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.
- Define how to measure and calculate changes in angular position (angular displacement) and the time derivatives angular velocity and angular 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?
Photogrammetry
- Field of View
- Exposure Time
- Frame Rate
- Focus
- Depth of Field
- Aperture
- f-stop
- Focal Length
|
 |
| Standard Photographic Apertures, Exposure Times, and Film Speeds |
| APEX value |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Aperture (f-stop) |
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 one-half.
Each faster film speed requires half the amount of light that the previous speed needed for proper exposure.
|
Calibration
Two-Dimensional
- Scaling Rod
- s = actual length (m) / digitized length (pixels)
- x = su
- y = sv
- Fractional Linear Transformation (FLT)
Three-Dimensional
- Direct Linear Transformation (DLT)
LINEAR KINEMATICS
Distance:The length of a curve or line
Displacement: Change of position (Straight-line distance from start to finish)
Time Derivatives
- Speed: Distance / Time
- Velocity: Displacement / Time
- Acceleration: Velocity / Time
Check units on page 20 of your book.
In the lab:
- Capture video of someone jumping.
- Digitize the height of the hip.
- Export the data into Excel.
- Calculate velocity and acceleration from the vertical position data.
- Create graphs of position, velocity, and acceleration versus time.
Mini-Project #1
Signal Noise and Data Smoothing
What are the sources of error that may lead to a noisy signal?
Example with laser velocity data & Peak Motus
How do we determine the appropriate filter settings (Filtered Data, Power Sprectrum)?
Accelerometers
Accelerometers use the peizoelectric effect.
We can go from position to velocity to acceleration. Can we go from acceleration to velocity to position?
ANGULAR KINEMATICS
- Segment angles
- Angular conventions
- Discontinuity Problems
- Joint angles
Angular Time Derivatives
The Connection Between Angular and Linear Motion
- Linear velocity: vT = ω r
- Linear acceleration: aT = α r
- Centripetal acceleration: ar = ω2 r
Electrogoniometers
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