Chapter 1  Objectives
 Examine how to describe a body's position
 Define how to determine the number of independent quantities (called degrees of freedom) necessary to describe a point or a body in space
 Define how to measure and calculate changes in linear position (displacement) and the time derivatives velocity and acceleration.
 Describe how to present the results of a kinematic analysis
 Explain how to directly measure position, velocity, and acceleration by using motion capture systems or transducers
DESCRIPTION OF POSITION
Is a runner 60 m from the start or 40 m from the finish?
Line up on the 20 yd line.
What is the position of my knee?
x, y, z, θx, θy, and θz
 How many camera views are needed to obtain x, y data?
 How many camera views are needed to obtain x, y, z data?
 How many points are needed to obtain θx, θy, and θz?
Calibration
TwoDimensional
 Scaling Rod
 s = actual length (m) / digitized length (pixels)
 x = su
 y = sv
 Practice with Dartfish
LINEAR KINEMATICS
Distance:The length of a curve or line
Displacement: Change of position (Straightline distance from start to finish)
Time Derivatives
 Speed: Distance / Time
 Velocity: Displacement / Time
 Acceleration: Velocity / Time
PROJECTILE MOTION
A Projectile is any body that has been set on its path by some force and continues in motion by its own inertia. (Gravity has a major effect on motion).
Examples of Projectiles include: Arrow, Basketball, Shotput, Human Body,Tigers
Let's begin simply with purely vertical motion
Now let's add horizontal motion
Horizontal and vertical components are independent
Equations of motion for projectiles
Characteristics of projectiles
Demonstration on what happens as initial conditions are altered
Another projectile cartoon
Practice Question:
Initial Velocity of Projectile
V = 20 m/s
at 27 degrees
from a height of 5m 
Flight Time = ?
Maximum Height = ?
Horizontal Displacement = ? 
Shot Put Example
METHODS FOR MEASURING AND ESTIMATING BODY SEGMENT PARAMETERS
 Cadaver studies
 Mathematical modeling
 Scanning and imaging techniques
 Kinematic studies
Segment mass = mass% (total mass)
Segment center of mass = proximal + length% (distal  proximal)
 x_{cm} = x_{proximal} + length% (x_{distal}  x_{proximal})
 y_{cm} = y_{proximal} + length% (y_{distal}  y_{proximal})
Calculating center of mass in a person
Practice calculating the center of mass in this situation
Moment of Inertia
Stability
Center of mass while airborne
ANGULAR MOTION
Online Book chapters 8 and 9
DIRECT LINEAR TRANSFORMATION
A procedure for generating threedimensional data from multiple twodimensional images.
 For camera 1, we can obtain two equations relating to the threedimensional object space.
 The L's represent camera constants (DLT parameters). In order to find out the values for the camera constants, we must have at least 11 unique equations. If we film enough points in the object space from at least two unique camera views, we can accomplish this.
 Typically, at least two cameras are used with at least 8 "control points" in the field of view.
 What is the minimum number of control points to solve the 11 camera constants?
 What is the benefit to using additional control points and camera views?
 Once the camera constants are solved, other objects in the object space can be filmed and threedimensional coordinates (x, y, z) can be determined.

 What is the minimum number of cameras to solve for x, y, and z?
 What is the benefit to using additional camera views?
Objectives: Cameras and optics
 Demonstrate an understanding of (and how they interact with each other)
 Depth of field
 Exposure time
 Shutter speed
 Frame rate
 Aperture
 Fstop
 Demonstrate an understanding of how video information is stored
 Demonstrate how to adjust the above characteristics on typical digital video cameras
Photogrammetry
 Field of View
 Exposure Time
 Frame Rate
 Focus
 Depth of Field
 Aperture
 fstop
 Focal Length
Standard Photographic Apertures, Exposure Times, and Film Speeds 
APEX value 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Aperture (fstop) 
1 
1.4 
2 
2.8 
4 
5.6 
8 
11 
16 
22 
32 
Exposure time (s) 
1 
1/2 
1/4 
1/8 
1/15 
1/30 
1/60 
1/125 
1/250 
1/500 
1/1000 
Film Speed (ISO or ASA) 
3 
6 
12 
25 
50 
100 
200 
400 
800 
1600 
3200 
APEX stands for the Additive Photographic Exposure System. Each increase in APEX value indicates a decrease in the light level by onehalf.
Each faster film speed requires half the amount of light that the previous speed needed for proper exposure. 
Demonstrations
 Motion Blur
 Field of View and Aperture
Binary Data
00000000 = 0 00000001 = 1 00000010 = 2 00000011 = 3 00000100 = 4 00000101 = 5
11111111 = 255
Photoshop Example of RGB data
640x480
 Data rate of 25Mbps = 3.125MB/s
 1 frame of video = 720 x 480 = 345,600 pixels
 30 frames of video per second
 60 fields of video per second
 This would be 345,600 pixels (8 bytes x 3 colors) x 30 frames = 248Mbps = 31 MB/s
HD 1080i
 1920x1080
 2,073,600 pixels (8 bytes x 3 colors) x 30 frames = 1492.99 Mbps = 186.6 MB/s
Ultra HD 4320p
 7680x4320
 33,177,600 pixels (8 bytes x 3 colors) x 60 frames = 47775.7 Mbps = 5971.97 MB/s
SD Cards
 Class 2  2 MB/s
 Class 4  4 MB/s
 Class 6  6 MB/s
 Class 10  10 MB/s
SPREADSHEETS
Ball toss
Ball toss filtered
Butterworth filter
Giant Swing
Giant swing with macro
Text file
Survey Calibration