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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

51 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationAmerican Society of Mechanical Engineers, Design Engineering Division (Publication) DE
PublisherPubl by American Soc of Mechanical Engineers (ASME)
Pages27-33
Number of pages7
Volume19-3
Editionpt 3
StatePublished - 1989
EventAdvances in Design Automation - 1989 - Montreal, Que, Can
Duration: Sep 17 1989Sep 21 1989

Other

OtherAdvances in Design Automation - 1989
CityMontreal, Que, Can
Period9/17/899/21/89

Fingerprint

Equations of motion
Kinematics
Jacobian matrices
Lagrange multipliers

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Nikravesh, P. E., & Gim, G. (1989). Systematic construction of the equations of motion for multibody systems containing closed kinematic loops. In 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.

American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. Vol. 19-3 pt 3. ed. Publ by American Soc of Mechanical Engineers (ASME), 1989. p. 27-33.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nikravesh, PE & Gim, G 1989, Systematic construction of the equations of motion for multibody systems containing closed kinematic loops. in 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.
Nikravesh PE, Gim G. Systematic construction of the equations of motion for multibody systems containing closed kinematic loops. In American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. pt 3 ed. Vol. 19-3. Publ by American Soc of Mechanical Engineers (ASME). 1989. p. 27-33
Nikravesh, Parviz E ; Gim, G. / Systematic construction of the equations of motion for multibody systems containing closed kinematic loops. American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. Vol. 19-3 pt 3. ed. Publ by American Soc of Mechanical Engineers (ASME), 1989. pp. 27-33
@inproceedings{d9e8fff0a9f94f71a7ec0d07c14e87cb,
title = "Systematic construction of the equations of motion for multibody systems containing closed kinematic loops",
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.",
author = "Nikravesh, {Parviz E} and G. Gim",
year = "1989",
language = "English (US)",
volume = "19-3",
pages = "27--33",
booktitle = "American Society of Mechanical Engineers, Design Engineering Division (Publication) DE",
publisher = "Publ by American Soc of Mechanical Engineers (ASME)",
edition = "pt 3",

}

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 -