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IJIRAE:: EFFECT OF WALL THICKNESS VARIATION IN HYPER ELASTIC SEMI-CYLINDRICAL FLUIDFILLED SILICONE RUBBER ROBOT FINGER ON ITS LOAD CARRYING CAPACITY

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In this paper the influence of thickness variation in the outer wall of semi-cylindrical hyper elastic, fluid filled silicone rubber robot finger on its load carrying capacity under static condition is studied. The shift of contact area, slip and the maximum tensile 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 models having different outer wall thicknesses are used for this analysis. The load carrying capacities of the fingers are determined for different 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.
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    International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163   Volume 1 Issue 8 (September 2014 )   www.ijirae.com __________________________________________________________________________________________________ © 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.Marappan  Department 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 silicone  rubber robot finger on its load carrying capacity under static condition is studied. The shift of contact area, slip and the maximum  tensile 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 models  having different outer wall thicknesses are used for this analysis. The load carrying capacities of the fingers are determined for  different 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 large variety of objects from very hard to soft . At the same time we can sense the texture of the objects and according to that the fingers deform and change the grasping force to avoid slipping. The deformation is an important factor in human hand’s ability to create a stable and encompassing grasps on the object. Many attempts have been made to simulate the human grasping in robot fingers [1,2]. The robot fingers having high stiffness do not deform more and they fail in effective grasping. Xydas et al [3,4] developed a contact model and studied soft contact mechanics using FEA and validated the results by experiments. Kwi-Ho Park et al [5] modelled a hemi spherical shaped soft finger tip for the robot finger 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. Xydas and 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 finger–tip. Kojii Murakami and Tsuyomu Hasegawa [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 elements having constant Young’s modulus and formulated an equation for the deformation of the finger tip. Takaniro Inoue and Shinichi 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 a finger model having outer finger pad of internal layers with fluid filled voids. This finger model gives good compliance and 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 work was 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 effect of 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 from the 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 Young’s modulus 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 the target surface and its deformation is ‘b’. Due to this compression, the pressure intensity of inside fluid is increased to ‘p’.    International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163   Volume 1 Issue 8 (September 2014 )   www.ijirae.com __________________________________________________________________________________________________ © 2014, IJIRAE- All Rights Reserved Page - 9 This inside pressure acting on the free curv ed surface, creates a tensile force in the finger layer and so it elongates by ‘δl’. 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 is considered 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 tensile force the wall thickness is reduced to ‘t 1 ’. The half contact width of finger with the object surface is ’w’ and new radius of the free curved surface is ‘R  1 ’, which is less than the srcinal 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 volume is constant, during deformation, some amount of fluid from the right side quadrant is shifted to left side. By equating the    International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163   Volume 1 Issue 8 (September 2014 )   www.ijirae.com __________________________________________________________________________________________________ © 2014, IJIRAE- All Rights Reserved Page - 10 volume reduction in right side, to the gaining of left side, the volume balancing is achieved. The finger model under equilibrium 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       International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2163   Volume 1 Issue 8 (September 2014 )   www.ijirae.com __________________________________________________________________________________________________ © 2014, IJIRAE- All Rights Reserved Page - 11 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   =  ℎ +    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   =  ℎ +    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  1  1.  The force acting on the free curve =  ×  1  1   This force is equal to the forces acting at the ends of the left side wall. So , it can be written as (  ×  1  1)  =[    +   (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 ′′ . After reaching the force and volume balance, orientation of the deformed shape, its shift along the direction of force and tensile stress 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 more radius of curvature and the left side wall more bulged with low curve radius. Also stress in the right side wall is increased than 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 tensile stress in the wall are found-out for 2 ,3, 4 and 6 mm outer wall thickness fingers.
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