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**