Derivation of the Equation of motion of a three-link-manipulator:

This part is necessary for programming Exercise 6 of
Introduction to Robotics
Mechanics and Control. The following parameters are specified:
Kg
Kg
Kg
For link 3 the center of mass is located at the origin of frame {3}
Inertia tensor for link 3 is:
The vector that locate each centre of mass relative to the respective link frame are:
Other usefull information:
is the position of link 3 in the frame of reference {2} is the position of link 2 in the frame of reference {1}
The outward iteration for link 3
because
The inward iteration for link 3
The inward iteration for link 2
force link 2
moment link 2
The inward iteration for link 1
force link 1
moment link 1
Extracting the torque components
Dynamic Equation