Derivation of Differential Equations of Motion for Three-segment and Four-segment Human Locomotive Models using Free-body Diagrams

C.S. Putcha and J.A. Hodgdon (USA)


Free-Body Diagram, Four-segment, Thigh, Trunk, Force, Moment


The modeling of a human body is the basis for study of human movement. This plays a key role, when the dynamics of corresponding human locomotive model is used to predict the forces and moments (torques) at joints of the human body. This area of research has applications in many practical fields of day-to-day life such as the medical field and the area of sports. A lot of work has been done in the area of human modeling for the last several years (Rahmani [1]; Pandy and Berme [2]; and Winter [3]). In this paper, equations of motion (which are essentially differential equations) are derived for a four segment model to predict forces and moments at joints of a human body using similar equations for a three-segment model existing in the literature (Rahmani [1]). The three segment model consists of foot, thigh and shank (leg), while the four-segment model consists of foot, thigh, shank (leg) and trunk of a human body. These equations of motion are derived using the free-body diagram approach using basic principles of dynamics rather than using Lagrangian mechanics principles (Winter [3]). The results of the human locomotive model considered in this research are: forces and moments at ankle, knee and hip joints for a three-segment model while for a four-segment model additional force and moment at the trunk joint are also considered.

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