Optimization of Fabric Manipulation during Pick/Place Operations

INTERNATIONAL JOURNAL OF CLOTHING SCIENCE AND TECHNOLOGY zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) Optimization of Fabric Manipulation during Pick/Place Operations zyxwvutsrqponmlkjihgfedcbaZYXWVUTS J.W. Eischen and Y.G. Kim zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIH North Carolina State University, Raleigh, North Carolina, USA zyxwvutsrqponmlkjihgfedcbaZYXWVU fabric coming into contact with a rigid object of arbitrary shape. To follow is a brief review of the literature that has influenced our work, particularly in the area of fabric material response and fabric drape. The earlier work on fabric mechanics was mainly concerned with measurement of flexural rigidity. Peirce[1] initiated research in the area of fabric bending behaviour and material properties measurement. He measured flexural rigidity and bending modulus of fabrics using the cantilever test, and also modelled a typical woven fabric. This model was widely used in later works. Abbott[2] reported on measurement of flexural rigidity of fabrics using five different experimental methods, especially the Peirce cantilever test. In 1960[3], he presented factors (clustering and rigidity factors) on the flexural rigidity of the fabric. Cooper[4] measured flexural rigidity of fibres, yarns and woven fabrics using the cantilever test. Research concerning fabric buckling behaviour followed. Dahlberg[5] conducted research on plate and shell buckling of fabrics and obtained load-deflection curves through experimentation. Fabric parts were modelled as thin plates, and analysed using Euler's column buckling formula. Lindbergzyxwvutsrqponmlkjihgfed et al.[6], using various commercial fabrics, analysed and discussed load-deformation curves obtained for shearing, plate buckling, and shell buckling. Lindberg[7] also discussed the phenomena of buckling for two fabrics A textile fabric is a very complex non-linear mechanical system. For many reasons, it is necessary to be able to predict the drape and deformation of fabric parts over complex objects while they are being manipulated during certain manufacturing operations. It is nearly impossible to obtain "closed form" mathematical solutions for such problems, and thus numerical methods are sought. The physical model used to make such predictions is of the utmost importance. Many researchers have modelled fabrics as an assemblage of their constitutent fibres or yarns. Such models have little practical value for general fabric structures due to the prohibitive number of such fibres and yarns. A very tempting modelling theme is to consider the fabric structure as a flexible continuum that undergoes arbitrarily large displacements and rotations. The effect of the interacting fibres (or yarns) is accounted for through the overall material response. In this research, certain fabric drape and manipulation problems are investigated where the fabric part is modelled as a very flexible beam (or strip). Thus, motion is restricted to bending in a single plane. To produce simulations, the analyst must provide data regarding: initial configuration of the fabric part, material properties, and external loads. The loading can consist of self-weight, prescribed forces at arbitrary points on the part, or prescribed displacements at arbitrary points on the part. The formulation includes the ability to ascertain the effects of the Financial support from the National Textile Center at North Carolina State University is gratefully acknowledged. International Journal of Clothing Science and Technology, Vol. 5 No. 3/4, 1993, pp 68-76, © MCB University Press, 0955-6222 68 Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) VOLUME 5 NUMBER 3/4 1993 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA fabric from a single test. Clapp and Peng[17] attached to each other. Grosberg and presented a comparison of linear and nonSwani[8] presented papers about bending and buckling of fabrics, and explained that linear bending models for predicting fabric bending behaviour is governed by a bending deformation in automated handling. A third rigidity factor and an internal frictional order moment-curvature relationship was couple. In research on the fabric bending used for non-linear material behaviour. curve, Chicurel and Suppinger[9] studied Simulations were performed for the laying of deformed configurations of a coplanar fabrics. The results were compared with crimped fibre with bending and stretching experimental data. deformations included. The minimum For problems involving three-dimensional potential energy principle was used. In 1963, fabric drape, the reader is referred to [18-37]. they presented a theory for three-dimensional Our research can be viewed as an extension crimped fibres with twisting deformation also and generalization of past work. Many of the included. Konopasek and Hearle[10] papers reviewed above deal with a specific formulated a model for three-dimensional geometry and set of loading/boundary fabric bending capable of treating large conditions. This article describes the results deformations. Moment-curvature equations, of a formulation that yields a general moment and force equilibrium equations, approach for solving problems where a wide curvature-orientation equations, and range of geometries and boundary/loading orientation-co-ordinate equations were used conditions are anticipated. This feature will to describe the fabric bending curve. The be illustrated through a set of numerical fourth order Runge-Kutta method was used examples below. for numerical integration of a large set of non-linear differential equations. LloydzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA et al.[11] studied folding of heavy fabric sheets. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA FORMULATION Simo, et al.[38,39] have recently presented a comprehensive finite element-based treatment of geometrically exact beam theory. We have adapted this theory for fabric drape and manipulation studies by including the effect of fabric contact with an arbitrary surface. The mechanical properties of the fabric including axial stiffness (EA) and bending stiffness (EI or "B") are required as input data. Currently, our implementation can handle a non-linear moment curvature response. A full description of the computational details of this formulation THE MODEL WAS AS EFFICIENT AS THAT OF THE FRICTION COUPLE THEORY Brown et al.[12] presented a paper about large deflection bending of woven fabrics in automated material handling, especially for layout of a fabric on a flat work surface. A computer program was developed based on Konopasek's theoretical formulation. Clapp and Peng[13] published a paper concerning buckling of woven fabrics. Their method was equivalent to the simplified version of Konopasek's technique, and used the Timoshenko beam theory. The claim was made that the model was as efficient as that of the friction couple theory. In their next paper[14], the effect of fabric weight was incorporated into a theoretical model based on Grosberg's[15] frictional couple theory. Clapp et al.[16] proposed a very simple experimental scheme to establish the complete moment-curvature response for a Fabric 1 40% polyester/60% cotton twill weave, orchid colour. Bleached, dyed, Finished, and preshrunk in a pure finish Fabric 2 65% polyester/35% cotton plain weave, blue colour. Bleached, dyed, Finished and preshrunk in a resin finish Fabric 3 100% cotton twill weave, yellow colour. Bleached, dyed, finished and preshrunk in a pure finish Fabric 4 65% polyester/35% cotton twill weave, cream colour. Bleached, dyed, finished and preshrunk in a resin finish TABLE I. Test Fabric Descriptions 69 INTERNATIONAL JOURNAL OF CLOTHING SCIENCE AND TECHNOLOGY Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) area A and the second moment of area I will be presented during the AARC were calculated according to A = t and I = conference and documented in future journal t3/12, respectively. Thus, A and I are based publications. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA on a 1 cm wide strip fabric. The weight per FABRIC MATERIAL PROPERTIES unit area is indicated by w. Figure 1 shows the Kawabata bending test We have performed simulations and for the four fabrics. From this test, a value experiments on a group of four test fabrics for bending rigidity is produced ("B" value). supplied by the Galey and Lord Company. This is effectively a bending rigidity (EI) per A description of these fabrics is shown in unit width of fabric. Recall that this value Table I. represents the average slope of the momentThe physical properties of these fabrics is curvature response at curvatures of 0.5 and shown in Table II. The thicknesszyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA t was 1.5 cm, for positive and negative curvatures. measured directly, while the cross sectional t (cm) A (cm2) I (cm4) (gmf/cm2) Fabric 1 Fabric 2 Fabric 3 Fabric 4 0.0292 0.0292 2.075 x 10-6 0.0165 0.0267 0.0483 0.0406 1,126 1,418 2,809 (EA)eff (gmf/cm) 1,515 0.067 0.0483 0.0406 (EI)eff 0.275 0.386 0.080 0.090 9.37 x 1.586X 5.58x (gmf-cm2/cm) 10-6 10-6 10-6 (GA)eff (gmf/cm) 1,126 1,418 2,809 1,515 0.0283 0.0149 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 0.0255 Fabric 1 Fabric 2 Fabric 3 Fabric 4 TABLE III. Effective Linear Elastic Properties of Four Test Fabrics (Per Unit Width, Warp Direction] TABLE II. Physical Properties for Test Fabrics 70 Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) VOLUME 5 NUMBER 3/4 1993 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA These values are reported in Table III as zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA RESULTS (EI)eff, for the warp direction. We term these Numerical simulations for a group of effective properties because neither E nor I is representative problems related to fabric measured directly. Since a fabric is not a manipulation and drape are presented next. homogeneous material, the A and I values These examples exhibit the capability of the calculated above are imprecise. However, by formulation to cope with large viewing A and I as true physical properties displacements/rotations and contact. and E as an effective property, we can Applications specific to textile mechanics are calculate an effective EA (axial rigidity). presented: folding, placement on a work These values are reported in the table also. surface, pick-up from a work surface. The transverse shear rigidity, GA (G = shear Optimization of fabric manipulator paths is modulus) of the fabric has been estimated to also discussed for the pick/place operations. be equal to the axial rigidity. Numerical All simulations use material properties experiments have shown relative insensitivity measured directly from actual fabrics, whose to the values of (EA)eff and (GA)eff for properties are listed above. Simulation results fabrics loaded primarily by their own self are compared with experiment in all cases. weight. Table IV shows polynomial curve fits to Fabric­folding Operation the actual moment curvature (M - x or M - K) Kawabata data. These non-linear Figure 2 shows a simulation and experimental equations are used in the simulations to results for a fabric folding operation. In this compare with results using the simple linear case, a 10 cm-long sample of fabric 1 is relationship M = (EI)effx. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA folded over on to itself. The right end of the Fabric Fabric Fabric Fabric Fabric Polynomial curve fit of actual M - x data (warp) ] 2 3 4 M M M M = = = = 0.34722x 0.39253x 1.53573x 1.34842x - 0.57762 x2 0.63481 x2 2.82874 x2 2.59202 x2 + + + + 0.54667 x3 0.58009 x3 2.84729 x3 2.87504 x3 - 0.23081 x4 0.23870 x4 1.27439 x4 1.41688 x4 + + + + 0.03544 0.03599 0.20789 0.25567 x5 x5 x5 x5 TABLE IV. Polynomial Curve Fit of ActualzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA M - x Data 71 INTERNATIONAL JOURNAL OF CLOTHING SCIENCE AND TECHNOLOGY shows results for fabric 2. Here the difference between the linear and non-linear results is even more striking. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ fabric is manipulated along a semi-circular path, while the left end is assumed fixed. Simulations were done using both a linear response for the bending rigidity and the full non-linear moment-curvature response. Linear elastic behaviour was assumed for the axial and transverse shear response. On comparing with the experimentally measured intermediate drape shapes, it is seen that incorporation of the non-linear bending response yields superior results. Figure 3 Fabric Place Operation Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) Figure 4 shows a simulation and experimental results for a fabric placing operation. Here a piece of fabric is initially suspended vertically with the bottom end just contacting the work surface. The top end of the fabric is then manipulated along a straight-line path. Figure 4 shows the results for a 10 cm-long strip of fabric 3. Figure 5 shows similar results for 72 Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) VOLUME 5 NUMBER 3/4 1993 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA fabric 4. Again, the simulated response using decrease the possibility of the fabric wrinkling near the fixed end. The objective is the non-linear moment curvature response to determine the path of the manipulator agrees very closely with experiment. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (not necessarily semi-circular) to accomplish this. Figures 7 and 8 show intermediate drape shapes for the linear and non-linear momentFabric Place Operation — Optimization curvature response for fabric 1. Figure 9 Figure 6 shows a schematic of what we term shows the required path for the manipulator in each case. an "optimum" place operation. The goal of the place operation is to lay a piece of fabric To illustrate the robustness of our approach, we show similar results including out on a work surface while minimizing the the effect of a rigid semi-circular constraint reaction force. The idea is to 73 Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) INTERNATIONAL JOURNAL OF CLOTHING SCIENCE AND TECHNOLOGY accomplish this. Figure 13 shows intermediate drape shapes for the non-linear momentcurvature response for fabric 1. Figure 14 shows the required path of the manipulator for each case. CONCLUSIONS A general large displacement beam theory has been used to formulate a finite elementbased numerical method for simulating fabric drape, manipulation and contact. A broad class of fabric mechanics problems including these effects can be solved effectively. Numerical results have been presented corresponding to real fabric materials. zyxwvutsrqponmlkjihgfe □ bump on the work surface. Figure 10 shows References the intermediate drape shapes for the non1. Peirce, F.T., "The Handle of Cloth as a linear response, and Figure 11 shows the The Journal of the Measurable Quantity",zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR required manipulator paths. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Textile Institute, Vol. 21, 1930, pp. T377-T416. 2. Abbott, N.J., "The Measurement of Stiffness in Textile Fabrics", Textile Research Journal, Vol. 21, 1951, pp. 435-44. 3. Abbott, N.J., Coplan, M.J. and Platt, M.M., "Theoretical Considerations of Bending and Creasing in a Fabric", Journal of the Textile Institute, Vol. 51, 1960, pp. T1384-T1397. 4. Cooper, D.N.E., "The Stiffness of Woven Textiles", Journal of the Textile Institute, Vol. 51, 1960, pp. T317-T335. 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Van West, B.P., Pipes, R.B. and Keefe, M., "A Applied Mechanics, Vol. 53, 1986, Simulation of the Draping of Bidirectional Fabrics Over Arbitrary Surfaces", Journal of pp. 849-63. 76 Downloaded by North Carolina State University At 07:34 01 August 2016 (PT) This article has been cited by: 1. Abdel-Fattah M. Seyam College of Textiles, NC State University, Raleigh, NC, USA Sanaa S. Saleh Textile & Apparel Section, Women's College, Ain Shams University, Cairo, Egypt Mamdouh Y. Sharkas Textile & Apparel Section, Women's College, Ain Shams University, Cairo, Egypt Heba Z. AbouHashish Textile & Apparel Section, Women's College, Ain Shams University, Cairo, Egypt . 2014. Shaped Seamless Woven Garments. Research Journal of Textile and Apparel 18:2, 96-107. [Abstract] [PDF] 2. Georgios T. ZoumponosMechanical and Aeronautics Engineering Department, University of Patras, Patra, Greece Nikos A. 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