In this paper, the problem of motion of controlled mechanical systems under a servo constraint
is considered. The servo constraint which is prescribed by the designer is supposed
to be non-ideal, that is, it does work in a virtual displacement. The second order form constraint
is introduced to obtain a closed-form (i.e., analytical form) control input. The final
servo control contains two parts: the first one generates the constraint force so that the
constraint is exactly followed, while the second one can be designed by the designer for the
facility, such as to compensate the effects of the friction force. After geometrical analysis
applied to the Coulomb friction forces, we found that they actually depend on the control
forces (i.e., the two are coupled). Application to a 3-DOF robot manipulator is made.
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