Structural Analysis of Parallel Mechanisms Using Conformal Geometric Algebra

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• 关键词：Conformal geometric algebra ; Parallel mechanism ; Position and orientation characteristic ; Symbolic computation ; Automatic derivation
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9834
• 期：1
• 页码：162-174
• 全文大小：797 KB
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  15.Li, H., Hestenes, D., Rockwood, A.: Generalized homogeneous coordinates for computational geometry. In: Sommer, G. (ed.) Geometric Computing with Clifford Algebras, pp. 27–59. Springer, Heidelberg (2001)
  16.Hildenbrand, D.: Geometric computing in computer graphics and robotics using conformal geometric algebra (Doctoral dissertation, Hildenbrand, Dietmar) (2006)
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• 作者单位：Lubin Hang (17)
  Chengwei Shen (17)
  Tingli Yang (18)
  
  17. Shanghai University of Engineering Science, Shanghai, 201620, China
  18. Changzhou University, Changzhou, 213016, China
  
• 丛书名：Intelligent Robotics and Applications
• ISBN：978-3-319-43506-0
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9834

文摘

The operable description of parallel mechanisms is the key to automatic derivation of structural analysis and synthesis. Conformal geometric algebra is introduced to describe robot mechanisms in this paper. A group of basis bivectors {e ₂₃, e ₃₁, e ₁₂, e _1∞, e _2∞, e _3∞} is established to express position and orientation characteristics of the joint axis. The union of each joint’s characteristics of serial mechanisms is defined via outer product operation and the intersection of each limb’s characteristics of parallel mechanisms is defined by shuffle product operation, respectively. In this work, a new algebraic symbol algorithm for end-effectors’ characteristics is proposed and proved validity via two case studies of 3-RRR and 4-URU PMs which is suitable for computer-aided derivation of mechanisms position and orientation characteristics.