**3.2 Two parallel modules disposed in a serial mode**

In the Figure 3, two parallel modules can be observed. We have disposed them in a serial configuration, leaving one parallel module rotated 180 degrees and disposed in a mirror mode behind the other, to achieve robust and stable postures, and at the same time, it allows to set up 90 degrees rotations (figure 5(b)) of the end-effector around of the free joint axis.

All different positions that these two attached modules are able to reach are summarized in Table 2.

In Figure 4(a), we can observe that the four linear actuators are set to off, and therefore the minimum elongation of the module is obtained.

However, if we need to perform a translation around the axis of the actuators without performing a rotation of the end-effector, we could use the image configuration 4(b) with the 4 actuators set to ON. In that way, there will not be any movement induced by rotational


b) π/4 rotation: Actuator 2

c) Actuator 1 and 2 ON

ON

Obviously, the different positions that this module is able to reach are given in Table 1:

*Actuator 1 Actuator 2 Translation Rotation*  0 0 0 0º 0 1 d1 45º 1 0 d1 -45º 1 1 d2 0º

In the Figure 3, two parallel modules can be observed. We have disposed them in a serial configuration, leaving one parallel module rotated 180 degrees and disposed in a mirror mode behind the other, to achieve robust and stable postures, and at the same time, it allows to set up 90 degrees rotations (figure 5(b)) of the end-effector around of the free joint axis. All different positions that these two attached modules are able to reach are summarized in

In Figure 4(a), we can observe that the four linear actuators are set to off, and therefore the

However, if we need to perform a translation around the axis of the actuators without performing a rotation of the end-effector, we could use the image configuration 4(b) with the 4 actuators set to ON. In that way, there will not be any movement induced by rotational

The Figure 2(c) refers to both actuators P1 and P2 set to ON.

a) Isometric view of the parallel

Fig. 2. Some views of the closed-chain module

Table 1. Positions from one parallel module

minimum elongation of the module is obtained.

**3.2 Two parallel modules disposed in a serial mode** 

module

Table 2.


Table 2. Positions from two parallel modules in a serial mode

Fig. 3. Two parallel modules to draw up a serial structure

joints. In this pose, it can be observed that the central sliders indicate the distance d2 between the base and the end-effector, obviously, they will be at its highest point of stretching.

However, it could be needed to reach some points in the workspace that are inclined at 90 degrees according to the base. In order to achieve this, and according to the Table 2, it could be observed in the Figure 5(b), that it can be obtained an inclination of 90 degrees, if the two mirror drives of each parallel module are switched alternately to ON and OFF.

In a similar way, if a 45 degrees inclination according to the base link was needed to reach, we could perform an actuation to ON of one of the linear actuators (figure 5(a)). This could be observed in the Table 2.

Design and Postures of a Serial Robot Composed by Closed-Loop Kinematics Chains 131

The robot in the Figure 1 consists of 2 + 2 parallel modules arranged to each other in a serial configuration and connected by a top link between two actuated rotational joints. According to this configuration, a three-dimensional movement of 90 and 180 degrees is possible to

*Actuator R1 Actuator R2 Translation Rotation*  0 0 0 0º 0 1 d1 90º 1 0 d1 -90º 1 1 d2 180º

achieve around the rotational axis of the joint, as shown in the Table 3:

Table 3. Positions of the rotational actuator

Fig. 6. Posture to a surface change of the structural frame

Fig. 7. Posture to evade a structural node: changing the plane

a) Minimum length. Frontal view.

b) Maximum length. Frontal view.

a) 45 degrees inclination b) 90 degrees inclination

Fig. 5. Different postures of the open-chain module
