Torquecharacteristics

1
Torque-characteristics

• A torque (moment of force) is a tendency of a
  force to cause rotation about a specific axis.
• A torque is not a force, but merely the effect of
  a force in causing rotation.

2
Torque-characteristics

• A gymnast wishes to execute a twist about their
  longitudinal axis while standing in the
  anatomical position. Using torque as the method
  of explanation, show how this can be achieved.

3
Centre of mass

• The centre of mass is the point about which the
  mass is evenly distributed.

A
Balance point
B
3 kg
C
2 kg
0.20 cm
0.30 cm
Clockwise torque
Counterclockwise torque
Torque A (3 kg 9.81 ms-2) 0.2 m 5.89 Nm
Torque b (2 kg 9.81 ms-2) 0.3 m 5.89 Nm
The centre of mass can be further defined as
the point which the sum of the torques equal
zero. ?Tcm 0
4
Link isolation

• To determine forces and moments acting at joint
  on body links, individual links can be separated
  from adjacent ones and then analysed in a FBD.
• The Link must be completely isolated from all
  other bodies and an external boundary link
  sketched. All known and unknown external forces
  must be listed by vector arrows.
• Internal forces acting between the particles of
  the segment cancel each other out, and with a
  rigid link do not change the link movement.

5
Link Isolation-Free-body diagram
6
Examples of torque and sport

• Torque from muscle, gravitational and ground
  reaction force.
• Levers and torque.
• Internal torques
• Static and dynamic examples of torque.

7
Commonly generated Torques a) muscle force b)
gravitational force c) ground reaction force MA
movement arm
8
Gravitational torques created by the weight of
body segments acting at a distance from the joint
in movements such as trunk flexion a) and an arm
lateral raise b) must be countered by muscular
torques acting in the opposite direction.
9
Contact forces such as ground reaction force (a)
and muscle force (b) create torques because their
line of action of the force does not go through
the CM or joint axis, respectively.
10
An example of an anatomical lever
11
Viewing muscle torque as a lever.Force
resistance is weight of the arm axis is elbow
effort force is muscle force and M effort is
moment arm
12
FBD of the biceps curl
13
Solution
Cos ? a/d a d cos ?
arm
a
elbow
?
forearm
d
Forearm weight
The cosine of the angle ? of the forearm is used
to calculate The moment arm when the forearm is
not parallel to the horizontal
14
Calculate tension in muscle for the static
example below
15
Dynamic analysis of the foot in walking
Ry
? -14.66 rad/s-2 Ax 1.35 ms-2 ay 7.65
ms-2 Rx 1.57 N Ry 20.3 N Mass of foot 1.16
kg I 0.0096 kg.m2
Moment ankle
Rx
ay
0.07 m
ax
0.07 m
CM
y
Weight
x
16
Dynamic example

• Newtons second law establishes the basis for the
  dynamic analysis.
• In the linear case (2-D)
• ?Fx max
• ?Fy may
• The angular equivalent is T Ia
• If a 0 motion is purely linear
• If ay and axis 0 the motion is purely rotational
• If a ay ax 0, a static case exists.

17
Solution

• The net ankle moment can be calculated.
• ?Torquescm (about CM) Icma
• Torque ankle Torque Rx Torque Ry Icma
• Rearranging
• Torque ankle Icma Torque Rx Torque Ry
• Torque (0.0096 -14.66) (0.7 20.3) (0.7
  20.3)
• Torque -0.141 Nm 0.11 Nm 1.421 Nm
• Torque ankle 1.17 Nm

18
Torques generated on the horse by the vertical
(Fy dx) and anteriorposterior force (Fx dy)
generate angular impulses about the centre of
mass of the vaulter.
19
Angular work

• Mechanical angular work is defined as the product
  of the magnitude of the torque applied against an
  object and the angular distance that the object
  rotates in the direction of the torque while the
  torque is being applied.
• Angular work T ??
• T Torque, ?? is the angular distance

20
Angular work applied

• When a muscle contracts and produces tension to
  move a segment, a torque is produced at the joint
  and the segment is moved through some angular
  displacement.
• The muscles that rotate the segment do mechanical
  angular work.
• Positive angular work is concentric and negative
  angular work is eccentric motion.

21
Work and single and bi-articular muscles

• Single muscle levers lose tension as they
  contract therefore, expend more energy that two
  joint muscles in the same action.
• Bi-articular muscles cross two joints such as,
  rectus femoris (flexion at the hip and extension
  at the knee) or the hamstring group (flex the
  knee and extend the hip).

22
Work and single and bi-articular muscles

• As two joint muscles contract, they do not lose
  length and therefore, are able to maintain
  tension.
• For example, the rectus femoris muscles lose of
  tension at the knee is balanced by an increase in
  tension at the hip. At the same time the
  hamstrings gain tension at the knee and lose it
  at the hip.
• Although one joint muscles can allow locomotion,
  two joint muscles are more efficient.

23
Angular power

• Angular power is defined as the angular work done
  per unit of time and is calculated as the product
  of angular velocity and torque.
• Angular power T ?

24
Angular power applied

• Muscle power is determined by calculating the net
  torque of the muscle acting across the joint and
  the angular velocity of the joint.
• The net muscle torque describes the net muscle
  activity and does not represent any one
  particular muscle.
• It does not account for biarticulate muscles or
  elastic energy.
• Because work completed by muscles is rarely
  constant with time, the concept of muscle power
  is therefore used.

25
Rotational kinetic energy

• Rotational kinetic energy may be defined as the
  angular analogs of mass, velocity, i.e. moment of
  inertia and angular velocity.
• Rotation ( R) KE ½ inertia (I) angular velocity
  (?)
• Therefore, the total energy of a system is
  defined as
• Total energy KE PE RKE

26
Lower limb energy in running

• A lower extremity segment undergoes both
  translation and rotational movements in running.
• If the body segment values of the lower leg are
  inertia 0.0393 kgm2, mass 3.53 kg, r 0.146
• RKE ½ I ?2
• 0.05 0.0393 ?2
• 0.0192 ?2
• KE ½ mv2
• 0.5 3.53 (0.146 ?)2 (note v ?r)
• 0.0376 ?2
• Notice that both are in ? terms hence a
  comparison can be made.

27
Work-energy theorem

• For linear W ?E
• For rotation W angular ? RE
• W angular ? (1/2 I?2)
• Angular work is the work done on an object and ?
  RE is the change in rotational kinetic energy
  about the centre of mass.
• To calculate total work done on the object
• Work ? KE ? PE ? RE
• Work ? (1/2 mv2) ? (mgh) ? (1/2 I?2)