A musculoskeletal multibody algorithm based on a novel rheonomic constraints definition applied to the lower limb

In this paper, a multibody model was developed in the framework of biotribology of lower limb artificial joints. The presented algorithm performs the inverse dynamics of musculo- skeletal systems with the aim to achieve a tool for the calculation of the joint reaction forces. The revolute joint, the cam joint, the spherical joint and the free joint were consid- ered in the analyzed lower limb system by introducing a novel analytical formulation of the rheonomic constraint equations based on the quaternions theory. Within the kinemati- cal analysis, the curved muscle paths were modeled by simulating their geodesic wrap- ping over bony surfaces while the muscle actuations were formulated through the Hill muscle model. The developed theoretical model was developed in MATLAB environment allowing to follow the classical musculoskeletal analysis pipeline: kinematical analysis, inverse dynamics, and static optimization, applied to the lower limb during the gait kine- matics. The validation of the results was obtained by comparing the calculated hip joint reactions with the ones obtained in vivo by Bergmann and calculated by Opensim soft- ware, showing a satisfactory agreement. The proposed model and algorithm represent a fully open and controllable synovial joint tribological configuration generator tool, useful to be coupled with numerical lubrication/contact models in the framework of the in silico artificial joints tribological optimization.