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Chapter 10: Terminology and Measurement in Biomechanics

Chapter 10: Terminology and Measurement in Biomechanics. KINESIOLOGY Scientific Basis of Human Motion, 11 th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Revised by Hamilton & Weimar. Objectives.

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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, 11th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Revised by Hamilton & Weimar

  2. Objectives 1. Define mechanics & biomechanics. 2. Define kinematics, kinetics, statics, & dynamics, and state how each relates 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 answers 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 is subject to laws and principles of force and motion.

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

  5. Statics and Dynamics • Biomechanics includes statics & dynamics. Statics: all forces acting on a body are balanced F = 0 - The body is in equilibrium. Dynamics: deals with unbalanced forces F  0 - 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 • Describes 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 relationships 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, kilogram, newton, liter, 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 contains. Weight: product of mass & gravity. Force: a measure of mass and acceleration. • 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. Speed 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 combinations.

  15. Combination of Vectors Fig 10.3

  16. Resolution of Vectors • Any vector may be broken down into two component vectors acting at a right angles to each other. • The arrow in this figure may 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. y x 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.

  19. y P=(13,5) 5 x 13 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

  20. y P 13.93 21o x Location of Vectors in Space • Polar coordinates for point P describes the line R and the angle it makes with the x axis. It is given as: (r,) • Distance (r) of point P from origin • Angle ()

  21. Location of Vectors in Space Fig 10.5

  22. Location of Vectors in Space • Degrees are measured in a counterclockwise direction. Fig 10.6

  23. Graphic Resolution • Quantities may be handled graphically: • Consider a jumper who takes off with a velocity of 9.6 m/s at an angle of 18°. • Since take-off velocity has both magnitude & direction, the vector may be resolved into x & y components. • Select a linear unit of measurement to represent velocity, i.e. 1 cm = 1 m/s. • Draw a line of appropriate length at an angle of 18º to the x axis.

  24. Step 1- Use a protractor to measure 18o up from the positive x-axis. Step 2- Set a reference length. For example: let 1 cm = 1 m/s. Step 3- Draw a line 9.6 cm long, at an angle of 18° from the positive x-axis. Step 4- Drop a line from the tip of the line you just drew, to the x-axis. Step 5- Measure the distance from the origin, along the x-axis to the vertical line you just drew in step 4. This is the x component (9.13cm = 9.13 m/s). • Step 6- Measure the length of the vertical line. This is the y-component (2.97cm = 2.97m/s). y 9.6 m/s 2.97 cm = 2.97 m/s 18° x 9.13 cm = 9.13 m/s Graphic Resolution

  25. Combination of Vectors • Resultant vectors 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.

  26. 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

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

  28. Another Graphic Method of Combining Vectors • Vectors added head to tail. • Muscles J & K pull on bone E-F. • Muscle J pulls 1000 N at 10°. • Muscle K pulls 800 N at 40°. Fig 10.10a

  29. 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

  30. Another Graphic Method of Combining Vectors • Measure line R & convert to N: • 4.4 cm = 1760 N • Use a protractor to measure angle: • Angle = 23.5° • Not limited to two vectors. Fig 10.10b

  31. Graphical 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.

  32. Any vector may be resolved if trigonometric relationships of a right triangle are employed. Same jumper example as used earlier. A jumper leaves the ground with an initial velocity of 9.6 m/s at an angle of 18°. Find: Horizontal velocity (Vx) Vertical velocity (Vy) y 9.6m/s 18o x Trigonometric Resolution of Vectors

  33. Fig 10.11 Trigonometric Resolution of Vectors Given: R = 9.6 m/s  = 18° To find Value Vy: Vy = sin 18° x 9.6m/s = .3090 x 9.6m/s = 2.97 m/s

  34. Fig 10.11 Trigonometric Resolution of Vectors Given: R = 9.6 m/s  = 18° To find Value Vx: Vx = cos 18° x 9.6m/s = .9511 x 9.6m/s = 9.13 m/s

  35. Trigonometric Combination of Vectors • If two vectors are applied at a right angle to each other, the solution process is also straight-forward. • If a baseball is thrown with a vertical velocity of 15 m/s and a horizontal velocity of 26 m/s. • What is the velocity of throw & angle of release?

  36. Fig 10.12 Trigonometric Combination of Vectors Given: Vy = 15 m/s Vx = 26 m/s Find: R and  Solution: R2 = V2y + V2x R2 = (15 m/s)2 + (26 m/s)2 = 901 m2/s2 R = √ 901 m2/s2 R = 30 m/s

  37. Fig 10.12 Trigonometric Combination of Vectors Solution: Velocity = 30 m/s Angle = 30°

  38. 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 determining the x and y components for each vector and then summing component to obtain x and y components for the resultant. • Consider the example with Muscle J of 1000 N at 10°, and Muscle K of 800 N at 40°.

  39. Muscle J R = (1000N, 10°) y = R sin  y = 1000N x .1736 y = 173.6 N (vertical) x = R cos  x = 1000N x .9848 x = 984.8 N (horizontal)

  40. Muscle K R = (800N, 40°) y = R sin  y = 800N x .6428 y = 514.2 N (vertical) x = R cos  x = 800N x .7660 x = 612.8 N (horizontal) Sum the x and y components

  41. Fig 10.13 Trigonometric Combination of Vectors Given: Fy = 687.8 N Fx = 1597.6N Find:  and r

  42. Fig 10.13 Trigonometric Combination of Vectors Solution:

  43. Value of Vector Analysis • The ability to understand and manipulate the variables of motion (both vector and scalar quantities) will improve one’s understanding of motion and the forces 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 resolution. • The same principles may be applied to any motion such as projectiles.

  44. Chapter 10:Terminology and Measurement in Biomechanics

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