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The role of the mass matrix in the analysis of mechanical systems

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Abstract

This paper proposes a simple, intuitive method of analyzing and understanding the mass matrix of a mechanical system. With very little calculation, it is possible to determine four important values that describe the inertia and inertial coupling of a mechanism: the locked effective inertia, the force coupling, the free effective inertia, and the acceleration coupling. These values can be determined for a system formulated in terms of joint coordinates, but when used with systems formulated in terms of workspace coordinates, this work provides a unified method of determining important, well-established concepts such as effective mass (particularly important in the field of human-robot interaction) and dynamic isotropy (an important consideration for robotic manipulators and haptic devices). Two examples are provided which highlight the use of this method to analyze robotic manipulators.

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  1. Deutsches Zentrum für Luft- und Raumfahrt, or German Aerospace Centre.

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Acknowledgements

The authors would like to acknowledge the support of Fonds de Recherche du Québec—Nature et Technologies, the National Sciences and Engineering Research Council of Canada, and CM-Labs Simulations, Inc.

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Authors and Affiliations

  1. Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, 817 Sherbrooke St. West, Montreal, Quebec, Canada, H3A 0C3

    Martin Hirschkorn & József Kövecses

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  1. Martin Hirschkorn
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  2. József Kövecses
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Correspondence to Martin Hirschkorn.

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Hirschkorn, M., Kövecses, J. The role of the mass matrix in the analysis of mechanical systems. Multibody Syst Dyn 30, 397–412 (2013). https://doi.org/10.1007/s11044-013-9369-4

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  • DOI: https://doi.org/10.1007/s11044-013-9369-4

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