Page 223 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

200 BIOMECHANICS OF THE HUMAN BODY

as seen in Fig. 8.2. The system is constrained to move within the r-θ plane and is acted upon by a
gravitational field of magnitude g, which acts in the negative vertical direction; r and θ are deter-
mined to be the only two generalized coordinates, since the motion of the mass is limited to movement
in the radial and transverse (r and θ, respectively) directions only. A model of this type can be used
as a mechanical analogy to structure an approach to investigate the dynamics of soft tissues such as
a muscle.
The velocity of the mass is given by

v = r e + rθ e θ
r
in the r-θ frame of reference or, in terms of the b , b , b frame of reference,
1 2 3
v = r b + rθ b 2 (8.5)
1
The origin of this reference frame is considered to be located at the pivot point, as seen in Fig. 8.2.
The kinetic energy of the system can be represented in vector form as
1
T = m(vv
• )
2 (8.6)

g

B b 2

b 1

θ r
c k / 2

k / 2 G
l 1

C
m

FIGURE 8.2 Single elastic body pendulum with two springs and one dashpot
(point G represents the center of gravity of the pendulum).
1