Transcript Kinetics versus kinematics for analyzing coordination during

Kinematics
D. Gordon E. Robertson, PhD
Biomechanics, Laboratory,
School of Human Kinetics,
University of Ottawa, Ottawa, Canada
Kinematic Analysis
• Description of motion
without consideration of
its causes
• Based on calculus
developed by Newton
and Leibnitz
Isaac Newton, 1642-1727
Kinematic Analysis
manual goniometer
• Linear position
– ruler, tape measure, optical
• Angular position
– protractor, inclinometer,
goniometer
optical goniometer
protractor
digital goniometer
Kinematic Analysis
• Linear velocity
– radar gun
– speedometer
– photo cells
– videography
• Angular velocity
– tachometer
– videography
radar gun
Kinematic Analysis
• Linear acceleration
– accelerometer
– videography
• Angular acceleration
accelerometers
– multi-axis accelerometry
– videography
multiple accelerometers
within a headform
Videography /
Motion Analysis
• Cinefilm, video, or infrared video
• Person is filmed and locations of
joint centres are digitized
• Body is modeled as a system of
connected segments
high-speed
cine-camera
Steps to Obtaining Valid
Kinematics
1. Film scaling factors, origin, and vertical or
horizontal references or calibrate volume
(statically and dynamically) for 3D studies.
2. Place reflective markers on the body and
record body mass, height, and segment
lengths and girths, as necessary for
modelling.
3. If planning to use Visual3D or similar
programs, film a static trial with the subject
standing motionless. Afterwards some
markers may be removed depending on the
model chosen (e.g., medial markers).
Static Trial
Subject can be aligned with
laboratory axis but this
is not necessary with a
full uOttawa marker set.
Include implements (bats,
racquets, epees, etc.) if
they are to be tracked.
Also include markers that
are only needed for
model calibration (e.g.,
medial knee, medial
ankle).
Steps to Obtaining Valid
Kinematics, cont’d
4. Film the motion trials. Keep a record of
each trial’s experimental condition (load
carried, terrain traversed, skill technique)
for future reference. These are best kept in
a database.
5. Convert or digitize the video images to
obtain the trajectories of the markers. For
automatic systems, such as, Vicon and
MAC, this step “reconstructs” 3D
trajectories from the various 2D camera
views.
Steps to Obtaining Valid
Kinematics, cont’d
6. Refine (scale) the digitized coordinates to
metric units (x, y, z) with respect to a
Newtonian (laboratory) frame of reference.
This process can be realized with a
Fractional Linear Transform (FLT) for 2D
studies. For 3D systems this step is part of
the reconstruction step (above) and uses a
Direct Linear Transform (DLT) or similar
algorithm.
Apply FLT or DLT to Refine
and Scale Data
These transforms scale the data from digitizer
units (e.g., pixels) to real units (m, cm, mm).
They also align the data with a specific
laboratory axis system that is usually stationary
and aligned with a least one force platform.
Example is a 2D FLT: x  c1u  c2 v  c3
1  c7 u  c8v
[(u, v) coordinates are
c4 u  c5v  c6
raw unscaled data from
the camera] y  1  c7 u  c8v
Steps to Obtaining Valid
Kinematics, cont’d
7. Examine data for “gaps” or erroneous data,
then fill the gaps or eliminate the erroneous
data using interpolation. Extrapolation (at
the beginning and end) should be avoided
but is possible.
8. Smooth the coordinates to remove high
frequency noise. One method uses low-pass
digital filtering (see next page), other
methods include quintic splines and Fourier
reconstruction.
Digital Filtering
Apply a smoothing technology such as digital
filtering to reduce high frequency “noise”
that increases exponentially in magnitude
with time differentiation, especially double
differentiation or higher.
xi  a0 xi  a1 xi 1  a2 xi  2  b1 xi1  b2 xi 2
a0  a2  ½a1
a0  a1  a2  b1  b2  10
.
Same equation is used for y and z coordinates.
Differentiation
9. Compute time derivatives using finite
difference calculus. Calculate first and
second derivatives using central difference
equations:
( xi1  xi1 )
v xi 
2 t
(v xi1  v xi1 )
a xi 
2 t
a x i  ( xi1  2 xi  xi1 ) /  t 2
• Use same equations for y and z coordinates.
• Adjustments are need for first and last data
or use padding points before and after trial.
Steps to Obtaining Valid
Kinematics, cont’d
10. Optionally, compute additional coordinates
such as segment centres of gravity or joint
centres of rotation and/or compute angular
kinematics such as segmental angles and
joint angles.
Motion Analysis
uOttawa Biomechanics Laboratory
Computerized Digitizing
Vicon and Visual3D motion analysis systems
2D Example: Sprinting
Stick figure representation
Start Phase
• No motion permitted when gun sounds
• No force on blocks 0.10 seconds before
gun sounds
• Gun fires and there is a delay before
sprinter hears gun (unless blocks have
speakers)
• Delay between when gun fires and
force is applied to blocks (time for
message to reach muscles at 6 m/s)
• Taller sprinters take longer to start
Acceleration Phase
• Each athlete has his/her own rate of
acceleration
• The whole race takes between 43 and 48
steps
• At maximum speed, stride length
(1 stride = 2 steps) is over 4.5 metres long!
• Can last to 70 metres
Last 60 Metres of Race
100
male: 12 m/s
90
80
70
female: 10 m/s
60
50
40
5
6
7
8
9
Race time (s)
10
11
Constant Velocity Phase
• athletes achieve maximum
constant velocity between 50 and
70 metres
• speed:
– 9 – 12 metres / second
– 32 – 43 kilometres / hour
• foot achieved twice this velocity
(86 km/h!)
Donovan Bailey sets
world record (9.835)
despite slowest
reaction time (0.174)
of finalists
Fastest Sprinter (in 1996)
Johnson or Bailey?
•
•
•
•
•
•
Johnson’s 200 m record = 19.32 s
Each half = 9.66 s?
Bailey’s 100 m record = 9.84 s
US reporters claim Johnson is faster?
Johnson had running start for last 100 m
At 12 m/s Bailey can run 100 m in 8.33 s,
200 m time could be 18.17 (new WR)!
• race in Toronto confirms Bailey is
Fastest Man in the World
3D Example: Fencing
U. Sydney biomechanics laboratory with
Motion Analysis Co. (MAC) infrared cameras
Eagle infrared camera
Kinematic Variables
• Markers (use absolute frame of ref.):
– linear positions, velocities, & accelerations
– X=forward, Y=lateral, Z=vertical, resultant
• Segments (use absolute frame of ref.):
– linear positions, velocities, & accelerations
– angular positions, velocities, & accelerations
• Joints (use relative frame of ref.):
– linear positions, velocities, & accelerations
– angular positions, velocities, & accelerations
(X=flex./ext., Y=ab./adduction, Z=int./ext. rotation)
• Total body (use absolute frame of ref.):
– linear positions, velocities, & accelerations
Visual3D Signals
(Kinetic_Kinematic folder)
All computed
variables for
the left thigh
(LTH) are listed
Center of mass of
the total body
(Model) is
shown in table
of Data Values
Visual3D images
stick figures
skeletal images
geometric segments
Paths of CofG and CofP
yellow is path of centre of gravity,
blue is path of centre or pressure
FP4
FP3
FP2
FP1
Joint Angles
Joint Angles
Right Hip
13.1
Angle (degrees)
12.3
50.0
100.0
-29.7
0.0
Right Knee
11.4
-35.3
Legend
50.0
red =
flex./ext.
100.0
green =
ab./ad.
Left Knee
-51.9
-82.8
0.0
102.2
Left Hip
22.0
-54.6
0.0
Angle (degrees)
73.7
50.0
-115.1
100.0
Right Knee
100.8
43.6
-15.0
0.0
50.0
% cycle
University of Ottawa - Fencing Fleche
0.0
% cycle
Angle (degrees)
80.8
100.0
50.0
100.0
Left Ankle
38.8
-23.3
0.0
50.0
100.0
% cycle
page 9
blue =
int./ext.
rotation
Problem Data
• What factors are missing that prevent calculating
accurate kinematics from this 16mm cinefilm?
Problems
1. Only 1 view, yet “subject” moved obliquely
in film plane
2. No timing marks to ensure film speed
3. No vertical or horizontal reference
4.Conclusion:
No scale factorfilm is unanalyzable.
5. No markers on “subject”
6. Only one trial was filmed
7. No body weight measurements
8. No force platforms
9. Some body parts were hidden