Module 9 : Robot Dynamics & controls
Lecture 31 : Robot dynamics equation (LE & NE methods) and examples
    3.
 Lagrangian formulation for Robot arm:

 

Figure 31.7 Robot link performing general plane motion

In general Robot link is performing general plane motion. In this case K.E. is sum of Rotational & Translational kinetic energies. Therefore

          
Inertia matrix should be computed in the same reference frame w.r.t. which angular velocity of link is defined.

Total kinetic energy of one robot link i is

 

summing for all joints the sum can be written as

                                                                          
  

where D(q) is a symmetric, positive definite matrix that is in general configuration dependent.The matrix D(q) is called the inertia matrix.We will see its significance later in the dynamical equation.

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