Closed-form kinematics for a spatial closed-chain mechanism modeling biped stance

This paper presents kinematic analysis of a spatial closed-chain mechanism with applications in the stance phase of human gait and in postural studies. Based on a specific sequence of body-fixed rotations and an appropriate set of independent coordinates, a closed-form solution has been successfully obtained by suitably imposing the kinematic constraints. This approach reduces the numerical stiffness index of the respective dynamic system from three to two, and provides a set of ordinary differential equations instead of differential/algebraic equations describing system dynamics. As a result, it allows more stable integration and more efficient direct dynamic simulation. This approach is not universal for all closed-chain mechanisms. However, it is anticipated that this approach will have valuable influence on modeling biped locomotion in biomechanics and robotics.