Civil Engineering Reference
In-Depth Information
10.5.2 Internal Transmission
The tension inside a muscle-tendon unit tries to pull together the origin and insert the muscle-tendon
unit across a joint. This generates torque about the articulation with the long bones, which are the lever
arms at which muscle pulls. The torque developed depends, hence, not only on the strength of the
muscle, but also on the effective lever arm, and on the pull angle. Figure 10.4 depicts these conditions
as a simplified scheme of the lower arm link L attached to the upper arm link U, articulated in the
elbow joint. The muscle has its origin at the proximate end of U. Its insertion point is at the distance
m from the joint on the link L. It generates a muscle force M, pulling at an angle a. The torque T gen-
erated by M depends on the lever arm m and the pull angle aaccording to
T
¼
m
M
sin a
(10
:
1)
This torque T then counteracts an external force H, acting perpendicularly at its lever arm h,
according to
T
¼
m
M
sin a
¼
h
H
:
(10
:
2)
10.5.3 External Application — “Body (Segment) Strength”
The final output of the biomechanical system is the torque or force (H in Figure 10.4) available at
the hand, foot, or other body segments for exertion to a resisting object. This object is usually
outside the body, but the resistance may be from an antagonistic muscle. The “body (segment)
strength” available for application to an outside object is of primary importance to the engineer,
designer, and manager.
The model depicted in Figure 10.4 shows that the amount of force (H) available at the body interface
with an external object depends on muscle force (M); lever arms (m and h); pull angle (a) which, in turn,
depends on the angle between the two links. If all of these are known, the body segment force can be
calculated from Equation (10.2)
H
¼
(m
=
h)
M
sin a
(10
:
3)
D
EFINITIONS
To help distinguish among muscle tension, its internal transmission, and the final exertion to an
outside object, it is useful to define terms as follows:
Muscle strength is the maximal tension (or force) that muscle can develop voluntarily between its
origin and insertion.
The best word to refer to this is “muscle tension” (in N
cm
2
) but the term strength
(force in N) is commonly used. If the variables m, h, aand H in Equation (10.2) are known, one
can solve for muscle force as follows:
mm
2
or N
/
/
M
¼
(h
=
m)
H
=
sin a
(10
:
4)
Internal transmission is the manner in which muscle tension transfers in the form of torque
inside the body along links and across joint(s) to the point of application to a resisting object.
If several link-joint systems in series constitute the internal path of torque (in N m or N cm)
transmission, each transfers the arriving torque by the existent ratio of lever arms (m and h in
the example shown earlier) until resistance is met, which is usually the point where the body
interfaces with an outside object. This transfer of torques is more complicated under dynamic
conditions than in the static case because of changes in muscle functions with motion, changes in
lever arms and pull angles, and because of the effects of accelerations and decelerations of masses.
Search WWH ::
Custom Search