### Abstract

This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

Original language | English (US) |
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Title of host publication | American Society of Mechanical Engineers, Design Engineering Division (Publication) DE |

Publisher | Publ by American Soc of Mechanical Engineers (ASME) |

Pages | 27-33 |

Number of pages | 7 |

Volume | 19-3 |

Edition | pt 3 |

State | Published - 1989 |

Event | Advances in Design Automation - 1989 - Montreal, Que, Can Duration: Sep 17 1989 → Sep 21 1989 |

### Other

Other | Advances in Design Automation - 1989 |
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City | Montreal, Que, Can |

Period | 9/17/89 → 9/21/89 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*American Society of Mechanical Engineers, Design Engineering Division (Publication) DE*(pt 3 ed., Vol. 19-3, pp. 27-33). Publ by American Soc of Mechanical Engineers (ASME).

**Systematic construction of the equations of motion for multibody systems containing closed kinematic loops.** / Nikravesh, Parviz E; Gim, G.

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

*American Society of Mechanical Engineers, Design Engineering Division (Publication) DE.*pt 3 edn, vol. 19-3, Publ by American Soc of Mechanical Engineers (ASME), pp. 27-33, Advances in Design Automation - 1989, Montreal, Que, Can, 9/17/89.

}

TY - GEN

T1 - Systematic construction of the equations of motion for multibody systems containing closed kinematic loops

AU - Nikravesh, Parviz E

AU - Gim, G.

PY - 1989

Y1 - 1989

N2 - This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

AB - This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

UR - http://www.scopus.com/inward/record.url?scp=0024914089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024914089&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0024914089

VL - 19-3

SP - 27

EP - 33

BT - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE

PB - Publ by American Soc of Mechanical Engineers (ASME)

ER -