Paradigms for Studying Motion of the System PDF

DR. CARLOS A. ESTRADA Motion of the System Paradigms for Studying McLester, J. & St. Pierre, P. Chapter 3: Paradigms for Studying Motion of the System. Applied B...

DR. CARLOS A. ESTRADA Motion of the System Paradigms for Studying McLester, J. & St. Pierre, P. Chapter 3: Paradigms for Studying Motion of the System. Applied Biomechanics: Concepts & Connections (2nd ed). Burlington, MA, J ones & Bartlett Learning, 2020.  2 Qualitative Motion Analysis (1 of 2)  Describes how the body ”looks” upon visual inspection as it performs skills  subjective and usually involves visual observation  Includes the system’s:  Position in space  Position of body parts relative to each other  Position of segments of body parts in relation to each other  3 Qualitative Motion Analysis (2 of 2)  Two general approaches to qualitative analysis:  composite approach:  Alsoknown as the total body approach, views the whole body as a system that progresses through phases as it refines movement patterns  component approach:  Usesthe same phase/stage method (defined as steps), but rather than looking at the body as a global system, it breaks the body down into component sections  4 Composite Approach  Total body approach often referred to as “developmental biomechanics”  Breaks down movement patterns into primary body part  However, the stages of skill progression are based on the product of all body parts in combination.  Each stage identifies important body parts used to perform the skill, and the number of stages can vary depending on the requirements necessary to perform a task.  5 Composite Approach  Figure 3.2: Total body composite approach applied to throwing.  6 Component Approach  Sometimes called “error analysis strategy”  Each primary body component is observed.  Each component has its own evaluative series of stages or phases that can be advanced independently of each other.  E.g. overhand throwing→ broken down into component parts, i.e. trunk, arms, and action of the feet  7 Component Approach Figure 3.3. - Developmental sequence of components of overhand throwing  8 Component Approach  So, performers could show evidence of mature skill performance in one part of the body, while other body segments are at less mature levels.  Qualitative and Quantitative Analyses are complementary toward one another, not competitive  Qualitative most commonly used; helps develop ability to visually analyze motion to rapidly isolate various factors affecting one’s performance.  9 Quantitative Motion Analysis (1 of 3)  Stems from the simple need for a deeper and more  Example applications: specific understanding of why  Enhance performance of elite the system moves the way athletes that it does  PTs and ATs have a need to  Some performers/practitioners quantify severity of injury and/or require more accurate info treatment success. that can only be measured  Biomechanical research—goal quantitatively of understanding human motion, optimizing sport performance, improving equipment design, and/or preventing injury  10 Quantitative Motion Analysis (2 of 3)  Scalar quantity:  A quantity that possesses only a magnitude but has no particular associated direction  For example:  Mass: quantity of matter of which a body is composed; a measure of a body’s inertia  inertia: a body’s resistance to having a state of motion changed by the application of a force  11 Quantitative Motion Analysis (3 of 3)  Vector quantity:  Can only be fully specified with a magnitude of appropriate units and a precise direction  For example:  Weight : a measure of the force with which gravity pulls upon an object’s mass  12 Quantitative Motion Analysis: Vectors Representing Forces  Arrows are used to represent forces in free-body diagrams.  Arrows are appropriate because all forces are vectors.  An arrow possesses certain specific characteristics that allow it to represent a vector quantity and therefore a force.  Forexample: a tip and tail, a length drawn to scale, and an imaginary path along which it would travel  13 Vectors Representing Forces  Direction: the way in which the force is applied  E.g. up, down, forward, backward, north, south, positive, negative  Orientation: alignment or inclination of the vector in relation to cardinal directions where angle (θ) is usually measured counterclockwise from the positive x-axis  E.g. vertical, 45° from horizontal  14 Vectors Representing Forces  Point of application: the point or location at which the system receives the applied force; usually defined by the tail of a vector  E.g. at the toes, 2cm from axis of rotation of elbow  Magnitude: amount or size of the applied force as depicted by drawing the length of the vector to scale  E.g. if scale is 1cm = 10N → 10cm = 100N force  Line of action: imaginary line extending infinitely along the vector through the tip and tail  15 Vectors in Frames of Reference (1 of 2)  We can specifically define the position of an object (the system) in space by establishing one or more frames of reference within a Cartesian coordinate system.  An origin (O) and 2 or 3 orthogonal axes (each passing through the origin and defining one spatial dimension) are used to define the coordinate frame of reference.  16 Vectors in Frames of Reference (2 of 2)  In biomechanics, need to describe single points, segments (represented w/ lines connecting points), and forces (represented by vectors or arrows).  In addition, various mathematical operations with vectors are necessary.  Because of these needs, it is sometimes more convenient and necessary to define a polar coordinate system and locate a point in space using its plane polar coordinates.  17 Polar Coordinate System (1 of 2)  Still has an origin (O) and multiple reference axes (one for each dimension).  The positive x-axis is often used as the reference axis.  Location of a given point is defined by its distance radius; r from the origin and by the angle (θ) between the chosen reference axis and the line formed by connecting the given point to the origin.  18 Polar Coordinate System (2 of 2)  θ is often measured counterclockwise from the positive x-axis.  So, a point with plane polar coordinates (r, θ) = (7.00 m, 55°) is located 7 m away from the origin at an angle of 55° above the reference axis.  19 Basic Trigonometric Functions  trigonometric functions can be used to analyze vectors.  Coordinate transforms are possible with the most basic trigonometric functions: 1. SOHCAHTOA  sin θ = side opposite θ  tan θ = side opposite θ hypotenuse side adjacent to θ  cos θ = side adjacent θ hypotenuse  20 Basic Trigonometric Functions  When the sides of a right angle are known, the _________ of the trigonometric function is used to calculate the angle:  21 Basic Trigonometric Functions The angles in a triangle add up to 180 degrees. Therefore: The remaining angle is 11.3 degrees.  22 Basic Trigonometric Functions  Coordinate transforms are possible with the most basic trigonometric functions: 2. Pythagorean theorem : r2 = x 2 + y 2 Aka A2 + B2 = C2  23 Basic Trigonometric Functions  Coordinate transforms are possible with the most basic trigonometric functions: 3. Trigonometry is based upon simple ratios of the lengths of two sides in a given triangle.  e.g., if θ in the polar coordinates is 55°, then the ratio of y to r is 0.819 (sin 55° = 0.819), i.e. the length of side y is 81.9% the length of side r.  The inverse function can be used to transform the ratio to the angle, i.e. sin-1 0.819 = 55° A surveyor is standing 50 feet from the base of a 24 large tree. The surveyor measures the angle of elevation to the top of the tree as 73.5°. How tall is the tree? tan 73.5° y ? tan 73.5° = 50 73.5° y = 50 (tan 73.5°) 50 y = 50 (3.375943) y = 168.80 feet A person is 200 yards from a river. Rather than walk 25 directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° 200 x (cos 60°) = 200 60° x x X = 400 yards  26 Special Properties of Vectors (1 of 2)  Vector equality:  Associative law of addition:  Two vectors are considered  The sum of three or more equal if they possess the same vectors is independent of magnitude and direction (A the grouping of the vectors = B). for addition. (A + B) + C = A + (B + C)  Commutative law of addition:  Vectorsbeing added must  When vectors are added together, the sum is possess the same units of independent of the order of measure addition (A + B = B + A).  27 Special Properties of Vectors (2 of 2)  Vector subtraction:  Negative of a vector: a vector that when added to the first gives a sum equal to zero (the vectors that have the same magnitude but point in opposite directions). A + (-A) = O  To subtract a vector from another, we add the negative vector to the first A – B = A + (-B)  28 Special Properties of Vectors (2 of 2)  Vector multiplication:  When multiplying (or dividing) a scalar by a vector, the product is a vector quantity e.g., scalar number = - 9, vector = A. The product of scalar x vector = -9A  Multiplying one vector by another results in another vector: A x B = C  Orientation of C is perpendicular to the plane formed by A and B  Because C’s plane is perpendicular to A and B, it is calculated: A x B x (sin θ) = C  29 Graphical Vector Analysis  Can be used to understand:  The multiple effects of one force  The resultant motion of the system that is acted upon by many different forces simultaneously  Resultant is a vector representing the sum of all the forces (vector sum) acting on a system  30 Vector Resolution (1 of 2)  Vector resolution: process by which individual directional component vectors of a single vector are determined  Component vectors: the individual vectors that represent each of the multiple effects that one vector represents  A force is capable of causing an object to have a rise and run, i.e. the applied force can cause a system to travel a given distance both vertically and horizontally  31 Vector Resolution (2 of 2)  A vector is resolved into two components: Y-axis  Horizontal component (parallel to the x-axis)  Vertical component (perpendicular to the x-axis) X-axis  32 Figure 3.17: Vector resolution using the parallelogram method Figure 3.18: Vector resolution using the chain method  33 Vector Composition (1 of 3)  Vector composition:  Two or more vectors are summed to determine a single resultant vector, i.e., a situation where multiple forces act upon a system, and we would like to find the resultant force vector  Resultant: a vector that represents the sum of all forces acting upon a system  Resultant motion of a system that we observe is composed of many individual forces  34 Vector Composition (2 of 3)  Forces may be applied simultaneously or sequentially.  Factors that affect complexity of vector composition:  Number of vectors  Relative directions and orientations of the vectors  Colinear Vectors: vectors having the same line of actions Vector Composition (3 of 3) 35  36 Connections: Functional Anatomy  Muscle groups produce force along multiple lines which converge in one resultant line.  Example: quadriceps, triceps  A single muscle force can have multiple directional effects.  Example: triceps creating rotary motion and stabilization forces at the elbow joint  37 Connections: Injury Science  Differences in Q angle related to gender  Q angle (quadriceps angle) is a rough estimate of femoral and tibial alignment.  Females generally have a larger Q angle due to wider hips (muscle insertion sites).  Larger Q angle deviation is correlated with patellofemoral pain.  38 Connections: Motor Control  Muscle forces control degrees of freedom (DOF).  Activation can create rotation/stabilization  Muscle force production is dependent upon the nervous system recruitment of specific muscles and an almost infinite range of motor units within any muscle.  39 Connections: Motor Development  Muscle forces provide motive forces for progressing though normal maturation.  Voluntary control of muscles results in the ability to move within an environment.  Efficient control of muscle forces allows bipedal locomotion and advanced motor skills.  40 Connections: Motor Learning  Practice and experience refine the recruitment and function of muscles.  Increases in strength  Increases in variety and precision  41 Connections: Pedagogy (1 of 3)  Quantitative and qualitative assessment of fitness and movement inform teaching.  Provide data to monitor student progress in fitness and motor skills.  Provide accountability for quality PE and athletic programs.  42 Connections: Pedagogy (2 of 3)  Quantitative examples:  FitnessGram: Photo Credit: https://apkpure.com/coach-s-eye/com.techsmith.apps.coachseye.free  Collectsdata on five components of physical fitness, i.e. aerobic capacity, muscular strength, muscular endurance, flexibility, and body composition  Coach’s Eye:  Softwarethat can provide specific anatomic information  43 Connections: Pedagogy (3 of 3)  Qualitative examples:  Test of Gross Motor Development (TGMD-3):  Data related to fundamental motor skills  Movement task sheets:  Designed to provide subjective data on fundamental movements and sport skills  44 Connections: Adapted Physical Education  Assessment is crucial to developing required Individualized Education Programs (IEPs).  Many children with disabilities can be assessed using typical PE methods.  Special tools exist for specific populations:  Bruininks-Oseretsky Test of Motor Proficiency  Peabody Developmental Scales