Biomechanical model of swimming rehabilitation after hip and knee surgery

As a low-to-moderate intensity rehabilitation exercise after hip and knee surgery, we propose a dynamical model of the legs motion through the water medium in freestyle and backstroke swimming. We formulate a general Kirchhoff-Lagrangian dynamics model of the legs-propulsion through the water in post-surgical rehabilitation swimming. We start by defining the two-leg-propulsion configuration manifold. This is composed of eight Euclidean groups of rigid motions in 3D space for each of the four leg segments. Next, we define Newton-Euler dynamics for each segment. This single segmental dynamics is further generalized into Lagrangian dynamics for the whole leg-propulsion system. Finally, the water effects are added in the form of Kirchhoff's vector cross-products. In agreement with orthopaedic recommendations for post-surgical rehabilitation, numerical simulation is performed on a simplified version of the full Kirchhoff-Lagrangian dynamics model, which we call the "robotic swimming leg" - with intentionally reduced number of (microscopic, non-sagittal) degrees-of-freedom. The purpose of this development is both qualitative, for medical and physiotherapist practitioners to study, and quantitative, for biomechanics experts to analyze and further develop.