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Volume 24 Issue 5
May  1998
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Journal of Beijing University of Aeronautics and Astronautics  > 1998  >  24(5): 603-606.
Han Lin, Liao Qizheng, Liang Chonggaoet al. Closed-Form Displacement Analysis of a Planar Fifth-Class Group with Lower Pairs[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(5): 603-606. (in Chinese)
Citation: Han Lin, Liao Qizheng, Liang Chonggaoet al. Closed-Form Displacement Analysis of a Planar Fifth-Class Group with Lower Pairs[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(5): 603-606. (in Chinese)
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Closed-Form Displacement Analysis of a Planar Fifth-Class Group with Lower Pairs

  • 1.

    Beijing University of Aeronautics and Astronautics,Dept. of Mechanical and Electronical Engineering

  • 2. Beijing University of Posts Telecommunications,Dept. of Mechanical and Electronic Engineering

  • Received Date: 16 Jul 1997
  • Publish Date: 31 May 1998
    Abstract
  • The closed-form displacement analysis of one kind of planar fifth-class groups with 8 links and 12 lower pairs is solved by the method of combining vector with complex number. First, the vector equations are established according to different loops. Then the equations are changed into the form of complex number. The problem is reduced to a single unknown equation after algebraic elimination. The input-output equation, which is proved to be a 42th degree polynomial equation, is obtained. It shows that this construction of fifth-class group has 42 structures. Last, a numerical example is studied. Four real roots are listed. The symbolic computation is carried out by computer algebra system Mathematica.

     

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  • 1. 曹惟庆. 机构组成原理. 北京:高等教育出版社,1983 2. 白师贤. 高等机构学. 上海:上海科学技术出版社,1988 3. 楼鸿棣,邹慧君. 高等机械原理. 北京:高等教育出版社,1990 4. Liand S, Matthew G K. Closed form kinematic analysis of planar assur Ⅱ groups. In:Bautista E, ed. The theory of machines and mechanisms Proceedings of the 7th World Congress, Spain, Sevilla:Copyright-Pdrgamon Books Ltd, 1987. 141~145 5. Radcliffe C W, Zlokolica M Z, Cveticanin L. Kinematic analysis of Assur groups of the third class by numerical solution of contraint equations. In:Bautista E, ed. The theory of machines and mechanisms Proceedings of the 7th World Congress, Spain, Sevilla:Copyright-Pdrgamon Books Ltd, 1987. 169~172 6. Gosslin C M, Merlet J P.The direct kinematics of planar parallel manipulators:special architectures and number of solution. MMT, 1994, 29(8):1083~1098
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