Analytic modelling of the dynamics of the four-bar mechanism: A comparison of some methods

J. P. Meijaard*, V. van der Wijk

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)

Abstract

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

Original languageEnglish
Title of host publicationProceedings ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Subtitle of host publicationVolume 5A: 42nd Mechanisms and Robotics Conference
Place of PublicationNew York, NY , USA
PublisherASME
Number of pages10
ISBN (Electronic)978-0-7918-5180-7
DOIs
Publication statusPublished - 2018
EventASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018 - Quebec City, Canada
Duration: 26 Aug 201829 Aug 2018

Conference

ConferenceASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018
Abbreviated titleIDETC/CIE 2018
CountryCanada
CityQuebec City
Period26/08/1829/08/18

Keywords

  • Dynamics (Mechanics)
  • Modeling
  • Equations of motion
  • Linkages
  • Virtual work principle
  • Algebra

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