### Abstract

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Original language | English (US) |
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Title of host publication | Proceedings of the ASME Design Engineering Technical Conference |

Pages | 1159-1170 |

Number of pages | 12 |

Volume | 4 |

Edition | PARTS A AND B |

DOIs | |

State | Published - 2011 |

Externally published | Yes |

Event | ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States Duration: Aug 28 2011 → Aug 31 2011 |

### Other

Other | ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 |
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Country | United States |

City | Washington, DC |

Period | 8/28/11 → 8/31/11 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering
- Computer Graphics and Computer-Aided Design
- Computer Science Applications
- Modeling and Simulation

### Cite this

*Proceedings of the ASME Design Engineering Technical Conference*(PARTS A AND B ed., Vol. 4, pp. 1159-1170) https://doi.org/10.1115/DETC2011-48383

**Multibody dynamics in generalized divide and conquer algorithm (GDCA) scheme.** / Poursina, Mohammad; Anderson, Kurt S.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the ASME Design Engineering Technical Conference.*PARTS A AND B edn, vol. 4, pp. 1159-1170, ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, United States, 8/28/11. https://doi.org/10.1115/DETC2011-48383

}

TY - GEN

T1 - Multibody dynamics in generalized divide and conquer algorithm (GDCA) scheme

AU - Poursina, Mohammad

AU - Anderson, Kurt S.

PY - 2011

Y1 - 2011

N2 - Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

AB - Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

UR - http://www.scopus.com/inward/record.url?scp=84863573380&partnerID=8YFLogxK

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U2 - 10.1115/DETC2011-48383

DO - 10.1115/DETC2011-48383

M3 - Conference contribution

SN - 9780791854815

VL - 4

SP - 1159

EP - 1170

BT - Proceedings of the ASME Design Engineering Technical Conference

ER -