Biomechanics Module Notes

Size: px

Start display at page:

Download "Biomechanics Module Notes"

Scarlett Kennedy
5 years ago
Views:

1 Biomechanics Module Notes Biomechanics: the study of mechanics as it relates to the functional and anatomical analysis of biological systems o Study of movements in both qualitative and quantitative Qualitative: non numerical description of a movement based on direct observation. Ex/ a coach s observation of an athletes performance to correct a flaw in the skill Quantitative: numerical result, the movement is analyzed numerically based on measurements from data collected during the performance of the movement. Ex/ physiotherapist have motion analysis tools to allow them to quantify the range of motion of the foot, movements impossible for the naked eye Mechanics: study of physical actions and forces o Statics: study of systems in a constant state of motion (all forces acting on the body are in balance/at equilibrium) o Dynamics: study of systems in motion with acceleration Kinematics: description of motion over time Kinetics: forces associated with body motion Functions of machines in body: 1. Balance multiple forces 2. Enhance forces to reduce amount of force needed to overcome a resistance 3. Enhance Range of Motion and speed of movement to move resistance further or faster than applied forces 4. Alter resulting direction of applied force Types of machines in body: Arrangement of musculoskeletal system provides 3 types: 1. Levers (Most common type) 2. Wheel/axles 3. Pulleys Each of these involves balancing or rotational forces about an axis Levers: A rigid bar that turns about an axis of rotation (fulcrum) Force applied to a lever causes a rotation about the fulcrum to cause movement against resistance o Ex: Bone = lever, joint =axis, muscles apply force Human movement occurs through organized use of levers Anatomical levers (as opposed to mechanical levers) cannot be changed, but can be used more efficiently o We have multiple redundant muscles and flexors that can be used for specific situations Types of levers: Depends on arrangement of axis, force and resistance

2 First class levers: axis placed between force and resistance (at the fulcrum) o Ex: scissors, skull rotating in c1 axis Force Axis Resistance Designed to produce balanced movements when axis is midway between force and resistance When axis is close to force = change in speed and Range of motion When axis is close to resistance = change in force of motion Force occurs at tendon Class of lever can change depending on contact surface Second class levers: resistance is between axis and force o Ex: person pushing another person in a wheelbarrow Axis Resistance Force Produce force movements o Small force can move large resistance (helps with body efficiency) Few that occur in the body Third class levers: force is between axis and resistance o Ex: chopsticks, contraction of arm Axis Force Resistance Designed to produce speed and Range of motion Includes most levers in body o Large amount of force to move small amount of resistance (inefficient) Factors in use of anatomical levers: Torque: moment of force (force magnitude x force arm) Turning effect of eccentric force Eccentric force: force applied in direction not in line with center of rotation of an object with a fixed axis (lengthening) No fixed axis: applied force not in line with object s center of gravity Force (moment) arm: perpendicular distance between location of force applied and axis (must be 90 degree) o Shortest distance from the axis of rotation to line of action o The greater the distance from the moment arm, the greater the amount of torque can be produced by force Ex: opening a door, the further away from the moment arm (hinge) the easier it is to open the door Factors impacting force production (levers): Resistance arm: distance between axis and point of resistance (not perpendicular) Inverse relationship between force and force arm

3 Inverse relationship between resistance and resistance arm Force components and resistance components proportional o Force x Force arm = Resistance x Resistance arm (static) Angle of pull o Rotary component, dislocating component and stabilizing component o One of these three depending on insertion o When line of force (inserting tendon) is perpendicular to the bone it is inserting on (90 degrees), dislocating and stabilizing components = 0, therefore all force is rotary Wheels and axles: Used to enhance range of motion and speed of movement Functions as form of lever o Ex: c1 atlas rotates about the c2 axis If either wheel or axle turns, so must the other (complimentary) Center of wheel and axle = fulcrum Radius of wheel and axle = force (moment) arm Moment arm = radius of wheel/radius of axle (2 nd class) Moment arm = radius of axle/radius of wheel (3 rd class) Pulleys: Single pulleys have a fixed axle and function to change effective direction of force being applied MA = 1 May be moveable and combined to form compound pulleys o Further increases MA Ex: fibularis longus everting the foot Laws of motion and physical activities: Motion cannot occur without force o Muscular systems are the source of force 2 types of motion: 1. Linear (translatory): motion along a line 2. Angular (rotary) rotation about an axis Both types of motion are related Linear Kinematics Kinematics: Branch of dynamics concerned with the description of motion Describing motion in terms of time, distance, velocity, and acceleration Does not deal with the forces causing motion Motions:

4 Linear Motion: (aka Translation) o Occurs when all points on a body or object move the same distance, in the same direction, and at the same time o Involves the study of linear movement through time o Rectilinear: Motion along a straight eg. Figure skating trunk rigid movement same through movement o Curvilinear: Motion along a curved path eg. Sky diving Angular Motion: (aka Rotary Motion) o Occurs when all points on a body of object move in circular move in circular about the same fixed central line or axis eg. Leg lifts hip fixed, & leg moving up and down. Muscles closer move less, than muscles further away General Motion: o Combination of linear and angular motion eg. Cyclist. Combination of linear & angular Linear Kinematics Quantities: Position Distance/displacement Speed/velocity Acceleration Position: Location in space relative to some reference Defined by x, y, z coordinates of a point Distance vs. Displacement: Units: meters (m) Distance Measure of the length of path followed Scalar change in position Measures how far you traveled regardless of direction Displacement Vector change in position magnitude & direction of motion Delta x= x2 x1, Delta y= y2 y1 Question: When will the distance traveled and the displacement be equal? Rectilinear motion When will the distance traveled and the displacement not b\e equal? Angular/non rectilinear motion Speed vs. Velocity Velocity o Rate of change of displacement with respect to time o Vector direction & magnitude of motion o Laws of vector addition tip to tail o Delta v= (x2 x1)/time

5 o Simply: v=d/t o Units meters/sec Speed o Rate of change of distance traveled with respect to time o Scalar o Units: meters/ second Q1: The winner of the men s 100 m at the 2004 Anthems Olympics completed the race in 9.85 s. what was his avg. velocity during this race? V=d/t Average velocity= displacement/time Average velocity= 100 m//9.85 s Average velocity = m/s Q2: A man leaves his house, drive 5 km west at 50 km/h, then drives back east 5 km at 40 km/h. what is his average velocity for the entire trip? 0km/h avg. velocity= total displacement/ total time avg. velocity= 0/ total time= 0 avg. speed= total distance/ total time avg. speed = 10 km/ (0.1 h h ) = 44.4 km First Central Distance Method Frame # s, time (s0, position (m) Vi= [(x i+1 ) (x i 1 )]/[(t i+1 ) (t i 1 )] Acceleration Acceleration: rate of change of velocity with respect to time (speeding up) A= (v2 v1)/time Vector Units; meters/sec/sec or m/ s 2 Q3: Which shot would a hockey goalie have a better chance of blocking a shot from 5 m away at 10 m/s or a shot 10 m away at 40 m/s? Angular Kinematics: Deals with angular motion Ex/ bike wheel Angular Quantities: Angular position Angular displacement Angular velocity Angular acceleration Angular Position: Angular Kinematics

6 Location relative to a defined spatial reference system The orientation of a line with another line or plane Theta = arc length/r = L/R o Theta = angular measurement in radians o L = arc length o R = radius 360 degrees = 2 Pi Radians Radian = 180/3.14 =57.3 degrees Assumption: the two radius are of equal length (forearm shoulder) Angular Displacement: Difference between the initial and final positions of a rotating object Change in absolute angular position experienced by a rotating line The angle formed between the final position and the initial position in radians Delta theta (change in displacement) = final position initial position Ex 1: diving o A diver performs a triple somersault with a full twist. What is the angular displacement around the transverse axis (around the hip)? What is her angular displacement around her longitudinal axis o Answer in revolutions? Degrees? Radians? o 3 rotations about the Transverse axis = 1080 degrees = 6 Pi Radians (18.5) o 1 full twist (revolution) about the longitudinal axis = 360 degrees = 2 Pi Radians (6.28) Ex 2: joint range of motion o The elbow and the knee have ranges of motion of approximately 150 degrees. What is the range of motion expressed in radians? o 150 degrees/57.3 degrees per radian = 2.62 radians How is angular displacement described? o o Positive angular motion or negative angular motion Right hand rule: the direction of the fingers curl indicates the positive angular direction if the right thumb points in the positive linear direction (plane) along the axis of rotation Angular displacement and gait (how someone walks) o Sagittal plane (flexion extension) o Frontal plane (abduction adduction) o Transverse plane (external internal) Angular Velocity: The rate of change of angular displacement Measured in radians per seconds Delta theta/delta time OR (final position initial position)/change in time Ex: RPMs, peak angular velocity of a soccer player s knee: 2400 deg/s = 6.7rev/s Angular Acceleration:

7 The rate of change of angular velocity Change in velocity (V f V i ) /change in time (T f T i ) Measured in radians per second 2 Ex: Runner s thigh o The angular velocity of a runner s thigh changes from 3 rad/s to 2.7 rad/s during a 0.5 s time period. What has been the average angular acceleration of the thigh? o Final velocity Initial velocity / Final time Initial time o (3 rad/s 2.7 rad/s) / 0.5 s o (0.3 rad/s) / (0.5 s) = 0.6 rad/s 2 Linear Kinetics Forces: Force: the push or pull on an object Newton s second law of motion o F = Mass x Acceleration o 1 newton = I kilogram x 1 meter/sec 2 o 1 newton = pounds or 1 pound = N Newton s laws of motion: Law of inertia o Object will remain in state of motion unless affected by external force o An inertia of an object is used to describe its resistance to motion o It is directly related to the mass of the object o The greater the mass, the greater the inertia Law of acceleration o The change of motion is proportional to the force impressed and is made in the direction of the straight line in which that force is impressed o All forces acting on an object, the mass and acceleration of an object

8 Law of action/reaction o To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal and directed to contrary parts o Forces act in pairs not isolation o When two objects interact, the force exerted by object A on object B is counteracted by a force equal and opposite exerted by object B on object A Question o If 2 hockey players collide, with one hockey player weighing 90 kg and exerting a force of 450 N, how much force would be exerted on an 80 kg hockey player? Answer: 450 N cannot assume acceleration of other player, law of action/reaction Types of forces: Internal forces: forces that act within the system of object whose motions is being investigated o Ex: muscles contracting (tensile forces), bone on bone forces (compressive forces) o Muscular forces: tensile forces (internal) Muscle extension o Bone to bone forces: compressive forces (internal) External forces: forces that act on an object as a result of its interaction with the environment o Ex: gravity o o Fluid forces (external)

9 Buoyancy Drag Lift o Contact forces (external) Normal reaction force/ground reaction force Ground under ideal Conditions provides an equal reactionary force when walking conditions provides an equal reactionary force when walking Ex: exerting 100 N into ground with leg, ground should produce 100 N of reactionary forces Friction force Internal forces often used to counteract external forces o Compression of intervertebral discs in spine by vertebrae Weight: The force due to gravity Gravity = 9.8 m/s 2 Weight has a magnitude o W = Mass x Gravity o Therefore o N = Mass x Gravity o N = Kg x M/s 2 Weight always acts on the center of mass and points towards the center of the earth Question: a woman has a mass of 50 kg, what is her weight? o W = mass x Gravity o W = 50 kg x 9.8 m/s 2 o W = N Question 2: what is the woman s mass and weight on the ISS where gravity is 8.7 m/s 2 o Mass is unaffected doesn t change (CONSTANT) o W = 50 Kg x 8.7 m/s 2 o W = 435 N Weight is a measurement of the forces of gravity, Mass is a measurement of weight without the forces of gravity Friction: The force acting over the area of contact between two surfaces in the direction opposite that of the motion Types of friction forces o

10 o Static o Kinetic Angular Kinetics Kinetic Principles: Inertia Impulse Work Power Kinetic Energy F = ma W= mg Inertia and Momentum: Inertia: Any object will resist any change in motion state Momentum (p): mass x velocity Lineman A has a mass of 100 kg and is traveling with a velocity of 4m/s when he collides with lineman B head on, who has a mass of 90 kg and traveling 4.5 m/s. If both players remain on their feet, what will happen? Identity one direction as being positive Calculate Momentum Lineman A: 100kg x 4m/s = 400kg m/s Lineman B: 90kg x 4.5m/s = 405 kg m/s Momentum of the system: P T = P(A) = P(B) = 400kg m/s 405 kg m/s = 5 kg m/s P/M = 5 kg m/s 190 kg = 0.03 m/s Lineman B will push Lineman A backward with a velocity of 0.03 m/s. Impulse: Any change in motion state depends on the applied force and the time over which it is applied Impulse = F x Time Impulse increases with o Increased force magnitude o Increased duration of application

11 Impulse Inertia Relationship: Impulse is equal to the change in momentum F x T = m (v u) o Where F = force o T = time o M = mass o U = initial velocity o V = final velocity A pitched ball with a mass of 1 kg reaches a catchers glove traveling at a velocity of 28 m/s. Q: How much momentum does the ball have? A: 28 kg m/s Q: How much impulse is required to stop the ball? A: 28 kg m/s Q: If the ball is in contact with the catchers glove for 0.5s during the catch, how much average force does the glove apply? A: F = I / T = 28kg m/s / 0.5s = 56 kg m/s 2 = 56 N Work: The amount of work done by the movement system is equal to the force applied and the distance over which it is applied U = F x d Positive work o Results when force and displacement are in the same direction. Indicated that force is acting to speed up the object Negative work o Results when force and displacement are in opposite directions. Indicated that the force is acting to slow down the object. (Friction) Ex: If a bike move displacement d: F pedal does positive work and F brake does negative work. Power: The rate of doing work production Power = work/time Units of Power: o SI: Watt (W) Kinetic Energy:

12 The amount of work done on a body or object is equal to the kinetic energy produced KE = ½. m. v 2 Units of KE = Units of Work (Joule) J = kg. m 2 / s 2 Potential Energy = m. g. h Applications to Biomechanics: Analysis of work can identify inefficient movement patterns or wasted effort Work and power can indicate whether muscles or forces are acting to generate brake motion. Power relationships indicate muscles are better at breaking motion than generating motion Energy relationships allow one to understand the relationships between applied forces, changes in speed, changes in height, and deformation. Possible Question: what is the point of work?

13 Angular Kinetics The causes of angular motion Torque: Force which causes a turning effect Torque = moment of force Torque = moment AKA rotary or angular force Moments: Applying a force at the Center of Gravity will cause linear motion Applying a force away from the Center of Gravity will produce a Torque o Results in Rotary Motion T = F. r o T = Moment o F = Force o R = Moment Arm (Radius) Units = Newton. Meter How much does the box weigh? 50N 1m away from center??? 2m away from center Is torque equal? Yes, the line is flat F 1 x D 1 = F 2 x D 2 F 2 = F 1 x D 1 / D 2 = 50N x 1M / 2 M = 25N Find the biceps force necessary to hold the 100N dumbbell in the static position shown. Force? 0.05 m 0.1 m 0.15 m 25N Force: 100N Torque of the upward motion = Torque of the downward motion Tu = Td

14 F 1 x D 1 + F 2 x D 2 (25 N x 0.15) + (100N x 0.3) Fb = (3.75Nm + 30 Nm) / 0.05m = 675 N Moment Arm: shortest (perpendicular) distance between a forces line of action and an axis of rotation In the body, moment arm of muscle is the perpendicular distance between muscle s line of pull and the joint center

Section 6: 6: Kinematics Kinematics 6-1

Section 6: 6: Kinematics Kinematics 6-1 6-1 Section 6: Kinematics Biomechanics - angular kinematics Same as linear kinematics, but There is one vector along the moment arm. There is one vector perpendicular to the moment arm. MA F RMA F RD F