describing motion describing motion part i the force-motion relationship photo reprinted from marey,...

DescribingMotion

DescribingMotion

PART I The Force-Motion Relationship

Photo reprinted from Marey, 1889.

X velocity-Time

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Movement is Motion – Motion is Movement

Laboratory Movement

Small Movement

Review of Math Review

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

More 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)

Arc length = 1 radius

Math Review

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 = aA

a

B

C

Math Application: important in signal processing

Sine function – continuous wave over angular position

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0

-10 180 360 degrees

Cosine function – continuous wave over angular position

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0

-1

Math Application: important in signal processing

Math Review

Website for sine and cosine waves

http://catcode.com/trig/trig08.html

Describing Motion = Kinematics

Kinematics describes the

Time – Geometry of Motion

or the

Movement Pattern

during static or dynamic activity

Two Fundamental Movement Patterns

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

Curvilinear Translation During Walking

Two Fundamental Movement Patterns

Rotation – Angular Movement – displacement around an axis

Principle means of

animal motion

Translation Through Rotation

A person stands up by rotating the hip, knee, and ankle joints

Animals rotate to translate

Animals are rotating machines

Animals translate by skillfully combining joint rotations

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°

Four Kinematic Variables or Motion Descriptors

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)

Biomechanics Laboratories

Position in a Linear 2D Reference Frame

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 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


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


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


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)

Displacement in a Linear Reference Frame

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

Resultant displacement between heel strike and toe off for:

Shoulder = 0.87 m

Met head = 0.10 m

Magnitude Result. Displ. = (Hor disp2 + Vert disp2)1/2

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)

Johnson vs Lewis100m, Seoul 1988

More information with shorter measurement intervalsNewsweek, 7-29-96

Gross body movement

Average vs. Instantaneous Velocity

Velocity

Velocity = rate of change of position

= amount of displacement per unit time


Linear velocity (v) = (Pf – Pi) / time (m/s)

Angular velocity () = (f - i) / time (/s or rad/s)

Simple Finite Difference TechniqueSimple Finite Difference Technique

Velocity: displacement / timeVelocity: displacement / time

vectorvector•magnitude: how fastmagnitude: how fast•direction: specification of “which way”direction: specification of “which way”

•This is motionThis is motion

Cyclic Movement – Angular Kinematics

Positive & negative slopes on position curve have positive and negative phases on the velocity curve

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Relationship Between Position and Velocity

Knee angular position & velocity curves during the stance phase of running

Knee Position/Velocity in Walking

Knee Angular Position

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Knee Position

contact Toe off


Knee Angular Position and Velocity

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Identify local minima and maxima: velocity = ??



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What is the sign of the velocity between local min & max?



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Identify inflection points : ?



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Identify inflection : local minima & maxima on velocity



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Knee Velocity

Identify local minima and maxima



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Knee Velocity

Identify inflection points

Second Order Finite Differences

• Use Project to demonstrate need.

Acceleration

Acceleration = rate of change of velocity

= change in velocity per unit time

change in velocity = change in motionchange in velocity = change in motion

Acceleration

Acceleration = rate of change of velocity

= change in velocity per unit time


Linear acceleration (a) = (Vf – Vi) / time (m/s2)

Angular acceleration () = (f - i) / time

(/s2 or rad/s2)

Acceleration

Acceleration due to gravity = g = 9.81 m /s2

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Position

Velocity

Describe shape of:Position curveVelocity curveAcceleration?

Acceleration

Acceleration due to gravity = g = 9.81 m /s2

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Describe shape of:Position curveVelocity curveAcceleration

Velocity – Acceleration Relation

Based on definition of acceleration, sketch the angular acceleration curve for this velocity curve

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Velocity – Acceleration Relation

Acceleration curve shows the slope of the velocity curve, including positive and negative directions

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Acceleration is our link to kinetics

• Important to understand the concept of positive and negative acceleration



• Parabolic motion: horizontal & vertical components

• release velocity• Peak velocity• contact velocity

Wayne WrightHuman Cannonball



• Parabolic motion: horizontal & vertical components

• release velocity• Peak velocity• contact velocity

Gymnast leaves ground at v v = 3m/s and v h = 4.2 m/s. Calculate velocities 0.25 seconds later.

Gymnast is at peak height (v v = 0 m/s). How fast is she traveling 0.25 m (vertical) later? What is vh?

Gymnast is falling at –1.5 m/s. How fast is she traveling 0.25s later? What about v h?

Constant Linear Velocity

• Acceleration = 0• what is force?

• Calculating final position of body

• Rearrange equation of velocity• Sprinter is 70 from start. Horizontal velocity of

11.5 m/s. Maintains for 1.7s. How far from start line?

So let’s imagine the force. 09/02/07: Labor Day occasion to commemorate lost railroad workers By Bill Kemp Archivist/Librarian, McLean County Museum of History Advertisement BLOOMINGTON -- On Feb. 25, 1921, "death came fantastic with horror" when a storage tank explosion tossed Harold Downey’s whirling, lifeless body 200 feet into the air. A Chicago & Alton Railroad boilermaker, Downey’s fatal accident reminds us of the untold number of railroad workers who lost their lives toiling in one of the more vital and dangerous industries in U.S. history. On that Friday afternoon, Downey, who worked at the C&A shops on Bloomington’s west side, was sent to repair a leaking gasoline storage tank. When he entered through a manhole at the top, his lighted torch ignited the escaping fumes."His body was propelled upwards with a force, the intensity of which can only be imagined," the Pantagraph reported.

Forensic Biomechanics

Complete the project available from the website.

General Kinematic Procedures

Linear data:

use position of body segments for descriptive stride characteristics (how far, high, etc)

use position, velocity, and acceleration for complex inverse dynamics (F = ma)

Angular data:

use joint angular position for direct comparisons

use joint angular velocity for joint power (P= T * )

General Kinematic Procedures

Other places: You name it, people use it.

Pelvic tilt

Hand displacement in reaching

Trunk vibrations in driving

Tibia accelerations in running (shock)

etc etc etc

Orthotic Effects on Kinematics

Kinematic Coordination in Running

Coordination between knee and subtalar motions

Kinematic Coordination in Running

AnklePosition: Soft vsStiffLandings

Use angular velocity to compare technique

Relation Between Kinematics & Kinetics

Kinetics causes kinematics

Force produces acceleration which ultimately causes a change in position

Kinematics causes kinetics ?

Position causes force??

Is this possible???

482 Advanced Biomechanics

• How many plan to enroll in this class for Spring 2008?

• Early registration is next week, do it at that time.

• Warning: if low enrollment, class will be cancelled, so sign up for an alternative class too.

Error in Kinematic Data

Calculations of derivatives introduces noise into the signal

Velocity has some error

Acceleration has more error

Error From Data Acquisition

Digitizing process introduces error in position data –

Markers move or vibrate relative to the joint center

System misses the marker

Markers are covered

Time vs Frequency

Human movement – low frequency

Digitizing error – high frequency

Derivatives increase high frequency error

Pos = sin 2 Vel = 2 cos 2

Fourier Analysis – Frequency Content

Single frequency

Two frequencies

Many frequencies

Digital Filters to Remove Error

Low pass filter allows low frequency signal to pass but filters out high frequency error

Cut off frequency ~ 5-15 Hz

Optimal filter techniques

Fourier Analysis

Optimal Filter

Finds point beyond which filtering does not change result

Digital Filter Demonstration

(Show digital filter program application)

Bench Press: filter the angular velocity and acceleration curves

80% 1RM BP, Narrow vs Wide Grip

Filtered Position – Good Acceleration

Filter position data to produce accurate velocity and acceleration data

We filter the linear horizontal & vertical position vs time data

Signal Processing

Data Filtering or smoothing vs. Curve fitting

y = 106.02x - 108.53

R2 = 0.9502

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Height

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Force by Contraction Velocity

y = 991.57x2 - 545.25x + 101.45

R2 = 0.9871

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Velocity (mm/s)

Fo

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Signal Processing

Complex and detailed mathematical topic

We provided only the slightest introduction

Summary – Kinematics

Kinematics describes the movement pattern in linear and angular reference frames

Kinematics is the outcome of Kinetics (the result not the cause)

describing motion describing motion part i the force-motion relationship photo reprinted from marey,...

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