Principal Vectors for Spatial Dynamical Analysis by Fischer

Svenja Stutzmann, Volkert van der Wijk*

*Corresponding author for this work

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

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Otto Fischer was during the late 19th and early 20th century the founder of 3-D human gait analysis. From motion recordings he calculated by hand the inverse dynamics of humans in motion, for which he discovered and used the principal vectors of a system of moving bodies. With the principal vectors the equations of motion and the kinetic energy can be written in a specific simple form with full geometric meaning and with reduced mass models with which system dynamics can be investigated in a simple way at link level. Fischer applied his theory mainly in its planar form. He also presented the theory of the spatial form by example of a serial two-link chain, however the explanations in the original texts in German are challenging to understand. This paper presents Fischer’s spatial form in a modern and understandable way.

Original languageEnglish
Title of host publicationNew Advances in Mechanisms, Transmissions and Applications
Subtitle of host publicationProceedings of the 6th MeTrApp Conference, 2023
EditorsMed Amine Laribi, Carl A. Nelson, Marco Ceccarelli, Saïd Zeghloul
ISBN (Print)978-3-031-29814-1
Publication statusPublished - 2023
Event6th IFToMM International Conference on Mechanisms, Transmissions, and Applications, MeTrApp 2023 - Poitiers, France
Duration: 24 May 202326 May 2023

Publication series

NameMechanisms and Machine Science
Volume124 MMS
ISSN (Print)2211-0984
ISSN (Electronic)2211-0992


Conference6th IFToMM International Conference on Mechanisms, Transmissions, and Applications, MeTrApp 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • equations of motion
  • kinetic energy
  • Principal vectors


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