Predictive Dynamics - Human Motion Simulation: Predictive Dynamics - page 109

Table 5.2

Four Cases of Swing Motion Examined with Predictive Dynamics

Motion Case Available Information

Simple swing without
oscillation

1 Boundary conditions

Oscillating motion 2 Boundary conditions

3 Boundary conditions and response at one

point

4 Boundary conditions and response at two

points

y

O

x

q

￿

l

mg

FIGURE 5.9
Single pendulum.

The pendulum pivots at the point O as shown in Figure 5.9 . The equation of
motion for a rigid bar subject to external torque is given as

mg l I q €

2 cos q

5 τ

(5.32)

1

where I is the moment of inertia, m is the mass, l is the length, q is the joint
angle, and is the external torque. The external torque is assumed to be a sinusoi-

dal function given as

τ

τ 5 :

1sin 5 t

ð Nm Þ

0 (5.33)

The geometrical and physical parameters of the rigid bar are taken as

0267 kgm 2 , m I 0 : 0 : 5 kg, and l 0 : 4 m. With the initial condition qð 0 Þ 5 0

5 5 5

and qð 0 Þ 5 0, the forward dynamics is solved by the ADAMS Runge-Kutta solver,

as shown in Figure 5.10 , which is considered the true solution of the system.