Unformatted text preview: Lecture 7 Kinematic Modeling EML 5595 Mechanics of the Human Locomotor System Outline 3D Rotations Noisy Data y Journal Article Review Lu and O'Connor (1999) Outline 3D Rotations Direction Cosine Matrices
^ ^ ^ a1 =  cos(q1 )n1 + sin(q1 )n 2 ^ ^ ^ a 2 =  sin(q1 )n1 + cos(q1 )n 2 ^ ^ a3 = n3 Matrix form:
N RA ^ n1 ^ n2 ^ n3 ^ ^ ^ a1 a2 a3 cos q1  sin q1 0 sin q1 cos q1 0 0 0 1 Finite Rotations Finite Rotations Rotation Sequences F R P =[ F R P ' ][ P ' R P '' ][ P '' R P ] F RP ^ f1 ^ f2 ^ f3 ^ p1 c1c 3  s1c 2 s 3 s1c 3 + c1c 2 s 3 s 2s 3 ^ p2  c1s 3  s1c 2 c 3  s1s 3 + c1c 2 c 3 s 2c 3 ^ p3 s1s 2  c1s 2 c2
^ ^ ^ 3  1  3 Coordinate Transformations
Let
Pi P
N O Pi Position ^ ^ ^ P CO P i = 1c1 + 1c 2 + 1c3
P P
CO Pi NO P i ^ ^ ^ = 3 n1 + 3 n 2 + 3 n 3 ^ ^ = dx n1 + dy n 2 + dz n 3 y^ P NOC O CO NO P N O CO P P N O Pi N O Pi = P CO Pi + P NOCO = N R C P CO Pi + P NOCO Coordinate Transformations
Rewrite 3 = 3 3 1 dx N R C 1 + dy 1 dz Transformation Matrix Computational Trick 3 3 = 3 1 N TC 1 1 1 1 N C T = 0 N RC 0 dx dy dz 0 1 Hip Joint Definition Hip Joint Definition Hip Joint Definition Knee Joint Definition
Now you develop a knee joint definition . . . Knee Joint Definition Knee Joint Definition Knee Joint Definition Question
How would you create a knee joint whose axis of rotation is not one of the coordinate system axes? Outline 3D Rotations Noisy Data y Sources of Kinematic Data Use kinematic data published in literature Measure external kinematics optical tracking, electromagnetic tracking Measure internal kinematics cine fluoroscopy, cine MRI, imbedded markers Develop a dynamic model kinematics determined by forces in muscles, ligaments, contacts Video Motion Data Video Fluoroscopy Data Example of Noisy Data
30 20 10 0 10 20 30 0 0.5 1 Time (s) 1.5 2 Raw 1 Hz signal 10 Hz noise SNR = 20 Sample rate 100 Hz 1st Derivative 1 D i i
5000 200 100 0 100 200 200 0 2nd D i i 2 d Derivative 0 0.5 1 Time (s) 1.5 2 5000 5000 0 0.5 1 Time (s) 1.5 2 Noisy Data Differentiation of Noisy Data Consider a 1 Hz signal contaminated with 10Hz noise, with a signaltonoise (SNR) ratio of 20: signalto x (t ) = 20 sin(6.28t) + sin (62.8t ); SNR = 20 x (t ) = 125cos(6 28t) + 62 8cos(62 8t ); SNR = 2 125cos(6.28t) 62.8cos 62.8t x (t ) = 785sin(6.28t)  3944sin (62.8t ); SNR = 0.2
The 2nd derivative of the noise is 5 times larger than the 2nd derivative of the signal! LowLowPass Filters SignalSignalNoise Overlap Ideally, signal and noise have minimal overlap Signal in Common Activities
Movement Activity Posture Gait (excluding heelstrike transient) Running Heelstrike Transient Maximum Frequency of Interest (Hz) 3 6 101015 100300 100 Noise Characteristics
Noise Source Skin movement artifact Partially obscured markers, interpolation errors p Camera switching, tracking errors Camera/digitizer noise Electrical interference Duration (ms) 100100200 Several frames 1 or more frames Continuous Intermittent (spike) or continuous ti Frequency Range (Hz) 110 Varies High (step) Broadband B db d (white) Usually high y g LowLowPass Filtering Effects
Pitching hand data Outline 3D Rotations Noisy Data y Journal Article Review Lu and O'Connor (1999) Problems with Kinematic Models What kinematic modeling problem do Lu and
O'Connor (1999) propose to address? Problems with Kinematic Models What kinematic modeling problem do Lu and O'Connor (1999) propose to address? What is their "new twist" for dealing with this problem? Problems with Kinematic Models What kinematic modeling problem do Lu and O'Connor (1999) propose to address? What is their "new twist" for dealing with this problem? What are some of the strengths and weaknesses of this proposed approach? p p pp Visualization of Concept Global optimization as defined by Lu and O'Connor (1999) is what we call "inverse kinematics" today. Desired pose 90 knee flexion 90 Blue markers Initial optimizer seed 0 knee flexion Red markers For Next Time Download and review kinematics handout Download and review momentum, inertia, and dynamics handout Download and read Remy and Thelen (2009) Journal of Biomechanics 32: 129134 129 ...
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This note was uploaded on 02/15/2012 for the course EML 5595 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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