ijirae:: effect of wall thickness variation in hyper elastic semi-cylindrical fluidfilled silicone...

8/10/2019 IJIRAE:: EFFECT OF WALL THICKNESS VARIATION IN HYPER ELASTIC SEMI-CYLINDRICAL FLUIDFILLED SILICONE RUBB

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International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163Volume 1 Issue 8 (September 2014) www.ijirae.com

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2014, IJIRAE- All Rights Reserved Page - 8

EFFECT OF WALL THICKNESS VARIATION IN

HYPER ELASTIC SEMI-CYLINDRICAL FLUID

FILLED SILICONE RUBBER ROBOT FINGER ON

ITS LOAD CARRYING CAPACITY

P.Subramaniam R.MarappanDepartment of Mechanical Engineering. Department of Mechanical Engineering

Sengunthar Engineering College. Tiruchengode, K.S.R College of Engineering, Tiruchengode,

Abstract -- In this paper the influence of thickness variation in the outer wall of semi-cylindrical hyper elastic, fluid filled siliconerubber robot finger on its load carrying capacity under static condition is studied. The shift of contact area, slip and the maximumtensile stress in finger wall are the factors which determine the load carrying capacity of the robot finger. An analytical model is

used to determine the deformation and shift of contact area at various applied loads. Hyper elastic silicone rubber finger modelshaving different outer wall thicknesses are used for this analysis. The load carrying capacities of the fingers are determined fordifferent combinations of normal and the tangential loads. Experimental load tests were also conducted on the actual finger

specimens to validate the analytical findings. It is found that the analytical findings are closer to the experimental results.

Keywords :Hyper elastic Finger, Silicone rubber, Contact area, Shift, Slip, Stress.

I. INTRODUCTION

We, human beings can manipulate different objects because of the dexterity of our fingers. We can handle largevariety of objects from very hard to soft . At the same time we can sense the texture of the objects and according to thatthe fingers deform and change the grasping force to avoid slipping. The deformation is an important factor in human

hands ability to create a stable and encompassing grasps on the object. Many attempts have been made to simulate thehuman grasping in robot fingers [1,2]. The robot fingers having high stiffness do not deform more and they fail ineffective grasping. Xydas et al [3,4] developed a contact model and studied soft contact mechanics using FEA andvalidated the results by experiments. Kwi-Ho Park et al [5] modelled a hemi spherical shaped soft finger tip for the robotfinger and performed a non linear finger analysis on its deformation. Biagiotti et al [6] modelled a hemispherical finger tip

having soft outer pad and rigid inner core to investigate their contact mechanics under normal and tangential loads. Xydasand Koa [7] used FEA analysis and verified the results with experiments to support their proposed power law = .Where is the radius of contact, is a constant depending on material and geometry of the finger tip, is a

constant which has the range of 0

, that depends on the finger tip material. Dan Reznik and Christian Laugier [8]

developed a computational model for the dynamics of semi circular deformable fingertip. Kojii Murakami and TsuyomuHasegawa [9] of Kyushu university developed a finger tip model equipped with soft skin and hard nail and validated

using experimental results. Takaniro Inoue [10] proposed an elastic model, which comprised of linear spring elementshaving constant Youngs modulus and formulated an equation for the deformation of the finger tip. Takaniro Inoue andShinichi Hirai [11] modelled a pair of hemispherical soft finger tips with 1-DOF grasping and manipulation of a rigid

object and validated by experiments. As an advancement in the finger modelling, Berselli and vassura [12] had designed afinger model having outer finger pad of internal layers with fluid filled voids. This finger model gives good complianceand damping property. Biagiotti et al [13] proposed a mechatronic design of finger model which is yet to be developed.

Still many attempts are being made on soft contact manipulation for humanoid like grasping. Any how very little workwas done on suitable finger material and its physical configuration. In this paper, fingers with different thickness outer

layer ,which are filled with viscous fluid in their core are subjected to different normal and tangential loads and the effectof wall thickness on their load carrying capacity is studied.

II. FINGER MODEL

A semi cylindrical shaped soft finger model made up of silicone rubber with adequate length and radius has been

designed [14]. The finger model is made as a thin skin like hyper elastic outer wall filled with incompressible fluid,which uniformly distributes the applied force to the wall. The force-deformation relationship has been formulated fromthe basic principles of mechanics. The radius of the semi cylindrical finger is taken as R and its outer wall thickness as

t. The length of the finger is taken as L and for simplicity of calculation it is considered as unity. The Youngsmodulus of finger material is E, which varies with applied load .The finger model is placed against a rigid flat

surface. Over the cross section of finger, the normal load W is acting. This causes compression of finger against thetarget surface and its deformation is b. Due to this compression, the pressure intensity of inside fluid is increased to p.


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This inside pressure acting on the free curved surface, creates a tensile force in the finger layer and so it elongates by l.The reduction in volume of the finger due to the compression is compensated by this elongation, with lateral bulging of

the finger as shown in figure 1. Due to symmetry of the finger with respect to vertical axis, one quarter section isconsidered for analysis.

Fig. 1 Finger deformation due to Normal load

At the balanced condition, a tangential force Ft is acting along the finger outer wall at the fixed ends. Due to this tensileforce the wall thickness is reduced to t1. The half contact width of finger with the object surface is w and newradius of the free curved surface is R1, which is less than the original radius R

III. GRASPING AND LIFTING

On the above deformed finger model, a tangential pulling force is applied along the contact area as shown in

figure 2.

Fig. 2 Application of tangential load along the contact area

This applied force causes force imbalance on both sides of the finger with respect to the vertical axis OP. The moment

caused by this force is balanced by a couple acting through the fixed ends creating a static balance. Since the fluid volumeis constant, during deformation, some amount of fluid from the right side quadrant is shifted to left side. By equating the


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volume reduction in right side, to the gaining of left side, the volume balancing is achieved. The finger model underequilibrium condition is shown in figure 3.

Fig. 3 Deformed finger model under force balanced condition

Considering unit length of finger, the area of contact is =2 1

Then, the contacting force =

= 2 1

Taking coefficient of friction between the rubber finger surface and the material as ,

The maximum load that can be lifted per unit length of finger , without slip

=2

Now, the finger shape is changed to accommodate the moment due to the force F as shown in figure-3.

The Moment created =( ) (Clockwise) (1)

Hence for the equilibrium, there should be a balancing anticlockwise moment.

It is = 2 (Anticlockwise).(2)

Here, N is the equivalent force to give required anticlockwise moment with respect to the centre O.

At equilibrium condition 2 =( ).

From this , N=()

Now this N is also acting along the Normal load


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So, the total upward force acting on the right side wall = +

Then, the tangential force acting in the right side wall, =

()

The elongation of the right side wall due to the tangential force is

=

()

Now, new arc length= +

On the free arc length, the inside pressure p is acting on its projected area and creates a force, which is

perpendicular to its chord MN.

Then, force acting on the free curve =

This force is equal to the forces acting at the ends of the wall. So , it can be written as

( ) =[+(sin90 2)] +[(cos90 2)]

.-----------(A)

Similarly, the tangential force in the left side wall is =

()

The elongation of the Left side wall due to this tangential force is

=

()

The new arc length= +

On the left side free arc length, the same inside pressure p is acting on its projected area and creates a force

which is perpendicular to its chord 11.

The force acting on the free curve = 11

This force is equal to the forces acting at the ends of the left side wall. So , it can be written as

( 11) =[+(sin90 2)] +[(cos90 2)]

.-----------(B)

The above equations (A) and (B) hold good for particular angle values of , respectively, when the force

balance is achieved. Using deformation parameters of the model such as inside pressure, tangential force and contact width,the force balancing has been achieved through iteration using a computer program by varying the value of . Afterreaching the force and volume balance, orientation of the deformed shape, its shift along the direction of force and tensilestress in the finger are calculated.

IV. SHIFT OF CONTACT AREA AND TENSILE STRESS IN FINGER WALL

Because of application of Tangential force F on the contacting area, it shifts in the direction of force. It is

measured from the shifting of the chord MN to the new orientation. This shift causes the right side free wall to get moreradius of curvature and the left side wall more bulged with low curve radius. Also stress in the right side wall is increasedthan the left side wall. The maximum tensile stress in the right side wall is calculated. Using a computer program, applying

different pre-stressing normal loads and tangential forces, the corresponding shift of contact area and maximum tensilestress in the wall are found-out for 2 ,3, 4 and 6 mm outer wall thickness fingers.


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V. EXPERIMENTAL LOAD TEST

Silicone rubber fingers similar to the analytical model were manufactured by liquid injection moulding as per ASTMD 695 standard. The mean radius of finger was 10 mm and the length of finger was 30 mm. The fingers having outer wallthickness of 2,3,4 and 6 mm are moulded for the load test. Figure 4 shows the sample silicone rubber fingers. The inner

cavity was filled with SAE 30 oil and the top opening was sealed by screwing a flat steel plate over it.

Fig. 4 Sample silicone rubber fingers

A special sliding table mechanism was designed and fabricated for the testing purpose. It consisted of a top sliding

table mounted over a bottom rigid plate and in-between them frictionless spherical steel balls are provided in horizontalsemi cylindrical guide ways. They freely roll in the guide ways to provide sliding motion to the top sliding table over thebottom one. Over this table, the fluid filled hyper elastic robot finger was rigidly fixed using a face plate.

The test was conducted in a compression testing machine, supplied by AVJ Engineering Industries, India. It has the

maximum loading capacity of 25 kN, with a least count of 0.01 N. A strain gauge load-cell was mounted with its fixed topplatform to measure the applied normal load. One mechanical dial gauge was fitted between the top and bottom platformsto measure the vertical compression and the other one between the fixed and moving table to measure the shift of contact

area of the finger. The accuracy of the dial indicators was 0.001 mm.

Fig.5 Slip and shift test set up for robot fingers


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The finger specimen was placed over the moveable bottom platform and rigidly fixed. The finger mounted slide wastied to a string, to the other end of which a dead-weight hanger was attached and suspended through a pulley mechanism

for loading purpose. Figure 5 shows the test set-up. By applying normal load on the finger, grasping contact was createdbetween the finger and the target surface. Then a tangential pulling load was slowly applied to the slide through the string,by the pulley and dead weight arrangement. By increasing the dead weight the horizontal shift was noted down until the

plate slipped. At slipping condition the tangential applied load and the normal load were noted down. The test was repeated

for three times and the mean value was taken for calculation. The experiment was repeated for different normal loads andthe shift , slip details were noted down . This was carried out for all the four different wall thickness fingers. Now, the

tangential loads at which slipping takes place are plotted against their respective applied normal loads. By takingcoefficient of friction between silicone rubber and steel surface as 0.6 [9], the slipping tangential load for the same appliednormal load is analytically calculated and also plotted in the same graph. The coefficient of friction assumed, gives the

slipping load, which is closer to that of experimental results.

VI. RESULTS AND DISCUSSION

In figure 6, shift of contact area and tensile stress in the finger layer are plotted against applied normal load for afinger with 2 mm wall thickness. By joining the slip points on the shift curve , the shift boundary is obtained. Similarly by

joining the slip points on the stress curve , the stress boundary is obtained.

Fig. 6 Safe working area of the finger with 2 mm wall thickness

The area trapped under these limiting boundary lines is the safe working area for the finger. Within these boundaries, as theapplied normal load is increased the shift of contact area is found to decrease, but the tensile stress in the wall increases.The tangential load lifting capacity of the finger, both experimental and theoretically assumed values are plotted against

applied normal load in figure 7(a). Contact area and the local normal load acting on the contact area are also plotted in thesame figure. It is seen that the theoretically assumed values of load lifting capacity of the finger is almost nearer to theexperimentally obtained values.

Fig.7(a) Variation of Contact area , Local normal load, Analytical and Experimental values of tangential load

against Applied normal load for a finger with 2 mm wall thickness.


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The deviation may be due to the assumed coefficient of friction, which seems to be slightly on the higher side for thematerial that is used. Normally these lines should be straight lines as the coefficient of friction between two materials will

be a constant, as it is a material property. But here the slope of these lines increase as the normal load increases, whichmeans that the apparent coefficient of friction increases.

It is seen from the same figure that the slope of contact area curve decreases, while that of the local normal load (as

shown in figure 7(a)) and inside fluid pressure (as shown in figure 7(b)) are increasing. It means that, when the applied

normal load is increased the local normal load increases with increased rate. This increased local normal load actuallydecides the load lifting capacity of the finger. That is, the coefficient of friction being constant, the higher values of local

normal load facilitates higher load carrying capacity, even though the applied normal load has not increased to that extent.Hence apparent coefficient of friction calculated based on applied normal load and load carrying capacity of the finger willkeep increasing.

Fig.7(b) Variation of Inside fluid pressure of finger against Applied normal load .

Figures 8 to 10 show the safe working areas of 3,4 and 6 mm wall thickness fingers.


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Inside

Fluid

Pressurein'N/sqmm'

App lied Normal load in 'N'


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As the wall thickness of the finger increases, the induced stress for equal applied normal loads reduces and hencethe stress lines are brought down. This leads to shifting of stress boundary towards the right side. As the wall thicknessincreases, for a particular applied normal load, slipping takes place earlier or for a lower value of horizontal load lifted as

shown in figure 11. The reason is that for thicker walls , the contact area is smaller and hence the local normal load issmaller and hence slip takes place for a lower value of tangential load. This is clear from the figure 12, in which localnormal loads are plotted against applied normal loads for different wall thickness fingers.

Fig. 11 Variation of tangential load that can be lifted without slip against

applied normal load of different wall thickness fingers

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

Tangentialloadatslip

in'N'

App lied nor mal Load in 'N'

2 mm wall finger

3 mm wall finger

4 mm wall finger

6 mm wall finger


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Fig.12 Variation of local normal load against applied normal load at slipping condition of different wall thickness fingers

VII. CONCLUDING REMARKS

When a hyper elastic, semi-cylindrical fluid filled robot finger made up of silicone rubber with a specific wallthickness is subjected to normal and tangential loads ,

1.

The tensile stress in the wall increases and the shift of contact area decreases as the normal load isincreased.

2. Stress and shift limits at slipping condition are the boundary lines for the finger to operate.3.

Under identical loading conditions as the finger wall thickness increases, the stress and shift of contactarea reduce.

4. Increasing the wall thickness increases the range of load lifted.5.

When applied normal load is increased the local normal load increases, with increasing rate giving anincrease in the value of apparent coefficient of friction.

6. For a particular value of applied normal load, finger with thin wall thickness is capable of lifting higherloads, as the local normal load is higher for this finger due to higher contact area and higher fluid

pressure.ACKNOWLEDGMENT

The authors wish to acknowledge the Sengunthar Educational Trust, Tiruchengode for providing facilities to dothis research work.

REFERENCE

[1] Mohammad Asim Farooqi, Takashi Tanaka, YukioIkezawa, Toru Omata and Kazuyuki Nagata (1999) Sensorbased control for the execution of re-grasping primitives on a multi fingered robot hand,Proceedings of IEEE

International Conference of Robotics and Automation, PP 3217-3223.[2] Takeshi Matsuoka, Tsutomu Hasegawa and Kyuhei Honda, (1999) A dexterous manipulation system with error

detection and recovery by a multi fingered robotic handProceedings of IEEE International Conference on

Intelligent robots Robotics and systems, PP 418-423.[3] Xydas. N, Koa. I (September -1999) Modeling of contact mechanics and friction limit surface for soft fingers

with experimental results, International Journal of Robotic research , 18(9): 941-950.

[4] Xydas. N, Imin Kaot, (2000) Influence of material properties and finger tip size on the power law equation forsoft fingers,Proceedings of the IEEE/RSJ International conference on intelligent robots and systems.

[5] Kwi-Ho Park, Byoung-Ho Kim and Shinichi Hiraj, (2003) Development of a soft finger tip and its modelingbased on force distribution Proceedings of IEEE International Conference of Robotics and Automation,PP 3269-3174.

[6] Biagiotti.L, Tiezzi.P, Vassura.G and Melchiorri.C, Modelling and controlling the compliance of a robot handwith soft finger pads, DEIS University of Bologna, Italy.

[7] Nicholas Xydas, Milind Bhagavat and Imin Kao, (2000) Study of soft finger contact mechanics using finiteelement analysis and experiments, Proceedings of IEEE International Conference of Robotics and Automation,

PP 2179-2183,

[8] Dan Reznik and Christian Laugier, Dynamic simulation and virtual control of deformable finger tip, Universityof California.


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[9] Koji Murakamii and Tsutomu Hasegawa , Design of robotic finger tip based on human-miemetic functions,Kyushu University

[10] Takahiro Inoue Shinichi Hiri, (2005) Elastic model of deformable finger tip for soft fingered manipulation,IEEE Transaction on Robotics, Vol.1 , No 11.

[11] Takahiro Inoue Shinichi Hiri, How Hemispherical soft fingertips enhance dexterity in Grasping and

manipulation , Kusatsu, Shiga-525-8577, Japan.

[12] Berselli.G, Vassura,G. (July 2010), Non linear Modeling and Experimental Evaluation of Fluid filled Soft padsfor robotic hands , 9-th Youth Symposium on experimental Solid Mechanics, Trieste, Italy ,

[13] Biagiotti.L, Lotti.F, Melchiorri.C and Vassura.G, (2003), Mechatronic design of Innovative Fingers forAnthropomorphic Robot Hands, Proceedings of IEEE International Conference of Robotics and Automation,PP 3187-3191,

[14] Subramaniam. P and Marappan. R , (2013) Semi Cylindrical Fluid Filled Hyper elastic Finger Model for SoftContact, International Journal of Engineering and Technology, Engg Journals Publications, Volume 5: 6 ,Page 1131-1137.

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