Walking Beam Transport Mechanism

Rasikh Tariq (ME113006)

Khawar Shahzad (ME113009)

Mohammad Adam (ME-113125)

Walking Beam Transport

Mechanism

A project report submitted to the

Department of Mechanical Engineering

in partial fulfillment of the requirements for the course of

MECHANICS OF MACHINES.

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Table of Contents

Abstract .......................................................................................................................................... 2

Project Accomplishment .............................................................................................................. 2

Project Learning Outcomes ......................................................................................................... 2

Project Strategy ............................................................................................................................. 2

Walking Beam Transport Mechanism ........................................................................................ 3

Computation process of the Project ............................................................................................ 3

Assumptions ............................................................................................................................... 4

Satisfaction of Grashof Condition ............................................................................................ 4

Position, Velocity & Acceleration Analysis ............................................................................. 4

MatLAB Program .................................................................................................................. 4

Fourbar Mechanism .............................................................................................................. 5

Cognates & Parallel Motion ..................................................................................................... 8

Conclusion ..................................................................................................................................... 8

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Abstract

This project aims for the utilization of kinematic synthesis (type, dimensional and number)

to fabricate a working physical model of an eight link transport mechanism. The mechanism to be

developed in its simplest form would perform the function of transporting boxes/articles which are

being fed onto two rails and are moved ahead one by one. The eight bar mechanism allows moving

more than one article as compared to its four bar counterpart. Transport mechanisms generally

move material and their application lies in various industries- manufacturing, assembly, packaging

etc.

Project Accomplishment

This project was accomplished in 4 steps.

1. Finding the linkages lengths that collectively yield “Straight-line Motion” using Nelson &

Hrones Atlas.

2. Finding cognates and parallel motion using acquired links length.

3. Theoretical design of mechanism and as well as position, velocity & acceleration analysis

(graphical and analytical) of the resulted fourbar mechanism.

4. Manufacturing of mechanism.

Project Learning Outcomes

After the accomplishment of this project we get acquainted with:

1. Using Nelson & Hrones Atlas.

2. Finding cognates and parallel motion of a given mechanism.

3. Position, velocity and acceleration analysis of any complex mechanism using graphical and

as well as analytical approach.

4. Usage of different machines in the accomplishment of project.

Project Strategy

This was not such an easy project as can be observed in animations. Our strategy for the

accomplishment of the project was:

Distribute the project load among the group members and

Accumulating and polishing all the tasks to make it presentable.

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Walking Beam Transport Mechanism

Following is the idyllic model of our project.

This is principally a fourbar mechanism using parallel motion having an objective of

transferring multiple boxes in a straight line. The links lengths are obtained using Nelson & Hrones

Atlas.

Computation process of the Project

Following are the theoretical links lengths and angle.

Type of Link Associated Symbol Theoretical

Lengths (m)

Prototype Lengths

(m)

Ground L1 .1584 0.066

Crank L2 0.072 0.03

Coupler L3 0.14832 0.0618

A to P point Position Vector AP 0.22032 0.0918

Angle <BAP ϑ 31o 31o

Rocker L4, L6 0.16776 0.0699

Following are the lengths and angle that comes after manufacturing of the mechanism.

Since, this was our first project also we don’t have good expertise of market and manufacturing so

there arises change in theoretical and actual manufacture mechanism. Analysis via software help

(MatLAB and AutoCAD) uses theoretical lengths whereas practical lengths are used for analysis

of manual computation.

Type of Link Associated Symbol Mechanism Lengths (m)

Ground L1 0.1584

Crank L2 0.0755

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Coupler L3 0.1275

A to P point position vector AP 0.2015

Angle <BAP Θ 36o

Rocker L4 0.162

Assumptions

Following are the assumption that we considered throughout the project.

Initially the crank angle (θ2) is 450

Crank is rotating with an angular velocity (ω2) is 30rpm or 0.5rps

Linear velocity at point “P” is the forward moving velocity of boxes.

Satisfaction of Grashof Condition

Following is the Grashof equation:

𝑆 + 𝐿 < 𝑃 + 𝑄

In which Ground both link adjacent to the shortest and you get a crank-rocker, in which

the shortest link will fully rotate and the other link pivoted to ground will oscillate. Ground the

shortest link and you will get a double-crank, in which both links pivoted to ground make complete

revolutions as does the coupler. Ground the link opposite the shortest and you will get a Grashof

double-rocker, in which both links pivoted to ground oscillate and only the coupler makes a full

revolution.

Position, Velocity & Acceleration Analysis

We use 4 methods to accomplish the position, velocity & acceleration analysis of this

project.

1. Graphical method using manual drawing.

2. Graphical method using CAD software.

3. Analytical method using manual computation of respective formula.

4. Analytical method using MatLAB software.

The graphical and analytical position, velocity and acceleration analysis using manual tactics

is attached with this document. Whereas, software based calculation are shown here:

MatLAB Program

Following is the MatLAB program of our project. As mentioned earlier, it uses theoretical

computation results.

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% Position, Velocity and acceleration analysis

a=0.072; % L2

b=0.14832; % length of link 3

c=0.16776; % Lenght of Link 4

d=.1584; % Lenght of Ground Link 1

% to calculate k1,k2, and k3

k1=d/a;

k2=d/c;

k3=(a^2-b^2+c^2+d^2)/(2*a*c);

% calculate a,b and c and theta4

for i=1:6:360;

theta2=i-1;

A=cosd(theta2)-k1-k2*cosd(theta2)+k3;

B=-2*sind(theta2);

C=k1-(k2+1)*cosd(theta2)+k3;

theta4(i)=2*atan((-B+sqrt(B^2-

4*A*C))/2*A)*180/pi;

end

%Calculating k4 and k5

k4=d/b;

k5=(c^2-d^2-a^2-b^2)/(2*a*b);

%Calculating D,E,F and Theta3

for i=1:6:360;

theta2=i-1;

D=cosd(theta2)-k1+k4*cosd(theta2)+k5;

E=-2*sind(theta2);

F=k1+(k4-1)*cosd(theta2)+k5;

theta3(i)=2*atan((-E+sqrt(E^2-

4*D*F))/2*D)*180/pi;

end

%CALCULATING OMEGA3

w_2=.5 %Units are radians per second.

w_3=(a*w_2/b)*(sin(theta4-theta2))/(sin(theta4-theta3));

%Units: Radian per second

w3=w_3*60 %Units: RPM

%CALCULATING OMEGA4

w_4=(a*w_2/c)*(sin(theta2-theta3))/(sin(theta4-theta3));

%Units: Radian per second

w4=w_4*60 %Units: RPM

%Calculating Acceleration

alpha2=30 %It is an assumed value of angular

acceleration

A1=c*sin(theta4)

B1=b*sin(theta3)

C1=alpha2*a*sin(theta2)+(a*w_2^2*cos(theta2))+(b*w_

3^2*cos(theta3))-(c*w_4^2*cos(theta4))

D1=c*cos(theta4)

E1=b*cos(theta3)

F1=alpha2*a*cos(theta2)-(a*w_2^2*sin(theta2))-

(b*w_3^2*sin(theta3))-(c*w_4^2*sin(theta4))

%plot(theta2,theta4)

plot(theta2,w_3)

plot(theta2,w_4)

Fourbar Mechanism

Following are the screenshots of the results yielded from fourbar mechanism.

FOURBAR MECHANISM USING THEORETICAL CALCULATIONS

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FOURBAR MECHANISM MADE USING ACTUAL LENGTHS OF

MANUFACTURED MECHANISM

POSITION ANALYSIS OF POINT "P"

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VELOCITY ANALYSIS OF POINT "P"

ACCELERATION ANALYSIS OF POINT "P"

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Cognates & Parallel Motion

We find the cognates and parallel motion of our mechanism and are attached at the end of

this report. Cognates are find out using same conventional method but we used another tactic to

find parallel motion.

Another common method of obtaining the parallel motion is to duplicate the same

linkage (i.e. the identical cognate), connect them with a parallelogram loop and remove the

two redundant links. This technique transforms our four linkage mechanism in eight linkage

mechanism.

Conclusion

After the accomplishment of this project we got acquainted with all the practical traits that

we are learning in our “Mechanics of Machines” course. This project helps us to grace our

academic knowledge and to prepare them to apply practically. We learnt some new techniques of

graphical linkage design like cognates and parallel motion. Furthermore, this project also improves

our grip on different software like fourbar mechanism, MatLAB and AutoCAD. This project also

helps us a lot to figure out different markets and possible machines to accomplish the

manufacturing of a mechanism.

Walking Beam Transport Mechanism

Engineering

Transcript of Walking Beam Transport Mechanism