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Chapter 10: Terminology and Measurement in Biomechanics

Chapter 10: Terminology and Measurement in Biomechanics. KINESIOLOGY Scientific Basis of Human Motion, 10 th edition Luttgens & Hamilton Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University. Objectives. 1. Define: Mechanics & Biomechanics

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Chapter 10: Terminology and Measurement in Biomechanics

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  1. Chapter 10:Terminology and Measurement in Biomechanics KINESIOLOGY Scientific Basis of Human Motion, 10th edition Luttgens & Hamilton Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University

  2. Objectives 1. Define: Mechanics & Biomechanics 2. Define: Kinematics, Kinetics, Statics, & Dynamics, and state how each related to biomechanics 3. Convert units of measure; metric & U.S. system 4. Describe scalar & vector quantities, and identify 5. Demonstrate graphic method of the combination & resolution of two-dimensional (2D) vectors 6. Demonstrate use of trigonometric method for combination & resolution of 2D vectors 7. Identify scalar & vector quantities represented in motor skill & describe using vector diagrams

  3. Mechanics • Area of scientific study that answer the questions, in reference to forces and motion • What is happening? • Why is it happening? • To what extent is it happening? • Deals with Force, Matter, Space & Time • All motion subjects to laws and principles of force and motion

  4. Biomechanics • The study of mechanics limited to living thing, especially the human body • An interdisciplinary science based on the fundamentals of physical and life sciences • Concerned with basic laws that effect forces on the state or rest or motion of humans

  5. Statics and Dynamics • Biomechanics includes: statics & dynamics Statics: all force acting on a body are balanced • The Body is in equilibrium Dynamics: deals with unbalanced forces • Causes object to change speed or direction • Excess force in one direction • A turning force • Principles of work, energy, & acceleration are included in the study of dynamics

  6. Kinematics and Kinetics Kinematics: geometry of motion • Describe time, displacement, velocity, & acceleration • Motion may be straight line or rotating Kinetics: forces that produce or change motion • Linear – causes of linear motion • Angular – causes of angular motion

  7. QUANTITIES IN BIOMECHANICSThe Language of Science • Careful measurement & use of mathematics are essential for • Classification of facts • Systematizing of knowledge • Enables us to express relationship quantitatively rather than merely descriptively • Mathematics is needed for quantitative treatment of mechanics

  8. Units of Measurement • Expressed in terms of space, time, and mass U.S. system: current system in the U.S. • Inches, feet, pounds, gallons, second Metric system: currently used in research • Meter, liter, kilogram, newton, second Table 10.1 present some common conversions used in biomechanics

  9. Units of Measurement Length: • Metric; all units differ by a multiple of 10 • US; based on the foot, inches, yards, & miles Area or Volume: • Metric: Area; square centimeters of meters • Volume; cubic centimeter, liter, or meters • US: Area; square inches or feet • Volume; cubic inches or feet, quarts or gallons

  10. Units of Measurement Mass: quantity of matter a body contain Weight: depends on mass & gravity Force: a measure of weight • Metric: newton (N) is the unit of force • US: pound (lb) is the basic unit of force Time: basic unit in both systems in the second

  11. Scalar & Vector Quantities Scalar: single quantities • Described by magnitude • Size or amount • Ex. Velocity of 8 km/hr Vector: double quantities • Described by magnitude and direction • Ex. Velocity of 8 km/hr heading northwest

  12. VECTOR ANALYSISVector Representation • Vector is represented by an arrow • Length is proportional to magnitude Fig 10.1

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

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

  15. Combination of Vectors Fig 10.3

  16. Resolution of Vectors • Any vector may be broken down into two component vectors acting at right angle to each other • Figure represent the velocity the shot was put Fig 10.1c

  17. 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

  18. Location of Vectors in Space • Position of a point (P) can be located using • Rectangular coordinates • Polar coordinates • Horizontal line is the x axis • Vertical line is the y axis • Coordinates for point P are represented by two numbers (13,5) • 1st number of x units • 2nd number of y units

  19. Location of Vectors in Space • Rectangular coordinates for point P are represented by two numbers (13,5) • 1st number of x units • 2nd number of y units • Polar coordinates for point P that describe line R make with x axis (r,) • Distance (r) of point P from origin • Angle ()

  20. Location of Vectors in Space Fig 10.5

  21. Location of Vectors in Space • Degree are measured in a counterclockwise direction Fig 10.6

  22. Graphic Resolution • Quantities may be handled graphically • Consider a jumper who take of with a velocity of 9.6 m/sec at an angle of 180 • Since take-off velocity has both magnitude & direction, the vector may be resolved • Select a linear unit of measurement to represent velocity, 1 cm = 1 m/sec • Draw a line of appropriate length at an angle of 180 to the x axis

  23. Graphic Resolution Given Velocity = 5.5 m/sec Angle = 180 Solution 1 cm = 1 m/sec Horizontal velocity x = 5.2 m/sec Vertical velocity y = 1.7 m/sec Fig 10.7

  24. Combination of Vectors • Resultant vector may be obtained graphically • Construct a parallelogram • Sides are linear representation of two vectors • Mark a point P • Draw two vector lines to scale, with the same angle that exists between the vectors

  25. Combination of Vectors • Construct a parallelogram for the two line drawn • Diagonal is drawn from point P • Represents magnitude & direction of resultant vector R Fig 10.8

  26. Combination of Vectorswith Three or More Vectors • Find the R1 of 2 vectors • Repeat with R1 as one of the vectors Fig 10.9

  27. Another Graphic Method of Combining Vectors • Vectors added head to tail • Muscle J, K pull on bone E-F • Muscle J pulls 1000 N at 100 • Muscle K pulls 800 N at 400 Fig 10.10a

  28. Another Graphic Method of Combining Vectors • 1 cm = 400 N • Place vectors in reference to x,y • Tail of force vector of Muscle K is added to Head of force vector of Muscles J • Draw line R Fig 10.10b

  29. Another Graphic Method of Combining Vectors • Measure line R & convert to N • 4.4 cm = 1760 N • Use a protractor to measure angle • Angle = 23.50 • Not limited to two vectors Fig 10.10b

  30. Trigonometric Resolution and Combination of Vectors • Method has value for portraying the situation • Serious drawbacks, when calculating results • Accuracy is difficult to control • Dependent on drawing and measuring • Procedure is slow and unwieldy • A more accurate & efficient approach uses trigonometry for combining & resolving vectors

  31. Trigonometric Resolution of Vectors • Any vector may be resolved if trigonometry relationships of a right triangle are employed • Same jumper example as used earlier Find: • Horizontal velocity (Vx) • Vertical velocity (Vy) Fig 10.7

  32. Trigonometric Resolution of Vectors Given: R = 9.6 m/sec  = 180 To find Value Vy: sin  = opp = Vy hyp R Vy = sin 180 x 9.6 = .3090 x 9.6 = 3.0 m/sec Fig 10.11

  33. Trigonometric Resolution of Vectors Given: R = 9.6 m/sec  = 180 To find Value Vx: cos  = adj = Vx hyp R Vx = cos 180 x 9.6 = .9511 x 9.6 = 9.1 m/sec Fig 10.11

  34. Trigonometric Combination of Vectors • If two vectors are applied at right angle to each other, the solution should appear reasonable obvious • If a baseball is thrown with a vertical velocity of 15 m/sec and a horizontal velocity of 26 m.sec • What is the velocity of throw & angle of release?

  35. Trigonometric Combination of Vectors Given: Vy = 15 m/sec Vx = 26 m/sec Find: R and  Solution: R2 = Vy2 + Vx2 R2 = 152+ 262 = 901 R = 901 R = 30 m/sec Fig 10.12

  36. Trigonometric Combination of Vectors Solution:  = arctan Vy/Vx  = arctan 15/26  = 300 Velocity = 30 m/sec Angle = 300 Fig 10.12

  37. Trigonometric Combination of Vectors • If more than two vectors are involved • If they are not at right angles to each other • Resultant may be obtained by determined the x and y components for each vector and then summing component to obtain x and y components for the resultant • Let’s consider the example with Muscle J; 1000 N at 100, and Muscle K; 800 N at 400

  38. Muscle J r = (1000N, 100) y = r sin  y = 1000 x .1736 y = 173.6 N (vertical) x = r cos  x = 1000 x .9848 x = 984.8 N (Horizontal) Fig on page 10-14 Or 309 in book

  39. Muscle K r = (800N, 400) y = r sin  y = 800 x .6428 y = 514.2 N (vertical) x = r cos  x = 800 x ..7660 x = 612.8 N (Horizontal) Fig on page 10-14 Or 309 in book Sum the x and y Components

  40. Trigonometric Combination of Vectors Given: y = 687.8 N x = 1597.6 Find:  and r Fig 10.13

  41. Trigonometric Combination of Vectors Solution: • = arctan y / x • = arcntan 687.8 1597.6 • = .4305 • = 23.30 R = 687.8 / sin 23.30 R = 687.8 / .3955 R = 1739 N Fig 10.13

  42. Value of Vector Analysis • The ability to handle variable of motion and force as vector or scalar quantities should improve one’s understanding of motion and the force causing it • The effect that a muscle’s angle of pull has on the force available for moving a limb is better understood when it is subjected to vector analysis • The same principles may be applied to projectiles

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