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Kinetostatic Modeling and Analysis of an Exechon parallel kinematic machine(PKM) Module

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Chinese Journal of Mechanical Engineering 2016年第1期29卷 33-44页

作者： ZHAO Yanqin JIN Yan ZHANG Jun School of Mechanical Engineering Anhui University of Technology School of Mechanical and Aerospace Engineering Queen's UniversityBelfastUK State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University

As a newly invented parallel kinematic machine（PKM）, Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method（FEM）. The equilibrium equations of the platform are derived with Newton＇s 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system＇s deflections. The platform＇s elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.

关键词： parallel kinematic machine substructure synthesis kinetostatic stiffness Exechon

Running Accuracy Analysis of a 3-RRR parallel kinematic machine Considering the Deformations of the Links

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Chinese Journal of Mechanical Engineering 2014年第5期27卷 890-899页

作者： WANG Liping JIANG Yao LI Tiemin Department of Mechanical Engineering Tsinghua University

parallel kinematic machines have drawn considerable attention and have been widely used in some special fields.However,high precision is still one of the challenges when they are used for advanced machine tools.One of the main reasons is that the kinematic chains of parallel kinematic machines are composed of elongated links that can easily suffer deformations,especially at high speeds and under heavy loads.A 3-RRR parallel kinematic machine is taken as a study object for investigating its accuracy with the consideration of the deformations of its links during the motion process.Based on the dynamic model constructed by the Newton-Euler method,all the inertia loads and constraint forces of the links are computed and their deformations are derived.Then the kinematic errors of the machine are derived with the consideration of the deformations of the links.Through further derivation,the accuracy of the machine is given in a simple explicit expression,which will be helpful to increase the calculating speed.The accuracy of this machine when following a selected circle path is simulated.The influences of magnitude of the maximum acceleration and external loads on the running accuracy of the machine are investigated.The results show that the external loads will deteriorate the accuracy of the machine tremendously when their direction coincides with the direction of the worst stiffness of the machine.The proposed method provides a solution for predicting the running accuracy of the parallel kinematic machines and can also be used in their design optimization as well as selection of suitable running parameters.

关键词： parallel kinematic machine dynamic model accuracy deformations

Compliance Modeling and Analysis of a 3-RPS parallel kinematic machine Module

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Chinese Journal of Mechanical Engineering 2014年第4期27卷 703-713页

作者： ZHANG Jun ZHAO Yanqin DAI Jiansheng School of Mechanical Engineering Anhui University of Technology Department of Informatics King's College London

The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric complexities. By using the screw theory, this paper explores the compliance modeling and eigencompliance evaluation of a newly patented 1T2R spindle head whose topological architecture is a 3-RPS parallel mechanism. The kinematic definitions and inverse position analysis are briefly addressed in the first place to provide necessary information for compliance modeling. By considering the 3-RPS parallel kinematic machine（PKM） as a typical compliant parallel device, whose three limb assemblages have bending, extending and torsional deflections, an analytical compliance model for the spindle head is established with screw theory and the analytical stiffness matrix of the platform is formulated. Based on the eigenscrew decomposition, the eigencompliance and corresponding eigenscrews are analyzed and the platform＇s compliance properties are physically interpreted as the suspension of six screw springs. The distributions of stiffness constants of the six screw springs throughout the workspace are predicted in a quick manner with a piece-by-piece calculation algorithm. The numerical simulation reveals a strong dependency of platform＇s compliance on its configuration in that they are axially symmetric due to structural features. At the last stage, the effects of some design variables such as structural, configurational and dimensional parameters on system rigidity characteristics are investigated with the purpose of providing useful information for the structural design and performance improvement of the PKM. Compared with previous efforts in compliance analysis of PKMs, the present methodology is more intuitive and universal thus can be easily applied to evaluate the overall rigidity performance of other PKMs with high efficiency.

关键词： compliance modeling parallel kinematic machine eigencompliance eigenscrew

kinematic DESIGN OF A RECONFIGURABLE MINIATURE parallel kinematic machine

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Chinese Journal of Mechanical Engineering 2003年第1期16卷 79-82页

作者： HuangTian DJWhitechouse 等 SchoolofMechanicalEngineering TianjinUniversityTianjing300072China SchoolofEngineering UniversityofWarwickConventryCV47ALUK

The kinematic design of a reconfigurable miniature parallel kinematic machineis dealt with. It shows that the reconfigurability may be realized by packaging a tripod-basedparallel mechanism with fixed length struts into a compact and rigid frame with which the differentconfigurations can be formed. Utilizing a dual parameter model, the influences of the geometricalparameters on the dexterous performance and the workspace/machine volume ratio are investigated. Anovel global performance index for the dimensional synthesis is proposed and optimized, resulting ina set of dimensionless geometrical parameters.

关键词： parallel kinematic machine Modularity kinematic design

Determination of servomotor parameters of a tripod-based parallel kinematic machine

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Progress in Natural Science:Materials International 2001年第8期 54-63页

作者：黄田赵兴玉王洋梅江平倪雁冰 China School of Mechanical Engineering Tianjin 300072 Tianjin University

This paper presents a comprehensive methodology to determine the servomotor parameters of a parallel kinematic machine according to the design specifications in terms of the cutting load, fast feed rate and accelerating capabilities. Due to the characteristics of the parallel format, the singular value decomposition technique is employed to determine the lower and upper bounds of the servomotor parameters such as the rated speed and torque. An approach is also developed to determine the maximum equivalent moment of inertia of the platform and struts reduced onto a servo axis , which therefore allows the accelerating capability of the servo system to be examined in terms of the maximum torque required. The effectiveness of this methodology is exemplified by the application to a tripod-based parallel kinematic machine for high-speed milling.

关键词： parallel kinematic machine inverse dynamics servomotor.

Dynamic Modeling and Eigenvalue Evaluation of a 3-DOF PKM Module

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Chinese Journal of Mechanical Engineering 2010年第2期23卷 166-173页

作者： ZHANG Jun LI Yonggang HUANG Tian School of Mechanical Engineering Tianjin University Tianjin 300072 China Tianjin University of Technology and Education Tianjin 300222 China

Due to the structural complexity, the dynamic modeling and quick performance evaluation for the parallel kinematic machines （PKMs） are still to be remained as two challenges in the stage of conceptual design. By using the finite element method and substructure synthesis, this paper mainly deals with the dynamic modeling and eigenvalue evaluation of a novel 3-DOF spindle head named the A3 head. The topological architecture behind the proposed A3 head is a 3-RPS parallel mechanism, which possesses one translational and two rotational capabilities. The mechanical features of the A3 head are briefly addressed in the first place followed by inverse position analysis. In the dynamic modeling, the platform is treated as a rigid body, the RPS limbs as the continuous uniform beams and the joints as lumped virtual springs. With the combination of substructure synthesis and finite element method, an analytical approach is then proposed to formulate the governing equations of motion of system using the compatibility conditions at interface between the limbs and the platform. Consequently, by solving the eigenvalue problem of the governing equations of motion, the distribution of lower natural frequencies of the A3 head throughout the entire workspace can be predicted in a quick manner. Modal analysis for the A3 head reveals that the distributions of lower natural frequencies are strongly related to the mechanism configuration and are axially symmetric due to system kinematic and structural features. The sensitivity analysis of the system indicates that the dimensional parameters of the 3-RPS mechanism have a slight effect on system lower natural frequencies while the joint compliances affect the distributions of lower natural frequencies significantly. The proposed dynamic modeling method can also be applied to other PKMs and can effectively evaluate the PKM＇s dynamic performance throughout the entire workspace.

关键词： dynamic modeling parallel kinematic machine natural frequency

parallel Mechanisms with Two or Three Degrees of Freedom

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Tsinghua Science and Technology 2003年第1期8卷 105-112页

作者：刘辛军汪劲松李铁民段广洪 Manufacturing Engineering Institute Department of Precision Instruments and Mechanology Tsinghua University

parallel manipulators for the machine tool industry have been studied extensively for various industrial applications. However, limited useful workspace areas, the poor mobility, and design difficulties of more complex parallel manipulators have led to more interest in parallel manipulators with less than six degrees of freedom (DoFs). Several parallel mechanisms with various numbers and types of degrees of freedom are described in this paper, which can be used in parallel kinematics machines, motion simulators, and industrial robots.

关键词： parallel manipulator parallel kinematic machine degree of freedom robot

The Virtual Product Design System for parallel machine Tools （PMTs）

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The Virtual Product Design System for Parallel Machine Tools...