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

Two-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