Mechatronic Design of a Soccer Robot for the Small-Size League of ...

Chapter 3: Kicking device
At the moment of impact, the conservation of impulse law can be used to
determine the velocity after the impact.
m plunger v plunger ,t1 + m bal v bal ,t1 = (m plunger + m ball ). v t2 (4.23)
Assuming that the velocity of the ball is zero before impact:
v t2 = m plunger v plunger ,t1
m plunger + m ball
( 4.24)
v t2 =
m plunger
2. α. F 0 − k. α²
m plunger
m plunger + m ball
(4.25)
C. Accelerating plunger and ball
This calculation is similar to those made in section A. The mass becomes the
combined mass of plunger and ball. Only the start conditions of the differential
equation change. Variable ‘x’ is equal to α at the start. The velocity is equal to v t2 at
the start and the acceleration at the start becomes:
F 0 − k. α
m total
x t = α − F 0
k
. cos ωt + v t2
ω . sin ωt + F 0
k
(4.26)
v t = ω. F 0
k − α . sin ωt + v t2. cos⁡(ωt) (4.27)
a t = ω 2 . F 0
k − α . cos ωt − v t2. ω. sin⁡(ωt) (4.28)
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