2. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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 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

3. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

4. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

5. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

6. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

7. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

8. © 2008 McGraw-Hill Higher Education. All Rights Reserved. QUANTITIES IN BIOMECHANICS The 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.

9. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

10. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

11. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

12. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

13. © 2008 McGraw-Hill Higher Education. All Rights Reserved. VECTOR ANALYSIS Vector Representation Vector is represented by an arrow Length is proportional to magnitude Fig 10.1

14. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Vector Quantities Equal if magnitude & direction are equal. Which of these vectors are equal? A. B. C. D. E. F.

15. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

16. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Combination of Vectors Fig 10.3

17. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

18. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

19. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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. x y

20. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Location of Vectors in Space Rectangular coordinates for point P are represented by two numbers (13,5). –1 st - number of x units –2 nd - number of y units P=(13,5) 13 5 x y

21. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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 (  ) x y 13.93 21 o P

22. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Location of Vectors in Space Fig 10.5

23. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Location of Vectors in Space Degrees are measured in a counterclockwise direction. Fig 10.6

24. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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 18 º to the x axis.

25. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Graphic Resolution Step 1- Use a protractor to measure 18 o 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). 18° 9.6 m/s x y 9.13 cm = 9.13 m/s 2.97 cm = 2.97 m/s

26. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

27. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

28. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Combination of Vectors with Three or More Vectors Find the R1 of 2 vectors. Repeat with R1 as one of the vectors. Fig 10.9

29. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

30. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

31. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

32. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

33. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Trigonometric Resolution of Vectors 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 (V x ) Vertical velocity (V y ) 18 o 9.6m/s x y

34. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Trigonometric Resolution of Vectors Given: R = 9.6 m/s  = 18 ° To find Value V y : V y = sin 18 ° x 9.6m/s =.3090 x 9.6m/s = 2.97 m/s Fig 10.11

35. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Trigonometric Resolution of Vectors Given: R = 9.6 m/s  = 18 ° To find Value V x : V x = cos 18 ° x 9.6m/s =.9511 x 9.6m/s = 9.13 m/s Fig 10.11

36. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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?

37. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Trigonometric Combination of Vectors Given: V y = 15 m/s V x = 26 m/s Find: R and  Solution: R 2 = V 2 y + V 2 x R 2 = (15 m/s) 2 + (26 m/s) 2 = 901 m 2 /s 2 R = √ 901 m 2 /s 2 R = 30 m/s Fig 10.12

38. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Trigonometric Combination of Vectors Solution: Velocity = 30 m/s Angle = 30 ° Fig 10.12

39. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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 °.

40. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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)

41. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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

42. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Trigonometric Combination of Vectors Given:  Fy = 687.8 N  Fx = 1597.6N Find:  and r Fig 10.13

43. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Trigonometric Combination of Vectors Solution: Fig 10.13

44. © 2008 McGraw-Hill Higher Education. All Rights Reserved. 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.

45. © 2008 McGraw-Hill Higher Education. All Rights Reserved. Chapter 10: Terminology and Measurement in Biomechanics