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

Compared to classical methods as Cardan, Fick and Euler angles which are based on homogeneous transformation, dual quaternions [1] offer an advantageous representation of a rigid transformation in 3D-space in many aspects. The dual quaternions have less computer memory cost, computer memory locations, since it needs 8 elements while classical methods require 12 elements, to describe a rotation composed with translation of a rigid body in 3D-space. Thus, the homogeneous transformation methods cost more storage and require a high computational time due to the nonlinearity of the end-effector coordinates. Moreover, these methods impose a well-defined rotation order. While, the dual quaternions method enables the reduction of the number of mathematical operations which leads automatically to minimize the computational cost [2]. Moreover, dual quaternions method permits to avoid discontinuities and singularities that arise from the Euler angle representation based on cylindrical polar coordinates to represent the motion of a rigid body in 3D-space [3].