0
Research Papers

Dynamic Behavior of Flexible Multiple Links Captured Inside a Closed Space

[+] Author and Article Information
A. M. Shafei

Department of Mechanical Engineering,
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

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 11(5), 051016 (Feb 25, 2016) (13 pages) Paper No: CND-15-1320; doi: 10.1115/1.4032388 History: Received October 01, 2015; Revised December 12, 2015

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 n 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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Wittenburg, J. , 1977, Dynamics of Systems of Rigid Bodies, Teubner, Stuttgart, Germany.
Chang, C. C. , and Peng, S. T. , 2007, “ Impulsive Motion of Multibody Systems,” Multibody Syst. Dyn., 17(1), pp. 47–70. [CrossRef]
Hurmuzlu, Y. , and Marghitu, D. B. , 1994, “ Rigid Body Collision of Planar Kinematic Chain With Multiple Contact Points,” Int. J. Rob. Res., 13(1), pp. 82–92. [CrossRef]
Goswami, A. , Thuilot, B. , and Espiau, B. , 1998, “ A Study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos,” Int. J. Rob. Res., 17(12), pp. 1282–1301. [CrossRef]
Chevallereau, C. , Westervelt, E. R. , and Grizzle, J. W. , 2005, “ Asymptotically Stable Running for a Five-Link, Four-Actuator, Planar Bipedal Robot,” Int. J. Rob. Res., 24(6), pp. 431–464. [CrossRef]
Tlalolini, D. , Aoustin, Y. , and Chevallereau, C. , 2010, “ Design of a Walking Cyclic Gait With Single Support Phases and Impacts for the Locomotor System of a Thirteen-Link 3D Biped Using the Parametric Optimization,” Multibody Syst. Dyn., 23(1), pp. 33–56. [CrossRef]
Tornambè, A. , 1999, “ Modeling and Control of Impact in Mechanical Systems: Theory and Experimental Results,” IEEE Trans. Autom. Control, 44(2), pp. 294–309. [CrossRef]
Liu, S. , Wu, L. , and Lu, Z. , 2007, “ Impact Dynamic and Control of a Flexible Dual-Arm Space Robot Capturing an Object,” Appl. Math. Comput., 185(2), pp. 1149–1159. [CrossRef]
Khude, N. , Stanciulescu, I. , Melanz, D. , and Negrut, D. , 2013, “ Efficient Parallel Simulation of Large Flexible Body Systems With Multiple Contacts,” ASME J. Comput. Nonlinear Dyn., 8(4), p. 041003.
Kövecses, J. , and Cleghorn, W. , 2003, “ Finite and Impulsive Motion of Constrained Mechanical Systems Via Jourdain's Principle: Discrete and Hybrid Parameter Models,” Int. J. Non-Linear Mech., 38(6), pp. 935–956. [CrossRef]
Heppler, G. R. , and Kariz, Z. , 2000, “ A Controller for an Impacted Single Flexible Link,” J. Vib. Control, 6(3), pp. 407–428. [CrossRef]
Boghiu, D. , and Marghitu, D. B. , 1998, “ The Control of an Impacting Flexible Link Using Fuzzy Logic Strategy,” J. Vib. Control, 4(3), pp. 325–341. [CrossRef]
Seidi, M. , Hajiaghamemar, M. , and Caccese, V. , 2015, “ Evaluation of Effective Mass During Head Impact Due to Standing Falls,” Int. J. Crashworthiness, 20(2), pp. 134–141. [CrossRef]
Khulief, Y. A. , and Shabana, A. A. , 1987, “ A Continuous Force Model for the Impact Analysis of Flexible Multibody Systems,” Mech. Mach. Theory, 22(3), pp. 213–224. [CrossRef]
Yigit, A. S. , Ulsoy, A. G. , and Scott, R. A. , 1990, “ Dynamics of a Radially Rotating Beam With Impact, Part 1: Theoretical and Computational Model,” ASME J. Vib. Acoust., 112(1), pp. 65–70. [CrossRef]
Yigit, A. S. , Ulsoy, A. G. , and Scott, R. A. , 1990, “ Dynamics of a Radially Rotating Beam With Impact, Part 2: Experimental and Simulation Results,” ASME J. Vib. Acoust., 112(1), pp. 71–77. [CrossRef]
Yigit, A. S. , Ulsoy, A. G. , and Scott, R. A. , 1990, “ Spring-Dashpot Models for the Dynamics of a Radially Rotating Beam With Impact,” J. Sound Vib., 142(3), pp. 515–525. [CrossRef]
Yigit, A. S. , 1994, “ Impact Response of a Two-Link Rigid-Flexible Manipulators,” J. Sound Vib., 177(3), pp. 349–361. [CrossRef]
Chapnik, B. V. , Heppler, G. R. , and Aplevich, J. D. , 1991, “ Modeling Impact on a One-Link Flexible Robotic Arm,” IEEE Trans. Rob. Autom., 7(4), pp. 479–488. [CrossRef]
Shabana, A. A. , 1997, “ Flexible Multibody Dynamics: Review of Past and Recent Developments,” Multibody Syst. Dyn., 1(2), pp. 189–222. [CrossRef]
Khulief, Y. A. , 2012, “ Modeling of Impacts in Multibody Systems: An Overview,” ASME J. Comput. Nonlinear Dyn., 8(2), p. 021012.
Krauss, R. , 2012, “ Computationally Efficient Modeling of Flexible Robots Using the Transfer Matrix Method,” J. Vib. Control, 18(5), pp. 596–608. [CrossRef]
Mohan, A. , and Saha, S. K. , 2009, “ A Recursive, Numerically Stable, and Efficient Simulation Algorithm for Serial Robots With Flexible Links,” Multibody Syst. Dyn., 21(1), pp. 1–35. [CrossRef]
Tong, M. M. , 2010, “ A Recursive Algorithm for Solving the Generalized Velocities From the Momenta of Flexible Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 5(4), p. 041002.
Changizi, K. , and Shabana, A. A. , 1988, “ Recursive Formulation for Flexible Multibody Systems,” ASME J. Appl. Mech., 55(3), pp. 687–693. [CrossRef]
Shabana, A. A. , Hwang, Y. L. , and Wehage, R. A. , 1992, “ Projection Methods in Flexible Multibody Dynamics. Part I: Kinematics, Part II: Dynamic and Recursive Projection Methods,” Int. J. Numer. Methods Eng., 35(10), pp. 1941–1966. [CrossRef]
Lugris, U. , Naya, M. A. , Gonzalez, F. , and Cuadrado, J. , 2007, “ Performance and Application Criteria of Two Fast Formulations for Flexible Multibody Dynamics,” Mech. Based Des. Struct. Mach., 35(4), pp. 381–404. [CrossRef]
Wasfy, T. M. , and Noor, A. K. , 2003, “ Computational Strategies for Flexible Multibody Systems,” ASME Appl. Mech. Rev., 56(6), pp. 553–613. [CrossRef]
Korayem, M. H. , and Shafei, A. M. , 2013, “ Application of Recursive Gibbs–Appell Formulation in Deriving the Equations of Motion of N-Viscoelastic Robotic Manipulators in 3D Space Using Timoshenko Beam Theory,” Acta Astronaut., 83, pp. 273–294. [CrossRef]
Korayem, M. H. , and Shafei, A. M. , 2015, “ A New Approach for Dynamic Modeling of n-Viscoelastic-Link Robotic Manipulators Mounted on a Mobile Base,” Nonlinear Dyn., 79(4), pp. 2767–2786. [CrossRef]
Korayem, M. H. , Shafei, A. M. , and Dehkordi, S. F. , 2014, “ Systematic Modeling of a Chain of N-Flexible Link Manipulators Connected by Revolute–Prismatic Joints Using Recursive Gibbs–Appell Formulation,” Arch. Appl. Mech., 84(2), pp. 187–206. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

An open kinematic chain of flexible links floating through the space

Grahic Jump Location
Fig. 2

Two imaginary links connected with n real links to model spatial motions

Grahic Jump Location
Fig. 3

Inertia matrix of the whole system in the flight phase

Grahic Jump Location
Fig. 4

Right hand side vector of governing equations for the flight phase

Grahic Jump Location
Fig. 5

A multiflexible-link chin in impact phase

Grahic Jump Location
Fig. 6

A two-flexible-link planar robotic manipulator confined within a square

Grahic Jump Location
Fig. 7

Angular positions of the joints

Grahic Jump Location
Fig. 8

Angular velocities of the joints

Grahic Jump Location
Fig. 9

Modal generalized coordinates of the links

Grahic Jump Location
Fig. 10

Modal generalized velocities of the links

Grahic Jump Location
Fig. 11

Positions of the joints in the refX1 direction

Grahic Jump Location
Fig. 12

Absolute velocities of the joints in the refX1 direction

Grahic Jump Location
Fig. 13

Positions of the joints in the refX2 direction

Grahic Jump Location
Fig. 14

Absolute velocities of the joints in the refX2 direction

Grahic Jump Location
Fig. 15

(a)(b) Configurations of the system at different times

Grahic Jump Location
Fig. 16

A single flying link confined inside a closed cube

Grahic Jump Location
Fig. 17

Angular positions of joints

Grahic Jump Location
Fig. 18

Angular velocities of the joints

Grahic Jump Location
Fig. 19

(a)–(b) Modal generalized coordinate and its derivative with respect to time

Grahic Jump Location
Fig. 20

(a)(c) Positions of the joints in refX1, refX2, and refX3 directions

Grahic Jump Location
Fig. 21

(a)(c) Absolute velocities of the joints in refX1, refX2, and refX3 directions

Grahic Jump Location
Fig. 22

Configurations of the system at impact moments

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In