Conference article

Performance Analysis of VON MISES’ Motor Calculus within Modelica

Tobias Zaiczek
Fraunhofer Institute for Integrated Circuits, Design Automation Division, Dresden, Germany

Olaf Enge-Rosenblatt
Fraunhofer Institute for Integrated Circuits, Design Automation Division, Dresden, Germany

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Published in: Proceedings of the 7th International Modelica Conference; Como; Italy; 20-22 September 2009

Linköping Electronic Conference Proceedings 43:30, s. 278-287

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Published: 2009-12-29

ISBN: 978-91-7393-513-5

ISSN: 1650-3686 (print), 1650-3740 (online)


This paper presents an alternative concept of modelling multibody systems within Modelica; the socalled motor calculus. This approach was introduced by R. VON MISES in 1924 and can be used to describe the dynamical behaviour of spatial multibody systems in a very efficient way. While the equations clearly take a very simple form in terms of motor algebra; the numerical efficiency is still an open question.

In the paper; first some fundamentals of motor calculus are summarized. An experimental implementation of motor algebra is used to measure and analyse the numerical efficiency and performance regarding the simulation time of VON MISES’ approach. Therefore; some components of the Modelica Multibody Standard Library were modified in order to compare both implementations. Finally; some examples are given to prove the applicability and correctness of the concept but also to serve as a basis for a discussion of the numerical performance. The chosen approach utilizes all object-oriented features provided by the modelling language. Besides; it gives reason for the present endeavours to introduce the possibility of operator overloading within Modelica.


Motor calculus; screw theory; rigid multibody system; Modelica; performance


[1] J. Angeles. Fundamentals of Robotic Mechanical Systems. Second Edition. NewYork; Springer-Verlag; 2003.

[2] R.S. Ball. A Treatise on the Theory of Skrews. Cambridge University Press; 1900.

[3] W.K. Clifford. Preliminary sketch of biquaternions. Proc. London Math. Soc.; 4:381–395; 1873.

[4] P. Fritzson. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley-IEEE Press; 2003.

[5] C. Heinz. Motorrechnung im X 1+3+3. Zeitschrift für Angewandte Mathematik und Mechanik(ZAMM); 67(11):537–544; 1987. doi: 10.1002/zamm.19870671105.

[6] R. von Mises. Motorrechnung; ein neues Hilfsmittel der Mechanik. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM); 4(2):155–181; 1924. doi: 10.1002/zamm.19240040210.

[7] R. von Mises. Anwendungen der Motorrechnung. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM); 4(3):193–213; 1924. doi: 10.1002/zamm.19240040301.

[8] seen on August 10th; 2009.

[9] M. Otter; H. Elmqvist; and S. E. Mattsson. The New Modelica MultiBody Library. In 3rd International Modelica Conference; Linköping; Sweden; November 3–4; 2003; Proc.; pages 311–330. The Modelica Association; 2003.

[10] B. Roth. Screws; motors; and wrenches that cannot be bought in a hardware store. In M. Brady and R. Paul (eds.): The First Internal Symposium on Robotic Research.; MIT Press; Cambridge (MA); pp. 679–693;.

[11] K. Sugimoto. Kinematic and Dynamic Analysis of Parallel Manipulators by Means of Motor Algebra. Journal of mechanisms; transmissions; and automation in design; vol. 109(1); pp 3–7; 1987.

[12] E. Study. Geometrie von Dynamen. Die Zusammensetzung von Kräften und verwandte Gegenstände der Geometrie. Teubner; Leipzig; 1903;

[13] H. Stumpf and J. Badur. On the non-abelian motor calculus. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM); 70(12):551–555; 1990.

[14] M.M. Tiller. Introduction to Physical Modeling with Modelica. Springer; 2001. doi: 10.1007/978-1-4615-1561-6.

[15] T. Zaiczek; O. Enge-Rosenblatt. Towards an Object-oriented Implementation of VON M ISES’ Motor Calculus Using Modelica. In 2nd International Workshop on Equation-Based Object-Oriented Languages and Tools; Paphos; Cyprus; July 3; 2008; Proc.; pages 131–140.

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