The effect of gravity on hand spatio-temporal kinematic features during functional movements

Abstract

Understanding the impact of gravity on daily upper-limb movements is crucial for comprehending upper-limb impairments. This study investigates the relationship between gravitational force and upper-limb mobility by analyzing hand trajectories from 24 healthy subjects performing nine pick-and-place tasks, captured using a motion capture system. The results reveal significant differences in motor behavior in terms of planning, smoothness, efficiency, and accuracy when movements are performed against or with gravity. Analysis showed that upward movements (g-) resembled transversal ones (g0) but differed significantly from downward movements (g+). Corrective movements in g+ began later than in g- and g0, indicating different motor planning models. Velocity profiles highlighted smoother movements in g- and g0 compared to g+. Smoothness was lower in g+, indicating less coordinated movements. Efficiency showed significant variability with no specific trends due to subjective task duration among subjects. This study highlights the importance of considering gravitational effects when evaluating upper-limb movements, especially for individuals with neurological impairments. Planning metrics, including Percent Time to Peak Velocity and Percent Time to Peak Standard Deviation, showed significant differences between g- and g0 compared to g+, supporting Fitts' law on the trade-off between speed and accuracy. Two novel indications were also introduced: the Target Position Error and the Minimum Required Tunnel. These new indicators provided insights into hand-eye coordination and movement variability. The findings suggest that motor planning, smoothness, and efficiency are significantly influenced by gravity, emphasizing the need for differentiated approaches in assessing and rehabilitating upper-limb impairments. Future research should explore these metrics in impaired populations to develop targeted rehabilitation strategies.

Fig 1. Experimental set-up.

(A) Environment: 9 Nexus Vicon infrared cameras (orange circles) and a custom-made library made of a table and a shelf. (B) Positioning of IR-reflective markers on subjects (1)C7, (2)T10, (3)Scapula, (4)Shoulder, (5)Arm, (6)Elbow, (7)Forearm, (8)Outer Wrist, (9)Inner Wrist, (10) Collar bone, (11)Sternum, (12)Knuckle (C) Proposed pick-and-place task: 3 movements from the desk to the shelf (M1-M3), 3 from shelf to desk (M4-M6), and 3 from desk to desk (M7-M9).

Fig 2. Physical set-up and a participant performing the proposed pick-and-place task.

Fig 3. Representations of absolute hand positions (A) and velocities (B) across each subject, repetition, and movement.

Each curve was normalized over their own duration thus velocity is expressed as m/path. M1-M3 can be grouped as g-, M4-M6 as g+, and M7-M9 as g0.

Fig 4. Representation of velocity peaks, number of peaks in the velocity profile and Movement Time distribution for each gravity condition.

(A) Each row represents the absolute hand velocities for either g⁻, g⁺, and g⁰ sets of movements. The maximum peak is marked in red meanwhile all the local maxima are marked as blue stars. (B) Distribution of number of velocity profiles presenting 1, 2, 3, or 4 local maxima. (C) Movement Time (MT) distribution for each gravity condition. The arrangement is positively skewed for g⁻ (1.43), g⁺ (1.77), and g⁰ (1.44).

Fig 5. Statistical distribution of kinematic metrics.

Graphs A, B, and C show the statistical distribution of PTPV, PTPSD, and SPARC metrics respectively. Each metric was calculated for three sets of movements (i.e. g-, in pink, g+, in violet, g0, in green). From these graphs it’s possible to notice how the distributions for PTPV, PTPSD, and SPARC metrics are comparable between g⁻ and g⁰, as the means are mostly aligned with respect to g⁺. Graph D reports the comparison between PTPV (in red) and PTPSD (in blue) for each gravity condition. Overall, maximum peak is reached before maximum standard deviation across subjects, trials, and movements.

Fig 6. Representation of Target Position Error and Minimum Required Tunnel metrics.

(A) 3D and 2D view of Target Position Error (TPE) metric defined as the sphere whose radius contains up to 95% of hand end-points. Sphere related to g⁻ (in pink) and g⁺ (in violet) are almost symmetrical and present radius of 3.33 and 3cm respectively. g⁰ sphere (in green) radius is 2.3cm. The small dots represent experimental data, each colored in accordance to the gravity condition they belong to. (B) Representation of the average standard deviations across subjects, trials and movements for g⁻, g⁺, and g⁰. Solid line is representative of 1 standard deviation, meanwhile dashed line of 3 standard deviations. The Minimum Required Tunnel (MRT) metric is defined as the integral between solid and dashed lines (Table 3), shaded in the graph.