DESIGN, SYNTHESIS AND SIMULATION OF FOUR BAR … · DESIGN, SYNTHESIS AND SIMULATION OF FOUR BAR...

297

Int. J. Mech. Eng. & Rob. Res. 2012 R R Gurpude et al., 2012

DESIGN, SYNTHESIS AND SIMULATION OF FOURBAR MECHANISM FOR WHEELS FOR CLIMBING

R R Gurpude1*, R D Ashkhedkar1, C C Handa1 and S K Choudhary1

*Corresponding Author: R R Gurpude,[email protected]

In this paper a mechanism is designed for the desired performance output of the machine andthese mechanisms are being used in case of climbing wheels. In cities the buildings are generallythree or four storied and it is not convenient and also financially not easy to fit electric liftseverywhere. A four bar lift can be used by old or disabled person to climb one floor as subjectedto lift. Hence a four bar mechanism to be implemented on every wheel to make the frame to bemoved and to make synthesis and simulation for same mechanism to track its actual path andto understand its motion of stair of height of 220 mm. Taking into consideration the availabledimensions of the four links a software is prepared with help of Fraudenstein’s equation beingcompared graphically with existing dimensions so as to calculate the actual deviation graphicallyand programmatically. Also the sensitivity of each link being carried out for variation of +1 mmand –1 mm in actual dimensions available.

Keywords: Four bar, Simulation, Synthesis

INTRODUCTIONThis paper reveals about design, synthesisand simulation of four bar mechanismfor guiding wheels for climbing mechanism.Machines consist of number of mechanismsfor their successful operation and to givedesired output. Mechanisms like four barmechanism, single slider crank mechanism,double slider crank mechanism, etc., are usedfor transmitting motion, force, torque, etc.

Generally a mechanism is designed for thedesired performance output of the machine

ISSN 2278 – 0149 www.ijmerr.comVol. 1, No. 2, July 2012

© 2012 IJMERR. All Rights Reserved

Int. J. Mech. Eng. & Rob. Res. 2012

1 Department of Mechanical Engineering, K D K C E, Nagpur, India.

and these mechanisms are being used in caseof climbing wheels. In cities the buildings aregenerally three or four storied and it is notconvenient and also financially not easy to fitelectric lifts everywhere. A chain lift can be usedby old or disabled person to clime one flooras subjected to lift.

In this project it is proposed to designsynthesis and simulate the chain liftmechanism of climbing mechanism.

For synthesis of mechanisms followingmethod:

Research Paper

298


• Function generation

• Path generation

• Body guidance

• Fraudenstein’s equation

It is time consuming to carry on the analysis,mathematical or graphical to simulate amechanism. Software is required to bedeveloped for the same purpose.

To design the basic mechanisms for findingdifferent positions, synthesize that mechanismsimulates it by taking or exist dimensions, aCAD model is to be developed.

Also an C-language software is beingprepared along with formulation ofFraudenstein’s equation so as to calculate thedeviation in dimensions by plotting graphs forvariation of about 5 degrees in input value andprogrammed values to find (x, y) co-ordinates

for different positions. And also the sensitivityof each link being carried out for variations of+1 mm and –1 mm in actual dimensionsavailable.

CONCEPTThe aim of the mechanism is, wheel to climbobstacles, steps, or slopes with a suitablesmooth path. The proposed four bar linkagecan be installed on each wheel of vehicle, whichtherefore can capable to climb stairs withsuitable comfortable motion. A straight linetrajectory for centre of wheel is ensured throughan easily controlled motion, and compactnessof mechanism design makes it suitable forstaircase climbing wheelchair for aidingpeople with disabilities.

Figure 1a, 1b, 1c and 1d shows the exactmotion for mechanism which will be actuallyimplemented on assembly wheels.

(a) The Position of the Wheel at the Stairon the Urge to Climb

(b) The Actual Locking Position of the Wheelat the Stair

(c) The Motion of Input Links and will Pullthe Wheel on Stair

(d) The Climbed Position of the Wheeland Locked Wheel

Figure 1: The Actual Concept

299


The Actual Mechanism

The actual mechanism consist of four links, i.e.,1.1, 1.2, 1.3 and 1.4 has an input link 1.5 whichis the slider makes input for mechanism andalso the Figure 2 shows the actual position ofmechanism along with wheel passing over theobstacles.

Degree of Freedom

1) Kutzbach criterion

n = 3(l – 1) – 2j – h

where l: Number of links

j: Joints

h: Number of higher pair

2) Grublers criterion

n = 3(l – 1) – 2j

where l: Number of links

j: Joints

Synthesis

There are several methods by which synthesiscan be carried out as discussed earlier. Outof which we will go for Fraudenstein’s equationbecause of advantage that all values are beingarranged in analytical manner and alsocalculation are being arranged simpleformulation hence will leads towards accuracyas compared to other methods as that of

Figure 2: The Four Bar Mechanism

Fixed LinkA

LNC

DX

xo

B

C

Openo

y

Y

1.1

1.4

1.5

1.6

1.3

1.2

Climbing-Wheel Mechanisms

22

1

Positioning Mechanism

Figure 1 (Cont.)

300


graphical which will leads to an huge error incase of small mistakes.

To solve resolving all forces in x-directionand y-direction on adding both we have

cos1

. cos1 + sin

1. sin

2 = k

1cos

1 –

k2cos

2 + k

3

cos(2 –

1) = k

1cos

1 – k

2cos

1 + k

3

where,

k1 = r

1/r

2, k

2 = r

1/r

4, k

3 = r

22 – r

32 + r

42 + r

12/r

2 . r

4

RESEARCH METHODOLOGY• Synthesis of climbing four bar mechanism

by Fraudenstein’s method.

• Preparation of cad model of synthesizedclimbing mechanism.

• Simulation of climbing mechanism.

The Actual Programme

#define PI 3.14

#include<stdio.h>

#include<conio.h>

#include<math.h>

void main()

{

float ab=220,bc=100,cd=111,da=97,A,B,C,D,E,F;

int theta;

float figh,figh1,figh2,beta,beta1,beta2,rtheta,i;

float x1=0.0,y1=0.0,x2,y2,x3,y3,x4=da,y4=0.0;

float k1,k2,k3,k4,k5,cnst1,cnst2,cnst3,cnst4;

clrscr();

printf(“Enter the value of theta\n”); scanf(“%d”,&theta);

rtheta=theta*PI/180;

printf(“x1=%f,y1=%f\n\n”,x1,y1);

x2=ab*cos(rtheta); y2=ab*sin(rtheta);

printf(“x2=%f,y2=%f\n\n”,x2,y2);

k1=da/ab; k2=da/cd;

k3=(pow(ab,2)-pow(bc,2)+pow(cd,2)+pow(da,2))/(2*ab*cd);

k4=da/bc; k5=(pow(cd,2)-pow(ab,2)-pow(bc,2)-pow(da,2))/(2*ab*bc);

A=(1-k2)*cos(rtheta)+k3-k1; B=-2*sin(rtheta);

C = k 1 + k 3 - ( 1 + k 2 ) * ( c o s ( r t h e t a ) ) ;D=(k4+1)*cos(rtheta)+k5-k1;

E=B; F=((k4-1)*cos(rtheta)+k5+k1);

cnst1=(-B+sqrt(B*B-4*A*C))/(2*A); cnst2=(-B-sqrt(B*B-4*A*C))/(2*A);

figh1=2*atan(cnst1)*180/PI; figh2=2*atan(cnst2)*180/PI;

cnst3=(-E+sqrt(E*E-4*D*F))/(2*D); cnst4=(-E-sqrt(E*E-4*D*F))/(2*D);

beta1=2*atan(cnst3)*180/PI; beta2=2*atan(cnst4)*180/PI;

for(i=-25;i<=70;i++)

{

if(figh1<0)

{

figh=figh1;

}

}

figh=figh2;

if(beta1>0)

{

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le 1

: C

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pari

son

of R

esu

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ph

ically a

nd

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gra

mm

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cally

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ut

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aual

Dim

ensi

on

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ph

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nc

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./A

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l.A

nal

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if.

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.

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bb

cc

dd

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x2Y

2-y2

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Y3x3

y3X

3-x3

Y3-

y3x4

y4

-

302


beta=beta1;

} else

{

beta=beta2;

}

printf(“figh=%f \n\n”,figh);

x3=cd*cos(figh*PI/180); y3=cd*sin(figh*PI/180);

printf(“x3=%f,y3=%f\n\n”,x3,y3); printf(“x4=%f,y4=%f\n\n”,x4,y4);

getch();

GRAPHICAL RESULTSSimulation

Step 1: Identify the problem.

Step 2: Formulate the problem.

Step 3: Collect and process real system data.

Step 4: Formulate and develop a model.

Step 5: Validate the model.

Step 6: Document model for future use.

Step 7: Select appropriate experimentaldesign.

Step 8: Establish experimental conditionsforums.

Step 9: Perform simulation runs.

Comparison

1. Curb assistive mechanisms forwheelchairs:

• Negative Point

– Increased frontal area rear requiredfor turning

Figure 3: Actual Graphs with Dimensional Results

Figure 4: The Actual Simulation

303


– Cannot operate backward

– Not available for or compatible withall type of wheel chair

• Feature

– Raise the crub negotiating ability of awheel chair’s front wheels

– Retrofitable to a wide range ofmanually propelled and powerd wheelchair

– Low cost

– Light weight

2. Lightweight wheelchair stair-climbingattachments:

• Features

– Stair-climbing ability

– Suitable to almost all stairs(max. stepheight up to 25cm scale mobile/ 21cmC-max)

– Compact

– Uses existing wheel chair-no transferrequired Lightweight(25kg plus wheelchair scalamobil

• Negative point

– Required special instruction regardingusage

– Dedicated assistant operated wheelchair-transfer required

Figure 5: Curb Assistive Mechanisms for Wheelchairs

Wheelchair Caster

Additional Wheel

Curb Curb

CurbCatcher

WheelchairCaster

a) Additional Wheel Illustration b) Additional Wheel Photo c) Curb Catcher Illustration

Figure 6: Lightweight Wheelchair Stair-Climbing Attachments

a) C-Max Stair-Climber b) Stair Edge Brakes c) Climber Operation

304


– Orbital motion tends to beuncomfortable for passenger

– Auto brake mechanism does not suitroughly surfaced stair

LITERATURE REVIEWLiterature review is an assignment of previoustask done by some authors and collection ofinformation or data from research paperspublished in journals to progress our task. It isa way through which we can find new ideas,concept. There is lot of literatures publishedbefore on the same task; only three to fourpapers are taken into consideration from whichidea of the project is taken.

Gonzalez (2008) explained the amechanism that aims a wheel to climbobstacles, steps, or slopes with a suitablesmooth path. The purposed at our entire barlinkage can be installed on each wheel ofvehicle, which therefore can capable to climbstairs with suitable comfortable motion. Astraight line trajectory for centre of wheel isensured through an easily controlled motion,and compactness of mechanism designmakes it suitable for staircase climbingwheelchair for aiding people with disabilities.

Morales and Feliu (2007) explained a newadvance in mobility assistance came withdevelopment of wheelchair of negotiationarchitectural barrier. The first commercialmodel was based on a single-section trackmechanism.

He also mentioned about a completemechanical and kinematic designmethodology of a new wheelchair withadditional properties like, a capability ofadapting to the new environment overcomingspecial profile characterized by obstacle with

vertical slopes, a capability to move system,in a comfortable way for passenger, overcontinuous smooth profile and a capability toascent and descent staircase. It is veryimportant to remark these new qualities areobtained without necessary of personalassistance. All mechanical designmethodology is described. Also sectionsinvolve description of different mechanicaldevices, the performance of thesemechanisms in real situation and mechanicalsynthesis design used to obtained a compactsolution. Also a kinematic designmethodology which performs the forward andinverse kinematic over smooth profile.Moreover, this methodology can be easilyparticularized to a special prof ilecharacterized by obstacles with verticalslopes. Also gives a short description ofexperimental prototype designed.

CONCLUSIONThe graphical and programme results arebeing analyzed and comparison is carried outresults into less than1% deviation .Also withvariations in dimensions as mentioned therewill be a very little variation in (x, y)co-ordinates for every single change indimensions out of which ,when change indimension for input link as compared to otherlink is very less as C-programmed. Henceinput link is more sensitive than the others.

REFERENCES1. Gonzalez A, Ottaviano E and Ceccarelli M

(2008), “A Generalized Performance onthe Kinematicfunctionallity of a Four-BarBased Mechanism for Guiding Wheels inClimbing Steps and Obstacles”, Journal ofMechanism and Machine Theory.

305


2. Gonzalez P Pintado (2006), “KinematicModel of New Staircase ClimbingWheelchair and its ExperimentalValidation”, in the International Journal ofRobotics Research, Vol. 9.

3. Morales R and Feliu V (2007), “KinematicModel of a New Staircase ClimbingMechanical and Kinematic DesignMethodology of a New Wheelchair withAdditional Capabilities”, Journal ofRobotic Research, Book Aided by Maki KHabib.

4. Murray J Lawn (2003), “Modeling of a Stair-Climbing Wheelchair Mechanism with HighSingle Step Capability”, IEEE.

5. Murray J Lawn (2002), “Study of Stair-Climbing Assistive Mechanisms for theDisabled”, Ph.D thesis, Graduate Schoolof Marine Science and Engineering,Nagasaki University, Nagasaki City, Japan.

6. Rafael Morales, Antino Gonzalez-Rodriguezand Angel G Gonzalez-Rodriguez (2010),“Mechanical Synthesis for Easy and FastOperation in Climbing and Walking Robot”.

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