Páginas: 13 (3039 palabras) Publicado: 5 de septiembre de 2012
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Mancilla Morales J. Arturo, F´ lix Beltr´ n Olga, Reyes Cortes Fernando, e a Palomino Merino Amparo, Vargas Trevi˜ o Aurora, Luis Ramos Arnulfo, BUAP, M´ xico n e arturo manc@hotmail.com, olga ﬂix@yahoo.com.mx, fernando.reyes@posgrados-fce-buap.mx

Resumen—The objective of this work is tomodel the phenomenon of friction using model friction in an anthropomorphic robot with two degrees of freedom. This will provide static friction models for application in a robot manipulator. Also, the properties of the dynamic model of a robot, which are necessary to use a model friction.

I-A. DYNAMIC MODEL OF ROBOTS WITH FRICTION The general dynamic equation of a robot manipulator is given by:˙ ˙ M(q)¨ + C(q, q)q + g(q) + f(τ ) = τ q (1) ˙ ¨ where q, q, q ∈ Rn×1 are vector of position, velocity and acceleration of robot joint, respectively, M(q) ∈ Rn×n is ˙ the matrix inertia, C(q, q) ∈ Rn×n is the matrix Coriolis and centripetal forces, g(q) ∈ Rn×1 is the pair gravitational ˙ f(τ, q) ∈ Rn×1 is the vector of friction, τ ∈ Rn×1 is the torque applied [5], [6], [7]. The effects of frictionin mechanical systems are complex phenomena that depend on many factors including the nature of the materials contact, including lubrication, temperature, etc.. For this reason, traditionally the friction forces and torques are modeled only approximately, while recognizing that they depend on the relative velocity between the bodies in contact. Thus, there are two classes of models of friction:static models in which the friction force or torque is given based on the instantaneous velocity between bodies, and dynamic models, which depend on the relative velocity [5]. In static models, friction is modeled by a vector f (q) ∈ Rn ˙ dependent only on the articular velocity q. The frictional ˙ effects are local, and f ( dot(q)) can be expressed as:   f1 (q1 ) ˙  f2 (q2 )  ˙   ˙ f(q) = (2)  . .   . fn (qn ) ˙ An important feature of the frictional forces is that they are dissipative: ˙ ˙ qT f (q) > 0 ˙ ∀q = 0 ∈ Rn Considering the viscous friction coefﬁcient Fv > 0 to describe the frictional force caused by the viscosity of lubricants. When combined with Coulomb friction, and consider the velocity as dot(q) = v we have:

I. I NTRODUCTION Is deﬁned as the force of frictionthat occurs between two media in contact, this being a force that opposes the motion against the other half (frictional force dynamics) or force that opposes the motion starts (Static friction force). Friction is present in the machines that incorporate parties relative motion. Research in the ﬁeld of control have not been capitalized adequately friction models available. Some research has producedpowerful tools for the theory of stability, nonlinear control, system identiﬁcation is not linear adaptive control and other areas, but these investigations are based on models friction of Leonardo Da Vinci or elementary physics [1]. These friction phenomena are always present when two media are in contact and forces are tangential to these that tend to produce relative motion. For this reasoncontrol problems of mechanical systems is essential to deﬁne handling these phenomena as they can place tracking errors, limit cycles, discontinuous movement (A dhe ren ing and gliding) and other problems affecting directly to the different types of control (position and movement) [1]. The friction appears in more than 60 % in the torque of the motor, damaging by 30 % control performance. In a carused about 20 % of the power motor to counteract the forces of friction. Friction causes wear and grip moving parts, and carried out a major engineering effort to reduce them. Moreover could not walk without friction, we could not hold a pencil, and if we could do, we could not writing; the wheeled transport would not be possible [1]. There is friction within the Stribeck effect, which represents...

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