EXSC 662 - Mechanical Analysis of Activity
Brigham Young University
Chapter 1 - Objectives

 

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

 

Calibration

Two-Dimensional



LINEAR KINEMATICS

Distance:The length of a curve or line

Displacement: Change of position (Straight-line distance from start to finish)

Time Derivatives


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)

  • xcm = xproximal + length% (xdistal - xproximal)
  • ycm = yproximal + length% (ydistal - yproximal)

 

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 three-dimensional data from multiple two-dimensional images.

  • For camera 1, we can obtain two equations relating to the three-dimensional 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 three-dimensional 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
    • F-stop
  • 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
  • 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.

 

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