Estimation of the muscle force distribution in ballistic motion based on a multibody methodology

Abstract

This work presents a general three-dimensional multibody procedure for studying the human body motion with emphasis on the locomotion apparatus. The methodology includes a three-dimensional biomechanical model, data acquisition techniques and an inverse dynamics approach. The biomechanical model is based on a multibody formulation using natural coordinates and consists of 16 anatomical segments modeled by 33 rigid bodies for a total of 44 degrees-of-freedom. The action of the muscles is introduced in the equations of motion of the multibody model by means of driver actuators defined as kinematic constraints. By associating a Lagrange multiplier to each muscle actuator the muscle forces became coupled with the biomechanical model through the Jacobian matrix of the underlying multibody system. A Hill type muscle model is used to calculate individual muscle forces. The model for the muscle apparatus comprises 43 muscle groups for each leg, which use the full three-dimensional lines of action for these muscles in their geometric description. The problem of the redundancy of the forces on the musculoskeletal structure is solved by using inverse dynamics and static optimization methods. In the process of describing the methodology the benefits of modeling in natural coordinates are highlighted. The methodology developed is demonstrated through its application to a case of ballistic motion, represented by the take-off to an aerial trajectory in order to estimate the joint torques and the muscle force distribution in the supporting leg. The time characteristics of the resultant net torques at the basic joints of the supporting leg and the time-varying muscle force patterns are presented and discussed. The results obtained are explained in terms of their relevance to the activity under study.

Keywords:

• Biomechanical models
• Natural coordinates
• Inverse dynamics
• Optimization

Acknowledgements

The authors want to acknowledge the support of FCT (The Fundação para e Ciência e Tecnologia) through the project POCTI/2001/EME/39976.