On the Computation of the Average of Planar Displacements

Q. Jeffrey Ge, Zihan Yu, Mona Arbab, Mark P. Langer

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

3 Scopus citations


In this paper, we present four parametric representations of a planar displacements and studied the problem of how to compute the average displacement from a set of given planar displacements using these representations. It has been shown that the optimal average displacement is obtained by using planar quaternions and the concept of relative displacements. Examples are provided to show the comparisons of these methods.

Original languageEnglish (US)
Title of host publicationProceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics
EditorsPierre Larochelle, J. Michael McCarthy
PublisherSpringer Science and Business Media B.V.
Number of pages11
ISBN (Print)9783030998257
StatePublished - 2022
Externally publishedYes
Event2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022 - Rapid City, United States
Duration: May 19 2022May 21 2022

Publication series

NameMechanisms and Machine Science
Volume118 MMS
ISSN (Print)2211-0984
ISSN (Electronic)2211-0992


Conference2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022
Country/TerritoryUnited States
CityRapid City


  • Averaging displacements
  • Means and variance
  • Planar quaternions

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering

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