Theoretical study of possible solutions for addressing the kinetic redundancy in lumbar spine by central nervous system

Human motor system is organized for execution of various motor tasks in different and flexible ways. This is mainly achieved by the way that central nervous system (CNS) uses the redundancy in musculoskeletal system. The kinetic redundancy in human musculoskeletal systems is a significant property by which central nervous system achieves many complementary goals. In this study, by explaining the definition and role of uncontrolled manifold for movement kinematics, the kinetic redundancy concept is explored in mathematical terms. The null space of the kinetically redundant system when certain joint moment and/or stiffness are needed is derived and discussed. In this paper, the mathematical methods have been developed for a simpler planar biomechanical model with 3 muscles in which the explained concepts have been utilized.