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

Denavit and Hartenberg based methods as Cardan, Fick and Euler angles describe the position and orientation of an end-effector in Three Dimensional (3D) space. However, the generation of unrealistic human posture in joint space constitutes the weak point to these methods because they impose a well-defined rotations order. A method to handle the transformation homogeneous performance uses the dual quaternions. Quaternions have proven themselves in many fields as providing a computational efficient method to represent a rotation, and yet, they can not deal with the translations in 3D-space. The dual numbers can extend quaternions to dual quaternions. This paper exploits dual quaternions theory to provide a fast and accurate solution to the forward, inverse kinematics and recursive Newton-Euler dynamics algorithm for 7 Degree of Freedom (DOF) human lower limb in 3D-space.