Conceptual Design
Research study shows a rich content of pipe robot design for different applications (Roman et al., 1993; Yaguchi & Izumikawa, 2012; Roh et al., 2001; Pfeiffer et al., 2000; Ryew et al., 2000), but few are really applicable for this research. To meet the specific requirements, the conceptual design of the robot’s mechanical system has a rectangular platform supported by four wheeled legs as illustrated in Figure 2. The four robot legs are identical and interchangeable, as are the wheels. The legs are assembled with the robot platform through two rotational joints located at the centre of the two ends of the platform.
Figure 2. The front view of the conceptual design of the pipe inspection robot
Suppose the origin of a Cartesian coordinate system is set coincidently at the centre point of the robot platform, with the Z-axis collinear with the pipe centre line, X-axis horizontal and Y-axis vertical, as illustrated in Figure 2. If the robot platform is placed horizontally inside the pipe with the center point of the line that joins the two rotational joints coincidently located at the origin of the Cartesian coordinate system, then the center line of the rotational joints for the robot legs is collinear with the pipe centre line as shown in Figure 2, where W the robot gravity force, R the pipe radius, Fa and Fb are the normal forces applied on the robot wheels. To simplify the analysis, the gravity forces of the robot legs are ignored; also assume the design of the robot is symmetric with respect to both the XOY and YOZ planes.
Angle θ is the angle measured in front view from the top surface of the robot platform to the robot leg. The assembly allows the robot legs to rotate around the centre of the rotational joint. This makes angle θ adjustable. When the robot platform is placed horizontally, as the design is symmetric, the assembled mechanism guarantees the centre of the gravity is always below the top surface of the platform. Under ideal conditions, the gravity centre of the robot should be on the Y-axis and in the longitudinal vertical plane that passes through the pipe centre line.
Force Analysis Without Payload
In the static state, with no payload on the robot platform, the symmetric design with respect to the XOY and YOZ planes assures the forces applied on the robot satisfy the equilibrium condition.
(1)(2) where
and
are the sum of the normal forces applied to the left and right sides of the robot wheels.
As a result:
(3)
Equation 3 indicates 
and 
changes with angle θ. The rational domain for angle θ is 
. For a unit mass, the θ -
graph is shown in Figure 3. The graph reveals that, when θ is less than 20 degrees and approaches to 0 degree, the value of 
increases rapidly and approaches to infinity. Apparently an applicable boundary for angle θ must be considered. Based on the θ -
graph, the lower limit for angle θ set at 20 degrees is a reasonable approach for the study of the normal forces applied on the robot wheels.
Figure 3. The 
-
graph