Tissue mechanics: mechanical properties of bone, muscle, tendon, etc.

1. Overall course plan • Tissue mechanics: mechanical properties of bone, muscle, tendon, etc. • Kinematics: quantification of motion, with no regard for the forces that govern motion • Kinetics: forces in human movement

2. Kinematics • 1-D linear kinematics • Angular kinematics • 2-D linear kinematics • Locomotion

3. Reading • Linear: Enoka chapter 1 pp. 3-23 • Loco: Enoka chapter 4 pp. 141-146 • Angular: Enoka chapter1 pp. 23-29

4. Kinematics • 1-D linear kinematics • Angular kinematics • 2-D linear kinematics • Locomotion

5. Video Kinematics • 60-6000 images/sec • Put markers on anatomical landmarks • Computer tracks marker position

6. Kinematics example video • http://www.vicon.com/applications/life_sciences.html • http://www.youtube.com/watch?v=USOYUMN5nwU • http://www.youtube.com/watch?v=IJ4tndpwL-o&mode=related&search= • http://www.youtube.com/watch?v=frNpkIH8_vo&mode=related&search=

7. Kinematics • 1D = movement in one direction. • e.g just the forward movement of a human runner during a sprint • 2D = movement in a plane, components in 2 directions • e.g. side view of hip of a person walking • 3D = movement anywhere in space • an owl swooping to catch jackrabbit, knee movements • Angular = movements that include rotation • e.g., a biceps curl, alligator biting, figure skater

8. 1 dimensional linear kinematics • Measurement Rules • Definitions of terms used in kinematics • Equations and examples for constant acceleration motion • 1D Kinematics example

9. Units • SI system • Length : meters (m) • Mass : kilograms (kg) • Time : seconds (s) • Other units • Angle : radians (rad) • 2p radians = 360o

10. Prefixes and Changing Units • Giga (G) 1x109 • Mega (M) 1x106 • Kilo (k) 1x103 • Deci (d) 1x10-1 • Centi (c) 1x10-2 • Milli (m) 1x10-3 When changing units, always be sure to CANCEL units appropriately!

11. 1 dimensional linear kinematics • Measurement Rules • Definitions of terms used in kinematics • Equations and examples for constant acceleration motion • 1D Kinematics example

12. Kinematics terms: position • position (r) =location in space • Units : meters (m) • Must be defined with respect to a baseline value or axis

13. Kinematics terms: Displacement • Displacement = Change in position = ∆r = (rf - ri) • rf = final position; ri = initial position • Units = meters (m) • Involves space and time rf Position r, (m) ri ti tf Time (s)

14. Kinematics terms: Velocity (v) • rate of change of position • vave = ∆r / ∆t • vinstantaneous = dr / dt (slope of position vs. time) • Units = m / s rf Velocity v, (m/s) Position r, (m) vi vf ri ti tf ti tf Time (s) Time (s)

15. Kinematics terms: acceleration (a) • rate of change of velocity • aave = ∆v / ∆t • ainstantaneous = dv / dt = slope of velocity vs. time • units = m / s2 rf Velocity v, (m/s) Position r, (m) vi vf ri ti tf ti tf Time (s) Time (s)

16. 1 dimensional linear kinematics • Measurement Rules • Definitions of terms used in kinematics • Equations and examples for constant acceleration motion • 1D Kinematics example

17. Special case: Constant acceleration • Example: Projectile motion when air resistance is negligible • Gravitational acceleration = 9.81 m / s2 • in the downward direction!!! • g = 9.81 m/ s2 • Useful for analyzing a jump (frogs, athletes), the aerial phase of running, falling

18. Projectile Motion • The only significant force that the object experiences while in the air will be that due to gravity • Flight time depends on vertical velocity at release and the height of release above landing surface

19. Symmetry in projectile motion • A comparison of the kinematics at the beginning and end of the flight reveals: • vi = - vf & vi2 = vf2 • ri = rf & rf - ri = 0

20. Equation 1 for constant acceleration • Expression for final velocity (vf) based on initial velocity (vi), acceleration (a) and time (t) vf = vi + at • If vi = 0 vf = at

21. Problem solving strategy • Define your coordinate system! • List all known variables (with UNITS!) • Write down which variable you need to know • (with UNITS!) • Figure out which equations allow you to solve for the unknown variable from the known variables.

22. Example using equation 1 • An animal jumps vertically. The animal’s takeoff or initial velocity is 3 m/s. How long does it take to reach the highest point of the jump? (Air resistance negligible). • - 0.3 s • 0.03 s • - 0.03 s • 0.3 s

23. Equation 2 for constant acceleration • Expression for change in position (rf - ri) in terms of initial velocity (vi), final velocity (vf), acceleration (a) and time (t). rf - ri = vit + ½ at2 • If vi = 0, then rf - ri = ½ at2

24. Example using equation 2 What was the net jump height of the animal in example #1. In other words, how high did it jump once its feet left the ground? • 46 m • 46 cm • 1.34 m • -1.34 m

25. Equation 3 for constant acceleration • An expression for the final velocity (vf) in terms of the inital velocity (vi), acceleration (a) and the distance travelled (rf - ri). vf2 = vi2 + 2a (rf - ri) • If vi = 0, then vf2 = 2a (rf - ri)

26. Example using Equation 3 A runner starts at a standstill and accelerates uniformly at 1 m/s2. How far has she travelled at the point when she reaches her maximum speed of 10 m/s?

27. Example using Equation 3 A runner starts at a standstill and accelerates uniformly at 1 m/s2. How far has she travelled at the point when she reaches her maximum speed of 10 m/s? • 5 m • 10 m • 50 m • 100 m

28. 1 dimensional linear kinematics • Measurement Rules • Definitions of terms used in kinematics • Equations and examples for constant acceleration motion • 1D Kinematics example

29. 1-D kinematic analysis of a 100 meter race • Question to answer: How long does it take to reach top speed? • Videotape the sprint • Measure the position of a hip marker in each frame of video

30. 100 meter sprint

31. 100 meter sprint vmax reached at 6 seconds, at 50 meters.

32. Acceleration (m / s2) 100 meter sprint vmax = 10 m/s aave = 1.66 m/s2 (0 - 6 seconds)

33. Kinematics • 1-D linear kinematics • Angular kinematics • 2-D linear kinematics • Locomotion

34.  Position • Linear symbol = r unit = meter • Angular symbol =  unit = radians or degrees 6.28 rad = 360°

35. Hip Knee Ankle Joint angles • Ankle: foot - shank • Knee: shank - thigh • Hip: thigh - trunk • Wrist • Elbow • Shoulder

36. Hip Knee Ankle Segment angles • Measured relative to a fixed axis (e.g., horizontal) Trunk Trunk Thigh Shank Shank

37. 2 ∆ 1 Displacement • Linear symbol = ∆r ∆r = rf - ri unit = meter • Angular symbol = ∆ ∆ = f - i unit = radian

38. Angular ---> linear displacement • s = distance travelled (arc) • s = radius • ∆ ∆ must be in radians 2 s ∆ 1 radius

39. Elbow Joint angle change: Flexion • Flexion: decrease in angle between two adjacent body segments • Bird’s eye view of arm on table Flexion

40. Joint angle change: Extension • Extension: increase in angle between two adjacent body segments Extension Elbow

41. Knee extension Knee extension

42. knee Knee FLEXION Knee flexion

43. A Squat Jump Hip ext Knee ext Ankle ext

44. EMG: Electromyography • Measures electrical activity of muscles • indicates when a muscle is active Hip ext Knee ext Ankle ext

45. Hip angle Hip extensor EMG Knee angle Knee extensor EMG Ankle angle Ankle extensor EMG 0 0.30 0.15 Time (s)

46. Alternative joint angle definition Full extension: alt = 0 (degrees or rad) norm alt

47. Knee angle (rad) 2 Run Enoka 4.5 Flex-Ext Flex-Ext 1 0 1 Small Flex-Ext Walk Flex-Ext 0 Flexion Swing Stance stance stance Time (% of stride)

48. Velocity • Linear • symbol = v • v = ∆r / ∆t • unit = meters per second • Angular • symbol =  = “omega”” •  = ∆ / ∆t • unit = radians per second • human body: we define extension as positive  ∆

49.  v r Linear velocity (v) & angular velocity () • v =  r

50. A person sits in a chair and does a knee extension. The knee angle changes by 0.5 radians in 0.5 seconds. What is the magnitude of the angular velocity of the knee, the linear velocity of the foot and the linear displacement of the foot? (Shank length is 0.5 meters) • 1 rad/s, 0.5 m/s, 0.25rad • 0.5 rad/s, 0.5 rad/s, 0.25rad • 1 rad/s, 0.5 m/s, 0.25 m • 0.25 rad/s, 0.5 m/s, 0.25m