2D AND 3D MOTION ANALYSIS
Name: Ilias Evdokimos Mystidis
Uco: 401509
Date: 3-12-2013
INTRODUCTION-AIM
The aim of this project is to calculate several parameters such as distace,time,speed and angles of a
particular sport of our choice. In order to be able to calculate-measure these parameters we will use
some computer programs and some simple mathematical equations. The sport that i have chosen for
this project is table tennis.
ANGLE
Cosine theorem: In any triangle ABC is:
a2 = b2 + c2 - 2bc cos a
b2 = a2 + c2 - 2ac cos b
c2 = a2 + b2 - 2ab cos g
the square of the triangle is equal to the sum of the squares of the other parties
reduced by twice the product of these parties and the cosine of the angle cordoned them.
Thus in order to calculate the angle i took 3 coordinates, 1-hand point, 2-elbow point and 3-shoulder
point.Then i used xcel program in order to find the value of the angles.
Point 1 Point 3 Point 1
x1 601 x1 424 x1 601
y1 452 y1 384 y1 452
Point 2 Point 2 Point 3
x2 428 x2 428 x2 424
y2 454 y2 454 y2 384
size 173,01156 size 70,1141926 size 189,61276
cos 2 = -0,046 cos 1 = 0,929 cos 3 = 0,411
2 = 92,61 1 = 21,68 3 = 65,71
control
180,00
Thus:
angle 1=21,68 ᵒ
angle 2=92,61ᵒ
angle 3=65,71ᵒ
HEIGHT
In order to find the height of the ball we need to know the height of the net and then by using om
formulas on the excel we can calculate the result.
distance
x y
Point1 779 442
Point2 779 356
d= 86,0 pixel 45,20 cm
1 pixel 0,52555 cm
calibration
x y
Point1 748 429
Point2 749 400
d= 29,0 pixlu 15,25 cm
Thus
Net=15,25 cm
Ball height=45,20 cm
DISTANCE
In order to calculate the distace that the ball reached from the raquet to the table we should know the
distace of the table –calibration factor , and then to use excel program using coordinates in order to
calculate it.
Table dimension =274 c m
distance
x y
Point1 389 455
Point2 701 391
d= 318,5 pixel 210,59 cm
1 pixel 0,661192 cm
calibration
x y
Point1 287 432
Point2 698 379
d= 414,4 pixlu 274 cm
Thus distance= 210,59cm
SPEED-TIME
In order to calculate the speed of the ball we must calculate the distance covered by the ball and the
time needed for the ball to land on the table.
time, speed
numer of frames
1 .1/25 0,04 s
0,04 speed
v=s/t 52,65
Thus
Time=0,04 s
Speed= 52,6 m/s -- 2,109/0,04=52,6 m/s