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An Improved Principal Coordinate Frame for use with Spatial Rigid Body Displacement Metrics

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Advances in Mechanism and Machine Science (IFToMM WC 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 73))

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Abstract

This paper presents an improved definition of a coordinate frame, entitled the principal frame (PF), that is useful for metric calculations on spatial rigid-body displacements. For a finite set of displacements a point mass model of the moving rigid-body is employed. Next, we compute the centroid and principal axes associated with the point mass locations. The PF is then determined from the principal axes. Here, a new algorithm for determining the PF from the principal axes is proposed. The PF is invariant with respect to the choice of the fixed coordinate frame as well as the system of units used; therefore, the PF is useful for left invariant metric computations. An example including a set of 10 spatial rigid-body displacements is presented to demonstrate the application and utility of the PF.

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Acknowledgments

We gratefully acknowledge the insightful discussions about metrics and the principal frame PF with Michal Juránek of Photoneo S.R.O. (https://www.photoneo.com). This work builds upon preliminary results reported in Refs. [1, 25, 2, 26].

Author information

Authors and Affiliations

  1. South Dakota School of Mines & Technology, Rapid City, SD, 57701, USA

    Pierre Larochelle

  2. SoftBank Robotics, Boston, MA, 01864, USA

    Venkatesh Venkataramanujam

Authors
  1. Pierre Larochelle
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  2. Venkatesh Venkataramanujam
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Corresponding author

Correspondence to Pierre Larochelle .

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Editors and Affiliations

  1. Robotics & Machine Dynamics Group, University of Mining and Metallurgy, Kraków, Poland

    Tadeusz Uhl

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Larochelle, P., Venkataramanujam, V. (2019). An Improved Principal Coordinate Frame for use with Spatial Rigid Body Displacement Metrics. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_32

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