Dynamic Principle of Center of Mass in Human Walking
Yifang Fan *
Center for Scientific Research, Guangzhou Institute of Physical Education, Guangzhou 510500, P.R. China
Yubo Fan
Key Laboratory for Biomechanics and Mechanobiology of Ministry of Education, School of Biological Science and Medical Engineering, Beihang University, Beijing 100191, P.R. China
Zhiyu Li
College of Foreign Studies, Jinan University, Guangzhou 510632, P.R. China
Mushtaq Loan
International School, Jinan University, Guangzhou 510632, P.R. China
Changsheng Lv
Center for Scientific Research, Guangzhou Institute of Physical Education, Guangzhou 510500, P.R. China
*Author to whom correspondence should be addressed.
Abstract
Assuming the ground reaction force of both feet to be the same in the same phase of a stride cycle, we establish the relationships between the time of initial foot contact and the ground reaction force, acceleration, velocity, displacement and average kinetic energy of center of mass. We employ the dispersion to analyze the effect of the time of the initial foot contact that imposes upon these physical quantities. We present results of an analytic and numerical calculation that studies the relationship between the time of initial foot contact and the ground reaction force of human gait and explores the dynamic principle of center of mass. Our study reveals that when the time of one foot's initial contact falls right in the middle of the other foot's stride cycle, these physical quantities reach extrema. An action function has been identified as the dispersion of the physical quantities and optimized analysis used to prove the least-action principle in gait. In addition to being very significant to the research domains such as clinical diagnosis, biped robot's gait control, the exploration of this principle can simplify our understanding of the basic properties of gait.
Keywords: Gait, center of mass, forward dynamics method, least-action principle, musculoskeletal system diseases