Page 51 - Anatomy of a Robot
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02_200256_CH02/Bergren 4/17/03 11:23 AM Page 36
36 CHAPTER TWO
Overshoot: Damping = .2
Frequency = 2.5
2
1.5
Position x Position x Position x Position x 0.5
1
0
0 2 4 6 8 10
Time tTime t
Time t
Time t
FIGURE 2-13 This bouncing weight overshoots by 50 percent
Spring
Force
Step input F = K * x
Mass
2 2
F = m * d x/dt
Friction
F = B * dx/dt
FIGURE 2-14 A second-order mechanical system with step input, spring,
weight, and friction
leave it up to the reader to calculate the rotation of the earth that would occur if every-
body on Earth starting walking in the same direction at once. For now, let’s consider the
ground stable.
We’re going to delve into physics and math here without a serious attempt to explain
how things work. Take heart that we will return to more familiar ground shortly and that
the results will be intuitive and usable.
