Journal of Automatic Control 2002 Volume 12, Issue 1, Pages: 46-55
doi:10.2298/JAC0201046M
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Open-chain analysis of single stance

Mizrahi Joseph, Brion Orly, Adam Dan

In this study we present a model by which the kinematics of single stance standing can be formulated and solved from forceplate measurements. A three-segment model with four rotation coordinates, two at the ankle and two at the hip, was developed as an open chain of linkages, with the trunk treated as the end-effector. Using the Denavit-Hartenberg notation, the trajectory of the center of mass (CoM) was evaluated by an iteration procedure, combining angular momentum principles with direct integration of the equations of motion. Kinematics and torques in the joints were thereafter solved. Single stance standing experiments were made on six healthy subjects and forceplate measurements served as input data for the model. The results show that the typical CoM excursion is within 2-3 cm roughly one order of magnitude higher than in double stance standing. Average oscillations of the joint angles ranged from 0.79 to 4.57 deg, with the higher values taking place in the hip sagittal rotation. The highest torques were coronal, at the hip, amounting to an average of 141 Nm. It was also found that when moving from ankle to hip the sequence of torque and angular displacement is inverted, indicating that the power delivered to the muscles at the distal/proximal joint is taken back by the muscles acting about the upper/lower joint. This provides evidence for the central strategy of the body to keep the CoM in a stable position.

Keywords: single-stance standing, open chain, center of mass trajectory, joint torques, redundancy

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