Forward dynamics of the lower limb based on constrained multibody dynamics
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In this thesis the forward dynamics of the lower limb is modeled as a constrained multibody dynamics problem. The equations of motion are developed using the Euler-Lagrange method. The constraints involved in the system are inequality constraints at position, velocity and acceleration levels. These constraints are incorporated into the equations of motion using the Lagrange multiplier technique. The constraint equations are posed as a linear complementarity problem (LCP) and are solved using Lemke's algorithm based on the dual phase simplex method used in the optimization problems. The surfaces used to model the contact dynamics between the skeletal surfaces are spheres. The actuation forces by the muscles are modeled using the Hatze's model for muscle dynamics. The results are found to be promising and motion of the lower limb system is found to be close to the actual motion. During the course of the project a new method to estimate the Jacobian of the manipulator is also developed. The purpose of this thesis was to develop a forward dynamics model for the motion of the lower limbs that could be used in the control of prostheses by the central nervous system.