Movement Forces

1. MovementForces MovementForces Figure reprinted from Marey, 1889.

2. Objectives • Review Newton’s laws of motion, and extend to angular motion. • Expand on the technique of the free body diagram • Define torque as a rotary force • Describe the forces due to body mass • Explain the forces exerted by the surroundings • To quantify the concept of momentum • To characterize the relation between work and energy

3. Ia. Law of Linear Inertia – An object will remain stationary or move with constant velocity until an unbalanced external force is applied to it “Constant velocity” – implies straight line (direction) Inertia – resistance Inertia quantified by mass (kg) Newton’s Laws of Motion

4. The Elevator Test: stand in elevator with knees flexed about 20 and press the UP button. Press the UP button - What happens? Perceiving the Law of Inertia

5. The Elevator Test: stand in elevator with knees flexed about 20 and press the UP button. Press the UP button - Why do your legs flex? Perceiving the Law of Inertia Upward force from elevator

6. The Seat Belt Test: what happens when you press on the brakes as you are driving or if you JAM on the brakes? Perceiving the Law of Inertia Trunk accelerates forward relative to thighs and car. The more you JAM on the breaks, the greater the acceleration. Rearward force applied to seat from wheels through chassis

7. 1. Inertia DOES NOT EQUAL Momentum (mv) i.e. kg is not kg m / s The downhill skier has inertia (which is constant) but it’s his/her momentum that is important 2. Inertia DOES NOT EQUAL weight (mg) i.e. kg is not kg*g Weight is a force vector, inertia is a scalar variable Law of Inertia – Linear Kinetics

8. Inertial forces – motion-dependent forces (but really acceleration-dependent forces) Forces causing acceleration of an object: F = ma TWO MOST IMPORTANT PROBLEMS: GROCERY BAG PHENOMENON and WALKING WITH A FULL CUP OF COFFEE Secondary problem: Back injuries during lifting Law of Inertia and Inertial Forces

9. Inertial Forces important in lifting Effective force: F = ma F = mg + mavert if avert = 0, F = mg Law of Inertia and Inertial Forces

10. Inertial Forces important in lifting Effective force: F = ma F = mg + mavert if avert = 0, F = mg Law of Inertia and Inertial Forces This is a squat from an standing position. When does the descent phase change to the ascent phase?

11. Inertial Forces important in lifting Effective force: F = ma F = mg + mavert if avert = 0, F = mg Law of Inertia and Inertial Forces

12. Inertial Forces important in lifting Effective force: F = ma F = mg + mavert if avert = 0, F = mg Law of Inertia and Inertial Forces

13. Inertial Forces important in locomotion (weight ~ 870N) Ground Reaction Force & Inertia

14. Free Body Diagram of the Foot in Locomotion (no torques indicated) ∑F = m a V GRF + A JRF + mg = ma A JRF = ma - V GRF - mg Law of Inertia and Inertial Forces Ankle JRF Foot mg Vertical GRF

15. Vertical joint reaction forces in walking and running (weight = 780 N) Note decrease in magnitude as move proximal on the leg. Law of Inertia and Inertial Forces

16. Vertical Joint reaction forces and inertial components in running (weight = 950 N) Foot inconsequential but trunk is significant Law of Inertia and Inertial Forces

17. This is GRFvertical 1. What type of jump? Inertial Forces in Jumping(like lifting) BW

18. Where is max knee flexion? • 2. Where is peak Velocity Vert? Inertial Forces in Jumping(like lifting) BW

19. Ib. Law of Angular Inertia – An object will remain stationary or rotate with constant angular velocity until an unbalanced external torque is applied to it Rotational Inertia – resistance Rotational Inertia = Moment of Inertia = I = mr2 Long, massive objects are hard to rotate – Tight rope walker phenomenon Newton’s Laws of Motion

20. Most important application of Moment of Inertia: Moment of Inertia for individual body segments – the amount of resistance to a change in rotation within each segment. Affects the rotational motion caused by muscle torques. Larger people – more mass and longer segments – have larger segment I values (7’ Basketballers) Moment of Inertia

21. Numerous techniques to calculate Segmental I values We use Segmental mass as % Body mass from Dempster (1955) and Hanavan model (1964) to predict location of segment center of mass (~43% of total length from proximal end) and segment I values Segmental Moment of Inertia

22. Dempster’s Data: standard set of anthropometric data including segment masses, location of segment center of mass, segment moments of inertia We use only segment mass as % body mass: Thigh = 10% Leg = 4.7% Foot = 1.5% Segmental Moment of Inertia

23. Hanavan model – models segments as frustrums of cones (cones with tips cut off) Segmental Moment of Inertia

24. Table 2.1 Regression Equations Estimating Body Segment Weights and Locations of the Center of Mass Proximal end Segment Weight (N) CM location (%) of segment Head 0.032 Fw + 18.70 66.3 Vertex Trunk 0.532 Fw – 6.93 52.2 C1 Upper arm 0.022 Fw + 4.76 50.7 Shoulder joint Forearm 0.013 Fw + 2.41 41.7 Elbow joint Hand 0.005 Fw + 0.75 51.5 Wrist joint Thigh 0.127 Fw – 14.82 39.8 Hip joint Shank 0.044 Fw – 1.75 41.3 Knee joint Foot 0.009 Fw + 2.48 40.0 Heel Note. Body segment weights are estimated from total-body weight (Fw), and the segmental center-of-mass (CM) locations are expressed as a percentage of segment length as measured from the proximal end of the segment.

25. Table 2.5 Segment Length, Mass, and Center-of-Mass (CM) Location for Young Adult Women (W) and Men (M) Length (cm) Mass (%) CM Location (%) Segment W M W M W M Head 20.02 20.33 6.68 6.94 58.94 59.76 Trunk 52.93 53.19 42.57 43.46 41.51 44.86 Upper torso 14.25 17.07 15.45 15.96 20.77 29.99 Middle torso 20.53 21.55 14.65 16.33 45.12 45.02 Lower torso 18.15 14.57 12.47 11.17 49.20 61.15 Upper arm 27.51 28.17 2.55 2.71 57.54 57.72 Forearm 26.43 26.89 1.38 1.62 45.59 45.74 Hand 7.80 8.62 0.56 0.61 74.74 79.00 Thigh 36.85 42.22 14.78 14.16 36.12 40.95 Shank 42.23 43.40 4.81 4.33 44.16 44.59 Foot 22.83 25.81 1.29 1.37 40.14 44.15

26. Table 2.6 Segmental Moments of Inertia (kg•m2) for Young Adult Women (W) and Men (M) About the Somersault, Cartwheel, and Twist Axes (Frontal, Sagittal, Vertical) Somersault Cartwheel Twist Segment W M W M W M Head 0.0213 0.0296 0.0180 0.0266 0.0167 0.0204 Trunk 0.8484 1.0809 0.9409 1.2302 0.2159 0.3275 Upper torso 0.0489 0.0700 0.1080 0.1740 0.1001 0.1475 Middle torso 0.0479 0.0812 0.0717 0.1286 0.0658 0.1212 Lower torso 0.0411 0.0525 0.0477 0.0654 0.0501 0.0596 Upper arm 0.0081 0.0114 0.0092 0.0128 0.0026 0.0039 Forearm 0.0039 0.0060 0.0040 0.0065 0.0005 0.0022 Hand 0.0004 0.0009 0.0006 0.0013 0.0002 0.0005 Thigh 0.1646 0.1995 0.1692 0.1995 0.0326 0.0409 Shank 0.0397 0.0369 0.0409 0.0387 0.0048 0.0063 Foot 0.0032 0.0040 0.0037 0.0044 0.0008 0.0010

27. Free Body Diagram of the Foot in Locomotion ∑F = m a V GRF + A JRF + mg = ma A JRF = ma - V GRF - mg Law of Inertia and Inertial Forces Ankle JRF Foot mg Vertical GRF

28. T = I  ( is angular acceleration of body) Torque around foot segment in running composed of ankle muscle torque, GRF torque, inertial torque Rotational Inertial Torques

29. Knee angular position and Hip & Knee Torques in Swing phase of Running Inertial torque (hip on thigh) and applied torque (knee muscles on shank) Rotational Inertial Torques Note: hip torque opposite to knee torque. Hip initially flexor to accelerate thigh forward. What does this do to shank? Note direction of Knee Torque. What role? What type of muscle activity? Same in latter half of swing phase. + Torque = flexion - Torque = Extension

30. IIIa. Law of Linear Reaction – When one object applies a force on a second object, the second object applies an equal and opposite force onto the first object “equal and opposite” – equal magnitude and opposite direction Basis for force platform measurements Newton’s Laws of Motion

31. Platform measures the reaction forces and torques to the forces and torques applied by the person Forces – reactions to human forces – 3 dimensional Torques – torques or “free moments” around the center of plate (My, Mx) or around the center of pressure (Mz) - My, Mx used only to help identify the position of the center of pressure (no biological information) Force Platforms and the Law of Reaction

32. Force Plate in Balance and Falling

33. Vertical force (Fz and Mz) Force Platforms Conventions Anteroposterior force (Fx and Mx) Walking direction Mediolateral force (Fy and My)

34. Must Calibrate voltage to force and torque: Sensitivity matrices from manufacturer (theoretical) and Applied known forces (experimental) Force Platform Calibration

35. 1. take values from main diagonal of sensitivity matrix (english) units are ((microvolts/volt) / lb ) or ((microvolts / volt) / ft-lb) 2. multiply sensitivity values by 4000 (amplifier gain) 3. multiply result by 10 (excitation voltage) 4. resultant product in units of microvolt/lb or microvolt/ft-lb 5. convert to SI system and N/Volt or Nm/Volt by: N/V = ((microvolt / lb) / (1 lb) * (1 lb) / (4.448 N) * (1 volt / 1000000 microvolt))-1 Nm/V = ((microvolt / ft-lb) / (1 ft-lb) * (1 ft-lb) / (0.3048 m * 4.448 N) * (1 volt / 1000000 microvolts))-1 Sensitivity Matrices

36. Sensitivity Matrices • Small Platform (N/v or Nm/v) • Fz=285.8612 Mz=14.68534 • Fy=72.77487 My=30.78452 • Fx= 72.67974 Mx= 30.81251

37. Calibrate vertical force with known weights – straight line is desired result Must reach force values typically measured Empirical Calibration for Voltage to Force

38. Center of Pressure A single point at which the applied GRF will produce the same linear and angular effects on the object Force is really applied under the entire object, CoP allows for pin-point application of the force vector needed for inverse dynamic analysis

39. Center of Pressure in Running CoP from Cavanagh, 1980

40. Center of Pressure in Walking

41. Accuracy of Center of Pressure Med Lat CoP – known distance from plate center to point under the foot Ant Post

42. Error in Center of Pressure Errors of 1 cm cause about 10% error in joint torques

43. Calculate Center of Pressure CoP – known distance from plate center to point under the foot Digitize the foot and the plate edge Calculate location of plate center from edge (e.g. large plate is 0.305 m edge to center) Calculate location of CoP under foot

44. Calculate Center of Pressure Fz Fx dz = .02 m CoP calculation – results are the distance between the exact center of plate and the CoP location My My = Fz(dx) + Fx(dz) dx = (My – Fx(dz)) / Fz dx – distance from center of plate

45. Center of Pressure in Locomotion Data for walking (solid), stair ascent (dash), stair descent (dots)

46. Center of Pressure vs. Center of Mass

47. IIIb. Law of Angular Reaction – When one object applies a torque on a second object, the second object applies an equal and opposite torque onto the first object “equal and opposite” – equal magnitude and opposite direction Evident in joint or muscle torques Newton’s Laws of Motion

48. Spring system has equal and opposite torques on levers which would rotate in opposite directions Equivalent to skeletal joint with muscle torque Law of Angular Reaction Why does only forearm rotate then in biceps curl?

49. Law of Angular Reaction – Inverse Dynamics & Muscle Torques

50. IIa. Law of Linear Acceleration – a force will accelerate an object in the direction of the force, at a rate inversely proportional to the mass of the object F = m a The basis for all biomechanics – forces cause motion Force – a pushing or pulling effect on an object Compression vs. tension vs. shear Newton’s Laws of Motion