The

static friction coefficient ([[my].sub.s]) of the beans was determined by the method outlined by Kaliniewicz et al.

Consequently, the

static friction torque for rotation is remarkably reduced to 10.5 gm (0.103 Nm), which approaches zero.

Employing generalised matrix inverses (GI), an intuitive and effective computation method of the

static friction forces is deduced, considering Gauss' least constraint principle.

Due to this stochastic nature, at each time, different control signal values are needed to overcome

static friction in the same specific position, and different values of minimum speed are required so that the valve does not grip during opening or closing procedure, being not compatible with traditional model-based controllers.

The reason for introducing [[epsilon].sub.f] in (5) is because the classical Coulomb friction model only defines the maximum

static friction for the stick state; the actual

static friction force can take on any value in the interval between zero and [f.sub.[sigma]][[mu].sub.s], depending on the magnitude of the total nonfrictional external force.

As shown in Figure 4, the motion of a curved surface slider is characterized by at least three phases, which corresponds to different friction factors: [[mu].sub.0] is the

static friction relative to the onset of motion; [[mu].sub.dyn] = [mu] is the dynamic friction during the sliding with velocity similar to the design one; [[mu].sub.1] is the friction factor corresponding to the change of velocity sign.

8, the net

static friction with the presence of magnetic flux passing through steel plate and platform is given by:

When [F.sup.(1).sub.s] cannot overcome the

static friction force [F.sup.(1).sub.f] (i.e., [absolute value of [F.sup.(1).sub.s]] [less than or equal to] [absolute value of [F.sup.(1).sub.f]]), mass [m.sub.1] does not have any relative motion to the belt, that is,

Halperin, "Experimental investigation of the elastic-plastic contact area and

static friction of a sphere on flat," Journal of Tribology, vol.

Moreover, the analytic conditions for stick and nonstick motions are developed, and the influence of the maximum

static friction torque and the driving torque on the stick motion is predicted numerically.