过约束与局部自由度对机构关节约束反力可解性的影响

王庚祥; 刘宏昭; 原大宁

doi:10.13433/j.cnki.1003-8728.2014.0603

过约束与局部自由度对机构关节约束反力可解性的影响

doi: 10.13433/j.cnki.1003-8728.2014.0603

1.
西安理工大学,机械与精密仪器工程学院西安 710048

基金项目:

国家自然科学基金项目(51275404)

陕西省重点学科建设专项资金项目

陕西高校省级重点实验室科研项目(2010JS080)

西安理工大学优秀博士学位论文研究基金项目(102-211209)资助

详细信息

作者简介:
王庚祥(1985-)，博士研究生，研究方向为并联机器人和机械设计及理论，wanggengxiang27@163.com

通讯作者:
刘宏昭，教授，博士，博士生导师，liu-hongzhao@163.com

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- 文章访问数: 206
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- 被引次数: 0
出版历程
- 收稿日期: 2012-10-13
- 刊出日期: 2015-06-10

Influences of Over-constraint and Local Degree of Freedom on the Solvability of Mechanism Joint Constraint Force

1.
School of mechanical and Precision Instrument Engineering,Xi'an University of Technology,Xi'an 710048

摘要

摘要: 利用静力学平衡方程研究了一种含局部自由度的4-SPS/CU无过约束并联机构的受力分析。写出了该机构的静力学平衡方程并得出其方程组中方程个数大于未知量的个数,采用局部转换矩阵去掉了该机构中局部自由度对应的力矩平衡方程使原来的超定方程变为静定方程。说明了对机构中局部自由度的预处理提高了静力学平衡方程的求解效率。为了系统的研究过约束和局部自由度对机构静力学平衡方程的影响,分别讨论了2阶至5阶过约束机构静力学平衡方程的可解性与机构中过约束与局部自由度的关系,制定了机构中局部自由度和过约束的判定方法。证明了机构中过约束与局部自由度对机构静力学平衡方程的可解性影响具有一般性,为机构的关节约束反力求解提供了理论基础。
- 关节反力 /
- 静力学 /
- 过约束 /
- 局部自由度
Abstract: The force analysis of a novel 4-SPS/CU parallel mechanism is investigated through statics vectorequilibrium equations. The equilibrium equations in which the equations' number is greater than the unknownvariables are formulated for this mechanism. It happens that the number of redundant equations is equal to the localdegrees of freedom, and redundant equations are abandoned by using the local switch matrix. Such preprocessingfor the local degrees of freedom can improve the efficiency of the solved statics equilibrium equations. In order tosystematically research the influence of the local degrees of freedom and over-constraint on the statics equilibriumequations, the relations between the solvability of statics equilibrium equations in the two to five orderoverconstrained mechanism and the local degrees of freedom, over-constraint are respectively discussed. Thejudgment method of the local degrees of freedom and over-constraint is established. It proves that the influences ofthe local degrees of freedom and over-constraint on the statics equilibrium equations are universal, which providesthe rationale for the solution of joint constraint forces.
- efficiency /
- Joint constraint force /
- local degree of freedom /
- matrix algebra

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参考文献(32)

[1]	Slavia alinic'.Determination of joint reaction forces in a symbolic form in rigid multibody systems [J].Mechanism and Machine Theory,2011,46: 1796-1810
[2]	Frczek J,Wojtyra M．On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and coulomb friction in joints [J].Mechanism and Machine Theory,2011,46: 312-334
[3]	李仁军,刘宏昭,李鹏飞．考虑非线性摩擦的混合输入机构动力学研究[J]. 机械科学与技术,2009,28(2): 222-226Li r J,Liu H Z,Li P F．Dynamic modeling of a hybrid machine with nonlinear friction considered [J].Mechanical Science and Technology for Aerospace Engineering,2009,28(2): 222-226 (in Chinese)
[4]	Wojtyra M．Joint reactions in rigid body mechanismswith dependent constraints [J]. Mechanism and Machine Theory,2009,44: 2265-2278
[5]	Lu Y,Shi Y,Huang Z,et al．Kinematics/statics of a 4-DOF over-constrained parallel manipulator with 3 legs [J]. Mechanism and Machine Theory,2009,44:1497-1506
[6]	Wojtyra M．Joint reaction forces in multibody systems with redundant constraints [J]. Multibody System Dynamics,2005,14: 23-46
[7]	黄勇刚,黄茂林,向成宣,等．无过约束少自由度并联机器人构型设计方法[J]. 中国机械工程,2009,20(2): 222-228Huang Y G,Huang M L,Xiang C X,et al．Synthesis method of non-over constrained lower-mobility parallel robots[J]. China Mechanical Engineering,2009,20(2): 222-228 (in Chinese)
[8]	Tsai M S,Yuan W H．Inverse dynamics analysis for a 3-PrS parallel mechanism based on a special decomposition of the reaction forces[J]. Mechanism and Machine Theory,2010,45: 1491-1508
[9]	Li Y,Xu Q．Kinematics and inverse dynamics analysis for a general 3-PrS spatial parallel mechanism[J].robotica,2005,23: 219-229
[10]	Du J L,Bao H,Cui C Z,et al．Dynamic analysis of cable-driven parallel manipulators with time-varying cable lengths [J]. Finite Elements in Analysis and Design,2012,48(1): 1392-1399
[11]	Lim W B,Yang G L,Yeo S H．A generic force-closure analysis algorithm for cable-driven parallel manipulators[J]. Mechanism and Machine Theory,2011,46: 1265-1275
[12]	Boudreau r,Nokleby S．Force optimization of kinematicallyredundant planar parallel manipulators following a desired trajectory[J]. Mechanism and Machine Theory，2012,56: 138-155
[13]	Xu Y D,Yao J T,Zhao Y S．Inverse dynamics and internal forces of the redundantly actuated parallel manipulators[J]. Mechanism and Machine Theory，2012,51: 172-184
[14]	Garg V,Nokleby S B,Carretero J A．wrench capability analysis of redundantly actuated spatial parallel manipulators [J]. Mechanism and Machine Theory，2009,44: 1070-1081
[15]	Jesus J Cervantes-Sanchez,JoseM．rico-Martinez,Salvador Pacheco-Gutierrez,et al．Static analysis of spatial parallel manipulators by means of the principle of virtual work[J].robotics and Computer-integrated Manufacturing,2012，28: 385-401
[16]	Lu Y．Using virtual work theory and CAD functionalities for solving active force and passive force of spatial parallel manipulators [J]. Mechanism and Machine Theory,2007,42: 839-858
[17]	崔冰艳,金振林．农业机器人新型肘关节的静力学性能分析[J]. 农业工程学报,2011,27(3): 122-125Cui B Y,Jin Z L．Analysis of statics performance for a novel elbow joint of agricultural robot[J]. Transactions of the CSAE,2011,27(3): 122-125 (in Chinese)
[18]	程佳,王宣银,李强,等．4TPS-PS 并联四自由度电动平台的受力特性研究[J]. 哈尔滨工业大学学报，2009,41 (1): 108-112Chen J,Wang X Y,Li Q,et al．Kinetostatic characters of parallel 4-DOF platform with 4TPS-PS structure[J].Journal of Harbin Institute of Technology,2009,41 (1):108-112 (in Chinese)
[19]	刘士昌,陈子明,刘婧芳,等．基于螺旋理论对单环空间 rSUr 机构受力分析[J]. 机械工程学报,2011,47(13): 23-28Liu S C,Chen Z M,Liu J F,et al．Force analysis of single ring spatial rsur mechanism based on screw theory [J]. Journal of Mechanical Engineering,2011,47 (3):23-28 (in Chinese)
[20]	Blajer W．On the determination of joint reactions in multibody mechanisms[J]. Transactions of the ASME，Journal of Mechanical Design,2004,126: 341-350
[21]	Geike T,McPhee J．Inverse dynamic analysis of parallel manipulator s with full mobility[J]. Mechanism and Machine Theory,2003,38: 549-562
[22]	Blajer W．An alternative scheme for determination of joint reaction forces in human multibody models[J].Journal of Theoretical and Applied Mechanics,2005,43(4): 813-824
[23]	Blajer W,Dziewiecki K,Mazur Z．Multibody modeling of human body for the inverse dynamics analysis of sagittal plane movements [J]. Multibody System Dynamics,2007,18(2): 217-232
[24]	赵燕,黄真．3-rPS 并联机构的主动力和约束力分析[J]. 燕山大学学报,2008,32(4): 299-303Zhao Y,Huang Z．The analysis of active forces and constraint reactions of 3-rPS parallel manipulator[J].Journal of Yanshan University,2008,32 (4): 299-303(in Chinese)
[25]	Song S M,Gao X．The mobility equation and the solvability of joint forces/torques in dynamic analysis[J].ASME Journal of Mechanical Design,1992,114:257-262
[26]	周玉林,刘磊,高峰．3 自由度球面并联机构 3-rrr静力全解[J]. 机械工程学报,2008,44(6): 169-176Zhou Y L,Liu L,Gao F．Full static solving of 3-DOF spherical parallel mechanism 3-rrr [J]. Chinese Journal of Mechanical Engineering,2008,44 (6): 169-176 (in Chinese)
[27]	赵燕,黄真．含过约束力偶的少自由度并联机构的受力分析[J]. 机械工程学报,2010,46(5): 15-21Zhao Y,Huang Z．Force analysis lower-mobility parallel mechanisms with over-constrained couples[J]. Journal of Mechanical Engineering,2010,46 (5): 15-21 (in Chinese)
[28]	韩先国,陈五一．基于运动约束解过约束并联机构变形协调方程[J]. 力学与实践,2005,27(3): 65-67Han X G,Chen W Y．The method to solve the compatibility equation of distortion of over constraint parallel manipulator based on kinematic constraint[J].Mechanics in Engineering,2005,27 (3): 65-67 (inChinese)
[29]	Song S M,Gao X C．The mobility equation and the solvability of joint forces/torques in dynamic analysis[J].ASME Journal of Mechanical Design,1992,114:257-262
[30]	王庚祥,原大宁,刘宏昭．空间 4-SPS/CU 并联机构运动学分析[J]. 农业机械学报,2012,43(3): 207-212Wang G X,Yuan D N,Liu H Z．Kinematics analysis of spatial 4-SPS/CU parallel mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery,2012，43(3): 207-212 (in Chinese)
[31]	王庚祥,刘宏昭,原大宁．空间 4-SPS/CU 并联机构的受力分析[J]. 农业工程学报,2012,28(22): 30-38Wang G X,Liu H Z,Yuan D N．Force analysis of spatial 4-SPS/CU parallel mechanism[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE),2012,28 (22): 30-38 (in Chinese)
[32]	黄真,赵永生,赵铁石．高等空间机构学[M]. 北京:高等教育出版社,2006 Huang Z,Zhao Y S,Zhao T S．Advanced spatial mechanism[M]. Beijing: Higher Education Press,2006