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Related Experiment Video

Updated: Jul 3, 2026

Three-Dimensional Finger Motion Tracking during Needling: A Solution for the Kinematic Analysis of Acupuncture Manipulation

Three-Dimensional Finger Motion Tracking during Needling: A Solution for the Kinematic Analysis of Acupuncture Manipulation

Published on: October 28, 2021

Three-dimensional arm movements at constant equi-affine speed.

Frank E Pollick¹, Uri Maoz, Amir A Handzel

¹Department of Psychology, University of Glasgow, United Kingdom. frank@psy.gla.ac.uk

Cortex; a Journal Devoted to the Study of the Nervous System and Behavior

|August 6, 2008

Summary

Researchers generalized the planar drawing power law to three-dimensional (3D) movements. This new 3D law, incorporating curvature and torsion, accurately predicts human 3D drawing speed-shape relationships.

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Area of Science:

Biomechanics
Human Motor Control
Robotics

Background:

The established planar power law links drawing speed to curvature (speed ∝ 1/curvature^(1/3)).
Explanations and deviations for 2D drawing speed-shape relationships are well-documented.
Three-dimensional (3D) drawing movement speed-shape dynamics remain under-explored.

Purpose of the Study:

To generalize the 2D power law for drawing movements to 3D space.
To investigate the role of curvature and torsion in 3D drawing speed-shape relationships.
To validate a new 3D power law against empirical human movement data.

Main Methods:

Derivation of a generalized 3D power law based on constant equi-affine speed.
The derived 3D law relates speed to curvature and torsion (speed ∝ 1/(curvature^(1/3) * torsion^(1/6))).
Empirical data collection from human 3D scribbling movements.

Main Results:

The proposed 3D power law significantly improves the prediction of speed-shape relationships compared to 2D models.
The inclusion of torsion in the 3D power law explains a greater variance in movement data.
Empirical exponents closely matched the theoretically predicted values.

Conclusions:

The generalized 3D power law provides a more accurate model for human drawing movements in three dimensions.
Torsion is a critical factor influencing speed-shape dynamics in 3D drawing.
This research bridges a gap in understanding motor control for complex 3D trajectories.