Research & ReviseActivity 2

Activity 2: Muscles and muscle groups.

Which muscle group must be active?Multiple muscle problemMaximal muscle torqueMuscle torque vs. arm positionMuscle force-length effect on torque

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Research & RevisePRS Q1

1. ShoulderAbductors

2. ShoulderAdductors

Activity 2 –muscles and muscle groups: Which muscle group must be active at the shoulder when performing the iron cross?

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Research & ReviseActivity 2 – PRS Q2

Activity 2 – Isolate the total arm+ring (arm-forearm-hand-ring combination) and draw a free body diagram. Neglect the weight of the total arm, lump the muscles into a single resultant force, and assume the shoulder joint is a frictionless hinge joint.

Compare your FBD with these:

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Research & RevisePRS Q2

Which of the following is a correct FBD of a gymnast’s arm + jig in holding the iron cross position? Assume the shoulder joint is frictionless and neglect the weight of the arm and the jig. T=Tension of the rope, M= Muscle force, J= Joint Reaction Force.

(A) T

MJ

(B)

T

M

J

(C)

M

(D) T

X

X

X

T

MJ

X

J

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Research & RevisePRS Q2

Which of the following is a correct FBD of a gymnast’s arm + jig in holding the iron cross position? Assume the shoulder joint is frictionless and neglect the weight of the arm and the jig. T=Tension of the rope, M= Muscle force, J= Joint Reaction Force.

Since the muscles act at an angle and pull away from the shoulder joint, the correct answer is:

T

M

J

(C)

X

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Research & RevisePRS Q3

1. ShoulderAbductors

2. ShoulderAdductors

Activity 2 –muscles and muscle groups: Repeat - Which muscle group must be active at the shoulder when performing the iron cross?

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Research & ReviseMuscle Force 1

Activity 2 – muscles and muscle groups

Assume that the two muscles marked below are the only active muscles at the shoulder. Can you find the force developed by each muscle to maintain equilibrium? (Consider the shoulder to be a frictionless hinge joint.)

1 Lat Dor

2 Pec Maj

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Research & ReviseMuscle Force 2

Activity 2 – muscles and muscle groups

How many unknown scalar quantities are in your free body diagram?

How many independent scalar equilibrium equations are applicable for this 2D problem?

1 Lat Dor

2 Pec Maj

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Research & ReviseMuscle Force 3

Activity 2 – muscles and muscle groups

How many unknown scalar quantities are in your free body diagram?

A) 1. B) 2. C) 3. D) 4.

1 Lat Dor

2 Pec Maj

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Activity 2 – muscles and muscle groups

How many unknown scalar quantities are in your free body diagram?The unknown scalar quantities are the two muscle forces, so the correct answer is:

B) 2.

1 Lat Dor

2 Pec Maj

Research & ReviseMuscle Force 3NextPrevious

Research & ReviseMuscle Force 4

Activity 2 – muscles and muscle groups

How many independent scalar equilibrium equations are applicable for this 2D problem?

A) 1 B) 2 C) 3 D) 4

1 Lat Dor

2 Pec Maj

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Research & ReviseMuscle Force 4

Activity 2 – muscles and muscle groups

How many independent scalar equilibrium equations are applicable for this 2D problem?The only applicable equation in this problem is derived from summing the moments about the shoulder joint, so the correct answer is:

A) 1

1 Lat Dor

2 Pec Maj

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Research & ReviseMuscle Force 5

Activity 2 – muscles and muscle groups

How would you define a statically indeterminate problem?

Can you think of ways the body might distribute forces between individual muscles to make this a statically determinate problem?

1 Lat Dor

2 Pec Maj

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Activity 2 – muscles and muscle groups

Assume that each of the three adductor muscles shown on the next slide generates its maximum possible force, Fmax,i. Derive expressions for the resultant muscle force, resultant direction, and its moment arm relative to the shoulder joint. Is the resultant muscle torque sufficient to hold a 5’ 10”, 160 lb gymnast in the iron cross position? Neglect weight of the arm.

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Research & ReviseMuscle Resource

Activity 2 – muscles and muscle groups, resources

insertion

origin

Muscle Insertion (x,y)(cm)

Origin(x,y)(cm)

Maximum Force (N)

Teres Major (+2.78, 0) (-11, -14) 1800

Latissimus Dorsi

(+1.5, 0) (-8, -28) 2700

Pectoralis Major

(+2.06, 0) (-9, -19) 4000

 

y

x

Origin & Insertion coordinates for arm in "iron cross" positionShoulder joint is at (0,0)

In class:What is maximum torque provided by Teres Major?

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Research & ReviseSegment Lengths

Activity 2 – muscles and muscle groups, resources

 

Segment Lengths(Expressed as a Percentage of Total Body Height)

Segment Males FemalesHead and Neck 10.75 10.75Whole Trunk 30.00 29.00Thorax 12.70 12.70Abdomen 8.10 8.10Pelvis 9.30 9.30Total Arm 32.90 33.30Upper Arm 17.20 17.30Forearm 15.70 16.00Hand 5.75 5.75Forearm and Hand 21.45 21.75Total Leg 47.90 50.60Thigh 23.20 24.90Leg 24.70 25.70Foot 4.25 4.25

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Research & ReviseArm Position 1

Activity 2 – muscles and muscle groups

What factors influence maximal muscle torque?

Would you expect maximal muscle torque at the shoulder to vary with arm position ?

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Research & ReviseArm Position 1

Activity 2 – muscles and muscle groups

If maximum muscle force F is independent of , would maximal muscle torque vary with arm position ?

Why or why not?

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Research & Revise

Activity 2 – muscles and muscle groups

How does muscle moment arm d vary with position ?

s

o

i

i

i

d

Muscle Length

Muscle moment arm, d

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Research & ReviseActivity 2 – muscles and muscle groups

How does Muscle Length vary with position ?

cos2

sin221

cos2

cos2

22

22

222

issi

sim

issim

issim

llll

lll

lllll

lllllCompute muscle length:

Note: Shoulder Joint is at (0,0)

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Research & ReviseActivity 2 – muscles and muscle groups

How does Muscle Force and Muscle Torque vary with position ?

cos2

sin

cos2

sin

22

22

iooi

ois

s

iooi

oim

llll

llFM

FMAM

llll

lllMAMoment Arm:

Muscle Torque:

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Research & Revise

Activity 2 – muscles and muscle groups

Experimental Observations:

Muscle Force vs. Length

Sarcomere Force vs. Length

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Research & Revise

Activity 2 – muscles and muscle groups

Muscle Force vs. Muscle Length (Quantitative Approach)

Does the force-length relationship for muscle influence the actual maximum

torque that can be developed by a muscle?

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Research & Revise

Activity 2 – muscles and muscle groups

Muscle Force vs. Muscle Length (Quantitative Approach)

forcepeak at lengthfiber

volumemuscle

/70100

force muscle Maximum

maximal is force whenlength Muscle

25.55.1225.6

2

0

0

0

2

00

PCSA

cmNpsik

PCSAkF

L

L

L

L

L

F

F

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Research & Revise

Activity 2 – muscles and muscle groups

Muscle Force vs. Muscle Length

Muscle Active Force-Length Relationship

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.4 0.6 0.8 1 1.2 1.4 1.6

L/Lo

F/F

0

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Research & Revise

Activity 2 – muscles and muscle groups

Through statics find the force necessary to hold the position assuming that the relative magnitudes of the forces remain the same

?

?

? 180040002700

: where0

TM

PM

LD

TMPMLD

S

F

F

F

FFF

M

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Research & Revise

Activity 2 – muscles and muscle groups

Through statics find the maximum mass of the gymnast for the muscle forces given to be sufficient to hold the iron cross position.

?BWmax

0

SM

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