The addendum for the generalized d'Alembert equations of motion

In this paper, the traditional generalized d'Alembert equations of motion (G_D) in the field of robot dynamics are extended to the circumstances as follows: 1 Considering the robots not only with rotary joints but also with translational joints. 2 Extending the application range of the G_D dynamic equations from the simple chained robots to the tree_structured robots.