where β is the angle between CD and BD. The mass of the robot
is 2.1 kg. The lengths of AB and BC are 130 mm and 160 mm
respectively. Assuming that η is 0.8, Fx and Fy can be calculated
from (7) to (9) in the condition of Fig. 6 (a) as 0.27 N and 6.70 N
respectively, in the condition of Fig. 6 (c) as -4.71 N and 2.32 N
respectively, and in the condition of Fig. 7 (a) as 0.48 N and 0.16
N respectively. The resultant force of Fx and Fy is Fxy which is
perpendicular to line C’O. Assuming that there is no slippage
between the wheels and the ground, the robot will incline in the
sides of the rectangle because of the rotational kinetic energy.
The maximum angular velocity of steering needs to be calculated
to avoid falling down of the robot. The rotational kinetic energy
is converted into the potential energy as
2
0 J / 2 mgh (10)
where J=mC’O2 is the moment of inertia of the robot, μ0 is the
angular velocity. The permitted maximum value of the angular
velocity can be calculated by using the same method as shown
in Fig. 8. As shown in Fig. 10, the resultant forces Fxy cross
AB, BC, and AD respectively when the robot is in the
proposed three conditions. The robot will incline in line AB,
BC, and AD. μ0 can be calculated by using (10) as 19.5 rad/s,
24.4 rad/s, and 199.2 rad/s respectively in the three conditions.
C. Wireless Charging System
The principle of wireless charging of the robot system is
shown in Fig. 11. The 220V (AC) voltage is converted to 12V
(DC) voltage. The transmitting circuit converts the 12V (DC)
to AC voltage for the wireless transmission of electrical
energy. The primary side coil transmits energy to the
secondary side coil wirelessly based on the principle of
electromagnet induction. The receiving circuit converts the
AC voltage of the secondary side coil into a DC voltage for
the battery charging.
The 3D model of the wireless charging system is shown in
Fig. 12. It is composed of a charging station and a battery
system. Fig. 12 (a) is the charging station composed of a
charging base, two transmitting circuit boards, and two
primary side coils. There are two chargers on the charging
where β is the angle between CD and BD. The mass of the robot
is 2.1 kg. The lengths of AB and BC are 130 mm and 160 mm
respectively. Assuming that η is 0.8, Fx and Fy can be calculated
from (7) to (9) in the condition of Fig. 6 (a) as 0.27 N and 6.70 N
respectively, in the condition of Fig. 6 (c) as -4.71 N and 2.32 N
respectively, and in the condition of Fig. 7 (a) as 0.48 N and 0.16
N respectively. The resultant force of Fx and Fy is Fxy which is
perpendicular to line C’O. Assuming that there is no slippage
between the wheels and the ground, the robot will incline in the
sides of the rectangle because of the rotational kinetic energy.
The maximum angular velocity of steering needs to be calculated
to avoid falling down of the robot. The rotational kinetic energy
is converted into the potential energy as
2
0 J / 2 mgh (10)
where J=mC’O2 is the moment of inertia of the robot, μ0 is the
angular velocity. The permitted maximum value of the angular
velocity can be calculated by using the same method as shown
in Fig. 8. As shown in Fig. 10, the resultant forces Fxy cross
AB, BC, and AD respectively when the robot is in the
proposed three conditions. The robot will incline in line AB,
BC, and AD. μ0 can be calculated by using (10) as 19.5 rad/s,
24.4 rad/s, and 199.2 rad/s respectively in the three conditions.
C. Wireless Charging System
The principle of wireless charging of the robot system is
shown in Fig. 11. The 220V (AC) voltage is converted to 12V
(DC) voltage. The transmitting circuit converts the 12V (DC)
to AC voltage for the wireless transmission of electrical
energy. The primary side coil transmits energy to the
secondary side coil wirelessly based on the principle of
electromagnet induction. The receiving circuit converts the
AC voltage of the secondary side coil into a DC voltage for
the battery charging.
The 3D model of the wireless charging system is shown in
Fig. 12. It is composed of a charging station and a battery
system. Fig. 12 (a) is the charging station composed of a
charging base, two transmitting circuit boards, and two
primary side coils. There are two chargers on the charging
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