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James W. DeVocht, DC, PhD

Module 1 Course Introduction and Basic Mechanics (Herzog Chapter 1 – by Herzog) Biomechanics (TECH71613). James W. DeVocht, DC, PhD.

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James W. DeVocht, DC, PhD

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  1. Module 1 CourseIntroduction and Basic Mechanics(Herzog Chapter 1 – by Herzog)Biomechanics (TECH71613) James W. DeVocht, DC, PhD

  2. Primary Text for Course Herzog, 2000 Clinical Biomechanics of Spinal ManipulationSecondary Texts Nordin & Frankel 2001: Basic Biomechanics of the Musculoskeletal System, 3rd EditionLeach, 2004:The Chiropractic Theories: A Textbook of Scientific Research, 4th EditionVarious other sources

  3. Grade based on: 2 exams (midterm & final) 7 quizzes (drop 2) Bonus points – no near misses of a grade Tour Research Center

  4. Nature of Science • Objective • Methodical • Forward looking

  5. Objectives of Science • Understand mechanisms (discover controlling factors) (often have to settle for describing) • Apply mechanisms (or behaviors) in new ways

  6. Limitations of Science • Describing is not understanding (fully) • Naming is not understanding • Limited to what is observable

  7. Basic BiomechanicsHerzog Chapter 1 – Walter Herzog • Focus on concepts – very limited math • Cover first 10 pages except two sections - The Scalar Product (page 3) - The Vector Product (page 4) • Will take portions from the rest of Chapter 1 • Additional terms and concepts are taken mostly from Nordin

  8. Scalars & Vectors Scalars quantities that have only magnitude temperature (degrees centigrade or Fahrenheit) speed (m/sec, ft/sec, km/hour, miles/hour) mass (kg) Vectors - have both magnitude and direction velocity (m/sec, ft/sec, km/hour, miles/hour) acceleration (m/sec/sec, or m/sec2) force, like weight (N, lbs) Herzog pages 1 & 2

  9. Direction of vectors is always given relative to some reference system (coordinate system) y 3 2 1 x 0 1 2 3 4 5 Cartesian Coordinate System – perpendicular (orthogonal) axes - what happens along one axis is independent of the other - usually oriented so that x is horizontal and y is vertical- in order for the length of the vector to represent its magnitude, the appropriate scale must be on the axes Herzog page 1

  10. Unit Vectors: magnitude of 1 in direction of each axis of a Cartesian coordinate system y 3 j 2 i 1 x 0 1 2 3 4 5 Normally used to define any arbitrary vector in terms of components Herzog page 2

  11. Adjustive Thrust (Force, Load) Consider line of drive

  12. Adjustive Thrust – expressed in normal and tangential components tangential component (parallel to the surface) normal component (perpendicular to the surface) Usually the normal and tangential components are measured, then the magnitude of the thrust is determined.

  13. Vector AdditionYields resultant vector when 2 vectors are applied to the same point on a rigid (non-deformable) body A B A + B = ?

  14. Graphic Vector Addition Parallelogram Rule

  15. Scalar Multiplication 3A = ? A 3A

  16. For the case of the normal component being 4N and the tangential component being 3N, a coordinate system can be defined as shown 4N 3N 2N 1N 0 1N 2N 3N 4N 5N 6N In this coordinate system, the thrust would be expressed in component form as T = 3Ni – 4Nj

  17. Determining the Magnitude of a Vector 4N 3N 2N 1N 0 1N 2N 3N 4N 5N 6N Pythagorean Theorem: the square of the hypotenuse is equal to the sum of the squares of the sides

  18. Using the Pythagorean Theoremto determine the magnitude of a vector T2= 32+42 = 9 + 16 = 25T = 5 T 4 3

  19. Components define the orientation and magnitude of a vector – not its location 4 3 2 1 0 1 2 3 4 5 6 Note that these 2 vectors are identical

  20. Vector Addition by Components 4 3 A + B 2 A 1 B -3 -2 -1 0 1 2 3 -2i + 2j + 3i + j = i + 3j A + B = Herzog page 3

  21. Scalar Multiplication(by components) 3 2 3A 1 A 0 1 2 3 4 5 6 7 8 A = 2i + j3A = 3(2i + j)3A = 6i + 3j Herzog page 3

  22. 3D, Right Handed, Cartesian Coordinate System (x, y,z) z x y All 3 axes are perpendicular (or orthogonal) to each other. Use right hand rule to determine direction of positive z.Events along one axis are independent of the others.

  23. Polar Coordinate System (r, q) r q origin reference line Good for describing rotation

  24. Moment (Torque): the tendency of a force to produce rotation about an axis 12 N 0.5 m Moment, M = F x L = 12N x 0.5m = 6Nm where F is the magnitude of the force and L is the length of the moment arm(shortest distance, or the perpendicular distance, from the pivot point to the line of the force)

  25. Sense of a moment If plate pivots at A, sense is clockwise Herzog Fig 1-14 If plate pivots at C, sense is counter clockwise If plate pivots at B, there would be no moment

  26. Center of Gravity For a rigid body, the point at which the sum of torques due to gravity is zero A force applied through the center of gravity tends to cause translation, not rotation

  27. If a body is rigid, can think of its mass as being concentrated at its center of gravity For a person in anatomical position, the cg is a few centimeters in front of the sacrum Panjabi & White p 35

  28. There may be nothing at the center of gravity

  29. The center of gravity may not be at the geometric center

  30. Conditions of Static Equilibrium SF = 0 SM = 0 Herzog p 10

  31. Free Body Diagrams Herzog Fig 1-9 adapted from Herzog Fig 1-11

  32. 20N 10N F What force F is needed to hold in static equilibrium? 1m 2m 1m + SM = 0 (20N)(1m) + F(2m) – (10N)(3m) = 0 20N + F(2) – 30N = 0 2F = 30N – 20N = 10N F = 5N

  33. 20N 10N F If we defined positive moments the other way: 1m 2m 1m + SM = 0 - (20N)(1m) - F(2m) + (10N)(3m) = 0 - 20N - F(2) + 30N = 0 - 2F = - 30N + 20N = - 10N - F = - 5N, so F = 5N

  34. Using Moments to Find Static Muscle Forces Perpendicular distance from pivot point to line of D is 0.031m (0.12m x sin15°) Figures 6.2A & B from Williams & Lissner, 1977

  35. Force Couple Equal but opposite forces offset equally from the center of rotation Tends to cause rotation, not translation

  36. Rotary Cervical Adjustment(example of a force couple)

  37. Newton’s First Law Herzog p 9 A particle will move at a constant velocity unless acted upon Hall Fig 3-1 inertia (the tendency) momentum (p = mv) Panjabi & White p 35, 37

  38. Newton’s Second Law F = ma Force = mass x acceleration Herzog p 10

  39. Newton’s Third Law For every action, there is an equal and opposite reaction (on different objects) Herzog p 10

  40. Recoilless Rifle R R (14 sec):http://www.youtube.com/watch?v=6zD-ZmSZ5vQ

  41. M16 Rifle http://www.youtube.com/watch?v=E0KQ07j0Db4&mode=related&search=

  42. Newton’s Laws of Motion 1. A particle will move at a constant velocity unless acted upon (inertia, momentum) 2. F = ma 3. For every action, there is an equal and opposite reaction (on different objects) Which 2 are not independent? Herzog p 10

  43. Newton’s Laws of Motion Apply to “particles” Apply in an inertial reference frame (IRF) That is, stationary or moving in uniform motion Empirically based Herzog p 9

  44. KinematicsAn analysis of an object or system that describes only motion, not forces • Distance traveled • Speed • Acceleration Herzog p 11

  45. Angular Displacement Angular Velocity (can have different linear velocity with the same angular velocity) Angular Acceleration Best described using polar coordinates

  46. KineticsAn analysis of an object or system that determines the forces involved as well as describing the motion (if any) 10 kg Herzog p 16

  47. If this system of forces is in static equilibrium, could this be drawn to scale?

  48. Work = Force x distance energy Potential energy = Wt x hKinetic energy = ½ mv2 http://video.google.com/videoplay?docid=8959221252413764426&hl=en Power = Work / time 100 N Herzog p 18

  49. Impulse, I = F x Dt with units of N-sec(I = Dp) Herzog p 20

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