Department of Mechanical and Aerospace Engineering University at Buffalo

Machines and Mechanisms II, Fall 2002

Final Project December 13, 2002

Group K: Erik Anthony Schuster Michael Oscar Scipione

David Douglas Sekuterski Elliot Abraham Shakeridge

Joseph Anthony Shiner Stephen Michael Spina Nathaniel Carl Stenz Amanuel G. Tecle

Introduction

The final project our MAE 412: Machines and Mechanisms Class design and

engineer a “catapult system” that must be able to launch a squash ball. The objective of

the project was to throw the ball a maximum distance and to have high accuracy in its

ability to hit a target. We were given a month to design and build a four bar mechanism.

An electric motor could be used to generate enough energy to launch the projectile. We

also had to analyze our design by using the various analytical methods that were taught in

lecture. With the use of computer software, we used Solid Edge to design and optimize a

prototype and simulate the launch. All of the projects must meet the same minimum

design requirements but there are certain design objectives that will result in greater

success. We were given the following design constraints to consider during the idea

generation process:

• The design must incorporate at least a 4-bar mechanism • It must primarily be constructed of wood • The design must be mounted to a base plate in order to be clamped onto a

table • The mechanism can never leave an operating window of 2’ x 2’ including the

base plate • The four, five, or six bar mechanism must be powered by one standard motor • There cannot be any part of the mechanism beyond the start plane • The design must able to launch the squash ball within a specified time limit • All designs must begin at an initial state where there is no stored potential

energy of any form (with the exception of the power source to the battery)

In designing the mechanism, our device will store the energy that is output from

the motor in a spring. Some additional constraints that we will have to consider are the

force of the spring which depends on the amount of distance that the motor can displace

the spring. Another consideration was the placement of the motor, the size of the

linkages, and the types of joints. Probably the most difficult consideration would be

determining how to draw the most power from our motor. Throughout the design phase,

there is potential for several complications that arise. Some constraints would have to be

clarified in order for us to develop an effective design. Many of the given constraints

were helpful and accommodating but there were others created problems with the

designing and manufacturing of our catapult.

In addition to the designing and building phases of our process, there are the

aspects of performance, testing, physical and virtual prototyping, analytical calculations,

and overall presentation of our project. The physical and virtual prototyping will include

the design creativity and the concepts behind our idea, the synthesis, analysis, simulation,

and optimization of our mechanism. The overall presentation of our project and its

performance include the ergonomics, synergy, appearance, and its ability to accomplish

the tasks. The most important requirements that our design must meet include meeting

all of the constraints, launching the ball with good range, having high accuracy in its

ability to hit a target, the ease of operation, and the satisfaction of meeting its timing

constraint. Once all of the constraints are established and the group understands the task

at hand, a successful design can be engineered.

Idea Generation Alternative 1

Our group came up with several good ideas by each member but only a select few

were considered. After the first meeting, we had a design idea for our project. The first

design that we had considered was the implementation of a flywheel that will be

connected to a four bar mechanism. The design would use the electric motor to spin the

weighted flywheel. The flywheel will spin and gather a string, resulting in potential

energy that will be stored as momentum to drive the four bar mechanism. When the

device reaches a predetermined condition such as time, rate of rotation, etc, the flywheel

would then transfer its momentum into a linear force that would cause the 4-bar to launch

the squash ball like a catapult. The four bar design had a long follower arm that would

hold the squash ball in a basket of some sort. The main reason for scrapping this idea was

the fact that we didn’t really have any experience with the physics of the flywheel and we

didn’t know how we were going optimize its effectiveness.

Alternative 2

Another device idea that the group considered was the use of a frictionless track

that would be designed like a channel in which a basket holding the squash ball would be

launched. The track would be lined with magnets. The basket or car carrying the squash

ball would have an oppositely charged magnet on its bottom surface. Ideally basket or

car would never come in contact with the track, thus eliminating any frictional losses. A

string will pass through a pulley and the other end of the string will be attached to a linear

compression spring. The motor would wind up the string by using the rotation of a four

bar mechanism. After several rotations of the input link, the spring would have developed

enough displacement to achieve a big enough force. The spring would push the car or

basket carrying the squash ball with a high force along the frictionless track and

projecting it a significant range. The configuration is similar to a pinball machine release

mechanism. Despite its crafty design and brilliance, the group was strongly encouraged

not to move forward with the plans because the four bar assembly was too simple and it

wasn’t used as the main throwing device in our design. It was just being used as a

method of winding the string to store energy in the spring.

Alternative 3

We tried to make the design a lot simpler from here on. The design called for the

use of a four bar mechanism with a long follower link that would be set to launch the

squash ball at its limiting condition of 45 degrees from the horizontal (theta 4 equal to

135 degrees). The follower link had the coupler, attached at a distance of one third of its

length from the base. The other two thirds would provide a higher velocity at the point of

interest where the squash ball would be released. The coupler and input links were going

to be the same size and a spring was going to be attached between joint number 2 and 4.

With joint number two being in between links 1 and 2, and joint number four the base

connection with link four. The spring would have no stored potential energy when the

limiting condition of the follower was set at 45 degrees form the horizontal. The motor

would be placed to the left of the assembly and a string would be attached to joint 2

where the end of the spring was attached as well. The motor would start pulling the

string back and storing sufficient energy in the spring and then it would be tripped. The

input and coupler links would be pulled back to the limiting condition by the spring and

the follower would swing around and release the ball at its limiting condition. This idea

was what we thought going to be our final decision but after some testing and virtual

prototyping in solid edge, we found a better design that was more effective.

Final Alternative

Our final design is similar to the previous design except that it uses a slider crank

as the 4-bar mechanism. The reason that we made some changes and decided to go

forward with this alternative is because its virtual prototype created on Solid Edge

Dynamic Designer was quite successful. While we were trying to simulate the response

of alternative 3, one of our astounded group members created a variation and it resulted

in significant success in the Dynamic Designer simulation. The final alternative is very

similar to alternative 3 except for the fact that it is a slider mechanism with the springs

attached to eye pins in the base and a dowel that extends through the slider. There are two

identical links that are attached to the input link, they represent the coupler and they just

slide on the base. A track is mounted to the base for support, guidance, and stability. A

brief description of our design will be offered in the next section of the report.

Description and Figures of Our Mechanism The type of mechanism

developed by our team was a

classic slider with the length of

link four equal to zero. The

slider moved along a plane

that intersected with the joint

between the input link and the

base (we often referred to it as

joint 1 or Ao in lecture). Almost every part of our design besides the trigger pin, dowels,

screws, springs, and squash ball holder was made out of wood. We wanted to make the

mechanism itself as light as possible but maintain good strength. The construction of the

base consisted of a rectangular piece of wood that had mounted on its face a track to

guide the slider, a base joint for the input link(throwing arm), the motor, some eye screws

to hold the springs and strings, and a well designed vertical wooden structure used to trip

the release mechanism. These features of

the base can be observed in the following

figures.

The throwing arm itself had

various small holes for adjustability and it

had a small platform that supported a cap

from a bottle of Edge Gel shaving cream

to hold the squash ball. The very top of the throwing arm was equipped with a simple

trigger mechanism that was shaped like a Z. The arm was pulled down by the electric

motor which gathered fishing line and once the arm reached a critical point, the trigger

mechanism would catch the wooden structure attached to the base causing it to rotate and

the fishing line to slide off. We also tied a thick rubber band around the throwing arm and

attached it to the base with some string.

When the projectile had been launched,

the rubber band provided a gradual

damping force to stop the arm without a

sudden force. Attached to the throwing

arm at a selected distance, was the

coupler link.

The coupler was actually two identical links that were connected to the throwing

arm with a small dowel. The coupler links had some holes drilled through them as well

for adjustability. As stated earlier, a dowel was extended through the two input links and

they were placed over the track that was mounted to the base. The last significant detail

to be mentioned is the arrangement of the springs. There were four springs in all, they all

had the same actual diameter and coil diameter but two of them were longer. The two

longer springs were attached to metal links that were in turn attached to the dowel

holding the identical input links along the track. The other sides of the two longer

springs were connected to some eye screws in the base. The other two smaller springs

were connected the same with one end on the same dowel and the other end into a

different set of eye screws.

Our design was probably the simplest out of all presented by the class. When the

electricity is supplied to the motor, it begins to rotate and wind up the fishing line that is

held by one end of the trigger release pin which is attached to the throwing arm. As the

arm is pulled down, the coupler links are spread apart from there original position and

they slide along the base track. While sliding of course, the springs attached to the dowel

at the end of the coupler are being pulled apart and the potential energy is being stored in

them. Once the motor pulls the arm close enough, the vertical structure trips the release

pin, the fishing line slides off and it allows the springs to pull the arm forward with a high

velocity. The holes in the throwing arm and couplers links allow us to choose the release

angle of the squash ball. We adjusted the throwing arm so its limit condition would be at

45 degrees from the base. The rubber band and the string tied to the base will stop the

motion of the throwing arm. The objective of the project was to successfully launch a

squash ball and our design reflected our efforts.

Physical Construction

The four bar mechanism is made up of wood. In the final physical

prototype, we used some special features. These features include a worm

gear box with a motor, springs, fishing string, trip mechanism, and powder

graphite. These features are used in make the mechanism with out violating

the constraint given as a guideline.

The gearbox is used to get smooth power and excellent torque. In

order to store energy we use four extension springs. Two springs were set up

on the crank joint. The other two springs are attached to the center or the

board and extend to the slider. As the motor winds the string, the crank

stretches the spring; it goes until the shooting (releasing) mechanism tripped

by the tripping mechanism. Then the energy stored on the springs shoot the

arm. We used fishing string in order to pull the arm with the help of the

motor. The fish net is tied on the trigger mechanism and goes back to the

motor. A string was used to stop the arm after the release mechanism was

triggered. It helps to stop the arm at the height of the string so that it shoots

the squash ball. It limits the motion of the arm. The poison of the string is set

in order the arm to have a 450 with board. The trip mechanism is a piece of

wood made to trip the release mechanism. It is attached at the very end of

the board. It has a square drilled part so it does not interfere with the

releasing mechanism. Powder graphite is used as a lubricant between the

slider and the board. It is also used on the joint between the crank and the

coupler.

Simulation Based Design Our four bar mechanism was simulated using Solid Edge/Dynamic Designer. The

lengths of the links could be altered within the computer program to simulate how far the

ball was thrown. We simulated our 3rd alternative along with our final design is solid

edge. The third alternative was only throwing the squash ball 20 feet where our final

design was throwing the squash ball 51 feet. Obviously we choose our final design based

on the difference between each simulated design.

The 3rd Alternative(20ft simulated)

The Final Alternative(51ft simulated)

Our final design for our slider crank was adjustable. It was constructed to adjust

the link lengths at the competition. During the accuracy competition we adjusted our

mechanism so that it threw exactly 15ft. This was done by changing the lengths of link 2

and link 3; we also removed 2 of 4 springs. Because of our adjustability, we were able to

get 2 of 3 accuracy bonus shots.

Analysis Section

The following are the position, velocity, and acceleration analysis of our final

design at a critical point. The critical point chosen was the release of the mechanism

after all of the potential energy was stored in the 4 springs. The initial velocity of r1 is

zero at this critical point. Additional points could be calculated by inserting different

initial values in to the matlab program.

The initial torque is calculated as if there were no springs attached to the slider.

The input torque, T12, is calculated between the ground link and link 2 to get the

acceleration needed.

Please see hand calculations and matlab code.

Dynamic Designer Prototype Our final 4-bar slider crank design was fully designed and analyzed in Solid

Edge/Dynamic Designer. It predicts that our 4 bar mechanism will throw the squash

ball a total distance of 51 feet. The following is an image of the balls path in solid edge.

The spring constant was calculated using a force gage from MLT-ACTS Testing

where Nate interned over this past summer. The spring was stretched and the distance

and force were recorded. The spring was stretched to a different position and the force

and position were recorded. Using the formula F = kx, the spring constant, k, was

calculated from the differences of the two positions. The total spring constant, ktotal, for

all four springs is 50.6 lb/in.

The following graphs were determined from solid edge. The angular velocity,

projection angle, and angular acceleration were all determined for link 2 (the throwing

arm) and link 3.

Angular velocity of link 2 with respect to the gound.

0.00 0.02 0.05 0.07 0.09 0.12 0.14 0.16 0.19 0.21 0.23Time (sec)

-1288

-1067

-846

-625

-404

-183

38

Ang

ular

Vel

- Z

(de

g/se

c)

Projection angle on link 2 from its initial position of 10 degrees

0.00 0.02 0.05 0.07 0.09 0.12 0.14 0.16 0.19 0.21 0.23Time (sec)

-32

-27

-21

-16

-11

-5

0

Pro

ject

ed A

ngle

- Z

(de

g)

Angular Acceleration on link 2 with respect to the ground.

0.00 0.02 0.05 0.07 0.09 0.12 0.14 0.16 0.19 0.21 0.23Time (sec)

-138241

-25575

87091

199758

312424

425090

537756

Ang

ular

Acc

el -

Z (

deg/

sec*

*2)

Angular Velocity of link 3 with respect to link 2

Projection angle on link 3 with respect to link 2

0.00 0.02 0.05 0.07 0.09 0.12 0.14 0.16 0.19 0.21 0.23Time (sec)

-55

-46

-37

-28

-18

-9

0

Pro

ject

ed A

ngle

- Z

(de

g)

0.00 0.02 0.05 0.07 0.09 0.12 0.14 0.16 0.19 0.21 0.23Time (sec)

-2178

-1805

-1431

-1058

-684

-311

62

Ang

ular

Vel

- Z

(de

g/se

c)

Angular Acceleration on link 3 with respect to link 2.

0.00 0.02 0.05 0.07 0.09 0.12 0.14 0.16 0.19 0.21 0.23Time (sec)

-138241

-25575

87091

199758

312424

425090

537756

Ang

ular

Acc

el -

Z (

deg/

sec*

*2)

Discussion of the Performance of Our Mechanism At the Competition

After a long wait it was our turn to show Dr. Krovi, other distinguished professors

from the Mechanical and Aerospace department, the judges, and our classmates what our

design was capable of. Our mechanism performed very effectively and we believe that

we surprised many people including ourselves. We invested much of our time into testing

and fine tuning rather then aesthetics and flashiness. Our investment paid off since our

mechanism recorded the all time distance record and made 2 out of 3 shots in the

accuracy contest. We should have gotten all three but the first one went in and out and we

were robbed. It was a shame that our group was one of the last to go because many of our

classmates and some of our professors had to leave. The motor performed extremely well

for us and throughout the designing and testing phases we were all quite impressed with

the power generated by it. During the competition, the motor was able to pull the

throwing arm down in less than twenty seconds. Overall the performance of our

mechanism was extremely successful and good enough to win the competition by a large

amount of distance. Our design performed so well that it destroyed the grading curve and

upset many of our classmates. Our group is very proud of our mechanism and the

valuable design experience gained from this project.

Future Design Changes

If we were given the opportunity to re-design our project there would be

numerous changes that could have been made. The first and most important aspect that

we could have changed was the procedure for testing that mechanism. We strictly

concentrated and its ability to launch the squash ball the furthest distance possible. There

was little or no emphasis on the accuracy part of the competition. Even though our design

still performed well, we could have spent more time practicing on its ability to hit targets

or throw the squash ball into buckets or garbage cans. By making our design fully

adjustable and the springs interchangeable, our mechanism was still able to hit some

targets after careful planning. Another change that we could have made would be the

length of the throwing arm since our mechanism never came close to exceeding the

restricted window. By increasing the length, the ball would have traveled even farther.

In addition we would have incorporated a pulley system and larger springs if more time

were permitted. Since the motor was able to bring the throwing arm to its release point in

two-thirds of the required time, we could have used larger springs to store more energy.

The pulley system would have made it easier for our motor the pull down the throwing

arm thus the larger springs could have been used. These two additions would have given

us more distance in our launch. Of course we would have had to consider using stronger

wood for the mechanism to prevent a disaster.

A minor detail that could have been implemented was a different method of

releasing the throwing arm. Instead of the trigger release pin that we used, we has a

device that we could have attached to the end of the throwing arm. The device has a

clamp on one end that the fishing line could have been held with and a trigger switch in

the middle. As the arm was moving downward, the device would move past a vertical

structure and the switch would be tripped, causing the clamps to open, and release the

fishing line. Another minor detail that we would have paid more attention towards is

appearance. Although our design was beautiful and brought tears to our eyes, we could

have at least slapped some paint on there like a few other groups did. We were not at all

concerned with the artistic view or our design, we just wanted it to perform effectively.

Some of the changes and implementations mentioned are not necessary and may

not increase the level of performance of our mechanism but they are some aspects that we

would consider if given the chance to develop another device. We were extremely happy

with our results but there is always room for improvement. I think we could have

definitely launched the squash ball farther than we did and we should have made all three

shots in the accuracy portion of the competition.