i] is a

generalized force corresponding to the ith quasi-coordinate, and k is the number of quasi-coordinates.

Thus, the elastic potential energy is determined as a

generalized force.

Generally for this purpose relation of the external torque vector with

generalized force through the Jacobian matrix of manipulator is used.

Q = the

generalized force applied to the ith generalized coordinate

3S(i)] can be transformed to the

generalized force vector [F.

The

generalized force vector is obtained using expression:

As input in the model, using actuators, can be chose between the

generalized force and position/speed/acceleration of the motor joints.

i] (t) is the component of the

generalized force acting along the [x.

The J-integral discovered independently by Rice (1968) and Cherepanov (1968) originated from a conservation law given by Eshelby (1951) who introduced an integral having the meaning of a

generalized force on an elastic singularity in a continuum lattice (Bui, 2006).

Which

generalized force gives the required gripping force?

2] are the

generalized forces vectors, superscript 'd' denotes rigid disc.

The resulting functions transform the motion description of the system from generalized displacements x and

generalized forces f([V.