Describing Motion

1. PART I The Force-Motion Relationship Describing Motion Describing Motion Photo reprinted from Marey, 1889.

2. X velocity-Time

3. Movement is Motion – Motion is Movement

4. Laboratory Movement

5. Small Movement

6. Systeme Internationale = Metric System Fundamental Units: mass in kg, linear distance in m, angular distance in rad, time in s All other physical measurements are derived from these variables: Force = N = kg*m / s2 Energy = J = kg*m2 / s2 Website for conversions http://catcode.com/trig/trig08.html Review of Math Review

7. Radian – the angle created by the arc on a circle with the length of the radius of the circle (~ 57.3 degrees) More review of Math Review Arc length = 1 radius

8. Trigonometry – sine, cosine, tangent, and inverse functions sin a = A/C, cos a= B/C, tan a= A/B sin-1 A/C = a, cos-1 B/C = a, tan-1 A/B = a Math Review C A a B

9. Sine function – continuous wave over angular position Math Application: important in signal processing +1 0 -1 0 180 360 degrees

10. Math Application: important in signal processing Cosine function – continuous wave over angular position +1 0 -1

11. Math Review Website for sine and cosine waves http://catcode.com/trig/trig08.html

12. Kinematics describes the Time – Geometry of Motion or the Movement Pattern during static or dynamic activity Describing Motion = Kinematics

13. Translation – Linear Movement – displacement from one point to another in either: Straight lines – rectilinear translation or Curved lines – curvilinear translation Animals can do both but curvilinear motion more common Two Fundamental Movement Patterns

14. Curvilinear Translation During Walking

15. Rotation – Angular Movement – displacement around an axis Principle means of animal motion Two Fundamental Movement Patterns

16. Animals translate by skillfully combining joint rotations Translation Through Rotation A person stands up by rotating the hip, knee, and ankle joints Animals rotate to translate Animals are rotating machines

17. Translation Related to Rotation Linear displacement and velocity related to the angular kinematics: s = r v = r Calculate Arc Length when radius = 1 cm and  = 90°

18. Position – location within the environment Displacement – the change in position with movement Velocity – rate of change of position Acceleration – rate of change of velocity (All variables are vectors) Four Kinematic Variables or Motion Descriptors

19. Biomechanics Laboratories

20. Heel Strike: Shoulder=1.01,1.34 Knee = 1.11, 0.47 Toe Off: Shoulder=1.87,1.35 Knee = 1.78, 0.44 Position in a Linear 2D Reference Frame

21. Position in an Angular Reference Frame Segment Angles – Angle between a body segment and the right horizontal from distal end of segment Trunk = 85° or 1.48 rad Arm = 95° or 1.66 rad

22. Position in an Angular Reference Frame Joint Angles – Angle between two body segments Shoulder = 20° or 0.35 rad Knee = ???

23. Generate Angular Position Data 1) Identify location of skeletal joints 2) Define joint angles 3) Calculate segment angles 4) Combine segment angles to calculate joint angles

24. Position in an Angular Reference Frame Acromion 1.10, 1.34 Greater Trochanter 1.05, 0.8 Lateral Knee 1.18, 0.5 Lateral Malleolus 1.23, 0.1 Heel 1.20, 0.02 5th Met 1.35, 0.08

25. Position in an Angular Reference Frame Joint angular position for obese and lean subjects while walking Obese less flexed at hip and knee and less dorsiflexed at ankle Obese walk in a more erect pattern

26. Displacement Displacement = difference between final and initial positions Linear displacement (d) = Pf – Pi (m) Angular displacement () = f - i ( or rad) Displacement does not necessarily equal distance (the length of the path traveled)

27. Horizontal displacement: heel strike to toe off Shoulder = 0.86 m Met Head = 0.09 m Total displ. Shoulder = 1.87,1.35 -1.01,1.34 0.86,0.01 Displacement in a Linear Reference Frame

28. Magnitude Result. Displ. = (Hor disp2 + Vert disp2)1/2 Displacement in a Linear Reference Frame Resultant displacement between heel strike and toe off for: Shoulder = 0.87 m Met head = 0.10 m

29. Linear Displacement During Walking Step length – forward displacement of one foot during swing phase Stride length – combined forward displacement of both feet during left and right swing phases

30. Linear Displacement During Walking Step length – mean value ~ 0.75 m for healthy adults, less for shorter, older, ill, or injured people Left and right step length symmetry Stride length – mean value ~1.5 m for healthy adults, less for shorter, older, ill, or injured people

31. Velocity Velocity = rate of change of position = amount of displacement per unit time “rate of change” = calculus concept of the derivative or slope Linear velocity (v) = (Pf – Pi) / time (m/s) Angular velocity () = (f - i) / time (/s or rad/s)

32. Gross body movement Johnson vs Lewis100m, Seoul 1988 More information with shorter measurement intervals Newsweek, 7-29-96

33. Average vs. Instantaneous Velocity

34. Velocity Velocity = rate of change of position = amount of displacement per unit time “rate of change” = calculus concept of the derivative or slope Linear velocity (v) = (Pf – Pi) / time (m/s) Angular velocity () = (f - i) / time (/s or rad/s) Simple Finite Difference Technique

35. Velocity: displacement / time • vector • magnitude: how fast • direction: specification of “which way” • This is motion

36. Cyclic Movement – Angular Kinematics Positive & negative slopes on position curve have positive and negative phases on the velocity curve

37. Cyclic Movement – Angular Kinematics Increasing + Positive & negative slopes on position curve have positive and negative phases on the velocity curve

38. Cyclic Movement – Angular Kinematics Decreasing + Increasing + Positive & negative slopes on position curve have positive and negative phases on the velocity curve

39. Increasing - Cyclic Movement – Angular Kinematics Decreasing + Increasing + Positive & negative slopes on position curve have positive and negative phases on the velocity curve

40. Increasing - Cyclic Movement – Angular Kinematics Decreasing + Increasing + Decreasing - Positive & negative slopes on position curve have positive and negative phases on the velocity curve

41. Cyclic Movement – Angular Kinematics Positive & negative slopes on position curve have positive and negative phases on the velocity curve

42. Relationship Between Position and Velocity Knee angular position & velocity curves during the stance phase of running

43. Knee Position/Velocity in Walking contact Toe off

44. Knee Position/Velocity in Walking Identify local minima and maxima: velocity = ??

45. Knee Position/Velocity in Walking What is the sign of the velocity between local min & max?

46. Knee Position/Velocity in Walking Identify inflection points : ?

47. Knee Position/Velocity in Walking Identify inflection : local minima & maxima on velocity

48. Knee Position/Velocity in Walking Identify local minima and maxima

49. Knee Position/Velocity in Walking Identify inflection points

50. Second Order Finite Differences • Use Project to demonstrate need.