Session: 07-05-01: Dynamics and Control of Biomechanical Systems

Paper Number: 167616

Rigid-Body Modeling and Rotational Center Localization in Quiet Stance Mechanics 

This paper presents an in-depth investigation of the static biomechanical behavior of the human foot through a combination of high-resolution kinematic measurements and force plate data. The study aims to validate the assumption that the foot, during quiet stance, can be modeled as a rigid structure with predictable rotational properties. Fourteen healthy subjects participated in controlled experiments, during which sensors were affixed to the navicular, metatarsal, and calcaneus regions. Data were recorded along the X, Y, and Z axes to capture detailed position information, and several key metrics—including the distance between the calcaneus and metatarsal, navicular height, and the inter-segmental angle defined by the calcaneus, navicular, and metatarsal—were computed to test the underlying hypotheses.

The first hypothesis proposes that during quiet stance, each distinct region of the foot behaves as a rigid body. In this configuration, minimal internal deformation is expected; the recorded positional data and inter-segment distances should remain nearly constant over time, thereby affirming a rigid-body model. The second hypothesis extends this notion by positing that the entire foot can be represented as a single rigid entity when the navicular is designated as the center of mass. By integrating the sensor data across all three regions, quaternion analysis is employed to compute both the rotation and pitch angles in the sagittal plane. The overall expectation is that even if small sliding movements occur, the kinematic behavior will conform predominantly to the rigid-body representation.

The third hypothesis focuses on the localization of the foot’s rotational center. It is anticipated that the rotational center is positioned near the metatarsal region—a prediction that is evaluated by comparing the root mean square (RMS) values derived from the movement data across the calcaneus, navicular, and metatarsal. A systematic decrease in RMS values from the calcaneus to the metatarsal would indicate that the center of rotation indeed lies closer to the metatarsal, supporting theoretical predictions and prior studies.

Experimental trials were conducted under controlled laboratory conditions with subjects standing on a calibrated force plate. The integration of kinematic data with kinetic measurements enabled a comprehensive statistical analysis of foot stability and rigidity. Results from these analyses demonstrate that the inter-segmental parameters remain largely invariant during quiet stance, validating the hypothesis of regional rigidity. Furthermore, the aggregated quaternion data provide compelling evidence that the overall foot motion adheres to a rigid-body model with the navicular as a viable center of mass. The observed RMS trends confirm the predicted proximity of the rotational center to the metatarsal region.

The outcomes of this study contribute significantly to the field of foot biomechanics by offering a robust framework for modeling the foot as a rigid structure during static conditions. These findings have immediate implications for the design of orthotic devices, the refinement of rehabilitation protocols, and the development of computational models that simulate foot mechanics. In summary, the integration of detailed kinematic data and force plate measurements substantiates the rigid-body paradigm and accurately localizes the rotational center, thereby advancing our understanding of static foot behavior.

Keywords: foot biomechanics, rigid-body modeling, sagittal plane, rotational center, kinematics, static stance.

Presenting Author: Esra Gözde Yalçın Yıldırım Roketsan

Presenting Author Biography: Esra Gözde Yalçın is an accomplished mechanical engineer and technical author with extensive experience in aerospace, defense, and automotive industries. A graduate of Middle East Technical University, she holds dual MSc degrees in Mechanical Engineering and Civil Engineering (Transportation) and is further advancing her expertise as a PhD candidate..

Currently serving as a Lead Mechanical Engineer at ROKETSAN, Esra has played a pivotal role in conducting advanced structural analyses and developing validated finite element models for high-performance mechanical components. Her proficiency with industry-standard tools such as MSC Patran, Nastran, ANSYS, and CATIA V6 has been instrumental in optimizing design integrity and ensuring compliance with rigorous safety standards across critical projects. Prior to her tenure at ROKETSAN, she contributed to strategic projects at organizations including TSE, Turkish Aerospace Industries, and TUBITAK, where her work spanned from unmanned underwater vehicles to Turkey’s first commercial helicopter.

Authors:

Esra Gözde Yalçın Yıldırım Roketsan
Kutluk Bilge Arıkan Ankara University
Senih Gürses Middle East Technical University