BIOMECHANICS OF SPORT AND EXERCISE
BIOMECHANICS OF SPORT AND EXERCISE EXSS 323
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This 20 page Class Notes was uploaded by Dr. Immanuel Sipes on Monday October 19, 2015. The Class Notes belongs to EXSS 323 at Oregon State University taught by M. Pavol in Fall. Since its upload, it has received 21 views. For similar materials see /class/224463/exss-323-oregon-state-university in EXERCISE AND SPORT SCIENCE at Oregon State University.
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Date Created: 10/19/15
Introduction to Biomechanics Objectives Define basic concepts in biomechanics Provide an overview ofthe sport clinical and occupational applications of biomechanics Subdivisions of Mechanics Kinematics The description of motion as a function of space and time The forces causing the motion are not considered Kinetics The relationship between the forces acting on a system and the motion ofthe system What is Biomechanics Mechanics Study ofthe action of forces on particles and mechanical systems a branch of physics System An object or group of interacting objects Bio Prefix for life or living organism Biomechanics Application of the principles of mechanics to the study of living organisms eg the human body and its parts Branches of Mechanics Statics Deals with systems in a constant state of motion Includes systems that are at rest lie not moving moving with a constant speed and direction Dynamics Deals with systems in which acceleration is present lie where speed or direction is not constant Who Uses Biomechanics PhysEdTeachers Coaches Athletes Personal Trainers Athletic Trainers Physicians Physical Therapists Occupational Therapists Engineers Researchers What is Biomechanics Used For Improving Physical Function eg surgery planning in Cerebral Palsy Musculoskeletal Health eg reducing injurious falls by older adults preventing bone loss in space Product Design eg athletic shoes prosthetics Forensic Biomechanics eg accident investigation What is Biomechanics Used For Improving Sports Performance Better technique amp training Better equipment eg klapskates Sports Injury Prevention Identifying safertechniques Training to reduce risk of injury Developing protective equipment eg knee brace Occupational Injury Prevention Ergonomics eg low back pain hand amp wrist trauma Injury Rehabilitation Identify when safe to return to activity Why Study Biomechanics Biomechanics Has many and wideranging applications within health and sport sciences Is used by professionals throughout health and sport sciences This course will provide a foundation for Understanding the mechanical principles underlying human movement Applying these principles to the analysis of human movement Understanding biomechanics will make you a more competent professional Newton s Laws Objectives Define linear kinetics internal amp external forces Introduce the concept of free body diagrams Understand and apply Newton s three laws of motion Linear Kinetics Kinetics Study of the relationship between the forces acting on a system and the motion ofthe system Linear Motion Translation All parts of an object or system move the same distance in the same direction at the same time Linear Kinetics The kinetics of particles objects or systems undergoing linear motion Questions to Think About Why might a decrease in the ability to control muscle forces impair standing balance When does a hockey player need to apply a net force to a puckthat is sliding across the ice In performing a bench press when do you need to apply the most force to the bar Why does taking too long of a stride during running tend to slow you down In what direction do you need to push on the ground in order to speed up and turn to the left Internal vs External Forces Internal Force applied to a system from within the system External Force applied to a system from outside the system Internal forces not included in mechanical analyses Fexterhal System F Internal F extemal2 F external Free Body Diagram 1st Law Law of inertia Diagram of the external forces and external torques acting on a system A body will maintain a state of rest or constant The first step in solving a problem in kinetics VBIOCW unless aeted Upon by an eXtemal force If there is no net external force acting on a body FWW If the body s center of mass is not moving it will remain motionless If the body s center of mass is in motion it will continue to move at a constant velocity i39e at the same speed in the same direction 2nd Law Law of Acceleration Effects of Force in 1D Net external force amp velocity 2 F m a ln same direction magnitude of velocity increases Opposite directions magnitude of velocity decreases where Z 393 net external force acting on a body Larger net force Igt largerfaster change in velocity m mass of the body 3 linear acceleration of the body center of mass Velocity Force Change in Velocity Increase in dir If there is a net external force acting on a body the acceleration ofthe body s center of mass is Decrease in dir Directly proportional to the net force Increase in dir lnversely proportional to the body s mass In the direction ofthe net force Decrease in dir Effects of Force in 2D A net external force can produce a change in speed lie in magnitude of velocity a change in direction a change in both speed and direction V a lt b h I C anges changes d speed V gt 39 hanges F gt direction changes F V direction 3rd Law Law of Reaction For every action there is an equal and opposite reaction If body 1 applies a force to body 2 then body 1 experiences a reaction force from body 2 Of the same magnitude At the same point In the opposite direction If reaction Analyzing Effects of Force in 2D ln 2D apply Newton s Laws separately in the X and y directions For Newton s 2quotd Law ZZFXmaX 2Fm ltgt Zlemay Note If FX and m are constant then aX is constant Can use laws of constant acceleration to analyze motion in X direction Same concept applies for y direction Example Problem 1 A 60 kg gymnast is hanging in a stationary iron cross position on the rings He pushes on each ring with a downward force of 2943 N and a mediallydirected force of 1071 N Le a force of 3132 N at 20 medial of downward What are the forces acting on the gymnast Will the gymnast remain stationary Example Problem 2 A 50 kg runner is running forward Her heel contacts the ground with her lower limb at 15 short of vertical relative to the ground in the sagittal plane Assume that this contact results in a force of 2 times body weight being directed up her lower limb What is the runners instantaneous linear acceleration just before and just after heel contact What if the lower limb angle had been 30 instead Questions to Think About Basic Concegts in Kinetics Why do boxing gloves help prevent injuries What types of applied forces would cause a muscle strain A herniated disk A blister Why is a hollow tube a good structure for bone Where will a bone tend to break when subjected to a lateral impact Objectives Why might a severe ankle sprain lead to an k Define basic concepts in kinetics including unstable an 3987 inertia mass force weight and stress Define the different types of loading Learn how materials behave under loading How does an overuse injury result from running Subdivisions of Mechanics lnertia amp Mass Inertia Concept relating to the difficulty with which an object s motion is altered Kinematics The description of motion as a function of space and time o The forces causing the motion are not considered Mass The quantity of matter composing an object Kinetics The measure of inertia for linear motion The property giving rise to gravitational attraction Units English slug SI kilogram kg The relationship between the forces acting on a system and the motion of the system Center of Mass Center of Gravity Point representing the average location of the mass of a body Position ofthe Center of Mass changes with changes in body configuration Motion ofthe Center of Mass represents the average motion of the body as a whole Actions of Forces Forces cause acceleration or deformation change in shape Often assumed that forces cause minimal deformation Relationship between net force F mass m and acceleration a of center of mass m 5 Units English pound lb 1 slug1 fts2 SI Newton N 1 kg1 ms2 1 lb 445N Force Mechanical interaction between an object and its surroundings The push or pull of one object on another Force is a vector It has a magnitude a direction a point of application quot3911 point of 5 application quot l 9 Net Force 0 Resultant force derived from the vector addition of two or more forces Reflects the net effect of all ofthe forces acting together 3 F4 E E I2 Concentrated vs Distributed Force Weight Concentrated Force The force due to gravity Le the pull of the Earth A force that is applied at a single point Weighthas magnitude Distributed Force A force that is applied over a distributed area Can be approximated by a concentrated force that has same net effect Where39 m mass g acceleration due to L L gravity 981 msz 322 sz Weight always acts at the center of mass points towards FW E T the center of the Earth ground F ground Example Problem 1 Compre88ion Ten8ion amp Shear Compression pressing or squeezing force directed normal perpendicular to a surface Tension pulling or stretching force directed normal to a su ace A woman has a mass of 50 kg What is her weight Does her weight depend on the position of her body In the International S ace Station orbitin 400 km above the Earth mpg acceleration due 3 gravity is Shear sliding or tearing force directed parallel about 87 ms2 What would the woman s mass be on the space station7 39 ri What would her weight be F Compression Tension Shear Deformations Under Loading Compression tension and shear deform the object under load Compression Tension Shear Example Problem 2 A boxer hits another boxer with a force of 450 N The contact area of the boxing glove is 0025 m2 What is the average stress over the area of contact Without the glove the contact area ofthe boxer s fist is 0005 m2 What would be the average stress over the area of contact if the boxer used his fist instead ofthe glove Stress amp Pressure Stress The force distributed over a given area where o stress 39 F total force applied A area force is applied over Units English pounds per square inch psi 1 lbin2 SI Pascal Pa 1 Wm2 Pressure stress due to a compressive force Bending Asymmetric loading that produces tension on one side of a body compression on the other Compressive and tensile stresses are greatest at the surface l El Crosssection V Torsion Load producing a twisting of a body Creates shearstresses Shear stresses are greatest at the surface Crosssection Tissue Response to Stress Muscle and bone adapt to the stresses applied over time Training loads increase tissue strength Underloading decreases tissue strength Underloan c amp39Atrophys 6 A c A Q quot quot39 H 39 Physrologlc 39 lt0 i i a Loa 3 U 139 l L i is j 7 In ad R J y 0 Stress Deformation Materials behave elastically at small loads Loads above the yield point create permanent plastic deformation Rupture or fracture occurs at the ultimate failure point Yield Point f Ultimate 3 Eastquot f Failu re 9 Region I Plastic point H L I A Region x Slope Stiffness ia Change in length Repetitive vs Acute Loading The stress required to cause a material to fail lie fracture or rupture decreases as number of loading cycles increases I With underloading Stress Causing Failure of Loading Cycles Torgue Objectives Define angular kinetics Define and learn to compute moment arms torque and resultant torques Introduction to resultant joint torques and anatomical torque descriptions Angular Kinetics Kinetics The relationship between the forces acting on a system and the motion of the system Angular Motion Rotation All points in an object or system move in a circle about a single axis of rotation All points move through the same angle in the same time Angular Kinetics The kinetics of particles objects or systems undergoing rotation Questions to Think About What anatomical and physiological factors affect a muscle s functional strength lie ability to control rotation at a joint How can we determine which muscle groups are most active during a movement task Why should a worker keep an object being lifted close to his or her torso in the transverse plane How might an athlete be able to compensate for weakness or fatigue ofthe semimembranosus What are some benefits and drawbacks of agonistantagonist cocontraction at a joint Torque or Moment A force applied through the center of mass will produce linear acceleration A force applied at any other point produces both linear acceleration and angular acceleration Torque Measure of extent to which a force will cause angular acceleration of an object Line of Action The line of action of a force is the imaginary line that extends from the force vector in both directions It s the line that the force pushes or pulls along f line of action of Computing a Moment Arm Determined by Distance d from axis of rotation to point at which force is applied Angle e at which force is applied Use trigonometry to compute moment arm di di d sin e Kw axis of rotation Moment Arm Shortest distance from a force s line of action to the axis of rotation Moment arm is always perpendicular to the line of action and passes through the axis of rotation i line of action ofF Kb moment arr of F x axis of rotation Moment Arm Examples axis of rotation 3 d I a d L d J y df d sin e g F F d 0 i F Td I Fd t Computing Torque Torque has a magnitude a direction or a speci c axis of rotation Magnitude of the torque T produced by a force is the force s magnitude F times its moment arm d1 rotati ggn Units nglish footpounds lb l E S Newtonmeters Nm Example Problem 1 Shown below are 4 muscles acting across a joint Which muscles have the largest and smallest force Moment arm Torque magnitude Direction of a Torque Positive torque Acts counterclockwise about axis of rotation Negative torque Acts clockwise about axis Determine direction using the right hand rulequot Place hand on force vector ngers towards tip Curl ngers around axis of rotat39on Torque acts in direction that ngers are curling T gt 0 T lt 0 9 axis of F F rotation Resultant Torques Resultant or net torque found by adding the torques abo t an axis taking the sign direction of each torque into account Resultant torque has same effect on rotation as the Tnet T1 39 T2 T3 Note In this example T andT3gt0 T7ltU Anen computing39TW Resultant Joint Torque The effects of all forces acting across a joint can be duplicated exacty by the combination of A resultant joint force acting at the joint center A resultant joint torque acting about the axis of rotation through the joint center Resultant joint force The vector sum of all forces acting across a joint Resultantjoint torque The sum ofthe torques about the joint axis due to these forces Note Forces that do not act across the joint eg weight are not included in the resultant joint force or torque Use of Resultant Joint Torque Typically joint contact force muscle forces ligament forces etc cannot be determined individually We can compute resultant joint forces and torques based on data measured external to the body Except near the limits of the anatomical range of motion the main contributors to the resultant joint torque are the muscles The resultant joint torque provides a simplified picture of which muscle groups are most active about a joint Example Fcuntact Tresultant knee joint center Fnams i k Faci gt F Tresultant Fquads dtquads Facl dtacl Fhams dtnarns Muscle Redundancy Multiple combinations of muscle force can create the same resultant joint torque Example For elbow of forearm shown below RJT 05mFbx 125mFbe025m Ft Fcun act Fbl FL 0 0 32 Fame 8 32 464 Fe 16 10 20 El D25 m El D5 m Fm 0 24 4 3 Anatomical Torques Positive amp negative torques depend on the spatial reference frame chosen gt Y gt Fquad Fquad knee knee T gt 0 T lt 0 X X To avoid this joint torques typically described by the joint motion that occurs if the segment moves in the direction of the torque eg Fquad produces a knee extension torque Linear amp Angular Motion Objectives Learn the relationships between linear and angular distance amp velocity for a body in rotation Understand the concepts of and know how to compute tangential and radial acceleration Linear amp Angular Motion The body is structured primarily to perform angular motion Many tasks require the body to produce linear motion either of the body or of an object Walking running Throwing kicking hitting an object The body achieves linear motion through rotation Need to understand how rotation and linear motion are related Questions to Think About What are two factors at the time of release that influence the speed of a softball pitch Why is it easier to hit a home run off an outside pitch than an inside pitch To travel faster at a given cadence should a cyclist use a larger or smaller rear chain ring At what point in her spin does a discus thrower need to release the discus so that it will stay in bounds Why do distance runners typically run in the inside lane of a track but sprinters prefer to run in lanes 4 or 5 Definition of a Radian Radian Angular displacement that results if a point travels around a circle by a distance equal to the radius A A6 1 radian Angular amp Linear Distance The curvilinear distance D traveled by a point on a rotating body is D r A9 D where r radius of rotation distance of point from axis of rotation r A9 change in angle in radians A o D in linear units eg m ft is fr tation r39 Linear amp Angular Velocity The linear velocity V of a point on a rotating body ls tangential to the path of motion in the direction of rotation Has a magnitude of where r radius of rotation w angular velocity in radians 39axis of rotation Example Problem 1 Two distance runners are racing Runner1 is at the inside ofthe first lane Runner 2 is on her shoulder at the inside of the second lane The inside radius of the track is 368 m Each lane is 11 m wi e What distance must each runner travel in going around the turn Finding the Tangential Direction Vpoints in the direction that the point is rotating and is directed i90 from the points angular position If 0 counterclockwise If 0 clockwise ie 0 gt 0 ie 0 lt 0 Example Problem 2 A baseball player swings a bat at 600 s He makes contact with the ball 40 cm from the axis of rotation with the bat angled 110 from the direction the ball is traveling What is the linear velocity of the bat at the point of impact What is the linear velocity at the point of impact if he makes contact at a distance of 80 cm instead Radial amp Tangential Velocity Changes As an object moves along a curved path Can change its speed along the path gtVelocity changes tangential to path of motion Constantly changes V2 direction to follow path gtVelocity changes perpendicular to path towards axis radial AV Avraqial tangentia V1 A change in velocity 39 39 39 AV I requires acceleration in radialI corresponding direction 39 031 axrs Radius of Rotation Distance amp Velocity The greater the radius of rotation r o The greater the curvilinear distance D for a given change in angle A9 The greater the magnitude of linear velocity v for a given angular velocity 03 DrA9 vrm if r1 gt r2 then D1 gt D2 v1 gt v2 Tangential Acceleration Acceleration along the path of motion Produces a change in linear speed aT gt 0 accel in direction along path aT lt 0 accel in direction lfrconstant rm roa aT 2 1 t2t1 a on on in radians2 Radial Acceleration Acceleration towards the axis of rotation Produces a change in direction V If r constant r IwIJ2 r v w in radians 3R Release of a Rotating Object Radial accel must be present for an object to move in a curved path The instant that the forces producing radial acceleration are removed an object becomes projected in the tangential direction v2 Without aR V with ER Linear Acceleration in Angular Motion The total linear acceleration of a body in angular motion is the vector sum of lts tangential acceleration aT along the path acts to change speed lts radial acceleration aR perpendicular to the path acts to change direction 3 3T2 3R2 Example Problem 3 The instant before a thrower releases the hammer the hammer ball is 15 m from the thrower s axis of rotation The cable is angled 80 clockwise from the desired throwing direction The hammer is rotating counterclockwise at 950 s 166 rads It is accelerating counterclockwise at 300 ls2 52 rads2 What is the linear velocity of the hammer ball at the instant before release The magnitude ofthe ball s linear acceleration at that instant What is the linear velocity of the hammer ball at the instant after release
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