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Technical Brief

A Refined Technique to Calculate Finite Helical Axes From Rigid Body Trackers

[+] Author and Article Information
Stewart D. McLachlin

Department of Mechanical and Materials Engineering, Western University,
London N6A 5B9 ON, Canada

Louis M. Ferreira

Department of Mechanical and Materials Engineering,
Western University,
London N6A 5B9 ON, Canada

Cynthia E. Dunning

Department of Mechanical and Materials Engineering,
Western University,
London N6A 5B9 ON, Canada
e-mail: cdunning@uwo.ca

1Corresponding author.

Manuscript received April 21, 2014; final manuscript received August 8, 2014; accepted manuscript posted August 27, 2014; published online November 5, 2014. Assoc. Editor: Guy M. Genin.

J Biomech Eng 136(12), 124506 (Dec 01, 2014) (4 pages) Paper No: BIO-14-1174; doi: 10.1115/1.4028413 History: Received April 21, 2014; Revised August 08, 2014; Accepted August 27, 2014

Finite helical axes (FHAs) are a potentially effective tool for joint kinematic analysis. Unfortunately, no straightforward guidelines exist for calculating accurate FHAs using prepackaged six degree-of-freedom (6DOF) rigid body trackers. Thus, this study aimed to: (1) describe a protocol for calculating FHA parameters from 6DOF rigid body trackers using the screw matrix and (2) to maximize the number of accurate FHAs generated from a given data set using a moving window analysis. Four Optotrak® Smart Markers were used as the rigid body trackers, two moving and two fixed, at different distances from the hinge joint of a custom-machined jig. 6DOF pose information was generated from 51 static positions of the jig rotated and fixed in 0.5 deg increments up to 25 deg. Output metrics included the FHA direction cosines, the rotation about the FHA, the translation along the axis, and the intercept of the FHA with the plane normal to the jig's hinge joint. FHA metrics were calculated using the relative tracker rotation from the starting position, and using a moving window analysis to define a minimum acceptable rotational displacement between the moving tracker data points. Data analysis found all FHA rotations calculated from the starting position were within 0.15 deg of the prescribed jig rotation. FHA intercepts were most stable when determined using trackers closest to the hinge axis. Increasing the moving window size improved the FHA direction cosines and center of rotation accuracy. Window sizes larger than 2 deg had an intercept deviation of less than 1 mm. Furthermore, compared to the 0 deg window size, the 2 deg window had a 90% improvement in FHA intercept precision while generating almost an equivalent number of FHA axes. This work identified a solution to improve FHA calculations for biomechanical researchers looking to describe changes in 3D joint motion.

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Figures

Grahic Jump Location
Fig. 2

Root mean square error (RMSE) of the X–Y intercept position in millimeters versus the moving window size (in degrees)

Grahic Jump Location
Fig. 1

Left: A custom machined jig that was capable of incremental planar rotations of 0.5 deg about a fixed hinge joint was used. Four Optotrak Smart Markers (rigid body trackers) were attached, two to the moving portion and two to the fixed portion (Body2_far not shown). Right: Transformation [t] matrices of a moving tracker Body1 with respect a reference Body2 (either a fixed tracker or the camera) were determined by the Optotrak software. The screw [s] matrix was then calculated for varying displacements (i.e., 1 → 2).

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