Predicting the Biomechanics of Walking - Human Motion Simulation: Predictive Dynamics - page 167

3

Front
heel

x

r 3

2

r 4

r 2 o z ZMP

r 1

Rear
toe

4

1

FIGURE 7.13
Foot support polygon (top view).

Left arm

η 1

y

x

Right leg

η 2

o

z

FIGURE 7.14
Arm-leg coupling motion.

7.9.3.1.5 Arm-leg coupling
It is believed that the arm-swing is performed to help balance the upper body dur-
ing walking to reduce the trunk moment in the vertical direction. Swinging arms
are not necessary or required for motion; however, that motion provides dynamic
balance.
In practice, it is difficult to measure the moment produced by the swing arm.
In this formulation, we introduce a two-pendulum model to represent arm-leg
coupling kinematics during the walking motion. The basic idea of the arm-leg
coupling constraint is that the arm-swing on one side counteracts the leg-swing
on the other side as depicted in Figure 7.14 , where the first pendulum

η 1 repre-
sents the left arm (from the left shoulder to the left wrist), and the second pendu-
lum

η 2 denotes the right leg (from the right hip to the right ankle).
The mathematical form of a coupling constraint is written as:

ðη 1 n z Þðη 2 n z Þ $ 0 (7.31)

where n z is the unit vector along the z-axis. It is important to note that the arm-
leg coupling constraint is imposed only on the swing directions of the arm and