**5. Dexterous Manipulation Verification Experiment**

In this section, an experiment is conducted on the improved experimental platform of the robot manipulator (shown in Figure 8a) to verify the dexterous manipulation of the robot manipulator, especially the dexterous manipulation of a certain processing point. An aluminum alloy casting automobile steering booster housing (shown in Figure 8b) was selected as the experimental object, and the dexterous manipulation verification experiment was carried out at the center hole on the cylindrical top of the booster housing (shown in Figure 8b).

**Figure 8.** Experimental platform and experimental object: (**a**) experimental platform of improved robot manipulator; (**b**) overall appearance of booster housing.

Experimental verification of the dexterous manipulation was carried out on the platform of the improved robot manipulator. When the last two axes *J4* and *J5* both matched the actual initial state (shown in Figure 8a), the first three axes *J1*, *J2* and *J3* were adjusted so that the tool tip of the end-effector reached the center hole on cylindrical top of the booster housing until the intersection of the last two axes *J4* and *J5* basically coincided with the center hole (shown in Figure 8b). Then the first three axes *J1*, *J2* and *J3* remained stationary, and only the last two axes *J4* and *J5* rotated within the motion range. The characterizations of the dexterous manipulation of the robot manipulator are shown in Figure 9. The enveloping surface of the dexterous manipulation verification experiment is shown in Figure 10.

**Figure 9.** Experimental validation of the dexterous manipulation (unit is radian): (**a**) ϕ<sup>4</sup> = 0, ϕ<sup>5</sup> = 0; (**b**) ϕ<sup>4</sup> = −π; ϕ<sup>5</sup> = 0; (**c**) ϕ<sup>4</sup> = −2π/3; ϕ<sup>5</sup> = π/6; (**d**) ϕ<sup>4</sup> = −π/6; ϕ<sup>5</sup> = π/3; (**e**) ϕ<sup>4</sup> = 0; ϕ<sup>5</sup> = π/2; (**f**) ϕ<sup>4</sup> = π/6; ϕ<sup>5</sup> = 2π/3; (**g**) ϕ<sup>4</sup> = 2π/3; ϕ<sup>5</sup> = 5π/6; (**h**) ϕ<sup>4</sup> = π; ϕ<sup>5</sup> = π.

**Figure 10.** Enveloping surface of the experiment validation for the dexterous manipulation.

When the last two axes *J4* and *J5* traversed the motion ranges [−π, π] and [0, π], respectively, as shown in Figure 9, it can be found that the total locus of the tool tip of the end-effector appeared as an approximate enveloping half-spherical surface with a downward open, as shown in Figure 10, and the center of the half-spherical surface was the intersection of the last two axes *J4* and *J5*. In addition, the total locus of the tool tip remained the same when the last two axes *J4* and *J5* traversed the motion ranges [−π, π] and [−π, 0], respectively. For the sake of simplicity, only the former case is illustrated in Figure 9. Note that the approximate enveloping half-spherical surface was not a strictly half-spherical surface, and the extremely small difference was caused by the structure parameter *e*, which was not strictly equal to zero due to assembly errors.

The above results of the dexterous manipulation experiment imply that the robot manipulator has a very high level of the dexterous manipulation and the orientation reachability. These available and excellent characterizations of the dexterous manipulation and the orientation reachability can provide appropriate and flexible manipulations and orientation adjustments with a very high level of dexterity for the robotic deburring of the robot manipulator.

#### **6. Robotic Deburring Experiments**

Two robotic deburring experiments were conducted on the experimental platforms of the robot manipulator in this section to show the effectiveness of the proposed robotic deburring tool path planning method and the proposed robotic deburring process parameter control method, and also to demonstrate the superiorly operational manipulation performance and the deburring ability of the robot manipulator.
