Page 284 - Flexible Robotics in Medicine

274 Chapter 12

Hence, the bending angle of each joint is as follows:

α 5 sin 21 L 1 2 L 2 5 sin 21 L 1 2 L 2 (12.5)
2d 2d

The total bending angle for the entire section is simply N 3 α, where N represents the
number of joints. From this, we can see that by determining the change in length between
two tendon wires, the bending angle can be calculated. The change in length can be varied
by the pulling of the tendon wires by the stepper motors.

12.2.2.2 Pulling length and velocity of stepper motors
To initiate a bending angle, the tendon wires needed to be pulled by the stepper motors.
Hence, we need to identify the pulling length and pulling velocity, which is dependent on
the stepper motors and its cm per minute (CPM) (stepper motor calculations). CPM can be
defined as follows:

ð f 3 60Þ
CPM 5 ;
ð n 3 S 3 MÞ
where f 5 frequency of the stepper motor, n 5 number of turns per cm (TPC), S 5 steps per
revolution, and M 5 micro-steps. There is then a need to derive the number of steps
required to move by 1 cm to initiate the bending of the sections in the horizontal axis
accurately to ensure the accuracy of the robotic platform in performing the required shapes.
Two possible ways have been identified:
• Move and measure method—a marker is used as a tool head to determine a 1000-step
line. Measure the line and divide 1000 by its length in centimeters.
• Step size calculation method—this approach is preferable, as it is relatively simpler to
calculate step size since it is based on the platform’s drive mechanism.

Secondly, since we are using a threaded rod-type drive mechanism, the number of TPC
plays an essential role in the calculation. The rods will be approximately 10 threads per cm.
The number of steps can then be calculated as follows:
Using a 200 step/revolution stepper motor (the most common type of stepper motors), it
would be 2000 steps per cm. The revolution per minute (RPM) of the stepper motor can be
determined in the Arduino code and setting the RPM of the stepper motors to be 300. The
required CPM is calculated as follows in Table 12.1.

From Table 12.1, the CPM of the stepper motors is calculated to be 60. This means that the
pulling velocity is 60 cm/min. Hence, for the pulling length to be 1 cm, the stepper motors
must revolve for approximately 1 second for each step.