CHAPTER 10: TERMINOLOGY AND MEASUREMENT IN BIOMECHANICS KINESIOLOGY Scientific Basis of Human Motion, 12th edition Hamilton, Weimar & Luttgens Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Revised by Hamilton & Weimar Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

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 use of trigonometric method for combination & resolution of 2D vectors. 6. Identify scalar & vector quantities represented in a motor skill & describe using vector diagrams.

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.

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.

The Study of Biomechanics Biology Mechanics Anatomy/ Physiology Kinematics Kinetics emg* Motion capture* Force plate/ transducer* Structure Function Statics (zero or constant velocity) Dynamics (acceleration) (ΣF=0) (ΣF≠ 0) * Tools used to collect biomechanics data in laboratories

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.

Kinematics and Kinetics Kinematics: geometry of motion Describes time, displacement, velocity, & acceleration. Motion may be in a straight line or rotating. Kinetics: forces that produce or change motion. Linear – motion in a line. Angular – motion around an axis.

Quantities in Biomechanics: Mathematics is 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.

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

Units of Measurement Length: Metric; all units differ by a multiple of 10. There are 10 millimeters in a centimeter 100 centimeters in a meter 1000 meters in a kilometer US; based on the foot, inches, yards, & miles.

Units of Measurement Mass: quantity of matter a body contains. Weight: product of mass & gravity. Force: the product of mass times 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.

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

VECTOR ANALYSIS Vector Representation Vector is represented by an arrow Length is proportional to magnitude Fig 10.1

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

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

Combination of Vectors Vectors may be combined be addition, subtraction, or multiplication. New vector called the resultant (R ). Vector R can be achieved by different combinations, but is always drawn from the tail of the first vector to the tip of the last. Fig 10.2

Combination of Vectors Fig 10.3

Resolution of Vectors Fig 10.1c Any vector may be broken down into two component vectors acting at a right angles to each other. The arrow in this figure represents the velocity of the shot.

Resultant displacement Resolution of Vectors Fig 10.4 Resultant displacement (R ) X displacement (A) Y displacement (B) What is the vertical displacement (A)? What is the horizontal d displacement (B)? A & B are components of resultant (R)

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

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 P=(13,5) 13 5 x y

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 () 21o 13.93 P x y

Location of Vectors in Space Fig 10.5

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

Trigonometric Resolution of Vectors 9.6m/s x y Any vector may be resolved if trigonometric relationships of a right triangle are employed. A soccer ball is headed with an initial velocity of 9.6 m/s at an angle of 18°. Find: Horizontal velocity (Vx) Vertical velocity (Vy)

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 Fig 10.7 I would rather leave the 2.97 m/s. At this stage I try to teach two place accuracy. They will need it later to avoid rounding errors.

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 Fig 10.7

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 volleyball is served with a vertical velocity of 15 m/s and a horizontal velocity of 26 m/s. What is the velocity of serve & angle of release?

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 Fig 10.8

Trigonometric Combination of Vectors Solution: Velocity = 30 m/s Angle = 30° Fig 10.8

Trigonometric Combination of Vectors Consider the example with Muscle J of 1000 N at 10°, and Muscle K of 800 N at 40°. 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) The slide explaining when to use trigonometric methods is no longer useful, since we have dropped graphic solutions.

Sum the x and y components 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 (horizontal) Sum the x and y components

Summed components Fy = 687.8 N Fx = 1597.6N Find:  and r Fig 10.9

Solution: Fig 10.9

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.