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.

翻译：Denavit-Hartenberg方法如Cardan、Fick和欧拉角可描述末端执行器在三维空间中的位置与姿态。然而，这些方法因强制规定明确的旋转顺序，在关节空间中生成不真实的人体姿态构成其缺陷。一种处理齐次变换性能的方法采用对偶四元数。四元数已在多个领域被证明是一种高效的计算旋转表示方法，但无法处理三维空间中的平移。对偶数可将四元数扩展为对偶四元数。本文利用对偶四元数理论，为三维空间中七自由度人体下肢提供快速精确的正向运动学、逆向运动学及递归牛顿-欧拉动力学算法。