Rasikh Tariq (ME113006)Khawar Shahzad (ME113009)Mohammad Adam (ME-113125)

Walking Beam Transport Mechanism

A project report submitted to theDepartment of Mechanical Engineering

in partial fulfillment of the requirements for the course ofMECHANICS OF MACHINES.

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 SymbolTheoretical Lengths (m)

Prototype Lengths (m)

Ground L1 .1584 0.066Crank L2 0.072 0.03Coupler L3 0.14832 0.0618A to P point Position Vector AP 0.22032 0.0918Angle <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

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Crank L2 0.0755Coupler L3 0.1275A to P point position vector AP 0.2015Angle <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 analysisa=0.072; % L2b=0.14832; % length of link 3c=0.16776; % Lenght of Link 4d=.1584; % Lenght of Ground Link 1% to calculate k1,k2, and k3k1=d/a;k2=d/c;k3=(a^2-b^2+c^2+d^2)/(2*a*c);% calculate a,b and c and theta4for 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 k5k4=d/b;k5=(c^2-d^2-a^2-b^2)/(2*a*b);%Calculating D,E,F and Theta3for 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 OMEGA3w_2=.5 %Units are radians per second.w_3=(a*w_2/b)*(sin(theta4-theta2))/(sin(theta4-theta3)); %Units: Radian per secondw3=w_3*60 %Units: RPM%CALCULATING OMEGA4w_4=(a*w_2/c)*(sin(theta2-theta3))/(sin(theta4-theta3)); %Units: Radian per secondw4=w_4*60 %Units: RPM%Calculating Accelerationalpha2=30 %It is an assumed value of angular accelerationA1=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.

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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"

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.

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