null

《机械工程前沿（英文）》 2014年第9卷第3期页码 233-241 doi: 10.1007/s11465-014-0312-z

摘要：

In this paper, a typical 3-degree of freedom (3-DOF) translational parallel kinematic machine (PKM) is studied and analyzed whose tool platform has only translations along X-, Y- and Z-axes. It consists of three limbs, each of which have arm and forearm with prismatic-revolute-revolute-revolute (PRRR) joints. Inverse kinematics analysis is carried out to find the slider coordinates and joint angles for a given position of tool platform. Stiffness modeling is done based on the compliance matrices of arm and forearm of each limb. Using the stiffness modeling the variations of minimum and maximum translational stiffness in the workspace are analyzed. For various architectural parameters of the 3-DOF PKM the tendency of variations on the minimum and maximum stiffness over the entire workspace is studied; and also the deflections of the tool platform along X, Y, and Z directions with respect to various forces are presented.

关键词： 3-DOF translational PKM inverse kinematics stiffness modeling translational stiffness