# The Kinematic Analysis of a Wind Turbine Climbing Robot Mechanism
## 4 Results and Discussion  
The study of the motion of the climbing robot travelling on the surface of the tower was tested through the MATLAB environment, which showed reasonable motion of the robot. The assumed velocities were to demonstrate full functionality of the kinematic modeling for the robot, where the results presented are very satisfactory. Theoretically, the robot can move in the specified movement states without changing its orientation by a proper combination of the four wheels' angular velocity. In fact, for this climbing robot, the commonly used movements are being studied to evaluate the effectiveness of the mecanum wheel as locomotion. Figure 6 shows the climbing robot wheel movement in different states. Moving all four wheels inwardly and outwardly causes an up-down movement of the robot on the tower, running the two wheels on one side in an opposite direction either inwardly or outwardly to those on the other side, which causes rotational movement to the tower and running one wheel on one side either inwardly or outwardly to those on the other side, which causes spiral movement. The robot has been designed in such a way that the wheels of the right or left side could be exchanged between them. The eight movement states are attained by adopting the wheel combination technique. The assumed velocity is 120 mm/s as it is provided in Table 3, to ensure a promising result with respect to climbing performance capability in a certain motion, particularly speed and stability. It is also assumed that there is no wheel slip on the tower as it climbs. The climbing modeled along the desired path as it moves to the wind turbine tower are shown in Figure 7. The motion of the robot along the tower allows examining the path as it goes in an up-down motion, rotation from left-right motion, spiral left-right, and upward-downward motion as shown in Figure 7a-d. The climbing model of the robot motions along the wind turbine tower with the height of 1200 mm and 330-400 mm tower diameter. The movement states of the robot are along the Z, Y and X axes. The angular speed for each wheel is assumed to be 3 rad/s, which is multiplied by each wheel's velocity both in up-down and rotational movements. For the spiral motion, the calculated distance travelled was based on the length of an Archimedean spiral. Thus, the total distance travelled by the robot is 8885 mm. To achieve the spiral movement the velocities of the two wheels are 5 rad/s each, and the other two wheels are zero. Travelling along the defined path provides the current pose of the robot. It is considered that a mecanum wheel has good stability in the motion process with enough adhesion to grip on the tower surface. The robot's ideal motion as shown in Figure 8 with robot velocity and total distance traveled. Figure 8a shows the up-down motion that the robot velocity is expected to increase from 0 mm/s to reach the maximum value of 120 mm/s as a commendable range with the corresponding tower distance that is within 0-1200 mm. Figure 8b shows the rotate motion that the robot velocity is expected to increase from 0 mm/s to reach the maximum value of 120 mm/s as a commendable range with the corresponding tower circumference within 0-1184 mm. Figure 8c shows the spiral motion the robot velocity is expected to increase from 0 mm/s to reach the maximum value of 170 mm/s as a commendable range with the corresponding ZY-axis from a total distance of 0-8885 mm. Table 3 also shows the 8 corresponding wheel directions up, down, rotate left, rotate right, spiral-left-upward, spiral-left-downward, spiral-right-upward and spiral-right-downward. For the up direction all four wheels are positioned inwardly to the tower surface and for down direction all four wheels are positioned outwardly to the tower surface. For the rotation to the left, the wheels 1 and 4 are facing outward while the wheels 2 and 3 are inward to the tower surface. For the rotation to the right, the wheels 1 and 4 are inward while the wheels 2 and 3 are outward to the tower surface.