Exam 1 Notes.docx

Biomechanics Exam 1 Study Guide =============================== Lecture 1 -- Intro to Biomechanics ---------------------------------- - Two types of biomechanical analysis Qualitative analysis Non-numeric evaluation of motion based on direct observation ----------------------- ----------...

Biomechanics Exam 1 Study Guide =============================== Lecture 1 -- Intro to Biomechanics ---------------------------------- - Two types of biomechanical analysis Qualitative analysis Non-numeric evaluation of motion based on direct observation ----------------------- ----------------------------------------------------------------------------- Quantitative analysis Numeric evaluation of motion based on data collected during the performance - Biomechanical research studies and/or quantifies... - Movement of different body segments & factors that influence movement - Deformation of biological structures & factors that influence deformity - Biological effects of locally acting forces on living tissues; effects such as growth and development or overload and injuries - The muscles in the rotator cuff are mainly producing force for stability instead of trying to lift the arm - Contributors to the study of biomechanics - Isaac newton - The emergence of the mechanical philosophy and Newton's Laws provided the impetus for the study of human movement and the tools to understand it Lecture 2 -- Fundamental Concepts --------------------------------- - Statics & Dynamics +-----------------------------------+-----------------------------------+ | Statics | Evaluation of systems that [are | | | not moving or that are moving at | | | a constant velocity] | | | and considered to be in | | | equilibrium (sitting in chair) | +===================================+===================================+ | Dynamics | Evaluation of systems [in | | | accelerated motion] | | | using kinetic and kinematic | | | approaches (rising from a chair) | | | | | | Takeaway point = the COM is | | | dynamically moving! | +-----------------------------------+-----------------------------------+ - Kinematics & Kinetics +-----------------------------------+-----------------------------------+ | Kinematics | Examines motion from a spatial | | | and temporal perspective without | | | regard for the forces causing | | | that motion | | | | | | Looks at movement without forces | +===================================+===================================+ | Kinetics | Examines and attempts to define | | | the forces causing (or resulting | | | from) a movement | | | | | | Forces causing movement | +-----------------------------------+-----------------------------------+ Activity Peak Vertical Ground Reaction Force -------------------- ------------------------------------- Walking 1.1 BW Running 2.8 BW VB spike landing 4.8 BW Somersault landing 13.6 BW - Vectors and Scalars +-----------------------------------+-----------------------------------+ | Vectors | Magnitude AND direction and point | | | of application | | | | | | Ex. Ray extends infinitely in one | | | direction | | | | | | Ex. 60 mph heading north | +===================================+===================================+ | Scalars | **Just magnitude** | | | | | | Ex. 60 mph | +-----------------------------------+-----------------------------------+ - Kinematic Quantities: Linear Kinematic Quantities: Linear ------------------------------ ------------------------------------------------------------------------------------------------------------ Displacement X; vector quantity, has direction, magnitude, point of direction, is the change in space from start to end Distance Actual length or path traveled; scalar Velocity Rate of change of position, slope of a line, vector Speed Acceleration Rate of change of velocity over time - Angular velocity -- rate of change of angular movement over time - Angular acceleration -- rate of change of angular velocity - Jerk: change in acceleration - Ex. People with PD have jerk in their movements - Kinematic Quantities: Angular Kinematic Quantities: Angular ------------------------------- ------------------------------------------------------- Angular displacement Theta, difference between initial and final positions Angular velocity Omega, rate of change of angular movement over time Angular acceleration Alpha, rate of change of angular velocity over time - Force - An interaction, push or pull, between two objects that can cause an object to accelerate positively or negatively - Examples - Gravitational force - Muscle force - Contact force - Buoyant force - Elastic -- tendons, TheraBand - Rigid body assumption - Rigid body: - An object in which the distance between every pair of points on the object remains the same - Body segments are often "grossly" represented in order to simplify the analysis - Assumption = all body segments are rigid (don't bend, don't deform) - Kinematic Quantities Linear Angular -------------- ------------------------------ --------- ------------------------------- -------- Time seconds S seconds S Displacement meter m radians R Velocity Meters per sec m/s Radians/sec r/s Acceleration Meters per second per second m/s\^2 Radians per second per second r/s\^2 - Review Questions - What are statics, dynamics, kinematics and kinetics? - Static -- not moving or constant velocity - Dynamic -- moving, acceleration/deceleration - Kinematics -- motion without force - Kinetics -- motion w/ force - What are examples of vectors and scalars? - Scalar = magnitude - Vector = more descriptive; magnitude AND direction - What is the difference between distance and displacement? Speed and velocity? +-----------------------------------+-----------------------------------+ | Distance | Displacement | +===================================+===================================+ | Scalar | Vector | | | | | Length of path traveled | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ | Speed | Velocity | +===================================+===================================+ | scalar | Vector | | | | | | Rate of change of position = | | | slope | +-----------------------------------+-----------------------------------+ - What is a force? - An interaction - Push/pull between 2 objects that can cause an object to accelerate positively or negatively - Ex. Gravity, muscle, contact, elastic, buoyant - What is a rigid body? Why is a rigid body assumption often made in biomechanics? - Assumption = an object in which the distance between every pair of points on the object remains the same - The assumption simplifies problems - Body segments are "grossly" represented to simplify the analysis (system) Lecture 3 -- Fundamental Concepts --------------------------------- - [7 fundamental units:] - Length - Mass - Time - *Electric current* - *Temperature* - *Amount of a substance* - *Luminous intensity* - [**LENGTH, MASS & TIME** are the fundamental units of physical space] - The rest are derived! - Qualitative - Nominal + ordinal - Quantitative - Interval scale and ratio scaled - Measuring and counting - Level of Accuracy - The level of accuracy is important, but it varies with circumstance - Measuring cloth in micrometers is absurd, but necessary for aircraft pads - Validity and reliability issues are related to the accuracy of a measurement - In this course, when in doubt, use 2 decimal spaces - Basic Concepts: Space - Space - Boundless 3D volume - Instruments: tape measures, optoelectronic devices, micrometers, anthropometers - Plane - Boundless 2D flat surface, no width - Line - Infinite series of points that are straight - Infinite length, no width or depth - Point - Also called a particle - A location in space that occupies no volume - Frames of Reference - Cardinal/relative frame of reference - Origin of axes usually set at center of gravity of body and moves w/ body - Newtonian/absolute frame of reference - Origin set at arbitrary point; does not move - Axes are also fixed and do not move - Right-handed axes are ISB standard - Based on the right hand system, counter-clockwise rotation around axis = positive - Rules for solving problems - Forces to the right are + - Forces upward are + - Counterclockwise rotation (torques) are + - Basic Concepts: Time - Event = designated instant in time - Temporal analysis = the study of the sequencing of or durations between events - Basic concepts: Mass - Mass is a fundamental property of a body which characterizes its resistance to change of motion (inertia) - Something with more mass has more inertia - Mass is also a body's gravitational potential - Only significant when the body is exceptionally large ex. Planet - Between small bodies gravitational forces are too small to affect their motions - Having mass means your have gravity - Newtonian Mechanics - Space, mass and time and independent of each other - Lines are infinitely straight - Mass is unchangeable - Time proceeds in uniform steps - Requires axis whose [origin is fixed in space] and not moving - Newton's laws describe the concept of a force - A force is dependent upon space, mass and time - Force is the action of one body upon another - Measured in newtons (N) - Newton's Laws of Motion 1. Bodies remain at rest or in uniform motion until acted upon by unbalanced forces 2. The acceleration of a body is proportional to the net force applied to the body (F = ma) 3. For every action, there is an equal and opposite reaction - Overview of Whiplash Injury - Most injuries occur at crash speeds below 12 mph and damage to car may be minimal - There may be little correlation between vehicle damage and magnitude of injury - Peak acceleration of the head is much greater than the peak acceleration of the vehicle - Whiplash Injury Phases - Phase 1 - Back and torso load the seat - Torso acceleration begins - High shear forces begin in neck - Spinal curves straighten & spine is compressed - Phase 2 - Vertical motion of torso + straightening of spine vertical rise of up 3.5 inches - Head snaps into full extension, extends overhead restraint and collapses it - Restraint acts as fulcrum - TMJ injury possible - Phase 3 - Head begins in forward motion - Torso descends in seat - Seat bounce increases occupant velocity to 30-70% more than car - Slack is taken out of shoulder harness - Phase 4 - Full deceleration of head, neck and torso - Aggravated by shoulder harness - High tension and shear forces in spine - Posterior ligamentous complex tension - Review Questions - What are the fundamental units of physics? - Length, mass, time - Give examples of derived units - Temperature, electric current, luminosity, amount of substance - Describe the difference b/t absolute and relative coordinate systems - Absolute - Axes are fixed to the ground and do not move - Origin set to some arbitrary point in the ground and does not move - Related to something singular in the room - X,y,z axes - Relative - Origin of axis set at center of gravity of the body - Moves w the body - Transverse, sagittal, frontal planes - Elbow relative to humerus - Can you resolve vectors in their x and y components? - Vx2 + Vy2 = V2 - X component cos - Y component sin - SOH CAH TOA - Can you add component vectors to get magnitude and direction of the resultant? Lecture 3.5 -- Quantifying Muscle Forces ---------------------------------------- - Musculoskeletal forces - Magnitude and direction of forces inside the human body - The interaction & application of Newton's law of acceleration on human body segments we can determine the magnitude and direction of forces inside the human body - Joint reaction force - 3 components - Normal component is typically directed into the joint surface and represents a compressive force - Most important contributor to joint reaction force is the force due to muscle activity - Difficult to measure JRF experimentally - Implant devices into joint - Calculate it using inverse dynamics - Muscle force - Muscles can only exert a PULLING force on a segment - Opposing set of muscles (agonists and antagonists) control movement around a joint - Magnitude of muscle force - To measure the magnitude of force directly, we must measure the force on the tendon - A surgical procedure characterized by the application of buckle transducers directly on the tendon allow us to directly measure muscle forces - Other Measures - Indirect measures (MMT, dynamometer, EMG) - Based upon the determination of CSA -- cross sectional area - CSA is a measurement of the end-on view of the area at the level at which the section has been made - Indicates the number of force-generating units (myofibrils) that are lying in parallel with the muscle - The more you have the more force you have - These measures can be obtained via cadaver dissection and through the use of imaging procedures (CT, MRI, US) - Cross Sectional Area (CSA) - There is a LINEAR RELATIONSHIP between maximal isometric force and CSA - Relationship is the same for both men and women - The slop of the regression line is referred to as Specific Tension or Normalized Force - Normal value = 30 N/cm\^2 - CSA x 30 = force area - Factors Involved in force-generating capacity - CSA of muscle accounts for only 50% of the variance in strength across individuals - It's not absolute; things modify it - FIVE factors contribute to variation - CSA varies along muscle length - Identification of all the muscles contributing to force generation - Keeping the antagonist muscles silent - (counters amount of force produced) - The assumption that the entire muscle mass can be activated - Muscles do not act as one big motor unit; fibers take turns - Variations in muscle architecture - Important!!! Maximum force - The maximum force a muscle can generate can be calculated knowing its CSA - Fm = specific tension x CSA - (Specific tension = 30 N/cm\^2) - Specific Tension Changes - Specific tension can change with activity - It is a functional measure of the number of myofibrils per unit of CSA - Specific tension of type 2 fibers declines with age - Electromyography -- EMG - Muscle force can be estimated from EMG - A measurement of electrical activity of skeletal muscles - Muscle force is controlled by the nervous system by means of electrical signals sent from motor neurons to muscle fibers - These signals (APs) can be recorded with special electrodes - What are we really measuring? - The sum of all APs transmitted on that muscle - The signal is filtered & amplified, transmitted to a computer for analysis - Signal Processing - Rectification - Taking all --'s and flipping and making +'s - Gives an average of muscle activity - Want all signals on x axis - Integration - Looking at area under the curve or root mean squared - Normalization - Power spectrum - Used to measure fatigue - Relating max activity to max force - RMS - Root mean squared - Taking --'s and making +'s - Useful w/ biofeedback - Power stroke - Make everything a sine wave smooth up & down waves - Look at medium frequency if shifting in one way or another, you assume fatigue or something is getting in the way of the signals - Power spectrum - 3 parts to understanding power spectrum relationship w/ EMG - 1\. Sine wave characteristics can be represented on a frequency plot - 2\. Even a square wave can be deconstructed into sine wave parts - 3\. Any wave can be deconstructed - Review Questions - What are MSK forces? - The interaction/application of newton's law of acceleration on human body segments we can determine the magnitude & direction of forces inside the human body - How is a muscle CSA used to determine muscle force? - Typically taken at the area of muscle that has the largest girth/diameter - Measurement of end-on view of the area at the level the section is being made - Ex. Transverse cut on gastroc - Indicates the \# of force generating units of myofibrils in parallel with muscle - Measurement can be taken using dissection, MRI, CT, US - The maximum force a muscle can generate can be calculated knowing its CSA - Fm = specific tension x CSA - (Specific tension = 30 N/cm\^2) - What is a "normal" value for specific tension? - 30 N/cm\^2 - What factors contribute to muscle force variation? - CSA varies along muscle length - ID all muscles contributing to force generation - Assumption that the entire muscle mass can be activated - Keeping the antagonist muscle silent - Variation in fiber architecture - Gastroc parallel fibers - Soleus pennate fiber arrangement - What is EMG? - EMG is the measure of electrical activity in skeletal muscles - Muscle force is controlled by the nervous system by means of electrical signal - Measure of sum of APs transmitted in that muscle Lecture 4 -- Kinematics and Kinematic Measurement Systems --------------------------------------------------------- - Kinematics = motion without regard to force producing the motion - Why measure motion? - Motion sometimes provides clues regarding pathology - Pre and post, compare to "norm" - Accelerations may be used to determine forces (F =ma) - Descriptive data can be used to evaluate change - Treatment effect, surgical outcome, comparison to normal - Basic Instrumentation - Man-instrument system - Person attached to transducers - Simple system - Transducer: converts energy from one form to another (volts) - Can the instrument do what is demanded of it? - Range: useable reading from the smallest expected value of the variable or parameter being measured to the largest - Sensitivity: - The amount of signal required to produce a unit of deflection. The sensitivity directly determines the resolution of the device, which is the minimum variation that can be accurately read - Linearity: the degree to which variations in the output of an instrument follow input variations - Frequency response: an instrument should be able to respond rapidly enough to reproduce the event being observed - Accuracy: (or precision) depends to a great extent on the errors or lack of errors to which an instrument is susceptible - Classification of Errors - Instrument errors - Mechanism errors -- errors in movement, etc. - Environmental errors -- likely when an instrument is used in an environment different from the one in which it was calibrated - Dynamic errors -- errors due to poor frequency response - Reading errors -- parallax, inadequate illumination, or excessively wide ink traces, etc. - Measurement errors - Systematic errors -- absolute accuracy vs relative accuracy - Ex. Ruler labeled wrong all measurements are off - Random errors -- errors that tend to cancel each other out if the measurement occurs over a long enough period of time - Ex. Using correctly labeled ruler but user's hands are shaky - Instrumented Motion Analysis (direct & indirect techniques) +-----------------+-----------------+-----------------+-----------------+ | Direct | Indirect | | | | Techniques | Techniques | | | +=================+=================+=================+=================+ | Temporal gait | To measure | Photography | Older | | measurement | cadence, stride | | techniques | | | length, gait | | reported in | | | cycle, single | | literature used | | | and double limb | | a single camera | | | support times, | | approach | | | graphic | | | | | displays of | | Single frame | | | foot-floor | | exposure w/ | | | contract | | strobe | | | patterns | | | +-----------------+-----------------+-----------------+-----------------+ | Electrogoniomet | An electrical | Video/High | Requires | | er | potentiometer | Speed Cameras | sufficient | | | that is | | light and frame | | | attached to a | | rate high | | | mechanical | | enough to | | | linkage. When | | eliminate | | | fit to body | | blurring of the | | | segments it | | fastest moving | | | provides a | | body parts | | | voltage output | | | | | that is | | | | | proportional to | | | | | joint position. | | | +-----------------+-----------------+-----------------+-----------------+ | Accelerometer | Is considered | Optoelectronics | Computer based | | | to be a direct | | system; single | | | technique but | | camera provides | | | is often used | | 2D (no depth), | | | to indirectly | | multiple | | | measure | | cameras for 3D | | | velocity and | | | | | position. | | 3D has to be 2 | | | Attach to body | | or more cameras | | | to measure | | | | | motion. | | | +-----------------+-----------------+-----------------+-----------------+ | | | Magnetic | 6DOF | | | | Tracking | | | | | | Gives real time | | | | | feedback | +-----------------+-----------------+-----------------+-----------------+ - Calibration & Reconstruction +-----------------------------------+-----------------------------------+ | Calibration | Reconstruction | +===================================+===================================+ | Relationships established that | Process of determining 3D | | relate the cameras to the lab | coordinates for imaged markers | | coordinate space and to | | | real-world dimensions | Actual coordinates are | | | "reconstructed" from independent | | Requires calibration frames w/ | camera views | | markers accurately placed at | | | defined locations | Uses 2 camera perspectives to | | | "triangulate" depth | | 3D calibration uses each cameras | | | view of the calibration object to | | | determine the location of the | | | cameras in the data collection | | | space | | +-----------------------------------+-----------------------------------+ - Review Questions - Why is motion analysis performed? - Motion can provide clues regarding pathology - Acceleration can be used to determine forces (F = ma) - Descriptive data can be used to evaluate change - Treatment effect, surgical outcome, comparison to normal - What is the difference between systematic and random error? +-----------------------------------+-----------------------------------+ | Systematic Error | Random Error | +===================================+===================================+ | Absolute accuracy vs relative | Errors that tend to cancel each | | accuracy | other out if the measurement | | | occurs over a long enough period | | Making a consistent error | | | somewhere | Ex. Using a ruler to measure but | | | your hand is shaking | +-----------------------------------+-----------------------------------+ - What is calibration? Reconstruction? +-----------------------------------+-----------------------------------+ | Calibration | Reconstruction | +===================================+===================================+ | Relationships established that | Process of determining 3D | | relate to the cameras to the lab | coordinates for imaged markers | | | | | Coordinate space to real world | Actual coordinates are | | dimensions | reconstructed from independent | | | camera view | | Requires calibration frames w/ | | | markers accurately placed at | Uses 2 camera perspectives to | | defined locations | triangulate depth | | | | | 3D calibration: uses each camera | Summates the data | | view of the calibration object to | | | determine location of the cameras | | | in the data collection space | | +-----------------------------------+-----------------------------------+ - Give examples of available technologies for motion measurement. - Direct - Temporal gait measurement - Electrogoniometer - Accelerometer - Indirect - Photography - Video/high speed camera - Optoelectronics - Magnetic tracking Lecture 5 -- Kinematic Data Processing -------------------------------------- - The main purpose of indirect movement analysis techniques is to obtain x, y, z coordinates of a point or a point in space. - Typically... - Joint-centers are marked by contrasting markers - Camera frame rates high enough to eliminate blurring of most rapidly moving body parts - Marker i.d. is typically performed manually - The data coordinates are processed further for analysis - The total process is time consuming - 2-D imaging techniques can obtain accurate and reliable measurements - Methods used to reduce error - To reduce perspective error: - Film plane set parallel with movement plane - Performer should move at right angles to the optical axis of the camera - Camera should be positioned as far away from action as possible - Maximize image size - Optical axis set relative to the movement of interest - Automated motion analysis (3D) - Markers are identified by the system in some automated fashion - Active markers are wired - Markers may be passive (reflective) or active (wired) - Computer performs analysis - Use of multiple cameras - Accuracy depends on camera placement - Sources of Systematic error in motion analysis - Poor calibration resulting from camera movement after calibration has been done - Misplacement of markers on subject - Marker movement - Obscured markers - Sources of random error in motion analysis - Marker shape changing (shadowing) - Discrete pixel size related to definition of marker (bit noise) - Time Varying Signals - Noise reduction in a time-varying signal - Signal is assumed to vary with time - Averaging would reduce the data to a constant - Filtering permits selective "subtraction" of unwanted signal (noise) - Low Pass Filtering (IMPORTANT) - Eliminates high frequency signals!!! - Saves (lets pass) the signal of interest - Filter frequency can be controlled - May result in some data degradation - Why filter??? - Velocities or accelerations often needed (ex. For momentum and force calculations) - Velocity = slope of position - Acceleration = slope of velocity - Jerk = slope of acceleration - Jounce = slope of jerk - Differentiation magnifies small changes in data - Differentiating anything amplifies the noise - Review Questions - What are sources of error in motion analysis? +-----------------------------------+-----------------------------------+ | Systematic Error | Random Error | +===================================+===================================+ | Poor calibration | Will zero out | | | | | Misplacement of markers | Shadowing change marker shape | | | | | Marker movement | Bit noise discrete pixel size | | | related to definition of marker | | Obscured markers | | +-----------------------------------+-----------------------------------+ - How can noise be reduced? Why would you want to do this? - Filtering or smoothing - To have more accurate data so you can get derivatives for that data - What special considerations are associated with manual image-based motion analysis? With automated? - 2D-manual - To reduce error: - Film in plane parallel to movement - Maximize image size - Try to place cameras far away from motion - 3D-automated - Ideally 3 cameras - Spread cameras out and calibrate them to each other - Can you give an example of something useful learned from motion analysis? - Can get an idea of impairment/pathology - Evaluate change at baseline - If given acceleration you can find the forces acting on the body Lecture 6 -- Linear Kinematics ------------------------------ - Positional change is exponential - Review types of motion - Translational: when all points of a body or object move the same distance over the same time - Angular motion: all points of body or object move through the same angle - General plane motion: combo of translational and angular - Computing Displacement - Digital data provides location of each point in space - Displacement of a single marker can be done from frame to frame - Delta (r) = r2 -- r1 (gives you difference in location) - Displacement vs pathway - IMPORTANT: displacement is a function of the sampling interval - As the sampling interval goes to zero, the displacement gets closer to the actual pathway - KEY = need more points to see path taken; think analog vs digital clock - Computing Velocity - Average velocity - Rate of change of position with respect to time - Instantaneous velocity - The slope of a line tangent to the position time curve - Slope at a particular instant time - A derivative is... - A fundamental mathematical tool used for many purposes - Differentiation: the process of finding the derivative of a function - One application -- computing velocity + acceleration - How to compute derivates in the real world a. First backwards difference a. No space to put this value in the graph b. Ex. 4-5 b. Central difference c. Don't need to shift data d. Ex. 5 = 6-4 - Computing Acceleration - Acceleration = rate of change of velocity w/ respect to time - Integration - Instantaneous velocity and relative position of the object can be calculated using the process of integration - Integration = anti-differentiation - Integration is the reversed operation of differentiation - Integration has many applications such as area, volume, work and energy computations - Riemann Sum - Approximating an integral by summing a series of rectangles - Review Questions - Can you describe the difference between differentiation and integration? +-----------------------------------+-----------------------------------+ | Differentiation | Integration | +===================================+===================================+ | What is happening at that instant | Working backwards -- ANTI | | | differentiation | | Instantaneous velocity | | | | Given acceleration going to | | Velocity to acceleration | velocity & displacement | | | | | Taking the derivative dx/dt | Getting data over a span of time | | | | | Gives the slope of the curve at | Using the area under the curve | | area | | | | Gives the area under the curve | | Rate of change of a function | between points | | | | | Position acceleration | Sum of function over a range | | | | | | Acceleration position | +-----------------------------------+-----------------------------------+ - Can you apply these techniques to position, velocity, and acceleration data? - Can you apply the constant acceleration equations? - - What is one problem with estimating forces using kinematic derivatives? - You have to estimate is - Not real time - You could be missing data - If the same frequency isn't high enough, you could be missing data Lecture 7 -- Angular Kinematics ------------------------------- - Computing Angular Velocity and Acceleration - Once a series of angles have been computed, then computing angular derivatives can be accomplished - Angular velocity = rate of change of angular position over time - Angular acceleration = rate of change of angular velocity over time - Angular units have to be converted to radians! - 1 rad = 57.3 degrees - Relationship between linear and angular components - In many human movements, the results are linear even though the motions of the segments are angular - There is a relationship between the linear and angular motions of a segment based on the previous definition of a radian - Angle-angle diagram - This diagram does NOT show time you can't tell how fast they're going - Shape of curve demonstrates pathology - Stiff knee graph would compress - Review Questions - How are absolute angles used to compute relative angles? - What is the relationship between angular position and angular velocity? - Can you describe the relationship between angular velocity and translational velocity? - Can you draw (approximate) the velocity plot if given a position plot?