## 3 Results
### Experimental Results  
An experimental investigation has been carried out on the technical feasibility of transporting objects on an inclined plane oscillating in its longitudinal direction, applying an additional asymmetry achieved through dynamic dry friction manipulations. The object's motion was achieved by tuning the control parameters \(\phi\) and \(\lambda\), where the dynamic effective dry friction was reduced between the object and the manipulated surface, and a frictional asymmetry was achieved. The amplitude of the sinusoidal harmonic oscillations was \(A=1.04\) mm, and the angular frequency was \(\omega=62.83\) rad/s. The kinetic friction coefficient between the manipulation surface and the upward-moving object was approximately \(\mu_{0}=0.24\), and the ratio was \(\langle{{{\mu}_{m}}}\rangle/{{{\mu}_{0}}}=1/4\). The average velocity sharply increased from \(\phi=0\) and reached the maximum between \(\phi=\pi/3\) and \(\phi=\pi/2\) at \(\lambda=\pi\), and then dramatically started to decrease until it reached \(\phi=2\pi/3\) at \(\alpha=0.035\) rad as shown in Figure 10a. At a higher inclination angle \(\alpha=0.1\) rad, the average velocity was notably decreased at \(\phi=\pi/2\) and \(\lambda=\pi\) due to the gravitational potential energy exerted on the moving object. Similarly, the average velocity was reduced at lower \(\lambda\) as a function of phase shift and reached a minimum at \(\lambda=2\pi/3\), as demonstrated in Figure 10b. Theseexperimental findings verified the modeling results, which revealed that the phase shift \(\phi\) had shown its effectiveness in controlling and changing the direction of the moving object at different inclination angles.  
The experimental investigation has proven the technical feasibility of the theoretical findings that the directional motion of the moving object can be controlled by changing \(\lambda\) and the phase shift \(\phi\). Figure 10(a) represents the variation of the average velocity depending on \(\lambda\). The average velocity was dramatically increased as \(\lambda\) increased between \(\pi/6\) and \(\pi/2\) and reached its maximum at \(\phi=\pi/4\). However, as the inclination angle increased to 0.1 rad, the average velocity significantly decreased due to the gravitational potential energy, as demonstrated in Figure 10(b). Similarly, the average velocity was notably increased as \(\lambda\) increased between \(\pi/6\) and \(\pi/2\). The average velocity reached the maximum at \(\phi=\pi/4\) and the minimum at \(\phi=\pi/2\). \(\lambda\) has revealed strong effectiveness in changing the velocity of the moving object at different inclination angles.  
Figure 10: Average transportation velocity vs. the phase shift \(\phi\): (**a**) \(\alpha=0.035\) rad, \(A=1.04\) mm, \(\omega=62.83\) rad/s; (**b**) \(\alpha=0.1\) rad, \(A=1.04\) mm, \(\omega=62.83\) rad/s, \(\mu_{0}=0.24\) and \(\langle\mu_{m}\rangle/\mu_{0}=1/4\).  
Different experiments have been performed at various inclination angles \(\alpha\) rad, as shown in Figure 12. The experiments have presented the influence of the inclined angle while the object was moving upwards. The average velocity steadily decreased as the inclined angle increased from \(\alpha=0\) rad to \(\alpha=0.1\) rad. The average velocity reached a maximum value at \(\phi=\pi/3\) and \(\lambda=\pi\), where \(A=1.04\) mm, \(\omega=62.83\) rad/s, \(\mu_{0}=0.24\) and \(\langle\mu_{m}\rangle/\mu_{0}=1/4\).