1. Factors Influencing Production of Muscular Tension and Applied Force n Force-velocity relationship - Fig 6.17, p 162 n Length - tension relationship - Fig 6.18, p 164 -Elastic and contractile components

2. Force- velocity relationship:

5. Active insufficiency: length- tension relationship:

6. Biomechanics of musculoskeletal system (pp 420-436) -Objectives n Identify the musculoskeletal machines and machine functions found in the human body n Identify elements of the lever n Define torque, quantify resultant torques, and identify the factors that affect resultant joint torques n Describe the concept of net torques and it’s use in estimating muscle force n Describe the elements of the wheel and axle and give examples in the musculoskeletal system of humans n Describe the concept of mechanical advantage associated with levers and wheel and axle

7. Musculoskeletal machine functions and machines n Most important machine functions found in the human body -provide advantage for ROM and speed (levers and wheel & axle) -change direction of applied force (pulley) n Three machines found in the body: -levers (ex. biceps brachii pulling on radius) -wheel and axle (rotator cuff muscles pulling on humerus) -pulley (patella, lateral malleolus of fibula)

8. Musculoskeletal Levers n Elements of levers - axis (joint center) -rigid bar (long bone) -motive and resistance torques (muscle pull, gravity, inertia), or moments n Concept of Net Torque n Law of levers (  CW torques =  CCW torques) -Force X Force Arm = Resistance X Resistance Arm - or Ff = Rr n Analysis of musculoskeletal lever system -Turning, or rotary component (Fd sin  ) -Stabilizing and dislocating component (Fd cos  )

9. Levers in the Human Body (all amplify movement at expense of force) Class III: Class :I

10. Wheel & Axle: Another movement amplifier!

11. Simple pulley: Changes direction of force application

12. Concept of Net Torque, concentric and eccentric contraction

13. Sample Problem #2, p 433

14. Analysis of elbow flexors: Note how angle of pull changes

15. Angle of Pull of Muscle & degree of force application Turning component equals Force times sin θ

16. Mechanical Advantage of Elbow Flexors

17. Length of Elbow Flexors as Joint Angle Changes

18. Additional problem #2, p 173: Length-tension, angle of pull combined Sine of

19. Mechanical advantage n Mechanical advantage is the output force (F) divided by input force (R) n Lever arrangements MA = output force (R) divided by input force (F) = force arm (f) divided by resistance arm (r) n Wheel and axle arrangements Very similar to lever arrangements with force applied to the axle, which is usually the case (e.g., shoulder joint in throwing) with radius of axle and radius of wheel equivalent to force arm (f) and resistance arms (r), respectively

20. Musculoskeletal pulleys, study questions n Pulleylike arrangements Only simple pulleys found in the body to change direction of force application n General considerations of musculoskeletal machines human body is built for speed & ROM - not force n Self-study questions -Introductory problems, p 445 - # 1,2,3,6,7

21. Assume force is applied perpendicular to the bar: a. In which position will the exercise be easier? b. If it takes 100 N to move the system at position 2, what will it take to lift it at positions 1 and 3? Hint: use the law of levers: Ff = Rr and solve for F Homework # 7 – Musculoskeletal machines: (due Monday, 3/15/04) Introductory problems, p 445 - # 4, 8 Additional problems, p 446 - #3 Exercise equipment problem illustrated below: