AUTOMA+`TED SEPAK TAKRAW BALL THROWING MECHANISM FOR
TRAINING
Tanakorn Tony Ontam
B. E., Khon Kaen University, 2000
B.S., California State University, Sacramento, 2008
THESIS
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
MECHANICAL ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
SUMMER
2010
AUTOMATED SEPAK TAKRAW BALL THROWING MECHANISM FOR
TRAINING
A Thesis
by
Tanakorn Tony Ontam
Approved by:
__________________________________, Committee Chair
Dr. Akihiko Kumagai
__________________________________, Second Reader
Dr. Yong Suh
______________________
Date
ii
Student: Tanakorn Tony Ontam
I certify that this student has met the requirements for format contained in the University
format manual, and that this thesis is suitable for shelving in the Library and credit is to
be awarded for the thesis.
________________________, Graduate Coordinator__________________
Dr. Kenneth Sprott
Date
Department of Mechanical Engineering
iii
Abstract
of
AUTOMATED SEPAK TAKRAW BALL THROWING MECHANISM FOR
TRAINING
by
Tanakorn Tony Ontam
This study of the first automated Sepak Takraw ball throwing mechanism presents the
design of a new mechanism which is able to generate common types of Sepak Takraw
ball motion. Sepak Takraw is a unique competitive ball sport where two teams of three
players kick the ball over a net with their feet. Kinematic data of ball motions were
acquired by measuring from actual Sepak Takraw games. Requirements of a Sepak
Takraw ball throwing mechanism were established and a prototype was designed,
manufactured and tested. Results showed that the Sepak Takraw ball throwing
mechanism is able to produce realistic Sepak Takraw ball motions and a reasonable
accuracy compared to expected projectile equations with a low standard deviation. The
mechanism can be used to help develop skills of Sepak Takraw players.
_____________________, Committee Chair
Dr. Akihiko Kumagai
____________________
Date
iv
ACKNOWLEDGMENTS
I would like to thank Dr. Akihiko Kumagai, the advisor of this thesis, for guiding
me throughout this study and the manufacturing process.
I would also like to thank Dr. Yong Suh who guided me in the designing process
using Pro/ENGINEER software.
I am thankful to staff and students who work at Engineering and Computer
Science (ECS) Tech Shop at California State University, Sacramento including Michael
Bell.
I am grateful to Wat Sacramento Buddhavanaram, USA Takraw Association, and
the U.S. Sepak Takraw team, who have been encouraging me to do this study. This work
would not have been possible without their support.
Special thanks to my family for their great support and encouragement.
v
TABLE OF CONTENTS
Page
Acknowledgments ...........................................................................................................v
List of Tables............................................................................................................... viii
List of Figures ............................................................................................................. viii
Chapter
1. INTRODUCTION .......................................................................................................1
2. OBJECTIVES .............................................................................................................9
3. METHODOLOGY AND DESIGN ............................................................................11
Kinematic Data ..........................................................................................................11
Design .......................................................................................................................17
Testing Validation .....................................................................................................31
4. RESULTS AND DISCUSSION.................................................................................37
Design Requirements Met ..........................................................................................37
Testing Results ..........................................................................................................39
5. CONCLUSION .........................................................................................................49
Improve Design/Future Study ....................................................................................49
Appendices ....................................................................................................................51
vi
Appendix A: Motor and Wheel Size Calculations for Ball Shooter ............................64
Appendix B: Projectile Calculations Using Wolfram Mathematica 7 .........................70
References ....................................................................................................................80
vii
LIST OF TABLES
Page
1. Table 3.1 Basic Kinematic Data of Four Movements in Sepak Takraw...............15
2. Table 4.1 The Suitable Tire Pressure of Wheels .................................................39
3. Table 4.2 The Suitable Gap Between Two Wheels .............................................40
4. Table 4.3 Maximum Range ................................................................................40
5. Table 4.4 Maximum Ball Velocity .....................................................................41
6. Table 4.5 Ball Feeder Efficiency at 6 Balls per Minute (10 Second Time Interval)
..........................................................................................................................41
7. Table 4.6 Standard Deviations, Average Length, and Number of Balls Missing
Target Area ........................................................................................................46
8. Table A.1 Ball Velocity of Four Movements Using a Speed Gun .......................52
9. Table A.2 Velocity of the Wheels and Velocity of the Balls Given Different RPM
..........................................................................................................................53
10. Table A.3 How Final Mechanism Met Design Requirements .............................55
11. Table A.4 Partial Automatic at 30 Degrees at a Launching Height of 3 Feet at 6
Second Time Interval (Tossing) .........................................................................56
12. Table A.5 Partial Automatic at 30 Degrees at a Launching Height of 3 Feet at 10
Second Time Interval (Tossing) .........................................................................57
13. Table A.6 Partial Automatic at 50 Degrees at a Launching Height of 3 Feet
(Tossing) ............................................................................................................59
14. Table A.7 Automatic Feed at 11.5 Degrees at a Launching Height of 6.5 Feet
(Serving & Spiking) ...........................................................................................60
viii
15. Table A.8 Automatic Feed at 11.5 Degrees at a Launching Height of 3.5 Feet
(Tossing) ..........................................................................................................62
16. Table A.9 Partial Automatic at 75 Degrees at a Launching Height of 2.5 Feet
(Setting) ...........................................................................................................63
ix
LIST OF FIGURES
Page
1. Figure 1.1 Dimensions of Official Sepak Takraw Court .......................................2
2. Figure 1.2 Sepak Takraw Game in Action. There Are Three Players on Each Side.
............................................................................................................................2
3. Figure 1.3 Test Ball. Sepak Takraw Ball Officially Approved by International
Sepak Takraw Federation (ISTAF) for Men’s Events ...........................................5
4. Figure 1.4 Four Main Types of Sepak Takraw Ball Movements Generated by
Athletes Include: a) Tossing b) Serving c) Setting and d) Spiking. .......................6
5. Figure 3.1 Illustration of Launching Point and Launching Angle of Sepak Takraw
Ball Movement in: a) Tossing b) Serving c) Setting d) Spiking ..........................13
6. Figure 3.2 Illustration of Projectile Motion.........................................................16
7. Figure 3.3 Block Diagram of Controllers ............................................................24
8. Figure 3.4 Pro/ENGINEER Computer Model of Sepak Takraw Ball Throwing
Mechanism Prototype Featuring Ball Shooter and Ball Feeder ...........................25
9. Figure 3.5 Pro/ENGINEER Computer Model of Sepak Takraw Ball Throwing
Mechanism Prototype Showing Ball Shooter......................................................26
10. Figure 3.6 Pro/ENGINEER Computer Model of Rotating Carousel Design Inside
Ball Feeder of Sepak Takraw Ball Throwing Mechanism. ..................................27
11. Figure 3.7 Base and Control Box of Sepak Takraw Ball Throwing Mechanism ..28
12. Figure 3.8 Ball Feeder, Ball Hopper and Ball Shooter of Sepak Takraw Ball
Throwing Mechanism ........................................................................................29
13. Figure 3.9 Ball Shooter and Telescopic Pole of Sepak Takraw Ball Throwing
Mechanism ........................................................................................................30
14. Figure 3.10 Ball Target Size Created in Pro/ENGINEER ...................................32
x
15. Figure 3.11 Experimental Set Up For Accuracy Testing of Ball Throwing
Mechanism. .......................................................................................................35
16. Figure 3.12 Flow Chart of Sepak Takraw Ball Throwing Mechanism.................36
17. Figure 4.1 Number of Balls Missing Target Based on Angle and Feeder Mode of
Mechanism ........................................................................................................46
18. Figure 4.2 Standard Deviation Based on Angle, Height, and Feeder Mode of
Mechanism ........................................................................................................46
19. Figure 4.3 Sepak Takraw Players Interacting with the Sepak Takraw Ball
Throwing Mechanism to Practice .......................................................................48
xi
1
Chapter 1
INTRODUCTION
The purpose of this thesis is to design a novel automated ball throwing
mechanism for training in the sport of Sepak Takraw. Sepak Takraw is a challenging,
point-based competitive team sport that is played both outdoors and indoors. The sport is
played by two opponent sides which have a 5.09 feet high net separating the court. The
court is the same size as a badminton court, which is 20 x 44 feet (Figure 1.1).
There are three players in a Sepak Takraw team, as seen in Figure 1.2. The sport
is similar to volleyball, except that the three players on each side cannot use their hands.
The game begins with one player tossing the ball by hand to the server (this is the only
time that hands are allowed in the game), then the server uses their foot to kick the ball
over the net (in Fig 1.1, the tosser is in position 1 and the server is in position 3). The
opponent side is then allowed to use any part of their body, except the arms, to make
contact with the ball and kick the ball over the net.
The rules of the game allow players to make contact to the ball up to three
consecutive times per side [1]. During the Sepak Takraw game, both teams will make
different powerful moves to kick and spike the ball to go to the opponent side and fall
within the boundary line of the court. See Fig. 1.1 for Sepak Takraw court dimensions, as
specified by the International Sepak Takraw Federation (ISTAF) [1].
2
Figure 1.1 Dimensions of Official Sepak Takraw Court
Figure 1.2 Sepak Takraw Game in Action. There Are Three Players on Each Side.
3
Although Sepak Takraw is a relatively new sport in the last thirty years in the
United States, the sport originated in Southeast Asia in the late 1500s. The sport is now
being played in many countries throughout the world, including the United States of
America, Canada, Brazil, India, China, Germany, Thailand, Malaysia, Switzerland,
Japan, and France, among other countries [1]. Sepak Takraw is also taught in schools and
universities in Physical Education and Kinesiology classes. There is a USA Takraw
Association, which is the organization that recruits players for the U.S. national team to
compete in the world championship. This world championship tournament includes both
men’s and women’s events, with teams participating from up to 30 countries. According
to USA Takraw Association’s website [2], the organization is trying to develop the sport
in this country by promoting Sepak Takraw through training, consulting, and hosting
tournaments around the country. It is clear that Sepak Takraw is a sport of growing
interest in the world market. In fact, Sepak Takraw is even featured in a new Nintendo
DS video game [3].
Although Sepak Takraw is a growing sport, there are a limited number of
advanced athletes and coaches available to train new players in the USA. Since the game
requires complex ball control skills, it is important for Sepak Takraw players to have
sufficient and thorough training. This training can be a time and labor-intensive process.
For example, during practice sessions, the U.S. national team members are trained by
coaches who use their labor and manual training techniques to generate a variety of ball
motion to train players. Manual training might involve throwing the balls by hand, or
4
hitting the balls with a wooden paddle to athletes for defense and offence drills. It is a
difficult and time consuming process because a Sepak Takraw coach’s arms will tire after
hitting 50 balls consecutively. For three hours per day of training sessions, a coach may
have to hit the ball repeatedly up to 300 times. In addition, the accuracy of humangenerated ball motion cannot be controlled, and this can effect development of athlete’s
kicking skills. Furthermore, kinematic data and analysis of this sport has not yet been
done to help Sepak Takraw athletes improve their skills.
One way to develop ball control and kicking skills and to address the other
training problems discussed above is to use an automated mechanism that generates
motion of the Sepak Takraw ball. Although there are ball throwing machines available
for other sports, such as baseball, volleyball, tennis, table tennis, and soccer, none of
these machines have been designed to specifically meet the needs of the unique sport of
Sepak Takraw. Sepak Takraw balls are very different in size, material, and structure from
others balls used in the sports described above. Sepak Takraw balls that are used to test in
this study are the official competition balls (Marathon Model MT 908) which are 0.39
pounds in weight. The balls have a hollow spherical shape 5 inches in diameter with
twelve pentagon-shaped holes around the ball surface (see Fig 1.3). The area of each hole
is 0.43 square inches. The ball is made from woven synthetic rattan material with a soft
rubber outer surface which has good bouncing characteristics and shock absorption [4].
5
diameter = 5 inches
Figure 1.3 Test Ball. Sepak Takraw Ball Officially Approved by International Sepak
Takraw Federation (ISTAF) for Men’s Events
Furthermore, the types of motion involved in Sepak Takraw, which can be
described as a unique blend of gymnastics, volleyball, soccer, hacky sack and martial
arts, are specific to the sport of Sepak Takraw [2]. See Figure 1.4 for the four main types
of ball motion generated in Sepak Takraw: tossing, serving, setting, and spiking. A ball
throwing mechanism that meets the unique motion and ball specifications of Sepak
Takraw doesn’t currently exist and needs to be developed and tested.
6
ө
ө
ө
ө
Figure 1.4 Four Main Types of Sepak Takraw Ball Movements Generated by Athletes
Include: a) Tossing b) Serving c) Setting and d) Spiking.
7
In order to find out what principles are used in other types of ball throwing
machines, research on the various types of commercially available ball machines was
done as a background of study. There are several ball throwing machines available on the
market. The most common principles involved with these machines are rotating lever
arm, propulsion system and two counter rotating wheels [5-6].
Furthermore, there are several studies of ball pitching machines [5-9], including
research that tested baseball pitching machines using different kinds of balls. These
studies showed that baseball pitching machines are being continuously improved to
imitate the desired motions of the baseballs. For example, Mish and Hubbard [5] found
that the pitching machine prototype that they studied could provide their required linear
and angular velocity of the ball with good accuracy and repeatable motions. Having a
machine throw balls to reproduce the throw of an adversary pitcher, can also be used to
improve batting technique of players [6]. Similarly, tennis serve simulation machines
have been developed and studied under repetitive and realistic serving conditions [9]. In
addition to baseball pitching and tennis serving machines, there are also commercial
mechanisms available for volleyball, football, cricket, and soccer ball throwing [10-12].
Currently there is no automatic training device for coaching and helping Sepak
Takraw players to improve their kicking skills commercially available on the market.
This study hopes to provide a new educational and training tool for youth and
professional Sepak Takraw players to practice repeatable drills and a variety of
8
movements to improve their ball control skills. Furthermore, the mechanism, along with
kinematic ball motion data, could be used to create Sepak Takraw training instructions
for schools as well as for amateur and professional athletes.
9
Chapter 2
OBJECTIVES
The objective of this thesis is to build a prototype of a Sepak Takraw ball
throwing mechanism to simulate different kinds of ball motion in the sport of Sepak
Takraw. The study will gather kinematic data for ball motion (for example, ball velocity
and ball launching position), which doesn’t currently exist for the sport of Sepak Takraw,
and then design an automated Sepak Takraw ball throwing device and prototype not yet
commercially available, to aid in the training of athletes to develop ball control skills.
The study and measurement of kinematic data of ball motion in actual performance of
Sepak Takraw players will inform the design of a machine that is both accurate and
capable of producing realistic ball motions in order to effectively train and challenge
players.
The mechanism will be operable using automated means, with little need for
human operation while the mechanism is launching the balls. According to the Longman
Advanced American Dictionary, automated means “using machines to do a job or
industrial process” [13]. With an automated Sepak Takraw ball throwing mechanism, the
goal is for the machine to help do the job of the coach or player, and for Sepak Takraw
players to potentially be able to practice by themselves the four main types of ball motion
generated in the sport, including tossing, serving, setting, and spiking (see Fig. 1.4). Or,
10
as one Sepak Takraw player summarized, “One machine, one man, four movements.”
[14].
The automated Sepak Takraw ball throwing mechanism will be designed to shoot
a variety of realistic ball motions over a range of velocities seen in the actual sport. The
use of this device in tests will provide experimental data to evaluate the performance of
the prototype.
Motion data will be compared between the automated mechanism
prototype and the expected results from mathematics equations.
Overview of This Thesis:
This thesis will detail and follow the design process of the automated Sepak
Takraw ball throwing mechanism. In Chapter 3, the detailed methodology, including
kinematic data used to inform the design, prototype design, and test set up process,
including the mathematical equations used, will be introduced and described. Chapter 4
will describe and evaluate the results of the final mechanism and experimental validation,
and include a discussion of these results. Chapter 5 will make conclusions as well as
recommendations for future study and expansion, followed by Appendices.
11
Chapter 3
METHODOLOGY AND DESIGN
The scope of this thesis includes gathering kinematic data on the types of ball
motion generated in Sepak Takraw and using this data and other research in order to
design and build a novel automated Sepak Takraw ball throwing mechanism to be used
for training athletes. The overall plan for the methodology and design of this study can be
described in three main parts:
1. Kinematic Data: Study and measure kinematic data of ball motion in actual
performance of Sepak Takraw players.
2. Design: Describe design specifications and requirements and generate computer
model of a prototype mechanism. Build, assemble and iteratively adjust prototype
to ensure mechanism is in working order.
3. Testing Validation: Generate projectile equations. Collect and compare ball
motion data generated by the prototype to the expected results to ensure machine
is capable of creating realistic Sepak Takraw ball motion.
Kinematic Data
In order to ensure that the ball throwing mechanism reproduces the actual ball
motion of Sepak Takraw players, kinematic data of ball motion in actual performance of
12
Sepak Takraw players was studied and measured by using a video camera and velocity
measuring devices at local Sepak Takraw games in Sacramento, California. The Sepak
Takraw players observed were intermediate in skill level; more advanced Sepak Takraw
players were not available locally for this study. The players’ heights ranged from 5 to 6
feet. A JVC digital video camera (Model: Everio, JVC, Japan) was used to record the
nature of the game and movements of the ball with actual Sepak Takraw players.
The videos collected from local Sepak Takraw games in Sacramento, California
were analyzed frame by frame for ball launching positions, launching angles, and
velocity. By studying videos of Sepak Takraw games, different moves that are used in the
game were found. There are four major movements that cause the ball to move in the air
during the Sepak Takraw game. Those four movements are: tossing, serving, setting and
spiking. Moreover, the position of a launching ball in reference to the ground as well as
the angle of the launching ball with respect to a horizontal plane were observed. The ball
releasing points vary depending on the height of the players, kicking skills and different
moves. See Fig. 3.1 for an illustration of some kinematics involved in the four main types
of ball motion observed in Sepak Takraw players: tossing, serving, setting, and spiking
respectively.
13
a)
c)
b)
d)
Figure 3.1 Illustration of Launching Point and Launching Angle of Sepak Takraw Ball
Movement in: a) Tossing b) Serving c) Setting d) Spiking
14
As seen in the above figure, the four movements can be described as follow:
•
Tossing: Ball is tossed by the tosser position (position 1 in Fig. 1.1) from 2-3 feet
high with a positive angle (+θ) in reference to the horizontal plane, to the server
position on the same side of the court.
•
Serving: Ball is kicked by the server (position 3 in Fig. 1.1) from 3-6 feet high
with a positive (+θ) or negative (-θ) angle in reference to the horizontal plane, to
the opposing side of the court.
•
Setting: Ball is kicked from 1.5-2.5 feet high with a positive angle (+θ) in
reference to the horizontal plane, to another player in the spiker position (position
2 in Fig. 1.1) on the same side of the court.
•
Spiking: Ball is spiked by spiker from 5-8 feet high with a positive angle (+θ) and
negative angle (-θ) in reference to the horizontal plane, over the net to the
opposing side of the court.
By observing the ball motion during the game it was also determined that the
Sepak Takraw ball can spin when it is kicked. There are two types of spin: top spin (ball
spins towards the same direction of ball travel) and under spin (ball spins in opposite
direction of ball travel). The ball spin characteristics vary by each movement. Table 3.1
details the ball spin characteristics, ball launching angle, ball travel distance, and ball
15
release height and end height for each of the four movements as acquired by analyzing
the video frame by frame.
Table 3.1 Basic Kinematic Data of Four Movements in Sepak Takraw
Movements
Ball position
(ft)
Releasing
End
height
height
Ball travel
distance (ft)
Ball launch
angle (degree)
min
max
min
max
Ball spin
characteristic
Top
Under
spin
spin
Tossing
2-3
3-6
12.2
16.2
0
60
No
Yes
Serving
3-6
3-6
13
36.7
-30
60
Yes
Yes
Setting
1.5-2.5
5-8
2
22
30
80
Yes
Yes
Spiking
5-8
5-8
5
44
-30
30
Yes
Yes
A Bushnell speed gun (Bushnell Speedster II Radar Gun Model #10-1900) was
used to measure the speeds of each of the four main ball moves that are generated in
Sepak Takraw games. The speed gun used a digital signal to capture the speed of the
moving Sepak Takraw ball. The speed gun provides accuracy at +/-1 mile per hour
(MPH) for measured speeds. The observer stood behind a Sepak Takraw player, aimed
the speed gun and pressed the trigger at the ball when the player released the ball (i.e.
tossed or kicked the ball). The speed gun was pointed to the ball in the same plane of ball
direction of travel. Table A.1 in the Appendix shows the ball velocities for tossing,
serving, setting and spiking motions. As seen in Table A.1, velocities of tossing and
setting were similar to each other, and they were lower in range than velocities of serving
and spiking. On the other hand, the velocities of serving and spiking were closer to each
16
other, but higher in value than tossing and setting velocities. Identifying the proper
velocities, angles, ranges of releasing heights, and types of motion seen in actual Sepak
Takraw games is important in determining the functional requirements needed for a
realistic ball throwing mechanism for Sepak Takraw.
The basic principles involved in each of the ball movements are based on
projectile motion. See Figure 3.2 for an illustration of projectile motion.
u
ө
y
h
x
Figure 3.2 Illustration of Projectile Motion
Knowing the basic kinematic data from the actual study of Sepak Takraw games
will help to determine the trajectory of the ball by using projectile principles. The
equations for calculating projectile motion are as follows:
y = h + (u sinθ) t – (gt2)/2
(3.1)
x= u (cosθ) t
(3.2)
17
The equation calculates the motion of the ball, where h is initial height, y is target
height, g is gravitational acceleration, t is time of flight, x is distance between releasing
point and target, u is initial velocity of the ball and θ is ball launching angle. The desired
end height to kick the balls is varied. Equations will be helpful to set up testing targets to
validate ball accuracy. Equations will be created with Wolfram Mathematica 7.0 [15].
Further detail on testing set up will be discussed later.
Design
The kinematic data from the previous section and requirements from the Sepak
Takraw players guided the design specification of the first prototype for the Sepak
Takraw ball throwing mechanism. Feedback from Sepak Takraw players in the USA was
also an important way to define requirements. In the USA, most Sepak Takraw games are
played outdoors and this prototype was designed to meet these conditions. To design a
ball throwing mechanism capable of being used for Sepak Takraw training it is important
that design specifications are identified.
18
Design Requirements
The prototype must be:
1) Portable: Transportable from one location to another location by vehicle.
2) Weight under 50 pounds: easy to take apart and assemble.
3) Partially Automatic: operating by itself or by using only a few controls.
4) Sufficient Ball Capacity: Able to contain up to 10 balls.
5) Battery powered: able to run the machine without electrical outlet.
6) Able to generate ball speeds from 10- 60 MPH.
7) Able to shoot the ball from 2-45 feet in distance.
8) Able to adjust ball release point from 2.5-8 feet high from the ground.
9) +/- 30 degree ball launching angle adjustable along a horizontal plane
10) +80 and -30 degree ball launching angle adjustable along a vertical plane.
11) Able to provide various time intervals of ball release: 6-10 balls/minute.
19
Principles and Design Overview
1. Ball Shooter
In reviewing the basic Sepak Takraw kinematics, a basic principle that needs to be
considered in the design of the Sepak Takraw ball throwing mechanism is projectile
motion. After observing Sepak Takraw ball motion in live matches and videos of the
games, observers also saw that the ball exhibits both translational and rotational motions.
The characteristic of these motions led to the decision to use the principle of the two
counter rotating wheels as the main ball shooter component of the mechanism. The two
wheels rotate in different directions, generating speed on the wheels’ surface which
imparts speed on a ball propelled between these wheels. Equation 3.3 is used to calculate
velocity of the wheel’s surface (v) where ω is angular velocity (rpm) of the wheel and
is radius of the wheel.
v= ω
(3.3)
According to Mish and Hubbard [5], the following equation can be used to
calculate ball linear velocity (
( and
) based on the velocities of the two points of contact
) between the wheels and the ball:
= ( + )/2
(3.4)
20
Table A.2 in the Appendix shows velocity of the wheels and velocity of the balls
given different RPM.
A spin may also be produced when the two wheels spin at different speeds. This
spin is imparted about an axis which is perpendicular to the ball linear velocity vector,
; the following equation [5] can be used to calculate the magnitude of this spin based
on the two linear velocities and
, radius of the ball:
ω = ( - )/2
(3.5)
The radius of the Sepak Takraw test ball is 2.5 inches. As seen in Table 3.1,
several Sepak Takraw movements impart spin on the ball; to create this type of spinning
ball motion using the Sepak Takraw ball throwing mechanism, the counter rotating
wheels need to spin at two different speeds; if the top wheel spins faster than the bottom
wheel it will create a top spin on the ball. On the other hand if the bottom wheel spins
faster than the top wheel, the ball will produce an under spin.
Since the Sepak Takraw ball is hollow with 12 holes around its synthetic rubber
surface, the two counter rotating wheels need to provide some cushion of the ball to help
propel the ball out; furthermore a hard solid wheel could break the ball; thus pneumatic
rubber wheels were selected as the wheel type so that the air pressure could cushion the
ball and help avoid ball damage. The two rubber wheels selected for the ball shooter were
9 inches in diameter and 1.5 inches in width. The diameter was based on the wheel
21
calculations found in Appendix A. The wheel surface is black, grooved and curved. The
two wheels should have a gap size between them that is a little less than the diameter of
the Sepak Takraw ball (5 inches) to allow for the wheels to press the ball out when it is
received in between the two wheels.
Since the mechanism must be portable, a 12 volt rechargeable battery (Fisher
Price, 12 V Power Wheels Battery, 9.5 Ah) was selected as the power source. The two
wheels are driven by two separate DC motors connected to this battery. See Appendix A
for the motor calculations used to determine the size of the motor that is suitable to
produce the required ball speeds of up to 60 miles per hour. The revolutions per minute
for a suitable motor to generate ball speed at 60 MPH is 3360 RPM (see Appendix A for
motor calculations). The motor commercially available that best meets these
requirements is the Protech DC motor (Protech 1/7 HP 12 VDC 3785 RPM PM Motor).
This motor has amperage of 13.1 amps and voltage 12 DC, with a speed of 3785 RPM.
Because the design requirements specify the need to adjust the launching angle
along a vertical plane, the mechanism of a rotating fixed axis between the frame and the
ball shooter was applied.
Changing the launching angle is important because the
different Sepak Takraw movements, such as serving and setting, depend on a variety of
angles, as seen in Table 3.1. This mechanism also allows horizontal angle adjustment.
This horizontal angle changing feature is mounted to a U shaped base which freely moves
along a vertical axis.
22
2. Ball Feeder
Since the mechanism must provide Sepak Takraw balls to the ball shooter
automatically, a ball feeder component was designed. The ball feeder needed to vary the
individual drop rate of balls by set time intervals. The design of the ball feeder also
needed to meet the size requirements of the Sepak Takraw ball, and hold a capacity of 10
balls at the smallest feeder size possible. Based on the principle of uniform rotation, a
rotating carousel was used as the mechanism to transport single balls in different time
intervals to the ball shooter. This component is what automatically rotates and drops the
Sepak Takraw balls at regular intervals (i.e. every 10 seconds) to the ball shooter. The
carousel is designed to hold four balls per rotation about a fixed axis, and consists of four
ball pockets; each pocket is 5.5 inches in diameter to allow the closest fit of the balls and
thus the most compact size.
The ball feeder also consists of a ball hopper where the balls are inserted into a
basket, with a diameter of 20 inches at the top and a diameter of 6 inches at the bottom, to
allow the balls to drop into the carousel one at a time. The rotating carousel is driven by
an 18.33 RPM 12 VDC Gear Motor with running torque 35 in-lb, amperage of 1.5 amps
and 12 volt DC. This motor was selected based on carousel motor calculations as seen in
Appendix A. The ball feeder can be taken apart from the ball shooter for ease of
transportation of the mechanism and for flexibility in using the mechanism.
23
3. Control box
Controllers are needed to switch the motors on, change the speed, and set ball
release time intervals. The mechanism design should be as simple as possible using only
a few controls. Three MX033 DC motor speed controls were selected for the mechanism
– two to control the ball shooter motor and one to control the ball feeder motor. These
controllers met the specifications for the motors used in the ball feeder and ball shooter,
and feature 12 VDC, 15 amp max, and Pulse with Modulation (PWM). In order to vary
the time interval of the ball release from the ball feeder, the DC motor speed controller is
used to modify time intervals of dropping balls in the ball feeder. Similarly the
controllers for the ball shooter are used to change the motor speed of the ball shooter and
in turn impact the launch speed of the ball. The three speed controllers are housed in a
control box with speed dials controlling their range. See Figure 3.3 for a block diagram of
the motor speed controllers for the Sepak Takraw ball throwing mechanism.
24
Figure 3.3 Block Diagram of Controllers
4. Base
Since the mechanism must be portable and needs to hold steady while the balls
are released, the base was designed with four lockable caster wheels that can swivel at
full 360 degrees of rotation. The top of the base is a 2.5 inch steel square tube 10 inches
in length, with four different holes along the length of the tube. The height can be
adjusted by lifting and placing a telescopic pole into the tube and inserting a bolt into the
hole to support the bottom of the telescopic pole. The telescopic adjustable pole is
attached to the base to further adjust the height of the mechanism, allowing for the range
of required ball releasing heights as seen in Table 3.1.
25
A computer model of the prototype mechanism was designed using
Pro/ENGINEER Schools Edition software which provides 3D design functions. See
Figures 3.4, 3.5, and 3.6 for Pro/ENGINEER software screenshots of the computer
drawings of the prototype design, featuring the ball feeder and ball shooter.
Figure 3.4 Pro/ENGINEER Computer Model of Sepak Takraw Ball Throwing
Mechanism Prototype Featuring Ball Shooter and Ball Feeder
26
Figure 3.5 Pro/ENGINEER Computer Model of Sepak Takraw Ball Throwing
Mechanism Prototype Showing Ball Shooter
27
Figure 3.6 Pro/ENGINEER Computer Model of Rotating Carousel Design Inside Ball
Feeder of Sepak Takraw Ball Throwing Mechanism.
The design of the prototype included detailed computer models, followed by
manufacturing and assembly. Fabrication was performed in the ECS Tech Shop at
California State University, Sacramento. Figures 3.7, 3.8 and 3.9, respectively, show
photographs of the automated Sepak Takraw ball shooting mechanism built, including the
base and control box, ball feeder, and ball shooter.
28
control box
base
Figure 3.7 Base and Control Box of Sepak Takraw Ball Throwing Mechanism
29
ball hopper
ball feeder
ball shooter
Figure 3.8 Ball Feeder, Ball Hopper and Ball Shooter of Sepak Takraw Ball Throwing
Mechanism
30
ball shooter
telescopic pole
Figure 3.9 Ball Shooter and Telescopic Pole of Sepak Takraw Ball Throwing Mechanism
31
Testing Validation
In order to test the accuracy of the machine in shooting out balls and the ability to
reproduce ball motion seen in Sepak Takraw, the following procedure was used:
1. Projectile equations:
Projectile equations were calculated by using Wolfram Mathematica (see
Appendix B), to predict the ball motion to simulate the motion of various moves involved
in a Sepak Takraw game. See Equations 3.1 and 3.2 for the projectile formulas. The
equations will help test the machine if it meets the predicted values. Figure 3.11
represents the experimental set up used to validate the accuracy of the ball throwing
mechanism in generating projectile motion that compares to these equations.
2. Set up target:
After the projectile equations were generated using the given data, the equation
should be able predict the target position. A target was created and placed on a stand
along the trajectory line of the ball. The target size was 25 inches in diameter (see Figure
3.10 below). The size of the ball (5 inches in diameter, represented by pink zone in Fig.
3.10) determined the target size. Ideally the ball should land within 7.5 inches of the
target (represented by the red and pink zones in Fig. 3.10), which is two ball widths away
from the center of the target. Landing in this zone will help to ensure that the player can
receive the ball to make effective movements.
32
Figure 3.10 Ball Target Size Created in Pro/ENGINEER
3. Set up mechanism:
After the target is set up, the mechanism will need to be set up based on the
projectile equations generated in Mathematica (see Appendix B). First, place the
mechanism at specified distance (x) with the ball shooter in line with the target. Second,
adjust the initial launching height (h) of the ball shooter. Third, adjust the launching angle
(θ). The angle of each test is set up by using an angle finder (Swanson, Magnetic C Angle
Finder) on the ball shooter between the two counter rotating wheels at the releasing point.
Fourth, adjust the initial speed (u) for the ball shooter by changing the RPM of the top
and bottom counter rotating wheels. A digital photo tachometer (DT-2234C+) is used to
measure the RPM of the counter rotating wheels. A speed gun is used to measure the ball
33
velocity. The basic experimental set up can be illustrated in Figure 3.11. See Appendix B
for details for each test’s projectile calculations. A video camera was placed behind the
ball throwing mechanism to observe if the machine replicates the ball motion and to
assist with data gathering. The following tests were set up:
•
Partial automatic at 30 degrees at a launching height of 3 feet at 6 second time
interval (tossing)
•
Partial automatic at 30 degrees at a launching height of 3 feet at 10 second time
interval (tossing)
•
Partial automatic at 50 degrees at a launching height of 3 feet (tossing)
•
Automatic feed at 11.5 degrees at a launching height of 6.5 feet (serving &
spiking)
•
Automatic feed at 11.5 degrees at a launching height of 3.5 feet (tossing)
•
Partial automatic at 75 degrees at a launching height of 2.5 feet (setting)
4. Insert ball into mechanism:
There are two ways to insert a ball into the ball shooter mechanism. See Fig. 3.12.
First, the ball can be inserted by ball feeder (automated). The ball will be placed into the
34
hopper by a human and then fall into the rotating carousel and dropped by gravity at the
bottom of the ball feeder into the ball shooter.
Second, the ball can be inserted into the mechanism by a human placing the ball
into the ball shooter directly (partial automated). A wood lever can be used by a human to
direct the ball into the ball shooter to keep the insert consistent.
5. Record ball position:
Record the location where the ball hit the target. The observer used a marking
pencil to mark the position where the ball places on the 25 inch diameter target area.
6. Repeat for consistency:
Repeat 50 times for each test to ensure a sufficient sample size and increase
precision in estimates.
35
ball
ball throwing mechanism
video
camera
target
initial height
target stand
target height
target distance
Figure 3.11 Experimental Set Up For Accuracy Testing of Ball Throwing Mechanism.
Not to Scale.
36
Figure 3.12 Flow Chart of Sepak Takraw Ball Throwing Mechanism
37
Chapter 4
RESULTS AND DISCUSSION
Design Requirements Met
After design and testing, the design requirements were reviewed and showed that
the Sepak Takraw ball throwing machine is capable of meeting 10 out of 11 design
requirements. See Table A.3 in the Appendix for details on how the mechanism met the
requirements. In summary, the final Sepak Takraw ball throwing mechanism was:
•
portable and fit in a car.
•
partially automatic for the ball shooter, automated for the ball feeder.
•
sufficient in ball capacity, fitting up to 10 balls.
•
battery powered.
•
able to generate ball speeds from 10-53 mph.
•
able to shoot the ball from 2-45 feet in distance.
•
able to adjust ball release point from 2.5-8 feet high from the ground.
•
+/- 30 degree ball launching angle adjustable along a horizontal plane
•
+80 and -30 degree angle adjustable along a vertical plane.
•
able to generate various time intervals of ball release.
38
The only one design requirement that wasn’t met was the weight of the machine
(lighter than 50 pounds). This requirement wasn’t met because the researcher selected the
material of steel for the ball shooter and adjustable pole parts of the prototype design due
to cost and experience of the researcher in working with the material. In the future, more
lightweight materials such as aluminum might be considered for the ball shooter to
minimize weight. Also some of the steel parts could be cut into smaller, lighter sizes with
more time and availability of the machine shop. The ball feeder was made out of wood,
which may have added weight. This material was picked due to availability of tools for
cutting and researcher experience using the tools. The researcher chose wood since it was
easier to cut into shape needed for the feeder box. In future designs, plastic could be used
to decrease weight of the ball feeder.
The manufacturing process took longer compared to the other process in this
study due to lack of tools, limited hours of the ECS Tech Shop, limited equipment,
limited tool experience, and other challenges of the hands-on manufacturing process for
the researcher. During the manufacturing process, the design was iteratively adapted to
ensure the machine worked in the desired way. For example, connecting the motor shaft
to the counter rotating wheels of the ball shooter and getting the wheels to spin without
vibration was a big challenge because the shaft was designed to be supported on one side
of the wheel. For future designs, the motor axis support must be more balanced with the
wheels and the shaft should be supported on both sides of the wheels to ensure stability
and increase performance and accuracy of the mechanism.
39
Overall the mechanism met the needs of Sepak Takraw players. The Sepak
Takraw ball throwing mechanism as designed can generate the tossing, serving, setting
and spiking ball motions which are needed to practice the unique sport of Sepak Takraw.
Testing Results
The following tests were done prior to the accuracy testing to determine suitable
pressure for the wheels, gap between the wheels, maximum velocity, maximum range,
and time interval of ball release to produce the most efficient ball motion.
Table 4.1 The Suitable Tire Pressure of Wheels
Tire
pressure
(psi)
10
15
20
Launching
angle
(degree)
45
45
45
45
45
45
45
45
45
Initial speed
(mph)
Spin/
No spin
Distance
(ft)
20
20
20
20
20
20
20
20
20
spin
spin
spin
spin
spin
spin
spin
spin
spin
41
38
45.4
41.3
47
45.5
38.5
36.7
39.5
Average
distance
(ft)
41.47
44.60
38.23
40
The most suitable pressure of the two tires was 15 psi, which propelled the ball to
the longest average distance, 44.60 feet. Thus the rest of the tests used this tire pressure.
Table 4.2 The Suitable Gap Between Two Wheels
Wheel gap
(inch)
4.5
4.75
Tire pressure
(psi)
Initial speed
(mph)
Spin/
No spin
Distance
(ft)
15
15
15
15
15
15
20
20
20
20
20
20
spin
spin
spin
spin
spin
spin
43.5
37
40
18.5
27
20.5
Average
distance
(ft)
40.17
22.00
The most suitable gap between two wheels was 4.5 inches, which shot the ball the
longer average distance, 40.17 feet, compared to a gap at 4.75 inches, which only shot the
ball to 22.0 feet.
Table 4.3 Maximum Range
Tire
pressure
(psi)
15
Launching
angle
(degree)
45
45
Initial speed
(mph)
Spin/No
spin
Distance
(ft)
Average
distance
(ft)
49
49
spin
spin
45.75
44
44.88
The maximum range found when tested at a 45 degree launching angle was 45.75
feet.
41
Table 4.4 Maximum Ball Velocity
Ball release point (ft)
Launching angle (degree)
5
0
Maximum ball velocity
(mph)
53
The maximum ball velocity recorded was 53 miles per hour.
Table 4.5 Ball Feeder Efficiency at 6 Balls per Minute (10 Second Time Interval)
Ball total
50
Number of balls passed
through
48
Number of balls stuck
2
At a feeding rate of 6 balls per minute, 48 out of 50 balls passed through the
rotating carousel of the ball feeder, which is 96% feeding efficiency.
42
The researcher used Wolfram Mathematica 7 as a tool to calculate projectile
equations used to predict target height for given angles and initial heights. Six tests
representing the various types of movements found in Sepak Takraw were done to
validate the accuracy of the ball motion generated by the mechanism. The experiment
showed that the Sepak Takraw ball throwing mechanism could meet the targets of
projectile equations by having reasonable standard deviation from calculated results.
The standard deviation method and equation were used to justify the accuracy of the
mechanism based on average length from target. The equation for standard deviation is as
follows:
(3.5)
σ: standard deviation
x: individual sample
: average
N: number of samples
As discussed in the methodology section, a 7.5 inch radius is acceptable distance
from the center of the target. The test results can show accuracy and consistency of the
ball motion generated by the throwing mechanism by using average values of the ball
43
distance from the target and standard deviation.
If the number for standard deviation is high it shows that the distribution of the
average values of the ball accuracy testing is spread all over and inconsistent. On the
other hand if the standard deviation is low then the results are close to the average values
and accuracy is consistent and acceptable. Assuming normal distribution of data (i.e. bell
curve), the standard deviation method [16] can be used to validate the expected landing
position of the balls in relation to the target. Using average length ( ) plus or minus
three standard deviation (σ) units, the lowest and highest lengths from the target can be
calculated, and 99.73% of all balls shot should fall within that range. In other words, 99
out of 100 balls will fall within the expected range.
The Tables with results of the standard deviation accuracy tests can be found in
the Appendix in Tables A.4, A.5, A.6, A.7, A.8 and A.9.
The first two projectile
accuracy tests, seen in Tables A.4 and A.5, were run to establish the best time interval to
use for the rest of the projectile accuracy tests. See Tables A.4 and A.5 for the standard
deviations for the tests for the following conditions:
•
30 degrees at 20 mph at 6 second time interval
•
30 degrees at 20 mph at 10 second time interval
According to the results of the tests, the machine performed better at the 10
second time interval (6 balls per minute) set up compared to the 6 second time interval
(10 balls per minute). This can be demonstrated by a lower standard deviation and
44
average value of length from target for the 10 second time interval (σ = 3.29 and 6.79
inches respectively) as compared to the 6 second time interval (σ = 4.67 and 8.3 inches
respectively). Assuming normal distribution, we can expect that 99.73% of the balls shot
to the target will fall within plus and minus three standard deviation (3σ) units of the
average length from the target, or within a range of 0 to 16.66 inches and 0 to 22.3 inches
for the 10 second time intervals and the 6 second time intervals, respectively. These
results are acceptable for professional players who have more kicking skills and are able
to kick the ball at 2-3 times the ideal range (7.5 inches). The results show that the 10
second time interval has a smaller average range compared to the 6 second time interval.
In addition, the 10 second time interval had fewer errors (2 out of 50 throws) compared to
the 6 second time interval (19 out of 50 throws) with the same experimental conditions.
Thus it was determined that the rest of the tests would be run using the 10 second time
interval. The researcher found that the 10 second time interval worked better and this
may be because the motor needs more recovery time to get speed back after a ball is
ejected from the two wheels.
Tables A.6, A.7, A.8 and A.9 outline the results of tests for the following
conditions:
•
50 degrees at 16 mph at 10 second time interval at initial height of 3 feet
•
11.5 degrees at 20 mph at 10 second time interval at initial height of 3.5 feet
•
11.5 degrees at 21 mph at 10 second time interval at initial height of 6.5 feet
•
75 degrees at 18 mph at 10 second time interval at initial height of 2.5 feet
45
Table 4.6 shows the standard deviations, average length from the target, range
based on plus and minus three standard deviations, and number of balls missing the target
area for those four tests. As seen in Table 4.6, the tests showed that lower ball launching
angles had a lower average length and standard deviation than the higher angles. Overall,
the results for standard deviation seen in Table 4.6 are acceptable for professional who
can kick the ball at double the ideal range (7.5 inches). In addition, the number of balls
missing the target were lower for the lower angles than the higher angles. See Figures
4.1 and 4.2 for bar graphs of these comparisons. Moreover, the standard deviation and
average lengths from the target of the balls dropped by automatic ball feeder mechanism
were lower compared to the results for balls using partial auto mode. This may be due to
the error from the human feeding the ball in partial auto mode.
46
Table 4.6 Standard Deviations, Average Length, and Number of Balls Missing Target
Area
Angle (˚)
Standard
deviation (σ)
11.5 (auto ball feeder,
3.5 ft)
11.5 (auto ball feeder,
6.5 ft)
50 (partial auto – 3 ft)
75 (partial auto – 2.5
ft)
Number of
balls missing
target area
4
3σ
(inch)
2.51
Average length
from target,
(inch)
5.93
2.36
6.99
14
14.07
2.93
2.65
7.81
8.95
18
28
16.6
16.9
30
25
20
15
10
5
0
13.46
11.5° (auto ball feeder, 3.5 ft)
11.5° (auto ball feeder, 6.5 ft)
50° (partial auto, 3 ft)
75° (partial auto, 2.5 ft)
number of balls that missed target
Figure 4.1 Number of Balls Missing Target Based on Angle and Feeder Mode of
Mechanism
3
11.5 ° (auto ball feeder, 3.5 ft)
2.5
2
11.5 °(auto ball feeder, 6.5 ft)
1.5
1
50 ° (partial auto, 3 ft)
0.5
75 ° (partial auto, 2.5 ft)
0
standard deviation
Figure 4.2 Standard Deviation Based on Angle, Height, and Feeder Mode of Mechanism
47
The causes of the variations may have been from:
•
Human – in partial auto mode (at angles above 11.5 degrees), the human pushed
the ball into the ball shooter using a wood lever
•
Machine – wheels’ vibration, wheel surface not flat, contact area, etc.
•
Measurement – since a human had to measure the distance from the target and
mark when the ball hit the target
•
Wheel surface - the contacting area between the wheels and the ball, since the
wheels are in a curve shape
•
Windy conditions – the conditions were windy on the day of the testing
•
Battery ran out of power - when the battery was low, the speed of the motor was
low too, and that reduced the ball speed
•
Drag force – drag force was neglected in the projectile equation motion analysis
•
Method – initial speed of the ball thrown may not have been the initial speed
when we used the speed gun
Even though there were some issues, overall when using the mechanism for
training, Sepak Takraw players were excited with the results of the first Sepak Takraw
ball throwing mechanism and the motions that could be created to do different moves. A
video screenshot of Sepak Takraw players testing the machine is found in Figure 4.3.
48
Figure 4.3 Sepak Takraw Players Interacting with the Sepak Takraw Ball Throwing
Mechanism to Practice
Feedback of Sepak Takraw players after trying the machine was positive. For
example, one player said that the machine can help him improve his kicking skills. In a
short period of time he said he was able to kick so many balls and the mechanism could
shoot the balls both to repeating spots and also randomly to challenge him. Another
player mentioned that when he practiced kicking the ball after it was served by the
mechanism, he felt like he received the Sepak Takraw ball from a professional player
because the ball was fast and had spin.
49
Chapter 5
CONCLUSION
The objective to build the first prototype for a Sepak Takraw ball throwing
mechanism was met. Results showed that the new Sepak Takraw ball throwing
mechanism is capable of recreating realistic Sepak Takraw ball motion and can even be
used by one person. Accuracy of the ball motion generated by the mechanism was
validated. The study also aimed to gather kinematic data that doesn’t currently exist for
the sport of Sepak Takraw, and the study met this objective.
The kinematic data and the principles used in this study can be useful for
research. Since an engineering study about Sepak Takraw has never been done before,
this study can be used as base standard information for future reference for others
interested in this kind of ball motion, ball mechanism, and the study of developing
kicking skills in Sepak Takraw.
Improve Design/Future Study
Since the maximum angle that can be used on automatic ball feeder mode is only
11.5 degrees, for future study, researcher needs to insert a part such as a counter weight
lever that can automatically push the ball in between the two counter rotating wheels.
This would allow more automated movement for all angles by not requiring "gravity" to
drop the balls from the ball feeder into the ball shooter. In addition, for serving and
50
spiking ball throwing, which are at heights of 5-8 feet tall, the mechanism’s ball hopper is
too tall for loading the balls into the feeder. In the future, ball feeder feeding efficiency
can also be improved by ensuring stability of the rotating carousel. For the adjustable
height telescopic pole, there can be an improvement by developing the pulley system to
make it easier to adjust the height of ball release.
Also, as mentioned earlier there needs to be better motor shaft support since now
it's only attached to one side of the wheel, and this can cause vibration on wheels.
Another improvement on the wheels would be to change the color of the wheels to a light
color, to avoid marking on the Sepak Takraw ball surface. In addition, increase the width
of the two counter rotating wheels and contact area of the ball to increase the area of
friction and grip needed to increase consistency to shoot the ball out of the ball shooter.
In the future prototype the researcher could also work with Sepak Takraw coaches
to create user training and a user manual on how to use the Sepak Takraw ball throwing
mechanism to improve athlete’s skills.
51
Appendices
52
Table A.1 Ball Velocity of Four Movements Using a Speed Gun
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Average
Tossing
11
12
13
10
Ball velocity (mph)
Serving
Setting
28
10
32
14
36
13
33
11
Spiking
34
36
36
30
10
12
12
12
13
12
14
13
12
15
13
12
13
10
15
13
14
13
12
12
13
34
31
30
32
34
28
25
26
26
25
24
17
18
31
26
28
27
28
25
24
25
11
12
14
15
12
14
13
16
15
14
13
12
14
15
13
14
16
14
12
15
13
26
23
28
21
28
30
35
32
30
30
37
37
40
31
44
42
27
31
33
44
40
12.62
26.86
13.67
32.81
53
Table A.2 Velocity of the Wheels and Velocity of the Balls Given Different RPM
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
ω1
(rpm)
300
350
400
450
500
550
600
650
700
750
800
850
900
950
1000
1050
1100
1150
1200
1250
1300
1350
1400
1450
1500
1550
1600
1650
1700
1750
1800
1850
1900
1950
ω2
r1 (in) v1 (in/s) (rpm) r2 (in) v2 (in/s) vball (in/s)
4.5
141.3
300
4.5
141.3
141.3
4.5
164.85
350
4.5
164.85
164.85
4.5
188.4
400
4.5
188.4
188.4
4.5
211.95
450
4.5
211.95
211.95
4.5
235.5
500
4.5
235.5
235.5
4.5
259.05
550
4.5
259.05
259.05
4.5
282.6
600
4.5
282.6
282.6
4.5
306.15
650
4.5
306.15
306.15
4.5
329.7
700
4.5
329.7
329.7
4.5
353.25
750
4.5
353.25
353.25
4.5
376.8
800
4.5
376.8
376.8
4.5
400.35
850
4.5
400.35
400.35
4.5
423.9
900
4.5
423.9
423.9
4.5
447.45
950
4.5
447.45
447.45
4.5
471
1000
4.5
471
471
4.5
494.55 1050
4.5
494.55
494.55
4.5
518.1
1100
4.5
518.1
518.1
4.5
541.65 1150
4.5
541.65
541.65
4.5
565.2
1200
4.5
565.2
565.2
4.5
588.75 1250
4.5
588.75
588.75
4.5
612.3
1300
4.5
612.3
612.3
4.5
635.85 1350
4.5
635.85
635.85
4.5
659.4
1400
4.5
659.4
659.4
4.5
682.95 1450
4.5
682.95
682.95
4.5
706.5
1500
4.5
706.5
706.5
4.5
730.05 1550
4.5
730.05
730.05
4.5
753.6
1600
4.5
753.6
753.6
4.5
777.15 1650
4.5
777.15
777.15
4.5
800.7
1700
4.5
800.7
800.7
4.5
824.25 1750
4.5
824.25
824.25
4.5
847.8
1800
4.5
847.8
847.8
4.5
871.35 1850
4.5
871.35
871.35
4.5
894.9
1900
4.5
894.9
894.9
4.5
918.45 1950
4.5
918.45
918.45
vball
(mph)
8.03
9.37
10.70
12.04
13.38
14.72
16.06
17.39
18.73
20.07
21.41
22.75
24.09
25.42
26.76
28.10
29.44
30.78
32.11
33.45
34.79
36.13
37.47
38.80
40.14
41.48
42.82
44.16
45.49
46.83
48.17
49.51
50.85
52.18
54
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
ω1
(rpm)
2000
2050
2100
2150
2200
2250
2300
2350
2400
2450
2500
2550
2600
2650
2700
2750
2800
2850
2900
2950
3000
3050
3100
3150
3200
3250
3300
3350
3400
3450
3500
3550
3600
3650
3700
3750
3800
r1 (in)
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.50
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
v1 (in/s)
942
965.55
989.1
1012.65
1036.2
1059.75
1083.3
1106.85
1130.4
1153.95
1177.5
1201.05
1224.6
1248.15
1271.7
1295.25
1318.8
1342.35
1365.9
1389.45
1413.00
1436.55
1460.1
1483.65
1507.2
1530.75
1554.3
1577.85
1601.4
1624.95
1648.5
1672.05
1695.6
1719.15
1742.7
1766.25
1789.8
ω2
(rpm) r2 (in)
2000
4.5
2050
4.5
2100
4.5
2150
4.5
2200
4.5
2250
4.5
2300
4.5
2350
4.5
2400
4.5
2450
4.5
2500
4.5
2550
4.5
2600
4.5
2650
4.5
2700
4.5
2750
4.5
2800
4.5
2850
4.5
2900
4.5
2950
4.5
3000 4.50
3050
4.5
3100
4.5
3150
4.5
3200
4.5
3250
4.5
3300
4.5
3350
4.5
3400
4.5
3450
4.5
3500
4.5
3550
4.5
3600
4.5
3650
4.5
3700
4.5
3750
4.5
3800
4.5
v2 (in/s) vball (in/s)
942
942
965.55
965.55
989.1
989.1
1012.65
1012.65
1036.2
1036.2
1059.75
1059.75
1083.3
1083.3
1106.85
1106.85
1130.4
1130.4
1153.95
1153.95
1177.5
1177.5
1201.05
1201.05
1224.6
1224.6
1248.15
1248.15
1271.7
1271.7
1295.25
1295.25
1318.8
1318.8
1342.35
1342.35
1365.9
1365.9
1389.45
1389.45
1413.00
1413.00
1436.55
1436.55
1460.1
1460.1
1483.65
1483.65
1507.2
1507.2
1530.75
1530.75
1554.3
1554.3
1577.85
1577.85
1601.4
1601.4
1624.95
1624.95
1648.5
1648.5
1672.05
1672.05
1695.6
1695.6
1719.15
1719.15
1742.7
1742.7
1766.25
1766.25
1789.8
1789.8
vball
(mph)
53.52
54.86
56.20
57.54
58.87
60.21
61.55
62.89
64.23
65.57
66.90
68.24
69.58
70.92
72.26
73.59
74.93
76.27
77.61
78.95
80.28
81.62
82.96
84.30
85.64
86.97
88.31
89.65
90.99
92.33
93.66
95.00
96.34
97.68
99.02
100.35
101.69
55
Table A.3 How Final Mechanism Met Design Requirements
Design Requirements
1
2
3
4
5
6
7
8
9
10
11
Portable: Transportable from one
location to another location by
vehicle.
Weight under 50 pounds: easy to
take apart and assemble.
Partially Automatic: operating by
itself or by using only a few
controls.
Sufficient Ball Capacity: Able to
contain up to 10 balls.
Battery powered: able to run the
machine without electrical outlet.
Able to generate ball speeds from
10- 60 MPH.
Able to shoot the ball from 2-45
feet in distance.
Able to adjust ball release point
from 2.5-8 feet high from the
ground.
+/- 30 degree ball launching angle
adjustable along a horizontal
plane
+80 and -30 degree angle
adjustable along a vertical plane.
Able to generate various time
intervals of ball release.
Design



How did the mechanism meet the
requirements
Transported machine in medium
sized car
Did not meet but each component
weighs under 50 pounds and
mechanism can be taken apart.
Ball feeder is automatic and
mechanism only has 3 controls.

Able to hold 10 balls at a time.

Used 12 Volt rechargeable
battery power.
Speeds up to 53 MPH were
observed using a speed gun.
Ball distances up to 45 feet were
observed.
Ball release points found at these
heights using telescopic
adjustable pole.
Used four swivel wheels to adjust
horizontal rotation.






Tilted ball shooter to adjust
vertical angles.
Ball release time intervals of 6
seconds and 10 seconds were
observed.
56
Table A.4 Partial Automatic at 30 Degrees at a Launching Height of 3 Feet at 6 Second
Time Interval (Tossing)
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Average
Length from target (in)
4
4.5
2.5
5.5
4.25
3.75
5.25
0.5
11
5.25
2.5
12
11.5
12.5
10.5
6
5.5
17
1
9.5
12
9.75
11.5
8.5
22
9.5
8.5
9.5
12.5
6.5
12.5
8.30
x-xbar
-4.31
-3.81
-5.81
-2.81
-4.06
-4.56
-3.06
-7.81
2.69
-3.06
-5.81
3.69
3.19
4.19
2.19
-2.31
-2.81
8.69
-7.31
1.19
3.69
1.44
3.19
0.19
13.69
1.19
0.19
1.19
4.19
-1.81
4.19
sum =
σ=
(x-xbar)^2
18.5761
14.5161
33.7561
7.8961
16.4836
20.7936
9.3636
60.9961
7.2361
9.3636
33.7561
13.6161
10.1761
17.5561
4.7961
5.3361
7.8961
75.5161
53.4361
1.4161
13.6161
2.0736
10.1761
0.0361
187.4161
1.4161
0.0361
1.4161
17.5561
3.2761
17.5561
677.0566
4.67
57
Table A.5 Partial Automatic at 30 Degrees at a Launching Height of 3 Feet at 10 Second
Time Interval (Tossing)
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Length from target (in)
6.5
2
4
11.25
11.25
9.25
9.75
1.5
6
2.25
9.75
11
11.5
8.75
8
11.5
11
8.5
11.5
12
11
9
7.5
9.5
5
6
9.25
5.5
2.25
11.75
4
2.5
6.5
5.25
3.5
x-xbar
-0.29
-4.79
-2.79
4.46
4.46
2.46
2.96
-5.29
-0.79
-4.54
2.96
4.21
4.71
1.96
1.21
4.71
4.21
1.71
4.71
5.21
4.21
2.21
0.71
2.71
-1.79
-0.79
2.46
-1.29
-4.54
4.96
-2.79
-4.29
-0.29
-1.54
-3.29
(x-xbar)^2
0.0841
22.9441
7.7841
19.8916
19.8916
6.0516
8.7616
27.9841
0.6241
20.6116
8.7616
17.7241
22.1841
3.8416
1.4641
22.1841
17.7241
2.9241
22.1841
27.1441
17.7241
4.8841
0.5041
7.3441
3.2041
0.6241
6.0516
1.6641
20.6116
24.6016
7.7841
18.4041
0.0841
2.3716
10.8241
58
No.
36
37
38
39
40
41
42
43
44
45
46
47
48
Average
Length from target (in)
5
6
2.5
2.5
4.5
9.75
4.5
5
2.5
3.5
7
3
4.5
6.79
x-xbar
-1.79
-0.79
-4.29
-4.29
-2.29
2.96
-2.29
-1.79
-4.29
-3.29
0.21
-3.79
-2.29
sum =
σ=
(x-xbar)^2
3.2041
0.6241
18.4041
18.4041
5.2441
8.7616
5.2441
3.2041
18.4041
10.8241
0.0441
14.3641
5.2441
519.4168
3.29
59
Table A.6 Partial Automatic at 50 Degrees at a Launching Height of 3 Feet (Tossing)
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Average
Length from Target (in)
9.5
6
6
2
9.5
7.5
7.25
6
9.5
11.75
11
10
10.05
10.25
5
5.25
12
11
12
10.25
9
10
5
5.5
4.5
2.5
2.25
7
6
12
6
8.5
7.81
x-xbar
1.69
-1.81
-1.81
-5.81
1.69
-0.31
-0.56
-1.81
1.69
3.94
3.19
2.19
2.24
2.44
-2.81
-2.56
4.19
3.19
4.19
2.44
1.19
2.19
-2.81
-2.31
-3.31
-5.31
-5.56
-0.81
-1.81
4.19
-1.81
0.69
sum =
σ=
(x-xbar)^2
2.8561
3.2761
3.2761
33.7561
2.8561
0.0961
0.3136
3.2761
2.8561
15.5236
10.1761
4.7961
5.0176
5.9536
7.8961
6.5536
17.5561
10.1761
17.5561
5.9536
1.4161
4.7961
7.8961
5.3361
10.9561
28.1961
30.9136
0.6561
3.2761
17.5561
3.2761
0.4761
274.4717
2.93
60
Table A.7 Automatic Feed at 11.5 Degrees at a Launching Height of 6.5 Feet (Serving &
Spiking)
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Length from Target (in)
6
8
5.5
7
6
4
7.5
3.25
3.5
3.5
4
2
6
4.5
6
10.5
3
4.5
7.75
10
11
11
8
3.25
2
10
10.5
5
7
8.5
3.75
7
8.5
4
x-xbar
0.07
2.07
-0.43
1.07
0.07
-1.93
1.57
-2.68
-2.43
-2.43
-1.93
-3.93
0.07
-1.43
0.07
4.57
-2.93
-1.43
1.82
4.07
5.07
5.07
2.07
-2.68
-3.93
4.07
4.57
-0.93
1.07
2.57
-2.18
1.07
2.57
-1.93
(x-xbar)^2
0.0049
4.2849
0.1849
1.1449
0.0049
3.7249
2.4649
7.1824
5.9049
5.9049
3.7249
15.4449
0.0049
2.0449
0.0049
20.8849
8.5849
2.0449
3.3124
16.5649
25.7049
25.7049
4.2849
7.1824
15.4449
16.5649
20.8849
0.8649
1.1449
6.6049
4.7524
1.1449
6.6049
3.7249
61
No.
35
36
37
38
39
40
41
42
43
44
45
46
Average
Length from Target (in)
8.25
6
4.5
3
6
3.5
8.5
5.25
3.5
3.5
4.5
4.5
5.93
x-xbar
2.32
0.07
-1.43
-2.93
0.07
-2.43
2.57
-0.68
-2.43
-2.43
-1.43
-1.43
sum =
σ=
(x-xbar)^2
5.3824
0.0049
2.0449
8.5849
0.0049
5.9049
6.6049
0.4624
5.9049
5.9049
2.0449
2.0449
288.9304
2.51
62
Table A.8 Automatic Feed at 11.5 Degrees at a Launching Height of 3.5 Feet (Tossing)
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Average
Length from Target (in)
6
9
6
6
5
8.5
7.25
4
7
11
4.5
11
8.5
4
4.5
6
3.5
4.5
8
6
8.5
2.75
12
8
5
5.5
7
6.75
4
7
11.5
9
10
8.5
9
7
6.99
x-xbar
-0.99
2.01
-0.99
-0.99
-1.99
1.51
0.26
-2.99
0.01
4.01
-2.49
4.01
1.51
-2.99
-2.49
-0.99
-3.49
-2.49
1.01
-0.99
1.51
-4.24
5.01
1.01
-1.99
-1.49
0.01
-0.24
-2.99
0.01
4.51
2.01
3.01
1.51
2.01
0.01
sum =
σ=
(x-xbar)^2
0.9801
4.0401
0.9801
0.9801
3.9601
2.2801
0.0676
8.9401
1E-04
16.0801
6.2001
16.0801
2.2801
8.9401
6.2001
0.9801
12.1801
6.2001
1.0201
0.9801
2.2801
17.9776
25.1001
1.0201
3.9601
2.2201
1E-04
0.0576
8.9401
1E-04
20.3401
4.0401
9.0601
2.2801
4.0401
1E-04
200.6861
2.36
63
Table A.9 Partial Automatic at 75 Degrees at a Launching Height of 2.5 Feet (Setting)
No.
1
2
3
4
5
7
8
9
10
11
12
13
14
16
17
18
19
20
21
22
Length from Target (in)
11
5.5
4
9.5
11.25
11
6.5
2.5
10
12
9.5
6
8.5
7.5
10
12
5
11
11
8
x-xbar
2.05
-3.45
-4.95
0.55
2.3
2.05
-2.45
-6.45
1.05
3.05
0.55
-2.95
-0.45
-1.45
1.05
3.05
-3.95
2.05
2.05
-0.95
(x-xbar)^2
4.2025
11.9025
24.5025
0.3025
5.29
4.2025
6.0025
41.6025
1.1025
9.3025
0.3025
8.7025
0.2025
2.1025
1.1025
9.3025
15.6025
4.2025
4.2025
0.9025
Average
8.59
sum =
σ=
155.0375
2.65
64
Appendix A
Motor and Wheel Size Calculations for Ball Shooter
Assumptions:
1) Ejecting 10 balls/minute
2) Maximum ball velocity is 60 MPH or 26.8 m/s
3) Powered by 12 volt battery
Given:
1) Ball mass is 177 grams or 0.39 lb
2) Shooting wheel diameter is 9 inches or 0.2286 m
3) Shooting wheel mass is 0.5 kg or 1.1 lbs
Free body diagram:
65
Solution
=(
r=
)/2
=
=
v = ωr
r = 4.5 in or 0.1143 m
ω=
= 234.5 rad/s
Convert to RPM:
= 37.32 revolutions/second
= 37.32∗60 revolutions/minute
= 2240 RPM
Motor without load requires RPM = 2,240
Assume that safety factor of load acting on motor shaft is 1.5.
∴ Suitable motor to generate ball speed at 60 mph is:
= 2240*1.5
= 3360 RPM or 351.8 rad/s
66
Calculate amount of kinetic energy for ejecting the ball at 60 MPH:
= m
= (0.177 kg)
= 63.56 J
Power to eject 10 balls per minute:
P1 = (
)/t
= 10* 63.56 J
= 635.6 J/min
=
J/s
P1 = 10.6 watts
There are two flywheels, so each wheel takes
∴one flywheel needs power of 5.3 watts
Energy stored in a shooting wheel:
= I
67
I= m
∴
= (0.5 kg)
= 0.00326 kg.
= I
=
(0.00326)
= 201.73 J
Power needed to store enough energy to eject 10 balls per minute (P2):
P2= (10*201.73 J)/ 60s
P2= 33.62 watt
= P1+P2
5.3 + 33.62 = 38.92 watt or 0.052 hp
Assume that the safety factor is 3
∴
= 3*0.52 = 0.156 hp
∴ Motor specifications needed for shooting balls at 60 MPH and 10 balls per minute are:
0.156 hp with 3360 rpm
68
Motor calculations for carousel of ball feeder
Assumptions:
1) The slowest ball feeding rate is every 10 seconds (6 balls/min) or 1.5 RPM. The
maximum ball feeding rate needed is 6 seconds (10 balls/min) or 2.5 RPM.
2) A maximum of 10 balls are contained in the ball feeder, and 4 balls can be contained
in the carousel at a time.
3) Time required for carousel to reach the desired angular velocity from resting position
is 0- 0.2 seconds (after turning on the switch).
4) Powered by 12 volt battery
Given:
1) Ball mass is 177 grams, or 0.39 lbs
2) Carousel diameter is16 inches, 5 inches thick
3) Carousel mass is 0.55 lbs
4) There are 4 ball pockets in the carousel, at 90 degree angles to each other (Figure 3.6)
Solution
69
)
= Angular acceleration (rad/ )
Moment of inertia of solid disk is m
I= (0.55+(4
when r=radius of the disk
))
I=67.52 lb.
1.5 RPM = 0.157 rad/s
=
.157 0.2 rad/
= 0.785 rad/
= 67.52 0.785
= 53 lb.in
Safety factor = 1.5
The desired motor should have torque that falls within the range of 53 to 79.5 lb.in and
provides at least 2.5 RPM.
70
Appendix B
Projectile Calculations Using Wolfram Mathematica 7
In[1]:=
In[2]:=
In[4]:=
Out[4]=
71
In[5]:=
In[6]:=
Out[6]=
In[7]:=
Out[7]=
Created with Wolfram Mathematica 7.0
72
In[44]:=
In[45]:=
In[11]:=
In[47]:=
Out[47]=
73
In[48]:=
In[50]:=
Out[50]=
In[51]:=
Out[51]=
Created with Wolfram Mathematica 7.0
74
75
Created with Wolfram Mathematica 7.0
76
In[59]:=
In[60]:=
In[11]:=
In[63]:=
Out[63]=
77
In[64]:=
In[65]:=
Out[65]=
In[66]:=
Out[66]=
Created with Wolfram Mathematica 7.0
78
In[67]:=
In[68]:=
In[11]:=
In[75]:=
Out[75]=
79
In[72]:=
In[73]:=
Out[73]=
In[74]:=
Out[74]=
Created with Wolfram Mathematica 7.0
80
References
[1] International Sepak Takraw Federation, “Laws of the Game SepakTakraw” in The
24th King’s Cup Sepaktakraw World Championship 2009 Program, Bangkok,
Thailand, July 2-7, 2009.
[2] USA Takraw Association [Online], Available: http://www.takrawusa.com.
[3] Hudson Soft Co. Ltd., “Deca Sports DS” Video Game, Nintendo DS, 2009.
[4] B. Lorhpipat and B. Lorpipatana, “Mkv Takraw Ball,” Patent No. 20070254754,
Patented Date November 1, 2007, U.S. Patent and Trademark Office.
[5] S.P. Mish and M. Hubbard, "Design of a full degree-of-freedom baseball pitching
machine” in Sports Engineering, vol. 4, pp.123-133, 2001.
[6] S. Sakai, J. Oda, S. Yonemura, K. Kawata, S. Horikawa, and H. Yamamoto,
“Research on the development of baseball pitching machine” in Journal of System
Design and Dynamics, vol. 1 no. 4, pp. 682-690, 2007.
[7] S. Daigh, Shooting device for free-surface impact studies, Bachelor of Science Thesis,
Massachusetts Institute of Technology, 2004.
[8] L.W. Alaways, Aerodynamics of the curve-ball: an investigation of the effects of
angular velocity on baseball trajectories, PhD Dissertation. University of
California, Davis, 1998.
[9] J. Kotze and S.R. Mitchell, “A tennis serve impact simulation machine” in The
Engineering of Sport 4, pp. 477-484, 2002.
[10] Sports Attack [Online]. Available: http://www.sportsattack.com.
81
[11] S. Morgan and D. Reese, “Ball Throwing Machine Useful in Practicing the Game of
Volleyball,” Patent No. 4254755, Patented Date March 10, 1981, U.S. Patent and
Trademark Office.
[12] S.S. Roy, S. Karmakar, N.P. Mukherjee, U. Nandy, and U. Datta, “Design and
development of indigenous cricket bowling machine” in Journal of Scientific &
Industrial Research, vol. 65, pp. 148-152, 2006.
[13] Pearson Education Limited, “Automated Definition”, in Longman Advanced
American Dictionary, p. 78, 2005.
[14] T.T. Ontam (private communication), 2010.
[15] Wolfram, Mathematica 7.0 [software]. Champaign, IL: Wolfram Research, Inc.,
2010.
[16] A. Kumagai, “Control Charts and Machine Capability” Handout, from Department
of Mechanical Engineering, California State University, Sacramento, Received
May 13, 2010.