Page 118 - Handbook of Biomechatronics

114 Naser Mehrabi and John McPhee

maximum normalized muscle force during lengthening. The numerical
values of the muscle parameters used in this research are reported in
Mehrabi and McPhee (2014a). The PE force of muscle (F PE ) is represented
by an exponential function:

L M m
k pe L opt 1 =E 0
e M 1
F PE ¼ (19)
e 1
k pe
m
where k pe (¼0.5) is a shape factor and E 0 is passive muscle strain at maximum
isometric force.
For steering with two hands, the total torque T d generated at the steering
wheel is as follows:

F f a, L M , V M Þ T d 0
ð
T d ¼ 2G SHS r (20)
F e a jj, θ, θð Þ T d < 0
where F f and F e are flexor and extensor muscle forces that, respectively, pro-
duce a clockwise and counterclockwise torque at the steering wheel, and θ
and r are the shoulder angle and the average moment arm of flexor and
extensor muscles, respectively; G SHS is a fixed ratio that projects the
moment of muscles produced at shoulder to the steering wheel. For simplic-
ity, the muscle length and velocity, and moment arms, are rearranged and
simplified to be only a function of shoulder angle and angular velocity
_
(i.e., L M ¼ L 0 rθ and V M ¼ rθ). Here, we assume that there is no muscle
co-contraction between flexor and extensor muscles, and the positive and
negative values of T d are produced by the flexor and extensor muscles,
respectively.
A simplified single-track model with a column-assist EPS steering system
as shown in Fig. 7B was developed to speed up the optimization procedures.
The driver torque T d transfers through a torsion bar to the steering pinion
and rotates the tires. The torque sensor measures the torsion bar twist and
sends it to the EPS system that regulates the assist torque (T a ). The following
equation describes the steering wheel, and the torque sensor dynamics:
€ _
J sw θ sw ¼ b sw θ sw + T tb + T d (21)

T tb ¼ K tb θ sw θ p (22)
where T d and T tb are the driver and the torsion bar torques, θ p is the pinion
angle, and θ sw , J sw , and b sw are the angle of rotation, the moment of inertia,
and the viscous damping coefficient of the steering column, respectively.