Graphic analysis of the linear and angular momentum of a dynamically balanced 1-dof pantographic linkage

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This article presents a graphical analysis method for the verification of the gravity force balance and shaking force and shaking moment balance of a 1-DoF pantographic linkage. First the joint velocities of the linkage are graphically found of which the procedure is well known. To obtain the linear and angular momentum graphically, the mass and inertia of each element are modeled with two equivalent masses about the center of mass of the element, resulting in a mass and inertia equivalent model with solely point masses. The velocities of these point masses are obtained and each velocity vector is multiplied with the respective mass value to obtain vectors that represent the linear momentum. For force balance it is shown that the sum of all linear momentum vectors form a polygon. Subsequently the linear momentum vectors with their moment arms are transferred into an angular momentum diagram which for moment balance shows to sum up to zero.

Original languageEnglish
Title of host publicationNew Trends in Mechanismsand Machine Science
Subtitle of host publicationEuCoMeS: European Conference on Mechanism Science
EditorsD. Pisla
Place of PublicationCham, Switzerland
ISBN (Electronic)978-3-030-55061-5
ISBN (Print)978-3-030-55060-8
Publication statusPublished - 2020

Publication series

NameMechanisms and Machine Science
ISSN (Print)2211-0984
ISSN (Electronic)2211-0992


  • Graphic analysis
  • Gravity force balance
  • Linear and angular momentum
  • Pantograph
  • Shaking force and shaking moment balance


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