KIN 3309 1nd Edition Lecture 9 Outline of Last Lecture I Human Movement Analysis II Kinematics III Linear Kinematics IV Collection of Kinematic Data V Spatial Reference Systems VI Cartesian Coordinate System VII 2 D Cartesian Coordinate System VIII Two Dimensional Reference System IX Quadrants in a Two Dimensional Reference System X Three Dimensional Reference System XI Three Dimensional Coordinate System XII Vectors and Scalars XIII Vector Magnitude XIV Distance from Origin XV Vector Components XVI Vector Direction XVII Vector Orientation XVIII Vector Orientation Standard XIX Vector Arithmetic XX Example 1a XXI Example 1b XXII Example 1c XXIII Example 1d XXIV Example 2a XXV Example 2b XXVI Example 2c XXVII Example 3 XXVIII Example 4 XXIX Position and Displacement XXX Example 5 XXXI Quiz Outline of Current Lecture These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII Human Movement Analysis Movements Occur Over Time Important Parameters Velocity v Velocity slope Velocity Estimation Finite Differentiation Instantaneous Velocity Average vs Instantaneous Velocity Graphical Example Constant Velocity Acceleration Instantaneous Acceleration Constant Acceleration Integration Finite Integration Example Riemann Sum Kinematic Analysis Gait Kinematics How to Solve Kinematics Problems Quiz Current Lecture Constant Velocity the xf is very important I Human Movement Analysis a II Movements Occur Over Time a Knowledge of the temporal patterns of a movement is critical in a kinematic analysis since changes in position occur over time b III Important Parameters a Position WHERE i Location in space relative to some reference point ii Linear and angular position s theta b Displacement Distance HOW FAR i c Velocity and Acceleration i IV Velocity v a V Velocity slope a VI Velocity Estimation a Velocity is the slope of a displacement time graph b Approximating velocity from displacement data employs finite differentiation i Differentiation gives the average velocity between displacement points c VII Finite Differentiation a Differentiation over one time interval calculates the velocity of a point midway between the frames b c First central differences method reduces sensitivity accuracy but aligns velocities with the same time frame as displacements d e VIII Instantaneous Velocity a Instantaneous velocity is the apparent velocity at any moment every point of time b The instantaneous velocity can be positive negative or zero c The instantaneous speed the magnitude of the instantaneous velocity d The instantaneous speed has no direction associated with it e IX Average vs Instantaneous Velocity a X Graphical Example a XI Constant Velocity a Indicates the instantaneous velocity at any instant during a time interval i Same as the average velocity during that time interval XII Acceleration a b Acceleration is used in everyday terms as a scalar c It is strictly speaking a vector d XIII Instantaneous Acceleration a The instantaneous acceleration is the limit of the average acceleration as change in t approaches 0 b XIV Constant Acceleration a Indicates the instantaneous acceleration at any instant during a time interval i Same as the average acceleration during that time interval XV Integration a There are times when it is more convenient to collect velocity or acceleration data than position data for biomechanical analysis b To compute displacement from velocity we use integration XVI Finite Integration a Finite differentiation calculates the slope of the curve b Finite integration calculates the area under the curve c XVII Example a b c d e XVIII Area A equals 3 m s x 6 s 18 m This is change in position from 0 6 s Area B equals 7 m s x 2 s 14 m Total change in position from 0 8 s is 32 m Riemann Sum a Finite integration approximates the area under curves as a series of rectangles i This is called the Riemann sum ii If change in t is small enough this is an accurate approximation iii XIX Kinematic Analysis a There are many uses of kinematic analysis b Sports scientists and coaches often use kinematics to characterize elite performance i E g analyzing a movement pattern golf club head speed c Ergonomists use kinematics to assess injury risk i E g assessing poor postures high task repetition d Doctors and physiotherapists also use kinematics i E g assessing walking gait with prostheses range of motion XX Gait Kinematics a Gait Cycle i Single sequence of functions by one limb ii Begins when reference foot contacts the ground iii Ends with subsequent floor contact of the same foot b Stance Phase i Reference limb in contact with the floor c Swing Phase i Reference limb not in contact with the floor d Single Support i Only one foot in contact with the floor e Double Support i Both feet in contact with floor f Cadence i Number of steps per unit time e g 100 115 steps min g Step Length i Distance between corresponding successive points of heel contact of the opposite feet h Stride Length i Distance between successive points of heel contact of the same foot i Support and non support swing phases are also of interest j In walking the time in the support phase is approximately 66 60 swing phase 34 40 k The relative time of cycle spent in the support phase decreases with increasing speed i Jogging 59 30 ii Full Sprint 25 20 l Changes associated with pathological function surface conditions i Increased support phase decreased swing phase ii Shorter step length iii Increased time in double support XXI How to Solve Kinematics Problems a Step 1 i Identify clearly what the problem is asking b Step 2 i Identify the information you are given c Step 3 i Identify relationships d Step 4 i Combine the given information and the relationships XXII Quiz a A sprinter is observed to run 50 meters in 7 5 seconds Calculate the speed of the sprinter in m sec i 50 m 7 5 s 6 67 m s b An individual runs 20 km in 89 minutes What was the average speed in meters per second i 0 27 ii 0 90 iii 3 75 20 89 0 23 km min then 23x 1000 60 3 75 m s iv 225 c During running 100 m a runner runs from the 20 to 30 meter mark in 60 frames of a video record If the video camera recorded data at 50 fps how fast was she running during this interval i 6 5 m s ii 36 m s iii 8 3 m s iv 0 167 m s d A sprinter moving in a straight line at constant velocity starts at a position of 10 meters