Biomechanics Guest Lecture - Kinesiology

1. Biomechanics Guest Lecture - Kinesiology Sean Collins

2. Why biomechanics? • How does biomechanics fit into kinesiology? • What is the difference between biomechanics and kinesiology? • How do biomechanics, kinesiology and exercise physiology complement one another?

3. Mechanics All motion is subject to laws and principles of force and motion F = ma Fundamental quantities: Mass (m), Length (l), Time (t) (also consider electric charge & temperature) Force = m (l x t-2) Why study mechanics?

4. Biomechanics The study of mechanics applied to living things Statics: all force acting on a body are balanced • Equilibrium (F1=F2) Dynamics: deals with unbalanced forces • (F1 ≠ F2) -> Δ acceleration

5. Kinematics and Kinetics Kinematics: geometry of motion • Describe time, displacement, velocity, & acceleration • Linear -motion in straight line; Angular - rotating Kinetics: forces that produce or change motion • Linear – causes of linear motion; Angular – causes of angular motion

6. Laws of Motion The Law of Inertia: Acceleration requires Force Law of Acceleration: • From: F = ma • Derive: a = F/m Equal and opposite: F = -F (equal, opposite, collinear)

7. Angular Displacement • The skeleton is a system of levers that rotate about fixed points when force is applied. • Particles near axis have displacement less than those farther away. • Degrees: • Used most frequently in measuring angular displacement.

8. Angular Velocity • C traveled farther than A or B • C moved a greater linear velocity than A or B • All three have the same angular velocity, but linear velocity of the circular motion is proportional to the length of the lever

9. Analytical Tool: Vector analysis • In biomechanics - Vector’s typically represent a Force and depicts its magnitude, direction, and point of application (note – can present quantities derived from Force (i.e. velocity) • Most simply represented as an arrow • Length is proportional to magnitude • Direction determined by its direction • Point of application considered conceptually

10. Scalar vs Vector Quantities Scalar: magnitude alone • Described by magnitude (Size or amount) • Ex. Speed of 8 km/hr Vector: magnitude and direction (minimally) • Described by magnitude and direction • Ex. Velocity of 8 km/hr heading northwest

11. Vector Quantities • Equal if magnitude & direction are equal • Which of these vectors are equal? A. B. C. D. E. F.

12. Combination of Vectors • Vectors may be combined: • addition, subtraction, or multiplication • New vector called the resultant (R) Fig 10.2 Vector R can be achieved by different combination

13. Combination of Vectors Fig 10.3

14. What is an example of combining vectors in biomechanics? • Every movement you observe is caused by resultant muscle force vectors – so what of “abnormal” movements?

15. Resolution of Vectors • Any vector may be broken down into component vectors in a coordinate system (i.e. Cartesian coordinate system) • Components are at right angles to one another • Coordinate system can be local or global • 2 vector components – 2 d planes • 3 vector components – 3 d space

16. Resolution of Vectors • What is the vertical velocity (A)? • What is the horizontal velocity (B)? • A & B are components of resultant (R) Fig 10.4

17. Location of Vectors in Space For 2 d (2 vector) planar analysis: • Horizontal line is the x axis • Vertical line is the y axis • Coordinates for a point are represented by two numbers (x,y) (13,5)

18. From Vectors to Movement • Vectors represent muscle force • Muscle forces act on bony lever systems and create Torque (also called Moments) • Torque is an angular (rotary) force and results in angular movement • Human movement is the sum of all Torques acting at all joints

19. Force Vectors • Force is a vector quantity • Magnitude • Direction • Point of Application • For a weight lifter to lift a 250 N barbell • Lifter must apply a force greater than 250 N, in an upward direction, through the center of gravity of the barbell

20. Point of Application • Point at which force is applied to an object • Where gravity is concerned, this point is always through the center of gravity • For muscular force, that point is assumed to be the muscle’s attachment to a bony lever • Technically, it is the point of intersection of • line of force and • mechanical axis of the bone

21. Direction of a force is along its action line Direction of muscular force vector is the direction of line of pull of the muscle Direction of gravity is vertically downward Gravity is a downward-directed vector starting at the center of gravity of the object Direction

22. Direction of Muscular Force Vector • Muscle angle of pull: the angle between the line of pull and the portion of mechanical axis between the point of application and the joint Fig 12.1

23. Angle of Pull • Force may be resolved into a vertical and a horizontal component • Size of each depends on angle of pull • A muscle’s angle of pull changes with every degree of joint motion • So do the horizontal & vertical components • The larger the angle (00 - 900), the greater the vertical and less the horizontal components

24. As seen here, the patella creates a larger moment arm (the perpendicular distance from the line of action to the axis of the joint) The patella allows this joint to favor rotary/angular/ movement force. Without it the force from the quads would be redirected towards the joint. Angle of Pull

25. Angle of Pull • Vertical component is perpendicular to the lever, and is called the rotary component (aka angular force or movement force) • Horizontal component is parallel to the lever, and is called the nonrotary component (aka stabilizing force) • Most resting muscles have an angle of pull < 900

26. Rotary vs. Nonrotary Components Angle of pull < 900 • As the angle of pull gets smaller, the moment arm decreases. • Nonrotary force is directed toward fulcrum • Stabilizing effect • Helps maintain integrity of the joint • Almost all of the force generated is directed back to the joint, pulling the bones together Fig 12.1a

27. Rotary vs. Nonrotary Components Angle of pull > 900 • Nonrotary force is directed away fulcrum • Dislocating component • It is called a dislocating force because the force generated is directed away from the joint • Muscle is at limit of shortening range and does not exert much force (Reminder: active insuficiency) Fig 12.1c

28. Rotary vs. Nonrotary Components Angle of pull = 900 • Force is all rotary/angular force • The moment arm is at its greatest length Angle of pull = 450 • Rotary & nonrotary components are equal Muscular force functions: • Movement • Stabilization

29. Drawing Vectors 1. Note the Axis of the Joint 2. Draw the Horizontal component - Parallel to Lever - Start at muscle intertions * 90˚ all rotary (movement force) * > 90˚ Distracting (force generated away form joint) * < 90˚ Compressive (force generated towards joint) 3. Draw Vertical Component - Perpendicular - Start at muscle insertions 4. Draw vectors ONLY long enough to make a perpendicular angle to the resultant vector.

30. Torque or Moment • The turning effect of an rotary force • Equals the product of the force magnitude and the length of the moment arm • Moment arm (later will divide the moment arm into the “effort” and “resistance” arm in certain situations) is the perpendicular distance form the line of force to the axis of rotation • Torque be modified by changing either force or moment arm Fig 13.2

31. Length of Moment Arm • Perpendicular distance from the direction of force to the axis of rotation • At 450 moment arm is no longer the length of the forearm • Can be calculated using trigonometry Fig 13.3

32. Length of Moment Arm • In the body, weight of a segment cannot be altered instantaneously • Therefore, torque of a segment due to gravitational force can be changed only by changing the length of the moment arm d Fig 13.4 W d W

33. Gluteus Medius

34. Hamstrings

35. Summation of Torques Movement is equal to the sum of Torques and Forces Forces that result in balanced torque do not produce rotary motion (i.e. a balanced scale); but the forces are summed and can produce linear motion (i.e. a canoe) Forces that result in an imbalance of Torque produce rotary motion (i.e. elbow flexion) Objects undergoing Rotary motion may exert Force that produces Linear motion (i.e. push up)

36. Principle of Torques • Resultant torques of a force system must be equal to the sum of the torques of the individual forces of the system about the same point • Must consider both magnitude and direction • In Biomechanics - Torques can be named by the movement • Biceps brachii creates an elbow flexion torque; Hamstrings create a knee flexion torque • When you know the movement a muscle creates as an agonist, you know the Torque its Force vector tends to create at that joint

37. Force Couple • The effect of parallel forces acting in opposite direction Fig 13.6 & 13.7

38. THE LEVER • A rigid bar that can rotate about a fixed point when a force is applied to overcome a resistance • They are used to; • overcome a resistance larger than the magnitude of the effort applied • increase the speed and range of motion through which a resistance can be moved

39. External Levers • Using a small force to overcome a large resistance • Ex. a crowbar • Using a large ROM to overcome a small resistance • Ex. Hitting a golf ball • Used to balance a force and a load • Ex. a seesaw

40. Anatomical Levers • Nearly every bone is a lever • The joint is the fulcrum • Contracting muscles are the force • Do not necessarily resemble bars • Ex. skull, scapula, vertebrae • The resistance point may be difficult to identify • May be difficult to determine resistance • weight, antagonistic muscles & fasciae

41. Lever Arms • Portion of lever between fulcrum & force points Effort arm (EA): • Perpendicular distance between fulcrum & line of force of effort Resistance arm (RA): • Perpendicular distance between fulcrum & line of resistance force

42. Classification of Levers Three points on the lever have been identified 1. Fulcrum 2. Effort point 3. Resistance point • There are three possible arrangements of these point • That arrangement is the basis for the classification of levers (based on mechanical advantage due to the moment arm of the effort or the resistance).

43. R E A First-Class Levers Fig 13.12 E = Effort A = Axis or fulcrum R = Resistance or weight

44. R A E Second-Class Levers Fig 13.13 E = Effort A = Axis or fulcrum R = Resistance or weight

45. R A E Third-Class Levers Fig 13.14 E = Effort A = Axis or fulcrum R = Resistance or weight

46. The Principle of Levers Any lever will balance when the product of the effort and the effort arm equals the product of the resistance and the resistance arm (Note this is a balanced torque system since E x EA = Torque E; R x RA = Torque R E x EA = R x RA -> no rotation Fig 13.16

47. Relation of Speed to Range in Movements of Levers • In angular movements, speed and range are interdependent • Note – this is the same concept as discussed for angular displacement and angular velocity

48. Selection of Levers • Skill in motor performance depends on the effective selection and use of levers, both internal and external Fig 13.19

49. Selection of Levers • It is not always desirable to choose the longest lever arm • Short levers enhance angular velocity, while sacrificing linear speed and range of motion • Strength (Force) needed to maintain angular velocity increases as the lever lengthens

50. Mechanical Advantage of Levers • Ability to magnify force • The “output” relative to its “input” • Ratio of resistance overcome to effort applied MA = R / E *MA = Mechanical Advantage • Since the balanced lever equation is, R / E = EA / RA • Then MA = EA / RA (Greater #, greater MA) • Used for comparisons – which of two or more possibilities gives the greatest MA? (Example – squat bar position)