This work presents a systematic method for the dynamic modeling of flexible multiple links that are confined within a closed environment. The behavior of such a system can be completely formulated by two different mathematical models. Highly coupled differential equations are employed to model the confined multilink system when it has no impact with the surrounding walls; and algebraic equations are exploited whenever this open kinematic chain system collides with the confining surfaces. Here, to avoid using the 4 × 4 transformation matrices, which suffers from high computational complexities for deriving the governing equations of flexible multiple links, 3 × 3 rotational matrices based on the recursive Gibbs-Appell formulation has been utilized. In fact, the main aspect of this paper is the automatic approach, which is used to switch from the differential equations to the algebraic equations when this multilink chain collides with the surrounding walls. In this study, the flexible links are modeled according to the Euler–Bernoulli beam theory (EBBT) and the assumed mode method. Moreover, in deriving the motion equations, the manipulators are not limited to have only planar motions. In fact, for systematic modeling of the motion of a multiflexible-link system in 3D space, two imaginary links are added to the real links of a manipulator in order to model the spatial rotations of the system. Finally, two case studies are simulated to demonstrate the correctness of the proposed approach.
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September 2016
Research-Article
Dynamic Behavior of Flexible Multiple Links Captured Inside a Closed Space
A. M. Shafei,
A. M. Shafei
Department of Mechanical Engineering,
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
e-mail: shafei@uk.ac.ir
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
e-mail: shafei@uk.ac.ir
Search for other works by this author on:
H. R. Shafei
H. R. Shafei
Department of Mechanical Engineering,
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
Search for other works by this author on:
A. M. Shafei
Department of Mechanical Engineering,
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
e-mail: shafei@uk.ac.ir
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
e-mail: shafei@uk.ac.ir
H. R. Shafei
Department of Mechanical Engineering,
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
Shahid Bahonar University of Kerman,
Kerman 76188-68366, Iran
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received October 1, 2015; final manuscript received December 12, 2015; published online February 25, 2016. Assoc. Editor: Ahmet S. Yigit.
J. Comput. Nonlinear Dynam. Sep 2016, 11(5): 051016 (13 pages)
Published Online: February 25, 2016
Article history
Received:
October 1, 2015
Revised:
December 12, 2015
Citation
Shafei, A. M., and Shafei, H. R. (February 25, 2016). "Dynamic Behavior of Flexible Multiple Links Captured Inside a Closed Space." ASME. J. Comput. Nonlinear Dynam. September 2016; 11(5): 051016. https://doi.org/10.1115/1.4032388
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