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Applied Mathematics and Mechanics

, Volume 8, Issue 10, pp 957–967 | Cite as

A matrix method of displacement analysis of the general spatial 7R mechanism

  • Chen Wei-rong
Article

Abstract

An input-output equation of the general spatial 7R mechanism is derived in this paper by using the method in [1] and applying the rotation matrices. The result is the same as [2], but the process of derivation is simpler. Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vecfors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation. Moreover, an algorithm, which consists of successive applications of row transformation and expansion based on Laplace’s Theorem, is given to evaluate the 16×16 determinant according to its characteristic, so that the evaluation is much simplified.

Keywords

Angular Displacement Displacement Analysis Direction Cosine Recurrence Formula Triple Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Chen Wei-rong, The displacement analysis and calculation of degrees of freedom of spatial mechanisms using the optimization method in graph theory,Mechanical Design 2 (1986). (in Chinese)Google Scholar
  2. [2]
    Duffy, J. and C. Crane, A displacement analysis of the general spatial 7-link, 7R mechanism,Mechanism and Machine Theory,15, 3-A (1980), 153–169.CrossRefGoogle Scholar
  3. [3]
    Chen Wei-rong, Analytical theory of space meshing,Journal of China Coal Society,11, 2 (1979), 49–64. (in Chinese)Google Scholar
  4. [4]
    Freudenstein, F., Kinematics: past, present and future,Mechanism and Machine Theory,8, 2 (1973), 151–161.CrossRefGoogle Scholar
  5. [5]
    Duffy, J.,Analysis of Mechanisms and Robot Manipulators, Edward Arnold, London (1980), 56–120.Google Scholar
  6. [6]
    Beijing University,Advanced Algebra, The People’s Education Publishing House, Bejing (1978), 87–91. (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1987

Authors and Affiliations

  • Chen Wei-rong
    • 1
  1. 1.Shanghai Second Polytechnical UniversityShanghai

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