**2. Structure Description and Related Research of the Robot Manipulator**

This section outlines the structure, experimental platforms and previous theoretical research of a developed five-degree-of-freedom (five-DOF) hybrid robot manipulator. The structure of the robot manipulator is shown in Figure 1. The robot manipulator, consisting of a 3-DOF (3T) parallel module and a 2-DOF (2R) serial module, is a newly developed 3T2R hybrid robot manipulator. The first three translational motion axes *J1*, *J2* and *J3* (consisting of ball screws) are driven by motor *M1*, *M2* and *M3*, respectively. The last two rotational motion axes *J4* and *J5* are driven by motor *M4* and *M5*, respectively. The axis *J6* is the end-effector which contains a high-speed motor spindle. The designed structure

parameter *e* is equal to zero, and the available range of the rotation angle is α ∈ [−π/4, π/4] because of the mechanical constraints.

**Figure 1.** Robot manipulator: (**a**) 3D model; (**b**) top view; (**c**) front view; (**d**) guideway module.

One of the most significant advantages of the robot manipulator is its dexterity in manipulation and orientation reachability. The last two rotational motion axes *J4* and *J5* as shown in Figure 1 are connected with an angle of 45◦ in order to realize the dexterous manipulation and the orientation adjustment of the robot manipulator end-effector. The end-effector can reach all orientations in the upper half of the complete spherical surface. Hence, the robot manipulator has the five-face machining ability in one setup. The detailed realizations are described as follows.

When the processing point of the end-effector coincides with the intersection of axes *J4* and *J5*, the position of the processing point of the end-effector can always keep at a same point (i.e., this point always coincides with the intersection), during the process of orientation adjustment in the upper half of the complete spherical surface only through the last two axes *J4* and *J5*. And the position of the processing point can be adjusted when translating the first three axes *J1*, *J2* and *J3*. This means that the manipulation and the orientation reachability of the robot manipulator characterize a very high level of dexterity.

It is necessary to note that some nonnegligible dynamic effects which caused by backlash of ball screws and robot manipulator structural deformations. It is very meaningful to investigate these effects of the backlash and structural deformations and to compensate for them if necessary. Some related research can be referred to [37–40].

Experimental platforms of the robot manipulator are shown in Figure 2. Among them, the improved platform is superior to the original one in mechanical structure on translational vertical axis assembly. The cylinder guide pillar module (shown in Figure 3c) of the improved platform, and the guideway

module (shown in Figure 1d) of the original one, are constituted by cylinder guide pillar and cylinder type support, and three sets of linear shafts and linear bearings, respectively. The former has greater torsional rigidity and strength of the vertical axis assembly around the vertical rotation axis than the latter. Finally, design structure and physical structure of the vertical axis assembly for the improved platform are shown in Figure 4.

**Figure 2.** Experimental platforms of robot manipulator: (**a**) original platform; (**b**) improved platform.

**Figure 3.** Improved cylinder guide pillar module: (**a**) cylinder guide pillar; (**b**) cylinder type support; (**c**) design structure diagram.

**Figure 4.** Vertical axis assembly of the improved platform: (**a**) design structure; (**b**) physical structure.

The reachable workspace of the robot manipulator based on structure parameters (Table 1) is shown in Figure 5. The top view and the front view of Figure 5 showed the range in the X, Y, and Z direction of the reachable workspace. Note that the shapes of the left end and the right end (in the top view of the Figure 5) are different. This is caused by the sway of the swing rod. The sway values are *L3*cosα and *L3*sinα in the *X* and *Y* directions, respectively. In the start phase, α increases from zero to the maximum attainable value (±π/4), and the sway value in the *X* and *Y* directions gradually decrease and increase, respectively. In the end phase, α decreases from the maximum attainable value (±π/4) to zero, and the sway values in the *X* and *Y* directions gradually increase and decrease, respectively. The mutual variation relationship is shown in Figure 5a.

In the previous research, kinematics analysis, dynamics analysis, dexterity analysis, multi-objective smooth trajectory planning and dynamic load-carrying capacity calculation, actual building of mechanical system and motion control system, and tests for the repeatability and accuracy of both the position and path for the five-DOF robot manipulator are conducted. For discussions of these domains and a more detailed listing of related research for the robot manipulator, see [41–44].

**Table 1.** Robot manipulator structure parameters (mm).

**Figure 5.** Reachable workspace of robot manipulator: (**a**) top view; (**b**) front view.
