Dynamics analysis of linear elastic planar mechanisms

Multibody System Dynamics

Volumn 17, Issue 1, 2007, Pages 1-25

  Liu, Jin Fan ^a   Yang, Jingzhou ^a   Abdel Malek, Karim ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Dynamic analysis; Hamiltonian form; Planar elastic mechanisms; Stiff system

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); ELASTIC MODULI; FINITE ELEMENT METHOD; HAMILTONIANS; NUMERICAL METHODS; PARAMETER ESTIMATION;

DYNAMIC ANALYSIS; HAMILTONIAN FORMS; PLANAR ELASTIC MECHANISMS; STIFF SYSTEMS;

LINEAR EQUATIONS;

EID: 33847278495     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11044-006-9031-5     Document Type: Article

References (61)

1. Al-Dwairi, A.F.: Modeling and dynamic analysis of a planetary mechanism with an elastic belt. Mech. Mach. Theory 39(4), 343-355 (2004)
2. Bakr, E.M., Shabana, A.A.: Geometrically nonlinear analysis of multibody systems. Comput. Struct. 23(6), 739-752 (1986)
3. Balachandran, B.: Dynamics of an elastic structure excited by harmonic and aharmonic impactor motions. J. Vib. Control 9(3/4), 265-279 (2003)
4. Berg, M.C., Amit, N., Powell, J.D.: Multirate digital control system design. IEEE Trans. Autom. Control 33(12) (1988)
5. Bloch, A.M., Robert, R.R.: Stability and Stiffening of Driven and Free Rotating Beams. American Mathematical Society, Providence, RI (1989)
6. Book, W.J.: Recursive Lagrangian dynamics of flexible manipulator arms. Int. J. Robot. Res. 3(3), 87-101 (1984)
7. Chen, C.T.: Linear System Theory and Design. Holt, Rinehart and Winston, New York (1984)
8. Chen, J.S., Huang, C.L.: Dynamic analysis of flexible slider-crank mechanisms with non-linear finite element method. J. Sound Vib. 246, 389-402 (2001)
9. Chu, S.C., Pan, K.C.: Dynamic response of a high speed slider-crank mechanism with an elastic connecting rod. ASME J. Eng. Ind. 97, 542-550 (1975)
10. Chunmei, J., Yang, Q., Ling, F., Ling, Z.: The nonlinear dynamic behavior of an elastic linkage mechanism with clearances. J. Sound Vib. 249(2), 213-226 (2002)
11. Claus, H., Schiehlen, W.: Dynamic stability and random vibrations of rigid and elastic wheelsets. Nonlinear Dyn. 36(2/4), 299-311 (2004)
12. Cleghorn, W.L., Chao, K.C.: Kineto-elastodynamic modeling of mechanisms employing linearly tapered beam finite elements. Mech. Mach. Theory 23(5), 333-342 (1988)
13. De Luca, A., Faina, R.: Dynamic properties and nonlinear control of robots with mixed rigid/elastic joints. In: Proceedings of the World Automation Congress (IEEE Cat. No.04EX832C), vol. 15(pt. 15, pp. 97-104), Hangzhou, China (2004)
14. Djerassi, D., Kane, T.R.: Equations of motion governing the deployment of a flexible linkage from a spacecraft. J. Astronaut. Sci. 33(4), 417-428 (1985)
15. Eberhard, P., Schiehlen, W.: Computational dynamics of multibody systems: history, formalisms, and applications. Trans. ASME J. Comput. Nonlinear Dyn. 1(1), 3-12 (2006)
16. Franklin, G.F., Powell, J.D., Workman, M.L.: Digital Control of Dynamic Systems. Addison-Wesley, Reading, MA (1990)
17. Gao, X., King, Z., Zhang, Q.: A hybrid beam element for mathematical modeling of high-speed flexible linkages. Mech. Mach. Theory 24(1), 29-36 (1989)
18. Goldstein, H.: Classical Mechanics. Addison-Wesley, Reading, MA (1980)
19. Goudas, I., Stavrakis, I., Natsiavas, S.: Dynamics of slider-crank mechanisms with flexible supports and nonideal forcing. Nonlinear Dyn. 35(3), 205-227 (2004)
20. Grishanina, T.V.: Dynamics of controlled motion of elastic systems subject to finite displacements and rotations. Mech. Solids 39(6), 132-144 (2004)
21. Gulyaev, V.I., Ikonnikov, A.N.: Dynamics simulation of crank mechanisms with elastic links. Problemy Prochnosti 5, 105-114 (2002)
22. Gulyaev, V.I., Zavrazhina, T.V.: Dynamics of a manipulation robot with flexible links and drive mechanisms. Mech. Solids 38(6), 13-22 (2003)
23. Hac, M.: Dynamics of flexible mechanisms with mutual dependence between rigid motion and longitudinal deformation of links. Mech. Mach. Theory 30(6), 837-847 (1995)
24. Haug, E.J., Arora, J.S.: Design sensitivity analysis of elastic mechanical systems. Comput. Methods Appl. Mech. Eng. 15, 35-62 (1978)
25. Haug, E.J., Ehle, P.E.: Second order design sensitivity analysis of mechanical system dynamics. Int. J. Numer. Methods Eng. 18(18), 1699-1717 (1982)
26. Haug, E.J., Sohoni, V.N., Kim, S.S., Seong, H.G.: Vehicle suspension dynamics optimization. In: Proceedings of the International Conference on Modern Vehicle Design Analysis, London (1983)
27. Haug, E.J., Wehage, R., Barman, N.C.: Design sensitivity analysis of planar mechanism and machine dynamics. ASME J. Mech. Des. 103, 560-570 (1981)
28. Haug, E.J., Wehage, R., Mani, N.K.: Design sensitivity analysis of large-scale constrained dynamic mechanical systems. ASME J. Mech. Transm. Autom. Des. 106, 156-162 (1984)
29. Ider, S.K., Amirouche, F.M.L.: Influence of geometric nonlinearities in the dynamics of flexible treelike structures. AIAA J. Guid. 12(6), 830-837 (1989)
30. Kane, T.R., Ryan, R.R.: Dynamics of a Cantilever beam attached to a moving base. AIAA J. Guid. 10(2), 139-151 (1987)
31. Kim, S.S.: A recursive formulation for flexible multibody dynamics. Ph.D. Dissertation, Department of Mechanical Engineering, University of Iowa (1988)
32. Lerbet, J.: Non-linear dynamics of elastic curvilinear systems. A new coordinateless approach. J. Appl. Math. Mech. 69, 917-924 (2005)
33. Marghitu, D.B., Hurmuzlu, Y.: Nonlinear dynamics of an elastic rod with frictional impact. Nonlinear Dyn. 10(2), 187-201 (1996)
34. Meirovitch, L.: Computational Methods in Structure Dynamics. Sijthoff & Noordhoff, The Netherlands (1980)
35. Meirovitch, L.: Dynamics and Control of Structures. Wiley Interscience, New York, 425pp (1990)
36. Meirovitch, L., Stemple, T.: Hybrid equations of motion for flexible multibody systems using quasicoordinates. J. Guid. Control Dyn. 18(4), 678-687 (1995)
37. Nagarajan, S., Turcic, D.A.: Lagrangian formulation of the equations of motion for elastic mechanisms with mutual dependence between rigid body and elastic motions. Part I: Element level equations. ASME J. Dyn. Syst. Meas. Control 112, 203-214 (1990)
38. Nagarajan, S., Turcic, D.A.: Lagrangian formulation of the equations of motion for elastic mechanisms with mutual dependence between rigid body and elastic motions. Part I: System equations. ASME J. Dyn. Syst. Meas. Control 112, 215-224 (1990)
39. Ogata, K.: Discrete-Time Control Systems. Prentice-Hall, Englewood Cliffs, NJ (1987)
40. Park, T.W., Haug, E.J.: A hybrid numerical integration method for machine dynamic simulation. ASME J. Mech. Transm. Autom. Des. 108, 211-216 (1986)
41. Romdhane, L., Dhuibi, H., Bel haudj Salah, H.: Dynamic analysis of planar elastic mechanisms using the dyad method. Proc. Inst. Mech. Eng. Part K (J. Multi-Body Dyn.) 217(K1), 1-14 (2003)
42. Rosenberg, R.M.: Analytical Dynamics of Discrete Systems. Plenum, New York (1977)
43. Sadler, J.P., Sandor, G.N.: A lumped parameter approach to vibration and stress analysis of elastic linkages. J. Eng. Ind. 95, 549-557 (1973)
44. Schiehlen, W., Guse, N., Seifried, R.: Multibody dynamics in computational mechanics and engineering applications. Comput. Methods Appl. Mech. Eng. 195(41/43), 5509-5522 (2006)
45. Shabana, A., Wehage, R.A.: Variable degree-of-freedom component mode analysis of inertia variant flexible mechanical systems. ASME J. Mech. Transm. Autom. Des. 105, 371-378 (1983)
46. Shabana, A., Wehage, R.A.: Spatial transient analysis of inertia-variant flexible mechanical systems. ASME J. Mech. Transm. Autom. Des. 106, 172-178 (1984)
47. Singh, S.N., Schy, A.A.: Control of elastic robotic systems by nonlinear inversion and modal damping. ASME J. Dyn. Syst. Meas. Control 108, 180-189 (1986)
48. Song, J.O., Haug, E.J.: Dynamic analysis of planar flexible mechanisms. Comput. Methods Appl. Mech. Eng. 24, 359-381 (1980)
49. Souh, B.Y.: A recursive dynamic formulation for flexible mechanisms. Ph.D. Dissertation, Department of Mechanical Engineering, University of Iowa (1990)
50. Tabor, M.: Chaos and Integrability in Nonlinear Dynamics. Wiley, New York (1989)
51. Thompson, B.S., Sung, C.K.: A variational formulation for the nonlinear finite element analysis of flexible linkages: theory, implementation, and experimental results. ASME J. Mech. Transm. Autom. Des. 106, 482-488 (1984)
52. Turcic, D.A., Midha, A.: Generalized equations of motion for the dynamic analysis of elastic mechanism systems. ASME J. Dyn. Syst. Meas. Control 106, 243-248 (1984)
53. Turcic, D.A., Midha, A.: Dynamic analysis of elastic mechanism systems. Part I: Applications. ASME J. Dyn. Syst. Meas. Control 106, 249-254 (1984)
54. Turhan, O.: Dynamic stability of four-bar and slider-crank mechanisms with elastic coupler. Mech. Mach. Theory 30(6), 871-882 (1995)
55. Usoro, P.B., Nadira, R., Mahil, S.S.: A finite element/lagrange approach to modeling lightweight flexible manipulators. ASME J. Dyn. Syst. Meas. Control 108, 198-204 (1986)
56. Van Loan, C.F.: Computing integrals involving the matrix exponential. IEEE Trans. Autom. Control AC-23(3) (1978)
57. Wang, Y.: Dynamics of an elastic four bar linkage mechanism with geometric nonlinearities. Nonlinear Dyn. 14(4), 357-375 (1997)
58. Wang, J., Liu, H., Yuan, D.: An efficient solution of the elastic mechanism non-linear differential equation of motion. Proc. ASME Des. Eng. Tech. Conf. 5A, 177-182 (2002)
59. Wayou, A.Y., Tchoukuegno, R., Woato, P.: Non-linear dynamics of an elastic beam under moving loads. J. Sound Vib. 273(4/5), 1101-1108 (2004)
60. Wu, S.C., Haug, E.J., Kim, S.S.: A variational approach to dynamics of flexible multibody systems. Mech. Struct. Mach. 17(1), 3-32 (1989)
61. Zavrazhina, T.V.: Dynamics of robot manipulator with elastically flexible links and drive mechanisms. J. Autom. Inf. Sci. 37(2), 55-65 (2005)