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All Theses and Dissertations
1971-5 A Study in the Design and Development of a Baseball Pitching Machine Neal M. Lundwall Brigham Young University - Provo
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BYU ScholarsArchive Citation Lundwall, Neal M., "A Study in the Design and Development of a Baseball Pitching Machine" (1971). All Theses and Dissertations. 7152. https://scholarsarchive.byu.edu/etd/7152
This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. 0 0 v 1. A STUDY IN THE DESIGN AND DEVELOPMENT
OF A BASEBALL PITCHING MACHINE
A Thesis
Presented to the
Department of Mechanical Engineering
Brigham Young University
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
by
Neal M. Lundwall
May 1971 This thesis, by Neal M. Lundwall, is accepted in its present form by the Department of Mechanical Engineering of Brigham Young
University as satisfying the thesis requirement for the degree of
Master of Science.
1121 Date ' ACKNOWLEDGMENT
The author wishes to express his appreciation to Dr. Richard
D. Ulrich for his many hours of counsel and assistance. Also, to
William 0. Hayes for his skill and assistance in the construction of the pilot model.
Sincere thanks is expressed to ray parents for their help and encouragement throughout the time spent on this thesis.
iii TABLE OF CONTENTS
ACKNOWLEDGMENT...... iii
LIST OF F I G U R E S ...... v
LIST OF T A B L E S ...... viii
Chapter
I. INTRODUCTION...... 1
Currently Available Machines Objectives
II. DESIGN ALTERNATIVES AND CHOICE OF A DESIGN ...... 5
Ball Accelerators Ball Spinners
III. THEORY AND DESIGN OF THE MACHINE CO M P O N E N T S ...... 11
The Impactor The Injector Assembly The Friction Spinner
IV. DEVELOPMENT AND IMPROVEMENTS...... 33
V. TESTING PROCEDURES AND R E SULTS...... 44
VI. RECOMMENDATIONS AND CONCLUSIONS ...... 51
Recommendations Conclusions
APPENDIX A - CONSIDERATIONS IN THE SELECTION AND DESIGN OF BASEBALL A C CELERATORS...... 54
APPENDIX B - PHYSICAL AND OPERATIONAL CHARACTERISTICS OF THE IMPACTOR...... 59
APPENDIX C - NOMENCLATURE...... 66
APPENDIX D - DATA ...... 69
iv LIST OF FIGURES
Figure Page
1. Currently available pitching machine ...... 2
2. Currently available pitching machine ...... 3
3. Air p i s t o n ...... 5
4. Four bar linkage...... 6
5. System without b a l l ...... 6
6. System with b a l l ...... 7
7. Impact or ...... 7
8. Mechanical ball spinner ...... 8
9. Friction ball spinner ...... 8
10. Impactor and friction spinner ...... 9
11. Impactor operation...... 10
12. Basic machine design ...... 10
13. Center of percussion...... 11
14. Impactor consisting of two b o d i e s ...... 13
15. The forces at point 0 after the imp a c t...... 13
16. Velocity of the ball before and after imp a c t...... 14
17. Size of impactor verses ball v e l o c i t y ...... 16
18. Impactor h e a d ...... 17
19. The completed impactor assembly ...... 18
20. Method of i n j e c t i o n ...... 20
21. Injection p a t h ...... 21
22. Synchronizer...... 23
23. Connection with the tension w i r e ...... 24
v 24. Cyclic movement of the synchronizer ...... 25
25. The friction s p i n n e r ...... 26
26. Analysis of the friction s p i n n e r ...... 27
27. The completed friction spinner ...... 31
28. The completed pilot m o d e l ...... 32
29. The four positions of the synchronizer...... 32
30. Impactor h e a d s ...... 34
31. Extrusion of rubber from h u b ...... 34
32. Redesign of the h u b ...... 35
33. Escape behavior...... 36
34. Probable position of ball at imp a c t...... 36
35. Damper mounted on injector ...... 37
36. Injector showing path of i n j e c t i o n ...... 38
37. Variations in direction after impact ...... 40
38. Impactor after a ball j a m m e d ...... 42
39. Injector without the tube ...... 42
40. Overhead injector ...... 42
41. The final i n j e c t o r ...... 42
42. The friction s p i n n e r ...... 42
43. The m o v i e ...... 42
44. The final pitching machine ...... 43
45. Canvas target with dispersion pattern ...... 44
46. Four orientations of the b a l l ...... 45
47. Consequence of the variation ...... 50
48. Impact against rubber cushion ...... 56
49. Impact against solid w a l l ...... 57
50. Impactor arm ...... 59
vi 51. Movement capabilities of the impactor a r m ...... 60
52. Impactor operation ...... 64
vii LIST OF TABLES
Table Page
1. Variances of the leather balls along the horizontal axis. . . 47
2. Variances of the leather balls along the vertical axis. .. . 47
3. Variances of both balls along the horizontal a x i s ...... 48
4. Variances of both balls along the vertical a x i s ...... 48
5. Leather covered b a l l s ...... 49
6. Leather and rubber covered balls ...... 49
7. Acceleration force and horsepower ...... 54
8. Coefficient of restitution ...... 55
9. Energy of impact...... 56
viii CHAPTER I
INTRODUCTION
Throughout history man has had the need of services which re quire great skill or tremendous strength or delicate consistency on the part of those who perform. Much of the time he has turned to the machine to accomplish these requirements.
Baseball pitching is a great skill or may even be called an art as there are few among the many who have an interest in the sport who can produce the desired effect with consistency over an extended period of time.
For this reason there are many who saw a need for a machine that had an ability to provide with consistency the skill of a great baseball pitcher. It was the purpose of this thesis to investigate, design and develop a machine which approached as closely as possible this goal.
Currently Available Machines
A brief survey of current commercial pitching machines showed that there are few choices available.
The design in figure la is probably the most commonly found design among those who use pitching machines. The machine throws the ball with a mechanical arm. As shown in figure lb, the flexible cable
A is in tension. An external force F rotates the arm assembly B in a counterclockwise direction until the cable A passes over the center of
1 2 rotation 0. At this time the force in the cable rotates the arm assem bly rapidly, accelerating the ball. The ball leaves the arm due to the centrifugal force.
This design is relatively inexpensive and is capable of high velocities. It currently sells for approximately $300.00 depending upon the model and can throw the straight fast ball up to 100 miles per hour. It is unable, however, to throw any type of curve ball.
Figure 1.— Currently available pitching machine
Another available design is capable of throwing curve balls in any direction and at speeds up to 120 miles per hour. It is shown in figure 2. It consists of two rotating rubber wheels which may operate at different angular velocities. The baseball rolls between the two wheels.
The machine is reported to be quite accurate, delivering 99 per cent in the strike zone. It is, however, relatively large and is currently priced at over twice the price of the previous pitching machine. 3
Figure 2.— Currently available pitching machine
Objectives
The design objectives of this thesis were:
1. To investigate various methods and devices to accelerate a baseball to velocities similar to those used in major league pitching, and also to investigate methods of imparting spin to the pitched ball.
2. To design and build a pitching machine that will deliver baseballs at speeds up to 132 feet per second and that will impart rotation to the baseball so as to produce the curve ball in any dir ection, including the fast ball and the knuckle ball (no rotation).
3. To test the machine for the above requirements and for repeatability.
4. To make a study of the flight of the ball as affected by several variables including the angular velocity of the ball, the for- 4 ward velocity of the ball, and the angle of the spin axis.
5. To use devices which may be produced with the lowest pos sible economic investment. CHAPTER II
DESIGN ALTERNATIVES AND CHOICE OF A DESIGN
Several designs were investigated and compared for size and weight, ease of construction, simplicity, and cost. Following is a list of some of the designs. First is a description of devices used to accelerate a baseball. Second is a description of devices used to apply spin or angular rotation to a baseball.
Ball Accelerators
Air Piston
The ball is accelerated linearly in the direction of the arrow by the force of an air piston.
Cylinder
Figure 3.— Air piston
5 Four Bar Linkage
The ball is accelerated linearly by a four bar linkage. By placing the ball holder at Ball's point on link C of a four bar rock er linkage, the ball holder will travel in almost a straight line as the links of the mechanism move. Thus, as link A rotates counter- clockwise, the ball holder B moves linearly from position 1 to po sition 2.(Figure 4)
Figure 4.— Four bar linkage
Resonating Accelerator
The ball is accelerated linearly by a resonating spring-mass system. If the holder A is without the ball, the resonating frequency of the spring-mass system is much higher than that of the driving force F. Therefore, the displacement of A is very small.(Figure 5)
Figure 5.— System without ball 7
If a ball Is added to A, Its mass Is Increased and the reson ating frequency of the system becomes the same as that of the driving force F. The displacement and velocity of the ball consequently become very great.(Figure 6) The ball is then released from A at the point of greatest forward velocity.
F
Figure 6.— System with ball
Impactor
The ball is accelerated by the impact of a rotating mass.
(Figure 7)
o
c )
Figure 7.— Impactor 8
Ball Spinners
Mechanical Spinner
The baseball is held between cup shaped holders which rotate
to spin the ball and separate to release the ball.(Figure 8)
Figure 8.— Mechanical ball spinner
Friction Spinner
The baseball slips between two surfaces each of which has a different coefficient of friction. The ball will tend to slip easier on one surface than the other and consequently will rotate.(Figure 9)
Figure 9.— Friction ball spinner
Because of its simplicity and small size, the impactor design was chosen as a ball accelerator for the pitching machine. Again, because of simplicity and the fact that there are no moving parts, the 9 friction spinner was chosen to apply ball spin.(Figure 10)
Friction Spinner / \ \ / \ V Impactor
Figure 10.— Impactor and friction spinner
Considering the operation of these components of the pitching machine, there became two possibilities for meeting the correct con ditions for impact:
1. The ball may be properly positioned in the path of the impactor. At the desired time of impact, the impactor may be ac celerated from rest at point A to a predetermined velocity at point
B where the impact will occur.(Figure 11a)
2. The impactor may rotate continuously at a fixed velocity.
At the desired time of impact, the ball may be synchronously placed into the path of the impactor.(Figure lib)
The second possibility was chosen for the design of the pitch ing machine. Thus, energy for the impact is stored in the rotating hammer, eliminating any need for external storage of energy which is quite often necessary for quick release mechanisms and which often requires the use of mechanical reducers. 10
Consequently, the basic design of the pitching machine became as shown in figure 12. It consisted of three major subdivisions:
1. The Impactor- a rotating hammer with power supply.
2. The Injector Assembly- a mechanism to inject the ball into the path of the impactor and a mechanism to synchronize the injection of the ball with the movement of the hammer.
3. The Friction Spinner- two surfaces, each of which has a different coefficient of friction and between which the moving ball slips.
Figure 12.— Basic machine design CHAPTER III
THEORY AND DESIGN OF THE MACHINE COMPONENTS
The Impactor
For any rotating rigid body used as an impactor, it is desir able that the force F of the impact be through the center of percus sion P.(Figure 13a) Thus, there will be no reactionary forces at the pivot point 0. If the impact were to take place through any other point than the center of percussion there would be reactionary forces at 0.
Figure 13.— Center of percussion
However, if the rigid body must rotate continuously about 0, it must have a counterbalance B.(Figure 13b) By adding this counter balance, the center of gravity is moved to 0.
Unfortunately, for any rigid body rotating about its center of gravity, its center of gravity is its center of percussion, also.
11 12
Thus, if it is desirable that there be no forces through the shaft of rotation^, it is necessary that the baseball impactor not be a rigid body. Rather, it must be two bodies, which pivot relative to each other at point Q.(Figure 14a) 2 In rotation , the centers of gravity and of each body and the common pivot Q will lie on a straight line G^— Q— G^. If body 2 is the heavier of the two and symmetrical about the line Q— G^, then the center of gravity 0 of the two bodies lies within body 2 and on the line Q— G^.(Figure 14b) Point 0 is also the pivot point around which the two bodies rotate. Then, due to centrifugal force, G^ will always remain in a straight line with Q, 0, and G^.
The center of percussion of body 1 now lies above its cen ter of gravity G^. Thus, if the force of impact is through P^, there
^Any rigid body rotating about its center of gravity 0 and experiencing a force F at some point A on the body will also exper ience a reactionary force H of the same magnitude but opposite in direction at the shaft of rotation.
Since during the impact of a baseball, the force may reach as high as 3,000 pounds (see Appendix A), it may be undesirable to have this force transmitted through the shaft. This transmitted force may be minimized if the body is elastic and able to bend between points 0 and A. 2 It is assumed that the two bodies are symmetrical about the plane of the paper and remain so during all movements. 13 will be no reactionary forces at Q, and consequently none at 0.
Figure 14.— Impactor consisting of two bodies
After an impact, however, of body 1 will no longer lie in a straight line with Q and G^. Thus, until centrifugal force can re store G^ onto the straight line, there will be a force F at 0 as shown in figure 15.
Figure 15.— The forces at point 0 after the impact 14
This is the only reaction to the impact which occurs at point
0. In application, however, it is small compared with the force of impact.(see Appendix B)
The first consideration in designing a pilot model impactor was size.
As an approximation, the ball will acquire the same speed after impact as that of the impactor before impact, if the mass of the impactor is at least two and one-half times that of the ball. This may be illustrated from figure 16.
Impactor Ball Impactor Ball
a. M = 2.5 m b .
Figure 16.— Velocity of the ball before and after impact
The impactor is travelling at velocity V^.(Figure 16a) The ball is stationary. After the impact the impactor is travelling at velocity V^, and the ball at velocity V^.(Figure 16b)
Using the principle of conservation of linear momentum, the 3 following equation may be written:
MxV^ + mxO = M x Vj +m x (1)
3 Nomenclature is given in Appendix C. 15
The coefficient of restitution of a baseball is approximately
.5 (see Appendix A).
Since (final impactor velocity) - (final ball velocity) e = ------(initial impactor velocity) - (initial ball velocity) then
(vx - 0)
V2 = V3 " -5 Vi <2>
Since M, m, and are known, equations (1) and (2) may be solved simultaneously for and yielding
V3 = 1.07 Vx
Thus, the final velocity of the ball is very close to V^.
By doubling the speed of the impactor, the ball velocity is also doubled.
V3 = 1.07 (2 x = 2.14 V3
By doubling the mass of the impactor (M = 5m) and using the same process as above to determine V3>
V3 = 1.25 V1
Thus it can be seen that a greater ball speed increase can be achieved by increasing the speed of the impactor than by increasing its mass.
Consequently, the radius of the impactor arm is determined for the most part by the maximum desired ball velocity. 16
For example, to pitch a ball at the desired speed of 132 feet per second, an impactor with a radius arm of one foot must have an angular velocity of 132 radians per second or 1260 revolutions per minute.(Figure 17)
132 feet per second feet per second 1 foot radians 132 radians per second second
Figure 17.— Size of impactor verses ball velocity
A smaller radius would require a larger angular velocity and thus, there is a trade off between the size of the impactor and the angular velocity of the same.
An impactor with the center of percussion located approximate
ly nine inches from the pivot point was chosen for the pilot model pitching machine.(Figure 18) This impactor was able to rotate within a circle of slightly more than one and one half feet in diameter. The required maximum angular velocity was approximately 1680 revolutions per minute which is close to the normal operating speed of synchronous electric motors.
The impactor face surface was one inch wide by two inches high
to which was bonded a one half inch thick rubber cushion. The upper
surface of the impactor head curved with a ten inch radius. Most of 17
1 inch
Figure 18.— Impactor head
the mass was toward the top. This geometry located the center of grav
ity and the center of percussion in the head where the ball would be hit.(Figure 18)
The remainder of the impactor assembly was built as shown in
figure 19. The hub was made of steel one inch thick by two inches wide by four inches high. The head rotating at 1750 revolutions per minute
exerted a centrifugal force of approximately 1250 pounds. A three-
eighths inch diameter grade 5 steel bolt was found sufficient to con
nect the head and hub. 18
Figure 19.— The completed impactor assembly 19
The head of the bolt floated inside the hub. A rubber cylinder located next to the head of the bolt held the bolt firmly in the hub, yet allowed the bolt to pivot inside the hub. Set screws prevented the bolt head from turning.
A cylindrical counterweight was connected to the hub with a one half inch diameter threaded rod. The cylinder, weighing 2.2 pounds, could be rotated for proper positioning along the threaded rod.
The entire assembly was mounted on the shaft of a variable speed motor.
The Injector Assembly
As was mentioned previously, the injector assembly consisted of
(1) the injector- a mechanism to place the ball into the path of the impactor, and (2) the synchronizer- a mechanism to synchronize the in jection of the ball with the movement of the impactor.
Injector
In considering a design for the injector, it was decided that the injection would be accomplished as shown in figure 20. The impact or may rotate at any designated angular velocity. The injection may
then be executed some time during the travel of the impactor from point B to point C. Movement of the tension wire A in the direction
shown by the arrow would rotate the lever assembly D and push the ball
into the path E of the impactor head.
Since the lever assembly D must move very rapidly, it was necessary that it be as light as possible yet have sufficient strength.
It was therefore necessary to know the energy and the approximate
force required to inject the ball in the most severe of cases. 20
Figure 20.— Method of injection
For an impactor angular velocity of 1750 revolutions per min ute, one revolution is completed in .034 seconds. Consequently, .017 seconds was chosen as a maximum allowable time to inject the ball.
This was a reasonable time since the impactor completes one half revo lution and may provide the injection motion during its downward stroke.
It was decided that the ball would be pushed into the path of the impactor by a lever with a 3.5 inch radius and that the ball would 21 initially be placed as close to the impactor path as possible to allow a minimum injection path.(Figure 21)
Figure 21.— Injection path
The equations of motion were applied to determine the required energy and force.
“b- V9’ (3)
Integrating equation (3) 22
e + c. (4)
0 = (5) t t I t + C2 S ls M • Since e « 0 at t « 0, - 0
6 = 0 at t = 0, C2 » 0.
Then,
1 “b t2 (6) e- 2 1 li s where e « 39 degrees ■ .681 radians
.017 seconds ci = foot-pound-second Xs - + mCl2.0 fcet)2 - 90-2 * 10 5 -5 2 Ib ■ 5.80 x 10 foot-pound-second Therefore,
1 \ (-017)2 2 90.2 x 10"5
4.26 foot-pounds. “b
Thus, if a constant moment of 4.26 foot-pounds is applied, the ball will be in position in .017 seconds. The energy required for this movement is 0 “ 4.26 x .681 ■ 2.90 foot-pounds. The con
stant force applied to the ball is:
4.26 foot-pounds F, 14.6 pounds 3.5 feet 12.0
Since the force applied to the lever assembly by the motion of
the impactor may be higher than average during part of the time of in
jection, a maximum force F, of thirty five pounds was used as a design b 23 parameter for the injector assembly.
The ball injector was built as shown in figure 28. When force was applied to the tension wire, the levers pushed the ball against the side of the tube.
Synchronizer
Since the injector mechanism was to be actuated by the move ment of the impactor, the synchronizer must engage the tension wire A with some point on the impactor so as to pull wire A a sufficient dis tance to properly inject the ball.
Referring again to figure 20, wire A may be engaged with the impactor any time after the head passes point B, but the injection of the ball must also be completed by the time the head passes point C.
The synchronizer was built using the components shown in fig ure 22. It consisted of four links. Link A— C was stationary. Link
A— B rotated 360 degrees about point A. Links B— D and C— D followed and moved as shown.
Figure 22.— Synchronizer 24
Another link E— F was placed behind link C— D and pivoted about point C.(Figure 23) Link E— F was connected to wire A at point
F. When it was desired to engage the synchronizer, a pin was inserted at point G between levers C— D and E— F. As lever C— D rotated clock wise, it also rotated lever E— F clockwise, pulling wire A downward.
Figure 23.— Connection with the tension wire
The total movement is described in figure 24. A pin was in serted at point G, locking levers C— D and E— F.(Figure 24a) As A— B rotated from point 1 to point 2, and from point 2 to point 3, C— D pulled E— F downward.(Figures 24a, 24b, and 24c)
As A— B rotated from point 3 to point 4, and from point 4 to point 1, C— D and E— F returned to their original positions.(Figure
24d) During the return, the pin was removed from point G so that as
A— B continued to turn in a clockwise direction, lever E— F would not come down again.
The four bar linkage used in the pilot model was a quick return 25
3
Figure 24.— Cyclic movement of the synchronizer mechanism. Lever A— B rotated 190 degrees to complete the downward stroke and 170 degrees to complete the return stroke. Figure 28 shows the synchronizer mounted on the pitching machine. The lever C— D was made from aluminum. Lever B— D was steel. Figure 29 shows the four positions in the cyclic motion of lever A— B .
The Friction Spinner
The friction spinner was the final addition to the pitching machine. It consisted of two flat parallel surfaces, each surface 26 having a different coefficient of friction.
The purpose of the friction spinner was to apply an angular velocity or spin to the baseball. It was intended to operate accord ing to the following description.
Referring to figure 25, as a ball travels from position 1 to position 2, the two flat surfaces A and B apply normal forces and
respectively. This results in two frictional forces and Fg acting on the ball. Since the force FL is larger than the force Fg, the ball tends to rotate counterclockwise as it passes between the surfaces.
Figure 25.— The friction spinner
For the analysis of the behavior of the ball between two such surfaces, four assumptions will be made;
1. The ratio of the normal forces and ^ is a constant.
Thus, the ratio of the tangential forces F and F is a constant. L b 2. The normal forces and Nj are equal. This also assumes that the ball will always travel in equal contact force with both sur faces . 27
3. The sliding coefficient of friction is unchanged as the velocity changes from position 1 to position 2.
4. The ball slips on both surfaces from position 1 to posi tion 2.
For a given ratio of the coefficients of friction, two tangen tial forces of the same ratio may be applied to the ball.(Figure 26a)
The relationship between F and F may be represented by F = n F , Lb Lb where n is the ratio of the larger coefficient of friction to the smal ler. The angle ^ represents the angular rotation of the ball from position 1 to position 2.(Figure 26b) The variable X describes the linear distance the ball travels between the two surfaces.
The equations of motion may now be written for the ball. Re ferring to figure 26a,
Position 1 Position 2
Figure 26.— Analysis of the friction spinner 28
(n - 1) Fg R * t + C. (8)
1 ^ FS R 2 * + (9) 5 *b
Also,
• • fl + fs (n + Fs X m m (10)
ft (n + 1) F£ X -m---- t + C j (ID
- (n + 1) F X -2 ------m — t: + C, 3 t + C. A (12)
To illustrate the operation of the friction spinner, an example will be used to calculate the loss of linear velocity incurred when a spin of 1800 revolutions per minute is applied to the ball. The ini tial velocity will be taken as 150 feet per second. The frictional forces Fg and F^ will be taken as .5 and 2.5 pounds respectively.
Then,
= 150 feet per second vi K = 0 hat 1800 revolutions per minute = 188.5 radians per second Fs = .5 pounds 2 m = .01 pound-second per foot -5 2 = 5.83 x 10 foot-pound-second *b R 25 .12 feet 29
Using equations (8) and (9), and since P * 0 at t * 0, * 0.
Since ^ * 0 at t = 0, * 0. Then,
• « (4) (.5) (.12) (j) = ^ f = 188.5 = ------— --- t 5.83 x 10 5
-2 t = 4.547 x 10 seconds.
Using equation (11), and since X = ■ 150 at t = 0, ■ 150, and
. "(6) (.5) (4.547 x 10“2)2 V = X ------+ 150 .01
Vf = 136.36 feet per second
In gaining an angular spin of 1800 revolutions per minute, the ball has decreased in velocity 13.64 feet per second. The length of travel required in the friction spinner is then, using equation (12),
(6) (.5) (4.547 x 10 2)2 1 X + (150) (4.547 x 10 2) 2 .01
X = 6.51 feet
To further illustrate the operation of the friction spinner, the energy equation will be used:
1 1 1 + + E, (13) 2 2 *1 2 m K
represents the energy lost to friction. Referring again to figure 26, (F^ + Fg) x X equals the energy used to produce angular ro
tation plus the energy lost to friction. Then equation (13) becomes,
1 + - I & 2 (14) 2 2 D *1 5 ” vf + CfL + rs) x x 30
Using the results of the previous example,
(pL + Fg) x X = (2.5 + .5) (6.51) = 19.53 foot-pounds
| m V2 = | (.01) (136.36)2 = 92.97 foot-pounds
| m V2 = | (.01) (150.00)2 - 112.5 foot-pounds
Then from equation (14), 112.5 = 92.97 + 19.53.
Since | 1^ 0)2 = 1.036 foot-pounds, Ef = 19.53 - 1.04 - 18.49
foot-pounds of energy lost to friction.
The question arose as to what length X of the friction spin
ner would give the most efficient operation. To determine this, the
following analysis was made.
If n = 5, then using equations (8), (11) and (12),
4 Fs R A (8) m
6 F, + V, (ID m
x = - | --- - t2 + Vi t (12) ra
If 0f, Vf , and X are all specified, the result is three equations in three unknowns: Fg , and t. Therefore,
(15)
(16)
Ef -
Equation (15) shows that Fg varies inversely with X since the
sum of the quantities within the brackets is a constant. Equations
(16) and (17) show that and E^ are constants. Therefore, accord
ing to equation (15), the trade off in the design of the friction
spinner is between the length X of the same and the frictional force
Fg applied to the ball.
The friction spinner was built as shown in figures 27 and 28.
It was part of a tube, the inside of which cleared the ball on all
sides by approximately .1 inch. The tube was lined with teflon to make the inside surface as slick as possible . The two friction sur faces were located in the last six inches of the tube, section A— B.
(Figure 27a) As shown in the end view, figure 27b, the tube wall act ed as the slick side of the spinner. The side with the greater coef
ficient of friction was constructed of a thin layer of rubber backed by an aluminum frame.(Figure 27c) The frame pivoted at A and was spring loaded at B . The contour of the rubber covered frame was such that as a ball passed by, a constant normal force was applied from points A to B.
b. a.
Figure 27 .— The completed friction spinner 32
Figure 28.— The completed pilot model
Figure 29.— The four positions of the synchronizer CHAPTER IV
DEVELOPMENT AND IMPROVEMENTS
After the completion of all working parts, the pitching ma chine was tested with a ball. To begin with, the impactor was rotated by hand and the synchronizer engaged. The impact followed, driving the ball down the tube.
The impactor was then driven with the motor. Starting at ap proximately fifty revolutions per minute, the synchronizer was again triggered with satisfactory results. This testing continued at in creases of 100 revolutions per minute with satisfactory operation un til approximately 700 revolutions per minute.
Beginning at about 700 revolutions per minute, the ball tended to jam in the tube at the time of the impact. This resulted in con siderable damage to the ball and also to machine components.
Figure 38 shows the impactor after a ball had jammed in the tube. Note the mispositioned counterweight. Note also that the im pactor head had rotated making it vulnerable to collision with other parts of the machine.
After several such occurences, it was evident that a redesign of some of the machine components was necessary. Following is an ac count of the changes necessary.
The Impactor
A new impactor was designed to correct the problems of the
33 34 original. Figure 30a shows the original impactor. Figure 30b shows the new design. Note that it is impossible for the new head to rotate.
Note also that the center of gravity of the new head is much farther to the rear of the connecting stem.
Figure 30.— Impactor heads
Another problem of the original impactor design was the tend ency of rubber to extrude out of the joint connecting the stem to the hub.(Figure 31)
Extruded rubber
Figure 31.— Extrusion of rubber from hub 35
The redesign cosisted of connecting the stem to the hub with a pin as shown in figure 32. The pin fit snuggly in the stem and ro tated in teflon bearings in the hub.
Figure 32.— Redesign of the hub
The Injector
Two theories were postulated as to the cause of the ball jam ming at the time of impact:
1. Due to the impact, the ball was expanding in diameter suf ficiently to unable it to pass through the tube.
2. During the injection, the ball passed into the path of the impactor, rebounded off the wall of the tube, and commenced to escape from the path of the impactor. Thus, when the impact occured, the ball was not properly centered.
To investigate the probability of these two theories, an in jector was constructed without the use of the guiding tube. Only the minimum physical boundaries were used to position the ball for the im- 36 pact.(Figure 39) Thus, very shortly after impact, the ball could free ly expand and proceed in a straight line normal to the face of the im- pactor head.
Unfortunately, even though the ball did escape freely upon im pact, it did not proceed in a line normal to the face of the impactor head.(Figure 33) Instead, it was found that at impactor speeds above
700 revolutions per minute, the ball escaped at a small angle to the right of the desired escape path.
Impactor head -Rubber tip -Desired escape path ------Escape angle
Actual escape path
Figure 33 .— Escape behavior
This indicated that the ball was probably positioned as shown in figure 34.
Injector stopping wall Impactor head
Figure 34.— Probable position of ball at impact
Further, the smearing of ink placed on the injector stopping 37 wall indicated that the ball had rebounded from the wall and was re turning at the time of impact.
The next injector was constructed with a damper in the stopping wall in an attempt to reduce the effects of the ball bouncing within the injector.(Figure 35)
Figure 35.— Damper mounted on injector
A three eighths inch thick piece of foam rubber was bonded to the framework of the injector. Then a piece of one eighth inch thick teflon was screwed in place and served as a striking plate.
The effects of the damper were noticeable but slight. At ma chine speeds above 700 revolutions per minute, the ball continued to escape the impact at an angle.
A third injector was built with the idea that it was better to inject the ball along the path of the impactor rather than to inject the ball at right angles to the path.(Figure 40) Thus, variations in the position of the ball along the path at the time of impact would not be as significant as variations in position of the ball at right angles to the path.
This injector had a problem similar to the previous injectors. 38 however. Although the ball could be easily injected in sufficient time, it was difficult to bring the injected ball to rest before the impact.
A fourth injector design was tried and proved sufficient to properly position the ball for the impact. Unlike the previous inject ors, the bouncing of the injected ball was used to advantage to bring the ball to rest. Since a baseball has a coefficient of restitution of .5, approximately seventy-five per cent of its kinetic energy is lost at each bounce. In the new injector, the ball had to bounce three times before it could proceed to bounce out of the injector. Figure 36 shows the injector and the travel of the ball within the same.
Figure 36.— Injector showing path of injection
The ball first struck a solid plate at a fourty-five degree angle to the ball injection. The rebounding ball then struck a plate normal to the travel of the ball. With the energy left after two bounces, the ball could return by the path which it entered.
For a standard baseball, and due to the fact that the injector finger locked into position, figure 36b, the bouncing of the ball 39 within the injector sufficiently decreased the ball's energy so that it came to rest between the two plates B and C before the impact. As will be pointed out later, high speed movies showed that the ball was at rest for a considerable portion of the time between the initial in jection and the impact. Figure 41 shows the injector mounted on the pitching machine.
The Friction Spinner
After the completion of a successful impactor and injector, attempts were made to add the friction spinner. The first attempt was to guide or channel the moving ball into a 3.5 inch inside diameter tube. Once in the tube, the principle of the friction spinner was to be applied.
A problem arose, however, in that if the moving ball made con tact with any of the guides, the ball bounced and deflected from its original path. Thus, the guides did not function to improve the path of travel of the ball as was intended, but rather proved to be an ob stacle. Consequently, variations in the direction of the ball due to the impact made the ball vulnerable to bouncing within the guides, re sulting in a loss of kinetic energy and an alteration in the direction of the ball.
The variations in the direction of the ball after the impact tended to be more in the vertical direction than in the horizontal.
(Figure 37)
The effect of the friction spinner was successfully applied for curving in the horizontal plane. Figure 42 shows two guides that were mounted on the pitching machine. One guide was constructed of one eighth inch thick teflon backed by an aluminum plate. The other AO
Figure 37.— Variations in direction after impact guide was one half inch thick rubber backed by a plate. The ball, af ter passing between the guides, was given enough spin to curve as much as four feet in a distance of sixty feet.
As a final check on the operation of the pitching machine, high speed movies were taken of the impact and spinning operations. These movies showed that the ball was injected into the path of the impactor in about the time the impactor had made one third revolution. The ball then bounced within the injector and came to rest. It remained at rest for approximately one half revolution of the impactor before the impact occurred.
After the impact, the ball travelled without rotation to the guides of the friction spinner. The movies then revealed that the friction spinner did not operate exactly as it had been assumed to op erate. Instead of the ball travelling between the guides with an equal force applied by each guide, it was found that the ball travelled its own path, pressed into the rubber for the full length of the rubber guide, then was deflected against the teflon guide, and bounced off the 41 same out of the friction spinner. Figure 43 shows the ball at the end of the rubber guide as it appeared in the movie. 42
38.
40.
42. 43.
Figure 38.— Impactor after a ball jammed Figure 39.— Injector without the tube Figure 40.— Overhead injector Figure 41.— The final injector Figure 42.— The friction spinner Figure 43.— The movie 43
PLATE III
Figure 44.— The final pitching machine CHAPTER V
TESTING PROCEDURES AND RESULTS
The pitching machine at this point was ready for testing to de
termine its operational properties. The following testing procedure was used to determine accuracy and repeatability.
A test area was set up in which a distance of sixty feet six
inches was marked off. The pitching machine was placed at one end and
a target backstop was placed at the other.
The target was constructed of canvas to stop the baseball with
out undue bouncing. A piece of chain link fence was located behind the
canvas to further break the motion of the baseball.
A chalk grid was drawn on the canvas target. The lines were
spaced three inches apart in both the vertical and horizontal direc
tions and numbered as shown in figure 45.
€> 6 5 BH 4 iLi1 7 II ? i -e -7 -I 0 .; 3 4 ,7 -4 ' 7 -1 -2 -3
f -4 -7 -6 __
Figure 45 .— Canvas target with dispersion pattern
44 45
Of particular interest was the size of the area on the target in which all of the balls would hit for one setting of the machine.
There were five variables in the operation of the machine which were thought could affect the dispersion of the balls on the target.
These variables were (1) the type of ball used, (2) the particular or ientation of the ball at the time of impact, (3) the hardness of the rubber tip on the face of the impactor, (4) the angular velocity of the impactor, and (5) the force applied to the ball by the friction spinner.
Two types of baseballs were used. One was the regulation leath er ball; the other a rubber covered practice baseball. Ten balls of each type numbered from one to ten were thought to represent a sample.
Each of the ten balls was of the same quality.
There were four different ball orientations which were thought could be significant. Figure 46 shows four orientations that the im pactor head saw at the time of impact.
#1 #2 #3 # 4
Figure 46.— Four orientations of the ball
The three hardnesses of the impactor were (1) a one half inch thick rubber cushion of about fourty durometer, (2) a one half inch 46 thick rubber cushion of approximately sixty five durometer, and (3) a one eighth inch thick teflon plate in front of the harder rubber cushion.
Three impactor angular velocities were chosen to represent the speed variable: 900, 1100, and 1300 revolutions per minute.
The tests were conducted without the use of the friction spin ner .
The balls were shot into the target. The round black circles in figure 45 represent the points of contact for a typical test.
Each test consisted of shooting ten balls. The ten positions were then recorded along both the horizontal and vertical coordinates.
From these ten positions, the variance along each axis was computed.
Tables 1,2,3, and 4 show the outlines for the tests conducted. The variance for each test is recorded in the appropriate column.
Tables 1 and 2 show the variances in the horizontal and ver tical directions respectively for leather balls only. Four orienta tions were used. Tables 3 and 4 show the variances in the horizontal and vertical directions respectively for both types of balls. Only two orientations of each ball type were used.
The variances in each table were analyzed by the Anovar com puter program at Brigham Young University to determine which variables were significant factors for the best performance of the machine. The results are shown in tables 5 and 6.
Table 5 shows that for leather balls in the vertical direction, the orientation of the ball at the time of impact was significant.
The orientation showing the least variance was orientation number two.
(Figure 46) 47
TABLE 1.
Variances of the leather balls along the horizontal axis
Impactor hardness
Soft Medium Hard Orien tation Impactor speed Impactor speed Impactor speed of the r.p.m. r .p .m. r .p .m. Daii 900 1100 1300 900 1100 1300 900 1100 1300
i 2.94 8.00 1.88 3.16 .94 3.34 1.96 1.60 .67
2 1.66 5.12 .90 1.07 .71 .49 1.43 2.77 1.17
3 7.21 1.43 2.72 4.22 3.51 1.66 2.00 5.07 6.00
4 5 .24 1.21 1.29 4.68 13.80 2.10 3.12 3.43 4.10
TABLE 2.
Variances of the leather balls along the vertical axis
Impactor hardness
Soft Medium Hard Orien- tation Impactor speed Impactor speed Impactor speed of the r .p .m. r • p .m • r.p.m. ball 900 1100 1300 900 1100 1300 900 1100 1300
1 9.07 16.32 12.00 12.40 7.18 16.18 6.62 10.28 2.90
2 .99 6.23 26.01 3.29 3.66 7.21 6.10 11.88 5.17
3 15.12 18.93 10 .01 6.24 14.77 8.77 13.29 16.32 14.54
4 13.21 20.10 24.01 13.51 15 .80 5.11 16.90 16.84 11.71 48
TABLE 3.
Variances of both balls along the horizontal axis
Impactor hardness
Soft Medium Hard Orien- tation Impactor speed Impactor speed Impactor speed of the r .p .m. r .p .m. r.p.m. ball 900 1100 1300 900 1100 1300 900 1100 1300
Leather cover
1 2.94 8.00 1.88 3.16 .94 3.34 1.96 1.60 .67
2 1.66 5.12 .90 1.07 .71 .49 1.43 2.77 1.17
Rubber cover
1 4.84 4.01 4.49 5 .07 1.96 2.04 1.14 6.71 .99
2 2.62 2.18 5.82 2.93 .93 4.68 3.29 5.57 2.94
TABLE 4.
Variances of both balls along the vertical axis
Impactor hardness
Soft Medium Hard Orien- tation Impactor speed Impactor speed Impactor speed of the r.p.m. r .p .m. r .p .m. ball 900 1100 1300 900 1100 1300 900 1100 1300
Leather cover — 1 9.07 16.32 12.00 12.40 7.18 16.18 6 .62 10.28 2.90
2 .99 6.23 26 .01 3.29 3.66 7.21 6.10 11.88 5.17
Rubber cover
1 2.99 5.96 3.34 1.34 5.33 5.48 3.61 4.10 3.12
2 9.16 1.79 6 .6 2 8.10 3.29 5.89 6.22 3.29 6.46 49
TABLE 5.
Leather covered balls
X coordinate Y coordinate
F Compar Signif F Compar Signif ratio ator icant ratio ator icant
Speed 1.45 3.34 No 1.40 3.34 No
Orientation 1.85 2.95 No 3.56 2.95 Yes
Hardness .17 3.34 No 2.76 3.34 No
The comparator is the value of the F ratio for significance at the five per cent level.
TABLE 6.
Leather and rubber covered balls
X coordinate Y coordinate
F Compar Signif F Compar Signif ratio ator icant ratio ator icant
Speed .89 3.33 No .94 3.33 No
Orientation .80 4.18 No .06 4.18 No
Ball 4.46 4.18 Yes 7.73 4.18 Yes
Hardness 2.24 3.33 No .96 3.33 No
Table 6 shows that there was a significance in the type of ball used. In the horizontal direction, the variance of the leather
balls was least. In the vertical direction, the variance of the rub
ber covered balls was least.
It was concluded that the variation in the vertical direction
resulted mostly from variations in the position of the ball within the
injector just before the impact. Figure 47a shows the impactor arm 50 and illustrates the variation in the y direction at the target as a result of the small variation 8 in the position of the ball. For ex ample, if 8 m one eighth inch, then, taking all other conditions of the impact to be equal, the variation in y at the target 4y = ten inch es. It was concluded that the balls varied in position depending upon how straight they bounced within the injector.(Figure 47b) The straightness of the bounce was a result of how the ball was injected.
Thus, some orientations gave the leather balls more of a tendency to bounce at an angle because of the threads rubbing on parts of the in jector. Also, the leather balls could bounce more within the injector than the rubber covered balls because, on the average, the leather balls were smaller in diameter.
It was concluded the variance of the leather balls in the hor izontal direction was less than that of the rubber covered balls be cause the leather balls as a group were softer. It was observed that approximately ten per cent of the time, the impact would impart a spin to the balls which would cause them to curve slightly to the right or to the left. This occurrence was more prevalent with the rubber cov ered balls, consequently, the greater variance.
Figure 47.— Consequence of the variation 6 CHAPTER VI
RECOMMENDATIONS AND CONCLUSIONS
Recommendations
In constructing another pitching machine several designs could be incorporated which may improve the operational smoothness of the present model.
For one, the injection force could be smaller if more time were allowed. By using a cam instead of the present synchronizer, the injection could be spread out over a larger portion of the impactor revolution. This would reduce the intensity of the bouncing of the ball within the injector. Also, the accuracy of the impacted ball in the vertical direction could be improved by better control of the pos ition of the ball before the impact.
The impactor could be simplified and made less vulnerable to wear if it were not jointed, but rather constructed as one piece able to bend with little resistance at the proper point. It is probable that much better side to side control of the impacted ball may be had with an impactor at least twice the width of the present.
The friction spinner is yet in need of considerable develop ment to carry out its function in a smooth and satisfactory manner.
Perhaps two surfaces could be built which follow the path of the ball instead of the ball following the surfaces.
Advantage could be taken of the structural rigidity of aluminum to make a light and attractive frame.
51 52
Conclusions
It has been observed that it is possible to accelerate a base ball to speeds in excess of ninety miles per hour and with appreciable control by use of the impact principle. Also, a baseball may be moved into the path of a rapidly rotating impactor in sufficient time for a smooth and straight impact.
It is also evident that a baseball which has been accelerated to speeds in the range of sixty to one hundred thirty two feet per sec ond is highly endowed with energy; and any attempt to alter or control its movement may be met with many problems.
Curve balls may be produced through the friction spinner if the ball passes through within acceptable tolerances. It is believed that further coordination of the friction spinner with the path of the base ball will provide a curving device of simple construction and good re peatability .
The pitching machine constructed for this thesis was relatively small, being only twenty inches in diameter. It is believed that such a model could be produced at a cost in the range of $100. to $150. APPENDIX A
CONSIDERATIONS IN THE SELECTION AND DESIGN OF
BASEBALL ACCELERATORS APPENDIX A
CONSIDERATIONS IN THE SELECTION AND DESIGN OF
BASEBALL ACCELERATORS
Mass of a Baseball
For a baseball weighing .3188 pounds, the mass is:
.3188 pounds 2 .009910 pound-second per foot 32.17 feet per second
Mass Moment of Inertia of a Baseball 2 Since for a sphere, I = .4 m R ,
2 1^ = .4 (.009910 pound-second per foot) (.1211 feet) -5 2 = 5.828 x 10 foot-pound-second
Acceleration Forces
The constant force and the horsepower required to accelerate a baseball weighing 144 grams to each of two speeds in a distance of 2.5 feet is shown in table 7.
TABLE 7.
Acceleration force and horsepower
Desired speed Required force Required horsepower m.p.h. lb.
60.0 15.3 1.22
100.0 42.5 5 .84
54 55
Coefficient of Restitution of a Baseball
A standard baseball was dropped from two different heights onto hard asphalt and the height of the rebound was measured in each case.
The velocity before impact was calculated for a free falling object in a vacuum. Likewise, the velocity after impact was calculated as the initial velocity required to lift a body to the rebound height. The coefficient of restitution was computed as the velocity after impact divided by the velocity before impact.
TABLE 8.
Coefficient of restitution
Drop Rebound Velocity Velocity Coefficient height height before impact after impact of restitution ft. ft. f .p .s. f.p.s.
1 12.0 3.8 27.8 15.6 .56
2 20.8 6.0 36.8 19.7 .54
Energy of Impact
The energy required to accelerate a standard baseball by the method of impact to each of several speeds is listed in table 9. It is
essentially equal to the loss of energy of the impactor. The mass of 2 the impactor was 2.5 times the mass of the ball or .025 pound-second
per foot. The coefficient of restitution of the impact was taken as
e = .50.
Force of Impact and Static Deflection
The static deflection X of a standard baseball was measured
against the crushing force. From this information an approximate
spring rate k was determined. The impact of the baseball against a 56
TABLE 9.
Energy of impact
Desired velocity Energy of of baseball impact f.p.s. m.p.h. ft.-lbs.
132 90.0 156
110 75.0 108
88 60.0 69
solid surface was then modeled as a spring-mass system. The required deflection X and the associated maximum force necessary to stop a base ball travelling at 150 feet per second are shown in figures 48 and 49.
Figure 48 represents the impact of the ball against one inch thick rub ber of approximately 65 durometer. Figure 49 represents the impact of the ball against a solid wall.
Force (pounds)
Displacement (inches) Figure 48.— Impact against rubber cushion 57
Force (pounds)
Figure 49.— Impact against solid wall APPENDIX B
PHYSICAL AND OPERATIONAL CHARACTERISTICS
OF THE IMPACTOR APPENDIX B
PHYSICAL AND OPERATIONAL CHARACTERISTICS
OF THE IMPACTOR
Physical Characteristics
Figure 50 gives several of the physical characteristics of the impactor arm.
Figure 50 .— Impactor arm
59 60
_I.
Figure 51.— Movement capabilities of the impactor arm
Figure 51 gives a description of the movement capabilities of the impactor arm. Line 0-Q-G represents the axis of the impactor.
The angle 9 represents the angle of deflection incurred from an impact.
The plane K-O-J rotates at a constant angular velocity u U ) ^ is also the angular velocity of the impactor arm. For the analysis, 61 points 0 and Q on the impactor arm remain fixed within plane K-O-J.
Therefore, in figure 51, the ball just prior to impact is represented by a ball approaching at velocity V^. The impactor arm just prior to impact lies on O-Q-K.
For the analysis, the result of an impact at point K is an angular velocity 6 imparted to the impactor arm. The counteracting moment Hg is 0-G x F. The force F is a component of the centrifugal force F exerted on G when 6 is greater than zero. The counteracting c moment H may be calculated as follows. s Referring to figure 51,
Fc = MA x (0-Q + Q-G) x U>1
F = F sin 4> ~ F
e = r + ?
sin £ m sin f 0-Q Q-G
For small angles, ±. . jl or s±.d 0-Q Q-G 0-Q
Q-G Q-G Therefore, Q = ^ +
6
H = F x Q-G = F (A) s c e 62
The velocity S of the arm after the impact may be calculated using the principle of conservation of linear momentum with the prop er coefficient of restitution.
m V, + M V . + M (B) b P 2 P
4 e = .5 = (C) V b
M is a point mass at the end of a 7.55 inch radius which has P a moment of inertia equal to 1^. For the impactor arm, = .0496.
If in figure 51 is 99 feet per second, then the solution of equa tions (B) and (C) gives = 24.7 feet per second. Consequently,
24.7 feet per second radians e 39.2 7.55 second 12.0 feet
The ratio of the velocity of the ball after Impact to the velo city of the impactor before impact is needed to determine the angular velocity of the impactor required to accelerate a ball to 99 feet per second. The momentum equation and the coefficient of restitution are again used:
M V c + m = M V, + m V 0 (D) p 5 6 p 7 8 V V 7 " 8 e = .5 = — (E)
where V is the initial velocity of the impactor, is the final velo city of the impactor, and V is the final velocity of the ball. From O these equations,
V "p V 1.250 V5 8 (M + m) P 63
Since the velocity of the ball is 99 feet per second, the velo city of the impactor must be 99-£■1.250 = 79.2 feet per second. This gives 6^ equal to 79.2 feet per second divided by .63 feet or =
125.7 radians per second.
Therefore, from equation (A),
.564 H = F (.0727) G [.083 J
- (Ma) (.564 + .083) 2 (.0727 )Q
= (5.46 x 10-2) (.647) (125.7)2 (.0727) 6
Hg = 40.5 6 foot-pounds
The following differential equation may be written:
• * 1.6 + 40.5 6 = 0 A Then,
0 + Q = 0 *A • • Q + 2065 0 = 0
Consequently,
6 - A cos(45.4 t) + B sin(45.4 t)
0 = -45.4 A sin(45.4 t) + 45.4 B cos(45.4 t)
Since 6 = 0 at t = 0, A = 0. Since Q = 39.2 at t = 0, B = .863. There
fore,
0 = .863 sin(45.4 t) (F)
0 = 39.2 cos(45 .4 t) (G) 64
Physically, the impactor arm is able to deflect 20.0 degrees
(©** 20.0 degrees). From equations (F) and (G), t at 20.0 degrees is
8.97 milliseconds. At 20.0 degrees, the impactor arm bottoms out and rebounds toward © = 0. The time required to return to the original position is, depending upon the coefficient of restitution between the steel parts of the arm, approximately twenty milliseconds. The suc cession of events is illustrated in figure 52.
Since the arm assembly is rotating at £*^= 125.7 radians per second, one revolution is completed in 50.0 milliseconds. The impact occurs at point A. The arm bottoms out at point B after 8.97 milli seconds. At point C, 6 = 0 and the arm is straight.
At 125.7 radians per second, the centrifugal force F£ ex erted on each side of the shaft is 557 pounds. As shown in figure 52, the resolved force exerted on the shaft when Q m 20.0 degrees is
195.5 pounds. Thus, when the impactor arm is bottomed out, the force
F^ is maximum. An additional force due to the impact between the steel parts of the arm is also added to F^, but is estimated to be less than fifty pounds. APPENDIX C
NOMENCLATURE APPENDIX C
NOMENCLATURE
Constant
Constant
Constant
Constant
Energy required to inject ball
Energy lost to friction
Force required to inject ball
Centrifugal force acting on impactor arm
Tangential force applied to ball by rough surface
Force on shaft due to impactor deflection
Tangential force applied to ball by smooth surface
Restoring moment acting on impactor arm
Mass moment of inertia of impactor arm
Mass moment of inertia of a baseball
I Mass moment of inertia of ball at extended radius s m Mass of a baseball
Mass of impactor
Mass of impactor arm
Moment applied to ball “b Moment applied to ball at extended radius *b M Point mass equivalent of impactor arm P
66 Ratio of coefficients of friction
Radius of ball
Time
Time of injection
Velocity of ball before impact
Linear velocity of ball after leaving friction spinner
Linear velocity of ball before entering friction spinner
Distance ball travels through friction spinner
Angular velocity of impactor arm
Angle of rotation of ball
Angular velocity of ball after leaving friction spinner
Angular velocity of ball before entering friction spinner
Angle of injection
Angle of deflection of impactor arm APPENDIX D
DATA APPENDIX D
TEST DATA
Coordinates of the Leather Balls in the Horizontal Direction
Impactor Speed Orien Ball number Ave. hardness tation 1 2 3 4 5 6 7 8 9 10
Hard 900 1 4 5 1 2 2 3 -1 3 4 2 2.5 2 5 2 4 6 4 4 4 5 5 2 4.1 3 1 0 2 1 2 5 3 10 4 1 2.9 4 0 0 2 2 4 -2 -3 0 -2 5 .4 1100 1 0 -1 4 2 0 0 2 4 0 2 1.0 2 -3 -2 1 4 0 2 0 0 -3 -2 - .3 3 0 -1 -3 -1 -1 0 0 0 -3 0 - .9 4 0 1 1 3 -4 0 -4 0 4 1 2.1 1300 1 -1 0 1 0 2 2 -2 -1 -1 -1 - .1 J H H VO W VO H H J
2 0 -1 2 1 1 3 -2 -4 0 -2 .7n 3 -2 1 2 2 4 3 0 2 2 1 1.5 4 0 1 1 -2 1 -1 1 -1 1 1 .2 Medium 900 1 0 -2 -2 1 -2 3 -3 0 0 -1 - .6 2 1 0 3 2 0 1 0 1 2 2 1.2 3 1 2 5 -1 -1 -1 2 -1 3 1 1.0 4 2 -1 -1 -1 -4 -2 0 4 0 0 - .3 1100 1 0 -1 -2 0 0 1 -1 -2 0 0 - .5 2 6 7 5 7 8 7 7 6 7 6 6.6 3 -1 -1 1 4 -1 3 -1 2 2 0 .8 4 2 -1 3 2 2 3 -2 12 2 3 2.6 1300 1 -3 -1 -1 -1 -1 0 4 1 -1 0 - .3 2 0 2 1 2 1 2 1 1 2 2 1.4 3 2 1 0 4 1 1 0 0 0 0 .9 4 3 3 2 3 1 5 6 4 4 3 3.6 Soft 900 1 0 2 -2 1 -2 1 -2 0 0 0 - .2 2 1 -3 1 0 0 0 0 1 -1 0 - .1
3 -1 -3 -3 -2 -4 0 -1 -3 0 -3 -2.0 Ui 0'vO4SwO'00OMn0JON)O' N) H O N) 4 -5 -1 0 0 -1 -3 -2 -4 0 -1 -1.7 1100 1 -3 -4 -5 -1 -3 -3 -5 -3 -5 -4 -3.6 2 -3 -2 -1 -1 -3 0 -2 -5 0 -4 -2.1 3 -1 -2 0 -2 -4 -3 -8 -1 -3 -4 -2.8 4 -3 -1 -1 -1 0 -2 0 -5 -1 -5 -1.9 1300 1 -5 -4 -4 -5 -4 -3 -5 -3 -4 -3 -4.0 2 -3 -3 -3 -2 -4 -2 -4 -5 -4 -5 -3.5 3 -5 -5 1 -3 -4 -4 -6 -7 -1 -6 -4.0 4 -3 -5 -3 -5 -1 -5 -2 -7 -3 -7 -4.1
69 70
Coordinates of the Leather Balls in the Vertical Direction
Impactor Speed Orien Ball numbe r Ave . hardness tation 1 2 3 4 5 6 7 8 9 10
Hard 900 1 0 -1 2 -4 2 -2 3 -7 -1 0 - .8 2 1 1 1 1 3 0 1 -1 1 1 .9 3 4 1 1 1 7 0 -8 0 -1 -2 .3 4 -1 0 4 4 1 1 2 -8 0 -4 - .1 1100 1 4 5 3 7 9 9 -4 5 9 2 4.9 2 3 1 -5 1 -3 -1 -3 -3 0 -3 -1.3 3 -5 -5 2 -3 7 -4 -6 -7 0 -5 -2.6 4 2 1 4 7 3 1 1 -10 2 -2 .9 1300 1 3 -1 -2 -2 7 -3 2 -1 6 1 1.0 2 -3 -6 -6 1 10 3 -9 0 0 -9 -1.9 3 2 0 7 4 3 0 0 -2 3 -4 1.3 4 7 0 8 7 11 7 7 -2 6 -4 4.7 Medium 900 1 6 0 6 2 8 8 8 -1 8 3 4.8 2 -4 -5 -2 -2 -4 -4 -7 -6 -2 -6 -4.2 3 -5 1 -5 -1 -1 -7 -5 -5 -2 -3 -3.3 4 -8 -7 -3 -1 0 -4 -10 -8 0 -7 -4.8 1100 1 -5 0 -1 -2 W -5 -6 -6 1 -3 -1.5 2 -5 -3 -3 -5 -3 -5 -7 -8 -3 -7 -4.9 3 -4 0 7 3 7 0 -3 -2 3 0 1.1 4 -1 -6 -1 -6 6 -2 -5 -7 1 -4 -2.5 1300 1 -1 1 1 2 9 -4 -1 3 8 0 1.8 2 -7 -3 -1 -6 -1 -6 -7 -6 0 -4 -4.1 3 -4 0 -4 0 3 -5 -3 -6 -4 -6 -2.9 4 -3 -5 -4 -6 7 -1 -3 -8 -2 -2 -2.7 Soft 900 1 -4 -2 -3 -2 -7 -4 -10 -5 -2 -3 -4.2 2 -3 -3 -3 -2 0 -2 -7 -7 -7 -5 -3.9 3 -7 -2 1 -3 2 -3 5 -5 2 -2 -1.2 4 -9 -7 -2 2 2 -5 -9 -6 -2 -7 -4.3 1100 1 -7 2 -2 -2 -2 -4 -7 -7 0 -6 -3.5 2 -5 -4 -4 -1 6 -4 -2 -6 -5 -4 -2.9 3 -5 -5 -6 3 6 -4 -5 -5 -3 -5 -2.9 4 -7 -4 2 -2 3 -7 -3 -7 1 -8 -3.2 1300 1 -2 -2 0 -1 0 -4 -1 -5 0 -2 -1.7 2 -8 -6 -7 -3 -5 -8 -10 -3 -8 -7 -6.5 3 3 5 -5 -6 -1 -5 -2 -5 -4 1 -1.9 4 3 -1 -3 -2 0 -3 W W -1 7 0 .0 71
Coordinates of the Rubber Covered Balls in the Horizontal Direction
Impactor Speed Orien Ball number Ave. hardness tation 1 2 3 4 5 6 7 8 9 10
Hard 900 1 6 4 5 8 4 2 6 7 2 8 5.2 2 4 1 5 3 1 4 5 2 1 2 2.8 1100 1 -1 3 0 3 -2 0 4 0 1 -1 .7 2 -1 -1 -1 -1 -1 -1 3 -3 -1 -1 - .8 1300 1 6 4 7 5 -1 5 5 4 4 5 4.4 2 4 2 5 1 -2 6 4 4 5 5 3.4 Medium 900 1 2 0 5 3 -1 1 1 -3 -1 1 .8 2 0 -1 4 -1 0 1 1 -1 0 3 .6 1100 1 1 0 0 0 -1 1 -3 -1 -1 2 - .2 2 -2 -1 -2 0 -1 -1 -2 -3 -3 -1 -1.6 1300 1 0 2 0 1 1 1 5 1 1 2 1.4 2 -3 -2 -2 -2 1 2 -2 2 -3 -4 -1.3 Soft 900 1 2 -1 0 0 -5 0 1 -1 -1 0 - .5 2 0 -3 -3 -1 -6 0 -1 -2 -1 -1 -1.8 1100 1 1 -4 -1 -5 -5 2 -5 -2 -4 -1 -2.4 2 1 0 1 1 -2 3 1 -5 0 3 .3 1300 1 5 3 2 3 2 3 2 4 3 4 3.1 2 2 0 5 3 4 5 4 3 3 6 3.5
Coordinates of the Rubber Covered Balls in the Vertical Direction
Impactor Speed Orien Ball number Ave . hardness tation 1 2 3 4 5 6 7 8 9 10 . UlhJU)-C'00O1(jJ-P'O'N5Cr>CO-t>J>00'-4 Hard 900 1 -3 -2 -3 -2 -4 -6 -5 -2 -2 0 -2.9 2 -6 -5 -7 -2 -3 -2 -7 -3 -2 3 -3.4 1100 1 4 9 1 4 3 8 4 4 4 7 4.8 2 0 -1 -1 3 -2 0 0 0 -1 -1 - .3 1300 1 -1 -1 -3 -3 0 0 0 -5 -1 1 -1.3 2 0 4 1 0 0 -2 0 7 0 2 1.2 Medium 900 1 -3 -2 -3 -4 -4 0 -3 -3 -2 -3 -2.7 2 0 -5 1 3 2 0 2 -2 5 3 .9 1100 1 6 2 2 1 2 6 0 1 4 6 3.0 2 5 2 5 3 3 6 0 2 2 4 3.2 1300 1 3 5 0 3 5 3 7 4 5 4 3.9 2 0 0 0 2 1 0 1 3 0 2 .9 Soft 900 1 -5 -3 0 -5 -3 0 -3 -3 0 -3 -2.5 2 3 -5 -3 -3 -1 -5 -3 -5 -3 -5 -3.0 1100 1 3 3 7 3 2 4 0 0 3 4 2.9 2 0 -1 -1 1 0 2 -3 -3 1 2 - .2
1300 1 -3 1 -1 -1 2 2 -3 0 0 0 - .3UN'OOUI'OOMOO'JMUWCCi-'O 2 1 3 0 -2 -2 -1 -6 0 -2 2 - .7 A STUDY IN THE DESIGN AND DEVELOPMENT
OF A BASEBALL PITCHING MACHINE
Neal M. Lundwall
Department of Mechanical Engineering
M.S. Degree, May 1971
ABSTRACT
The designs and performance capabilities of currently avail able pitching machines were investigated. Several other designs were considered in a search for a machine of simple construction and low cost which could pitch baseballs at speeds up to 132 feet per second and which could produce the fast ball, the curve, the sinker, and other effects attributed to ball spin during the pitch.
A design using the principle of impact was decided upon and a full sized model was constructed. The baseball was accelerated from rest to an initial velocity by the impact of a rubber tipped rotating hammer. Spin was applied to the ball as it passed between two sur faces having different coefficients of friction.
Performance tests showed that the machine could pitch at the desired speed and with an accuracy of 97 per cent within a strike zone of 21 inches wide by 30 inches high. Spinning balls would curve as much as four feet to the right or left in a distance of 60 feet. Recommendations are given for design alterations that may give im proved performance in future machines.
COMMITTEE APPROVAL:
7 Ar&t 117/ Date