Kinematics and Dynamics Modeling of 7 Degrees of Freedom Human Lower Limb Using Dual Quaternions Algebra

Abstract: Denavit and Hartenberg-based methods, such as Cardan, Fick, and Euler angles, describe the position and orientation of an end-effector in three-dimensional (3D) space. However, these methods have a significant drawback as they impose a well-defined rotation order, which can lead to the generation of unrealistic human postures in joint space. To address this issue, dual quaternions can be used for homogeneous transformations. Quaternions are known for their computational efficiency in representing rotations, but they cannot handle translations in 3D space. Dual numbers extend quaternions to dual quaternions, which can manage both rotations and translations. This paper exploits dual quaternion theory to provide a fast and accurate solution for the forward and inverse kinematics and the recursive Newton-Euler dynamics algorithm for a 7-degree-of-freedom (DOF) human lower limb in 3D space.