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. 2017 Nov;231(5):758-775.
doi: 10.1111/joa.12667. Epub 2017 Aug 15.

A Quantitative Evaluation of Physical and Digital Approaches to Centre of Mass Estimation

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Free PMC article

A Quantitative Evaluation of Physical and Digital Approaches to Centre of Mass Estimation

Sophie Macaulay et al. J Anat. .
Free PMC article

Abstract

Centre of mass is a fundamental anatomical and biomechanical parameter. Knowledge of centre of mass is essential to inform studies investigating locomotion and other behaviours, through its implications for segment movements, and on whole body factors such as posture. Previous studies have estimated centre of mass position for a range of organisms, using various methodologies. However, few studies assess the accuracy of the methods that they employ, and often provide only brief details on their methodologies. As such, no rigorous, detailed comparisons of accuracy and repeatability within and between methods currently exist. This paper therefore seeks to apply three methods common in the literature (suspension, scales and digital modelling) to three 'calibration objects' in the form of bricks, as well as three birds to determine centre of mass position. Application to bricks enables conclusions to be drawn on the absolute accuracy of each method, in addition to comparing these results to assess the relative value of these methodologies. Application to birds provided insights into the logistical challenges of applying these methods to biological specimens. For bricks, we found that, provided appropriate repeats were conducted, the scales method yielded the most accurate predictions of centre of mass (within 1.49 mm), closely followed by digital modelling (within 2.39 mm), with results from suspension being the most distant (within 38.5 mm). Scales and digital methods both also displayed low variability between centre of mass estimates, suggesting they can accurately and consistently predict centre of mass position. Our suspension method resulted not only in high margins of error, but also substantial variability, highlighting problems with this method.

Keywords: biomechanics; centre of gravity; inertial properties; mass properties; validation; volumetric modelling.

Figures

Figure 1
Figure 1
Pictures showing marker positions in bricks (A), and birds (B) as well as the standardised posture used for all bird specimens.
Figure 2
Figure 2
Stages of the suspension methodology performed in this study. (A) Suspension of object for Qualisys capture. At least three different suspension positions were captured for each object. (B) After the multiple Qualisys runs for the same specimen were matched, the specimen markers are aligned, and the various lines of suspension are now distributed around the specimen. (C,D) Two hypothetical 3D lines plotted in two, 2D graphs. Note that in (C), the lines have equal x values at y = 0.5, but at y = 0.5 in (D), they have different z values, and therefore do not intersect in 3D space. (E) Two hypothetical, non‐intersecting curves, highlighting the point of closest approach (CPoA) on each line, and the resulting mean CPoA.
Figure 3
Figure 3
Stages of the scales methodology performed in this study. (A) Photograph of the experimental set‐up, with the duck specimen. (B) Schematic of experimental set‐up, showing specimen resting on plank, lying on the two scales. The distance between supports (L) and distance from proximal plank edge to proximal support (ΔL) are indicated. These data combined with mass readings from the two scales enable calculations of CoM position. (C) Rendering of Brick1, after marker data from three data captures was matched, showing the position of the three planks aligned with the three axes, and the three, 1D CoM positions plotted. These are then combined to give a 3D, final CoM prediction from the method.
Figure 4
Figure 4
Render of Brick1 from the top (A), left side (B) and front (C) depicting the method for calculating the geometric centre (CoMG). This was calculated by taking the mean of three pairs of Qualisys markers, one pair per axis. CoMx, CoMy and CoMz then combine to give the final xyz co‐ordinates for a 3D CoMG.
Figure 5
Figure 5
Predicted CoM positions displayed on renders of Brick1 (A–C), Brick2 (D–F) and Brick3 (G–I), shown from the left (A,D,G), front (B,E,H) and top (C,F,I). Predicted CoM positions are shown for each methodology, coloured according to the key. In cases where multiple CoM positions were available for the initial suspension and scales methods, only the CoM from the first runs are displayed here, for clarity.
Figure 6
Figure 6
Predicted CoM positions displayed on renders of chicken (A–C), buzzard (D–F) and duck (G–I), shown in cranial view (A,D,G), left lateral view (B,E,H) and dorsal view (C,F,I). Predicted CoM positions are shown for each methodology, coloured according to the key. In the chicken and buzzard, multiple suspension CoMs are shown along with multiple scales CoMs in the chicken.
Figure 7
Figure 7
(A) Graph displaying 3D distances from brick geometric centre (CoMG) to the CoM positions predicted by the methodologies listed on the x axis. (B) Graph displaying 3D distances from our ‘best guess’ bird digital CoM (CoMD 1) to the CoM positions predicted by the methodologies listed on the x axis. (C) 3D differences between geometric centre (bricks)/best guess digital CoM (birds) and CoM predictions produced by the methods studied here, normalised by maximum side length (bricks)/cranio‐caudal body length (birds).
Figure 8
Figure 8
Renders of Brick1 (A–C), chicken (D–F) and buzzard (G–I) displaying the broad spread of centre of mass positions predicted by the suspension methodology with three repeats (orange) and 10 repeats (red).

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