## Recursive dynamic algorithm of open-chain multibody system.(English)Zbl 1407.70010

Summary: Open-chain multibody systems have been extensively studied because of their widespread application. Based on the structural characteristics of such a system, the relationship between its hinged bodies was transformed into recursive constraint relationships among the position, velocity, and acceleration of the bodies. The recursive relationships were used along with the Huston-Kane method to select the appropriate generalized coordinates and determine the partial velocity of each body and to develop an algorithm of the entire system. The algorithm was experimentally validated; it has concise steps and low susceptibility to error. Further, the algorithm can readily solve and analyze open-chain multibody systems.

### MSC:

 7e+56 Dynamics of multibody systems
Full Text:

### References:

 [1] Hooker, W. W.; Margulies, G., The dynamical attitude equations for an $$n$$-body satellite, Journal of the Astronautical Sciences, 12, 123-128, (1965) [2] Hooker, W. W., A set of r dynamical attitude equations for an arbitrary n-body satellite having r rotational degrees of freedom, AIAA Journal, 8, 7, 1205-1207, (1970) · Zbl 0195.54802 [3] Roberson, R. E.; Wittenburg, W., A dynamical formulation for an arbitrary number of interconnected rigid bodies with reference to the problem of satellite attitude control, Proceedings of the 3rd IFAC Congress [4] Wittenburg, J., Dynamics of Systems of Rigid Bodies, (1977), Teubner · Zbl 0363.70004 [5] Ho, J. Y. L., Direct path method for flexible multibody spacecraft dynamics, Journal of Spacecraft and Rockets, 14, 2, 102-110, (1977) [6] Kane, T. R.; Levinson, D. A., Formulation of equations of motion for complex spacecraft, Journal of Guidance and Control, 3, 2, 99-112, (1980) · Zbl 0435.70027 [7] Kane, T. R.; Levinson, D. A., Dynamics, Theory and Applications, (1993), New York, NY, USA: McGraw-Hill, New York, NY, USA [8] Kane, T. R.; Likins, P. W.; Levinson, D. A., Spacecraft Dynamics, (1993), New York, NY, USA: McGraw-Hill Book, New York, NY, USA [9] Haug, E. J.; Wu, S. C.; Kim, S. S., Dynamics of flexible machines, a variational approach, Proceedings of the IUTAM/IFTOMM Symposium on Dynamics of Multibody Systems [10] Haug, E. J., Computer-Aided Kinematics and Dynamics of Mechanical Systems, (1989), Boston, Mass, USA: Allyn and Bacon, Boston, Mass, USA [11] de Jalón, J. G.; Bayo, E., Kinematic and Dynamic Simulation of Multibody Systems, (1994), New York, NY, USA: Springer, New York, NY, USA [12] Huston, R. L.; Liu, Y. W., Dynamics of Multibody Systems, (1987), Tianjin, China: Tianjin University Publishing House, Tianjin, China [13] Huston, R. L., Multi-body dynamics including the effects of flexibility and compliance, Computers and Structures, 14, 5-6, 443-451, (1981) [14] Huston, R. L., Methods of analysis of constrained mechanical systems, Mechanics of Structures Machines, 17, 2, 135-144, (1989) [15] Huston, R. L., Computer methods in flexible multibody dynamics, International Journal for Numerical Methods in Engineering, 32, 8, 1657-1668, (1991) [16] Huston, R. L.; Kamman, J. W., Validation of finite segment cable models, Computers and Structures, 15, 6, 653-660, (1982) · Zbl 0491.73089 [17] Wang, S.-X.; Yun, J.-T.; Shi, J.-R.; Liu, Y.-W., Roadmap of research on modeling and control strategy for flexible manipulators, Robot, 24, 1, 86-92, (2002) [18] Wang, J.; Hong, J.; Liu, Y., A new modeling method for rigid-elastic coupling systems, Journal of Vibration Engineering, 16, 2, 194-197, (2003) [19] Jin, G.-G.; Liu, Y.-W.; Wang, S.-X.; Zhang, D.-J., Generally flexible multi-body system dynamics in consideration of dynamic stiffening terms, Journal of Harbin Institute of Technology, 37, 1, 101-103, (2005) [20] Liu, Z.-Y.; Hong, J.-Z., Research and prospect of flexible multi-body systems dynamics, Chinese Journal of Computational Mechanics, 25, 4, 411-416, (2008) · Zbl 1187.70002 [21] Qian, Z.; Zhang, D.; Liu, J.; Hong, J., Impact dynamic modeling and simulation of robots with flexible links and flexible joints, Journal of Nanjing University of Science and Technology, 37, 3, 415-421, (2013) [22] Duan, Y.-C.; Zhang, D.-G.; Hong, J.-Z., Partition method for impact dynamics of flexible multibody systems based on contact constraint, Applied Mathematics and Mechanics: English Edition, 34, 11, 1393-1404, (2013) [23] Zhang, Q.; Tang, Q.; Peng, Y.; Wang, H., Dynamics of Parachute-Capsule Recovery System, (2013), Beijing, China: National Defense Industry Press, Beijing, China [24] Zhang, Q., Research on the Dynamics of the Parachute Recovery Systems of Manned Spacecraft, (2003), Changsha, China: National University of Defense Technology, Changsha, China [25] Di, D., Research on Some Dynamic Problems of Large Parachute Recovery System of Manned Spacecraft, (2011), Changsha, China: National University of Defense Technology, Changsha, China [26] Wang, H., Research on Bull Whipping and Dynamic Stability of Large Parachute System, (2011), Changsha, China: National University of Defense Technology, Changsha, China
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.