The Law of Inner Product of Computation for Robot Dynamics in Lagrange Equation

Using Lagrange the second type equation of mechanics to set up computation of robot dynamics is an effective method that used frequently. But it is quite acomplicated one.It must be simplified being introduced differential translation and differential rotation by pual,and an approximate solution is obtained at last.
In this paper,on the base of the Lagrange equation of the dynamics in the computation method,the concept of inner product in the linear space can be introduced and the law of inner product can be obtained too. The quite a simplicated equation can be apply to compute the dynamic equation of robot-1 in our university