Biomechanical Effects of Arm Endpoint Stiffness During Three-Dimensional Isometric Force Maintenance

Abstract

Arm endpoint stiffness reflects stable hand-environment interaction under varying forces. While this stiffness has been studied extensively in two-dimensional (2D) isometric tasks, its generalization to three-dimensional (3D) space remains unclear. We used a cable-driven device and the perturbation-based approach to measure 3D arm endpoint stiffness while ten healthy subjects produced isometric forces in 14 spatial directions. We investigated the biomechanics of 3D arm endpoint stiffness during isometric force maintenance through the characteristics of stiffness matrix and stiffness ellipsoid. The maximum stiffness component in the x-axis suggests that the arm endpoint stiffness is mainly affected by the constraints from ligaments and articulations during 3D isometric force maintenance. The shoulder's role as the primary stabilizer in transverse movements is also reflected. Collinear stiffness ellipsoid pairs showed similar volumes, indicating antagonistic muscle co-contraction plays a key role in maintaining stiffness stability across collinear force directions. The largest variation observed in the secondary axis reflects individual muscle contributions. These findings enhance understanding of 3D arm endpoint stiffness and guide robotic design.