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Invariant geometric characteristics of spatial arm motion

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Abstract

This paper examines up to third-order geometric properties of wrist path and the first-order property of wrist trajectory (wrist speed) for spatial pointing movements. Previous studies report conflicting data regarding the time invariance of wrist-path shape, and most analyses are limited to the second-order geometric property (straightness, or strictly speaking, curvature). Subjects performed point-to-point reaching movements between targets whose locations ensured that the wrist paths spanned a range of lengths and lay in various portions of the arm’s spatial workspace. Movement kinematics were recorded using electromagnetic sensors located on the subject’s arm segments and thorax. Analysis revealed that wrist paths tend to lie in planes and to curve more as movement speed decreases. The orientation of the wrist-path plane depends on the reaching task but does not vary significantly with movement speed. The planarity of wrist paths indicates that the paths have close to zero torsion—a third-order geometric property. Wrist-speed profiles showed multiple peaks for sufficiently slow and long lasting movements, indicating deviation from the well-known, bell-shaped profile. These kinematic findings are discussed in light of various motor control theories.

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Notes

  1. Tasks 6 and 7 and Tasks 3 and 8 are similar. The wrist paths of these two sets of movements are similar, and so Tasks 7 and 8 are not included in the data analysis of this paper.

  2. The rate of curvature change with respect to the arc length is the ‘in-plane’ third-order geometric property of a curve. This property has not been studied in this work or elsewhere in the motor control/biomechanics literature. Together with torsion, it provides a complete third-order local characterization of a spatial curve.

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Acknowledgments

Support was provided by grant no. IIS-0937612 from the National Science Foundation. The authors wish to thank Mr. Julian Corona for his assistance in data collection, and the reviewers of this paper for their insightful comments.

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Authors and Affiliations

  1. Department of Kinesiology, The Pennsylvania State University, University Park, PA, USA

    Satyajit Ambike

  2. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, USA

    James P. Schmiedeler

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  1. Satyajit Ambike
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  2. James P. Schmiedeler
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Correspondence to Satyajit Ambike.

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Ambike, S., Schmiedeler, J.P. Invariant geometric characteristics of spatial arm motion. Exp Brain Res 229, 113–124 (2013). https://doi.org/10.1007/s00221-013-3599-9

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