Quantification of the Mechanical Properties in the Human-Exoskeleton Upper Arm Interface During Overhead Work Postures in Healthy Young Adults

Abstract

Exoskeletons transfer loads to the human body via physical human-exoskeleton interfaces (pHEI). However, the human-exoskeleton interaction remains poorly understood, and the mechanical properties of the pHEI are not well characterized. Therefore, we present a novel methodology to precisely characterize pHEI interaction stiffnesses under various loading conditions. Forces and torques were applied in three orthogonal axes to the upper arm pHEI of 21 subjects using an electromechanical apparatus. Interaction loads and displacements were measured, and stiffness data were derived as well as mathematically described using linear and non-linear regression models, yielding all the diagonal elements of the stiffness tensor. We find that the non-linear nature of pHEI stiffness is best described using exponential functions, though we also provide linear approximations for simplified modeling. We identify statistically significant differences between loading conditions and report median translational stiffnesses between 2.1 N/mm along and 4.5 N/mm perpendicular to the arm axis, as well as rotational stiffnesses of 0.2 N·m/° perpendicular to the arm, while rotations around the longitudinal axis are almost an order of magnitude smaller (0.03 N·m/°). The resulting stiffness models are suitable for use in digital human-exoskeleton models, potentially leading to more accurate estimations of biomechanical efficacy and discomfort of exoskeletons.

Keywords: exoskeleton; interaction stiffness; interface mechanics; mechanical characterization; physical human-robot interaction; physical human–exoskeleton interaction; upper arm; wearable robot.

Figure A1

(a) A curved rail facilitates the repositioning of the drive unit. At the same time, a vertical axis enables the cart’s rotation (highlighted with red arrows) to achieve various configurations of the measurement setup. These configurations allow torques and forces (white arrows) in the distoproximal (top), caudocranial (middle), or lateromedial (bottom) directions. (b) CAD of fixtures (forearm support, upper arm support, shoulder brace), upper arm attachment (pHEI), and drive unit connected to the pHEI adapter via a load cell and linkage. (c) Image of the load cell connecting the drive unit’s output shaft and the linkage. (d) CAD of drive unit illustrating the translational drive (motor and spindle) moving the rotational drive back and forth, thereby creating translations/forces (white arrows). The rotational drive generates torques around the output shaft (white curved arrows). (e) Picture of the pneumatic upper arm attachment, including the adapter, two braces, inserts for circumference adjustment, and pressure cuffs, connected to a pressurized air supply via tubes.

Figure A2

(a,b) The first 8 of 40 translational movements from one measurement. (a) Measured relative displacement of the arm attachment to the arm over time (black line) and a representative slope (blue) with the corresponding maximum (highlighted by a blue circle). (b) Measured force on the arm attachment over time and a representative slope (red) with the corresponding maximum (highlighted by a red circle). (c) The highlighted force slope from (b) is plotted against the displacement slope from (a) (measured primary data). A correction determines the distance to the force’s zero-crossing and shifts the curve accordingly, ensuring the corrected trajectory passes through the origin. (d) Various regression models are fitted to the curve, illustrated here by an exponential function.

Figure A3

Regression models fitted to measurement data from all subjects (dotted gray lines) for all loading conditions (positive (+) and negative (−) translations and rotations in distoproximal, caudocranial, and lateromedial axes). Fittings to all data are shown as dashed lines (SGR), while continuous lines depict averaged individual stimulus regressions (ISR). Linear regressions appear in blue, and exponential functions are shown in red.

Figure A4

FE-models of simplified arm pHEI under different loading conditions ((a) perpendicular force, (b) distoproximal force, (c) perpendicular torque, (d) distoproximal torque). Loads, depicted as white straight arrows representing forces and white curved arrows representing torques, were applied on the surface of the arm attachment (gray), either directly (d) or via auxiliary cylinders ((a) via one cylinder, (b,c) via two opposite cylinders for symmetry). The bone (yellow) was fixed to the ground. Deformations of the arm (red) are indicated with respect to the initial position (transparent) and exaggerated for better visibility in (a,b).

Figure 1

(a) Schematic overview of the measurement setup in CAD (computer-aided design, SolidWorks 2021, Dassault Systèmes, Vélizy-Villacoublay, France). (b) Subject secured in the setup via fixtures, connected to the support frame. A load cell connects the drive unit and the upper arm attachment (not connected to the support frame) via a linkage. (c) Load axes, types, and directions. The setup can exert load types, including forces (white arrows) and torques (white curved arrows) along three orthogonal axes (distoproximal, caudocranial, and lateromedial) in both positive and negative directions at the center of the pHEI. Mocap markers are indicated on the upper arm attachment (blue) and the arm (red). (d) The relative motion (d_R) of the attachment to the arm is calculated as the difference in movement between the pHEI (d_pHEI) and arm (d_A) mocap markers.

Figure 2

Linear (L) and exponential (E) fittings applied to the measurement data of one subject (a) and all subjects (b) under a specific loading condition (positive rotation about the lateromedial axis). (a) The gray graphs display the ten selected individual stimuli. The means and standard deviations of the corresponding regression functions (ISR) are plotted with continuous lines surrounded by a colored area, while the direct fittings to all ten individual stimuli of one subject (SSR) are plotted with broken lines. (b) The figure shows the curves for all the stimuli from all subjects (gray lines), the regression functions fitted directly to this data (SGR, broken blue and red lines), and the means of all ISR fittings (continuous blue and red lines).

Figure 3

Box plots of the slopes of the ISR linear regression models as a measure of interaction stiffness for the different loading conditions, each with the median (black line), interquartile ranges (gray box), whiskers, and outliers (gray circles). Additionally, the means are indicated (red lines), which can also be found in Table A1 (Appendix B.1). Interaction stiffness values are provided for positive (+) and negative (−) translations (a) and rotations (b) in all three loading axes (distoproximal, lateromedial, and caudocranial).