Systematic modeling of a chain of N-flexible link manipulators connected by revolute-prismatic joints using recursive Gibbs-Appell formulation. (English) Zbl 1298.70004
The authors discuss the rather complex title problem using a recursive Gibbs-Appell formulation. The manipulator links are represented as Euler-Bernoulli beams. The effect of gravity as well as longitudinal, transverse, and torsional vibrations are considered. What complicates the analysis is the inclusion of both prismatic as well as flexible joints. The end result is a systematic algorithm for developing the governing equations of motion for very general N-link manipulator systems.
Considering the subject matter, the paper is somewhat detailed. Nevertheless, it provides a basis for engineers and designers needing to develop motion equations for large flexible multibody systems. The paper is then likely to be of interest and use to both theoreticians and designers.
Considering the subject matter, the paper is somewhat detailed. Nevertheless, it provides a basis for engineers and designers needing to develop motion equations for large flexible multibody systems. The paper is then likely to be of interest and use to both theoreticians and designers.
Reviewer: Ronald L. Huston (Cincinnati)
MSC:
| 70E55 | Dynamics of multibody systems |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
References:
| [1] | Geradin M., Cardona A.: Flexible Multibody Dynamics: A Finite Element Approach. Wiley, New York (2001) |
| [2] | Dwivedy S.K., Eberhard P.: Dynamic analysis of flexible manipulators, a literature review. Mech. Mach. Theory 25(7), 749-777 (2006) · Zbl 1095.70005 · doi:10.1016/j.mechmachtheory.2006.01.014 |
| [3] | Brener H.: Elastic Multibody Dynamics/A Direct Ritz Approach. Springer, Berlin (2008) · Zbl 1147.70002 · doi:10.1007/978-1-4020-8680-9 |
| [4] | Pan Y.C., Scott R.A., Ulsoy A.G.: Dynamic modeling and simulation of flexible robots with prismatic joints. J. Mech. Design 112, 307-314 (1990) · doi:10.1115/1.2912609 |
| [5] | Yuh J., Young T.: Dynamic modeling of an axially moving beam in rotation: simulation and experiment. Trans. ASME J. Dyn. Syst. Meas. Control 113, 34-40 (1991) · doi:10.1115/1.2896355 |
| [6] | Al-Bedoor B.O., Khulief Y.A.: General planar dynamics of a sliding flexible link. J. Sound Vib. 206(5), 641-661 (1997) · doi:10.1006/jsvi.1997.1129 |
| [7] | Basher, H.A.: Modeling and simulation of flexible robot manipulator with a prismatic joint. In: Conference Proceedings—IEEE SoutheastCon, Art. No. 4147428, pp. 255-260. (2007) |
| [8] | Farid M., Salimi I.: Inverse dynamic of a planar flexible-link manipulator with revolute-prismatic joints. Proc. ASME Int. Mech. Eng. Congr. Expo. 2, 347-352 (2001) |
| [9] | Khadem S.E., Pirmohammadi A.A.: Analytical development of dynamic equations of motion for a three-dimensional flexible manipulator with revolute and prismatic joints. IEEE Trans. Syst. Man Cybern. B Cybern. 33(2), 237-249 (2003) · doi:10.1109/TSMCB.2003.810439 |
| [10] | Kalyoncu M.: Mathematical modeling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint. Appl. Math. Model. 32(6), 1087-1098 (2008) · Zbl 1145.70305 · doi:10.1016/j.apm.2007.02.032 |
| [11] | Theodore R.J., Ghosal A.: Modeling of flexible-link manipulators with prismatic joints. IEEE Trans. Syst. Man Cybern. B Cybern. 27(2), 296-305 (1997) · doi:10.1109/3477.558822 |
| [12] | Chalhoub N.G., Chen L.: A structural flexibility transformation matrix for modeling open-kinematic chains with revolute and prismatic joints. J. Sound Vib. 218(1), 45-63 (1998) · doi:10.1006/jsvi.1998.1779 |
| [13] | Gurgoze M., Yuksel S.: Transverse vibrations of a flexible beam sliding through a prismatic joint. J. Sound Vib. 223(3), 467-482 (1999) · doi:10.1006/jsvi.1999.2155 |
| [14] | Gaultier P.E., Cleghorn W.L.: A spatially translating and rotating beam finite element for modeling flexible manipulators. Mech. Mach. Theory 27(4), 415-433 (1992) · doi:10.1016/0094-114X(92)90033-E |
| [15] | Tadikonda S.K., Baruh H.: Dynamics and Control of a translating flexible beam with a prismatic joint. Trans. ASME J. Dyn. Syst. Meas. Control 114, 422-427 (1992) · doi:10.1115/1.2897364 |
| [16] | Bauchau O.A.: On the modeling of prismatic joints in flexible multi-body systems. Compute. Methods Appl. Mech. Eng. 181(1-3), 87-105 (2000) · Zbl 0968.74042 · doi:10.1016/S0045-7825(99)00065-1 |
| [17] | Wang P.C.K., Wei J.D.: Vibration in a moving flexible robot arm. J. Sound Vib. 116(1), 149-160 (1987) · doi:10.1016/S0022-460X(87)81326-3 |
| [18] | Chang J.R., Lin W.J., Huang C.J., Choi S.T.: Vibration and stability of an axially moving Rayleigh beam. Appl. Math. Model. 34(6), 1482-1497 (2010) · Zbl 1193.74075 · doi:10.1016/j.apm.2009.08.022 |
| [19] | Kazemi, M., Ghayour, M.: Effect of intermediate location and time-varying end mass on the dynamic response of a flexible robot manipulator in tracing multi-straight-line path. Adv. Mater. Res. pp. 463-464, 1246-1251, (2012) |
| [20] | Buffinton K.W.: Dynamic of elastic manipulators with prismatic joints. Trans. ASME J. Dyn. Syst. Meas. Control 114(1), 41-49 (1992) · Zbl 0775.93144 · doi:10.1115/1.2896506 |
| [21] | Book W.J.: Recursive lagrangian dynamics of flexible manipulator arms. Int. J. Robotics Res. 3(3), 87-101 (1984) · doi:10.1177/027836498400300305 |
| [22] | Changizi K., Shabana A.A.: Recursive formulation for the dynamic analysis of open loop deformable multibody systems. Trans. ASME J. Appl. Mech. 55(3), 687-693 (1988) · Zbl 0663.70001 · doi:10.1115/1.3125850 |
| [23] | Kim S.-S., Haug E.J.: A recursive formulation for flexible multibody dynamics, Part I: open-loop systems. Comput. Methods Appl. Mech. Eng. 71(3), 293-314 (1988) · Zbl 0679.73045 · doi:10.1016/0045-7825(88)90037-0 |
| [24] | Shabana A.A., Hwang Y.L., Wehage R.A.: Projection methods in flexible multibody dynamics. Part I: kinematics, Part II: dynamic and recursive projection methods. Int. J. Numer. Methods Eng. 35(10), 1941-1966 (1992) · Zbl 0780.73103 · doi:10.1002/nme.1620351002 |
| [25] | Fissette P., Samin J.C.: Symbolic generation of large multibody system dynamic equations using a new semi-explicit Newton/Euler recursive scheme. Arch. Appl. Mech. 66(3), 187-199 (1996) · Zbl 0844.70001 · doi:10.1007/BF00795220 |
| [26] | Znamenacek J., Valasek M.: An efficient implementation of the recursive approach to flexible multibody dynamics. Multibody Syst. Dyn. 2(3), 227-251 (1998) · Zbl 0928.70007 · doi:10.1023/A:1009761925675 |
| [27] | Ider S.K., Amirouche F.M.L.: Nonlinear modeling of flexible multibody systems dynamics subjected to variable constraints. Trans. ASME J. Appl. Mech. 56(2), 444-450 (1989) · Zbl 0711.73137 · doi:10.1115/1.3176103 |
| [28] | Hwang Y.L., Shabana A.A.: Decoupled joint-elastic coordinate formulation for the analysis of closed-chain flexible multibody systems. Trans. ASME J. Mech. Design 116(3), 961-963 (1994) · doi:10.1115/1.2919476 |
| [29] | Kim S.-S., Haug E.J.: A recursive formulation for flexible multibody dynamics, Part II: closed-loop systems. Comput. Methods Appl. Mech. Eng. 74(3), 251-269 (1989) · Zbl 0724.73293 · doi:10.1016/0045-7825(89)90051-0 |
| [30] | Keat J.E.: Multibody system order n dynamics formulation based on velocity transform method. J. Guid. Control Dyn 13(2), 207-212 (1990) · Zbl 0699.70005 · doi:10.2514/3.20538 |
| [31] | Lai H.J., Haug E.J., Kim S.-S., Bae D.S.: A decoupled flexible-relative co-ordinate recursive approach for flexible multibody dynamics. Int. J. Numer. Method Eng. 32(8), 1669-1689 (1991) · Zbl 0759.70005 · doi:10.1002/nme.1620320810 |
| [32] | Nikravesh P.E., Ambrosio J.A.C.: Systematic construction of equations of motion for rigid-flexible multibody systems containing open and closed kinematic loops. Int. J. Numer. Method Eng. 32(8), 1749-1766 (1991) · Zbl 0757.70002 · doi:10.1002/nme.1620320814 |
| [33] | Stelzle W., Kecskemethy A., Hiller M.: A comparative study of recursive methods. Arch. Appl. Mech. 66(1-2), 9-19 (1995) · Zbl 0861.70007 |
| [34] | Vukobratovic M., Potkonjak V.: Applied Dynamics and CAD of Manipulation Robots. Springer, Berlin (1985) · Zbl 0563.93026 · doi:10.1007/978-3-642-82198-1 |
| [35] | Desoyer K., Lugner P.: Recursive formulation for the analytical or numerical application of the Gibbs-Appell method to the dynamics of robots. Robotica 7, 343-347 (1989) · doi:10.1017/S0263574700006743 |
| [36] | Mata V., Provenzano S., Cuadrado J.I., Valero F.: Serial-robot dynamics algorithms for moderately large number of joints. Mech. Mach. Theory 37, 739-755 (2002) · Zbl 1126.70303 · doi:10.1016/S0094-114X(02)00030-7 |
| [37] | Mata V., Provenzano S., Cuadrado J.I, Valero F.: Inverse dynamic problem in robots using Gibbs-Appell equations. Robotica 20(1), 59-67 (2002) · doi:10.1017/S0263574701003502 |
| [38] | Korayem M.H., Shafei A.M.: 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 Astronautica 83, 273-294 (2013) · doi:10.1016/j.actaastro.2012.10.026 |
| [39] | Korayem M.H., Shafei A.M., Shafei H.R.: Dynamic modeling of nonholonomic wheeled mobile manipulators with elastic joints using recursive Gibbs-Appell formulation. Sci. Iran. Trans. B Mech. Eng. 19(4), 1092-1104 (2012) |
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