**6. Robot workspace**

138 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

cos sin 0 cos \* sin cos 0 sin \* 0 01 0 0 00 1

5 5

6 6

cos 0 sin 0 sin 0 cos 0 0 100 00 01

10 0 0 00 1 0 01 0 00 0 1

8 8

cos 0 sin 0 sin 0 cos 0 0 100 00 01

*d a* 

2R 0 L2 0 -90º

7R 0 L6 0 90

7 8 8

cos 0 sin 0 sin 0 cos 0 0 100 00 01

3 4 4 44

4 5 5

5 6 6

4

5

6

6 7

8

Below, the Table 4 indicates the D-H Parameters of the 8 DoF of the model:

*T*

Table 4. D-H Parameters table of the serial model

*Joint* 

1R

3R

4R

5R

6R

8R

*T*

*T*

*T*

*T*

4 4 44

*H H*

(47)

(48)

(49)

(50)

(51)

 

 

 

 

> 

 

6

 

 

*<sup>1</sup>*+90º H1 0 90º

*<sup>3</sup>* 0 0 90

*<sup>4</sup>* 0 H4 0

*<sup>5</sup>* 0 0 -90

*<sup>6</sup>* 0 0 -90

*<sup>8</sup>* 0 0 -90

*L*

A preliminary study of the workspace that could reach a set up of 2+2 parallel modules arranged in a serial mode, with actuated rotational joints, have been performed. The goal was to check if it was able to climb a three-dimensional cross-linked structure.

Fig. 10. 3D model of the serial robot with D-H convention axis

For one of the possible workspaces, some of the mathematical combinations of the robot actuators have been obtained, and a vector with all of them has been generated. This vector has been used to obtain different final points of the end-effector. Therefore, every element of the vector will be every final point of the previously described.

We have obtained a 210 elements vector (Figure 11) as a result of the ten joints of the real model. In this vector, the interferences between links were not taken into consideration.

On the other hand, a cross-linked structure and a robot model have been simulated through SolidWorks. The goal was to check if the robot was able to reach enough workspace points and, at the same time, to perform a plane change in the cross-linked structure, and all of this has been shown in the Figures 6 and 7 with the simulated model.

Design and Postures of a Serial Robot Composed by Closed-Loop Kinematics Chains 141

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**8. References** 

Fig. 11. 1024 points work space

## **7. Conclusions**

Some years ago, new robotic devices with a large number of degrees of freedom and binary actuators were developed to achieve a large motion workspace, to be capable of large fine motion, and have a small-stowed volume. Applications as inspection and maintenance tasks require them to adapt the robot to this kind of hostile environment.

In this way, a new reconfigurable binary climbing robot with closed-chains disposed in an open-chain architecture, has been presented.

Related works has been reviewed at the Section 2, as well as important features and applications of some climbing and walking robots.

Sometimes, the kinematics solution of parallel mechanisms requires using redundant sensors to establish a control loop because it becomes quite complicated. In this chapter, a binary actuators solution is presented, so a sensor-less feature is included.

Linear actuators are directly connected to the base and to the end-effector of the parallel modules, so these actuators are at the same time structural elements of the complete serial robot, and they work in a simultaneous way, which gives them the ability to handle loads much greater than its own weight.

The schematic design of the robot, description of the geometry and main postures have been also provided in the Section 3. In this Section, also has been studied in an independent way the parallel module, the two parallel modules disposed in a serial mode, and the complete robot composed by 2+2 Parallel modules arranged in a serial mode.

Moreover, an analysis of the forward and inverse kinematics of the parallel module, and forward kinematics of the complete serial robot are discussed in the Sections 4 and 5.

Finally the discrete workspace of the robot has been represented in the Section 6.

Future works will consist on determine the inverse kinematics solution of the serial robot, to implement the control system and applying path-planning algorithms to move the robot around of the cross-linked structure.
