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## Describing Motion

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**PART I The Force-Motion Relationship**Describing Motion Describing Motion Photo reprinted from Marey, 1889.**Systeme Internationale = Metric System**Fundamental Units: mass in kg, linear distance in m, angular distance in rad, time in s All other physical measurements are derived from these variables: Force = N = kg*m / s2 Energy = J = kg*m2 / s2 Website for conversions http://catcode.com/trig/trig08.html Review of Math Review**Radian – the angle created by the arc on a circle with the**length of the radius of the circle (~ 57.3 degrees) More review of Math Review Arc length = 1 radius**Trigonometry – sine, cosine, tangent, and inverse**functions sin a = A/C, cos a= B/C, tan a= A/B sin-1 A/C = a, cos-1 B/C = a, tan-1 A/B = a Math Review C A a B**Sine function – continuous wave over angular**position Math Application: important in signal processing +1 0 -1 0 180 360 degrees**Math Application: important in signal processing**Cosine function – continuous wave over angular position +1 0 -1**Math Review**Website for sine and cosine waves http://catcode.com/trig/trig08.html**Kinematics describes the**Time – Geometry of Motion or the Movement Pattern during static or dynamic activity Describing Motion = Kinematics**Translation – Linear Movement – displacement from one**point to another in either: Straight lines – rectilinear translation or Curved lines – curvilinear translation Animals can do both but curvilinear motion more common Two Fundamental Movement Patterns**Rotation – Angular Movement – displacement around an**axis Principle means of animal motion Two Fundamental Movement Patterns**Animals translate by skillfully combining joint rotations**Translation Through Rotation A person stands up by rotating the hip, knee, and ankle joints Animals rotate to translate Animals are rotating machines**Translation Related to Rotation**Linear displacement and velocity related to the angular kinematics: s = r v = r Calculate Arc Length when radius = 1 cm and = 90°**Position – location within the environment**Displacement – the change in position with movement Velocity – rate of change of position Acceleration – rate of change of velocity (All variables are vectors) Four Kinematic Variables or Motion Descriptors**Heel Strike: Shoulder=1.01,1.34**Knee = 1.11, 0.47 Toe Off: Shoulder=1.87,1.35 Knee = 1.78, 0.44 Position in a Linear 2D Reference Frame**Position in an Angular Reference Frame**Segment Angles – Angle between a body segment and the right horizontal from distal end of segment Trunk = 85° or 1.48 rad Arm = 95° or 1.66 rad**Position in an Angular Reference Frame**Joint Angles – Angle between two body segments Shoulder = 20° or 0.35 rad Knee = ???**Generate Angular Position Data**1) Identify location of skeletal joints 2) Define joint angles 3) Calculate segment angles 4) Combine segment angles to calculate joint angles**Position in an Angular Reference Frame**Acromion 1.10, 1.34 Greater Trochanter 1.05, 0.8 Lateral Knee 1.18, 0.5 Lateral Malleolus 1.23, 0.1 Heel 1.20, 0.02 5th Met 1.35, 0.08**Position in an Angular Reference Frame**Joint angular position for obese and lean subjects while walking Obese less flexed at hip and knee and less dorsiflexed at ankle Obese walk in a more erect pattern**Displacement**Displacement = difference between final and initial positions Linear displacement (d) = Pf – Pi (m) Angular displacement () = f - i ( or rad) Displacement does not necessarily equal distance (the length of the path traveled)**Horizontal displacement:**heel strike to toe off Shoulder = 0.86 m Met Head = 0.09 m Total displ. Shoulder = 1.87,1.35 -1.01,1.34 0.86,0.01 Displacement in a Linear Reference Frame**Magnitude Result. Displ. = (Hor disp2 + Vert disp2)1/2**Displacement in a Linear Reference Frame Resultant displacement between heel strike and toe off for: Shoulder = 0.87 m Met head = 0.10 m**Linear Displacement During Walking**Step length – forward displacement of one foot during swing phase Stride length – combined forward displacement of both feet during left and right swing phases**Linear Displacement During Walking**Step length – mean value ~ 0.75 m for healthy adults, less for shorter, older, ill, or injured people Left and right step length symmetry Stride length – mean value ~1.5 m for healthy adults, less for shorter, older, ill, or injured people**Velocity**Velocity = rate of change of position = amount of displacement per unit time “rate of change” = calculus concept of the derivative or slope Linear velocity (v) = (Pf – Pi) / time (m/s) Angular velocity () = (f - i) / time (/s or rad/s)**Gross body movement**Johnson vs Lewis100m, Seoul 1988 More information with shorter measurement intervals Newsweek, 7-29-96**Velocity**Velocity = rate of change of position = amount of displacement per unit time “rate of change” = calculus concept of the derivative or slope Linear velocity (v) = (Pf – Pi) / time (m/s) Angular velocity () = (f - i) / time (/s or rad/s) Simple Finite Difference Technique**Velocity: displacement / time**• vector • magnitude: how fast • direction: specification of “which way” • This is motion**Cyclic Movement – Angular Kinematics**Positive & negative slopes on position curve have positive and negative phases on the velocity curve**Cyclic Movement – Angular Kinematics**Increasing + Positive & negative slopes on position curve have positive and negative phases on the velocity curve**Cyclic Movement – Angular Kinematics**Decreasing + Increasing + Positive & negative slopes on position curve have positive and negative phases on the velocity curve**Increasing -**Cyclic Movement – Angular Kinematics Decreasing + Increasing + Positive & negative slopes on position curve have positive and negative phases on the velocity curve**Increasing -**Cyclic Movement – Angular Kinematics Decreasing + Increasing + Decreasing - Positive & negative slopes on position curve have positive and negative phases on the velocity curve**Cyclic Movement – Angular Kinematics**Positive & negative slopes on position curve have positive and negative phases on the velocity curve**Relationship Between Position and Velocity**Knee angular position & velocity curves during the stance phase of running**Knee Position/Velocity in Walking**contact Toe off**Knee Position/Velocity in Walking**Identify local minima and maxima: velocity = ??**Knee Position/Velocity in Walking**What is the sign of the velocity between local min & max?**Knee Position/Velocity in Walking**Identify inflection points : ?**Knee Position/Velocity in Walking**Identify inflection : local minima & maxima on velocity**Knee Position/Velocity in Walking**Identify local minima and maxima**Knee Position/Velocity in Walking**Identify inflection points**Second Order Finite Differences**• Use Project to demonstrate need.