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Torque
Objectives:•^
Define angular kinetics
-^
Define and learn to compute moment arms,torque, and resultant torques
-^
Introduction to resultant joint torques andanatomical torque descriptions
Questions to Think About
•^
What anatomical and physiological factors affecta muscle’s functional strength (
i.e.
ability to
control rotation) at a joint?
-^
How can we determine which muscle groups aremost active during a movement task?
-^
Why should a worker keep an object being liftedclose to his or her torso in the transverse plane?
-^
How might an athlete be able to compensate forweakness or fatigue of the semimembranosus?
-^
What are some benefits and drawbacks ofagonist-antagonist cocontraction at a joint?
Angular Kinetics
Kinetics •^
The relationship between the forces acting on asystem and the motion of the system Angular Motion (Rotation) •^
All points in an object or system move in a circleabout a single axis of rotation. All points movethrough the same angle in the same time Angular Kinetics •^
The kinetics of particles, objects, or systemsundergoing rotation
Torque (or Moment)
•^
A force applied through the center of mass willproduce linear acceleration
-^
A force applied at any other point produces bothlinear acceleration and angular acceleration
-^
Torque = Measure of extent to which a force willcause angular acceleration of an object
F
F
a
a
Line of Action
•^
The line of action of a force is the imaginary line thatextends from the force vector in both directions
-^
It’s the line that the force pushes or pulls along
F
line of action of F
Moment Arm
•^
Shortest distance from a force’s line of action to theaxis of rotation
-^
Moment arm is always perpendicular to the line ofaction and passes through the axis of rotation
F
axis of rotation
line of action of F
90°
moment arm
of F
Computing a Moment Arm
•^
Determined by:– Distance (d) from axis of rotation to point at which
force is applied
) at which force is applied
•^
Use trigonometry to compute moment arm (
d
)⊥
F
axis of rotation
d
d
⊥^
= d sin
Moment Arm Examples
axis of rotation
F
F
d
F
F
d⊥
d
= d sin⊥
θ
θ
d
⊥^
= d sin
θ
θ d
d
d
d⊥
Resultant Joint Torque
•^
The effects of all forces acting across a joint canbe duplicated
exactly
by the combination of:
- A resultant joint force acting at the joint center– A resultant joint torque acting about the axis of
rotation through the joint center
•^
Resultant joint force
= The vector sum of all
forces acting across a joint.
-^
Resultant joint torque
= The sum of the torques
about the joint axis due to these forces.
-^
Note: Forces that do not act across the joint (e.g.weight) are not included in the resultant jointforce or torque.
Example
Fcontact
Fhams
Facl
knee joint center
tibia
d⊥
hams
d⊥
quads d⊥
acl
Fquads
Fcontact Fresultant Fhams
Facl
Fquads
T^ resultant
T
resultant
= (F
quads
d ⊥quads
) + (F
acl
d ⊥acl
) – (F
hams
d ⊥hams
)
Use of Resultant Joint Torque
•^
Typically, joint contact force, muscle forces, ligamentforces,
etc.
cannot be determined individually
•^
We
can
compute resultant joint forces and torques
based on data measured external to the body
-^
Except near the limits of the anatomical range ofmotion, the main contributors to the resultant jointtorque are the muscles
-^
The resultant joint torque provides a simplifiedpicture of which muscle groups are most activeabout a joint
Muscle Redundancy
•^
Multiple combinations of muscle force can create thesame resultant joint torque
-^
Example:
For elbow of forearm shown below:
30°
Ft
Fcontact
Fbi
Fbr 0.25 m
0.05 m
0.025 m
FW
= 8 N
0.10 m
RJT
0
Fbr
20
10
16
Fbi
8
Fcontact
32
0
0
Ft
(^
)^
(^
)^
(^
)^
t
br
bi^
F m F m F m
RJT
Anatomical Torques
•^
Positive & negative torques depend on the spatialreference frame chosen:
-^
To avoid this, joint torques typically described bythe joint motion that occurs if the segment movesin the direction of the torque( e.g.
F
quad
produces a knee extension torque) Fquad
knee
Fquad
knee
x
y
x
y
T > 0
T < 0
