SKEDSOFT

Newton-Euler Formulation

For the sake of clarity, the manipulator is assumed to be an open-link chain, having revolute joints. The development can be extended to other types of manipulators in a straightforward manner.

 Consider the ith link of an n-link manipulator, as shown in Figure. The Newton-Euler equations for this link consist of the force momentum equations:

and the moment-angular momentum equations about the centroid Ci of the link:

The following notation has been used:

ƒ_i-1=force vector at the i-1th joint of the ith link.

N_i-1=moment (torque) vector at the i-1th joint of the ith link.

g=vector representing acceleration due to gravity.

m_i=mass of the ith link.

I_ci=moment of inertia matrix of the ith link about Ci.

u_ci=velocity of the centroid of the ith link.

w_i=angular velocity vector of the ith link.

r_a,b=position vector from point a to point b.

Next, by substituting: