The Spatial Pantograph and Its Mass Balance

Volkert van der Wijk*

*Corresponding author for this work

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

1 Citation (Scopus)


This paper presents the spatial version of the well-known pantograph linkage. While the traditional pantograph is a planar parallelogram linkage with 1 internal degree of freedom (DoF) and four moving links connected with solely revolute pairs, the general spatial pantograph is a linkage with 3 internal DoFs in which the four moving links are connected with spherical joints and two additional out-of-plane links are connected with universal joints. The out-of-plane links constrain the linkage to maintain the essential parallelogram and also constrain all links to move similarly. This is necessary for full controllability and also for inherent force balance, which is obtained for specific conditions on the mass distribution of the links. The force balance conditions are given and also a reduced version of the spatial pantograph linkage with 2 internal DoFs is presented which has five moving links connected with solely universal joints.

Original languageEnglish
Title of host publicationAdvances in Robot Kinematics 2022
EditorsOscar Altuzarra, Andrés Kecskeméthy
ISBN (Electronic)978-3-031-08140-8
ISBN (Print)978-3-031-08139-2
Publication statusPublished - 2022
Event18th International Symposium on Advances in Robot Kinematics, ARK 2022 - Bilbao, Spain
Duration: 26 Jun 202230 Jun 2022

Publication series

NameSpringer Proceedings in Advanced Robotics
Volume24 SPAR
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264


Conference18th International Symposium on Advances in Robot Kinematics, ARK 2022


  • Inherent force balance
  • Pantograph linkage
  • Spatial kinematics
  • Static balance


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