diff --git "a/designv11-2.json" "b/designv11-2.json" new file mode 100644--- /dev/null +++ "b/designv11-2.json" @@ -0,0 +1,8861 @@ +[ + { + "image_filename": "designv11_2_0001278_j.ymssp.2003.08.002-Figure14-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001278_j.ymssp.2003.08.002-Figure14-1.png", + "caption": "Fig. 14. Points of measurements.", + "texts": [ + " Moreover, the connection between the stator frame and the yoke ring is not perfect: the yoke ring of small machine is generally mounted hot. Consequently, hammer or shaker excitation is not as efficient as perfect cylinders and identification with the modal analysis software is not so easy. Despite these drawbacks, tests with hammer and shaker have been performed. The stator is suspended with a strap (Fig. 13) and not with an elastic rubber band because of the structure weight. Eight measurement points are taken around the stator in three plans as it is shown in Fig. 14. Measurements are not easy to perform because of the cooling ribs; consequently, modifications were performed to the hammer and the shaker: * the hammer tip is modified in order to hit the yoke ring between two ribs, * the accelerometer is manually held with a special extension piece when the shaker excites the structure. An example of frequency response is given in Fig. 15. A mode 2-2D deformation calculated by Starr software is shown in Fig. 16. The results given by each method are presented at Table 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003008_cdc.1986.267558-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003008_cdc.1986.267558-Figure1-1.png", + "caption": "Fig . 1. The one l i n k f l e x i b l e arm", + "texts": [], + "surrounding_texts": [ + "uh(e,e,u,P) = g ( e , e , u , P )\ng ' - h l 2 ( u h ( e , e , u , u ) ) f l ( e l u h ( e , e , u , u ) , ~ ~ ( e , e , ~ , u ) ) +\n.. . (20)\n- ~ , , ( u ~ ( e , e , ~ , u ) ) ~ , ( e , u ~ ( e , e , u , u ) ) +\n-~~~(~h(e,e,u,u))h(e,e,u,~) +\nI I ~ ~ ( P ~ ~ $ 8 ,U,V))U\nwhere i t is unders tood tha t 5 and & a r e t o t a l d e r i v a - t i v e s a l o n g t h e s o l u t i o n s o f (12 ) and (13).\nOnce h i s determined f rom the manifold condi t ion ( Z O ) , the des i red reduced order sys tem i s de f ined by combining (12) and (19) as\ne = - h l l ( P ~ ( e , e , u , ~ ) ) f l ( e , ~ ~ ( e , e , u , ~ ) , ~ ~ ( e , e , u , P ) ) +\n- h 1 2 ( ~ h ( e , e , u , u ) ) ~ 2 ( 6 , ~ ~ ( e , e , u , ~ ) ) T + (21)\n-h,,(~~(e,i,u,~i))~(e,e,~,u) T +\nh l l ( u h ( 8 , e , u , u ) ) u\nThis ystem is of t he same d i m e n s i o n a s t h e r i g i d s y s - tem (18), but i t i n c o r p o r a t e s t h e e f f e c t s o f t h e f l e x i - b i l i t y t h r o u g h t h e i n t e g r a l m a n i f o l d d e f i n e d b y (19). T h i s p o i n t i s h e l p f u l s i n c e , i n t h e f o l l o w i n g s e c t i o n , i t w i l l be shown tha t an approx ima te l i nea r i z ing cont r o l f o r (21) can be synthes ized , p rovided tha t the func t ions h and u a re expanded to any o rde r i n P.\nAPPROXIMATE FEEDBACK LINEARIZING CONTROL\nThe computation of a l i n e a r i z i n g c o n t r o l u ( e , B , v , V ) f o r ( 2 1 ) , where v is a new inpu t t o t he sys t em [8], i s complicated by the need to so lve the man i fo ld cond i t ion ( 2 0 ) f o r &. A p rac t i ca l computa t iona l approach i s based on expanding the func t ion h i n (19) a s [ 71\n- h(B,8,u,P) = b ( O , f i , u ) + ? h , ( e , e , u ) + ... (22)\nand cor respondingly the cont ro l u a s\nu ( e , e , v , P ) = u,(e,e,v) + pu,(e,e,v) + ... ( 2 3 )\nwhere i t can be recognized that and uo a r e t h e f u n c - t i ons i n t roduced i n (14 ) - (16 ) . The expansions (22) and (23) s h a l l be s u b s t i t u t e d in (20) t o y i e l d a s e t of eqs . in which the l ike powers of p on b o t h s i d e s a r e t o be qua ted . This p rocess is u s u a l l y v e r y t e d i o u s , b u t i t can be performed using a symbolic manipulat ion language. For the system ( 1 2 ) and (13) a l l t h e f o l l o w i n g express ions have been obta ined us ing REDUCE:\nu 0 : 0 = -a22(g$+E12(g)uo ( 2 4 )\n' : '$0 5, -e-e 22 - -O 22 - -1 -12 - u 1 i 2 ( 9 $T)g (0)h -E (0)h +G (0) 1 .*\n2 '. . - P : = -2%ehl2(g)(&,)(&,) +\ne t c . , w i t h A = det (M(2)) and the bars over h12 and H i n d i c a t e tha? the terms have been scaled by A t h l s 2 2 p o s i t i o n is n e c e s s a r y s i n c e t h e mass ma t r ix is f t h c t i o n of u . The f i r s t l i n e of ( 2 4 ) can be s o l v e d f o r ho as i n ( 1 6 ) ( A c a n c e l s o u t ) 0\n(16 ' )\na n d , a f t e r o b t a i n i n g t h e r i g i d s y s t e m (18) (neg lec t ing a term O(u)), so can be des igned . Knowing u,,, Lo i s a l s o known and $, can be e x p l i c i t l y computed a s\nThe second l ine of (24) then can be solved for hl as\n-1 0 2 2 - 4 E t 2 2 - -e-e 2 2 - 4 h = - A G-'(O)h + 8%-'(0) ( 0 $ T ) i ( 0 ) h + (26)\nwhich, when s u b s t i t u t e d i n (21) . g ives\nThe c o n t r o l s uo and u1 can be designed and so f o r t h . This process can be cont inued up t o any o rde r i n P. In the fo l lowing i t is assumed t h a t t h e f i r s t o r d e r c o r - r ec t ion t e rm is s u f f i c i e n t t o a c c o u n t f o r t h e f l e x i b i l - i t y i n t h e r e d u c e d o r d e r s y s t e m ( 2 7 ) .\nThe ze ro rde r con t ro l t e rm can be chosen as t h e l i n e a r i z i n g c o n t r o l\nwhere v is a new inpu t t o the sys t em. As f a r a s t h e f i r s t o r d e r c o n t r o l term is concerned , i t t u r n s o u t t h a t , i f o n l y o n e mode i s used to approximate the def lec t ion (m = 1 i n ( l ) ) , i t is poss i - b l e t o d e s i g n u1 so as t o o b t a i n h l = 0 , i . e .\nE x t e n d i n g t h i s t e c h n i q u e t o g r e a t e r o r d e r t e r m s l e a d s t o a v e r y i n t e r e s t i n g r e s u l t : t h e i n t e g r a l m a n i f o l d z can be forced to the s low manifold Eo and the reduce! order system behaves by des ign as t h e r i g i d s y s t e m .\nIn prac t ice , however , more than one mode may be requ i r ed t oapprox ima te he de f l ec t ion . In t ha t ca se E12(g) is n o t i n v e r t i b l e and the above technique i s no t appl icable anymore. This is n o t s u r p r i s i n g s i n c e t h e f l e x i b l e l i n k arm is n a t u r a l l y a d i s t r i b u t e d p a r a r a e t e r system which can never be completely \"s t i f fened\" by one c o n t r o l a c t u a t o r c o - l o c a t e d w i t h j o i n t l o c a t i o n [31. By examining eq. (271, however, a d i f f e r e n t s t r a t e g y c a n be adopted. The f i r s t o r d e r c o n t r o l t e r m , i n d e e d , c a n be chosen as\nwhich cance ls the t e rm in P. With t h e c o n t r o l s u (28) and u1 i n (30) t h e f i r s t o r d e r r e d u c e d o r d e r 0 sys- in tem r e s u l t s t h e n\nwhich y p r e s e n t s t h e o v e r a l l s y s t e m l i n e a r i z e d up t o o rde r u f o r t r a j e c t o r i e s i n t h e n e i g h b o r h o o d o f 2\nI f a j o i n t r a j e c t o r y B ( t ) i s t o be t r ackedy ' the new inpu t v can be se t a s ( inve r se mode l t echn ique )\nwhere k and k a r e p o s i t i o n a n d v e l o c i t y g a i n s . In Ease thx fast dynamics i s n o t s t a b l e , o r e v e n t u - a l l y i s o n l y l i g h t l y damped, a n a d d i t i o n a l f a s t c o n t r o l term ust be added to the control u given by ( 2 3 ) , adopt ing a c o m p o s i t e c o n t r o l s t r a t e g y [ 7 , 4 ] . In t h i s way s o l u t i o n s o u t s i d e t h e i n t e g r a l m a n i f o l d may", + "way s o l u t i o n s o u t s i d e t h e i n t e g r a l m a n i f o l d may \" rap idly\" f low a long the fas t mani fo ld (paramet r ized by t h e s low va r i ab le s ) t o t he i n t eg ra l man i fo ld wh ich becomes a n a t t r a c t i v e s e t . T h i s is a s e p a r a t e d e s i g n i s s u e a n d is beyond the purpose of t h i s p a p e r .\nCONCLUDING REMARKS\nI n t h i s p a p e r t h e c o n c e p t of a n i n t e g r a l m a n i f o l d has been adopted with the purpose of ob ta in ing a more accura te reduced order model for a one l i n k f l e x i b l e arm. The e f f e c t s of t h e f l e x i b i l i t y a l o n g t h e s t r u c t u r e have been incorpora ted in the reduced order model up to t h e f i r s t o r d e r . T h i s i s s u e is very impor tan t s ince i t has been shown how a f eedback l i nea r i z ing con t ro l can be synthes ized for the reduced order model , a lmost in t he same way a s i t is done f o r a r i g i d arm. One c r u c i a l po in t is t h a t u s i n g t h e c o n t r o l s t r a t e g y p r o p o s e d i n (22)-(32) requires the measurements of the joint angle , ve loc i ty , acce l e ra t ion and j e rk ( s ee (25 ) , (28 ) and (32 ) ) . As a ma t t e r of f a c t one has pos i t ion encoders and t achomete r s ; acce l e ra t ion and j e rk t hus need t o be r e c o n s t r u c t e d a n d t h i s may c a u s e s t a b i l i t y p r o b l e m s . Furthermore th fas t dynamics is r e q u i r e d t o b e a s y m p t o t i c a l l y s t a b l e o t h e r w i s e a n a d d i t i o n a l f a s t c o n - t ro l t e rm must be added to the cont ro l ( 2 3 ) . An altern a t i v e s t r a t e g y may be based on a combination of 'act i v e ' modal feedback control and 'passive' damping so as t o i n c r e a s e t h e s t r u c t u r a l damping [9]. A l l t hose t o p i c s will c o n s t i t u t e t h e s u b j e c t of f u t u r e r e s e a r c h .\nREFERENCES\n[l] W.J. Book, \"New c o n c e p t s i n l i g h t w e i g h t arms,\" 2nd I n t . Symp. Robotics Research, Kyoto, Japan, Aug. 1984.\nv a r i a b l e f e e d b a c k c o n t r o l o f e l a s t i c r o b o t i c s y s - tems,\" 1985 ACC, Boston, MA, June 1985.\n[3] B. S i c i l i a n o , B.-S. Yuan and W.J. Book, \"Model r e f - e r ence adap t ive con t ro l f a one l i n k f l e x i b l e arm,\" 25th IEEE CDC, Athens, Greece, Dec. 1986. [4] B. S i c i l i a n o and W.J. Book, \"A s i n g u l a r p e r t u r b a - t i o n a p p r o a c h t o c o n t r o l o f l i g h t w e i g h t f l e x i b l e man ipu la to r s , \" In t . J . Robot ics Research, subm. f o r publ., 1986. [5] V.A. Sobolev, \"Integral manifolds and decomposi t ion o f s ingu la r ly pe r tu rbed sys t ems , \" Sys t . , Con t r . L e t t e r s , v o l . 5, pp. 1169-1179, Dec. 1984. [6] N . Feniche l , \"Geometr ic s ingular per turba t ion theor y f o r o r d i n a r y d i f f e r e n t i a l e q u a t i o n s , \" J . D i f f . Equations, vol. 31, pp. 53-98, 1979.\nAn overview, ' ' Automatica, vol. 21 , no. 3, pp.\n[2] S.N. Singh and A.A. Schy, \"Decomposition and s t a t e\n[7] P.V. Rokotovic , \"Recent t rends in feedback des ign:\n225-236, 1985. p] T . J . Tarn, A.K. Bejczy, A . I s i d o r i and Y. Chen,\n\"Nonlinear feedback in robot arm c o n t r o l , \" IEEE CDC, Las Vegas, NV, Dec. 1984.\nCetinkunt and T. A l b e r t s , \"Combined approaches t o l i gh twe igh t arm u t i l i z a t i o n , \" 1985 ASME Winter Annual Meet ing, Miami, FL, Nov. 1985.\n[PI W.J. Book, S.L. Dickerson, G. Has t ings , S." + ] + }, + { + "image_filename": "designv11_2_0003271_0167-2789(87)90047-9-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003271_0167-2789(87)90047-9-Figure1-1.png", + "caption": "Fig. 1. Nullclines of system (2.1). Parameter Gf = 0.9.", + "texts": [ + " The form of the functions f ( A ) and g(A) and the value of the constants D A and D s chosen for the computations are [ 4 A , f(A)=~-Gf(A-ga), A ~ A - , A - < A < A +, A > A +, (2.3) where A + = (15g\u00a2 + Grg,,)/(15 + Gf). The function g(A) is defined by 1.82, A < 0.01, g ( A ) = 0.06, 0.01 0.95. The values of D A and D s are chosen as 1.0 and 0.0, respectively, while g~ and go are assumed to be 0.1 and 1.0, respectively. The nullclines for this piecewise linear kinetic model are shown in fig. 1. The parameter Gf represents the excitability of the active medium and is the control parameter in our numerical experiments. As the value of Gf increases the threshold value of the perturbation required to excite the system decreases. The system of partial differential equations (PDE) (2.1) and (2.2) was solved numerically using the standard finite difference techniques on the supercomputer CYBER 205 at Purdue university. The scheme employed was explicit Euler integration and the grid sizes chosen for computation were (41 x 41 x 41) or (51 x 51 \u00d7 51)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003052_bit.20361-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003052_bit.20361-Figure1-1.png", + "caption": "Figure 1. a: Photograph of bioreactor CC-25R showing PreSens Oxygen Probe (1), 150-Am gap around shaft for aeration (2), sampling ports (3). b: Schematic diagram of CC-25R showing location of fluid sampling port (S), 150-Am aeration gap (G), oxygen probe (O), thermocouple (T). Not to scale.", + "texts": [ + " The bioreactor used in this study, denoted CC-25R, was a modified constant stress rheometer (Stresstech, Rheologica Instruments AB, Sweden), the measurement system having been replaced with concentric cylinders, 25 mm and 27 mm in diameter, respectively, to give an annulus 1 mm wide and 35 mm high: the inner cylinder was machined from solid PTFE rod and had a 30-degree cone at the base, while the outer cylinder was furnished with a number of ports to facilitate insertion of a thermocouple, an oxygen-monitoring probe and a number of 20G needle tips through which samples of fluid were taken (Fig. 1a,b). Rotation of the inner cylinder was under computer control, and its speed monitored continuously by a microprocessor tachometer CURRAN AND BLACK: OXYGEN TRANSPORT IN A TAYLOR FLOW BIOREACTOR 767 (RS Components, Corby, UK). The bioreactor was housed in an enclosure maintained at 37 F 0.3jC and purged with filtered air (5% CO2) at atmospheric pressure. Aeration of the cell culture medium was achieved through a 150-Am air gap (G) between the shaft of the rotating inner cylinder and the housing, where the free surface at the top of the annulus was exposed to the air within the enclosure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002684_j.jmatprotec.2004.09.041-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002684_j.jmatprotec.2004.09.041-Figure3-1.png", + "caption": "Fig. 3. Excavator workspace.", + "texts": [ + " It ilustrates how the algorithm transforms matrix hybrid graph of the mechanical system into a block diagram structure, which was described in details in works [1,2]. This program makes it possible to test 2D and 3D complex systems containing linear couplings attracted to kinematic and dynamic excitations. This model of the excavator adapted to numerical analysis provides us with an example of the technical adaptation of the mentioned transformation method in GRAFSIM program [7]. The excavator is produced in the \u201cWarynski\u201d Factory in Warsaw (Poland). Main dimensions of the excavator model are presented in Figs. 1 and 2 and workspace in Fig. 3. Through the excavator idealisation we get a 2D phenomenological discrete model (Figs. 4 and 5). Inertial elements, in the shape of the main excavator body with the engine (1), the jib (2), the arms (3, 4), the bucket (5) as well as the operator\u2019s seat along with the operator (6) have been determined. Hydraulic actuators move the excavator\u2019s arms and E-mail address: grzegorz.wszolek@polsl.pl. are modelled by elastic\u2013dumping elements (9, 11, 12, 14). 924-0136/$ \u2013 see front matter \u00a9 2004 Elsevier B" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001445_bf01833299-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001445_bf01833299-Figure5-1.png", + "caption": "Fig. 5. The PUMA 562 (UNIMATION\u00ae).", + "texts": [ + " This kind of reductions can be performed manually or by several dedicated programmes (MACSYMA, SMP, REDUCE, ... ). Finally, in order to reduce the size of the output, intermediate auxiliary variables can be used to replace each product of trigonometrical functions. These variables are produced by taking the relation order into account so it is as easy as before to find the possible combinations of barycentric parameters and the regression vectors. 3.3. APPLICATION TO THE PUMA ROBOT The PUMA 562 (UNIMATION\u00ae) is a serial six degrees of freedom manipulator with revolute joints (Figure 5). Assuming here that the influence of the wrist is negligible, only the first three joints are considered. Three body-fixed frames have been introduced for the dynamic modelling. In the reference configuration, when the wrist is located straight above the shoulder, all these frames are aligned with the inertial frame {~0} attached to the bedplate. The physical characteristics (geometry and mass distribution) of each body are given in Table 1. According to the symbols defined in Table 1, the barycentric parameters and the dynamic model are obtained automatically by the software ROBOTRAN: 172 P" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000095_ac0104532-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000095_ac0104532-Figure7-1.png", + "caption": "Figure 7. Cyclic voltammograms for the oxidation of 0.1 mM dopamine (in pH 7.4 citrate/phosphate buffer) at a carbon cylinder electrode obtained in (a) October 1998 and (b) December 2000. Scan rate, 100 mV s-1.", + "texts": [ + " Therefore, electrodes with a long-term stability are most desirable in such work to obtain useful and meaningful results. However, adsorption of polar impurities often causes fouling of carbon electrodes,43 giving rise to unstable or gradually deteriorating background and analyte signals. The nonpolar and relatively oxygen-free carbon surface obtained by pyrolysis of acetylene, as demonstrated above, is likely to render the carbon cylinder electrodes less prone to the adsorption of polar impurities, hence reducing the effects of electrode fouling and prolonging the life span of the electrodes. Figure 7 shows two cyclic voltammograms for the oxidation of 0.1 mM dopamine (in pH 7.4 citrate/phosphate buffer) at the same carbon cylinder electrode obtained over a period of 26 months apart. Despite being stored in air, the electrode still exhibited sigmoidal-shaped voltammograms with a mere 8% increase in the limiting current after such an extended period. Clearly, based on the electrochemical parameters determined from the two voltammograms summarized in Table 3, there has only been a minimal change in the surface chemistry of the electrode over the specified period, demonstrating the long-term response stability of the carbon cylinder electrodes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002434_11538356_44-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002434_11538356_44-Figure4-1.png", + "caption": "Fig. 4. Depending on w \u03b8 , elbow may be in joint 1\u2019s limit region", + "texts": [ + " + is equal to: cos( ).(| |.| |)) ( ). )6 _ lim RC zr r r r rF H W M H\u03b8 \u2212 \u2212r r r . (21) Because of the similarity between joints 2 and 6, the same method can be used to map joint 2 limits to the Redundancy Circle. In such a case, joint 2\u2019s maximum for the current configuration may be reached when the elbow, the wrist and the shoulder link are on the same plane. Joints 1, 3 and 5 are all roll angles and their limits on the RC can be calculated similarly. Thus we only present joint 1\u2019s limit on the RC. Figure 4 shows the span of elbow based on the RC. There would be 4 cases. Figure 5 shows all possible mapping of joint 1\u2019s limit violation on the RC. The maximum wrist angle would be calculated based on equation: sin( /(| | sin( )))_ max a R rw u w\u03b8 \u03d5= \u22c5 . (22) For case (b), the limit on the RC can be calculated using the following equations: cos( / ) tan( 1_ lim ).| |.sin( ) 2 a h R h J rw M w PI \u03b3 \u03b8 \u03d5 \u03b1 \u03b3 = = \u2212 = \u00b1 . (23) in which \u03b1 represents the prohibited Redundancy Angle. As it was mentioned earlier the same approach is used to calculate the joint limit mapping for joints 3 and 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002687_cdc.2004.1428715-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002687_cdc.2004.1428715-Figure4-1.png", + "caption": "Fig. 4. Computation of the elevation angle. The vector labeled with \u201cx-axis\u201d is aligned with the nose of the aircraft (body-frame).", + "texts": [ + " The values of \u03c3az(R) and \u03c3min(R) generally depend on the distance R between the target UCAV and the radar because in choosing the most favorable elevation one is constrained by the UCAV\u2019s maximum descent rate. To understand how, we use the following equations: sin(\u03b8el + \u03b8pitch) = h R , sin(\u03b8pitch + \u03b1att) = d v , where h denotes the UCAV\u2019s altitude, R its distance to the radar, v its velocity, d its descent rate, \u03b8pitch the pitch angle with respect to the horizontal plane, and \u03b1att the angle of attack (cf. Figure 4). Therefore \u03b8el = arcsin h R \u2212 \u03b8pitch = arcsin h R \u2212 arcsin d v + \u03b1att. Therefore the minimum elevation angle is given by \u03b8min el (R) := arcsin hmin R \u2212 arcsin dmax vmin + \u03b1min, where hmin denotes the lowest admissible altitude, dmax the maximum descent rate, vmin the minimum speed, and \u03b1min the minimum angle of attack \u03b1min. Figure 3 shows \u03c3max, \u03c3az(R), and \u03c3min(R) versus the distance R. From the plots in Figure 3, we conclude that there are four distinct radial regions around a radar, which should be considered separately by path planning algorithms: 1) The first region Rred corresponds to distances from the target UCAV to the radar in the interval [0, Rmin), where Rmin is obtained by intersecting the curves for \u03c3burn(R) and \u03c3min(R)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003364_iros.2006.282077-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003364_iros.2006.282077-Figure3-1.png", + "caption": "Fig. 3, for the two portions of the walking cycle, the hip joint angles for the two legs are given by", + "texts": [ + " QXYZ Is the ZMP frame TXYZ i the Truhk frame HXY is the Thigh frame KXYZ is the Sharik frame AXYZ is the Fo t frame All Y axes are of direction ( x z' X3\\\\Az A IX xX 0 Fig. 2 Seven-link bipedal robot and its coordinate systems. Gait synthesis for this robot involves the determination of the hip-pitch and knee-pitch angles for each of the legs. The ankle-pitch angles are set to be such that both feet are always maintained to be parallel to the ground. A natural human walking gait is cyclical. Referring to human gait analysis [8], typical shapes of trajectories for hip and knee angles in one cycle of locomotion can be represented by Fig. 3. The trajectories for both legs are identical in shape but are shifted in time relative to each other by half of the walking period. For example 0lh for the left hip is identical to 0rh for the right hip, except that 0lh is time shifted by (t6-to)12 with respect to 0rh . The gait period is given by 27/ coh where COh is defined as the gait frequency in rad/sec. It can also be noted that the joint angle trajectories have certain \"offsets\". The values of offsets influence the biped's posture during walking", + " They can be divided into an upper portion, oh+ ' for which oh > ch, and a lower portion, 06h for which oh < h. Therefore, referring to where Orh and Olh are the right and the left hip joint angles, respectively. Similarly, the right knee joint angle trajectory for different portions of the walking cycle is given by te[to,t4)I rk =Okl (t+t6 t1) t E [t4, t5) rk = 0k2 (2) t E [ts I t6 ]I 69k = 69kl (t ts where 0k] is the knee joint trajectory from the beginning of swing phase, denoted by t5 for the right knee in Fig. 3, to the instant in the support phase when the knee joint is locked, denoted by t4 in Fig. 3. Ok2 is the locked angle for the knee joint. Similarly, referring to Fig. 3, the joint angle for the left knee is given by t E[to, t ) Olk = tgkl (t + t6 t2) t E[ts,I t2 ) Slk =Ok2 3 t [t2,16]6 llk = 0kl (t t2) where t1 is the instant when the stance knee is locked and t2 is the instant when the walking phases of the two legs are switched. From Fig. 3, it can be noted that all the upper and lower portions of the trajectories resemble part of a sinusoid. As such, a Fourier series representation for these curves is chosen which will not involve too many higher order terms. The general FSF is expressed as f(t 1 2;zi (4)f(t) 2 ao + L ai sin(T t)+ bi cos( t) (4) As discussed all the joint trajectories during a gait cycle can be divided into two portions. Each portion can be viewed as an odd function output according to the intersection with the angle axis. Therefore the sine series in the Fourier series function is simplified a Truncated Fourier Series (TFS) is used to model each portion as follows n f(t) = Z ai siniot + cf : i=l ;T T where ai, n, and cf are constants to be determined and co is the fundamental frequency, defined as a walking stride-frequency here, determined by the period T, which is half of T. Using (1), (2), (3) and (5), and by inspection of the curves in Fig. 3, the TFS for the hip joints' trajectories are derived as n 0 ~~~~YRh Aisin Ct)h (t -th+ ) + Ch(6 0rh'0fl{ ~ t)+c (6) r~h I Olh n Oh = R * isinicoh (t- th) + C where 6Ch = T 1(t3 - to) =T (t6 - t3) , which also determines the walking stride-frequency; Ai and Bi are constant coefficients, Oh+ and Oh the upper and the lower portion, respectively of the hip joint trajectory, and t+ and th are time-shift values according to (1). R is an amplitude scaling parameter used for changing the step-length. Initially, R is set to 1", + "2) where xi, yi, and zi are the coordinates of the centroid of link I; mi is mass; Iix and .ix are the centroidal moment of inertia and angle value, respectively, about X-axis; Iy and Qiy are the corresponding parameters for the Y axis; and g is the gravitational constant. Only (8.1) is used here since we only consider the sagittal plane motion. B. Optimization strategy GA In order to generate the desired joints' trajectories for stable walking, a suitable set of coefficients Ai, Bi, Ci and parameters Ch, Ck, tl, t2 (refer to Fig. 3) need to be obtained. t1 is the instant when the knee of the stance foot starts to lock and t2 is the instant when the walking phases of the two legs are switched. Genetic Algorithm (GA) [12] was used to search for the abovementioned coefficients. To achieve a natural walking gait while maintaining stable walking, an objective function to be minimised is of the form fT Wlf\u00b1+ W2f2 + W3f3 +w44 (9) where f' = sum of the distances of the ZMP from the centre of the footprint over a walking cycle; f2= standard deviation of the ZMP over a walking cycle; f3= root mean square of the error of the speed of the trunk from the desired speed over a whole walking cycle; 14= leg strike speed; and w1, W2, W3, and W4 are the corresponding assigned weighting factors" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002137_ias.2000.881132-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002137_ias.2000.881132-Figure1-1.png", + "caption": "Fig 1 1 - Conductor distnbution per angle unity", + "texts": [ + " To solve 1, for example, knowing vi, we need to relate i, with hi. This is possible using 2 once Am, is known. To obtain hm, , we consider only the fundamental component of the resultant spatial magnetomotive force distribution produced by all the winding\u2019s currents. Supposing that in a given instant of time the maximum value FM of the referred magnetomotive force distribution is in a generic position a, 0-7803-6401-5/00/$10.00 Q 2000 IEEE defined along the reference axis 8, of which origin is the magnetic axis of phase \u201ca\u201d, as shown in Fig. 1, the magnetomotive force distribution is given by: being K, a constant which relates the number of turns of phase \u2018Y and the winding factors for the fundamental harmonic. The term C2K,i, cos(8 - 8,) is defined in Appendix -\u201cf we get: Fig. I - Spatial distribution of magnetomotive force For a three phase induction machine with symmetric windings in both stator and rotor, with the rotor quantities referred to the stator, and making in 3, FM = - , where, K = K, (i = a, b, C, A, B, c>, e, = o0, eb = -120\u00b0, e, = 120\u00b0, eA = t l R , eB = eR - 120\u00b0, ec = 8 R + 120\u00b0, being 8 R the angle between the phase \u201ci\u201d axii of stator and rotor, from 2, 3 and 5, FM 2K The magnetomotive force mmf(8) produces a resultant f, = C-cosei hi (i = a,b,c,A,B,C) distribution of magnetic flux density B(8)", + " e.: From eqs. 05,I.l and 1.2, we get: hmi = Fh (E)cos[h(a - 8i )] h Kphi factors. and &hi are, respectively, the step and distribution B. force. Obtention of the Spatial distribution of Magnetomotive Supposing that the stator winding of phase \u201ci\u201c has Ni turns, distributed in the several slots along the stator surface (Fig. I.l), in such a way that the conductor distribution ni(B) has an approximate sinusoidal variation along the unity, the magnetomotive force is given by: stator per angle From Fig. 1.1 and eq. 1.4 we get: f m ( 8 ) = 2Ki iicos(f3 - Bi) (I.5$ C. Procedures to separate the iron losses. For the three phase induction machine described in the paper, the parameters of the equivalent circuit were determined using the no load and blocked rotor tests. The machine is a 1.5 Kw, 1720 rpm, 60 Hz, AN - 220/380 V - 6.9013.99 A. The values of the parameters in ohms were calculated as: Where Rs, Xs, RR, XR e Xm are, respectively, the stator resistance, the stator leakage reactance, rotor resistance, the rotor leakage reactance and the magnetizing reactance", + " The procedure to separate the iron losses are folowing described. The induction machine, with stator windings in wye connection, was driven at synchronous speed by means of a synchronous motor. Different values of rms voltages were applied to the induction machine stator, up to the point saturation was reached. For each value of applied voltage the instantaneous values of phase voltage vi and phase current ii were registered. Under synchronous speed and considering the magnetic saturation, the equivalent circuit of the induction machine is as shown in Fig. 1.2, where the magnetizing reactance is represented by a non linear dipole. Rs=3.11,R~=3.80,Xs=3.18,X~=3.18,Xm=72.6 e ipl =Rm where: and Pfei - iron losses in the phase \u201ci\u201d; Ei - rms value of e.m.f. of phase \u201c2\u2019 The iron losses are obtained as: Pfei = Pi - Rs(Iefi)* Where: 1 T P, =-jvl i ,dt Iefi - current in phase \u201ci\u201d, rms value; In Fig. 1.2 e, - instanteous value of the induced e.m.f.; Rm - is the resistance which indicates the iron losses; imi - is the instantaneous current in phase \u201ci\u201d without the iron losses; ip, - is the instantaneous current in phase \u201ci\u201d due to the iron losses. From Fig. 1.2, the induced electromotive force is given by: di e , = v, -Rs i , -Ls -L dt From eq. 1.6, using the Fourier series to decompose the so that we can get its derivative with a better current accuracy, and by knowing the values of Rs and Ls, we get ei. From Fig. 1.2:" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003664_j.automatica.2007.01.024-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003664_j.automatica.2007.01.024-Figure1-1.png", + "caption": "Fig. 1. Biped angles and control torques.", + "texts": [ + " E{J u sto} = x\u0304T 0 Pu 0 x\u03040 + tr[Pu 0\u03040] + N\u22121\u2211 k=0 tr[Pu k+1Qe + (KuT k R\u0302u kKu k) k], E{J p sto} = x\u0304T 0 Pp 0x\u03040 + tr[Pp 0\u03040] + N\u22121\u2211 k=0 tr[Pp k+1Qe + (KpT k R\u0302p kK\u0304p k + K\u0304pT k R\u0302p kKp k \u2212 KpT k R\u0302p kKp k) k], where R\u0302u k BTPu k+1B+Rc. Using optimality yields the following stochastic version of Theorem 6. Theorem 7. For the stochastic system represented by (22) and (23) with the same state and control weighting matrices, the following performance ordering holds: E{J u sto} E{J c sto} E{J p sto}. (39) The example demonstrated here is the discretized dynamics of the biped locomotion used in Hemami and Wyman (1979). As shown in Fig. 1, the motion is described by six-dimensional state vector xk =[ 1 2 3 \u03071 \u03072 \u03073]T whose first three components describe the angles of the first leg, the trunk, and the second leg, respectively, and whose last three components are the associated angular velocities. The control input to the biped is three-dimensional torque uk = [u1 u2 u3]T. The biped with both feet on the ground is described by xk+1 = Axk + Buk where the numerical values of A and B can be obtained by discretizing (with 0.05 s sampling time) the model in Hemami and Wyman (1979)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002094_robot.1988.12303-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002094_robot.1988.12303-Figure2-1.png", + "caption": "Fig. 2. Execution of LNAV with backtracking (from 4 to 5 along 2).", + "texts": [], + "surrounding_texts": [ + "Now we analyze the algorithm LNAV for its correctness and its performance. We first state a result.\nResult 1 181: The local VG is graph connected and every point in obstacle-free space is seen from some vertex of local VG. 0\nIt is direct to see that global V G satisfies the same properties stated above. A close look at the algorithm LNAV reveals the following property. Proposition 1: The order in which R visits the new obstacle vertices (while executing algorithm LNAV from s to g) is equivalent to performing a depth first search on global V G with s as a starting node.\nDepending on the locations of s and g, R (executing LNAV) will visit a subset of the vertices of global VG. In the worst-case, R would visit all the nodes. Now, combining the above two results we show that the algorithm LNAV correctly navigates R from the source points to the destination point g . Theorem 2.1: Algorithm LNAV navigates R from s to g in a finite amount of time. U\nThe execution of LNAV by R involves operations such as scans, movements and computation. The time taken for navigating from s to g is a function of the time taken to perform\nthese operations. These parameters are estimated in the following theorem. Theorem 2.2: In executing algorithm LNAV, (i) the number of scan operations is at most N+1, (ii) the total distance traversed is at most equal to twice the length of the depthjirst tree, of global VG, rooted at s . 0\nThe computational complexity of the algorithm LNAV is given in the following theorem. Theorem 2.3: In executing the algorithm LNAV, (i) the storage required is 0 ( N 2 ) , (ii) Complexity of path planning is 0 ( N 3 ) , (iii) complexity ofstack operations is o ( ~ ' 1 . 3. LEARNED NAVIGATION\nIn this section we present the algorithm GNAV which implements a restricted form of \"learning\". The algorithm LNAV is modified such that the adjacency lists that are generated after each scan are stored in a partially-built global V G called GVG. Note that the GVG contains the visited destination points of the navigation mission as nodes (along with their visibility information) in addition to the nodes corresponding to the obstacle vertices. Let the modified LNAV be called LNAV1. Now the navigation mission is executed as follows: For each traversal from di to di+l , a scan is performed from di and the GVG is augmented with the adjacency information of di. Then a node d' nearest to di+l is computed. A shortest path to d * is planned on GVG. Note that di is graph node. R moves to d* along the edges of GVG. From d* to di+l the navigation is carried out using LNAV1. The details of algorithm GNAV are given below:\nalgorithm GNAV(di , d i+ l ) 1 . scan and obtain seen-part, from di , of the terrain; 2. augment the visibility graph; 3. if (di+l is directly reachable) 4. move to di+l; 5 . else 6. 7. 8. 9. LNAVl(d* , d i+ l ) ; 10. if ( ( i + l ) # M ) compute the d* , the vertex nearest to di+l; compute the shortest path to d* ; move to d * on GVG;\n1 1 . GNAV(di+l d + 2 ) ; endif\nendif;\nConsider the traversal from di to di+l . The navigation from di to d * is along edges of GVG, and hence is collisionfree. The navigation from d* to di+l is correctly carried by LNAVl (theorem 2.1). Hence we have the following theorem. Theorem 3.1: Algorithm GNAV correctly executes the navigation mission. 0\nWe note that the GVG at any stage is dependent on the exact nature of the navigation mission. The GVG, at any stage, will be more complete if the destination points are scattered", + "around the terrain rather than clustered to a small region. Since, our learning is \"incidental\", i.e., the terrain model of a region is built only in the regions R moves into, we can only make probabilistic statements about the learning. Theorem 3.2: The terrain model converges to complete local VG with probability of one, i f every obstacle vertex and edge has a non-zero probability of being seen during some scan operation while executing the navigational course. The terrain model will be completely built in N +2M scans, then (i) execution of each traversal takes two scan operations i f N is unknown, no scan operations i f N is known, (ii) the planned path is optimal from di to d * , i f N unknown, and the entire path is optimal i f N is known. 0\nWhile executing the algorithm GNAV, the global visibility graph CVG contains nodes corresponding to the destination points (at most M in number) of the navigational mission in addition to the nodes corresponding obstacle vertices (at most N in number). Hence the number of nodes in the graph used by GNAV is at most N+M. A straightforward extension of Theorem 2.2 results in the following theorem. Theorem 3.3: I n executing the navigation mission, using GNAV (i) the number of scan operations is at most N +2M, (ii)\nthe total distance traversed is at most 2C (depth jirst tree\nrooted at di ).O The computational complexity of GNAV is estimated in the following theorem. Theorem 3.4: In executing the navigation mission, using GNAV (i) the storage complexity is O( (N+M)2) , (ii) the complexity of stack operations is O(MN2), (iii) the complexity of path planning is 0 ( ( N + M ) 3 ) . 0 4. EXAMPLE\nLet us compare the performance of the algorithm GNAV over repeated application of algorithm LNAV. We consider the terrain of Fig. 3. The Fig. 4 through 6 present seven traversals carried out using algorithms GNAV and LNAV. Note that the global information available to GNAV enabled it to navi-\nU\ni = l", + "gate better compared b LNAV. In Fig. 7 we show the relative performance of these two algorithms in terms of the number of scan operations. Notice the decrease in the number of scans performed by GNAV as R traverses in the terrain. Similar phenomenon is seen in the number of localized concavities entered by R in Fig. 8. 5. CONCLUSIONS\nIn this paper we presented an algorithm to navigate a point robot through a sequence of destination points amidst unknown stationary polygonal obstacles in a two dimensional terrain. The algorithm implements learning in the way of building a global terrain model by integrating the sensor information obtained during the course of navigation. This global model is used in planning the future navigational paths. This approach prevert8s the robot from getting into localized detours, and also results in better navigational course, in an average case, compared to the algorithms without learning. The proposed algorithms are implemented in language C on a simulator for HERMIES-I1 robot running on I B W C ." + ] + }, + { + "image_filename": "designv11_2_0000690_0094-114x(96)00018-3-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000690_0094-114x(96)00018-3-Figure2-1.png", + "caption": "Fig. 2. Two-dimensional GSPPM considered for simulation.", + "texts": [ + " In the present work, the direct kinematics solver is started from this predicted value, t~, to find out the correct values of xk. Equation (2) is used to calculate ~k from the measured ]. These values of xk and ~k are then used in (14) to update the dynamic 86 Soumya Bhattacharya et al. parameters. As/~ approaches r, ~k tends to Xk and computational time taken to solve the direct kinematics further reduces. The process continues till a specified level of convergence is attained. A 3DOF planar manipulator in the horizontal plane (shown in Fig. 2) is chosen for the verification of the proposed algorithm. The exact values of various important kinematic dimensions are listed in Table I. The dynamic equations of the planar manipulator are formulated for the purpose of predicting states of the parallel manipulator. The expression of total energy for the parallel manipulator is given in the Appendix. The regression model requires the determination of the range space of AH of (11). One may try to calculate it numerically, but the authors feel that the numerical method has less dependability, because one can calculate the basis set or the identifiable set of r0 from the observation matrix [~V]T[~] only when the trajectory, on which [~] is calculated, is persistently exciting [11]", + " If a given trajectory gives rise to the smallest eigenvalue equal to zero then the experimenter has no method to identify the exact cause of it. It may be either due to the choice of some unidentifiable/~0 or the trajectory On-line parameter estimation scheme 87 may not be persistently exciting. In order to avoid this difficulty the authors reformulated the energy expression symbolically, as done in [17], in such a way that no two columns of [~] are linearly dependent on the other columns. It is observed that the moments of inertia of two parts (parts 1 and 2 in Fig. 2) of each leg are dependent, but their sum is an independent dynamic parameter. Some dynamic parameters, e.g. the mass of part 1 (Fig. 2), do not contribute to the energy of the system. Those parameters belong to the null space of [~'] and hence are excluded from the identifiable set of dynamic parameters. It is observed in the Appendix that the system has 16 independent dynamic parameters. In the present paper, the results of six simulation runs are presented. The optimization involved in the direct kinematics is solved by successive quadratic programming. The numerical integration of the dynamic equation is performed using the Ranga-Kutta technique with adaptive step size control", + " A P P E N D I X rap--mass of the top platform Lz--moment of inertia of the top platform C,p--X-component of the product of centroidal distance from Xm and mass of the top platform C~p--y-component of the product of centroidal distance from Xm and mass of the top platform mj--mass of the second part of the ith leg l~:~--moment of inertia of part I about z of XL~ 12:i--moment of inertia of part 2 about z of XM~ C~--x-component of the product of centroidal distance of part 2 of the ith leg and its mass measured with respect to X M , C,--y-component of the product of centroidal distance of part 2 of the ith leg and its mass measured with respect to XMi X, y--position of X~ with respect to X0 0--angular position of X~ with respect to X0 ~t,--angle between the x-axis of XLi and the line joining the origin of XL~ and XM~ measured in the counter clockwise direction Then the total energy of the planar GSPPM described in Fig. 2 is, 1/2((2 2 + .C)mp + O:L: + (J~ cos 0 - 2 sin O)C~o - 0(9 sin 0 + 2 cos O)C,~) + 1/2 ~ ((1 ~a, + ~2)m, i = l '~ \"2 + atrL=, + ct, h=, + 2l,~,:C~, - 2[~,C,,)." + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001769_tmag.2003.810533-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001769_tmag.2003.810533-Figure2-1.png", + "caption": "Fig. 2. Rotor and parameter definition of the first test motor. (a) Segmented Halbach cylinder rotor. (b) Definition of parameters (P = 4,K = 3).", + "texts": [ + " In other words, with this type of rotor, the cogging torque due to the fabrication errors, if any, can be generated selectively and can be estimated easily. Manuscript received June 18, 2002. The authors are with Hitachi Research Laboratory, Hitachi, Ltd., Ibaraki 319-1292 Japan (e-mail: masashi@hrl.hitachi.co.jp). Digital Object Identifier 10.1109/TMAG.2003.810533 Fig. 1 illustrates how the segmented stator of the first test motor is fabricated. The laminated stator core consists of 12 teeth and a ring-shaped back yoke. The teeth, each combined with a concentrated winding coil, are inserted into the inner grooves of the back yoke. Fig. 2(a) shows the segmented Halbach cylinder rotor, made for the investigation, with 10 poles ( ) and three Nd\u2013Fe\u2013B PM blocks per pole ( ). The 30 PM blocks each have sectoral cross sections and they are uniformly magnetized prior to assembling them into a cylindrical shape. The directions of magnetizations in each PM block are depicted in Fig. 2(b) when and . The magnetization direction of a PM block with a central angular position is given by [2]. Assuming that its stator core is slotless and infinitely permeable, as shown in Fig. 2(b), and the recoil permeability of the PM blocks is that of the vacuum , according to the regular function treatment reported in the literature [4], we can show that the fundamental ( -pole) magnetic flux density in the air gap, defined in complex form as as a function of the point , is expressed as (1) 0018-9464/03$17.00 \u00a9 2003 IEEE where (2) (3) is the residual magnetic flux density of the PM blocks, is the outer radius of the rotor shaft, is the inner radius of the stator core, is the outer radius of the PM, and is the complex conjugate of " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001390_02783640122068128-Figure17-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001390_02783640122068128-Figure17-1.png", + "caption": "Fig. 17. Three-axis force sensor: (a) exploded assembly drawing of the flexure and single-axis load cells, (b) photograph of the flexure with clear LexanTM vacuum chamber and one load cell, and (c) flexure with four load cells in place.", + "texts": [ + " To explore the applicability of force-guided coordination in the minifactory environment, we chose to undertake a collection of insertion (\u201cpeg-in-hole\u201d) tasks. In our sample task, the courier robot carried a plate bearing a chamfered hole, and a manipulator observed forces on a peg as it was inserted into the hole. By performing a rendezvous operation, the two agents were able to exchange state, sensor, and command information with one another and act as a single 4-DOF device to reliably perform the insertion task. The details of the particular force sensor carried by the manipulator (shown in Fig. 17) were described in DeLuca, Rizzi, and Hollis (2000). at GEORGIAN COURT UNIV on April 22, 2015ijr.sagepub.comDownloaded from We have undertaken a number of experiments to evaluate the performance of the distributed agent pair performing this task. To accomplish this, we have deployed a control architecture that minimizes interagent communication by making use of algorithmically simple control schemes. Impedance control provides one such simple class of control policies and accomplishes stable interaction with an environment by converting the system to a form that naturally performs the task (Hogan 1985; Anderson and Spong 1988; Chiaverini, Siciliano, and Villani 1999)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002523_1.1637627-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002523_1.1637627-Figure2-1.png", + "caption": "Fig. 2 Schematic illustration of the crest and valley height fluctuations", + "texts": [ + " We show, however, that the presence of an error of form could improve tightness if its amplitude is slightly smaller than the groove average depth. The system under study is schematically shown in Fig. 1. The ring gasket is modelled as a system formed by joining normally a rough textured surface and a smooth one. The rough surface is representative of surfaces obtained by face turning. This machining process classically leads to a textured surface characterized by a spiral groove. As discussed for instance in @8#, the regular motion of the cutting tool leads to a quite regular spiral structure. This structure is illustrated in Fig. 2. Naturally, the spiral is however not perfect owing to various phenomena ~small vibrations of the cutting tool, local heterogeneities, . . . !. As schematically illustrated in Fig. 2, there exist small scale height fluctuations on both the valley and summit ~crest! of the groove, see for instance @8# for more details. In particular, this small scale disorder leads to the possibility of radial leak paths as will be discussed further below. The two surfaces are pressed together by applying a given load. This process leads to the deformation of asperities and reduces the local apertures between the two surfaces. The general problem is then to predict the leak as a function of the applied load. Obviously, increasing the load leads to reduce the distance between the mean planes of the two surfaces. It is therefore qualitatively equivalent to increase the load or to reduce this mean distance. For the sake of simplicity, the analysis presented in this paper is performed using parameters characterizing the distance between the surfaces, rather than the load. Leak Paths. As illustrated in Fig. 2, for low and moderate loads, leak is possible through passages associated with the local fluctuations of the crest height between two laps of the valley. These passages represent a series of shortcuts forming radial leak 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Jou Downloaded From paths. For a sufficient ~high! load, the passages on the crest disappear and the only leak path becomes the valley of the spiral. This leak path is termed the circumferential leak path. For intermediate loads the fluid will follow combinations of circumferential leak path sections and radial paths", + " Preliminary results, @11#, indicate that JANUARY 2004, Vol. 126 \u00d5 49 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F this geometrical erosion model is satisfactory in the case of plastic deformation of asperities. It may be surmised that it is also satisfactory when the smooth surface is made of a soft coating. In the present model, the geometrical erosion rule models the deformation of the crest. Deformation of the smaller scale asperities, such as the fluctuations schematically depicted in Fig. 2, is included implicitly in the variation of \u00ab ~\u00ab>0! since the radial passages are described in an average sense only in the present model. Another important characteristics of machined surfaces is that the roughness local slopes are small, that is in the present context a/l!1. In this section, we derive analytical expressions giving the leak trough the model ring gasket for two different transport phenomena. The first one is the transport by diffusion of a species through a stagnant fluid induced by a concentration difference between the ring inner domain and the outer one" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001600_j.vibspec.2003.09.005-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001600_j.vibspec.2003.09.005-Figure1-1.png", + "caption": "Fig. 1. Atom assignments for isonicotinic acid (a), nicotinic acid (b), and lithium isonicotinate (c).", + "texts": [ + " The NMR data are gathered in Table 7 (1H NMR) and Table 8 (13C NMR) for isonicotinates and in In case of isonicotinates, the chemical shifts of protons in pairs: 3a and 5a, and 2a and 6a are the same. The differences in chemical shifts of protons along metal series are small. However, comparing to free isonicotinic acid (Table 7), all protons are shifted diamagnetically. This suggests, that all metals cause decreasing in ring current intensity and along with the literature data decrease in aromaticity [16\u201318]. The chemical shifts of protons numbered 3a and 5a are smaller than chemical shifts of protons numbered 2a and 6a (Fig. 1c). That means that electronic charge density is bigger around positions 3a and 5a compared to positions 2a and 6a. The same effect is observed in case of carbon atom chemical shifts. The chemical shifts of carbon atoms in positions 2 and 6 are bigger than chemical shifts of carbon atoms in positions 3 and 5. The differences between chemical shifts of carbon atoms along metal series are small. Exclusively in case of caesium salt, the chemical shifts of all carbon atoms are shifted significantly comparing to free ligand. In case of nicotinates, the chemical shift of all protons are different. In Table 9, it is seen that electronic charge density is lowest around proton situated between carboxylic group and nitrogen in the ring. This is characteristic for all complexes and for free ligand as well. Highest density is observed around proton in position 5a\u2014opposite to carboxylate anion and nitrogen (Fig. 1b). In case of all positions, protons are shifted diamagnetically comparing to free ligand\u2014the ring current intensity decreases under complexation process. Although changes along metal series are irregular, the effect of ring current decrease is the evidence for affecting the electronic charge in the aromatic ring by metal ion complexed to the carboxylate anion. The chemical shifts of carbons of nicotinates change along the metal series only slightly. In case of nicotinates the exclusive effect of caesium is not observed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure2.21-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure2.21-1.png", + "caption": "Fig. 2.21. Rod shaving", + "texts": [ + "20, makes it possible to remove the suface layer of 0.2\u20130.7mm in the radius by the cutter with four cutting edges. Since the surface as peeled is rough, the light reduction by polishing roll can be normally carried out to make the surface roughness less than 10\u03bcm Rmax. By using the peeling machine, it becomes possible to have the surface defects removed completely and have any preferable diameter. The tapered bar can be also manufactured by the numerical control. As for the shaving machine shown in Fig. 2.21, the application can be for the wire diameter less than 15mm. This process is that the wire goes through the cutting die of cylindrical shape of which the inner diameter is the finish diameter. Although the cutting speed is higher than that of peeling machine, the cutting depth is around 0.1\u20130.15mm in the radius. Although a partial flaw removal machine is the method of not carrying out all circumference and full length cutting, pinpointing (above) the flaw position with an eddy current machine, and removing only the portion and is good for the surface flaw removal and improvement in size accuracy, but removal of a decarburization layer cannot be performed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000070_s0043-1648(97)00297-4-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000070_s0043-1648(97)00297-4-Figure6-1.png", + "caption": "Fig. 6. Analysis of the contact surface during the steady-state step of the upsetting-sliding Inst.", + "texts": [ + " Solving this system leads to an expression of the mean CouIomb's friction coefficient # defined by the ratio of the two previous stresses as a function of global mechanical parameters, i.e., geometry and lorces: Iz =I # -p+ q( Ft/ F.) I/[ q - ( 6-p)( F,/ F.) I (2) where. ($ is the spring back in the normal direction at leaving contact, p is the penetration, q is the length of the contact surface and takes into account the front bulge at incipient contact co, and F~ and F n are the experimental forces in tangential and normal directions ( Fig. 6). The parameters 6 and (o are numerically determined from the finite element simulation of the test alid take into account the real contact surface between the indenter and the specimen. The calculated mean Coulomb's friction coefficient can be used for the finite element computation of the forming process with a very good agreement between numerical and experimental results, This has been shown in previous work focused on the identification of the mean Coulomb's friction coefficient in wire drawing contact conditions [ 31" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000866_3.11408-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000866_3.11408-Figure6-1.png", + "caption": "Fig. 6 Undeformed configuration of the structure.", + "texts": [], + "surrounding_texts": [ + "We consider a hybrid coordinate dynamical system and assume that the Lagrangian L = T\u2014V9 in which T is the kinetic energy and V is the potential energy, can be written in the general form L = L ( f , P, #/ ,#/ , w/, w/, w/, w/), where Qi = Qi(t) (i = 1,2,... ,m) are generalized coordinates describing rigid-body motions of the hybrid system and wy = w/(P,0 (j = 1,2,...,\u00ab) are distributed coordinates describing elastic motions relative to the rigid-body motions of an undeformed body-fixed spatial position P. We define q and w generalized coordinate vectors such as q = [q\\, #2, \u2022 \u2022 \u2022 , qm]T and w = [w\\, w 2 , . . . , wn]T. Overdots designate derivatives with respect to time, and primes designate derivatives with respect to the spatial position. First we consider the case that there is only one elastic domain. For convenience, we assume that the Lagrangian consists of three terms such as L =LD + \\DL dD +LB, where D is the domain of the undeformed flexible body; LD is the discrete portion of L and is a function of t, q, and q in the Lagrangian; L is the Lagrangian density that is a function of q, q,w,w,w', w\", and (P,t);LB, which is a function of H>(/), w(l), H>'(0\u00bb w'(0\u00bb <7> and q, is the *'boundary term\" portion of the Lagrangian energy functional, which in turn depends on the boundary motions. Next, we consider the nonconservative virtual work of hybrid systems. The virtual work can be written in the form WM = QTdq + \\D/Tb\\v dD +/r6w(/) +/2r6>v '(/). Here, Q is the nonconservative generalized force vector associated with #, / is the nonconservative generalized force density vector associated with w, dq and 5w are associated virtual displacements, and ffbw(l) and /2 r6>v'(/) are the nonconservative virtual work that depends on the boundary forces and associated boundary virtual displacements. If w is a linear displacement vector, then f\\ is the nonconservative boundary force vector associated with dw(l) and/2 is the nonconservative boundary torque vector associated with 5w'(l). Now we consider the simplest case of one spatial variable 1443 D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1444 LEE AND JUNKINS: LAGRANGE'S EQUATIONS and derive an explicit version of Lagrange's equations for this class of hybrid systems. Usually, one spatial variable is used to identify the undeformed flexible body position in one domain. For certain symmetric configurations (for example, see Ref. 6), one spatial variable can represent multiple domains if symmetric or antisymmetric deformation is assumed. We assume that the kinetic energy, potential energy, and Lagrangian are expressed by Eqs. (1), (2), and (3), respectively, and q = q(t), w = w(x,t), and w(l) represents w(x,t)\\i. Also, we suppress the appearance of t everywhere for notational compaction. T=TD(q,q)+\\ f(q,q,w,w,w',w\")dx (1) so that L = T- V = LD(q,q) + (3) where LD = TD- VD, L = T-V, and LB = TB- VB. The nonconservative virtual work of the hybrid system is given by fT(x)5wdx+f?dw(l)+f?dw'(l) (4) where f\\ is the nonconservative force vector applied at the boundary, and/2 is the nonconservative torque vector applied at the boundary. The extended Hamilton's principle can be stated as 5q = dw = 0 at t = tl9t2 (5) The variation of L yields dL dt = dL dL dL a\u00a3 a\u00a3 \u2014 dq + \u2014 dq+ \u2014 dw + \u2014 dw + \u2014\u2014 dw' dq * dw dw dw' dw\" dw dq dq dw(l) (6) The symbolic integration by parts is tedious (see Ref. 1) but can be carried to completion to obtain the following results. Equation (5) can be written as (5L+5Wnc)dt dt\\dqj }hdq lodt\\dq dLB dq dt\\dq d_(dL^ dt\\dw dL -r-dw d \u2014dx dL -dw' d2 ( dLr UJ-j \\ V I UJ-i \\ \u2022R^r\\ -\u0302 -7 ) + T-1 ( T-7 +/ 6w \u0302 d^a \u2014 ' 7 3;c2 \\5>v BL (7) In the preceding equation and elsewhere in the present paper, if F is a function of t, x9 q(t\\ q(t), w(x,t), w(x,t), w'(x,t), w\"(x,t), >v(/), >V(/), w'(l), and w'(l), then the derivative dF/dt is defined as dF dF dF dq dF dq dF dw dF dw_ _ _ I _ _ f_ i _ _ f_ i _ _ i _ _ dt ~ dt dq dt dq dt dw dt dw dt dF w' dt dF dw(l) dt dw\" dt dw(l) dt dF dw'(l) dF dw'(l) dt dt Thus, dF/dt refers to the partial derivative of F, regarding it as \"a function of the independent variables t and x,\" whereas dF/dt refers to the so-called \"explicit\" partial derivative of F regarded as a function of the independent variables t, x, q, <7, w, H% w', w\", H>(/), H>(/), >v ' ( / ) , and iv^/). If t does not appear explicitly, then of course dF/dt =0. If F does not depend on w (and derivatives thereof), then dF/dt reduces to the usual definition of total derivative of F(t,q,q). In our original developments we denoted d/df ( ) by 5/d t( ), but decided this notation was confusing because of the use of d to denote variations. Using the usual arguments on the arbitrariness and independence of the variations dq(t), dw(x,t), and the boundary variations, the preceding equation gives the governing differential equations and the boundary conditions. First, we consider the integrand associated with dq. Since L is expressed by Eq. (3), the first term of Eq. (7) is dL d (dL\\ \u2014 - \u2014 (T- +6 tlLdq dt\\dqj * Therefore, based on the arbitrariness of dq and the independence of dq, dw, and the boundary variations, we conclude that the preceding integral, hence, the bracketed integrand, must vanish, so that we obtain the classical form for Lagrange's equations: (8)dq dq We see that the discrete coordinates satisfy the usual form of Lagrange's equations. However, because of the integrations of Eq. (3) over the elastic domain, L and therefore the resulting differential equations must be considered functions of the discrete coordinates, the elastic coordinates, and their space-time derivatives. To obtain the partial differential equations governing w(x,t), we consider the integrand associated with dw. The second term of Eq. (7) becomes / , J /o _ dw dx\\dw dx2\\dw\" D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1445 Because dw is arbitrary and independent of dq and the boundary variations, the bracketed term must vanish, and this provides the partial differential equations: _d fdL\\ _dLL d_ f dL\\ _ d^_ ( dL\\ = fT dt\\dwj dw + dx\\dw') dx2\\dw\")~'f ( } Equations (8) and (9) can be found in Refs. 2 and 7, and these are derived in Ref. 2 for a three-dimensional case. Next, we consider the boundary conditions. From the last two terms of Eq. (7), we obtain the following symbolic variational statements from which the spatial boundary conditions can be obtained: dL dw\" dw' (10) (11) Equations (8) and (9) generate directly the coupled hybrid system of ordinary and partial differential equations, and the variational statements of Eqs. (10) and (11) directly generate the associated boundary conditions. Thus, we have an explicit generalization of Lagrange's equations for nonconservative distributed parameter systems that have one elastic domain but that may undergo large motions and have discrete boundary masses, forces, and moments. Now we consider a more general case that has more than one elastic domain, i.e., we consider a system of flexible bodies. For simplicity, we consider each elastic body to be beamlike, with only one spatial variable (x/). Analogous, but more complicated, developments can be carried out in this case. Let us assume that the kinetic energy, potential energy, and Lagrangian are expressed by Eqs. (12), (13), and (14), respectively. We introduce n one-dimensional elastic domains \u00a3>/ (/ = !,...,\u00ab), X f t D i , where /0 .<*/- . ->w w ( / , i ) ; and w(l), w'([), and w'(l) are defined in a similar manner. In the general case, f1 and V1 are functions of q, q, w/, w/, w/, w\", w([), w(l), H>'(/), and w'(l), and TB and VB are functions of w(l), w([)9 w (l_), w'(/), q, and q. We assume the following structure for Tand V: ' T=TD(q,q) r7/ + E/=u/0 l . (12) (13) The Lagrangian is, therefore, L = r- V (14) where LD = TD- VD, Ll= f1- Vf, and LB = TB- VB. The nonconservative virtual work of the hybrid system is given by /o,. (15) where // is the nonconservative force vector applied at the boundary (at ;c/ = //) of domain D/, and/2 is the nonconservative torque vector applied at the boundary of domain Df . We use the extended Hamilton's principle that can be stated as =0 (16) After carrying out the variation of L and symbolic integration by parts (see Ref. 1), then Eq. (16) can be written in the following compact form: (dL+dWnc)dt i \\dw/ \\ dLB ^ d^ dLj tdWi(lj) dt [ dw-( = 0 where L = Kidt (17) (18) (14) Then by using the previous definitions and the usual arguments on the arbitrariness and independence of the variations, we can obtain the following relatively simple equations that are the generalizations of Eqs. (8-11): d 9L dt \\dq 3L dq (19) dw D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1446 LEE AND JUNKINS: LAGRANGE'S EQUATIONS ,,dw\" dLE dw{(li) dLB (22) Equations (19) and (20) generate directly the coupled hybrid system of ordinary and partial differential equations, and the variational statements of Eqs. (21) and (22) directly generate the associated boundary conditions. Actually, Eqs. (8-11) are the special case (n = 1) of the preceding equations. Thus, we have an explicit generalization of Lagrange's equations, for a large family of hybrid systems that consist of interconnected rigid and elastic bodies. Each elastic body is to be beamlike and can have several dependent distributed variables, but only one independent spatial variable. In essence, we have done the integrations by parts once and for all for a large class of systems. Thus, the governing equations become quite analogous to the discrete version of Lagrange's equations, i.e., through appropriate derivatives of energy functions. The utility of these equations [Eqs. (19-22)] can be appreciated by considering several examples. Illustrative Examples Simplest Class of Problems When there is only one domain for the elastic motion and there are no boundary dependent terms in the Lagrangian, then the preceding developments are especially simple. The system Lagrangian L is expressed as L =LD + \\\\QL dx, and then Eqs. (8-11) or, more generally, Eqs. (19-22) are simplified to the following form: 1 (MA.a* r dt \\dqj dq * (8) -Idt a\u00a3 dw d ( dL dx\\dw' dL d / dL dw' dx\\dw\" = 0 /o = 0 (23) (24) /o For this simplest class of problems, it is apparent that the boundary conditions do not make allowance for lumped masses, springs, and similar forces at the boundaries, and obviously the preceding equations do not apply to multilink flexible body chains. rigid hub, radius 1 _. Rigid Hub with a Cantilevered Timoshenko Beam With reference to Figs. 1 and 2, we consider a rigid hub with a cantilevered flexible appendage. The appendage is considered to be a uniform flexible beam, and we make the Timoshenko assumptions. The beam is cantilevered rigidly to the hub. Motion is restricted to the horizontal plane, and a control torque u(t) acting on the hub (normal to the plane of motion) is the only external effect. Figure 2 shows the kinematics of deformation of a beam that undergoes shear deformation in addition to pure bending. In this example, we neglect the velocity component -yB9 which is perpendicular to the>> direction. Under these assumptions, the kinetic and potential energies of this hybrid system are as follows: T = >/2/hub02 + dx K = i where E = Young's modulus of the beam / = moment of inertia of cross section about centroidal axis p = constant mass/unit length of the beam k = shear coefficient G = modulus of rigidity A = area of cross section on which shear force acts 7hub = moment of inertia of the rigid hub 6 - hub inertial roration y = elastic deformation a = rotation of cross section Therefore, the Lagrangian is expressed by following equation: L = LD + 1 L dx ' 'o M P(y L J /o L +xey+= >/2/hub02 + -EI(a')2-kGA(a-y')2\\ dx The discrete and distributed coordinates for this case are 6, w(x>t) = [y OL]T and the only external force is u(t), so g = u and/=0. From Eqs. (8) and (9) and the Lagrangian, we get the governing differential equations for this hybrid system: d26 pi fd2oi d20 *T TT + TTA \\dt2 dt2 \\ dx \u2014T dx2 = o Boundary conditions are obtained by Eqs. (23) and (24): \\ .o, = 0 Fig. 2 Kinematics of deformation of a Timoshenko beam. Since X/0) = 0, a(/o) = 0, and dy(l) and da(l) are free, the D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1447 kGA(a- \u2014 = 0 Extensions to Include General Boundary Conditions We consider the case in which the kinetic, potential, and Lagrangian energy functional depend on the boundary motion (at * = /). So there exist LB, /i, and /2. The boundary conditions presented in this section make allowance for the lumped masses and the springs at the boundaries. We also assume that there is only one domain for the elastic motion. So L is expressed as L = LD + J/ L dx + LB . Then we can use Eqs. (8-11). Flexible Three-Body Problem (Hub, Beam, and Tip Mass) With reference to Fig. 3, we consider a rigid hub with a cantilevered flexible appendage that has a finite tip mass. The appendage is considered to be a uniform flexible beam, and we make the Euler-Bernoulli assumptions of negligible shear deformation and negligible distributed rotatory inertia. The other assumptions are identical to the first example, except considering the tip mass and the rotatory inertia of the tip mass. The kinetic and potential energies of this hybrid system are as follows: T = 1 + - + Vim [/0+>(/)]2 1 V=- Ax where m is the mass of the tip mass and 7tip the rotatory inertia of the tip mass. Therefore, the Lagrangian may be expressed as L = LD + L dx + LB )]2+i/2/ t i p[0+.y'(/)]2 The discrete and distributed coordinates for this case are q ( t ) = 0, w(x,t)=y and the only external force is w(0> so Q = u, / = 0, f i - 0, and From Eqs. (8) and (9), the governing equations for this hybrid system are #0 /hub^ 'tip d20 dt2 d20 82y d20 d2 = u d20 =0 Boundary conditions are obtained from Eqs. (10) and (11) by inserting the descriptive variables, dx2 \\dx Since X/o)=J>'(A>) = 0, and dy(l) and d y ' ( l ) are free, the boundary conditions are the following: At x = /0: Atx = l El El dx2 y - 0 and y' = 0 = m [/0 +y(l)] (shear force) = - /tip [6 + y' (/)] (bending moment) Axial Vibration of a Rod With reference to Fig. 4, we consider the rod in axial vibration.7 For simplicity, we assume that the rod has uniform properties along the axial coordinates. In this case, there are no discrete coordinates. Then the kinetic and potential energies of this system are as follows: T=- pii2dx Jo V=- where E is Young's modulus of the rod, A the area of cross section, AT the spring constant, p the constant mass/unit length of the rod, and u the axial displacement u =u(x,t). Therefore, the Lagrangian may be expressed as L = L dx + LR 1 f L = - [Pu2-EA(u')2]dx- Y2Ku2(L) 2 Jo and there is no external force, so Q =0, / = 0, /i = 0, /2 = 0, and w(x,t) = u(x,t). Governing equations for this system fol- D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1448 LEE AND JUNKINS: LAGRANGE'S EQUATIONS low immediately from the Eq. (9) as and the boundary condition variational statement is obtained by Eq. (10): -EAu'du [-Ku(L)]du(L) = ( Since \u00ab(0) = 0, and du(L) is free, the boundary conditions are as follows: At x = 0: u =0 At x = L: EAu' = 0 More General Cases: Multiple-Connected Elastic Bodies We consider more general cases in which L is expressed as L =LD+ /0|. There is more than one elastic domain, i.e., we consider a system of flexible bodies. The governing equations for the hybrid system are obtained from Eqs. (19) and (20), and the boundary conditions are obtained from Eqs. (21) and (22). Two-Link Flexible Manipulator Model We consider a planar two-link flexible manipulator as shown in Fig. 5. Each link is modeled as a uniform flexible beam, and we make the Euler-Bernoulli assumptions. This system has two spatial variables x\\ and x'2t and elastic motions relative to the rigid-body motions are described by y\\(x\\,t) and y2(x2,t), respectively. In this example, we neglect the velocity components that are perpendicular to the y\\ and y2 directions. This system is controlled by the torque inputs u\\ and u2 as shown in Fig. 5. The kinetic and potential energies of this hybrid system are as follows: 1 T=- V \u2014 \u2014 I EI\\ I ~~\u2014 ) dxi ~h \u2014 I El-y ( \u2014\u2014 ) dx? O I \\ ^V2 / 0 I \\ /iv^ / ^ J 0 \\ \"-\u0302 1 / Z J 0 \\ ax2 / where p/ is the assumed constant mass/unit length of the /th beam, \u00a3!// the assumed constant bending stiffness of the /th beam, // the length of the /th beam, yf the elastic deformation of the /th beam, and m2 the mass of the second beam. L2dx2L=\\ L1 dxl Jo = 1 I V2pl( dx, dx2 The discrete and distributed coordinates for this case are Qi = 0i(0, q2 = 02(t) The nonconservative virtual work is expressed by the following equation: f ( *y\\\\ 6 > 2 - ( 6 > 1 + -^ L \\ ox\\ u2562 - u25\\ -\u2014 Therefore, and = [ul-u2 To apply Eqs. (19-22), first we record L1, L2, and LB. In this example, LB is identical to L since LD does not exist: /=! o The resulting coupled system of nonlinear hybrid differential equations and the boundary conditions are obtained from Eqs. (19-22) as the following eight equations: 0! equation: /w2/i [/i81 +^i(/i ,0] t = itl \u2014 u2 02 equation: /2 P2x2(x202+y2)dx2+ D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1449 Boundary conditions of beam 1: At*i = 0: y\\ = 0, y{ = 0 At *! = /!: _ a2vi = -u2 -0i) = 0, 0 at \u2014 w2(/2)sin a- - w3sin(a: + /3)] j b\\ + [>Vi(/i)-/2a! sin a- w2(/2)sin a - w3(a + /3)cos(a + /3) + 0 [/i - /2sin a - w2(/2)cos o; + /3)-w3cos(o:- = i - I2a cos a - w2(/2)cos a + w2(/2)o; sin o;dt .(a + /3)cos(a +18) \u2014 w4cos I {a + /3)sin(o; + f}) \u2014 0 [wi(/i) + /2cos a - w2(/2)sin a s(o; + j3) - w4sin(o; + /5)] | \u0302 i + j Wi(/!) \u2014 I2a sin a \u2014 w2(/2)sin a. \u2014 W2(l2)a cos a. - X4(a + |8)sin(ce + /3) - w4sin(a + jS) - w4(o: + j8)cos(ce +18) + 0 [/i - /2sin a - w2(/2)cos ce \u2014 JC4sin(a + jS) \u2014 w4cos(a + /?)] j \u0302 2 ^ = _d/?. *dg6 d^ = j - I2a cos ce - >V2(/2)cos a + w2(/2)a sin ce 2cos a - w2(/2)sin a] j S\\- - I2a sin a - w2(/2)sin a - W2(l2)a cos o; + 0 [/! - /2sin o; - w2(/2)cos a] j 52 For convenience of notation, we introduce The nonconservative forces are given through the expression of virtual work as follows: = (ui + u2 + w3)<50 Applying Eqs. (19-22) yields the following nonlinear equations of motion. Nonlinear Equations of Motion 6 equation: /o2 at ' o 3 d ? /4 ^ '04 ^ + m2 \u2014 (v5^ = MI + w2 + i equation: d 11 TS equation: , p 2 idV equation: 3 + V2 2/?2 3) - 1 =0 D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1451 + l \"3|dV 4- v P4 v4 2B4 3)-i w2 equation: '2^-T=0dx\u00a3 w2(/2) equation: '3 \u00ab3 '\u00ab F d 04 \u2014 = \u00a32/2 = (dw2/dx2)\\/2 equation: 'o, C'4 UP4 -(K J/o, Ld? 4U47 4- V2\u00a347) - V4U48 - V2\u00a3| d*4 1\u0302 ,2 vv3 equation: = 0 w4 equation: P4 where w3 = w3 - w30 and w4 = w4 - w40. The constants \u0302 4{ and .B/ that are functions of the states related to the overall structure are presented in the Appendix. Summary and Conclusion In this paper, emphasis has been placed on the multibody case. An explicit version of the classical Lagrange's equations that cover a large family of multibody hybrid discrete distributed parameter systems is symbolically derived. The resulting equations can be efficiently specialized to obtain not only the hybrid governing integro-differential equations but also the associated boundary conditions. These resulting equations enable us to avoid the very tedious system-specific variational arguments and integration by parts. These equations can be generalized further to consider three-dimensional elastic solid bodies. 2 = - cos a, Appendix >| 1 ___ ... A 2 ___ ___ /3 D! ___ -y^ l?^ ___ 1 SI J \u2014\u2014 VV\\ } VT. J \u2014\u2014 I/j -t-* J \u2014\u2014 A} , JD J \u2014\u2014 1 v42 = \u2014 d, >12 = \u2014 vvi(/i) \u2014 Jt2cos a + w2sin a. A2 = -x2cos a 4- w2sin ce ^ = jc2a sin a + w2sin a -f w2o; cos a 4- JC20 sin o; 4- W20 cos of 52 = 1, B2 = l\\ - *2sin o; - W2cos a B2 = -;c2sin ce - w2cos o; ,62 = -JC2o; cos a. - W2cos a 4- w2a sin a - x26 cos ce + w20 sin o: B2 = \u2014 sin a, #! = \u2014 (a 4- 0)cos ce ^^ -0 Al = - Wi(/!) - /2cos o; + w2(/2)sin a - X3cos(a: + 0) A\\-~ /2cos a + w2(/2)sin o; + x3cos(a: + J3) + w3sin(o; y43 4 = /2o: sin a. + w2(/2)sin a + w2(/2)a cos a. + 120 sin o: + w2(/2)0 cos a - Xi(6t + /3)sin(a + j8) + w3sin(a + 0) + w3(\u00ab + /3)cos(a: + /3) - JC30 sin(a + /3) + w30 cos(o: ^43 5 = - cos a, 1\u03023 6 = (QJ + 0)sin a j + /j)sin(a /3)cos(a cos(a 30 cos(a = (a = /i - /2sin a - w2(/2)cos a + x3sin(a + /3) - w3cos(a + /3) l = -I2sma - w2(/2)cos o; + x3sin(ce + ]8) \u2014 w3cos(o; + /3) 3 4 = - /2ce cos a - w2(/2)cos a + W2(l2)a sin a - /20 cos a + w2(/2)^ sin ce + JC3(ce + /3)cos(a + ]8) - W3cos(o; + j8) + w3(o; + jS)sin(a + j8) + X30 cos(a + j8) + w30 sin(o: + /3) 53 5 = - sin a, \u00a33 6 = - (a + (9)cos a I - W3cos(o: + j8) w3(a 4- j8)sin(a + /3) + X30 cos(o: 4- j8) 4- w30 sin(ce + /3) ?| = -sin(a + |8), J?3 10 = - (a. 4- j8 4 = - Wi(/i) - /2cos a 4- w2(/2)sin a - x4cos(a 4- /3) D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1452 LEE AND JUNKINS: LAGRANGE'S EQUATIONS w2(/2)sin a. - *4cos(a: w4sin(a A4 = I2a sin a + w2(/2)shi a. + W2(l2)a cos a. + /20 sin a. cos a + X4(a + /3)sin(a + j8) + w4sin(o; + j8) 3)cos(a + 18) + x40 sin(a + j8) + w40 cos(a 4 = - cos a, ^i5 = (a + 0)sin a = w4sin(a w4(a + /3)cos(a: + j3) + x40 sin(a + j8) + w40 cos(o: 44 9 = - cos(a + 18), ^l]0 = (a + jS + (9)sin(oj + j8) i - /2sin a - w2(/2)cos a - JC4sin(o; + 0) - w4cos(a + /3) - /2sin a - w2(/2)cos o: - X4sin(a + j8) - w4cos(a + /3) - I26i cos a - w2(/2)cos o: + w2(/2)a: sin a. - /20 cos o; w2(/2)0 sin a - x4(a + /3)cos(a + j8) - w4cos(a + 0) w4(cx + /3)sin(a: + 18) - JC40 cos(a + j8) + w40 sin(a: ^4 = - sin a, #1 = - (d + 0)cos a ^4 = - JC4sin(a + j3) - w4cos(a j8) - w4cos(a: - x40 cos(a + j8) + w40 sin(o; 54 10 = - (a + j8 + 0)cos(a - /2cos a + w2(/2)sin a A\\ = - /2cos a + w2(/2)sin a l = I2ct sin a + w2(/2)sin a + w2(/2)a cos a: + /20 sin a + w2(/2)0 cos a Al = - cos a, A$ = (a + 0)sin a J?6 ! = 1, B\\-l\\- /2sin a - w2(/2)cos a B\\= - /2sin a - w2(/2)cos o: \u2014 \u2014 I2a cos ce - w2(/2)cos a + w2(/2)a sin a - /20 cos a + w2(/2)0 sin a B5 6= -sin a, #| = ~(0 + Acknowledgments This work was supported by the Air Force Office of Scien- tific Research under Contract F49620-89-C-0084 and by the Texas Higher Education Coordinating Board, Project 999903- 231. We are pleased to acknowledge productive discussions with the following colleagues: H. Bang, N. Hecht, Y. Kim, L. Meirovitch, Z. Rahman, S. Skaar, and S. Vadali. The technical and administrative support of S. Wu and R. Elliott is appreciated. References e, S., and Junkins, J. L., \"Explicit Generalizations of La- grange's Equations for Hybrid Coordinate Dynamical Systems,\" Dept. of Aerospace Engineering, Texas A&M Univ., Technical Kept. AERO 91-0301, College Station, TX, March 1991. 2Meirovitch, L., \"Hybrid State Equations of Motion for Flexible Bodies in Terms of Quasi-Coordinates,\" Journal of Guidance, Control, and Dynamics, Vol. 14, No. 5, 1991, pp. 1008-1013. 3Berbyuk, V. E., and Demidyuk, M. V., \"Controlled Motion of an Elastic Manipulator with Distributed Parameters,\" Mechanics of Solids, Vol. 19, No. 2, 1984, pp. 57-65. 4Low, K. H., and Vidyasagar, M., \"A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems,\" ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 110, June 1988, pp. 175-181. 5Pars, L. A., A Treatise on Analytical Dynamics, Cambridge Univ. Press, London, 1965, Chap. 2-4. 6Junkins, J. L., Rahman, Z., and Bang, H., \"Near-Minimum-Time Maneuvers of Flexible Vehicles: A Liapunov Control Law Design Method,\" Mechanics and Control of Large Flexible Structures, edited by J. L. Junkins, Vol. 129, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, 1990, pp. 565-593. 7Meirovitch, L., Computational Methods in Structural Dynamics, Sijhoff & Noordhoff, Leyden, The Netherlands, 1980. 8Hailey, J. A., Sortun, C. D., and Agrawal, B. N., \"Experimental Verification of Attitude Control Techniques for Slew Maneuvers of Flexible Spacecraft,\" AIAA Paper 92-4456, Aug. 1992. 9Junkins, J. L., and Bang, H., \"Maneuver and Vibration Control of Nonlinear Hybrid Coordinate System Using Liapunov Stability Theory,\" AIAA Paper 92-4458, Aug. 1992. D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08" + ] + }, + { + "image_filename": "designv11_2_0003804_j.conengprac.2006.10.015-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003804_j.conengprac.2006.10.015-Figure3-1.png", + "caption": "Fig. 3. TVC\u2014bottom view.", + "texts": [ + " The servoactuators are not equipped with position transducers, but the position feedback is provided indirectly, by measuring the actual thrust vector direction from the center line of the vehicle. The nozzle swiveling, usually less then 10 , is measured by the angular transducers mounted in axes of the gimbal\u2019s universal joint, Fig. 2. The servoactuators are mounted 90 apart around the circumference of the engine. As a result, the motion of a single servoactuator produces rotation of both gimbal axes. On the other hand, the coupling between the dynamics of the two servoactuators have been neglected. Fig. 3 shows the bottom view of the TVC system. Obviously, the TVC system is symmetrical with respect to the longitudinal axis of the body frame, hence the analysis shall be done for one nozzle engine. The nozzle engine is moved by two servoactuators SA1 and SA2. Servoactuators are supported by the body frame, while cylinder pistons are connected to the gimbal frame. An Oxyz coordinate system, fixed to the body frame, is introduced with the origin in the center of the gimbal. The gimbal frame performs rotation around two independent axes of the gimbal" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002709_vetecs.2005.1543794-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002709_vetecs.2005.1543794-Figure1-1.png", + "caption": "Figure 1. Notations of determining a CRDP using NLP-based approach", + "texts": [ + " 1) NLP-based approach Using NLP-based approach, a CRDP is periodically determined by an energy-constrained objective function (1) with an iteration policy. Its purpose is to minimize cluster coverage overlapping by considering the energy of each CH which comprises the Delaunay triangle. As an NLP method for solving (1), we use a \u2018Limited Memory BFGS (L-BFGS) method\u2019 [10-12], one of the most efficient NLP methods for solving unconstraint optimization problem. For more details about L-BFGS method, refer to \u2018Appendix A. L-BFGS Method\u2019. The notations of determining a CRDP using NLP-based approach is depicted in Figure 1. Note that other values except the angular values can be transmitted to the sink; however, all the CHs should know these values. Taking communication overheads into account, it is desirable to compute these at sink node rather than CHs since a sink node is less energy constrained than CHs or sensor nodes. The sink node eventually obtains the energy state of each CH and the positions of each CH from the each CH. Each angular value is computed by the second law of cosine in the sink node. ( )2 2 2 1 2 3 1 2 3 1 1 2 3 1 cos 2 N N N N N N N N N N \u03b8 + \u2212 = \u22c5 \u22c5 ( )2 2 2 2 3 1 2 3 1 2 2 3 1 2 cos 2 N N N N N N N N N N \u03b8 + \u2212 = \u22c5 \u22c5 ( )2 2 2 2 3 3 1 1 2 3 2 3 3 1 cos 2 N N N N N N N N N N \u03b8 + \u2212 = \u22c5 \u22c5 where Ni denotes coordinates of each CHi, each coordinates consists of a pair (xi, yi)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003223_j.talanta.2006.03.042-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003223_j.talanta.2006.03.042-Figure1-1.png", + "caption": "Fig. 1. Graphica", + "texts": [ + " Curves 1\u20136 indicate IDE esponses to concentrations of 12.6, 18.6. 24.4, 30, 35.4 and 0.52 M of ABTS\u2022+, respectively. Increase in the concentraion of ABTS\u2022+ resulted in increased current responses in both athodic and anodic part of voltammograms. This phenomenon s indicated in Fig. 3b which shows linearity between current esponse of IDE, determined at potential of 100 mV, in the above entioned concentration range of ABTS\u2022+. Initially, measureents with applied buffer solution containing only 1 mM ABTS designated as \u201co\u201d in Fig. 1) resulted in low residual current. As vident in Fig. 3b, the current responses are a linear function f the bulk concentration of the radical form of ABTS, i.e. the urrent response is linear for those constituents of redox couple hich were present in the measured sample in lower concentra- alant t w s 3 p a b a w E t s a 1 t c r t h F i w c p 1 p t 6 i h w A c 2 a b 3 A y t i u t a 1 S. Milardovic et al. / T ion. Also, the current response should be negligible in the case hen only one constituent of the redox pair existed in the bulk olution" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002557_b:jmsc.0000020001.34413.e5-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002557_b:jmsc.0000020001.34413.e5-Figure2-1.png", + "caption": "Figure 2 The cyclic voltammograms recorded in acetonitrile + 0.01 M TBABF4 solution of (a) pure PMth, (b) pure PFu prepared from BFEE + EE (mole ratio 2:1) solution containing each monomer and (c) copolymer prepared at 1.2 V from BFEE + EE (mole ratio 2:1) solution containing 0.1 M 3-methyl thiophene and 0.05 M furan. Scan rate: 20 mV/s.", + "texts": [ + " This may be due partly to some change in the electrochemical environment such as electrode roughness caused by successive deposition of the two monomers during the course of current-potential curve measurements and due partly to the influence of the low electric conductivity accompanying the incorporation of furan ring in the copolymer chain. In addition, it should be noticed that the oxidation potential of the mixture of furan and 3-methyl thiophene is about 1.10\u20131.20 V, which is between the oxidation potentials of two monomers, indicating that the two monomers are oxidized alternately and the copolymer chains are composed of alternate furan and 3-methyl thiophene units. The copolymerization is carried out under different potentiostatic conditions. Fig. 2 shows the cyclic voltammogram of the copolymer prepared at 1.2 V vervus Ag/AgCl/0.1 M KCl, together with those of pure PMth and pure PFu. Only one anodic/cathodic peak current couple appears in the copolymer film, which is different from those of PMth and PFu. The appearance of one redox peak of the copolymer indicates uniform redox properties, which is accordance with the current-potential curve in the solution containing 0.1 M 3-methyl thiophene and 0.05 M furan in Fig. 1b. Furthermore, another noticeable feature is that both the cathodic current and the anodic one are higher than those of pure PMth and pure PFu" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003698_3-540-36268-1_60-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003698_3-540-36268-1_60-Figure6-1.png", + "caption": "Fig. 6. MOD 2 experimental rover", + "texts": [ + " The rear wheels are coupled by a differential, and the front wheels are joined by an Ackerman steering linkage. The rover has tunable independent, spring-damper suspensions for the wheels, and deformable rubber tires. For model validation, this rover does not need to carry the full sensor and computation package described above. A three-axis accelerometer and flash memory module are mounted to the vehicle for recording body accelerations. A high-speed gasoline-powered rover is currently being developed, and will carry the full sensor and computation package described above (see Figure 6 and Table 2). It has a top speed of 27 m/s, and will be controlled via two inputs: throttle to the engine driving the rear wheels, and a front wheel steering servo. The rear wheels are mounted to single drive axle, and the front wheels are joined by an Ackerman steering linkage. The front suspension is an I-beam configuration, while the rear suspension is a four-link trailing arm design. Both front and rear suspensions are tunable spring-dampers. The vehicle has rubber tires. Braking is achieved with a clutch-mounted friction brake" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure2.24-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure2.24-1.png", + "caption": "Fig. 2.24. Magnetic particle detector", + "texts": [ + " (8) Inspection process The main inspection items for steel bars are dimension, length, bend, surface defect and internal defect. The surface and internal defect should be inspected carefully for spring steel. Besides the visual inspection of surface defects, the non-destructive testing such as magnetic particle flaw detection, leakage magnetic flux detection, or eddy current flaw detection can be applied. The magnetic particle flaw detection is the method of magnetizing the product, and collecting magnetic particles around the defect to make the defects visible, as shown in Fig. 2.24 [1]. The leakage magnetic flux detection is the method of detecting the flux leaked from the defect directly, by a magnetic sensor instead of magnetic particles, as shown in Fig. 2.25 [2]. The eddy current flaw detection is the method of catching the defect by the eddy current disturbance when the alternating magnetic field is applied to the product. There is the through type method using circumferential through-type coil, where the bar can pass through the fixed coil and the rotating eddy probe coil method, where the detection coil rotates around the bar with high-speed, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000826_a:1024575707338-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000826_a:1024575707338-Figure7-1.png", + "caption": "Figure 7. Caster wheel moving at a forward speed v; (a) back view and (b) side view.", + "texts": [ + " As an example of a flexible multibody system with non-holonomic constraints we will analyse the kinematic (or static) shimmy of a caster wheel of an aircraft landing gear. Kantrowitz [21] was the first who analysed this kinematic shimmy and demonstrated the phenomena in an experimental setup. The mass of the airplane is assumed large with respect to the caster wheel assembly, so that the attachment point of the yoke to the airplane may be assumed to move forward at a constant speed v. Then in Figure 7, which is a back view and side view of the assembly, point B is the point where the yoke is hinged to the airplane. To demonstrate the principal mechanism for the kinematic shimmy we will assume that the caster length (trail) and the caster angle (rake angle) are zero, resulting in the wheel centre A and the contact point C of the wheel vertically under B. For the wheel-surface contact we will assume a finite contact area with zero longitudinal slip, zero lateral slip, and zero spin; these are the three non-holonomic conditions on the system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001782_00207170410001711648-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001782_00207170410001711648-Figure1-1.png", + "caption": "Figure 1. Two inverted pendulums on carts.", + "texts": [ + " As the tracking error, ei\u00bc xi xir, will converge exponentially to zero, the state xi can track the desired state xri asymptotically and finally the following asymptotic tracking property is achieved lim t!1 jyi\u00f0t\u00de yri\u00f0t\u00dej \u00bc 0: \u0153 Remark 3: Compared with the DNASFC, the DNAOFC employs an HGSPO to estimate the system states and perturbation. The HGSPO is an extendedorder (ri\u00fe 1)th-order observer but its design does not need the detailed system model. Consider a system composed of two inverted pendulums on two carts, interconnected by a moving spring, shown in figure 1. This system was studied as an example in the literature of decentralized control (Shi and Singh 1992, Da 2000). Assume that the pivot position of the moving spring is a function of time and it can change along the full length of the pendulums. In this example the motion of the carts is specified as sinusoidal trajectories. The input to each pendulum is the torque ui, i\u00bc 1, 2, applied to the pivot point. It is desired to control each pendulum with mass independently so that each pendulum tracks its own desired reference trajectory while the connected spring and carts are moving" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000832_1097-0126(200102)50:2<197::aid-pi606>3.0.co;2-1-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000832_1097-0126(200102)50:2<197::aid-pi606>3.0.co;2-1-Figure7-1.png", + "caption": "Figure 7. Relation between: (A) logarithm of the initial rate of polymerization and 1/T (K\u00ff1); (B) log k2/T versus 1/T (K\u00ff1).", + "texts": [ + "0638 mol l\u00ff1) solution under nitrogen atmosphere was carried out at 5, 10 and 15\u00b0C for different periods of time. The percentage conversion was calculated at different time intervals and the data are given in Table 4 from which it is clear that both the initial and overall reaction rates increase with temperature, while the speci\u00aec viscosity and ac conductivity values decrease with increasing temperature. The apparent activation energy (Ea) of the aqueous polymerization of 3-chloroaniline was calculated by plotting log Ri against 1/T, which gave a straight line (Fig 7A). From the slope we can calculate \u00ffEa/2.303R. The apparent activation energy for this system is 13.674 104 J mol\u00ff1. The aqueous oxidative polymerization of 3-chloroaniline develops in three steps: This step is the reaction between dichromate ion and hydrochloric acid which can be discussed as follows: (i) The orange red dichromate ions Cr2O2\u00ff 7 are in equilibrium with HCrO\u00ff4 in the pH range 2\u00b16, but at pH values below unity 1 the main species is H2CrO4. The equilibria are as follows: HCrO\u00ff4 H2CrO4 Cr2O2\u00ff 7 H2O ", + " The enthalpy and entropy of activation for the polymerization reaction can be calculated from the k2 values of the following equation: Reaction rate k2 HCl 1:0 oxidant 0:9 monomer 0:75 The values of k2 at different temperatures were calculated and the enthalpy (DH*) and entropy (DS*) of the activation associated with k2 were calculated using the Eyring equation k2 RT=Nh eDS=R e\u00ffDH=RT 202 Polym Int 50:197\u00b1206 (2001) where k2 is the rate constant, R is the universal gas constant, N is the Avogadro number and h is the Plank constant. By plotting log k2/T versus 1/T (Fig 7B) we obtained a linear relationship with a slope of \u00ffDH*/2.303R and an intercept of log (R/Nh) DS*/2.303R. From the slope and intercept, the values of DH* and DS* were found to be 13.674 104Jmol\u00ff1 and \u00ff295.12 J mol\u00ff1 K\u00ff1, respectively. The negative value of DS* could be explained by the activated complex and products being more solvated by water molecules than the reactants.31 The activated complex formation step is endothermic, as indicated by the positive value of DH*. The contributions of DH* and DS* to the polymerization rate constant seem to compensate each other" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002523_1.1637627-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002523_1.1637627-Figure1-1.png", + "caption": "Fig. 1 Schematic illustration of a machine turned static ring gasket", + "texts": [ + " Furthermore, the analysis also suggests that the transition could be confirmed by combining diffusion flux and viscous flow rate measurements. In a second part of the paper, we discuss the influence of errors of form ~waviness! on the leak. It is generally admitted that errors or form are detrimental to tightness. We show, however, that the presence of an error of form could improve tightness if its amplitude is slightly smaller than the groove average depth. The system under study is schematically shown in Fig. 1. The ring gasket is modelled as a system formed by joining normally a rough textured surface and a smooth one. The rough surface is representative of surfaces obtained by face turning. This machining process classically leads to a textured surface characterized by a spiral groove. As discussed for instance in @8#, the regular motion of the cutting tool leads to a quite regular spiral structure. This structure is illustrated in Fig. 2. Naturally, the spiral is however not perfect owing to various phenomena ~small vibrations of the cutting tool, local heterogeneities, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003340_iembs.2006.260243-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003340_iembs.2006.260243-Figure2-1.png", + "caption": "Fig. 2. Cut-away view of NFI linear actuator.", + "texts": [], + "surrounding_texts": [ + "I. INTRODUCTION\nEEDLE-FREE delivery of a liquid drug can be achieved by pressurizing the drug and rapidly ejecting it through a narrow orifice, thereby creating a high speed jet which can readily penetrate skin and underlying tissue. Typically, this technique requires a pressure of 10 to 60 MPa to be developed on the drug over a few milliseconds, and then maintained for up to 100 ms.\nNeedle-free drug delivery has several advantages over needle-based delivery, particularly when many successive injections are required or injection discomfort is a major concern. However, in order for NFI devices to become ubiquitous, they need to be controllable, repeatable, portable, and inexpensive.\nUntil very recently, most of the portable devices developed for jet injection have relied on springs [1] or compressed gases [2]-[4] to store and then rapidly release energy in order to create the high pressures required. A major drawback of these energy storage and delivery methods is that they allow very little control of the pressure applied to the drug during the time course of injection. However, recent studies have proposed that the pressure time-course (pressure profile) has an important effect on the quantity and depth of drug delivery [5], [6].\nManuscript received April 3, 2006. This work was supported in part by Norwood Abbey, Inc. of Victoria, Australia.\nA. J. Taberner is a Research Scientist with the Bioinstrumentation Lab, Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA02139. (phone 617 324 6052, e-mail: taberner@mit.edu)\nN. C. Hogan is a Research Associate with the Bioinstrumentation Lab, Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA02139. (e-mail: hog@mit.edu)\nN. B. Ball is a Masters candidate with the Bioinstrumentation Lab, Mechanical Engineering Department, Massachusetts Institute of Technology, Cambridge, MA02139. (email: nball@mit.edu)\nI. W. Hunter is Hatsopoulos Professor of Mechanical Engineering and Director of the Bioinstrumentation Laboratory, Massachusetts Institute of Technology, Cambridge, MA02139. (email: ihunter@mit.edu)\nAn alternative, superior approach to jet drug delivery is to store energy in electrical form, and impose a time-varying pressure-profile on the drug volume through the use of a monitored and servo-controlled electromechanical actuator [7]. Monitoring force, pressure, or delivered drug volume allows the time course and volume of drug delivery to be tightly defined, and controlled in real-time.\nLinear Lorentz-force (voice-coil) actuators are a form of electromechanical motor that can generate the high force, pressure, and stroke length required for jet drug delivery. Their inherent bi-directionality allows the applied pressure to be controlled and even reversed when necessary. However, commercially available voice-coil actuators that meet the power demands of this application are typically too large, heavy and expensive to be appropriate for a portable hand-held NFI device.\nWith the recent advent of comparatively inexpensive high energy density rare-earth magnets (Nd-Fe-B) it is now possible to construct quite compact, yet sufficiently powerful voice coil actuators for jet drug delivery. Additionally, high energy and power density capacitors allow sufficient energy to be locally stored and delivered rapidly to effect a needle-free injection in a portable, handheld device.\nIn this paper we discuss the design and performance of a portable NFI system based on a custom voice-coil actuator.\nN\n1-4244-0033-3/06/$20.00 \u00a92006 IEEE. 5001", + "Our portable system, with a mass of about 0.5 kg, is recharged from either a battery powered dock (~90 s recharge time) or a high voltage supply (~1 s recharge time) and provides a single injection per recharge. A second, computer-controlled bench-top device is used as a test-bed for evaluating drug and device performance.\nII. DESIGN\nThe portable NFI delivery device consists of a disposable commercially-available 300 \u03bcl NFI ampule (Injex\u2122 Ampule, part# 100100) attached directly to a customdesigned moving-coil Lorentz force actuator.\nThe syringe is screwed into the front plate of the NFI device, and the syringe piston is captured by a snap-fitting on the front of the moving coil. Drug can then be gently drawn into the syringe by the motor, from a vial, with the aid of a vial adapter (Injex\u2122 vial adaptor, part# 200203.) Alternatively, the syringe can be pre-filled or manually filled prior to loading into the device. The orifice at the tip of the syringe has a diameter of 165 m; the piston diameter is 3.16 mm.\nThe moving voice coil consists of 582 turns of 360 \u03bcm diameter enameled copper wire wound (using a custommade coil winding machine) six layers deep on a thin-walled former. The voice-coil former is machined from Acetal copolymer (rather than a metal such as aluminum) in order to minimize the moving mass (~50 g), and to avoid the drag caused by induced eddy currents in a conducting former. The total DC resistance of the coil is 11.3 .\nAs the voice coil moves in the motor, it slides freely and smoothly on the inside of the same steel extrusion from which the magnetic circuit is constructed. This approach obviates the need for the extra size and length of a separate linear bearing. Holes in the rear of the casing allow air to escape freely.\nFlexible electrical connections are made to the moving coil by means of plastic-laminated copper ribbons. The position of the voice coil actuator is monitored by a 10 k linear potentiometer with > 1 kHz bandwidth.\nThe magnetic circuit (Fig. 3) consists of two 0.4 MN/m2 (50 MGOe) NdFeB magnets inserted into a 1026 carbonsteel casing. Care was taken in this design to avoid stray magnetic field leaking from the device due to magnetic flux saturation in the steel. The magnetic flux density B in the field gap was approximately 0.6 T.\nIn our portable NFI device, the voice coil motor is energized from a low inductance electrolytic capacitor. The bench-top test system is driven by a 4 kW linear power amplifier, controlled by a PC-based data acquisition and control system running in National Instruments Labview\u2122 7.1. This approach readily allows for a variety of voltage waveforms to be tested on the device, while its current and displacement performance is monitored and recorded.\nIII. RESULTS\nThe performance of our jet injector voice-coil motor has been quantified by measuring its frequency response, step response and its open-loop repeatability. Additionally we confirmed its efficacy by injecting red dye into post-mortem guinea-pig tissue.\nA. Frequency response\nThe frequency dependent properties of the voice-coil motor can be quantified in terms of the magnitude of its electrical and electro-mechanical admittance (Fig. 4). The electrical admittance (formed by the series resistance and inductance of the voice coil) is approximately that of a first order R-L filter (R = 11.3 , L = 4.6 mH) with a cut-off frequency of approximately 400 Hz. The no-load", + "electromechanical admittance (velocity per unit of sinusoidal current) provides a measure of the voice coil motor\u2019s responsiveness to driving current.\nB. Step response\nThe force sensitivity of a voice coil motor quantifies the relationship between voice coil current and developed force. For a pure Lorentz-force motor, force sensitivity is the product of the magnetic flux density and the total length of coil in the magnetic field. Our voice coil motor has a force sensitivity of 10.8 \u00b1 0.5 N/A averaged along the length of its stroke, reaching a peak of 11.5 N/A at mid-stroke.\nBy applying a brief 200 V potential to the voice coil, more than 200 N of force can be imposed upon the syringe piston. This generates fluid pressure of ~20 MPa (comparable to that generated by conventional, commercially-available jet injectors) which is sufficient to effect jet injection of a 250 L volume of drug (Fig 5). The instantaneous power consumed by the voice coil under these conditions is 4 kW, but because the injection is completed in a mere 50 ms, there is negligible heating of the coil (<10 \u00b0C).\nThe electrical time constant of the voice coil current is 0.4 ms. As the current increases, force rapidly develops on the piston, compressing the rubber tip against the fluid, and accelerating the fluid through the orifice. The resonance of the rubber piston tip decays after a few milliseconds, and the piston reaches a steady state velocity which appears to be mostly determined by the mechanics of the fluid flow through the orifice. Bernoulli\u2019s equation for inviscid, steady, incompressible flow gives the relationship between velocity and pressure as:\nPv 2 (1)\nBy taking repeated voltage step response measurements (increasing the voltage step in 10 V increments up to 200 V) and fitting to the steady state piston velocity (t > 20 ms), the steady-state jet velocity was computed and then plotted against pressure (Fig. 6). Figure 6 confirms the modeled predictions of Equation (1) and demonstrates that our device is capable of generating the jet velocities that are required for effective jet delivery.\nC. Repeatability\nThe open-loop repeatability of the NFI system was tested by using a shaped voltage waveform to eject a nominal volume of 50 \u03bcl. The voltage waveform consisted of an initial pulse (180 V, 3 ms) to penetrate the skin surface, followed by a follow-through pulse (20V, 30 ms) to obtain the total required volume of delivery. The device was fired four times per syringe refill, 100 times in total. The current and displacement waveforms (averaged over 100 repetitions) are shown in Fig. 7." + ] + }, + { + "image_filename": "designv11_2_0000081_s001700170034-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000081_s001700170034-Figure4-1.png", + "caption": "Fig. 4. Schematic diagram of triangle facet and the working direction, is the normal vector of facet, B is the working direction.", + "texts": [ + " Feygin and Pak [12] developed a slicing rule based on the positive or negative value of the slope of the part to ensure the presence of an extra working tolerance for post processing. However, this often results in the above-mentioned ambiguous conditions. Thus, a method based on the slope of the part is not suitable. To solve these problems, a positive tolerance slicing method and a negative tolerance slicing method are proposed. The results of slicing are shown in Figs 3(c) and 3(d), respectively. As mentioned earlier, an STL file is capable of describing the normal vectors and the coordinates of the three vertices of a trianglar facet. Referring to Fig. 4, let the unit vector of the RP working direction be B, the normal vector of each triangle face be , and the angle between each triangle face and horizontal axis be . The user determines the preferred orientation based on such factors as machining precision, machining time, part strength, and difficulty of waste material removal (for LOM). Next, the orientation of each triangle face is calculated based on the inner product (dot) value of the normal direction of each triangle face and the RP working direction (B), i", + " B = D (4) where, = nii + njj + nkk, and B is the working direction of the RP process. Then, if D = 0, the intersection point at z value is the exact contour. if D 0, the intersection point at z value is the positive tolerance. if D 0, the intersection point at z value is the negative tolerance. Hence, if D = 0 during the slicing process, this means that the contour is vertical. In other words, the contour of the intersection point overlaps the original contour and so it maintains the exact contour without producing any error. If D 0 (a positive slope in the case of Fig. 4), this implies that the angle between the contour and the working direction is smaller than 90\u00b0, and cutting along the intersection point contour naturally forms a positive tolerance. If D 0 (a negative slope in the case of Fig. 4), this implies that the angle between the contour and working direction is larger than 90\u00b0, and cutting along the intersection point contour causes a negative tolerance. Hence, if the user requires a positive tolerance and finds D 0 in the calculation, the original intersection point should be replaced by the intersection point of the previous layer (z = slicing height \u2212 one layer thickness) (i.e. the bottom up slicing method mentioned earlier). If D 0, top down slicing should be used to ensure the extra working tolerance and avoid the problem of overcut" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001859_robot.1996.503850-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001859_robot.1996.503850-Figure5-1.png", + "caption": "Figure 5: Experimental setup.", + "texts": [ + " The identified parameters are shown in Table 2. The results in general are not comparable because of the different definitions of miisi and i n i , although for the Sarcos Dextrous Arm it turns out that mi'si, = ' f i i a : because all skew angles are ai = n/2 . The y-components though are different. To verify the identification result, we computed the gravity torque from the identified parameters. Results agree with those computed from the assumed parameters. 6 Experiments Experiments were then performed on the Sarcos Dextrous Arm Slave (Figure 5). The Sarcos Dextrous Arm Slave is an advanced hydraulic manipulator with 7- DOF revolute joints and a 3-DOF, 3-fingered gripper (Figure 2). Each joint is instrumented with high precision position and torque sensors, whose readings are accessible from the user level computer via a low level joint controller and mid level computer [13]. Work has been done to calibrate both the kinematic model and the joint sensor parameters [5, 71. We applied the identification procedures of Section 4 to the data we sampled during the torque sensor offset calibration in [ll]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002634_1.1609486-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002634_1.1609486-Figure1-1.png", + "caption": "Fig. 1 Schematic of lip seal", + "texts": [ + " While a great deal of experimental observations had been made, it is only over the last decade that those observations have been organized to construct conceptual models of the lip seal @1#. Based on those conceptual models, mathematical models have also been constructed @2\u20136#. While these latter models have been extremely useful in elucidating the basic physics of the lip seal, they are not yet suitable as design tools due, primarily, to the very large computation times that they require. Analysis of the hydrodynamics of the seal\u2019s lubricating film has been particularly time consuming. Figure 1 is a schematic of a typical lip seal. It has long been known that, in a successful seal, a thin ~micron scale! lubricating film of the sealed liquid separates the lip from the shaft under normal operating conditions @7#. This film prevents mechanical and thermal damage to the lip, and reduces wear. Thus, a central objective of a seal design must be the creation of a fluid film with desirable characteristics ~e.g., of optimum thickness, stable, etc.!. It is also well known that the asperities on the lip surface, in the sealing zone, play a dominant role in maintaining the film and preventing leakage @8#" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003079_iros.2004.1389781-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003079_iros.2004.1389781-Figure1-1.png", + "caption": "Fig. 1. Definition of SymboLr. (ai: paramem far pose e; . (bi: relrion between discrete lime t. information d, action a. and pose P.", + "texts": [], + "surrounding_texts": [ + "Proceedings of 2004 1EEORS.J International Conference on Intelligent Robots and Systems September 28 -October 2,2004, Sendai, Japan\nExpansion Resetting for Recovery from Fatal Error in Monte Carlo Localization\n- Comparison with Sensor Resetting Methods Ryuichi UEDA, Tamio ARAI and Kohei SAKAMOTO Toshifumi KIKUCHI and Shogo KAMIYA\nDepanment of Precision Engineering, School of Engineering, The University of Tokyo\n{ ueda, arai-tamio, sakamoto} @prince.pe.u-tokyo.ac.jp\nDepartment of Precision Mechanics, School of Science and Engineering, Chuo University\ntkikuchi@sensor.mech.chuo-u.ac.jp show-5 @arc.mech.chuo-u.ac.jp\nAbstracl-Though Monte Carlo localizalion is a popular method Cor mobile robot localization, il requires a method Cor recovery of large estimation error in itself. In this paper, a recovery melhod, which is named an expansion resetting method, is newly proposed. A blending OC the expansion melting method and another, which is called the sensor resetting melhod, is also proposed. We then compared our methods and olhen in a simulated RoboCup environment. Tlpical accidents for mobile robots were produced in the simulator during trials. We could grasp the chanrcterktia of each method. Especially, the blending melhod was robust ngainsl the kidnapped robot problems.\nI. INTRODUCTION\nMonte Carlo lcxalization has been popular in recent years. It is the application of panicle filters for mobile robot localization by Fox, Dcllacrt el al. 111, 121. MCL is a lightweight algorithm while it can represent a mathematical model for estimation well. That is because computational load is concentrated around estimated poses of robots in MCL.\nA Bayes filter is the mathematical model that is represented by MCL. It can he applied to mobile robot localization when the pose changes with Markov process, and when information about the pose is stochastically obtained based on the pose. An estimation result, which is reprrsented by a probability distribution, is always maintained in a Bayes filter. It is renewed when a robot moves or obtains sensor information. Since those assumptions are generally suitable for the case of mobile robot localization, MCL and other methods based on Bayes filters work successfully.\nHowever, accidents that are contrary to these assump tions exist around a robot even though they do not occur frequently. Bayes filters cannot deal with unconsidered accidents because this kind of mathematical model can only he formed on some suppositions. Once an accident occurs and a large error emerges, Bayes filters cannot recover from the error for a long time. Moreover, there are limitations for rigid implementation of a Bayes filter even if we use MCL. Though the concentration of computation around estimated poses is effective for reducing the load, it means that MCL does not treat other poses seriously, As a result, MCL is still worse at a fatal error than Bayes filters.\nBayes filters and MCL therefore require any exception handling so as to he robust against any accident. An easy\nbut practical method for the exception handling is reserrbtg. This method stops a Bayes filter when a fatal error is suspected. After that it reconstructs an initial probability distribution for the filter.\nLenser er al. have proposed a sensor resetring method in 131. This method measures the extent of contradiction hetween the pose estimation and the latest sensor information. If the extent is over a threshold, the method reconstructs a probability distribution that reflects both the previous probability distribution and the latest sensor information. Wrong information sometimes causes needless resettings in this method. GutmaM and Fox have given an improved method of the sensor resetting in 141. This method restricts excessive reaction of the sensor resetting when sensor information is noisy. However, there is anxiety that this method restricts some required resettings.\nIn this paper, we tackle this problem with a novel resetting method, which is named an expansion resetting method. This method constructs a probability distribution after a resetting not based on the latest sensor information hut based on the previous probability distribution. The average of the distribution can be preserved and the harmful effect of a resetting can be inhibited by this method. Simultaneously, the expansion resetting method enables a MCL method IO recover from large errors if it is used with the sensor resettings together. We also propose a concise way to use both of them.\nIn the next section, Bayes filters, MCL, and their problems are described. Our resetting methods and sensor resetting methods are explained in Section m. Simulations for comparison between the methods are conducted in Section IV. We conclude this paper in Section V.\n11. MONTE CARLO LOCALIZATION\nA. Buyes Filters The pose of a mobile robot on a flat environment is usually represented by the set of x , y and 8. As shown in Fig.l(a), (x,y) denote the position of the robot, and B denotes its orientation based on a coordinate system. We define & as a point in the xy0-space and e* as the actual pose of the robot. A space X that contains all possible e' is also defined. Moreover, the following symbols:\ns discrete time: T = 0 , 1 , 2 , . . . , t - 1, t , t + 1,. . , ,\n24481 0-7803-84634/04/$20.00 WO04 IEEE", + ". available information at T = t: dt, and the robot's action while t 5 T < t + 1: at\nare given for formulation. They are shown in Fig.l(b). A self-localization problem is formulated with these symbols. The problem is to solve the following probability:\nB t ( X ) = L b t ( C ) d I ! = PI{!; E X l d t , a t - i , d t - ~ ,\n( 1 )\nwhere X denotes any region in X and ht(e) is the probability density of C = e*. Initial probability density function (pdf) ho affects the character of a localization problem. If bo converges around actual pose P, it is called posirion rracking. If e* is unknown and bo is set as an uniform distribution, it is called a global localiwtion pmblem.\nWhen the set of all possible d and the set of all possible action a are represented by 'D and A respectively, Bayes filters require that the followin% probability densities can be measured for VC E X I Vel E X, Va E A, and V d E 'D at any time step. . CIC',a - p(C1E';a): the probability density that e =\non condition E' = et and a = at (Markov\n. dl t - p(d/C): the probability density that d = dt on condition e = I!;. If d is a discrete quantity, probability P(dje) is required as its substitution.\nat--2,dt-zrat--3.. . . , d l , no, bo}>\nproperty)\nA Bayes filter can be formulated as\np(El!', at-l)ht_l(E')de', and (2)\n(3)\nEq.(2) and Eq.(3) denote a Markov process and the Bayes theorem respcctively. Basically, they are calculatcd alternately.\nB. Monle Carlo localization A Bayes filter is implemented with various methods according to conditions. For global localization problems, particle filters [I], [2], [SI and multi hypothesis trackings (MHT) [6] , [7] are frequently used. A MHT executes many Kalman filters at once. The cenler pose of each Kalman filter is a hypothesis of the robot's pose. An algorithm that generales and eliminates hypotheses is required for a MHT. On the other hand, particle filters approximate\nBayes filters more directly than MHTs. They are sometimes compared from various standpoints [4], [7]. We think that the combination of a Bayes filter and a resetting method can be used in various conditions while its behavior is easy to understand.\nParticle filters for mobile robot localization have been named Monte Carlo localization (MCL). This method utilizes particles sr ) ( i = 1,2, . . . ,A') that drift in the xy8-space for approximation of &-, and bt. The particles share weight whose total is one. The weighted distribution of particles approximates the probability distributions.\nFigure 2 shows the algorithm of MCL. sr ) =\nthe xy8-space and its weight, denotes a particle. These processes approximate Eq.(2) and Eq.(3) respectively. The larger the number of particles N is, the more the approximation is expected. In general, many particles are required when ht is uncertain. Decision of a proper number of particles is studied by Fox [SI.\nC. Z7ze Problem It is the fatal state for MCL when there is no particle around actual pose e'. MCL cannot approximale the probability distribution at the region where no particle exists.\nThis fatal case oftcn occurs due to not only the lack of particles, but also any accident that goes against the suppositions of a Bayes filter. These accidents cannot he enumerated without omission. However, we can write the worst result hy such an accident with only one expression:\n(!;)(xt ( ' (1) ~g~),Or)),w~)), which is the set of its pose in\nBt(Y) = bt(e)dC = 1 (P 6 Y c X). (4)\nTherefore, a recovery method from the state of this equation can enable an MCL method to be robust.\nIncidentally, kidnapped mbor problems frequently become subjects for research as one of the fatal cases. The kidnap refers to the situation that a robot that knows its pose well is moved anywhere. This case can be also represented by Eq. (4).\n111. RESETTING METHODS\nNote that any Bayes estimation does not work well with wrong prior knowledge. Therefore, we must handle the problem beyond the limits of Bayes filters.\nThe following process: 1) stop a Bayes filter when the state like Eq.(4) is detected, 2) start the Bayes filter with new bo, is a possible way for this problem. This method is called a resetting method and is used in MCLs.", + "Though Thrun er al. have pointed out that these kinds of method does not have theoretical validity in [91, it does not contradict with Bayes filters. That is because Bayes filters do not restrict the condition of bo as long as it is not wrong.\nA. Sensor Resetring\nfor the trigger of resetting [IO]. a is explained by The sensor resetling uses cy, which is shown in Fig.2,\na = JxP(41!')bi(E')del (5 )\nin a Bayes filter. When the following value\n0 = 1 - a/a, (00, : a positive threshold) (6)\nbecomes positive, panicles are placed based on the pdf:\nB. Hysteresis Sensor Resetring There is the possibility that the above method arouses needless resettings if information is noisy. In [4] by Gutmann er al., there is the description that the University of Washington team used the following resetting method in RoboCup 2002 four legged robot league.\nInstead of Eq.(6), this method computes 0 with the following procedures:\nwoni +- mnia + (1 ~ vooi)a~onp (8) e r h m - Ilrmna. i- (1 - Ilrho\")a*O\" (9)\nB = 1 - arhon/(alongcyrh)i (10)\nwhere 0 5 qooi i< 'Ishon 5 1 and they are constants. u~hOn/cqoni becomes less than ah after a continues to be small. Therefore, a resetting may not occur by single wrong information. In this paper, this method is called the hysteresis sensor resetting.\nC. Expansion Resetring We have used another resetting method since RoboCup 2002 in our localization method (Uniform Monte Carlo localization, [Il l) . This method is called the expansion reserring. We generalize it and propose its use for MCL. It initializes the pdf as\nboncw = f [btl (11)\nwhen > 0. This equation only explains that only bt is used for allocation of particles. A more important thing than Eq.(ll)*is that mapping f acts as boocw becomes vaguer than bt. After that, boncu, - f [boB.,] is repeated every input of new information d until 4 of Eq.(6) becomes zero or less.\nIn the case of MCL, mapping f expands the region where panicles exist as shown in Fig.3. The extent of expansion on each axis should be roughly in proportion to the interval in which particles exist. This resetting method has the following property if there is no perceptual aliasing. . If bt is not wrong, the expansion stops soon.\n. If b, is completely wrong, thc expansion usually supplies panicles near correct pose e..\nTherefore, this method avoids the discard of accurate bt when wrong information is singly obtained.\nD. Blending of Resetring Merhods\nFor solving the perceptual aliasing problems or other special problems, the above methods can be blended with some ways. For example, the followin_e choice is possible when 8 > 0 with Eq.(6). . if particles exist in a small region: expansion resettings\nThis procedure regards bt as important if it converges. Otherwise the procedure attaches imponance to sensor information.\notherwise: sensor resettings\nIV. SIMULATION\nThe three resetting methods and a normal Monte Carlo localization are compared. Though blended methods referred in m-D also deserve to he compared, we concenlrate on the comparison of the simple methods.\nA. RoboCup Four Legged Robor League\nIn RoboCup four-legged robot league 1121. a team uses four sets of lion-like pet robots, ERS-210, as swcer players. Each robot has three DoF in each leg and in the head as shown in Fig.4(a). The CPU in the robot is an MIPS I92MHz. with 32MB of RAM. It has a CMOS camera on its nose, whose resolution is 176x 144. The size of a soccer field shown in FigA(c) is 4.2 x 2.7[m]." + ] + }, + { + "image_filename": "designv11_2_0000113_s0924-0136(00)00570-7-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000113_s0924-0136(00)00570-7-Figure3-1.png", + "caption": "Fig. 3. Parameters of the generated tooth pro\u00aele.", + "texts": [ + " In practice, the proper shaper cutter parameters are usually estimated according to the desired gear pro\u00aeles. In this section, several numerical examples are studied to investigate how the shaper cutter parameters affect the generated tooth pro\u00aele. In addition, the optimization method is adopted to determine adequate shaper cutter parameters to meet the prescribed gear pro\u00aele. Several parameters of the generated tooth pro\u00aele must be initially de\u00aened to quantitatively describe the generated tooth pro\u00aele. Fig. 3 depicts a generated tooth pro\u00aele and its pro\u00aele parameters. In Fig. 3, curve MN is the working part on the generated gear. The coordinates of point M (initial point of chamfer) can be determined by solving the nonlinear equations of the chamfer region and the involute region simultaneously. Similarly, the coordinates of point N (the initial point of the \u00aellet) can be determined by solving the non-linear equations of the involute region and the \u00aellet region simultaneously. In the chamfer region, hc denotes the height of the chamfer and yc represents the chamfer angle, formed by a horizontal line and the chamfer", + " Obviously, a larger hu leads to a shorter working part and therefore a smaller contact ratio of the gear. The tip chamfer and the \u00aellet of the gear tooth are generated by the semi-topping and the protuberance of the shaper cutter, respectively. Therefore, investigations on the effects of shaper cutter parameters on the tooth pro\u00aele fall into two parts: the effect on the chamfer region and the effect on the \u00aellet region. Table 1 lists some major design parameters of the shaper cutter and the generated gear employed in the following investigations. According to Fig. 3, the tip chamfer on the generated tooth pro\u00aele has two parameters, yc and hc, denoting the angle and height of the chamfer, respectively. On the other hand, as shown in Fig. 1, the semi-topping on the shaper cutter also has two parameters ys and xd. Parameter ys is the angle formed between the semi-topping and a horizontal line and parameter xd is the involute polar angle of point D. Based on the developed mathematical model of the generated gear tooth and the design parameters listed in Table 1, the effects of parameters xd and ys on the generated tooth pro\u00aele are investigated and illustrated in Fig. 4. Meanwhile, Fig. 5 summarizes the effects of xd and ys on the two chamfer parameters, yc and hc. According to Fig. 5(a), although xd increases with an increase of hc, yc remains nearly unchanged. As Fig. 5(b) indicates, yc increases but hc decreases as ys increases. In sum, the parameter xs affects the chamfer height hc while the semi-topping angle ys dominates the chamfer angle yc. According to Fig. 3, two parameters, umax and hu are relevant to the undercut and \u00aellet region of the generated tooth pro\u00aele, which are affected by the three protuberance parameters r, hp and yp of the shaper cutter, as shown in Fig. 1. Parameter r refers to the radius of curve BC, hp denotes the height of the protuberance, and yp represents the angle formed by line AB and a horizontal line. Several numerical examples are applied to investigate how the three shaper cutter parameters r, hp and yp affect the tooth pro\u00aele parameters umax and hu, individually" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000380_2000-01-0357-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000380_2000-01-0357-Figure7-1.png", + "caption": "Figure 7. Exemplar Modified Nicolas-Comstock longitudinal force", + "texts": [], + "surrounding_texts": [ + "5 All models of the combined tire force, regardless of the formulation, must provide realistic results. To do this, the following performance criteria are proposed for the process of combining the transverse and longitudinal components: 1. the combined longitudinal force component Fx(s,\u03b1) should approach the longitudinal component Fx(s) as \u03b1 \u2192 0, i.e. Fx(\u03b1,s)|\u03b1 \u2192 0 \u2192 Fx(s); 2. the combined transverse force component Fy(s,\u03b1) should approach the transverse component Fy(\u03b1), as s \u2192 0, i.e. Fy(\u03b1,s)|s \u2192 0 \u2192 Fy(\u03b1); 3. the combined force, F(\u03b1,s), must be friction limited, 4. the combined tire force F(\u03b1,s) must agree at least approximately with experimental results; and 5. the combined tire force F(\u03b1,s) should produce a force equal to \u03bcFz in a direction opposite to the velocity vector for a locked wheel skid (s = 1) for any \u03b1. It is instructional to begin the investigation of combined tire friction forces by looking at the concept referred to as the \"friction circle\" [see for example, Warner, et. al. (1983)]. This concept asserts that the total available friction force at the tire-road interface is given by Fmax = \u03bcFz, and its direction lies opposite to the direction of the resultant velocity vector, VR. The concept further asserts that if the vector sum of the longitudinal force and transverse force is less than Fmax, the tire will continue to track and rotate. Experiments show that tires exhibit properties that differ from the theoretical friction circle. Differences in longitudinal and transverse coefficients of friction due to such attributes as tread patterns, tire construction and tire geometry, lead to different longitudinal and transverse limiting forces. Consequently, the friction circle actually is better described as a friction ellipse. An expression for the friction ellipse can be written as: (11) Equation 11 illustrates mathematically the concept that if a steering input is introduced while braking or if brakes are applied while steering, less capacity is available for each individual force than when braking or steering alone. This leads to the situation, for example, where a steering input to a wheel under severe braking (but not fully locked) can increase the force to Fmax, causing the tire to slide out and begin to skid. COMBINATION MODELS \u2013 While Equation 11 is useful for an intuitive understanding of the physical conditions at the tire-road interface under combined loading, it provides only a bound on the resultant force. For quantitative use of the combined force, an equation for F(\u03b1,s), not an equality, is needed. Various models have been proposed over the years. See for example Nicolas and Comstock (1972), Bakker, et. al. (1987), Wong (1993), and Schuring, et. al. (1996).\nThe model proposed by Nicolas and Comstock is based on two conditions. The first is that the resultant force, F(\u03b1,s) for s = 1, is collinear with and opposite to the resultant velocity, VR. The second condition is that as \u03b1 is varied from 0 to \u03c0/2, the resultant force F can be described by an ellipse of semi-axes Fx and Fy. Semiaxis Fx is the longitudinal friction force defined by a \u03bcx slip curve for \u03b1 = 0 and semi-axis Fy is the transverse friction force predicted by an appropriate equation for s = 0. They produce the following expressions:\n(12)\n(13)\nNote that from these two equations the ratio of Fy(\u03b1,s) to Fx(\u03b1,s) is always (tan\u03b1)/s.\nEach equation is easily evaluated for a given s and \u03b1 by first evaluating Fx(s) and Fy(\u03b1). However, for either \u03b1 = 0 and/or s = 0, the expressions as defined above are undefined. In particular, when \u03b1 = 0, there is no transverse force on the tire, i.e. Fy| \u03b1=0 = 0 by definition. With both \u03b1 and Fy(\u03b1) equal to zero, both the numerator and the denominator of the two equations goes to zero. This is inconvenient as it is expected that Fx(s,0) should reduce to Fx(s). Similarly, with s and Fx(s) equal to zero, both the numerator and the denominator of the two equations goes to zero. As given above the Nicolas-Comstock equations do not satisfy all of the criteria presented earlier. For small values of s and \u03b1, where it is expected that Fx(s,\u03b1) \u2192 Fx(s) and Fy(s,\u03b1) \u2192 Fy(\u03b1), the equations produce bias factors as is now shown.\nFor small values of \u03b1 and s, the tire is operating in the linear region of the force curves (see figures 3 and 5). Therefore, linear approximations can be used for the longitudinal and transverse forces using the wheel slip stiffness and the sideslip stiffness presented earlier. Hence, Fx(s) \u2248 Css and Fy(\u03b1) \u2248 C\u03b1\u03b1 and tan\u03b1 \u2248 \u03b1. Introducing these approximations into equations 12 and 13 yields:\n(14)\n(15)\nThis shows that the Nicolas-Comstock equations have biased slopes in the combined linear regions of the tire force curves.\nx 2\nx 2 z 2\ny 2\ny 2 z 2\nF ( , s)\nF +\nF ( , s)\nF 1 \u03b1 \u03bc\n\u03b1\n\u03bc \u2264\nx x\ns\nF ( , s)= F (s) C\nC + C \u03b1\n\u03b1 \u03c0\n\u03b1\n\u03b1 2 2\nwhere 0 < << / 2 and 0 < s << 1\ny y s\ns\nF ( , s)= F ( ) C\nC + C \u03b1 \u03b1\n\u03b1 \u03c0 \u03b1 2 2 where 0 < << / 2 and 0 < s << 1", + "6 In considering the Nicolas-Comstock equations relative to the first and second performance criteria, two conditions are examined, that of straight-ahead braking (s = 1 and \u03b1 = 0) and transverse sliding (s = 0 and \u03b1 = \u03c0/2). Using these values in Equations 12 and 13 yields the conditions of 0/0 and \u221e/\u221e, respectively. This demonstrates that the Nicolas-Comstock equations also do not meet the first and second performance criterion. The bias factors shown in Equations 14 and 15 and the failure of the Nicolas-Comstock equations to meet the performance criteria can be mitigated by appropriate modification of the equations. Modified equations are presented and investigated in the next section and will be referred to as the Modified Nicolas-Comstock (MNC) equations. Typical plots of the force predicted by the MNC tire friction force model are presented. The capability of the model to match actual tire behavior is presented using data recorded by the SAE. A new way of graphically presenting the force plots is also presented. THE MODIFIED NICOLAS-COMSTOCK MODEL \u2013 The following Modified Nicolas-Comstock equations are proposed to correct the deficiencies discussed above: (16) (17) Equations 16 and 17 provide the tire force components for any combination of the parameters \u03b1 and s such that 0 \u2264 \u03b1 \u2264 \u03c0/2 and 0 \u2264 s \u2264 1 for any pair of functions Fx(s) and Fy(\u03b1). The equations have a relatively simple form for use in vehicle dynamic simulations. They easily can be extended for the range of sideslip angle such that 0 \u2264 \u03b1 \u2264 2\u03c0. It can be seen that Fx(\u03b1,s) and Fy(\u03b1,s) as given by Equations 16 and 17 approach Fx(s) and Fy(\u03b1) respectively for 0 < \u03b1 << \u03c0/2 and 0 < s << 1, when Fx(s) \u2248 CSs and Fy(s) \u2248 C\u03b1\u03b1. A typical means of viewing models of the combined forces is to plot the combined forces for given values of \u03b1 over the full range of s as shown in Figure 6 or for given values of s over the full range of \u03b1. An alternative means to viewing the equations is used here by displaying the data over the full range of both independent variables in one three-dimensional plot. Figures 7 and 8 are examples.\nx x y\ny x\nx 2\nF ( , s)= F (s) F ( )\ns F ( )+ F (s)\ns C + ( - s ) F (s)\nC\n\u03b1 \u03b1\n\u03b1 \u03b1\n\u03b1\u03b1\n\u03b1\n2 2 2 2\n2 2 2 2\ntan\n1 cos\u22c5\ny x y\ny x\ny s\ns\nF ( , s)= F (s) F ( )\ns F ( )+ F (s)\n( - s ) F ( )+ C\nC\n\u03b1 \u03b1\n\u03b1 \u03b1\n\u03b1 \u03b1 \u03b1 \u03b1\n2 2 2 2\n2 2 2 2 2\ntan\n1 cos sin\ncos \u22c5", + "7\nThe fourth performance criteria presented earlier requires that the combined tire force F(\u03b1,s) must agree at least approximately with experimental results. Heavy truck tire force data was collected through sponsorship of the SAE and has been made available for general use [Anonymous, 1995]. In addition to combined force data, free rolling cornering and straight line braking data were collected as part of the project. This individual force data has been used here with an optimization algorithm to determine the appropriate coefficients for the BNP formula, B, C, D, and E, for longitudinal forces versus s (straight line braking) and lateral forces versus \u03b1 (free rolling cornering). Figures 9 and 10 show the data with the accompanying BNP curve generated by the fitting process for one normal force, Fz = 20,604 N.\nindividual data points. The BNP coefficients and formulas then were used with the modified Nicolas-Comstock equations to compute the combined force for braking and steering F(\u03b1,s). A set of data was selected to compare the experimental to the analytical. The data chosen shows the combined force for a 295/75|275/80R22.5 truck tire for a slip angles of \u00b14\u00b0 [Anonymous, 1995]. The resulting plot comparing the experimental and analytical data is shown in Figure 11. The comparison shown in Figure 11 indicates that a good fit for the combined force can be obtained from MNC equations using just free-rolling cornering and straight line braking data.\nindividual data points.\nExperimental data shown by \u2666 and .\nA model for the combined frictional force at the tire-road interface based on a modified version of the modified Nicolas-Comstock equations (MNC) has been presented. The model, in conjunction with the BNP equations or any other tire force model, provides a simple algebraic means of finding the two tire force components over a full range of combined wheel slip and side slip angles. The only requirement needed to implement the model is the availability of the straight line braking and free rolling cornering data for given conditions. By specifying the friction limits, \u03bcxFz and \u03bcyFz, the MNC equations yield acceptable results for the prediction of the combined force at the tire-road interface. They can be used for vehicle dynamics simulations and also are useful for accident reconstruction applications." + ] + }, + { + "image_filename": "designv11_2_0000530_s0045-7825(02)00308-0-Figure9-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000530_s0045-7825(02)00308-0-Figure9-1.png", + "caption": "Fig. 9. Geometry, finite element mesh and material data for cylindrical panel.", + "texts": [ + " The total number of modified Newton\u2013Raphson iterations for every 50 load increments and the corresponding CPU time in seconds required for the formation and factorization of the tangent stiffness matrix, the forward and backward substitutions, the calculation of the residual forces and the total required time are depicted. The computations were performed on a Pentium III 1000 MHz processor. This example considers the large displacement elasto-plastic material behaviour of a cylindrical panel under a concentrated vertical load with reference value f0 \u00bc 1 kN. The curve edge nodes of the panel are assumed to be free in all directions while the nodes along the sides are hinged (fixed against translation). The geometric and material properties of the shell example are shown in Fig. 9. The yield stress is taken ry \u00bc 0:001 kN/mm2. Due to the symmetry of the problem, only one quarter of the panel is discretized with a mesh of 800 TRIC elements. The results obtained are compared with those in the literature from [17] where a Reissner\u2013Mindlin type kinematics assumption and layered finite element approach is considered. The load factor versus the vertical displacement under the force f is plotted in Fig. 10. The spread of equivalent plastic stress through the upper surface of the discretized quarter of the shell at load factor k \u00bc 0:0035 is presented in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001278_j.ymssp.2003.08.002-Figure25-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001278_j.ymssp.2003.08.002-Figure25-1.png", + "caption": "Fig. 25. Picture of the studied DSSRM.", + "texts": [ + " Then, the natural frequency is found accurately: a sinusoidal current of fixed frequency is adjusted so that the response magnitude is maximal. Fig. 24 shows the acceleration of statoric deformations obtained with such a device. Table 5 presents the results. Practical results are significantly modified. Indeed, radial natural frequencies are lower than the stator itself and important mode 2 additional frequencies appear. It shows the difficulties to analyse a complex structure. Mode 0-2D and 2-3D are correctly determined by each method, especially when the simple frame made of varnished metal sheets is considered. Fig. 25 shows the whole DSSRM. It has no feet for the reason that its fixation is axial. As for the previous induction machine, the analytical method takes into account the stator frame alone: it is considered as the main resonant part. So, the results of the last part are kept. FE model does not take into account cooling ribs or feet, but the stack of metal sheets alone. This machine is also suspended and three tests (modal hammer, shaker and magnetic excitatory) are performed. Measurements are not influenced by any internal cooling system because the machine has no fan" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000970_1.2816998-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000970_1.2816998-Figure4-1.png", + "caption": "Fig. 4 Comparison of thermal bend and second bending mode", + "texts": [ + "asme.org/about-asme/terms-of-use from the differential input. The latter produces a temperature differential locally across the journal, which results in a bend. Similar arguments apply to the backward whirl case when the journal is eccentric, although the heat input will always be smaller. Since linearity is assumed, the forward and backward whirl effects can be superimposed. For the purpose of illustration, further argument will be re stricted to the forward circular whirl case. Referring to Fig. 4, the thermal distortion of the rotor when stationary is shown to affect only the overhangs. Imagine for simplicity that the over hang mass is concentrated at the ends and the thermal bend 6 localized at the bearings. Also consider 8 arising thermally from an orbit at the bearing, denoted by vector q, then: 8 = T(t, \u00a3l)q (4) where 8 defines both magnitude and direction relative to rotor axes. T is a complex number varying with time and speed. Consider now a small bend 0, imposed on this rotor at the bearing location" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003614_10402000701739271-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003614_10402000701739271-Figure1-1.png", + "caption": "Fig. 1\u2014Schematic of washer bearing system (view into y-axis).", + "texts": [ + " The model provides predictions of frictional torque, bearing temperature, hydrodynamic lift, and other indicators of bearing performance. The numerical model and theoretical pre- dictions confirm the experimental results, showing that the bear- ing under consideration is very susceptible to the mechanisms of thermoelastic instability (TEI) and thermoviscous distress (TVD). Thermal Effects: Boundary Lubrication; Hydrodynamic Bearings; Washers; Gears; Asperity Contact This work investigates the physical phenomena that distress a thrust washer bearing system (see Fig. 1). This is a continuation of a body of work that includes both experimental (Jackson and Green (2), (3)) and numerical (Jackson and Green (4)) investigations. In Jackson and Green (4), however, the washers were considered rigid and no mechanical or thermal deformations were considered. The current work will expand on these results by including thermomechanical deformation to give a more realistic physical model. 1Present Address: Department of Mechanical Engineering, Auburn University, Auburn, AL 36849-5341 (robert", + " For the deformations resulting from mechanical pressures the solution for a uniform pressure on a rectangular region, from Johnson (31) is used: \u03c0 E 1\u2212v2 (uz)mech ptot = (x + a) ln { (y + b) + [(y + b)2 + (x + a)2]1/2 (y \u2212 b) + [(y \u2212 b)2 + (x + a)2]1/2 } + (y + b) ln { (x + a) + [(y + b)2 + (x + a)2]1/2 (x \u2212 a) + [(y \u2212 b)2 + (x \u2212 a)2]1/2 } + (x \u2212 a) ln { (y \u2212 b) + [(y \u2212 b)2 + (x \u2212 a)2]1/2 (y + b) + [(y + b)2 + (x \u2212 a)2]1/2 } + (y \u2212 b) ln { (x \u2212 a) + [(y \u2212 b)2 + (x \u2212 a)2]1/2 (x + a) + [(y \u2212 b)2 + (x + a)2]1/2 } [2] where ptot = p + Fcont/Ai is the sum of the fluid film pressure, p, and average contact pressure, Fcont/Ai , in the polygonal region having 2\u00b7a and 2\u00b7b as its dimensions and an area Ai , and x and y are the location on the surface in relation to the center point of the polygonal region. (uz)mech is the surface deformation due to the mechanical pressure. The total surface displacement, uz, is calculated as uz = (uz)mech + (uz)therm . Then by using superposition, the surface deformation for the entire half-space due to an arbitrary heat and load distribution is approximated for the carrier and gear surfaces shown in Fig. 1. In regions where asperities between surfaces come in close proximity, the asperities can influence the lubrication flow. In this mixed lubrication regime, there is only a thin film of lubricant separating the surfaces, and the micro-topography of the surfaces greatly affects the flow of the lubricant. This work models a thin fluid film between the carrier, the washer, and the gear, as shown in Fig. 1. To consider this effect, this work employs the ubiquitous (Patir and Cheng (32), (33)) flow factors and the modified form of the Reynolds equation (see Jackson and Green (4) for more details). The modified Reynolds equation is discretized using a finite difference scheme, and the fluid pressure, p, is solved at each nodal location on the bearing, which is used to find the nodal forces. This work uses the statistical elasto-plastic asperity contact model derived in Jackson and Green (34), (35) and confirmed for a broad range of material properties by Quicksall, et al", + " The force and moment balance depend ultimately on the location and orientation of the washers and gear. Thus the problem is formulated as a nonlinear set of four equations with four unknowns. These equations are dependent on the governing physical equations of the thrust washer bearing and consider asperity contact, mixed and full-film lubrication, and heat generation and balance. The unknowns are the axial location of each component, z, and the tilt of each component about the x and y-axis, \u03b3 x and \u03b3 y (see Fig. 1). The gear is able to translate in the z direction but has a fixed tilt, \u03b3 tilt, about the y-axis and so accounts for only one degree of freedom. The washer is able to tilt about the x- and y-axis and also move along the z-axis and so has three degrees of freedom. The four unknowns are explicitly zw, zg, (\u03b3 x)w, and (\u03b3 y)w . The above methods are coupled through their boundary conditions and so they must be satisfied simultaneously. This is done by use of the Newton-Raphson iterative method. In addition, variable underrelaxation is used to further enhance convergence" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002348_j.engfailanal.2004.12.016-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002348_j.engfailanal.2004.12.016-Figure8-1.png", + "caption": "Fig. 8. Circumferential stress at the inner side of the wheel tyre at y = 67.5 mm (roof-ridge) in dependence of the angle u for the loading case straightforward driving (assembly + Q-load) for a wheel diameter of 862 mm.", + "texts": [ + " At the \u2018\u2018roof-ridge\u2019\u2019 of the wheel tyre the circumferential stress is about 50 MPa. The analysis of the loading case \u2018\u2018straightforward driving\u2019\u2019 yield positive circumferential stresses that heavily vary in circumferential as well as axial direction. Fig. 7 shows the stress distribution in the area of the wheel/rail contact. The highest circumferential stress can be observed at the \u2018\u2018roof-ridge\u2019\u2019 in the symmetrical plane of the loaded wheel. For the loading case straightforward driving for Q = 98 kN a maximum stress rmax = 220 MPa will develop. As can be seen in Fig. 8, the circumferential stress, which is responsible for the fatigue crack growth, rapidly decreases in circumferential direction. A minimum can be observed for u = 45 with rmin = 6 MPa. In the range between u +45 and u = +90 the stresses are approximately equal to the assembly stresses. Fig. 8 shows the circumferential stresses at the inner side of the wheel tyre for a half turn of the wheel. It can be seen, that for any full turn of the wheel one loading cycle is passed through. For Q = 98 kN thus a stress amplitude ra = 107 MPa, a mean stress rm = 113 MPa and an R-ratio = +0.03 is effective. Those maximum stresses occur at the \u2018\u2018roof-ridge\u2019\u2019 (y = 67.5 mm). In the loading case straightforward driving the stresses decrease towards the shoulders of the wheel tyre (Fig. 9). Also the R-ratio R = rmin/rmax depends on the y-coordinate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001614_s0890-6955(02)00013-5-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001614_s0890-6955(02)00013-5-Figure3-1.png", + "caption": "Fig. 3. Photo of the developed ultra-high-speed grinding spindle unit.", + "texts": [ + " A continuous-duty, alternating-current (AC) squirrel cage motor element of 15 kW capacity was integrated to the spindle unit. Around the power zone, a coolant jacket with wider area is built in to disseminate the heat generated. Control to the AC squirrel cage motor is achieved using a frequency controller. A precise locating diametrical recess was included in the spindle nose for ease of wheel changing. Cartridge design was followed and safety against thermal seizure was included. Table 1 gives the specifications and Fig. 3 shows a photo of the developed spindle unit. The hybrid angular contact ball bearings are brought together by point contact and, upon loading, local deformation enlarges to form surface contact. Deformation of the rolling element was investigated using Hertz\u2019s theory and with application of the following conditions: use of silicon nitride (Si3N4) rolling elements; consideration of centrifugal forces due to high speed; and effect of oil/air mist lubrication on the rolling element. The rolling element is subjected to centrifugal force Fc, normal force Fn, frictional moment due to gyroscopic spin Mg and reaction forces F1, F2, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002129_j.scriptamat.2003.09.023-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002129_j.scriptamat.2003.09.023-Figure4-1.png", + "caption": "Fig. 4. Sampling positions for SEM and TEM samples. SEM samples (a)\u2013(c): (a) top of the drill hole, (b) at a depth of 50 mm, (c) at a depth of 90 mm and TEM samples (1)\u2013(4): (1) at a depth of 21 mm, (2) 41 mm, (3) 64 mm and (4) 95 mm (cross-section sample).", + "texts": [ + " Mechanically drilled, shot peened, electrochemical drilled and laser treated Ti6Al4V samples were investigated. The mechanically drilled connecting rod samples were delivered from the material testing lab of Volkswagen AG Wolfsburg. The drill hole has a diameter of 4 mm and a length of 100 mm. It is a so-called deep drill hole [8]. The following parameters were used: rotational speed 2450 min 1, rotational speed of the work piece 350 min 1, motion speed 40 mm/min. Samples of the drill hole surface were taken at different positions, see Fig. 4. Fig. 5 shows SEM-micrographs of the drill surface. In contrast to the starting point of the drill hole (Fig. 5(a)), strong deformations are visible at 50 and 90 mm, Fig. 5(b) and (c). Samples taken at a drill depth of 50 mm show a deformation zone with a thickness of about 10 lm and at a depth of 90 mm the deformation zone is about 20 lm. To investigate the vanadium concentration changes in TEM, four samples from different drill depths were taken, according to Fig. 4. The results of the maximum vanadium concentration in these samples are shown in Fig. 6. The maximum pseudo-temperature occurs at the end of the drill hole and is very close to the b-transus-temperature of Ti6Al4V alloy. At the starting point of the drill hole, the temperature was about 490 K higher, when compared with the unprocessed material. Between the start of the drill hole and the end a linear increase of about 5 K/mm can be approximated. This increase is probably caused by insufficient coolant supply [9]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000184_20.877712-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000184_20.877712-Figure2-1.png", + "caption": "Fig. 2. Skewing principle of 2D n-disks model.", + "texts": [ + " For the magnetic vector potential, we use the derivative of the magnetic energy considering the magnetic flux density constant. This method is easy to implement with the help of the local derivative of the jacobian matrix. III. 2D DISKS AND 2D\u20133D MODELS A. 2D Skewed Slots Model In this approach, the skewed slot effects are taken into account by a third dimension discretization. The skewed part of the axial length \u201c \u201d is cut into \u201c \u201d disks from an ideal 2D machine, by planes perpendicular to the shaft [1], [9]. Two adjacent disks are rotated by an angle of \u201c ,\u201d where corresponds to the total angle of the skew (Fig. 2). The winding and bar currents are assumed to be continuous from one disk to another. For each section, the magnetic field equation is solved by a 2D FEM, in connection with the stator and rotor electric circuit equations. B. 2D\u20133D Models In a 3D usual case, is a function of , the space coordinates, and may be split into three components. In the particular case of machines with skewed rotors, we may suppose that, in the stator, is oriented and invariant in the direction of the feeding currents. It means that, for the nodal discretization, is the only component non equal to zero" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002151_0957-4158(92)90038-p-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002151_0957-4158(92)90038-p-Figure4-1.png", + "caption": "Fig. 4. Epitaxy centrifuge: the rotor with the crucible is suspended within the container with no contact. The magnetic bearings are completely outside the container and the bearing forces are acting through the container wall.", + "texts": [ + " This possibility of influencing the characteristics by software allows the bearings to be made 'intelligent' (Table 1). The next two sections will show some actual examples. For the Max-Planck-Institute of Solid State Research in Stuttgart, Germany, we have built a special centrifuge, where solid state substrates can be covered in a well-defined way with very thin multi-layers [6]. To achieve this, a crucible rotates following a predefined speed program in a container under ultra-high-vacuum conditions (Fig. 4). There are intentions to upscale this liquid phase epitaxy process for generating semiconductors of the highest quality. In collaboration with a Swiss company, we built a magnetically supported milling spindle, which currently is launched as a prototype. The cutting power is about 35 kW, the rotation speed is up to 40,000 rpm, and the cutting speed for aluminium is up to 6000 m sec. This high-speed milling offers advantages with respect to the milling process and production costs. An extensive description is given in [7]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003910_robot.2006.1642348-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003910_robot.2006.1642348-Figure6-1.png", + "caption": "Fig. 6. Error model derivation.", + "texts": [], + "surrounding_texts": [ + "The kinematic model presented in Section II assumes that all the linear actuators are mounted perfectly in parallel. This is difficult to achieve for most installations, unless expensive calibration equipment is utilised. The other approach taken in this paper is to extend the nominal kinematic model with a set of four new parameters for each linear rail, two error offsets and two error orientations. The analytical inverse kinematics of this extended model has also been calculated and is presented in this section. Given this new kinematic model, there is no longer any requirement on parallel actuator rails. In fact, the rails could be mounted at large angles to each other if this would benefit the application. Since an analytical inverse kinematics solution for the error kinematic model has been calculated, the extended kinematic model can replace the nominal kinematic model in the feed-forward path of a fast real-time control system. The error parameters are shown for one of the rails in Fig. 5. Since taking into account these errors undermines the inherently simple geometry of the original model, a new method of finding the inverse kinematics was derived by defining the rail joints from both the tool reference and the rail reference and solving simultaneously. For all but the third rail position, this is a simple task, but due to the triangular configuration of the arms, solving for the third rail becomes quite complex. The derivation is shown in equations (9) to (14) with variables as defined in Figs. 5 and 6. x3 = x \u2212 sin(\u03b1)(L4 + L3d cos(\u03b3)) (9) y3 = y \u2212 L3d sin(\u03b3)) (10) z3 = z \u2212 cos(\u03b1)(L4 + L3d cos(\u03b3)) (11) x3 = X3 cos(\u03c63) cos(\u03b83) (12) y3 = yerror3 + X3 cos(\u03c63) sin(\u03b83) (13) z3 = zerror3 + X3 sin(\u03c63) (14) where the lowercase variables x3, y3 and z3 denote the new Cartesian location of rail 3 given the introduced error variables \u03b3, \u03c6, yerror3 and zerror3. Solving for the X3 rail position yields a quartic equation with an analytic solution found at [8] with only one valid solution for the given configuration. From this, the variable \u03b1 can be found and subsequently, the rail positions X1 and X2 can be found by solving a sphere and a line simultaneously. These computations yield the inverse kinematics of the Gantry-Tau with errors in rail position and orientation accounted for. The model has been successfully tested in simulation (as shown in Fig. 7 with exaggerated error parameter values)." + ] + }, + { + "image_filename": "designv11_2_0003136_robot.1995.525495-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003136_robot.1995.525495-Figure4-1.png", + "caption": "Figure 4: Planar 3-dof, 3RRR parallel manipulator", + "texts": [ + " Then, we have this type of singularity whenever the two types of singularities converge. By inspection of eq.(22), it is obvious that the ith row of K vanishes only if vi = 0. In this case, we have a degenerate manipulator. Such a manipulator is irrelevant for our study and is thus left aside. 3.1.1 Planar 3-dof, 3RRR parallel manipulator: The three types of singularities discussed above are investigated here, for a particular case of the foregoing class of manipulators, with three RRR legs, as shown in Fig. 4. It is recalled that the first type of singularity occurs when the det,erminant of J vanishes. Upon assigning Ai = E, Ci = E and E; = 1, eq.(20) yields for i = 1 or 2 or 3 rTEq, = 0, (28) - 1550 - This type of configuration is reached whenever ri and qi, for i = 1 or 2 or 3, are parallel, which means that one or some of the legs are fully extended or fully folded. At these configurations, the motion of one actuator, that corresponding to the fully extended or fully folded leg, does not produce any motion of M along the axis of the corresponding leg" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002969_pime_proc_1985_199_093_02-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002969_pime_proc_1985_199_093_02-Figure2-1.png", + "caption": "Fig. 2 Beam on two supports", + "texts": [ + " In the case, however, of a flexible shaft with many frequencies in the running range it may (11))l. Proc Instn Mech Engrs Vol 199 No C1 14 P G MORTON well be possible to deal with the lower modal distributions of unbalance in this direct fashion. The principle and accuracy of the technique can be demonstrated just as well on a stationary beam as on a rotating shaft. Since the normal modes of a uniform beam can be expressed analytically, it is convenient to consider the case of such a beam on two damped supports. Figure 2 shows a thin uniform beam split up into (n - 1) equal elements and forced in one plane. The force Fij at the j th node for the ith 4 mode is given by: The finite element equations take the following form: L where Z is the complex support impedance matrix. The relative magnitudes of K and Z determine the influence of the support. Rewriting equation (14) we obtain : where k is the dimensionless shaft stiffness matrix and, for two supports: and Z, is bearing impedance. Solutions were obtained for \u2018hard\u2019 and \u2018soft\u2019 supports with n = 20" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001769_tmag.2003.810533-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001769_tmag.2003.810533-Figure5-1.png", + "caption": "Fig. 5. Cogging torque computation due to a single roundness error.", + "texts": [ + " According to the principle of virtual work, the change of air-gap magnetic energy due to , , is roughly the attraction force applied to the tooth multiplied by . So, we have (6) where is the stacking length, is the slot pitch in radians, is the number of slots, and is still the inner radius of the stator core. Since the cogging torque is calculated from , from (6) we get (7) As anticipated, the cogging torque in (7) due to a single roundness error has cycles per revolution. In order to verify (7), we compare cogging torques obtained with the finite-element analysis (FEA) and (7), using the parameters of the test motor: T, mm, mm, mm, and mm. Fig. 5 illustrates a magnetic flux distribution in the test motor when a single roundness error is given. When m, for example, the ratio of cogging torque amplitudes calculated with the FEA and (7) is about 0.95. We see that the torques obtained in two different ways agree very well. Next we consider a cogging torque when every tooth has a particular roundness error. Let denote the roundness error of the th tooth. In superposing cogging torques due to each roundness error, we need to take into account that the phase advance of the cogging torque, given in (7), per slot pitch is rad" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002653_j.jmatprotec.2004.04.360-Figure13-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002653_j.jmatprotec.2004.04.360-Figure13-1.png", + "caption": "Fig. 13. Maximum and minimum principal stresses in the substrate at the end of the process.", + "texts": [ + " It shows that: (i) the clad\u2013substrate interface experiences the highest PEE values; (ii) a uniform PEEQ distribution exists along the whole perimeter of the valve seat; (iii) the maximum permanent distortions lie in a very limited zone below the clad\u2013substrate interface. In Fig. 12 the displacement distributions along the two principal directions of the plane 1\u20133 are presented. It results that the element displacements along the valve seat perimeter are opposite to the clockwise clad deposition because of the thermal contraction. In Fig. 13 the maximum and minimum principal stresses in the substrate are shown. It is evident that substrate elements experienced tensile stresses, since they were constrained by adjacent inner and colder elements. Also the effects of different boundary conditions on the strain distribution within the workpiece at the end of laser cladding treatment were numerically investigated: constrains on the lateral surface of the workpiece were also considered in order to simulate the presence of the engine block around the cylinder" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002715_j.robot.2005.03.006-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002715_j.robot.2005.03.006-Figure1-1.png", + "caption": "Fig. 1. Mobile manipulator syste a differentially driven platform.", + "texts": [ + " These techniques result in increased flexibility and improve performance both by finding collisionfree paths in cases where the original method fails and by considerably decreasing the length of the calculated paths. Finally, the method is successfully implemented to a large variety of simulated motion planning problems involving cluttered environments, including the parallel parking and crack-sealing problems. For simplicity, this paper focuses on a mobile system, which consists of a two degree-of-freedom manipulator mounted on a differentially driven mobile platform, see Fig. 1. However, the developed methodology can be applied to systems with N d.f. manipulators, or to car-like mobile platforms. The mobile system consists of two subsystems, the holonomic manipulator and its nonholonomic base. The Cartesian coordinates of joint H and end-point E m with with respect to the world frame, see Fig. 1, are given by, xH = xF + l1 cos(\u03d5 + \u03d11) yH = yF + l1 sin(\u03d5 + \u03d11) (1) xE = xF + l1 cos(\u03d5 + \u03d11) + l2 cos(\u03d5 + \u03d11 + \u03d12) yE = yF + l1 sin(\u03d5 + \u03d11) + l2 sin(\u03d5 + \u03d1 + \u03d12) (2) where (xF, yF) is the position of the mounting point F of the mobile platform, \u03d5 the platform orientation, \u03d11 and \u03d12 represent the manipulator joint angles, and l1 and l2 denote the manipulator link lengths. Eqs. (1) and (2) show that the end-point position depends on the position of the mounting point and on the orientation of the platform. If the configuration of the mobile platform is known, one can plan manipulator trajectories according to well-established methods. Therefore, solving the platform planning problem facilitates greatly the planning of manipulator trajectories. As shown in Fig. 1, the mobile platform is driven by two independent wheels. We assume that the speed, at which the system moves is low, and therefore the two driven wheels do not slip. This constraint, written for the manipulator mounting point F, is described by x\u0307F sin\u03d5 \u2212 y\u0307F cos\u03d5 + \u03d5\u0307l = 0 (3) w F p c m o E d w p o u v w(xF, yF, \u03d5) = \u03d5 (7) Eqs. (5)\u2013(7) constitute a transformation (xF, yF, \u03d5) \u2192 (u, v, w), which is defined at every point of the configuration space. This transformation greatly facilitates path planning", + " It can be seen that for some w=\u03d5, the obstacles in the u\u2013v\u2013w space are still an ellipse, a circle and a rectangle, while the centers of all families of obstacles lie on helicoids. The transformation developed above refers to the manipulator mounting point F of the platform. However, when it comes to obstacle avoidance, it is obvious t m a we study how a point on the platform or on the manipulator is mapped through the transformation for point F given by Eqs. (5)\u2013(7). To this end, we consider point R on the platform, with coordinates (\u03beR, \u03b7R) expressed in the coordinate frame (\u03be, \u03b7) parallel to the platform coordinate frame (X, Y) with origin at point F, see Fig. 1. Its Cartesian coordinates relative to the world frame are given by, xR = xF(\u03beR cos\u03d5 \u2212 \u03b7R sin\u03d5) (12a) xR = xF(\u03beR sin\u03d5 \u2212 \u03b7R cos\u03d5) (12b) Substituting Eq. (12) into Eqs. (5)\u2013(7) for both points F and R and after simple manipulations we conclude that: uR(w) = u(w) \u2212 \u03b7R (13a) vR(w) = v(w) \u2212 \u03beR (13b) Eq. (13) can be used to take into consideration additional points of interest when planning a collision-free path, e.g. corners of the vehicle. o m e 4 l f fi hat other points of the platform and of the manipulator ust be taken into account to ensure obstacle avoidnce for the whole system", + " During system motion, the manipulator may be moving with respect to its base. The relative manipulator motion (path and trajectory) can be planned easily using n boundary conditions, e.g. end-point initial and final position and velocity. A simple solution to this problem is to use polynomials of order n\u2212 1. Then, the n polynomial coefficients, and thus the joint path, are calculated by solving a system of n linear equat c d t t a c m p p f b o t t T i Example 1. To illustrate the obstacle avoidance method described above, we consider the system depicted in Fig. 1 navigating in the workspace depicted in Fig. 5, where a circular, an elliptic and a triangular obstacle exist. For the simulation, the following values were chosen: total motion time 6 s, initial configuration (xin F , y in F , \u03d5 in, \u03d1in 1 , \u03d1 in 2 ) = (\u22120.2 m, 0.5 m,\u221290\u25e6,\u221240\u25e6,\u221250\u25e6) and final desired configuration (xfin F , y fin F , \u03d5 fin, \u03d1fin 1 , \u03d1 fin 2 ) = (1 m, 2 m, 120\u25e6, 40\u25e6,\u2212130\u25e6). Note that choosing a different total time will make the system move faster or slower, but will have no effect on the Cartesian path of the platform" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002103_tsmcb.2003.810439-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002103_tsmcb.2003.810439-Figure8-1.png", + "caption": "Fig. 8. Three-dimensional manipulator with revolute and prismatic joints.", + "texts": [ + " 6 and 5, it is shown that consideration of two terms of the asymptotic expansion give sufficient accuracy and addition of the another terms is not necessary. The vibrational behavior of the manipulator link is shown in Fig. 7 during retraction of the length of link. It is observed in simulation that during retraction of the link, the frequency increases and the amplitude of the modal variable decreases. V. VERIFICATION OF THE REPRESENTED METHOD In order to verifying the results of the proposed method, we consider the flexible manipulator with a prismatic joint (see Fig. 8) studied in [17]. Using the proposed method, one can solve the dynamic equations of motion and compare the results with the ASM method. Figs. 9 and 10 show the accuracy of the proposed method with respect to the ASM method. VI. CONCLUSION In this paper, using a fictitious rigid link model, the motion of the robot is decomposed into rigid motions and elastic deformations. The kinematics equations are obtained without discretization. Furthermore, dynamic equations of motion for the longitudinal, torsional, and bending vibrations are derived using the Jourdain\u2019s principle and the Gibbs-Appell notation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001278_j.ymssp.2003.08.002-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001278_j.ymssp.2003.08.002-Figure1-1.png", + "caption": "Fig. 1. Structure geometry.", + "texts": [ + " It is first applied to smooth rings but a special transformation allows to take into account the weight of the stator teeth. Poisson ratio is not required in this part. The advantage of this analytical method is a fast determination of stator radial and tangential natural frequencies. It considers that the stator is the most responsive part compared to the rotor, the ball bearings or the flanges. The laws established by Jordan [7] are rewritten [8,9] using the Timoshenko theory [10] about the smooth free rings of infinite length. Fig. 1 shows used variables and selected notations: * Ra: internal radius, * Rc: average radius of the yoke, * ec: radial thickness of the yoke, behind the slots, * L: length of the frame, * L0: distance between the booth supports of the rotor shaft, * d: diameter of the shaft. If mode 0 and steel are considered, it is obtained: F0 \u00bc 837:5 Rc ffiffiffi D p : \u00f01\u00de For a smooth ring, D \u00bc 1: If the ring is toothed, it is obtained: D \u00bc weight of the yoke \u00fe weight of the teeth weight of the yoke : \u00f02\u00de When m \u00bc 1; the natural frequency corresponds to the deflections of the rotor shaft; in this case this frequency is noted f1: f1 \u00bc 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3Ed4 8\u00f0L0\u00de3103\u00bdL\u00f04R2 a d2\u00de \u00fe 0:5L0d2 s : \u00f03\u00de For mX2; two kinds of natural frequencies are used, comparatively to the radial vibrations Fm and the longitudinal vibrations Fc;m: Fm \u00bc F0 ec 2 ffiffiffi 3 p Rc mm ffiffiffiffiffiffiffi m\u00fe p ; \u00f04\u00de Fc;m \u00bc F0m ; \u00f05\u00de where m \u00bc m2 1 and m\u00fe \u00bc m2 \u00fe 1: The previous simplified analytical laws have been rewritten [8,9] more accurately: m \u00bc 0 : F 0 \u00bc O; \u00f06\u00de m \u00bc 1 : F 1 \u00bc O ffiffiffi 2 p ; \u00f07\u00de mX2 : F m \u00bc O ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ga \u00fe m\u00fe ffiffiffiffi Y p 2\u00f03G2m \u00fe 1\u00de s ; \u00f08\u00de where Y \u00bc m2 \u00fe \u00fe G2\u00f02am\u00fe 4m2m2 \u00de \u00fe G4\u00f0a2 12m2m3 \u00de; a \u00bc 4m4 m2 3; O2 \u00bc E rR2 c ; G \u00bc e2 c 12R2 c : Usually, a finite element software is used to establish models of mechanical systems" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000183_3-540-45501-9_4-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000183_3-540-45501-9_4-Figure2-1.png", + "caption": "Fig. 2 Normal indentation \u03b4 = \u03b4B + \u03b4 \u2032 B of spherical contact surfaces.", + "texts": [ + " Let non-conforming bodies B and \u2032 B come into contact at an initial contact point C, as shown in Fig. 1a. Suppose that in a neighbourhood of C the surfaces of the bodies have radii of curvature RB and R \u2032 B respectively; i.e. both bodies are smooth in the contact region. At the initial contact point C the surfaces have a common tangent plane and normal to this plane is the common normal direction n3. Let bodies with initial surface curvatures RB \u22121 and R \u2032 B \u22121 be compressed by a normal force F3 as shown in Fig. 2; as the compressing force increases the common area of contact spreads from C to include a small region around C. The perimeter of this contact area has radius a. Hertz showed that for compatible normal displacements within the contact area, there is an elliptic distribution of contact pressure p(r) between the bodies, p p0 = 1\u2212 r 2 a2 1 /2 , r \u2264 a . (10) Contact Problems for Elasto-Plastic Impact in Multi-Body Systems 197 where r is a radial coordinate originating at C and p0 = p(0) is the maximum pressure which occurs at the center of the contact area" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000894_ac9801667-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000894_ac9801667-Figure2-1.png", + "caption": "Figure 2. Schematic of the stages in the construction of the thinring platinum electrode. (a) The capillary is pulled to a fine point and (b) rotated using a motor and coated evenly with platinum paint. (c) After curing the platinum paint film, the pulled end of the capillary is insulated using epoxy resin and (d) polished flat using a home-built polishing wheel, equipped with micropositioners.", + "texts": [ + "9 Under relatively low volume flow rates and pressure conditions, it is shown that mass-transfer rates in excess of 2 cm s-1 can be readily achieved, making this technique very attractive for electroanalysis and kinetic studies. Chemicals. All solutions were prepared from Milli-Q (Millipore Corp.) reagent water. Solutions were prepared from potassium ferrocyanide trihydrate (Aldrich, ACS grade) at a concentration of either 0.002 or 0.005 mol dm-3 in 0.2 mol dm-3 potassium chloride (Fisons, AR grade) solutions, the latter serving as a supporting electrolyte. Electrodes. The procedure for the fabrication of the thin platinum ring capillary electrodes is outlined in Figure 2. Borosilicate capillary tubes (Clark Electromedical, Reading, U.K., 2.0- mm o.d., 1.2-mm i.d.; Chance Glass, Leicester, U.K., 2.0-mm o.d., 0.5-mm i.d.) were heated and pulled to a fine point using a Narishighe (Tokyo, Japan) PB7 vertical micropipet puller. The capillary was then attached to a home-built motor that rotated the horizontally held capillary about its cylindrical axis, and the narrower end was coated evenly with a platinum organometallic complex (Bright Platinum Paint, Cookson Matthey Ceramics, Stoke-on-Trent, U" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000007_acc.1999.786615-Figure10-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000007_acc.1999.786615-Figure10-1.png", + "caption": "Figure 10: Switching control law for one stable subsystem and one unstable subsystem of opposite directions.", + "texts": [], + "surrounding_texts": [ + "In this section, we consider the reachability problem for the switched system (1) consisting of two subsystems with unstable foci w d derive switching control laws. 2.1 Unstable Subsystems We first review some stability results from [8]. We shall say that a subsystem is of clockwise (counterclockwise) direction if starting from any nonzero initial condition in the phase plane its trajectory is a spiral around the origin in the clockwise (counterclockwise) direction. Let x = ( ~ 1 ~ x 2 ) ~ be a nonzero point on W2 plane, and denote fi = Alx = ( a l , a ~ ) ~ , fz = AZX = ( ~ 3 ~ ~ 4 ) ~ . We view x , fl and fz as vectors in Wz and define B i , i = 1,2 to be the angle between x and fi measured counterclockwise with respect to x (Si is confined to -n 5 Si < n). So Bi is positive (negative) if vector fi is to the counterclockwise (clockwise) side of x . Also as in [8] we define the regions { X I - 'IT 5 B; ( f ; ) 5 -5 or 5 5 B i ( f i ) < n} A n Eis = = = { x l x T f i ( z ) = xTAix 5 0 } , i = 1 ,2 { X I - 5 5 S ; ( f i ) 5 0 or 0 5 O i ( f i ) 5 2) 'IT A E;, = { x l x T f i ( x ) = X ~ A ~ X 2 01, i = 1,2. To design stabilizing switching control laws, we identify the following two distinct cases. Case 1. Two Subsystems of the Same Direction Without loss of generality, assume that both subsystems of (1) are of clockwise direction. We define the following conic regions. Ri = Ei, n E2u, Rz = Eiu n Ezs, R4 Re o3 = E l , n Ez, n (21aza3 - 0 1 0 4 I o}, 0 5 = El, n Ez, n {zlazas - ala4 5 0}, = E18 n Ezs n (XIaza3 - ala4 2 0 } , El , n Ez, n {X1a20,3 - ala4 2 0). = The conic switching law proposed in [8] is as follows: switch the switched system to subsystem 1 whenever the system state enters RI, R3, Rg and switch to subsystem 2 whenever the system state enters R2, 0 4 , as. The following theorem concerns the stabilizability of the switched system (see [SI). Note that this is a necessary and sufficient condition as opposed to other literature results. Theorem 2.1 Let 11 be a ray that goes through the origin. Let x o # 0 be on 11. Let x* be the point on 11 where the trajectory intersects 11 for the first tame after leaving 20, when the switched system evolves according to the conic switching law. The switched system (1) with subsystems with unstable foci and of the same direction is asymptotically stabilizable i f and only i f 11x*11z < 11x0112 by the conic switching law. Example 2.1 illustrates how the conic switching law works. 0-7803-4990-6/99 $10.00 0 1999 AACC 2955 Example 2.1 Figure 1 shows a simple circuit system consisting of two dependent sub-circuits. For every sub-circuit, there is a switch to connect the sub-circuit to one of the two voltage dependent current source circuits. so there are four possible switch combinations which would provide us with four subsystems. Here we assume that the switches for both sub-circuits can only be both at position 1 or both at position 2 simultaneously. This reduces the number of possible switch combinations to two. I t i s not di f icul t t o derive the following differential equations for the circuit (V = [Vel, VealT) . Both switches are at position 1: V = [ :2 '3\" ] V. Both switches are at position 2: V = [ -lo -1 2 j . :Dl The switched system consists of two unstable subsystems with foci at the origin and is asymptotically stabilizable by the conic switching law. Figure 2 shows the system trajectory Case 2. Two Subsystems of Opposite Directions Assume that subsystem 1 is of clockwise direction while subsystem 2 is of counterclockwise direction. We introduce the following conic regions. f rom initial point [(v,, (o), V , 2 ( ~ ) ] T = [2,2]'. 0 521 = E18 nEzs, 522 = Eiu flEz,, 0 3 = El, n Ez, n (xIaza3 - m a 4 2 0}, Q4 = E,, n EZu n (d(az(33 - (31(34 I o} , as = El, n Ezs n (xIaza3 - (3104 2 0} , 526 = El, fl E z S n ( 2 ] ( 3 2 ( 3 3 - 5 0). Theorem 2.2 concerns the stabilizability of the switched system (see [8]). Theorem 2.2 The switched system (1) with two subsystems with unstable foci and of opposite directions is asymptotically stabilizable i f and only i f I n t ( R 1 ) U Int(523) U Int(R5) # 0. If the switched system is asymptotically stabilizable, then the conic switching law can also be obtained as in [8] which makes the system asymptotically stable. The conic switching law is as follows: first, by following subsystem 1, force the trajectory into one of the conic regions 521, Q 3 , 525, and then switch to another subsystem upon intersecting the boundary of the region so as to keep the trajectory inside the region. Remark: The conic switching laws can also be extended to switched systems consisting of second-order LTI subsystems 2.2 Reachability Results In the following discussion, we assume that the switched system consists of unstable subsystems but is asymptotically stabilizable. Assume that xi # 0 and xt # 0 are given nonequilibrium initial and target points on Rz plane, respectively. We want to find a switching control law so as to drive the state of the system from x ; to x t . We consider the following two cases. Case 1. Two Subsystems of the Same Direction Without loss of generality, assume both subsystems are of clockwise direction. It is known that the conic switching law will make the system asymptotically stable. Now consider the trajectory starting from x t with time going backwards, i.e., consider the trajectory C- for -t, t 2 0 by following the conic switching law. It is clear that this trajectory would be away from the origin in a counterclockwise fashion. Let 1; be the ray that goes through the origin and x i . Let It be the ray that goes through the origin and q. Let x* = z(-t') be the point on C- that satisfies the following conditions. 1. The trajectory E = { x ( - t ) E C-10 < t 5 t ' } intersects It at least once. 2. t' is the minimum possible t such that condition 1 is satisfied and x(- t ' ) is on 1; and l l ~ ( - t * ) l l 2 2 l l ~ i112 . To obtain a switching control sequence, we let the system start from xi at t = 0 following the trajectory of subsystem 1. Since subsystem 1 is unstable, it is clear that if the switched system stays at subsystem 1 for sufficiently long time, z(t) will be outside the region formed by E and pzut of li(the region inside the bold curves in Figure 3(a)). By this we conclude that there exists a time instant tl such that the trajectory intersects E for the first time, i.e., X I = x ( t 1 ) E E. So by the above discussion, we can adopt the following switching control law. Switching control law: S tep 1. Let the system trajectory start f rom x; at t = 0 following the trajectory of subsystem 1 until it intersects E for the first t ime at tl o n x1 = x( t1) . Step 2. After it reaches 2 1 = z( t l ) , let the system ewolve following the conic switching law. which are not necessarily with foci (see [8]). 0 Example 2.2 Consider the circuit system as in Example 2.1. The switched system is reachable since it is asymptotically stabilizable. Figure 4 shows the system trajectory from xi = [-2, -2IT t o zt = [-0.5, 0.5IT and the corresponding switching sequences b y using the switching control law. shows that the d-stabilizability problem is readily solved by some small modification of the aforementioned results. Similarly to Section 2.1, we will discuss the following two cases. Case 1. Two Subsystems of the Same Direction Assume both subsystems are of clockwise direction. Using the same notation as in Case 1 in the Section 2.1, we propose the following conic switching law: switch the switched system to subsystem 2 whenever the system state enters 01, R3, R5 and switch to subsystem 1 whenever the system state enters R2, R4, R6. The following theorem concerns the d-stabilizability of the switched system. Theorem 3.1 Let 61 be a ray that goes through the origin. Let xo # 0 be on 11. Let x* be the point on 11 where the trajectory intersects 11 for the first t ime after leaving 20, when the switched system evolves according to the conic switching law. The switched system (I) with subsystems with stable foci and of the same direction is d-stabilizable i f and only if llx*112 > ( ( ~ 0 1 1 2 by the conic switching law. Case 2. Two Subsystems of Opposite Directions Assume subsystem 1 is of clockwise direction and subsystem 2 is of counterclockwise direction. Since the switched system is as mptotically stabilizable, In t (R l ) .U Int(R3) U Int(R5) # We assume R is one conic region from the possible nonempty sets 521, R3 and 0 5 which is between the two rays I 1 and h(Figure 3(b)). Consider the following trajectory C-. Starting from xt, let the system trajectory go backwards in time by following subsystem 1 until it intersects 12 for the first time by z* at -t*, then let the trajectory going backwards in time following the conic switching law in R. In this way, we can get the trajectory C- as depicted in Figure 3(b). Now let the system start from xi at t = 0 following the trajectory of subsystem 1. Since subsystem 1 is unstable, it is clear that if the switched system stays at subsystem 1 for sufficiently long time, x(t) will intersect C-. By this we conclude that there exists a time instant t i such that the trajectory intersects C- for the first time at X I = x(t1). By the above discussion, we can adopt the following switching control law. Switching control law: Step 1. Let the system trajectory start from xi at t = 0 following the trajectory of subsystem 1 until it intersects Cfor the first t ime at tl on XI = x(t1). Step 2. After it reaches 2 1 = x ( t l ) , let the system evolve following the corresponding subsystems associated with the points on the trajectory C- . The above switching control law can drive the system state from xi to xt via only a finite number of switches. 0 3 Reachability of Switched Systems with Two Stable Subsystems In the present section, we consider reachability problem for the switched systems (1) consisting of two subsystems with stable foci and derive switching control laws. 3.1 Stable Subsystems If both subsystems are stable, then the stabilizability of the switched system can be easily established if we simply let the system stay at one subsystem and do not apply any switches. Yet we may ask a converse question: can we find a control law such that the switched system can be \"destabilized\", in other words, the trajectory of the switched system can be made unbounded. It is not quite difficult to see that such a control law can be found if the switched system with two unstable subsystems X = -Alx, X = - A ~ x , (3) is asymptotically stabilizable. Formally, we defined dstabilizability as follows. Definition 3.1 An switched system (1) with two stable subsystems is said to be d-stabilizable i f and only i f the corresponding switched system (3) with two unstable subsystems is asymptotically stabilizable. A close look at the result for two unstable subsystems Example 3.1 shows how the conic switching law works. Example 3.1 Figure 5 shows a simple circuit system consdsting of two dependent sub-circuits with coeficients daflerent t o Example 2.1. I t can be readily obtained that: -3 2 [ -13 -1 1. Both switches are at position 1: V = Both switches are at position 2: V = [ 1; :\"I. T h e switched system consists of two stable subsystems with foci at the origin and is d-stabilizable. Figure 2 shows the system trajectory from initial point [(V,,(O), K,(O)lT = Case 2. Two Subsystems of Opposite Directions Assume subsystem 1 is of clockwise direction and subsystem 2 is of counterclockwise direction. With the same notation as in Case 2 of Section 2.1, the following theorem concerns the d-stabilizability of the switched system. [0.2,0.2]*. 0 2957 Theorem 3.2 The switched system ( 1 ) with two subsystems with stable foci of opposite directions is d-stabilizable if and only if I n t ( R z ) U Int (R4) U I n t ( 0 6 ) # 0 . If the switched system is d-stabilizable, then a conic switching law can also be obtained. The conic switching law is: first, by following subsystem 1, force the trajectory into one of the conic regions Rz, 524, 0 6 , and then switch to another subsystem upon intersecting the boundary of the region so as to keep the trajectory inside the region. 0 3.2 Reachability Results Consider the switched system (1) with two stable subsystems. In the following discussion, we assume that the switched system is d-stabilizable. The switching control law can be obtained by some modifications of the discussion in Section 2.2. Case 1. Two Subsystems of the Same Direction Assume that both subsystems are of the clockwise direction. Since the switched system is d-stabilizable, the conic switching law will \"destabilize\" the system asymptotically. Therefore, for this switched system, if we consider the trajectory starting from x; with time going forward, i.e., consider the trajectory C+ for t , t 2 0 by following the conic switching law. It is clear that this trajectory would be farther and farther from the origin in a clockwise fashion. Let 1, be the ray that goes through the origin and x i . Let It be the ray that goes through the origin and x t . Let x* = x ( t * ) be the point on C+ that satisfies the following conditions. 1. The trajectory E = { x ( t ) E C+IO < t _< t'} intersects l ; at least once. 2. t' is the minimum possible t such that condition 1 is satisfied and x ( t * ) is on It and Ilx(t')llz 2 11xt112. To obtain a switching control sequence, we let the system start from zt and going backwards in time following subsystem 1, since subsystem 1 is stable, the backward trajectory will not be stable. So as the discussion in Case 1 in Section 2.2, the backward trajectory will intersects E for the first time at x1 = x( t1) . Switching control law: Step 1. Let the system trajectory start from xi at t = 0 following conic switching law until i t reaches X I . Step 2. After it reaches 21, let the system switch to subsystem 1 and evolve following Subsystem 1. Such a switching control law drives the system state from xi to xt via only a finite number of switches (Figure 7(a)). So we propose the following switching control law. Example 3.2 Consider the circuit system in Example 3.1. The switched system is reachable since at is d-stabilizable. Figure 4 shows the system trajectory from x; = [0.2, 0.2IT to xt = [4,-4IT and the corresponding switching sequences b y Case 2. Two Subsystems of Opposite Directions Assume subsystem 1 is of clockwise direction and subsystem 2 is of counterclockwise direction. Since the switched using the switching control law proposed above. 0 system is d-stabilizable, I n t ( R z ) U l n t ( R 4 ) U I n t ( R s ) # 8. We assume R is one conic region from the possible nonempty sets 0 2 , and !& which is between the two rays I 1 and lz(Figure 7(b)). Consider the following trajectory C-. Starting from x t , let the system trajectory go backwards in time by following subsystem 1 until it intersects 12 for the first time by x* at - t* , then let the trajectory going backwards in time following the conic switchieg law in R. In this way, we can get the trajectory C- as depicted in Figure 7(b). Now let the system start from xi at t = 0 following the trajectory of subsystem 1. Since subsystem 1 is stable, it is clear that if the switched system stay at subsystem 1 for sufficiently long time, x ( t ) will intersect C-. By this we conclude that there exists a time instant tl such that the trajectory intersects C- for the first time at x1 = x( t1) . Switching control law: S tep 1. Let the system trajectory start from x; at t = 0 following the trajectory of subsystem 1 until it intersects C - f o r the first time at tl on X I = x ( t 1 ) . Step 2. After it reaches x1 = x ( t l ) , let the system evolve following the corresponding subsystems associated with the points on the trajectory C-. The switching control law can drive the system state from x; to xt via only a finite number of switches. 0 4 Reachability of Switched Systems with One Stable and One Unstable Subsystems If the switched system (1) consists of stable subsystem 1 and unstable subsystem 2, we note that the switched system must be both asymptotically stabilizable (by just following subsystem 1) and d-stabilizable (by just following subsystem 2). For reachability, there are two cases to be discussed, where the first case is similar to Case 1 in Section 2.2 and the second case is slightly different from Case 2 in Section 2.2. Case 1. Two Subsystems of the Same Direction Let the trajectory C- be the trajectory starting from xt with time going backwards by following subsystem 1. Let z* = x ( - t \" ) be the point on C- that satisfies: 1. The set E = { x ( - t ) E C-10 < t 5 t'} intersects It at least once. 2. t* is the minimum possible t such that condition 1 is satisfied and x(- t ' ) is on Z; and ~ ~ x ( - t * ) ~ ~ ~ 2 11xi11~. Let the system start from 2; at t = 0 and follow subsystem 2. Since subsystem 2 is unstable, by the similar reason as in Case 1 in Section 2.2, the trajectory will intersect E at X I = x( t1) for the first time. Switching control law: Step 1. Let the system start from x ; at t = 0 and follow subsystem 2 until it reaches X I . Step 2 . After it reaches 21, let the system switch to subsystem 1 and evolve following subsystem 1. The switching control law requires only one switch to So we propose the following switching control law. We propose the following switching control law. solve the reachability problem. I3 Case 2. Two Subsystems of Opposite Directions Assume in ( l ) , subsystem 1 is of clockwise direction and subsystem 2 is of counterclockwise direction. Then we identify the following two sub-cases. a. If 3c > 0 such that A1 = -cA2, then CA', = C- Az' Ci, = CA', for any initial point 20 # O (See Section 2 of [8]). Therefore zt is not reachable from z; if zt is neither on Ci, nor on Ci,. b. If there does not exist c > 0 such that A1 = -cAz, then there exists at most two lines on which A l z = k A ~ z for some k # 0 (See Section 2 of [SI). In view of the 0, introduced in Section 2.1, we can find a conic region in which either 1011 + lSzl < r or 1011 + l0zl > T holds for every point. For (01 I + 102 I < T case, we can obtain a switching control law similar to Case 2 in Section 3.2 (Figure lO(a)). For 101 I + 10, 1 > T case, we can obtain a switching control law similar to Case 2 in Section 2.2 except that we choose subsystem 2 between zi and 2 1 (Figure lO(b)). 0 5 Several Subsystems Consider the switched system (1) consisting of several second-order LTI subsystems with foci. The reachability results in Sections 2, 3 and 4 are readily extended to several subsystems as shown in the following. Case 1. All Subsystems with Unstable Foci We assume that the switched system is asymptotically stabilizable. If all subsystems are of the same direction, then we adopt the similar method as in Case 1 of Section 2.2 to drive z; to zt. If K(K > 0) subsystems S;, . . . , S, are of clockwise direction and M(M > 0) subsystems SF,. . . , SG are of counterclockwise direction (K+ M = N), then we can use one of the following methods . 1. If Sf,. . . , S- are asymptotically stabilizable, then adopt the similar mettod as in Case 1 of Section 2.2. 2. If S:, . . . , S+ are asymptotically stabilizable, then adopt the similar metgod as in Case 1 of Section 2.2. 3. If there exists Sz: and Sj' such that the switched system consisting of S,T and S: is asymptotically stabilizable, then adopt the similar method as in Case 2 of Section 2.2. Case 2. All Subsystems with Stable Foci The discussion is similar to the above case. Case 3. K Subsystems with Stable Foci and M Subsystems with Unstable Foci In this case, as long as there is one stable subsystem and one unstable subsystem satisfying the condition of Case 1 or the condition (b) in Case 2 of Section 4, we can always adopt the method therein. 6 Stabilizability and Reachability Now we state the relationship between stabilizability and reachability. Without loss of generality, we just consider switched systems (1) with two subsystems. If a switched system is reachable, then it must be asymptotically stabilizable and d-stabilizable. This is not difficult to show. For asymptotic stabilizability, we can start from z, and drive the state to zt which are on 1; and 11?t11z I qIIzj!lz, q < 1. Continuing this way, we can asymptotically stabilize the system. d-stabilizability can be similarly shown. Combined with the results in Sections 2, 3 and 4, we can readily prove the following theorem which provides us with a necessary and sufficient condition for the reachability of the switched systems. Theorem 6.1 Consider the second-order switched systems (1) consisting of two LTI subsystems with foci. If there does not exist c # 0 such that A1 = cA2, then the switched system is asymptotically stabilizable and d-stabilizable if and only i f i t is reachable. 7 Conclusions This paper considers the reachability problem for switched systems consisting of second-order LTI subsystems with foci and it is concerned with switching control laws to drive the state from zi # 0 to zt # 0. Necessary and sufficient conditions for reachability are also obtained. The method to obtain a switching control law is constructive and it is based on the conic switching laws proposed in [8, 91. Various cases are discussed according to the stability and directions of subsystems. Additional details can be found at: http://vvv.nd.edu/-isis/tech.html. References [l] M. S. Branicky, Stability of Switched and Hybrid Systems, In Proc. of 33rd CDC, pp.3498-3503, 1994. [2] M. S. Branicky, Multiple Lyapunovfunctions and other analysis tools for switched and hybrid systems, IEEE Trans. on Automatic Control, vol. 43, 1998, pp.475-482. p] B. Hu, X. Xu, A. N. Michel and P. J. Antsaklis, Roustness of Stabilizing Control Laws for a Class of Secondorder Switched Systems, to appear In Proc. 1999 ACC, 1999. [4] H. K. Khalil, Nonlinear Systems, 2nd Edition, Prentice-Hall, 1996. p] D. Liberzon, A. S. Morse, Benchmark problems in staility and design of switched systems, submitted to IEEE Control Systems Magazine. [6] P. Peleties and R. DeCarlo, Asymptotic stability of m-switched systems using Lyapunov-like functions, Proc. of ACC, pp.1679-1684, Boston, June 1991. y] S. Pettersson, B. Lennartson, Stability and Robustness or Hybrid Systems, In Proc. 35th CDC, Kobe, Dec, 1996, [8] X. Xu, P. J. Antsaklis, Stabilization of SecondOrder LTI Switched Systems, ISIS Technical Report isis-99-001, Department of Electrical Engineering, University of Notre Dame, January 1999. (http://w.nd.edu/-isis/tech.html) [9] X. Xu, P. J. Antsaklis, Design of Stabilizing Control Laws for Second-Order Switched Systems, to appear in Proc. of 14th IFAC world congress, 1999. pp. 1202-1207. 2959" + ] + }, + { + "image_filename": "designv11_2_0001994_s0924-0136(02)00954-8-Figure13-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001994_s0924-0136(02)00954-8-Figure13-1.png", + "caption": "Fig. 13. The three lasers comparison: tw influence on weldability of K40 hard metals to steel. Fig. 14. Cracking of high resistant joints submitted to bending.", + "texts": [ + " Regarding the speed influence in K40 samples it can be observed that a higher strength value occurs for a speed of 1.75 m/min (which corresponds to the same optimum point, in terms of heat input, observed in power influence). After this point the resistance decreases (as expected for higher speeds). For K10 samples the mechanical behaviour is better for higher heat inputs (lower speeds). This could be due to the fact that K10 tips have higher thermal conductivity, requiring higher heat input. Fig. 13 shows the tw influence on the behaviour of K40 samples when welded by the three different laser systems (Nd:YAG (cw), Nd:YAG (pw) and CO2 (cw)). It is clear that Nd:YAG (cw) laser present better results for smaller tw (0.1\u2013 0.2 mm). By contrary the (pw) Nd:YAG and (cw) CO2 lasers exhibit better results for higher tw, due to the high heat input used and higher spot size, respectively. During the bending tests it was possible to observe the cracking mode. Figs. 14 and 15 show the two kinds of fracture that takes place in these joints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003280_1.2174027-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003280_1.2174027-Figure6-1.png", + "caption": "FIG. 6. Pendulum rotating at the angular frequency of .", + "texts": [ + " This suggests that the rotationalmode vibration is independent of liquid properties and thus does not follow the physics of surface-tension-controlled vibration, whose angular frequency is given by balancing the pressure due to inertial R2 2 and capillary force /R , where and are the density and surface tension, respectively: / R3 1/2. Images of Fig. 4 b confirm that the surface area change during the rotation, thus the role of surface tension force is insignificant. Then the remaining candidate for restoring force is gravity. By balancing the centripetal force R3R 2 with the gravitational force R3g , we find g /R 1/2, which is consistent with the experimental results. The experimentally found relationship between and R for the rotational mode is similar to that of the rotating pendulum with the moment arm R. In Fig. 6, the centripetal force mr 2 is balanced by the gravity mg tan , where m is 1/2 the pendulum mass. For small , we get = g /R . An- ownloaded 02 Jun 2013 to 129.174.21.5. This article is copyrighted as indicated in the abstract. Re other facet of analogy between the pendulum oscillation and the lowest drop oscillation mode is that the resonance frequencies of the lateral vibration and of the rotation are identical in each system. In this Letter, we have shown that the lowest oscillation mode of a pedant drop is the rotation around the longitudinal axis, whose frequency g /R 1/2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003910_robot.2006.1642348-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003910_robot.2006.1642348-Figure2-1.png", + "caption": "Fig. 2. Kinematic parameters in XZ-plane.", + "texts": [ + " The inverse kinematics of the Gantry-Tau with one triangular link are relatively easy to find analytically. Consider the kinematic definitions in Figs. 1, 2 and 4. The Y1, Y2, Y3 and Z1, Z2, Z3 coordinates of the linear actuators are all fixed while X1, X2 and X3 are the variable linear actuator positions. Let X ,Y ,Z be the coordinates of the tool centre point (TCP). Let (Xa, Ya, Za), (Xd, Yd, Zd) and (Xf ,Yf ,Zf ) be the coordinates of the points A, D and F on the moving platform as defined by Fig. 2 and 4. These coordinates are relative to the TCP origin, but specified in the stationary global coordinate frame given by the redundant angle rotation \u03b1. If the coordinates of the points A, D and F are known, then the 8 solutions (all combinations of the two solutions for each actuator) for the inverse kinematics are given by equations 0-7803-9505-0/06/$20.00 \u00a92006 IEEE 4199 (1)-(3). X1 = X + Xf \u00b1 \u221a L2 1 \u2212 (Y1 \u2212 (Y + Yf ))2 \u2212 (Z1 \u2212 (Z + Zf ))2 (1) X2 = X + Xa \u00b1 \u221a L2 2 \u2212 (Y2 + Yoffs \u2212 (Y + Ya))2 \u2212 (Z2 \u2212 (Z + Za))2 (2) X3 = X + Xd + S \u221a L2 3d \u2212 (Y3 \u2212 Yoffs \u2212 (Y + Yd))2 \u2212 (Z3 \u2212 (Z + Zd))2 (3) where S equals \u00b11, L3d is the length of the link in parallel with the triangular pair and Yoffs is an offset in the Ydirection relative to the actuator for the arms A and D. The variable S is introduced for actuator 3 and later used in the solution for the angle \u03b1. For a Gantry-Tau with all links parallel, all the platform points relative to the TCP remain constants in the entire workspace, which makes it possible to solve the forward kinematics analytically as in [1]. For the triangular link configuration, however, all the platform points are functions of the redundant variable \u03b1, as illustrated in Fig. 2. To solve the inverse kinematics of the triangular Tau structure, an analytical expression for \u03b1 is found first. By inspection of Fig. 2 and 4 in the TCP frame \u03b1 is given as follows. cos \u03b1 = \u2212Zd L4 (4) where L4 is the Z-coordinate distance between the TCP and the points C, D and E in the TCP coordinate frame. A similar inspection in the global frame yields cos \u03b1 = Z + Zd \u2212 Z3\u221a (X + Xd \u2212 X3)2 + (Z + Zd \u2212 Z3)2 (5) Since L2 3d = (X+Xd\u2212X3)2+(Y +Yd\u2212(Y3\u2212Yoffs))2+(Z+Zd\u2212Z3)2 (6) equation (5) can be rewritten as cos \u03b1 = Z + Zd \u2212 Z3\u221a L2 3d \u2212 (Y + Yd \u2212 (Y3 \u2212 Yoffs))2 (7) By combining equations (4) and (7), Zd can be found. Zd = L4(Z3 \u2212 Z)\u221a L2 3d \u2212 (Y + Yd \u2212 (Y3 \u2212 Yoffs))2 + L4 (8) The solution for Zd depends only on known variables" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002084_cdc.2001.980701-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002084_cdc.2001.980701-Figure1-1.png", + "caption": "Figure 1: The 2DOF helicopter apparatus.", + "texts": [ + " The user logs on and posts control parameters from a remote client to a web server that is connected to the plant. The server re- ceives the parameters and uses these in an appropriate controller to control the physical plant. There are also a camera and a microphone next to the plant to capture the response of the plant in real time. The captured data are then sent to the user so that the user has a realistic feel of applying his algorithm to the real plant. We choose a 2-degree-of-freedom flight simulator [7], 2DOF helicopter, as the control plant. As shown in Figure 1, the 2DOF helicopter consists of a model mounted on a fixed base. The model has two propellers driven by DC motors that are mounted at the two ends of a rectangular frame. The motors are mounted a t 90 degrees such that one causes pitch and the other causes yaw of the helicopter. The helicopter frame is free to rotate on a vertical base equipped with a slip ring. Electrical signals to and from the helicopter are channeled through the slip ring to eliminate tangled wires, reduce friction and allow for unlimited and unhindered yaw" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000934_bf00163025-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000934_bf00163025-Figure1-1.png", + "caption": "Fig. 1. Mechanical model of the lamprey: Muscle segment M s consists of a spring of stiffness/z s, a dashpot with damping coefficient 7s and forcing term F~. The N light rods of length are smoothly jointed, with masses m placed at each pivot and at both ends. The rods are controlled by arms of length w fixed at right angles to each of their midpoints. 0~ and ~b are respectively the angle between the sth rod and the x axis and the angle between adjacent rods in the sth segment", + "texts": [ + " As a consequence it is numerically simpler to obtain detailed information concerning the ensuing motion, in particular the steady-state motion and the phase delays that occur between activation and curvature. The two essential ingredients of the model are the mechanical representations of the muscle segments and body tissue and the mathematical representation of the force produced by the muscles based on the observed pattern of ventral root activity. We construct here a planar continuum model for the mechanical structure of the lamprey body. Initially the body is assumed to consist of N rods connected by (N - 1) tissue segments, as depicted in Fig. 1, with the mechanical properties being described by a linear stiffness, a linear velocity dependent damping and a time dependent forcing term. The forcing term represents the tension generated within the muscle protein filaments; the viscoelastic properties of the muscle are lumped together with those of the notochord, skin, and other tissues in the stiffness and damping terms. In the real animal the swimming muscles are symmetric about the midline, and there is strict left-right alternation of muscle tension development", + " The positioning of the masses in the model seems reasonable since in the real animal the mass of the animal is symmetrical along the axial midline. The equations of motion corresponding to the angular coordinates for such a discrete system described above are given by Bowtell and Williams (1991) as: t ~ N+I f2m (N -- s + 1) \"Oicos(Oi -- 02) -k E i=1 i=s+l (N - i + 1)Oicos(Os - Oi) + N+I Z i=s+l ( N - i + 1 )O~s in (Os- Oi) - ( N - s + 1),=1i 0{sin(0,-0~)) + m E ( N - s + 1)(- Yo sin0s + j~o cos 0s) = 5 (G~ sin(qS~/2) - Q_ 1 sin(qSs- a/2)) + w ( G ~ c o s ( O J 2 ) - G ~ aCos(q~s-1/2)) s = 1 , . . . , N . (1) Assuming the notation of Fig. 1 the resultant force Gs in the sth muscle segment due to the damping, stiffness and forcing terms is given explicitly by: Xs )\u00a2s ~ = - \"~ 7 - ~s 7 - F ~ ( O , (2) where the extension xs of the dashpot and spring is calculated relative to a natural length position at q~ = 0 and is thus given by xs = f(cos(4~J2) - 1) - 2wsin(~b,/2). The dummy variables Go and Gx are set equal to zero and dot represents differentiation with respect to time. The equations governing the motion of the head coordinates (Xo, Yo) are given (Bowtell and Williams 1991) by: f N N0 - N + 1 i=~1 (N - i + 1)[-02 cos(0i) + 0isin(0~)], (3) I N Yo = X + ~ i~1 (N - i + 1) [02 sin(0i) - Oicos(Oi)] " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000988_i2003-00618-2-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000988_i2003-00618-2-Figure1-1.png", + "caption": "Fig. 1 \u2013 Stability boundary of the homogeneous state of an active fiber in the presence of polymerization and depolymerization of filaments. Insets indicate the density profiles of the corresponding unstable modes. Along the solid line the homogeneous state loses stability via a Hopf bifurcation towards solitary waves; the dotted line indicates a pitchfork bifurcation towards contracted states. The bifurcations occur as the parameter B exceeds a critical value Bc. L is the system size, F characterizes a stabilizing nonlinearity and \u00b5 characterizes depolymerization rates. Parameters are (A+E/\u00b5)/L3 = 1.5 \u00b7 10\u22123, D/L2 = 0.01, \u03b5/\u00b5L = 0.05, \u03bd = \u00b5, A = A1, A2 = 0, B = B1 = B2 = B\u03041/2 = B\u03042/2, E = E1 = E2 = E\u03041 = E\u03042 = E\u03031 = E\u03032, 2F = F1 = F2 = F3 = F4 = F\u03041 = F\u03042 = F\u03043/3 = F\u03044/3.", + "texts": [ + " These terms control the average filament concentration and polarization and lead to a coexistence of three different homogeneous steady states. These homogeneous states are given by i) c = p = 0, ii) c = p = 1/(\u00b5+\u03bd), and iii) c = 1/\u00b5 and p = 0. States i) and ii) are unstable with respect to homogeneous perturbations and will not be considered further. State iii) is stable against such perturbations. As a consequence, a linear stability analysis of this state reveals a bifurcation with an unstable mode of finite wave vector q which introduces a new length scale in the system, see fig. 1. As above, this bifurcation is either stationary or of Hopf type, depending on the value of \u03b5. We find that the critical mode is characterized by a phase shift of \u03c0/2 between c and p. This mode corresponds to a sarcomer-like periodic arrangement of filaments in the fiber, see fig. 2. It is also similar to polarity sorting observed in ref. [3], which can be understood if the dynamics of motor densities is taken into account [12]. The case of a fully oriented bundle needs to be discussed separately, Here, we assume that filaments of one orientation only appear in the system and that filaments of opposite orientation are not generated by polymerization events" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000178_19.816137-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000178_19.816137-Figure1-1.png", + "caption": "Fig. 1. Harmonic drive components.", + "texts": [ + "ndex Terms\u2014 Built-in torque sensor, harmonic drive, intelligent sensor, Kalman filter, misalignment torque, positioning error, rosette strain gauge, torque ripples. I. INTRODUCTION DEVELOPED in 1955 primarily for aerospace applications, harmonic drives are high-ratio and compact torque transmission systems. Every harmonic drive consists of the three components illustrated in Fig. 1. The wave generator is a ball bearing assembly with a rigid, elliptical inner race and a flexible outer race. The flexspline is a thin-walled, flexible cup adorned with small, external gear teeth around its rim. The circular spline is a rigid ring with internal teeth machined along a slightly larger pitch diameter than those of the flexspline. When assembled, the wave generator is nested inside the flexspline, causing the flexible circumference to adopt the elliptical profile of the wave generator, and the external teeth of the flexspline to mesh with the internal teeth on the circular spline along the major axis of the wave generator ellipse" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure2.129-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure2.129-1.png", + "caption": "Fig. 2.129. Prinpiple of rotation probe type eddy current testing machine [8]", + "texts": [ + " Furthermore, in order to detect flaws formed in the wire-making process nondestructively, eddy current tests are performed on the overall length of the wire. In this case, if the flaws are harmful, they are marked and removed later, to ensure that the material with the surface flaws cannot be used for coiled springs. There are two types of eddy current testing: a through type in which the wire is passed through a fixed eddy current coil and a rotation type in which an eddy current probe coil rotates around wire at a high speed (see Fig. 2.128 and Fig. 2.129). \u00a91 Patenting Patenting is heat treatment process, where high-carbon steel wire is continuously transformed to microstructure of fine pearlite, either by isothermal cooling or continuous cooling. In practice, wire rod, traveling continuously, is first held above the A3 point, and subsequently cooled down below the A1 point to be transformed to pearlite. Figure 2.100 shows a schematic of TTT diagrams of this heat treatment. Several kinds of cooling media, used in the patenting for the transformation of wire, include lead, air, and sand that is floated and fluidized by a mixture of air and combustion gas", + " Occasionally flaws can occur in the subsequent wire drawing process, therefore, an eddy current flaw detector can be applied either during the wire drawing process and/or after the quenching and tempering process. The eddy current test has two types, that is, a through coil type with differential method and rotation probe type with a probe coil rotating in a spiral manner. Each has its own characteristics. In general flaw detection, reliability is improved by applying these two methods independently or in combination. The features of the through coil type and the rotation probe type are shown in Table 2.21, and schematics of both types are shown in Fig. 2.128 and Fig. 2.129 [8]. With regard to wire drawing, just like piano wire, a continuous drawing machine and a single head drawing machine called single block can be used for large reduction and small reduction, respectively. Oil quenching and tempering, the focal process of manufacturing oil tempered wire, is heat-treatment where drawn material is continuously quenched and tempered. Figure 2.130 shows an example of oil quenching and tempering treatment equipment. From the viewpoint of metallurgy, this quenching and tempering can be classified into the following three processes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001488_j.1934-6093.2003.tb00162.x-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001488_j.1934-6093.2003.tb00162.x-Figure6-1.png", + "caption": "Fig. 6. State trajectory from initial point (1, 0).", + "texts": [ + " That means that in a steady state, the pendulum exhibits oscillations around the point (0.1- 0.0018, 0) = (0.0982, 0), with the frequency \u2126 = 99.3s\u22121 and the amplitude of the fundamental frequency component: 4 1 4 / ( ) 5.20 10 ,x a pA c W j rad\u03c0 \u2212= \u2126 = where 1( ) 4[ ( ) ( ) /(1 ( ) ( ))],a p a p pW s W s W s W s W s\u2212 = \u22c5 \u2212 \u22c5 011 ( ) 1c x t= + \u2192 \u221e \u2245 Run simulation of the original equations and compare the results with the frequency domain analysis. The transient process in the state space is presented in Fig. 6. The frequency of chattering determined from the simulations is \u2126sim = 99.7s\u22121, and the output average steady state value is x01sim = 0.0019rad, which closely match the frequency domain analysis. A frequency domain approach to the analysis of fast and slow motions in a sliding mode system with chattering is proposed. It is demonstrated that both the fast and the slow motions can be analyzed as the motions in a certain equivalent relay system. A methodology of bringing an original sliding mode system to the equivalent relay form is given" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003872_tpas.1980.319846-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003872_tpas.1980.319846-Figure3-1.png", + "caption": "Fig. 3. Root loci =0.5, a = 0.05", + "texts": [ + "04 -0.524\u00b1j2.04 root locus branches associated with the rotor poles to -l.00\u00b1j27.2 be bent more to the right. This effect causes the real part of the rotor poles of the full model to become in- Speed Response (rad/sec) for a lN-m Step Change in creasingly smaller in comparison with that of the re- Load Torque duced order model. Full Modelc For a < 1 the constant speed stator poles are 4 closer to the imaginary axis than the constant speed 10 x Awr (t) = 1.070 - 0.0586 exp(-0.950t) rotor poles (see Fig. 3(a) and (,)). This gives rise -2.075 exp(-0.522t) cos(2.04t + 1.06) to the possibility of the stator poles being dominant 5 for some parameter region. For the normal range of a +3.38X10 exp(-l.O0t) cos(27.2t-0.074) and s , this parameter region is not present until a Reduced Model: is below some value less than 0.8 and greater than 0.5. 4 There is no equivalent to the stator poles in the re- 10 x Aw (t) = 1.070 - 0.0586 exp(-0.949t) duced order model and hence according to the criterion -2.075 exp(-0", + "2 2 2 -2Ao: K( +ac a -W soC)/C of volts/hertz control on induction machine dynam- ic response\", Conference Record, IEEE IAS Annual Note - The steady state gain of the derived transfer Meeting, Oct. 1979. functions for the reduced order model was checked and found to be equal to the [9] A. R. Miles, D. W. Novotny, \"Transfer functions of full model the slip-controlled induction machine\", IEEE Trans. IAS, vol. IA-15, no. 1, pp. 54-62, Jan./Feb. 1979. 2059 Discussion high frequency operation and equal rotor and stator resistance, representing a transition region. With respect to Figure 3, which is the rotor- Stephen B. Kuznetsov (Imperial College, London, England): A concise, resistance-dominant root-locus plot, the difference between the full and powerful and unified theory of the transient response of induction reduced order models is clearly brought out and in addition, the effect machines to load torque and input frequency fluctuations has been of varying slip frequency is seen to be rather dramatic. There is one presented. The analysis, in using a linearized model to describe the question with respect to Appendix A" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000344_s0266-3538(99)00174-8-Figure14-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000344_s0266-3538(99)00174-8-Figure14-1.png", + "caption": "Fig. 14. The dimensions of a typical cell in the DJ-N sample.", + "texts": [ + " In this mechanism, merely the energy dissipated by the compression of the generators of the truncated conical shell is accounted. By noting that our SJ, DJ and DJ-N samples all possess a linear or bi-linear stress\u00b1strain relation in their tensile behaviour, this analysis concludes that in Stage 3 a linear relation, as given by equation (B3), can be established between the compression force and the vertical displacement; whilst the slope of the force-displacement curve can be predicted accordingly by the following simple expression: d P3 total d w n Rh 2H Ep cos2 8 As shown in Fig. 14, the actual dimensions of a cell in the DJ-N samples are: b 17 ; R 4:8mm; H 7:2mm; h 1:0mm: The mechanical properties of the DJ-N samples can be found from Tables 2 and 3. By employing these data, the force-displacement relationship predicted from our theoretical models almost coincides with the experimental curve presented in Fig. 10 for the same sample. The agreement is very good. In particular, the transition from Stage 1 (i.e. the inversion of the partial spherical shell) to Stage 2 (the plastic collapse of the truncated spherical cap at its base) is found to happen at the following state: Displacement w=h 1:5; Total force Ptotall=Mo 53" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002374_iros.1992.587321-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002374_iros.1992.587321-Figure5-1.png", + "caption": "Fig. 5 Types of opposition (adapted from [16])", + "texts": [ + " The platform push is a non-prehensile grasp; non-prehensile grasps are not considered in this work. 196 of freedom of individual fingers by the analysis of the functional roles of forces being applied in a grasp [ 131. Iberall et al. [14] define opposition space as \"the area within the coordinates of the hand where opposing forces can be exerted between virtual finger surfaces in effecting a stable grasp.\" They show that prehensile grasps involve combinations of the three basic oppositions shown in Fig. 5. Opposition space is an important concept in characterizing grasps. 2.4 We now illustrate how the contact web can be used to identify the grasp. We start with the simplest type of opposition, namely, pad opposition, and then proceed to side opposition. The detailed analyses involving these oppositions in the next two subsections constitute the main ideas that embody the mathematical framework for grasp recognition. Note that these analyses are done from the geometrical perspective. This is motivated by the fact that humans classify a grasp irrespective of the hand orientation and without explicit static analysis of the grasp" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002348_j.engfailanal.2004.12.016-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002348_j.engfailanal.2004.12.016-Figure6-1.png", + "caption": "Fig. 6. Finite-element mesh for the ICE-wheel with a diameter of 862 mm.", + "texts": [ + " This enormous effort is required due to the geometry of the wheels, the multi-dimensional prestressing of the rubber blocks and the spatial loading situation, especially when regarding all loading cases that might occur in service. So, e.g., the highest stresses develop at the side shoulders of the wheel tyre for rolling turn and track switch crossing. But even for straightforward driving the stress state becomes threedimensional. All following investigations refer to the accident s wheel with a diameter of 862 mm. Fig. 6 shows the finite-element mesh of the ICE-wheel. For reasons of symmetry it is sufficient to just take the half of the wheel into consideration. The symmetry conditions in the cross section and the bearings are fulfilled by appropriate kinematic boundary conditions. The forces defined in Fig. 4 act in the upright symmetry plane and have to be cut in halves, as only the half of the wheel is calculated. In the finite-element analyses of the loading cases the rubber blocks are fixed at their positions by the form and frictional fit resulting from contact with the wheel tyre and the rim", + " The finite-element meshes for the wheel tyre, wheel centre, detachable ring and solid shaft are built up with hexahedral brick elements with 8 nodes and linear ansatzfunctions for the displacements, which are recommended for contact analyses. The material constants for steel are E = 210000 MPa and v = 0.3. The finite-element meshes for the rubber blocks consist of hexahedral brick elements also with 8 nodes but hybrid ansatzfunctions. For the rubber the material law of MOONEY-RIVLIN with the material constants C10 = 2.90 MPa and C01 = 0.726 MPa is applied. The finite-element mesh of Fig. 6 incorporates approximately 130,000 elements with more than 150,000 nodes. In the FE-system \u2018\u2018rubber-sprung wheel\u2019\u2019 a triple non-linearity is inherent: Non-linearity due to the non-linear material behaviour of the rubber blocks. Geometrical non-linearity due to the big deformations of the rubber blocks. Structural non-linearity due to the contact between the parts of the wheel. For the finite-element analysis a two-stage approach is necessary. At first the wheel has to be assembled, and the resulting stresses of this process have to be determined" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002687_cdc.2004.1428715-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002687_cdc.2004.1428715-Figure1-1.png", + "caption": "Fig. 1. Cooperative Radar Jamming", + "texts": [ + " INTRODUCTION Concealment through Electronic Counter-Measures (ECM), more commonly referred to as jamming, consists of transmitting some form of noise to swamp a probing radar signal. Jamming is often used to conceal aircraft from the radars that guide Surface-to-Air Missiles (SAMs). We consider a scenario in which a group of Unmanned Combat Air Vehicles (UCAVs) uses jamming to avoid threats posed by SAMs. Jamming is typically classified as: self-protection or support depending on whether it is used to protect the aircraft that transmits the ECM noise signal or a different aircraft. Figure 1 shows both forms of jamming: the D-labeled UCAV is engaged in self-protection jamming, whereas the A, B, C UCAVs are engaged in support jamming. Note that the ECM signal transmitted by D can also provide some form of concealment for A, B, C (and vice-versa) however it is must less efficient because it transmits from outside the main lobe of the antenna that is being used to track the other aircraft. This paper is mostly focused on Escort Jamming (EJ), which is a form of support jamming in which aircraft flying This paper is based upon work supported by DARPA under the Space and Naval Warfare Systems Center, San Diego, Contracts Number N66001-01-C-8076 and N66001-04-M-R700" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002146_tmag.2004.838746-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002146_tmag.2004.838746-Figure7-1.png", + "caption": "Fig. 7. Cross section of the rotor.", + "texts": [ + " When magnetizing, adjusting the relative position of the stator winding and rotor magnetic poles, make sure their axes are overlapped, and then electrify the stator winding and magnetize the permanent magnet [4]. The applied current in each stator pole is 2 10 A. Use 2-D planar magnetostatic field to calculate, and the magnetic field strength distribution along line \u201ccd\u201d (in Fig. 3) is shown in Fig. 6. It can be seen that the magnetic field strength distribution is not very even, but every point is fully magnetized, so the post-assembly magnetization has the same effect as component magnetization. Then the surface flux density of the rotor is calculated with 2-D FEM. The calculated model is shown in Fig. 7. The surface flux density magnitude versus distance from point 1 to point 5 is shown in Fig. 8. To be verified by the following experiment, the flux density that is vertical to the surface is shown in Fig. 8, too. To avoid the influence of the boundary and be smoother, the surface flux densities are obtained from the points that are 0.1 mm away from the surface. Two prototype motors were manufactured and tested. One is of component magnetization and the other is of post-assembly magnetization. For the latter one, one phase of the stator windings is used as the magnetizing coil, and the axes of the stator winding and rotor pole are positioned at the same location by tooling. On the rotor surface (Fig. 7), the flux densities of five points are measured with tesla meter (for the post-assembly magnetization motor, the rotor is taken out to measure), and the values are shown in Table I. It can be seen that the surface flux densities of the component magnetization rotor and post-assembly magnetization rotor are consistent. These values are drawn in Fig. 8, too. Since what the tesla meter measured is the flux density vertical to the surface, so it can be seen from Fig. 8 that the tested values are in good agreement with the calculated flux density vertical to the surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000853_s0010-938x(03)00098-2-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000853_s0010-938x(03)00098-2-Figure3-1.png", + "caption": "Fig. 3. Configuration of C-ring specimen.", + "texts": [ + " Laser beam is a high energy density power and can produce deep penetration. So it can penetrate the sleeve and weld it with the tube. The designed welding equipment is illustrated in Fig. 1. Fig. 2 shows the designed structure. In the structure, the sleeve is concave so that it is easier to be deformed in the axial direction. The C-ring test specimens were prepared under ASTM G 38-73 code [13]. The dimension of C-ring machined from the tube was as follows; Outer diameter of 22.2 mm, thickness of 2.4 mm, width of 19 mm as shown in Fig. 3. Two holes were drilled to compress the C-ring by bolt and nut. The procedure for corrosion test is important because corrosion of heat exchanger tubes occurs mainly as stress corrosion caused by many factors. C-ring test is suitable for the small size of tube. The bending stress applied on C-ring by forcing with bolt and nut. The relationship between cracking and corrosive environment was evaluated. The residual stresses of specimens were measured by XRD before corrosion test. The applied stress was calculated theoretically according to the following [10]: Dof \u00bc Do D D \u00bc pf D2 i 4EtZ where Do is outer diameter of C-ring before forcing; Dof is outer diameter of C-ring after forcing; f is applied stress; D is variation of outer diameter; Di is inner diameter; E is Young\u2019s modulus; Z is correction factor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003344_cdc.2006.376915-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003344_cdc.2006.376915-Figure2-1.png", + "caption": "Fig. 2. Convertible VTOL", + "texts": [ + " The pitch, roll and yaw torques required for controlling the flying vehicle in hover are obtained from the speed difference between the two rotors and the control surfaces (aileron, elevon). The altitude of the vehicle is regulated by increasing or decreasing the propeller thrust. The roll torque is obtained from the difference of the rotors\u2019 angular velocities. Since the control surfaces are submerged in the propeller slipstream (prop-wash), the aerodynamic forces are generated with the elevon and ailerons deflection to provide the pitch and yaw motion respectively [see figure 2]. Let I={iIx , jIy , kI z } denote the right hand inertial frame. Let B={iBx , jBy , kB z } denote the rigid-body frame with origin at the gravity center. Let the vector q = (\u03be, \u03b7)T denote the generalized coordinates where \u03be = (x, y, z)T \u2208 3 denotes the translation coordinates relative to the frame I, and \u03b7 = (\u03c8, \u03b8, \u03c6)T \u2208 3 describes the vehicle orientation 1-4244-0171-2/06/$20.00 \u00a92006 IEEE. 69 expressed in the classical yaw, pitch and roll angles (Euler angles) commonly used in aerodynamic applications [1]", + " The time derivative \u2126\u0307 = W\u0307n\u03b7\u0307+ Wn\u03b7\u0308 is \u2126\u0307 = \u239b \u239d \u2212c\u03b8 \u03b8\u0307\u03c8\u0307 \u2212 s\u03b8\u03c8\u0308 + \u03c6\u0308 \u2212s\u03c6s\u03b8 \u03b8\u0307\u03c8\u0307 + c\u03c6c\u03b8\u03c6\u0307\u03c8\u0307 + c\u03b8s\u03c6\u03c8\u0308 \u2212 s\u03c6\u03c6\u0307\u03b8\u0307 + c\u03c6\u03b8\u0308 \u2212c\u03c6s\u03b8 \u03b8\u0307\u03c8\u0307 \u2212 s\u03c6c\u03b8\u03c6\u0307\u03c8\u0307 + c\u03c6c\u03b8\u03c8\u0308 \u2212 c\u03c6\u03c6\u0307\u03b8\u0307 \u2212 s\u03c6\u03b8\u0308 \u239e \u23a0 (4) 2) Moment of inertia: Matrix I represents the body moment of inertia whose value basically depends on the body mass distribution (for detail see [2]) and is decomposed as I = \u239b \u239d Ixx Ixy Ixz Iyx Iyy Iyz Izx Izy Izz \u239e \u23a0 (5) where Ixx = \u222b m (y2 + z2)dm, Ixy = Iyx = \u222b m \u2212(xy)dm Iyy = \u222b m (x2 + z2)dm, Ixz = Izx = \u222b m \u2212(xz)dm Izz = \u222b m (x2 + y2)dm, Iyz = Izy = \u222b m \u2212(yz)dm Notice that the aircraft is considered as a flat sheet aligned with the y\u2212 z plane [see figure 2]. Hence the application of the previous expressions to the convertible VTOL leads to a diagonal matrix I = \u239b \u239d Ixx 0 0 0 Iyy 0 0 0 Izz \u239e \u23a0 (6) A. Translational motion 1) Body frame: The equation (1) describes the transla- tional motion and may be rewritten as \u239b \u239d mu\u0307 mv\u0307 mw\u0307 \u239e \u23a0+ \u239b \u239d p q r \u239e \u23a0\u00d7 \u239b \u239d mu mv mw \u239e \u23a0 = \u239b \u239d fx fy fz \u239e \u23a0+RI\u2192B \u239b \u239d 0 0 \u2212mg \u239e \u23a0 (7) where the RI\u2192B transformation is such that RI\u2192B = (RB\u2192I)T . After some simple computations the equation (7) is rewritten as m(u\u0307 + qw \u2212 rv) = fx + s\u03b8mg m(v\u0307 \u2212 pw + ru) = fy \u2212 c\u03b8s\u03c6mg m(w\u0307 + pv \u2212 qu) = fz \u2212 c\u03b8c\u03c6mg or equivalently u\u0307 = \u2212(qw \u2212 rv) + fx/m \u2212 s\u03b8g (8) v\u0307 = \u2212(\u2212pw + ru) + fy/m + c\u03b8s\u03c6g w\u0307 = \u2212(pv \u2212 qu) + fz/m + c\u03b8c\u03c6g with fx = La1 \u2212 La2 \u2212 Le fy = 0 fz = Tr1 + Tr2 \u2212 (De + Da1 + Da2) where Tri and Dri (for i = 1, 2) represent the thrust and the drag forces of the propeller respectively, Le and Lai denote the elevator and aileron lift forces respectively, De and Dai denote the elevon and aileron drag forces respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002389_cm.970060606-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002389_cm.970060606-Figure5-1.png", + "caption": "Fig. 5 . A model of the bending movement of the two-tubule bundle. (a) Two outer-doublet microtubules are associated over their entire lengths by dynein arms (black projections). This causes a shearing force between the tubules (small arrows indicate direction of the shearing). (b) The bundle is bent by the shearing force because its proximal end is not allowed to move. The bundle continues to bend until the maximal curvature reaches a critical value. (c) When the bundle bends exceedingly, the dynein cross-bridges become unstable and dissociate at the site of the maximal curvature (asterisk). (d) The", + "texts": [ + " Since the two microtubules could be separated by as much as 1 pm, it is highly unlikely that any extendable inter-doublet links retain the connection between them. Such interdoublet links, if any, must be capable of being reversibly disconnected [Warner, 19831, at least in this two-microtubule system. A similar dissociation/reanealing behavior of doublet microtubules has recently been observed by Brokaw [ 19861 in sea urchin sperm axonemes. DISCUSSION All these observations led us to a model to explain the behavior of the two microtubules (Fig. 5). When they lie side-by-side in the presence of Mg-ATP, they interact with each other to cause a shearing force. This force bends the two-tubule bundle that has a proximal end that is firmly fixed (a). As dynein arms have been known to cause an adjacent microtubule to slide tipward [Sale and Satir, 19771, the dynein arms working in this pair should be those on the outer, convex edge microtubule. The bundle may continue to bend, with decreasing speed due to an increasing internal elastic force, until its maximal curvature exceeds a critical value (b)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000733_70.795797-Figure14-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000733_70.795797-Figure14-1.png", + "caption": "Fig. 14. Truss model for coplanar four contact points.", + "texts": [ + " 13 shows several kinds of the mode of internal force. We consider the case where the four contact points are coplanar. For simplicity, we assume that no three points are collinear. The 3 Equation (22) holds also for the case where fh and fk are parallel and in the same direction, and for the case where fh and fk are on the line going through Ch and Ck and in the opposite direction. We regard these cases as ones where the two forces intersect at an infinity point. The same argument holds for (15) too. virtual truss is given in Fig. 14. This truss is not rigid and the internal force shown in the figure by the four shaded arrows (they are all assumed to be normal to the plane including the four contact points), for example, cannot be expressed by a linear combination of the axial forces of the truss model only. To obtain a representation of all the internal forces, we place a fictitious joint (or contact point) CF5 that is not coplanar with the original four contact points to obtain an augmented truss model as shown in Fig. 15" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003666_0278364907080737-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003666_0278364907080737-Figure7-1.png", + "caption": "Fig. 7. Simulation of the hybrid controller operating in the visible set of a three beacon landmark. The initial configuration is q0, the controller switches at time ts in position qs and the final configuration is q f . (a) Configuration space plotted on x y 5 5 arctan y x for readability purpose. (b) Top view. The visual beacons are represented by the large black dots. The gray areas violate the visual constraints. (c) and (d) State variables and energy plots.", + "texts": [ + " Note that in figure 6 the robot executes a parallel parking maneuver in the plane. Although it is well known that for the unicycle the parallel parking motion is required to move sideways, the trajectory obtained on the plane is a natural consequence of moving on a level set of the navigation function. Moreover, the navigation function enforces that the robot does not hit the obstacles, since doing that would require puncturing the level sets away from the goal. A representative numerical simulation for the visual serving problem described in Section 2 is illustrated in figure 7. Since the navigation function , presented in equation (9), is defined in a convex set and has a unique critical point at q , all of its level sets are topological spheres. The inputs (40), (41) and (39) are computed using the nonholonomic constraint (12) and the navigation function (9). Table 2 compiles the simulation results. We now present the results of our implementation of the visual servoing algorithm using the robot RHex (Saranli et al. 2001) in three steps. In Section 4.1, we outline the hardware and software components that comprise the image processing pipeline" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000667_s0045-7825(03)00241-x-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000667_s0045-7825(03)00241-x-Figure5-1.png", + "caption": "Fig. 5. Sketch of a limit cycle including the transition points A and B.", + "texts": [ + " That random model of friction force is not coupling, which can be separated into deterministic and random parts. In this paper, a simple friction system, shown in Fig. 4, is considered, which has been studied by Popp [23]. For this system without external excitation, the classic research had shown that for stick\u2013slip motion, the trajectory in phase area consists of a straight line and a curve, which stand for stick and slip motions respectively [13]. This straight line is called as the singular line and the points of inflection as transition points. In Fig. 5, the transition points are described from stick to slip as A and from slip to stick as B. For this forced system, after neglecting of influence of the external excitation at slip mode a circle map for the deterministic stick\u2013slip motion has been derived by [23]. In reality random exists on friction systems. It is well known that the friction coefficient itself is randomly fluctuating and the transition points also fluctuating in a random manner. In addition, the motion of the support may possess random, for example the ground motion during an earthquake" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003654_tmag.2006.871423-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003654_tmag.2006.871423-Figure2-1.png", + "caption": "Fig. 2. 3-D finite-element mesh of rotor core considering lamination.", + "texts": [ + " In addition, the analyzed region is reduced as one-bar pitch of the rotor using the following periodical boundary condition with the difference of the electric angle [4]: (7) (8) where is the number of rotor slots per pole pair, and are the surfaces which are defined at the one-bar pitch interval. The magnetic saturation is estimated approximately by the sum of the harmonic magnetic fields with the iterative calculations based on the Newton\u2013Raphson method. The losses generated at the rotor including the interbar current loss are calculated at this step. Fig. 2 shows the 3-D finite-element mesh applied to the second step analysis, whose region is a one-bar pitch of the rotor. The rotor core region is each subdivided into an electrical steel plate, whose thickness is 0.5 mm. The number of subdivisions along the axis is 200 in this case. The gap elements [5], which represent the magnetic resistance between the steel plates, are inserted into every layer due to the stacking factor. The insulation between the plates is considered by assuming the axial direction conductivity of the plate as zero" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure2.22-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure2.22-1.png", + "caption": "Fig. 2.22. Centerless Grinder Fig. 2.23. Drawing process", + "texts": [ + " Although the cutting speed is higher than that of peeling machine, the cutting depth is around 0.1\u20130.15mm in the radius. Although a partial flaw removal machine is the method of not carrying out all circumference and full length cutting, pinpointing (above) the flaw position with an eddy current machine, and removing only the portion and is good for the surface flaw removal and improvement in size accuracy, but removal of a decarburization layer cannot be performed. The grinding processing by the centerless grinder is shown in Fig. 2.22. Although the surface roughness less than 5 \u03bcm and the dimensional accuracy can be obtained, the grinding amount is less than 0.15mm in the diameter for one grinding. Therefore, it is unsuitable to be applied for intermediate surface 2.1 Steel Material 69 removing. Although the application to hot rolled round bars can be seen, the application to peeled bar or cold drawn bar can be said to be normal. Since the cold drawing process shown in Fig. 2.23 is not the processing for removing the surface layer such as peeling or grinding, the removal of surface defects is not possible" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003752_jsl.26-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003752_jsl.26-Figure7-1.png", + "caption": "Figure 7. Diagrams of the dominating influence of the physical/chemical factor (a) and the geometric factor (b) on the value of the shear stress in the composition of the lubricating grease with thickener. 1 = grease without thickener; 2 = with the influence of the geometric factor; 3 = with the influence of the geometric and the physical/chemical factors.", + "texts": [ + " It is the result of the different structure of the bentonite grease as compared with the grease thickened by the lithium soap. The interrelations of the complexes of plates of bentonite clay is much smaller than the interrelations of the surface-active fibres of the lithium soap. That is why the addition of the thickener in the form of graphite flakes, MoS2 or powdered PTFE to the lithium grease significantly reduces the bonds between soap fibres, while in the case of bentonite grease it is only an additional thickener. It was presented on Figure 7 and as it follows from Figure 7(a), the influence of the physical/chemical factor is bigger than that of the geometric factor. Figure 7(b) shows the dominance of the geometric factor. The similar phenomenon was observed by Vergne and Pratt [8] in their research on different grease compositions. The results of this work are of great significance in establishing the resistances of flow of compositions in automated central lubrication system. The results of the research bring the following conclusions: \u2022 The solid lubricant applied to the lubricating grease in order to improve its tribological properties influences its rheological properties, influencing mainly the changes in the values of the shear stress in grease compositions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003482_005-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003482_005-Figure2-1.png", + "caption": "Figure 2. Photo of the rotating bow and the violin. Disc (D), two bearings (B) and lever (L).", + "texts": [ + " Meinel [21] also constructed a bowing machine. He used an infinite rosined stripe. Our reason for developing the rotating bow was that the LDV measurements need a repeatable, long and well-defined vibration signal to allow the modal analysis of the signal. Since the measuring time sometimes exceeds 10 min, ordinary bowing by hand was not possible, and it is not stable enough. A rotating bow was therefore constructed from which the violin string can be excited continuously and repeatedly for more than 15 min, see figure 2. It consists of a dc-engine (24 V) driven disc (D) of PMMA and is hinged like a pendulum in a frame supported by two bearings (B). The normal bowing force on the string can easily be changed by moving a small mass along the lever (L), and the rotational speed is controlled by a dc-voltage supply. The diameter and the thickness of the disc are 110 mm and 6 mm, respectively. The edge of the rotating disc was slightly rounded. It was rosined in the same way prior to all measuring series. Any change in the sound from the bowed violin was not detected by the measuring microphone during 20 min bowing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001222_2000-01-0095-Figure9-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001222_2000-01-0095-Figure9-1.png", + "caption": "Figure 9. Five-rod suspension - kinematic scheme", + "texts": [ + " It is expected that the principle of geometrical force superposition can be applied on condition that the main stiffness coefficients kt in radial (ktr) and axial (kta) directions are influenced by the magnitude of maximum deformation in both modes in a similar way, described by modified formulas (5): \u03b2\u03b2 \u03b2\u03b2 sin)(cos)( ,sin,cos aarr ar xFxFF xxxx += == 7 The model developed for cylindrical, elastomeric bushings was used in the simulation of spatial forced vibration of the wheel carrier in a multi-link vehicle suspension. A five-rod rear-wheel suspension [3] was taken as an example (Figure 9). This type of suspension contains eight cylindrical bushings which act as spherical joints providing desired kinematic properties, and introducing considerable compliance to the mechanism. Geometrical data and most important mass and inertia data for this example were determined by measurements carried out on a disassembled production vehicle suspension. The suspension model was built using the ADAMS software. The dimensional data are given in millimetres and include: \u2022 Coordinates of characteristic points: A1 = [-102" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000515_ic960722k-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000515_ic960722k-Figure8-1.png", + "caption": "Figure 8. Idealized orbital interaction diagrams for oxygen \u03c0 orbitals (px or py), the chromium dxz or dyz orbital, and the porphyrin e orbital: (a) electron-releasing substituent; (b) electron-withdrawing substituent.", + "texts": [ + " As discussed above, an increase in \u03c0-bonding character is usually accompanied by a decrease in P values, due to expansion of the dxy orbital. However, this is not the case. With an increase in \u03c0-bonding character of the CrVdO moiety, the P value is increased, suggesting a contraction of the dxy orbital. This is explained by the electron-withdrawing effect of the porphyrin ring induced by an electronegative meso-substituent. Since an oxochromium(V) porphyrin has C4V molecular symmetry, the dxz and dyz orbitals in the chromium(V) ion form bonding molecular orbitals with the e orbitals of porphyrin (Figure 8). Thus, an electronwithdrawing substituent in the porphyrin ring decreases the electron density on chromium(V). Since this electron-abstrac- tion effect cancels the \u03c0-electron-donation effect of the oxo ligand, the electron density on the chromium(V) ion is not increased, even when the \u03c0-bonding character of CrVdO is increased. This leads to a contraction of the dxy orbital, and results in a decrease in the P value with an increase in the electronegativity of the substituent. The contraction of the dxy orbital is also reflected in |a(53Cr)|", + " Since the spins in the 1s and 2s orbitals are induced by an exchange interaction with the spin in the dxy orbital of the chromium(V) ion, an increase in |a(17O)| with an increase in the electronegativity of the meso-substituent suggests a strengthened CrVdO bond and/or a decrease in CrdO bond length. This is consistent with an increase in \u03c0-bonding character of the CrVdO moiety expected from the change in the g value. Generally speaking, an increase in the electronegativity of the meso-substituent results in the \u03c0-bonding character of the CrVdO moiety being strong, the spin density around the oxo ligand large, and the electron density of the CrdO moiety small (Figure 8). On the basis of the above discussion, we wish to make some comments on the mechanism of the oxochromium(V) porphyrin epoxidation reaction. In general, as a particular chemical bond becomes stronger, the bonding component of the involved molecular orbital becomes more energetically stabilized while the antibonding component concomitantly becomes more destabilized. Thus, the increase in \u03c0-bonding character of the CrdO moiety observed here would suggest that the \u03c0-antibonding orbital of CrdO is destabilized in energy with an increase in electronegativity of the meso-substituent" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001898_s0924-0136(03)00467-9-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001898_s0924-0136(03)00467-9-Figure4-1.png", + "caption": "Fig. 4. In this study, both the left and the right side members were produced by tube bending and hydroforming. The initial tubes were straight round extruded aluminium profiles (outer diameter = 110 mm). The figure is from [1].", + "texts": [ + " However, the weight of the body structure can be reduced by up to 50% using aluminium and new forming and joining techniques, Fig. 3. 0924-0136/$ \u2013 see front matter \u00a9 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0924-0136(03)00467-9 Sapa Profiles and Volvo Car Corporation have, therefore, been studying tube bending and hydroforming with extruded aluminium profiles during the recent years. In a joint project, Sapa and Volvo manufactured a complete underbody. Side member left and side member right (hereafter referred to as the right and the left side member) were two of the components in this underbody, Fig. 4. These side members, which go from bumper to bumper, were manufactured by: (i) bending a straight (hollow with a circular cross-section) extruded aluminium profile and (ii) hydroforming this bent profile. The side members were produced in co-operation with AP&T Lagan AB and SwePart Verktyg AB. The present paper is an account of how these side members were made. The selected material was Sapa 6063-T4, which corresponds to AA6063-T4. Tubes with circular cross-section were used. The outside tube diameter was 110 mm, whilst the tube wall thickness was 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001189_6.2000-4442-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001189_6.2000-4442-Figure2-1.png", + "caption": "Figure 2: Resize and reorient/re-target maneuvers for spacecraft formations.", + "texts": [ + " Observation of the interference pattern for different values of (u,v) allows measurement of the complex mutual coherence function n(u,v). The van Cittert-Zernike result is that the inverse Fourier transform of /j,(u, v) gives the desired irradiance pattern J(x, y) of the celestial body. Two basic formation maneuvers are required to sample the irradiance pattern: namely formation expansion and formation reorientation. Motion between stars requires a formation re-target maneuver. In this paper we will refer to resize, reorient and retarget maneuvers as \"elementary formation maneuvers\" (EFM). Figure 2 shows the position and attitude requirements in order to maintain sensor lock, for expansion maneuvers and for reorientation/retarget maneuvers. An expansion maneuver (see Figure 2a) requires that the relative attitude be maintained while the spacecraft spacing is varied. On the other hand, both reorientation and re-target maneuvers (see Figure 2b) require that the relative attitude between spacecraft be varied at the same rate as the formation to maintain sensor lock. To implement these types of maneuvers there exists three approaches to formation flying found in the literature. These approaches have application to the coordination of spacecraft, multiple robots, and aircraft. They are the leader-following,5\"8 behavioral,9 and virtual structure10\"12 approaches. In leader-following, one vehicle is designated as the leader, while the rest of the vehicles are designated as followers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003769_1.2779892-Figure10-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003769_1.2779892-Figure10-1.png", + "caption": "Fig. 10 Transitory finite singularity of Y-motion generators with two coaxial H pairs", + "texts": [ + " If the open chain s a PHP array, the angle between the two P pairs can change and he chain generates Y motion when the P pairs are not parallel and ay become transitorily singular in a possible posture with tranitory parallel P pairs. Both cases are shown in Fig. 8. In a chain with two H pairs having parallel axes and equal itches, an undesired finite motion may happen when two H pairs re coaxial. It is an inadequate chain for a Y-motion generator if he coaxial H pairs are adjacent, as shown in Fig. 9. Otherwise, it ig. 8 Finite singularity of PPH and PHP Y-motion generators ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 is a transitory singularity of Fig. 10. Clearly, these finite singularities are special geometric cases of the infinitesimal singularities. As a matter of fact, in these chains with internal finite mobility, one can detect that three parallel H axes, which may go to infinity, are located in a plane. Moreover, based on the above findings, the possible singular postures of Y-motion generators with hinged parallelograms are readily deduced. 4.1 Translational Parallel Manipulators With Three 4DOF Limbs. Symmetrical parallel manipulators that position an end effector by 3DOF pure translations are synthesized by implementing in parallel three limbs, each limb generating Schoenflies also spelt Sch\u00f6nflies, \u201coe\u201d and \u201c\u00f6\u201d being equivalent in German 4DOF motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003668_robot.2007.363142-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003668_robot.2007.363142-Figure1-1.png", + "caption": "Fig. 1. Model of a four-wheel rover", + "texts": [ + " This controller implies a low-level control method that aims to regulate the slip rate of one wheel, since the traction force generated by the rotation of the wheel at the contact patch depends on the wheel slip. Limitations and required sensors are also pointed out. Finally, this control scheme is evaluated in dynamic simulation. The results show an improvement of motion control when implementing the model-based traction control. II. SYSTEM MODELLING We consider a skid-steering vehicle with four independent electrically driven wheels. The kinematic and geometric parameters of the vehicle are shown on figure 1. The center of mass G is located at the center of the platform. See Tab. I for a description of notations. \u03c8 is the orientation of the vehicle relatively to (O, x). Several modeling frameworks can be used to calculate the forces involved in the wheel-soil interaction process. We use an extended version of the terramechanic model introduced by Bekker ([4],[5]). We assume that the entire wheel is very stiff compared to the ground and we can consider that the wheel is rigid (Fig. 2). 1-4244-0602-1/07/$20" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003773_tac.2007.904323-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003773_tac.2007.904323-Figure3-1.png", + "caption": "Fig. 3. The implicit function method.", + "texts": [ + " Since x(t; ; 0; 0) = 0, 8t 2 , it is @xF (t; 0; x(t; ; 0; 0)) = 0 1 l 0 , which has the eigenvalues p l and p l and normalized eigenvectors W = 1p l+ 1 1p l ; 1p l : Then 0 0(t; ) = W e p lt 0 0 e p lt W 1, 8t; 2 , which im- plies that 8t; 2 , 0 0(t; ) has the eigenvalues e p lt, e p lt and constant eigenvectors given by the columns of W ; therefore @yP( ; 0; 0) = 0 0(T + ; ) I; 8t 2 and (13) holds. Since f( ; 0; 0)j0 Tg is a compact subset of 3, by the implicit function theorem, we can find > 0 and a C1 map y : [0; T ] [ ; ] ! B((0;0); ) (where B((0;0); ) denotes the closed ball in 2 of center (0,0) and radius ), represented in Fig. 3, such that y( ; 0) = 0; 8 2 [0; T ] P ( ; s; y( ; s)) = 0; 8( ; s) 2 [0; T ] [ ; ] f( ; s; y( ; s)) j( ; s) 2 [0; T ] [ ; ]g = ( ; s; y) 2 [0; T ] [ ; ] B ((0; 0); ) such that P( ; s; y) = 0g (15) that is, y( ; s) is the only solution of P( ; s; y) = 0, inside [0; T ] [ ; ] B((0; 0); ) @yP ( ; s; y( ; s)) is invertible 8( ; s) 2 [0; T ] [ ; ]: (16) The aim of the following is to prove that map y( ; s) can be prolongated at least to s = 1, 8 2 [0; T ] (see Fig. 4). A maximality procedure is used that requires the definition of suitable sets and functions, whose use is related to Lemma 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000866_3.11408-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000866_3.11408-Figure8-1.png", + "caption": "Fig. 8 Position vectors and applied torques.", + "texts": [ + " This model is specifically motivated by the hardware experimental configuration under study at the Naval Postgraduate School by Agrawal et al.8 Each elastic domain consists of a beam element connected through two discrete mass elements. The only rigidbody motion is rotation 0 of the hub, and this rigid-body motion forms highly nonlinear coupling effects with other substructures. In this example, we include the velocity components in the x direction as well, which result in a centrifugal force effect. Three control torque actuators are assumed to be available as in Fig. 8: one (u\\) at the rigid hub and the other two (u2,u3) at the discrete mass elements. Recently, Junkins and Bang9 have used this model for application of their globally stabilizing control law. The kinetic and potential energies for this system are expressed as functions of the position and velocity coordinates as 2T = [(piRi)(Ri 02 + m2R5(R5) and The position vectors for the four flexible appendages and two discrete mass elements can be represented as in Fig. 8 with respect to the body-fixed axes BI and S2 as follows: R_2 = (l\\ - x2sin a. - w2cos a) b{ [wi(/i) + JC2cos a. - w2sin a] b2 D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1450 LEE AND JUNKINS: LAGRANGE'S EQUATIONS \u00a3?3 = [/i-/2sin a- w2(/2)cos a - #3 sin(a + (3) - w3cos(a + /3)] b\\ + [wi(/i) + /2cos a - w2(/2)sin a. - JC3cos(a + /3) - w3 sin(ce + /3)] 62 R4= [/! - /2sin a - w2(/2)cos a. - *4sin(cx + /" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002653_j.jmatprotec.2004.04.360-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002653_j.jmatprotec.2004.04.360-Figure2-1.png", + "caption": "Fig. 2. Set of clad elements.", + "texts": [], + "surrounding_texts": [ + "In this study a sequentially-coupled thermal-stress analysis was performed to simulate the laser cladding process both in the steady-state and in the transient conditions (either when the laser beam begins to irradiate the workpiece and at the end of the process). In fact both stress and strain distributions are temperature-dependent; nevertheless the effects of plastic deformations caused by the residual stresses on the temperature field can be neglected, since no external loads are applied. Thus two FE models were developed: the first one for the uncoupled heat transfer analysis (to get the temperature distribution); the second one for the stress analysis (assigning as input the previously calculated temperature field). Further details on the numerical modeling of the laser cladding process are in [5]." + ] + }, + { + "image_filename": "designv11_2_0002573_cdc.1985.268837-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002573_cdc.1985.268837-Figure5-1.png", + "caption": "Fig. 5. Final path for case 2 (NS = 40).", + "texts": [], + "surrounding_texts": [ + "Fitting thls geometflc path with a spline usually gives an 'i such that (2.4) holds fo r q(t) I q(t,ll(r)t+fl(t),r). The f i t must be carried out under the boundary conditions (2.2) and as explained in Step 3 depends on r. I f the geometric path i s consistent with the boundary conditions, (2.4) holds over a wide range of r. The same cannot be said for the constralnt (2.3). If r is small, the motions are fast, u(t,a,r) i s large and the satislaction of (2.3) i s unlikely. Conversely, (2.3) usually holds i f z i s large. Our experience with both interior and exterior penalty functions for #, shows that the minimization algorithm converges best i f one uses reasonable guesses for r and exterior penalty functions 4 so that the\ninit ial violat ion of (2.3) i s permissible.\nV. Two Dimensional Cartesian nanipulator\nThe f i r s t example treats a modification of the Cartesian manipulator described in [a]. As shown in Figure I , the task i s t o translate and rotate the payload K1 i n the plane from position A to posit ion B in minimum time, avoiding the obstacles K2, ..., K?. The dynamics are given by\ni.ji(t) + $(t) = ui(t), = 1,2,3 , (5.1 )\nw h m ql(t) and qZ(t) specify the translation, q3(t) i s the rotation and the ui(t), 1 = 1,2,3, are the associated motor control voltages. The in i t ia l and terminal conditions are\nq(0) = (2,2,0), q(r) = ( 1 8,2,0), $0) = {(r) = (O,O,O), (5.2)\nand there are l imit constraints on ql(t), q2(t) and ui(t), i = 1,2,3, given by\n0 6 ql(t) s 20, 0 6 q2(t) 6 IO, I u'(t) I s I , i = 1,2,3. (5.3)\nFlnally, the obstacle avoidance conditions are\ndij(q(t)) 2 0.1, t c [O,rI, (i,j) c I = { (i,2) ,..., (1,7) 1. (5.4)\nThese equations and inequalities correspond to (2,1)-(2.4) in the general formulation.\nThe payload K1 i s 0.8 units wide and 2 units long. Only K, is dependent on q. In particular, T,(q) i s a rotation matrix dependent on q3, pl(q) = (qr,q2), K i = C, , i = 2 ,..., 7, and the sets 9 , i = 1 ,..., 7, may be inferred from Figure 1.\nthe solution far case one. The minimization process pmceeded smoothly in each ca6e taking about 10 minutes for case one and 30 minutes for case two on a Hams 800 computer. The payload trajectories are qualitatively identical, but case one produced smoother, perhaps easier t o reproduce, inputs, with less than a 7% degradation i n the final time.\nVI. Interacting Thne-Dimensional nanipulatofs\nThe second example consists of two three-degree-of-freedom cylindrical manipulators cooperatively interacting in a three-dimensional workspace as shown i n Figure 8. The task i s t o move the payload K, of the f i r s t manipulator from position A to position B i n minimum time. The second manipulator is allowed to move f r o m i t s in l t ia l position, provided it returns, and the objects K1, ... ,Kg, must not coll ide with each other. The dynamics of the system are given by\nul(t) = ~ J l - k l q z ~ t ~ + m 2 ~ q z ~ t ~ ~ z ~ ~ 1 ~ t ~ + ~ 2 m 2 q z ~ t ~ - k l ~ ~ 1 ~ t ~ ~ 2 ~ t ~ - 2 1 l ~ 1 ~ t ~ ,\nu5tt) = m~~s(t)+(k2/2-m5qstt))(i14(t))2-215~5tt),\nu W = msrq\"(t)-go)-216~6(t), (6.1 )\nwhere q'(t), i = l , ..., 6, specify respectively the rotation, radial translation and vertical translation of the arm K, and the arm K8, u'(t), 1=i, ..., 6, are the associated motor torques/forces, go i s the magnitude of the acceleration due to gravity, tii, i=l,...,6, are viscous fnction coefficients,\nand Jl,m2,m~,J4,m5,ms,ki,k2 are inertialmass parameters. The in i t ia l and terminal conditions are\nq(0) = 40, q(r)=qf, $O)=$r)= (0,0,0,0,0,0), (6.2)\nand there are l imit constraints on q(t), u(t), given by\nq W , q5tt) c lrO,rllr qYt), q'tt) c Izo,z11 ,\nI u?t) I s ai, I ui(t)+ci$(t) I 6 bi, i = I,. ..,6, (6.3)\nwhere ro,rI, are radial translatlon limits, 20.21, are vertical translation Hmits, the zy , i=l,.. , 6, result f rom motor current limits, ana 9, ci, i=l, ...,6, result from power supply voltage l im i t s [SI. The obstacle avoidance conditions are", + "The payload K, i s modelled as the spherical extension of a singleton and the sets KZ, ... ,K8, are modelled as spherical extensions of line segments. The distances between these objects may be analytically expressed using (3.3) and a formula expressing the distance between a line segment and either a point or another line segment. Of course, transformations are required. In particular: Tl(q)-TZ(q)=T3(q) and T5(q)=T&q)=T7(q) are rotation matrices dependent on q1 and q' respectively; p,(q),p,(q), depend on q', i= t ,2,3; ps(q), u6(q), depend on qi,\nin4,5,6; p3(q) depends on qi, i=1,3; p,(q) depends on qi, i%6; K4=C4, KE% are fixed.\nThe inequality constraints on qi, i=2,3,5,6, and those of (6.4) are enforced using interior penalty functions of the form (5.51, and the inequality constraints on u(t) are enforced using exterior penalty functions of the form 6.6).\nAs the data and results for this example take considerable space t o present In detail, they w l l l be presented a t the conference.\nVII. Conclusion\nThe minimum time path planning problem has been formulated i n terms of an optimal-control problem with special state constraints that ensure obstacle avoidance. A direct approach to i ts solut ion has also been presented which guarantees time optimality by combining, the dcterminatlon of the geometrfc path wi th the deteninat lon of the time h i s t o y of the path. The computations are expensive, but as evidenced by the examples, the formulation and solution approach are directly applicable t o complex problems including multiple manipulators interacting in a three-dimensional workspace.\nJ3EWEMm\nT. Lozano-Perez, 'Spatial plannlng: a configuration space approach,' E T m Compur., vol. C-32, pp. 108- 120, Feb. 1983.\nJ.Y.S. Luh, 'An anatomy of industrial robots and their controls,' /H T m &&#at. L-m&, vol. AC-28, pp. 133- 153, Feb. 1983.\nJ.Y.S. Luh and C.E. Campbell, 'Minimum distance collision-free path planning for Industrial robots with a prismatic joint; XFf Tmns. A&\"t. Cm&, VOI. AC-29, PP. 675-680, Aug. 1984.\nJ.E. Bobrow, S. Dubowsky, and J.S. Gibson, 'On the optimal control of robotic manipulators with actuator constraints,' in Pmc. &tmA L-mtc Cum::, San Francisco, CA, pp. 782-787, June 1983.\nK.G. Shin and N.D. UcKay, 'Uinimum-time control f robotic manipulators with geometric path constraints,' /ffF T m x . Aurumix, Curie, vol. AC-30, p ~ . 53 1-54 1, June 1985.\nK.G. Shin and N.D. BcKay, 'Selection of near-minimum time geometric paths for robotic manipulators,' /\u20acE T m . Aukmat. L 'onk , to appear.\nE. G. Gilbert and D.W. Johnson, 'Distance functions and their application to robot path plannmg i n the presence of obstacles,' in P m . ffghteenth dnn. Con/: hfannatim sCi8mes Jnd &stems, Princeton University, Princeton, NJ, Bar. 1984.\nE.G. Gilbert and D.W. Johnson, 'Distance functions and their application to robot path planning i n the presence of obstacles,' l m u l of Rabatics imU.4uCwnati&, vol. RA- I , pp. 2 1-30, Mar. 1985.\nR.P. Paul, hb&t ~ i p c / a c w X . Ms&mtics, Avpmuniy Jnd C#&v/. Cambridge, FA: Bass. Inst. Tech., 198 1.\n[ l o ] F.H. Clarke, QWmi.?atima#dMnsmooM anSlysis. New York: Wiley, 1983.\n[ I 11 R.O. Barr and E.G. Gllbert, 'Some efficient algorithms for a class of abstract optimization problems arising in optimal control,' 1EE Pms. duhmst. Cane.., vol. AC-14, pp. 640-652, Dec. 1969.\nn\nSide vlew\ni\nI '--' I '--' Flg. 8. Interacting three-dimenslonal cylindrical manlpulaton.\ni 121 P. Wolfe, 'Finding the nearest point i n a polytope,' in t%ft&mutical PfupmmingStu@, VoI. 1 I , No. 2. U.L. Balinski, Ed. Amsterdam North-Holland, Oct. 1976, pp. 128- 149.\n[ I31 L.L. Schumaker, Wine fmtim &sic Ti?eogr New York: Wiley, 1981.\n[ I41 A.V. Fiacco and G.P. UcCormick, hm/inewPm~mming: Squential LhcmstraiheUHinimitarian TecMiVs. New York: Wiley, 1968.\n1151 D.F. Shanno and K.H. Phua, 'Remark on algorithm 500: Rinimization 01 unconstralned multivariate functions,' AC/'I ~mns. mm. saftw., vol. 6, pp. 618-622, Dec. 1980.\n1161 J.Y.S. Luh, U.W. Walker, and R.P. C. Paul, 'On-line computational scheme fo r mechanical manipulators,' Tms. ASMJ Dgnmic 4qsl: &?as. Litntc, vol. 102, pp. 69-76, June 1980.\n1171 B.W. Walker and D.E. O m , 'Efficient dynamic computer simulation of robotic mechanlsms,' in pmc d i n t Aukmat. ~-m& Lmf:, tharlottesville, VA, June 1981." + ] + }, + { + "image_filename": "designv11_2_0002149_robot.1994.351010-Figure3.2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002149_robot.1994.351010-Figure3.2-1.png", + "caption": "Figure 3.2. Mobile Robot on Two Treaded Tracks", + "texts": [ + " Analysis is limited to motion in the plane, so all vectors presented here assume the basis, [el,e2IT. Except for O R i T i , which is a constant with respect to the object frame, all vectors are assumed to be functions of time (i.e., Po = Po ( t ) ) . The equations of motion for the object in two dimensions are expressed by equations (3.1) and (3.2). Fi is the force applied to the object by robot i, m, is the mass of the object, and Z, is the rotational inertia of the object about its z-axis through its center of mass. MOPO = z& i I Z 9 , = O R i x 4 (3.2) i The robots are represented by Figure 3.2. The treaded tracks are idealized as point contacts with the ground, and each track assumes a velocity, v1 and v2. The distance between the two tracks is r. The motion of the robot is described in terms of its velocity as, (3.3) (3.4) 1 1 VL = +v,+v,), 0 = ;(v,-v*), where VL is the total linear velocity, and w is the angular velocity of the robot. It is assumed that the robot is in rigid rolling contact with the ground and cannot move sideways. Let VL = [vx,vylT and let L = L ( 8 ) = [cos8,sin8]*, where 8 is defined for the robot as in Figure 3.2. L is a unit direction vector that describes the direction the robot is facing. Since the robot cannot move sideways,L must be collinear to the robot's velocity vector, ~ v sin8 Y or, vx sin0 - v y cos8 = 0 (3.5) Equation (3.5) is a nonholonomic velocity constraint. It makes the space of admissible velocities for the robot smaller than the robot's configuration space. Most mobile robot configurations are bound by a similar constraint. 4.0 Pseudoinverse solution The pseudoinverse is commonly used to find force setpoints for the actuators in grasping robotic hands and walking vehicles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000057_jsvi.1998.1859-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000057_jsvi.1998.1859-Figure1-1.png", + "caption": "Figure 1. Schematic of a deploying beam system.", + "texts": [ + " The model developed accounts for all the dynamic coupling terms, as well as the stiffening effect due to beam reference rotation. In previous studies, most researchers employed the Euler beam theory to study the flexible vibrations [2, 5, 6, 11, 12, 14, 15] and the dynamic stability [1, 7, 13, 15] of an axially moving beam. However, the Timoshenko beam model, the tip mass effect, the external force and its corresponding axial motion were not formulated completely. In this paper, the deployment of a flexible beam as shown in Figure 1 is considered. The flexible beam slides in and out of the rigid wall. At any instant, a part of the beam is outside the rigid support and is free to vibrate, while the remaining part of the beam is inside the wall and is restrained from the deformation in the transverse direction. Hamilton\u2019s principle [16] is employed to formulate the governing equations of the axial moving beam which is modelled by four separate beam models. In these formulations, an external force is applied, and the rigid-body motion and flexible vibrations are found to be non-linearly coupled. 2. FORMULATION OF THE GOVERNING EQUATIONS There are four separate models, Timoshenko beam model, Euler beam model, simple-flexible model and rigid-body model, which can be used to describe an axially moving beam. Hamilton\u2019s principle is employed to derive the governing equations of motion for the system shown in Figure 1. The axially moving beam is supported by a rigid wall while a mass (M) is attached at its free end. An external force P is applied at the left-hand side of the beam. In what follows, the governing equations of the system are derived using Timoshenko beam theory which retains the effects of the shear deformation and rotary inertia. A reduction process of the system equations through the other three theories is sequentially presented. 2.1. The length of the beam outside the wall is l(t) while the beam length inside the wall is \u2212s(t). The main point of the dynamic formulation is that the axially moving beam of the internal x(t)$60+, l(t)7 is free to vibrate while the other interval x(t)$6\u2212s(t), 0\u22127 is constrained in the j direction. In Figure 1, a fixed Cartesian coordinate oxy is used to describe of the problem. It is assumed that the beam has mass density (r), flexural rigidity (EI) and cross-sectional area (A). Position vector of any material point (x(t), y) of the axially moving before deformation is r= x(t)i+ yj, (1) where i, j are the unit vectors of the fixed coordinate. It is worth noting that the beam is deployable and x(t) is a function of time. The displacement field of the Timoshenko beam is U=[u(x(t), t)\u2212 yc(x(t), t)]i+ v(x(t), t)j, (2) where u(x(t), t) and v(x(t), t) represent the axial and the transverse displacements of the beam respectively, and c(x(t), t) is the slope of the deflection curve due to bending alone" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003149_12.952212-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003149_12.952212-Figure2-1.png", + "caption": "Figure 2 - Passband of an ideal velocity - adapted lowpass filter. The passband has the shape of a parallel -epiped. The no-", + "texts": [ + "org/ on 06/16/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx In the following, we assume an ideal velocity- adapted lowpass filter H(fx,fy,ft) = for -Fx < fx < Fx and -F Y < fy < Y and -V x fx -Vyfy -Ft < ft Vxfx -Vyfy +Ft (6) l 0 else The vector (Vx,Vy) will be denoted by nominal velocity of the velocity- adapted lowpass. Fx and F are its horizontal and vertical bandwidths, and Ft is its nominal temporal bandwidth. The passband of the ideal velocity- adapted lowpass has the form of a parallelepiped (Fig. 2). The frequency response of the velocity- adapted lowpass is separable into a lowpass operating along the nominal motion -trajectory, a horizontal lowpass, and a vertical lowpass. The spectrum of a signal which contains translatory motion according to (1) and (2), and which is spatially bandlimited according to (3), passes the velocity- adapted lowpass (6) without any loss of spatial resolution, if Fx.Ivx -Vx I +Fy .Ivy-Vy I < Ft (7) Thus, there exists a diamond - shaped \"passband\" of a velocity- adapted lowpass in the velocity plane, which is depicted in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000980_0379-6779(94)90051-5-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000980_0379-6779(94)90051-5-Figure2-1.png", + "caption": "Fig. 2. (a) Vol tammograms of films of poly(2) synthesized and analysed in CH3CN with the same electrolyte: (1) 0.1 M LiC104, (2) 0.1 M NaCIO4. Potential sweep rate, 20 mV/s. (b) Vol tammograms of films of poly(2) synthesized in acetonitr i le+0.5 M LiCIO4 and analysed in acetoni tr i le+0.1 M NaCIO4 (successive scans 1 to 5).", + "texts": [ + " However, for polypyrrole substituted with aza 18-crown-6 (poly(2)) significant differences in the cyclic voltammograms are observed depending on the cations. In a first step, the polymers were synthesized and analysed with the same electrolyte. When the electropolymerization is carried out with Li + instead of Bu4N +, no modification of the electrochemical properties are observed. When a film of poly(2) is realised in the presence of Na \u00f7 or K + ions, and analysed with the same ions, a distinct change of the original voltammetric response is observed (Fig. 2(a)). The curves show that the current peak is shifted towards positive potentials and that the charge reversibly exchanged is lowered, which indicates that the polymers become more difficult to oxidize. On the other hand, when a film of poly(2) is grown in the presence of Bu4N + and analysed in a solution containing Na + or K + instead of Li + or NBu4 +, the anodic wave gradually shifts to higher potentials and stabilizes at 0.5 and 0.54 V(SCE) for Na + and K +, respectively. The effect of concentration of the electrolyte has also been examined" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001891_s0301-679x(03)00074-4-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001891_s0301-679x(03)00074-4-Figure1-1.png", + "caption": "Fig. 1. Hole-entry journal bearing system.", + "texts": [ + ": +91-01332-285603; fax: +91- 01332-273560. E-mail address: sshmefme@iitr.ernet.in (S.C. Sharma). 0301-679X/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0301-679X(03)00074-4 turbo-machinery, machine tool spindles, precision grinding spindles, liquid rocket pumps etc. due to their ability to provide superior performance and relative easy in manufacturing as compared to conventional recessed journal bearings. The geometry of hole-entry journal bearing configurations is shown in Fig. 1. Due to rapid technological developments, the bearings are often required to operate under more stringent and severe operating conditions. Worldwide bearing designers are concentrating their research efforts to establish reliable design data so that the bearings operate quite satisfactorily under the given operating conditions. When the fluid-film bearings operate under high speed, heat is generated within the oil film due to shearing of the lubricant and temperature rise of the lubricant fluidfilm and the bearing surface takes place", + " The thermoelastohydrostatic (TEHS) analysis of a hole-entry hybrid journal bearing system involves a fluid-film thickness equation, Reynolds equation, a restrictor flow equation, the 3-D elasticity equation, the energy equation, a lubricant viscosity\u2013temperature equation and the heat conduction equation along with appropriate boundary conditions for the respective domains. These governing equations may be basically divided into two sub-categories as fluid and solid domains as described in the following subsections. The fluid domain equations comprise of fluid-film thickness, Reynolds, viscosity\u2013temperature relation, restrictor flow and energy equations. Fig. 1c shows the schematic representation of the fluid-film thickness profile of a hole-entry journal bearing system subjected to thermoelastic deformation of the bearing and thermal deformation of the journal. The nondimensional form of the fluid-film thickness equation for a rigid journal bearing system is expressed as: h\u0304 h\u03040 h\u0304 where h\u03040 is the fluid-film thickness of a rigid bearing system when the journal center is in the equilibrium position and is given as h\u03040 1 X\u0304Jcosa Z\u0304Jsina where h\u0304 is the perturbation on the fluid-film thickness due to dynamic conditions. For a hole-entry hybrid journal bearing system undergoing elastic and thermal deformation, the modified fluid-film thickness (Fig. 1c) is expressed as [5] h\u0304 h\u03040 h\u0304 d\u0304p fb d\u0304T fb d\u0304T J (1) where d\u0304p fb, d\u0304T fb are the values of dimensionless radial deformations in the bush due to fluid-film pressure and rise in bush temperature respectively at the fluid-film bush interface and d\u0304T J is the radial deformation of the journal due to temperature rise. The experimental study carried out by Dowson et al. [2] reported that the variation of journal temperature in the circumferential direction is negligible. Therefore, the journal is considered as an isothermal element of the bearing system. As the journal is assumed to be an axisymmetric body with uniform temperature, its thermal displacement is related to the linear thermal expansion coefficient and is expressed as [5] d\u0304T J aJTr 1 c\u0304 (T\u0304J 1). (2) Fig. 1 shows the geometric details of a hole-entry hybrid journal bearing system. The fluid-film pressure is governed by Reynolds equation and for the flow of an incompressible lubricant in the clearance space of a journal bearing system it is expressed in non-dimensional form as [13,14]: \u2202 \u2202a h\u03043F\u03042 \u2202p\u0304 \u2202a \u2202 \u2202b h\u03043F\u03042 \u2202p\u0304 \u2202b s \u2202 \u2202a 1 F\u03041 F\u03040 h\u0304 \u2202h\u0304 \u2202t\u0304 (3) where F\u03040, F\u03041, and F\u03042 are the non-dimensional viscosity functions defined as F\u03040 1 0 1 m\u0304 dz\u0304 F\u03041 1 0 z\u0304 m\u0304 dz\u0304 and F\u03042 1 0 z\u0304 m\u0304 z\u0304 F\u03041 F\u03040 dz\u0304" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000175_02783640122067264-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000175_02783640122067264-Figure1-1.png", + "caption": "Fig. 1. Small planar 2R robot centered at the origin.", + "texts": [ + " In a different approach, it is shown in Lloyd and Hayward (1998) that the reparameterization described in Lloyd (1996) can sometimes be applied to the workspace itself, such that all motions planned within this transformed workspace have well-behaved joint velocity profiles. When using the above-mentioned techniques, it can be difficult to place explicit limits on acceleration, particularly if there are to be no deviations from the path and a time-efficient motion is desired. The reason why can be demonstrated using the planar 2R robot in Figure 1, by considering the behavior of joint q2 when the robot is driven along a straight line into the singularity at the outer workspace boundary (Fig. 2). Doing this at constant speed produces a large spike in q\u03072 (solid line, Fig. 2B). The high velocity associated with this spike can be dealt with fairly easily: as the singularity is approached, one may scale the path velocity s\u0307 in direct proportion to the minimum singular value of J (similar to the method of Chiacchio and Chiaverini 1995). This has the effect of roughly \u201cclipping\u201d |q\u03072| to some maximum value (Fig", + " This is done assuming that x\u0308 is constant between knots, making this integration fairly easy to perform. Our algorithm directly handles both ordinary singularities (i.e., those not associated with self-motion) and linear selfmotion singularities (i.e., those for which the self-motion forms a straight line in joint space).1 The so-called wrist singularity is probably the most common example of a linear self-motion singularity. Both types of singularity can be illustrated by the planar 2R manipulator of Figure 1, with link lengths l1 = l2 = 1. Our attention will be restricted to the values of q1 arising from straight-line motions along the x axis, as shown in Figure 3. Ordinary singularities exist at x = \u00b12, where the x-axis intersects the outer workspace boundary and the two solution branches defined for x \u2208 (\u22122, 2) meet. A linear self-motion singularity exists at x = 0, where the manipulator folds up on itself and can spin freely about the q1 axis without affecting the tip\u2019s position. Now consider a path along the x-axis defined by x(s) = s, y(s) = 0, for s \u2265 \u22122" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000866_3.11408-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000866_3.11408-Figure1-1.png", + "caption": "Fig. 1 Rigid hub with a cantilevered Timoshenko beam.", + "texts": [], + "surrounding_texts": [ + "We consider a hybrid coordinate dynamical system and assume that the Lagrangian L = T\u2014V9 in which T is the kinetic energy and V is the potential energy, can be written in the general form L = L ( f , P, #/ ,#/ , w/, w/, w/, w/), where Qi = Qi(t) (i = 1,2,... ,m) are generalized coordinates describing rigid-body motions of the hybrid system and wy = w/(P,0 (j = 1,2,...,\u00ab) are distributed coordinates describing elastic motions relative to the rigid-body motions of an undeformed body-fixed spatial position P. We define q and w generalized coordinate vectors such as q = [q\\, #2, \u2022 \u2022 \u2022 , qm]T and w = [w\\, w 2 , . . . , wn]T. Overdots designate derivatives with respect to time, and primes designate derivatives with respect to the spatial position. First we consider the case that there is only one elastic domain. For convenience, we assume that the Lagrangian consists of three terms such as L =LD + \\DL dD +LB, where D is the domain of the undeformed flexible body; LD is the discrete portion of L and is a function of t, q, and q in the Lagrangian; L is the Lagrangian density that is a function of q, q,w,w,w', w\", and (P,t);LB, which is a function of H>(/), w(l), H>'(0\u00bb w'(0\u00bb <7> and q, is the *'boundary term\" portion of the Lagrangian energy functional, which in turn depends on the boundary motions. Next, we consider the nonconservative virtual work of hybrid systems. The virtual work can be written in the form WM = QTdq + \\D/Tb\\v dD +/r6w(/) +/2r6>v '(/). Here, Q is the nonconservative generalized force vector associated with #, / is the nonconservative generalized force density vector associated with w, dq and 5w are associated virtual displacements, and ffbw(l) and /2 r6>v'(/) are the nonconservative virtual work that depends on the boundary forces and associated boundary virtual displacements. If w is a linear displacement vector, then f\\ is the nonconservative boundary force vector associated with dw(l) and/2 is the nonconservative boundary torque vector associated with 5w'(l). Now we consider the simplest case of one spatial variable 1443 D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1444 LEE AND JUNKINS: LAGRANGE'S EQUATIONS and derive an explicit version of Lagrange's equations for this class of hybrid systems. Usually, one spatial variable is used to identify the undeformed flexible body position in one domain. For certain symmetric configurations (for example, see Ref. 6), one spatial variable can represent multiple domains if symmetric or antisymmetric deformation is assumed. We assume that the kinetic energy, potential energy, and Lagrangian are expressed by Eqs. (1), (2), and (3), respectively, and q = q(t), w = w(x,t), and w(l) represents w(x,t)\\i. Also, we suppress the appearance of t everywhere for notational compaction. T=TD(q,q)+\\ f(q,q,w,w,w',w\")dx (1) so that L = T- V = LD(q,q) + (3) where LD = TD- VD, L = T-V, and LB = TB- VB. The nonconservative virtual work of the hybrid system is given by fT(x)5wdx+f?dw(l)+f?dw'(l) (4) where f\\ is the nonconservative force vector applied at the boundary, and/2 is the nonconservative torque vector applied at the boundary. The extended Hamilton's principle can be stated as 5q = dw = 0 at t = tl9t2 (5) The variation of L yields dL dt = dL dL dL a\u00a3 a\u00a3 \u2014 dq + \u2014 dq+ \u2014 dw + \u2014 dw + \u2014\u2014 dw' dq * dw dw dw' dw\" dw dq dq dw(l) (6) The symbolic integration by parts is tedious (see Ref. 1) but can be carried to completion to obtain the following results. Equation (5) can be written as (5L+5Wnc)dt dt\\dqj }hdq lodt\\dq dLB dq dt\\dq d_(dL^ dt\\dw dL -r-dw d \u2014dx dL -dw' d2 ( dLr UJ-j \\ V I UJ-i \\ \u2022R^r\\ -\u0302 -7 ) + T-1 ( T-7 +/ 6w \u0302 d^a \u2014 ' 7 3;c2 \\5>v BL (7) In the preceding equation and elsewhere in the present paper, if F is a function of t, x9 q(t\\ q(t), w(x,t), w(x,t), w'(x,t), w\"(x,t), >v(/), >V(/), w'(l), and w'(l), then the derivative dF/dt is defined as dF dF dF dq dF dq dF dw dF dw_ _ _ I _ _ f_ i _ _ f_ i _ _ i _ _ dt ~ dt dq dt dq dt dw dt dw dt dF w' dt dF dw(l) dt dw\" dt dw(l) dt dF dw'(l) dF dw'(l) dt dt Thus, dF/dt refers to the partial derivative of F, regarding it as \"a function of the independent variables t and x,\" whereas dF/dt refers to the so-called \"explicit\" partial derivative of F regarded as a function of the independent variables t, x, q, <7, w, H% w', w\", H>(/), H>(/), >v ' ( / ) , and iv^/). If t does not appear explicitly, then of course dF/dt =0. If F does not depend on w (and derivatives thereof), then dF/dt reduces to the usual definition of total derivative of F(t,q,q). In our original developments we denoted d/df ( ) by 5/d t( ), but decided this notation was confusing because of the use of d to denote variations. Using the usual arguments on the arbitrariness and independence of the variations dq(t), dw(x,t), and the boundary variations, the preceding equation gives the governing differential equations and the boundary conditions. First, we consider the integrand associated with dq. Since L is expressed by Eq. (3), the first term of Eq. (7) is dL d (dL\\ \u2014 - \u2014 (T- +6 tlLdq dt\\dqj * Therefore, based on the arbitrariness of dq and the independence of dq, dw, and the boundary variations, we conclude that the preceding integral, hence, the bracketed integrand, must vanish, so that we obtain the classical form for Lagrange's equations: (8)dq dq We see that the discrete coordinates satisfy the usual form of Lagrange's equations. However, because of the integrations of Eq. (3) over the elastic domain, L and therefore the resulting differential equations must be considered functions of the discrete coordinates, the elastic coordinates, and their space-time derivatives. To obtain the partial differential equations governing w(x,t), we consider the integrand associated with dw. The second term of Eq. (7) becomes / , J /o _ dw dx\\dw dx2\\dw\" D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1445 Because dw is arbitrary and independent of dq and the boundary variations, the bracketed term must vanish, and this provides the partial differential equations: _d fdL\\ _dLL d_ f dL\\ _ d^_ ( dL\\ = fT dt\\dwj dw + dx\\dw') dx2\\dw\")~'f ( } Equations (8) and (9) can be found in Refs. 2 and 7, and these are derived in Ref. 2 for a three-dimensional case. Next, we consider the boundary conditions. From the last two terms of Eq. (7), we obtain the following symbolic variational statements from which the spatial boundary conditions can be obtained: dL dw\" dw' (10) (11) Equations (8) and (9) generate directly the coupled hybrid system of ordinary and partial differential equations, and the variational statements of Eqs. (10) and (11) directly generate the associated boundary conditions. Thus, we have an explicit generalization of Lagrange's equations for nonconservative distributed parameter systems that have one elastic domain but that may undergo large motions and have discrete boundary masses, forces, and moments. Now we consider a more general case that has more than one elastic domain, i.e., we consider a system of flexible bodies. For simplicity, we consider each elastic body to be beamlike, with only one spatial variable (x/). Analogous, but more complicated, developments can be carried out in this case. Let us assume that the kinetic energy, potential energy, and Lagrangian are expressed by Eqs. (12), (13), and (14), respectively. We introduce n one-dimensional elastic domains \u00a3>/ (/ = !,...,\u00ab), X f t D i , where /0 .<*/- . ->w w ( / , i ) ; and w(l), w'([), and w'(l) are defined in a similar manner. In the general case, f1 and V1 are functions of q, q, w/, w/, w/, w\", w([), w(l), H>'(/), and w'(l), and TB and VB are functions of w(l), w([)9 w (l_), w'(/), q, and q. We assume the following structure for Tand V: ' T=TD(q,q) r7/ + E/=u/0 l . (12) (13) The Lagrangian is, therefore, L = r- V (14) where LD = TD- VD, Ll= f1- Vf, and LB = TB- VB. The nonconservative virtual work of the hybrid system is given by /o,. (15) where // is the nonconservative force vector applied at the boundary (at ;c/ = //) of domain D/, and/2 is the nonconservative torque vector applied at the boundary of domain Df . We use the extended Hamilton's principle that can be stated as =0 (16) After carrying out the variation of L and symbolic integration by parts (see Ref. 1), then Eq. (16) can be written in the following compact form: (dL+dWnc)dt i \\dw/ \\ dLB ^ d^ dLj tdWi(lj) dt [ dw-( = 0 where L = Kidt (17) (18) (14) Then by using the previous definitions and the usual arguments on the arbitrariness and independence of the variations, we can obtain the following relatively simple equations that are the generalizations of Eqs. (8-11): d 9L dt \\dq 3L dq (19) dw D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1446 LEE AND JUNKINS: LAGRANGE'S EQUATIONS ,,dw\" dLE dw{(li) dLB (22) Equations (19) and (20) generate directly the coupled hybrid system of ordinary and partial differential equations, and the variational statements of Eqs. (21) and (22) directly generate the associated boundary conditions. Actually, Eqs. (8-11) are the special case (n = 1) of the preceding equations. Thus, we have an explicit generalization of Lagrange's equations, for a large family of hybrid systems that consist of interconnected rigid and elastic bodies. Each elastic body is to be beamlike and can have several dependent distributed variables, but only one independent spatial variable. In essence, we have done the integrations by parts once and for all for a large class of systems. Thus, the governing equations become quite analogous to the discrete version of Lagrange's equations, i.e., through appropriate derivatives of energy functions. The utility of these equations [Eqs. (19-22)] can be appreciated by considering several examples. Illustrative Examples Simplest Class of Problems When there is only one domain for the elastic motion and there are no boundary dependent terms in the Lagrangian, then the preceding developments are especially simple. The system Lagrangian L is expressed as L =LD + \\\\QL dx, and then Eqs. (8-11) or, more generally, Eqs. (19-22) are simplified to the following form: 1 (MA.a* r dt \\dqj dq * (8) -Idt a\u00a3 dw d ( dL dx\\dw' dL d / dL dw' dx\\dw\" = 0 /o = 0 (23) (24) /o For this simplest class of problems, it is apparent that the boundary conditions do not make allowance for lumped masses, springs, and similar forces at the boundaries, and obviously the preceding equations do not apply to multilink flexible body chains. rigid hub, radius 1 _. Rigid Hub with a Cantilevered Timoshenko Beam With reference to Figs. 1 and 2, we consider a rigid hub with a cantilevered flexible appendage. The appendage is considered to be a uniform flexible beam, and we make the Timoshenko assumptions. The beam is cantilevered rigidly to the hub. Motion is restricted to the horizontal plane, and a control torque u(t) acting on the hub (normal to the plane of motion) is the only external effect. Figure 2 shows the kinematics of deformation of a beam that undergoes shear deformation in addition to pure bending. In this example, we neglect the velocity component -yB9 which is perpendicular to the>> direction. Under these assumptions, the kinetic and potential energies of this hybrid system are as follows: T = >/2/hub02 + dx K = i where E = Young's modulus of the beam / = moment of inertia of cross section about centroidal axis p = constant mass/unit length of the beam k = shear coefficient G = modulus of rigidity A = area of cross section on which shear force acts 7hub = moment of inertia of the rigid hub 6 - hub inertial roration y = elastic deformation a = rotation of cross section Therefore, the Lagrangian is expressed by following equation: L = LD + 1 L dx ' 'o M P(y L J /o L +xey+= >/2/hub02 + -EI(a')2-kGA(a-y')2\\ dx The discrete and distributed coordinates for this case are 6, w(x>t) = [y OL]T and the only external force is u(t), so g = u and/=0. From Eqs. (8) and (9) and the Lagrangian, we get the governing differential equations for this hybrid system: d26 pi fd2oi d20 *T TT + TTA \\dt2 dt2 \\ dx \u2014T dx2 = o Boundary conditions are obtained by Eqs. (23) and (24): \\ .o, = 0 Fig. 2 Kinematics of deformation of a Timoshenko beam. Since X/0) = 0, a(/o) = 0, and dy(l) and da(l) are free, the D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1447 kGA(a- \u2014 = 0 Extensions to Include General Boundary Conditions We consider the case in which the kinetic, potential, and Lagrangian energy functional depend on the boundary motion (at * = /). So there exist LB, /i, and /2. The boundary conditions presented in this section make allowance for the lumped masses and the springs at the boundaries. We also assume that there is only one domain for the elastic motion. So L is expressed as L = LD + J/ L dx + LB . Then we can use Eqs. (8-11). Flexible Three-Body Problem (Hub, Beam, and Tip Mass) With reference to Fig. 3, we consider a rigid hub with a cantilevered flexible appendage that has a finite tip mass. The appendage is considered to be a uniform flexible beam, and we make the Euler-Bernoulli assumptions of negligible shear deformation and negligible distributed rotatory inertia. The other assumptions are identical to the first example, except considering the tip mass and the rotatory inertia of the tip mass. The kinetic and potential energies of this hybrid system are as follows: T = 1 + - + Vim [/0+>(/)]2 1 V=- Ax where m is the mass of the tip mass and 7tip the rotatory inertia of the tip mass. Therefore, the Lagrangian may be expressed as L = LD + L dx + LB )]2+i/2/ t i p[0+.y'(/)]2 The discrete and distributed coordinates for this case are q ( t ) = 0, w(x,t)=y and the only external force is w(0> so Q = u, / = 0, f i - 0, and From Eqs. (8) and (9), the governing equations for this hybrid system are #0 /hub^ 'tip d20 dt2 d20 82y d20 d2 = u d20 =0 Boundary conditions are obtained from Eqs. (10) and (11) by inserting the descriptive variables, dx2 \\dx Since X/o)=J>'(A>) = 0, and dy(l) and d y ' ( l ) are free, the boundary conditions are the following: At x = /0: Atx = l El El dx2 y - 0 and y' = 0 = m [/0 +y(l)] (shear force) = - /tip [6 + y' (/)] (bending moment) Axial Vibration of a Rod With reference to Fig. 4, we consider the rod in axial vibration.7 For simplicity, we assume that the rod has uniform properties along the axial coordinates. In this case, there are no discrete coordinates. Then the kinetic and potential energies of this system are as follows: T=- pii2dx Jo V=- where E is Young's modulus of the rod, A the area of cross section, AT the spring constant, p the constant mass/unit length of the rod, and u the axial displacement u =u(x,t). Therefore, the Lagrangian may be expressed as L = L dx + LR 1 f L = - [Pu2-EA(u')2]dx- Y2Ku2(L) 2 Jo and there is no external force, so Q =0, / = 0, /i = 0, /2 = 0, and w(x,t) = u(x,t). Governing equations for this system fol- D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1448 LEE AND JUNKINS: LAGRANGE'S EQUATIONS low immediately from the Eq. (9) as and the boundary condition variational statement is obtained by Eq. (10): -EAu'du [-Ku(L)]du(L) = ( Since \u00ab(0) = 0, and du(L) is free, the boundary conditions are as follows: At x = 0: u =0 At x = L: EAu' = 0 More General Cases: Multiple-Connected Elastic Bodies We consider more general cases in which L is expressed as L =LD+ /0|. There is more than one elastic domain, i.e., we consider a system of flexible bodies. The governing equations for the hybrid system are obtained from Eqs. (19) and (20), and the boundary conditions are obtained from Eqs. (21) and (22). Two-Link Flexible Manipulator Model We consider a planar two-link flexible manipulator as shown in Fig. 5. Each link is modeled as a uniform flexible beam, and we make the Euler-Bernoulli assumptions. This system has two spatial variables x\\ and x'2t and elastic motions relative to the rigid-body motions are described by y\\(x\\,t) and y2(x2,t), respectively. In this example, we neglect the velocity components that are perpendicular to the y\\ and y2 directions. This system is controlled by the torque inputs u\\ and u2 as shown in Fig. 5. The kinetic and potential energies of this hybrid system are as follows: 1 T=- V \u2014 \u2014 I EI\\ I ~~\u2014 ) dxi ~h \u2014 I El-y ( \u2014\u2014 ) dx? O I \\ ^V2 / 0 I \\ /iv^ / ^ J 0 \\ \"-\u0302 1 / Z J 0 \\ ax2 / where p/ is the assumed constant mass/unit length of the /th beam, \u00a3!// the assumed constant bending stiffness of the /th beam, // the length of the /th beam, yf the elastic deformation of the /th beam, and m2 the mass of the second beam. L2dx2L=\\ L1 dxl Jo = 1 I V2pl( dx, dx2 The discrete and distributed coordinates for this case are Qi = 0i(0, q2 = 02(t) The nonconservative virtual work is expressed by the following equation: f ( *y\\\\ 6 > 2 - ( 6 > 1 + -^ L \\ ox\\ u2562 - u25\\ -\u2014 Therefore, and = [ul-u2 To apply Eqs. (19-22), first we record L1, L2, and LB. In this example, LB is identical to L since LD does not exist: /=! o The resulting coupled system of nonlinear hybrid differential equations and the boundary conditions are obtained from Eqs. (19-22) as the following eight equations: 0! equation: /w2/i [/i81 +^i(/i ,0] t = itl \u2014 u2 02 equation: /2 P2x2(x202+y2)dx2+ D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1449 Boundary conditions of beam 1: At*i = 0: y\\ = 0, y{ = 0 At *! = /!: _ a2vi = -u2 -0i) = 0, 0 at \u2014 w2(/2)sin a- - w3sin(a: + /3)] j b\\ + [>Vi(/i)-/2a! sin a- w2(/2)sin a - w3(a + /3)cos(a + /3) + 0 [/i - /2sin a - w2(/2)cos o; + /3)-w3cos(o:- = i - I2a cos a - w2(/2)cos a + w2(/2)o; sin o;dt .(a + /3)cos(a +18) \u2014 w4cos I {a + /3)sin(o; + f}) \u2014 0 [wi(/i) + /2cos a - w2(/2)sin a s(o; + j3) - w4sin(o; + /5)] | \u0302 i + j Wi(/!) \u2014 I2a sin a \u2014 w2(/2)sin a. \u2014 W2(l2)a cos a. - X4(a + |8)sin(ce + /3) - w4sin(a + jS) - w4(o: + j8)cos(ce +18) + 0 [/i - /2sin a - w2(/2)cos ce \u2014 JC4sin(a + jS) \u2014 w4cos(a + /?)] j \u0302 2 ^ = _d/?. *dg6 d^ = j - I2a cos ce - >V2(/2)cos a + w2(/2)a sin ce 2cos a - w2(/2)sin a] j S\\- - I2a sin a - w2(/2)sin a - W2(l2)a cos o; + 0 [/! - /2sin o; - w2(/2)cos a] j 52 For convenience of notation, we introduce The nonconservative forces are given through the expression of virtual work as follows: = (ui + u2 + w3)<50 Applying Eqs. (19-22) yields the following nonlinear equations of motion. Nonlinear Equations of Motion 6 equation: /o2 at ' o 3 d ? /4 ^ '04 ^ + m2 \u2014 (v5^ = MI + w2 + i equation: d 11 TS equation: , p 2 idV equation: 3 + V2 2/?2 3) - 1 =0 D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1451 + l \"3|dV 4- v P4 v4 2B4 3)-i w2 equation: '2^-T=0dx\u00a3 w2(/2) equation: '3 \u00ab3 '\u00ab F d 04 \u2014 = \u00a32/2 = (dw2/dx2)\\/2 equation: 'o, C'4 UP4 -(K J/o, Ld? 4U47 4- V2\u00a347) - V4U48 - V2\u00a3| d*4 1\u0302 ,2 vv3 equation: = 0 w4 equation: P4 where w3 = w3 - w30 and w4 = w4 - w40. The constants \u0302 4{ and .B/ that are functions of the states related to the overall structure are presented in the Appendix. Summary and Conclusion In this paper, emphasis has been placed on the multibody case. An explicit version of the classical Lagrange's equations that cover a large family of multibody hybrid discrete distributed parameter systems is symbolically derived. The resulting equations can be efficiently specialized to obtain not only the hybrid governing integro-differential equations but also the associated boundary conditions. These resulting equations enable us to avoid the very tedious system-specific variational arguments and integration by parts. These equations can be generalized further to consider three-dimensional elastic solid bodies. 2 = - cos a, Appendix >| 1 ___ ... A 2 ___ ___ /3 D! ___ -y^ l?^ ___ 1 SI J \u2014\u2014 VV\\ } VT. J \u2014\u2014 I/j -t-* J \u2014\u2014 A} , JD J \u2014\u2014 1 v42 = \u2014 d, >12 = \u2014 vvi(/i) \u2014 Jt2cos a + w2sin a. A2 = -x2cos a 4- w2sin ce ^ = jc2a sin a + w2sin a -f w2o; cos a 4- JC20 sin o; 4- W20 cos of 52 = 1, B2 = l\\ - *2sin o; - W2cos a B2 = -;c2sin ce - w2cos o; ,62 = -JC2o; cos a. - W2cos a 4- w2a sin a - x26 cos ce + w20 sin o: B2 = \u2014 sin a, #! = \u2014 (a 4- 0)cos ce ^^ -0 Al = - Wi(/!) - /2cos o; + w2(/2)sin a - X3cos(a: + 0) A\\-~ /2cos a + w2(/2)sin o; + x3cos(a: + J3) + w3sin(o; y43 4 = /2o: sin a. + w2(/2)sin a + w2(/2)a cos a. + 120 sin o: + w2(/2)0 cos a - Xi(6t + /3)sin(a + j8) + w3sin(a + 0) + w3(\u00ab + /3)cos(a: + /3) - JC30 sin(a + /3) + w30 cos(o: ^43 5 = - cos a, 1\u03023 6 = (QJ + 0)sin a j + /j)sin(a /3)cos(a cos(a 30 cos(a = (a = /i - /2sin a - w2(/2)cos a + x3sin(a + /3) - w3cos(a + /3) l = -I2sma - w2(/2)cos o; + x3sin(ce + ]8) \u2014 w3cos(o; + /3) 3 4 = - /2ce cos a - w2(/2)cos a + W2(l2)a sin a - /20 cos a + w2(/2)^ sin ce + JC3(ce + /3)cos(a + ]8) - W3cos(o; + j8) + w3(o; + jS)sin(a + j8) + X30 cos(a + j8) + w30 sin(o: + /3) 53 5 = - sin a, \u00a33 6 = - (a + (9)cos a I - W3cos(o: + j8) w3(a 4- j8)sin(a + /3) + X30 cos(o: 4- j8) 4- w30 sin(ce + /3) ?| = -sin(a + |8), J?3 10 = - (a. 4- j8 4 = - Wi(/i) - /2cos a 4- w2(/2)sin a - x4cos(a 4- /3) D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1452 LEE AND JUNKINS: LAGRANGE'S EQUATIONS w2(/2)sin a. - *4cos(a: w4sin(a A4 = I2a sin a + w2(/2)shi a. + W2(l2)a cos a. + /20 sin a. cos a + X4(a + /3)sin(a + j8) + w4sin(o; + j8) 3)cos(a + 18) + x40 sin(a + j8) + w40 cos(a 4 = - cos a, ^i5 = (a + 0)sin a = w4sin(a w4(a + /3)cos(a: + j3) + x40 sin(a + j8) + w40 cos(o: 44 9 = - cos(a + 18), ^l]0 = (a + jS + (9)sin(oj + j8) i - /2sin a - w2(/2)cos a - JC4sin(o; + 0) - w4cos(a + /3) - /2sin a - w2(/2)cos o: - X4sin(a + j8) - w4cos(a + /3) - I26i cos a - w2(/2)cos o: + w2(/2)a: sin a. - /20 cos o; w2(/2)0 sin a - x4(a + /3)cos(a + j8) - w4cos(a + 0) w4(cx + /3)sin(a: + 18) - JC40 cos(a + j8) + w40 sin(a: ^4 = - sin a, #1 = - (d + 0)cos a ^4 = - JC4sin(a + j3) - w4cos(a j8) - w4cos(a: - x40 cos(a + j8) + w40 sin(o; 54 10 = - (a + j8 + 0)cos(a - /2cos a + w2(/2)sin a A\\ = - /2cos a + w2(/2)sin a l = I2ct sin a + w2(/2)sin a + w2(/2)a cos a: + /20 sin a + w2(/2)0 cos a Al = - cos a, A$ = (a + 0)sin a J?6 ! = 1, B\\-l\\- /2sin a - w2(/2)cos a B\\= - /2sin a - w2(/2)cos o: \u2014 \u2014 I2a cos ce - w2(/2)cos a + w2(/2)a sin a - /20 cos a + w2(/2)0 sin a B5 6= -sin a, #| = ~(0 + Acknowledgments This work was supported by the Air Force Office of Scien- tific Research under Contract F49620-89-C-0084 and by the Texas Higher Education Coordinating Board, Project 999903- 231. We are pleased to acknowledge productive discussions with the following colleagues: H. Bang, N. Hecht, Y. Kim, L. Meirovitch, Z. Rahman, S. Skaar, and S. Vadali. The technical and administrative support of S. Wu and R. Elliott is appreciated. References e, S., and Junkins, J. L., \"Explicit Generalizations of La- grange's Equations for Hybrid Coordinate Dynamical Systems,\" Dept. of Aerospace Engineering, Texas A&M Univ., Technical Kept. AERO 91-0301, College Station, TX, March 1991. 2Meirovitch, L., \"Hybrid State Equations of Motion for Flexible Bodies in Terms of Quasi-Coordinates,\" Journal of Guidance, Control, and Dynamics, Vol. 14, No. 5, 1991, pp. 1008-1013. 3Berbyuk, V. E., and Demidyuk, M. V., \"Controlled Motion of an Elastic Manipulator with Distributed Parameters,\" Mechanics of Solids, Vol. 19, No. 2, 1984, pp. 57-65. 4Low, K. H., and Vidyasagar, M., \"A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems,\" ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 110, June 1988, pp. 175-181. 5Pars, L. A., A Treatise on Analytical Dynamics, Cambridge Univ. Press, London, 1965, Chap. 2-4. 6Junkins, J. L., Rahman, Z., and Bang, H., \"Near-Minimum-Time Maneuvers of Flexible Vehicles: A Liapunov Control Law Design Method,\" Mechanics and Control of Large Flexible Structures, edited by J. L. Junkins, Vol. 129, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, 1990, pp. 565-593. 7Meirovitch, L., Computational Methods in Structural Dynamics, Sijhoff & Noordhoff, Leyden, The Netherlands, 1980. 8Hailey, J. A., Sortun, C. D., and Agrawal, B. N., \"Experimental Verification of Attitude Control Techniques for Slew Maneuvers of Flexible Spacecraft,\" AIAA Paper 92-4456, Aug. 1992. 9Junkins, J. L., and Bang, H., \"Maneuver and Vibration Control of Nonlinear Hybrid Coordinate System Using Liapunov Stability Theory,\" AIAA Paper 92-4458, Aug. 1992. D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08" + ] + }, + { + "image_filename": "designv11_2_0001669_1.1609493-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001669_1.1609493-Figure2-1.png", + "caption": "Fig. 2 Expansion of the apparent contact area of a macroscopic Hertzian contact and the accompanied increase in the number of fractal domains in contact for a normal load increased from \u201ea\u2026 P to \u201eb\u2026 P\u00bfDP", + "texts": [ + " For a macroscopic Hertzian contact, the apparent contact area, Aa , is related to the normal load, P, by @25# Aa}P2/3 (4) and the maximum Hertzian pressure, p0 , is given by p0 53P/(2Aa). Thus, p0}P1/3 (5) The distribution of the apparent pressure in the Hertzian contact region with a radius, ra , is given by p~x ,y !5p0@12~x/ra!22~y /ra!2#1/2 (6) Macroscopic Spherical Surfaces With Sub-Domains. Dividing the spherical surface into sub-domains of squares with the side length set equal to the upper limit for fractal characterization, Lu , the area of each sub-domain is, then, equal to Lu 2 ~Fig. 2~a!!. The density of these sub-domains, or fractal domains, is given by h51/Lu 2, and the normal load on each sub-domain, Pd , is related to the apparent pressure on the sub-domain, p, by Pd5pLu 2. It is assumed that the relationship between the real contact area of a sub-domain ~fractal domain!, Ar f , and the normal load on a subdomain, Pd , follows a power law Ar f5CdPd b (7) where Cd is a constant coefficient. The real contact area, Ar , can be obtained by integrating the real contact area of each subdomain, i", + " Fractal-regular surfaces give a closer-to-linear area-load relationship because, when the normal load increases, the expansion of the apparent area of the macroscopic contact increases the number of fractal domains in contact. Thus, the required amount of increase in the average load on a fractal domain is reduced. This effect corresponds to making use of a smaller segment of an originally nonlinear area-load curve. Hence, the nonlinearity originated from the fractal model is suppressed for fractal-regular surfaces. The expansion of the apparent contact area of the macroscopic contact region, Aa , and an accompanied increase in the number of fractal domains engaged in contact are shown schematically in Fig. 2 for a normal load increased from P to P1DP . The expected slight distortion of the grid of fractal domains due to lateral displacements is neglected for simplicity. The power spectral density function of a fractal-regular surface is equal to the sum of those of the macroscopic regular shape and the fractal structures. The Fourier expansion of the function for a parabolic surface profile given by Eq. ~3! in a fundamental interval, 2Lm/2(/), w(l), H>'(0\u00bb w'(0\u00bb <7> and q, is the *'boundary term\" portion of the Lagrangian energy functional, which in turn depends on the boundary motions. Next, we consider the nonconservative virtual work of hybrid systems. The virtual work can be written in the form WM = QTdq + \\D/Tb\\v dD +/r6w(/) +/2r6>v '(/). Here, Q is the nonconservative generalized force vector associated with #, / is the nonconservative generalized force density vector associated with w, dq and 5w are associated virtual displacements, and ffbw(l) and /2 r6>v'(/) are the nonconservative virtual work that depends on the boundary forces and associated boundary virtual displacements. If w is a linear displacement vector, then f\\ is the nonconservative boundary force vector associated with dw(l) and/2 is the nonconservative boundary torque vector associated with 5w'(l). Now we consider the simplest case of one spatial variable 1443 D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1444 LEE AND JUNKINS: LAGRANGE'S EQUATIONS and derive an explicit version of Lagrange's equations for this class of hybrid systems. Usually, one spatial variable is used to identify the undeformed flexible body position in one domain. For certain symmetric configurations (for example, see Ref. 6), one spatial variable can represent multiple domains if symmetric or antisymmetric deformation is assumed. We assume that the kinetic energy, potential energy, and Lagrangian are expressed by Eqs. (1), (2), and (3), respectively, and q = q(t), w = w(x,t), and w(l) represents w(x,t)\\i. Also, we suppress the appearance of t everywhere for notational compaction. T=TD(q,q)+\\ f(q,q,w,w,w',w\")dx (1) so that L = T- V = LD(q,q) + (3) where LD = TD- VD, L = T-V, and LB = TB- VB. The nonconservative virtual work of the hybrid system is given by fT(x)5wdx+f?dw(l)+f?dw'(l) (4) where f\\ is the nonconservative force vector applied at the boundary, and/2 is the nonconservative torque vector applied at the boundary. The extended Hamilton's principle can be stated as 5q = dw = 0 at t = tl9t2 (5) The variation of L yields dL dt = dL dL dL a\u00a3 a\u00a3 \u2014 dq + \u2014 dq+ \u2014 dw + \u2014 dw + \u2014\u2014 dw' dq * dw dw dw' dw\" dw dq dq dw(l) (6) The symbolic integration by parts is tedious (see Ref. 1) but can be carried to completion to obtain the following results. Equation (5) can be written as (5L+5Wnc)dt dt\\dqj }hdq lodt\\dq dLB dq dt\\dq d_(dL^ dt\\dw dL -r-dw d \u2014dx dL -dw' d2 ( dLr UJ-j \\ V I UJ-i \\ \u2022R^r\\ -\u0302 -7 ) + T-1 ( T-7 +/ 6w \u0302 d^a \u2014 ' 7 3;c2 \\5>v BL (7) In the preceding equation and elsewhere in the present paper, if F is a function of t, x9 q(t\\ q(t), w(x,t), w(x,t), w'(x,t), w\"(x,t), >v(/), >V(/), w'(l), and w'(l), then the derivative dF/dt is defined as dF dF dF dq dF dq dF dw dF dw_ _ _ I _ _ f_ i _ _ f_ i _ _ i _ _ dt ~ dt dq dt dq dt dw dt dw dt dF w' dt dF dw(l) dt dw\" dt dw(l) dt dF dw'(l) dF dw'(l) dt dt Thus, dF/dt refers to the partial derivative of F, regarding it as \"a function of the independent variables t and x,\" whereas dF/dt refers to the so-called \"explicit\" partial derivative of F regarded as a function of the independent variables t, x, q, <7, w, H% w', w\", H>(/), H>(/), >v ' ( / ) , and iv^/). If t does not appear explicitly, then of course dF/dt =0. If F does not depend on w (and derivatives thereof), then dF/dt reduces to the usual definition of total derivative of F(t,q,q). In our original developments we denoted d/df ( ) by 5/d t( ), but decided this notation was confusing because of the use of d to denote variations. Using the usual arguments on the arbitrariness and independence of the variations dq(t), dw(x,t), and the boundary variations, the preceding equation gives the governing differential equations and the boundary conditions. First, we consider the integrand associated with dq. Since L is expressed by Eq. (3), the first term of Eq. (7) is dL d (dL\\ \u2014 - \u2014 (T- +6 tlLdq dt\\dqj * Therefore, based on the arbitrariness of dq and the independence of dq, dw, and the boundary variations, we conclude that the preceding integral, hence, the bracketed integrand, must vanish, so that we obtain the classical form for Lagrange's equations: (8)dq dq We see that the discrete coordinates satisfy the usual form of Lagrange's equations. However, because of the integrations of Eq. (3) over the elastic domain, L and therefore the resulting differential equations must be considered functions of the discrete coordinates, the elastic coordinates, and their space-time derivatives. To obtain the partial differential equations governing w(x,t), we consider the integrand associated with dw. The second term of Eq. (7) becomes / , J /o _ dw dx\\dw dx2\\dw\" D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1445 Because dw is arbitrary and independent of dq and the boundary variations, the bracketed term must vanish, and this provides the partial differential equations: _d fdL\\ _dLL d_ f dL\\ _ d^_ ( dL\\ = fT dt\\dwj dw + dx\\dw') dx2\\dw\")~'f ( } Equations (8) and (9) can be found in Refs. 2 and 7, and these are derived in Ref. 2 for a three-dimensional case. Next, we consider the boundary conditions. From the last two terms of Eq. (7), we obtain the following symbolic variational statements from which the spatial boundary conditions can be obtained: dL dw\" dw' (10) (11) Equations (8) and (9) generate directly the coupled hybrid system of ordinary and partial differential equations, and the variational statements of Eqs. (10) and (11) directly generate the associated boundary conditions. Thus, we have an explicit generalization of Lagrange's equations for nonconservative distributed parameter systems that have one elastic domain but that may undergo large motions and have discrete boundary masses, forces, and moments. Now we consider a more general case that has more than one elastic domain, i.e., we consider a system of flexible bodies. For simplicity, we consider each elastic body to be beamlike, with only one spatial variable (x/). Analogous, but more complicated, developments can be carried out in this case. Let us assume that the kinetic energy, potential energy, and Lagrangian are expressed by Eqs. (12), (13), and (14), respectively. We introduce n one-dimensional elastic domains \u00a3>/ (/ = !,...,\u00ab), X f t D i , where /0 .<*/- . ->w w ( / , i ) ; and w(l), w'([), and w'(l) are defined in a similar manner. In the general case, f1 and V1 are functions of q, q, w/, w/, w/, w\", w([), w(l), H>'(/), and w'(l), and TB and VB are functions of w(l), w([)9 w (l_), w'(/), q, and q. We assume the following structure for Tand V: ' T=TD(q,q) r7/ + E/=u/0 l . (12) (13) The Lagrangian is, therefore, L = r- V (14) where LD = TD- VD, Ll= f1- Vf, and LB = TB- VB. The nonconservative virtual work of the hybrid system is given by /o,. (15) where // is the nonconservative force vector applied at the boundary (at ;c/ = //) of domain D/, and/2 is the nonconservative torque vector applied at the boundary of domain Df . We use the extended Hamilton's principle that can be stated as =0 (16) After carrying out the variation of L and symbolic integration by parts (see Ref. 1), then Eq. (16) can be written in the following compact form: (dL+dWnc)dt i \\dw/ \\ dLB ^ d^ dLj tdWi(lj) dt [ dw-( = 0 where L = Kidt (17) (18) (14) Then by using the previous definitions and the usual arguments on the arbitrariness and independence of the variations, we can obtain the following relatively simple equations that are the generalizations of Eqs. (8-11): d 9L dt \\dq 3L dq (19) dw D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1446 LEE AND JUNKINS: LAGRANGE'S EQUATIONS ,,dw\" dLE dw{(li) dLB (22) Equations (19) and (20) generate directly the coupled hybrid system of ordinary and partial differential equations, and the variational statements of Eqs. (21) and (22) directly generate the associated boundary conditions. Actually, Eqs. (8-11) are the special case (n = 1) of the preceding equations. Thus, we have an explicit generalization of Lagrange's equations, for a large family of hybrid systems that consist of interconnected rigid and elastic bodies. Each elastic body is to be beamlike and can have several dependent distributed variables, but only one independent spatial variable. In essence, we have done the integrations by parts once and for all for a large class of systems. Thus, the governing equations become quite analogous to the discrete version of Lagrange's equations, i.e., through appropriate derivatives of energy functions. The utility of these equations [Eqs. (19-22)] can be appreciated by considering several examples. Illustrative Examples Simplest Class of Problems When there is only one domain for the elastic motion and there are no boundary dependent terms in the Lagrangian, then the preceding developments are especially simple. The system Lagrangian L is expressed as L =LD + \\\\QL dx, and then Eqs. (8-11) or, more generally, Eqs. (19-22) are simplified to the following form: 1 (MA.a* r dt \\dqj dq * (8) -Idt a\u00a3 dw d ( dL dx\\dw' dL d / dL dw' dx\\dw\" = 0 /o = 0 (23) (24) /o For this simplest class of problems, it is apparent that the boundary conditions do not make allowance for lumped masses, springs, and similar forces at the boundaries, and obviously the preceding equations do not apply to multilink flexible body chains. rigid hub, radius 1 _. Rigid Hub with a Cantilevered Timoshenko Beam With reference to Figs. 1 and 2, we consider a rigid hub with a cantilevered flexible appendage. The appendage is considered to be a uniform flexible beam, and we make the Timoshenko assumptions. The beam is cantilevered rigidly to the hub. Motion is restricted to the horizontal plane, and a control torque u(t) acting on the hub (normal to the plane of motion) is the only external effect. Figure 2 shows the kinematics of deformation of a beam that undergoes shear deformation in addition to pure bending. In this example, we neglect the velocity component -yB9 which is perpendicular to the>> direction. Under these assumptions, the kinetic and potential energies of this hybrid system are as follows: T = >/2/hub02 + dx K = i where E = Young's modulus of the beam / = moment of inertia of cross section about centroidal axis p = constant mass/unit length of the beam k = shear coefficient G = modulus of rigidity A = area of cross section on which shear force acts 7hub = moment of inertia of the rigid hub 6 - hub inertial roration y = elastic deformation a = rotation of cross section Therefore, the Lagrangian is expressed by following equation: L = LD + 1 L dx ' 'o M P(y L J /o L +xey+= >/2/hub02 + -EI(a')2-kGA(a-y')2\\ dx The discrete and distributed coordinates for this case are 6, w(x>t) = [y OL]T and the only external force is u(t), so g = u and/=0. From Eqs. (8) and (9) and the Lagrangian, we get the governing differential equations for this hybrid system: d26 pi fd2oi d20 *T TT + TTA \\dt2 dt2 \\ dx \u2014T dx2 = o Boundary conditions are obtained by Eqs. (23) and (24): \\ .o, = 0 Fig. 2 Kinematics of deformation of a Timoshenko beam. Since X/0) = 0, a(/o) = 0, and dy(l) and da(l) are free, the D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1447 kGA(a- \u2014 = 0 Extensions to Include General Boundary Conditions We consider the case in which the kinetic, potential, and Lagrangian energy functional depend on the boundary motion (at * = /). So there exist LB, /i, and /2. The boundary conditions presented in this section make allowance for the lumped masses and the springs at the boundaries. We also assume that there is only one domain for the elastic motion. So L is expressed as L = LD + J/ L dx + LB . Then we can use Eqs. (8-11). Flexible Three-Body Problem (Hub, Beam, and Tip Mass) With reference to Fig. 3, we consider a rigid hub with a cantilevered flexible appendage that has a finite tip mass. The appendage is considered to be a uniform flexible beam, and we make the Euler-Bernoulli assumptions of negligible shear deformation and negligible distributed rotatory inertia. The other assumptions are identical to the first example, except considering the tip mass and the rotatory inertia of the tip mass. The kinetic and potential energies of this hybrid system are as follows: T = 1 + - + Vim [/0+>(/)]2 1 V=- Ax where m is the mass of the tip mass and 7tip the rotatory inertia of the tip mass. Therefore, the Lagrangian may be expressed as L = LD + L dx + LB )]2+i/2/ t i p[0+.y'(/)]2 The discrete and distributed coordinates for this case are q ( t ) = 0, w(x,t)=y and the only external force is w(0> so Q = u, / = 0, f i - 0, and From Eqs. (8) and (9), the governing equations for this hybrid system are #0 /hub^ 'tip d20 dt2 d20 82y d20 d2 = u d20 =0 Boundary conditions are obtained from Eqs. (10) and (11) by inserting the descriptive variables, dx2 \\dx Since X/o)=J>'(A>) = 0, and dy(l) and d y ' ( l ) are free, the boundary conditions are the following: At x = /0: Atx = l El El dx2 y - 0 and y' = 0 = m [/0 +y(l)] (shear force) = - /tip [6 + y' (/)] (bending moment) Axial Vibration of a Rod With reference to Fig. 4, we consider the rod in axial vibration.7 For simplicity, we assume that the rod has uniform properties along the axial coordinates. In this case, there are no discrete coordinates. Then the kinetic and potential energies of this system are as follows: T=- pii2dx Jo V=- where E is Young's modulus of the rod, A the area of cross section, AT the spring constant, p the constant mass/unit length of the rod, and u the axial displacement u =u(x,t). Therefore, the Lagrangian may be expressed as L = L dx + LR 1 f L = - [Pu2-EA(u')2]dx- Y2Ku2(L) 2 Jo and there is no external force, so Q =0, / = 0, /i = 0, /2 = 0, and w(x,t) = u(x,t). Governing equations for this system fol- D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1448 LEE AND JUNKINS: LAGRANGE'S EQUATIONS low immediately from the Eq. (9) as and the boundary condition variational statement is obtained by Eq. (10): -EAu'du [-Ku(L)]du(L) = ( Since \u00ab(0) = 0, and du(L) is free, the boundary conditions are as follows: At x = 0: u =0 At x = L: EAu' = 0 More General Cases: Multiple-Connected Elastic Bodies We consider more general cases in which L is expressed as L =LD+ /0|. There is more than one elastic domain, i.e., we consider a system of flexible bodies. The governing equations for the hybrid system are obtained from Eqs. (19) and (20), and the boundary conditions are obtained from Eqs. (21) and (22). Two-Link Flexible Manipulator Model We consider a planar two-link flexible manipulator as shown in Fig. 5. Each link is modeled as a uniform flexible beam, and we make the Euler-Bernoulli assumptions. This system has two spatial variables x\\ and x'2t and elastic motions relative to the rigid-body motions are described by y\\(x\\,t) and y2(x2,t), respectively. In this example, we neglect the velocity components that are perpendicular to the y\\ and y2 directions. This system is controlled by the torque inputs u\\ and u2 as shown in Fig. 5. The kinetic and potential energies of this hybrid system are as follows: 1 T=- V \u2014 \u2014 I EI\\ I ~~\u2014 ) dxi ~h \u2014 I El-y ( \u2014\u2014 ) dx? O I \\ ^V2 / 0 I \\ /iv^ / ^ J 0 \\ \"-\u0302 1 / Z J 0 \\ ax2 / where p/ is the assumed constant mass/unit length of the /th beam, \u00a3!// the assumed constant bending stiffness of the /th beam, // the length of the /th beam, yf the elastic deformation of the /th beam, and m2 the mass of the second beam. L2dx2L=\\ L1 dxl Jo = 1 I V2pl( dx, dx2 The discrete and distributed coordinates for this case are Qi = 0i(0, q2 = 02(t) The nonconservative virtual work is expressed by the following equation: f ( *y\\\\ 6 > 2 - ( 6 > 1 + -^ L \\ ox\\ u2562 - u25\\ -\u2014 Therefore, and = [ul-u2 To apply Eqs. (19-22), first we record L1, L2, and LB. In this example, LB is identical to L since LD does not exist: /=! o The resulting coupled system of nonlinear hybrid differential equations and the boundary conditions are obtained from Eqs. (19-22) as the following eight equations: 0! equation: /w2/i [/i81 +^i(/i ,0] t = itl \u2014 u2 02 equation: /2 P2x2(x202+y2)dx2+ D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1449 Boundary conditions of beam 1: At*i = 0: y\\ = 0, y{ = 0 At *! = /!: _ a2vi = -u2 -0i) = 0, 0 at \u2014 w2(/2)sin a- - w3sin(a: + /3)] j b\\ + [>Vi(/i)-/2a! sin a- w2(/2)sin a - w3(a + /3)cos(a + /3) + 0 [/i - /2sin a - w2(/2)cos o; + /3)-w3cos(o:- = i - I2a cos a - w2(/2)cos a + w2(/2)o; sin o;dt .(a + /3)cos(a +18) \u2014 w4cos I {a + /3)sin(o; + f}) \u2014 0 [wi(/i) + /2cos a - w2(/2)sin a s(o; + j3) - w4sin(o; + /5)] | \u0302 i + j Wi(/!) \u2014 I2a sin a \u2014 w2(/2)sin a. \u2014 W2(l2)a cos a. - X4(a + |8)sin(ce + /3) - w4sin(a + jS) - w4(o: + j8)cos(ce +18) + 0 [/i - /2sin a - w2(/2)cos ce \u2014 JC4sin(a + jS) \u2014 w4cos(a + /?)] j \u0302 2 ^ = _d/?. *dg6 d^ = j - I2a cos ce - >V2(/2)cos a + w2(/2)a sin ce 2cos a - w2(/2)sin a] j S\\- - I2a sin a - w2(/2)sin a - W2(l2)a cos o; + 0 [/! - /2sin o; - w2(/2)cos a] j 52 For convenience of notation, we introduce The nonconservative forces are given through the expression of virtual work as follows: = (ui + u2 + w3)<50 Applying Eqs. (19-22) yields the following nonlinear equations of motion. Nonlinear Equations of Motion 6 equation: /o2 at ' o 3 d ? /4 ^ '04 ^ + m2 \u2014 (v5^ = MI + w2 + i equation: d 11 TS equation: , p 2 idV equation: 3 + V2 2/?2 3) - 1 =0 D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 LEE AND JUNKINS: LAGRANGE'S EQUATIONS 1451 + l \"3|dV 4- v P4 v4 2B4 3)-i w2 equation: '2^-T=0dx\u00a3 w2(/2) equation: '3 \u00ab3 '\u00ab F d 04 \u2014 = \u00a32/2 = (dw2/dx2)\\/2 equation: 'o, C'4 UP4 -(K J/o, Ld? 4U47 4- V2\u00a347) - V4U48 - V2\u00a3| d*4 1\u0302 ,2 vv3 equation: = 0 w4 equation: P4 where w3 = w3 - w30 and w4 = w4 - w40. The constants \u0302 4{ and .B/ that are functions of the states related to the overall structure are presented in the Appendix. Summary and Conclusion In this paper, emphasis has been placed on the multibody case. An explicit version of the classical Lagrange's equations that cover a large family of multibody hybrid discrete distributed parameter systems is symbolically derived. The resulting equations can be efficiently specialized to obtain not only the hybrid governing integro-differential equations but also the associated boundary conditions. These resulting equations enable us to avoid the very tedious system-specific variational arguments and integration by parts. These equations can be generalized further to consider three-dimensional elastic solid bodies. 2 = - cos a, Appendix >| 1 ___ ... A 2 ___ ___ /3 D! ___ -y^ l?^ ___ 1 SI J \u2014\u2014 VV\\ } VT. J \u2014\u2014 I/j -t-* J \u2014\u2014 A} , JD J \u2014\u2014 1 v42 = \u2014 d, >12 = \u2014 vvi(/i) \u2014 Jt2cos a + w2sin a. A2 = -x2cos a 4- w2sin ce ^ = jc2a sin a + w2sin a -f w2o; cos a 4- JC20 sin o; 4- W20 cos of 52 = 1, B2 = l\\ - *2sin o; - W2cos a B2 = -;c2sin ce - w2cos o; ,62 = -JC2o; cos a. - W2cos a 4- w2a sin a - x26 cos ce + w20 sin o: B2 = \u2014 sin a, #! = \u2014 (a 4- 0)cos ce ^^ -0 Al = - Wi(/!) - /2cos o; + w2(/2)sin a - X3cos(a: + 0) A\\-~ /2cos a + w2(/2)sin o; + x3cos(a: + J3) + w3sin(o; y43 4 = /2o: sin a. + w2(/2)sin a + w2(/2)a cos a. + 120 sin o: + w2(/2)0 cos a - Xi(6t + /3)sin(a + j8) + w3sin(a + 0) + w3(\u00ab + /3)cos(a: + /3) - JC30 sin(a + /3) + w30 cos(o: ^43 5 = - cos a, 1\u03023 6 = (QJ + 0)sin a j + /j)sin(a /3)cos(a cos(a 30 cos(a = (a = /i - /2sin a - w2(/2)cos a + x3sin(a + /3) - w3cos(a + /3) l = -I2sma - w2(/2)cos o; + x3sin(ce + ]8) \u2014 w3cos(o; + /3) 3 4 = - /2ce cos a - w2(/2)cos a + W2(l2)a sin a - /20 cos a + w2(/2)^ sin ce + JC3(ce + /3)cos(a + ]8) - W3cos(o; + j8) + w3(o; + jS)sin(a + j8) + X30 cos(a + j8) + w30 sin(o: + /3) 53 5 = - sin a, \u00a33 6 = - (a + (9)cos a I - W3cos(o: + j8) w3(a 4- j8)sin(a + /3) + X30 cos(o: 4- j8) 4- w30 sin(ce + /3) ?| = -sin(a + |8), J?3 10 = - (a. 4- j8 4 = - Wi(/i) - /2cos a 4- w2(/2)sin a - x4cos(a 4- /3) D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08 1452 LEE AND JUNKINS: LAGRANGE'S EQUATIONS w2(/2)sin a. - *4cos(a: w4sin(a A4 = I2a sin a + w2(/2)shi a. + W2(l2)a cos a. + /20 sin a. cos a + X4(a + /3)sin(a + j8) + w4sin(o; + j8) 3)cos(a + 18) + x40 sin(a + j8) + w40 cos(a 4 = - cos a, ^i5 = (a + 0)sin a = w4sin(a w4(a + /3)cos(a: + j3) + x40 sin(a + j8) + w40 cos(o: 44 9 = - cos(a + 18), ^l]0 = (a + jS + (9)sin(oj + j8) i - /2sin a - w2(/2)cos a - JC4sin(o; + 0) - w4cos(a + /3) - /2sin a - w2(/2)cos o: - X4sin(a + j8) - w4cos(a + /3) - I26i cos a - w2(/2)cos o: + w2(/2)a: sin a. - /20 cos o; w2(/2)0 sin a - x4(a + /3)cos(a + j8) - w4cos(a + 0) w4(cx + /3)sin(a: + 18) - JC40 cos(a + j8) + w40 sin(a: ^4 = - sin a, #1 = - (d + 0)cos a ^4 = - JC4sin(a + j3) - w4cos(a j8) - w4cos(a: - x40 cos(a + j8) + w40 sin(o; 54 10 = - (a + j8 + 0)cos(a - /2cos a + w2(/2)sin a A\\ = - /2cos a + w2(/2)sin a l = I2ct sin a + w2(/2)sin a + w2(/2)a cos a: + /20 sin a + w2(/2)0 cos a Al = - cos a, A$ = (a + 0)sin a J?6 ! = 1, B\\-l\\- /2sin a - w2(/2)cos a B\\= - /2sin a - w2(/2)cos o: \u2014 \u2014 I2a cos ce - w2(/2)cos a + w2(/2)a sin a - /20 cos a + w2(/2)0 sin a B5 6= -sin a, #| = ~(0 + Acknowledgments This work was supported by the Air Force Office of Scien- tific Research under Contract F49620-89-C-0084 and by the Texas Higher Education Coordinating Board, Project 999903- 231. We are pleased to acknowledge productive discussions with the following colleagues: H. Bang, N. Hecht, Y. Kim, L. Meirovitch, Z. Rahman, S. Skaar, and S. Vadali. The technical and administrative support of S. Wu and R. Elliott is appreciated. References e, S., and Junkins, J. L., \"Explicit Generalizations of La- grange's Equations for Hybrid Coordinate Dynamical Systems,\" Dept. of Aerospace Engineering, Texas A&M Univ., Technical Kept. AERO 91-0301, College Station, TX, March 1991. 2Meirovitch, L., \"Hybrid State Equations of Motion for Flexible Bodies in Terms of Quasi-Coordinates,\" Journal of Guidance, Control, and Dynamics, Vol. 14, No. 5, 1991, pp. 1008-1013. 3Berbyuk, V. E., and Demidyuk, M. V., \"Controlled Motion of an Elastic Manipulator with Distributed Parameters,\" Mechanics of Solids, Vol. 19, No. 2, 1984, pp. 57-65. 4Low, K. H., and Vidyasagar, M., \"A Lagrangian Formulation of the Dynamic Model for Flexible Manipulator Systems,\" ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 110, June 1988, pp. 175-181. 5Pars, L. A., A Treatise on Analytical Dynamics, Cambridge Univ. Press, London, 1965, Chap. 2-4. 6Junkins, J. L., Rahman, Z., and Bang, H., \"Near-Minimum-Time Maneuvers of Flexible Vehicles: A Liapunov Control Law Design Method,\" Mechanics and Control of Large Flexible Structures, edited by J. L. Junkins, Vol. 129, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, 1990, pp. 565-593. 7Meirovitch, L., Computational Methods in Structural Dynamics, Sijhoff & Noordhoff, Leyden, The Netherlands, 1980. 8Hailey, J. A., Sortun, C. D., and Agrawal, B. N., \"Experimental Verification of Attitude Control Techniques for Slew Maneuvers of Flexible Spacecraft,\" AIAA Paper 92-4456, Aug. 1992. 9Junkins, J. L., and Bang, H., \"Maneuver and Vibration Control of Nonlinear Hybrid Coordinate System Using Liapunov Stability Theory,\" AIAA Paper 92-4458, Aug. 1992. D ow nl oa de d by C A R L E T O N U N IV E R SI T Y L IB R A R Y o n Ju ne 2 1, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 14 08" + ] + }, + { + "image_filename": "designv11_2_0003205_an9840901019-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003205_an9840901019-Figure1-1.png", + "caption": "Fig. 1. Lumincscence sampling system. (a) Side view of the system.", + "texts": [], + "surrounding_texts": [ + "Instrumental A Turner Model 430 spectrofluorimeter (Sequoia-Turner, Mountain View, CA) was used together with a laboratorybuilt chopper to discriminate phosphorescence from fluores- mm and (4) 11.1 mm Pu bl is he d on 0 1 Ja nu ar y 19 84 . D ow nl oa de d by M em or ia l U ni ve rs ity o f N ew fo un dl an d on 1 7/ 09 /2 01 3 19 :0 1: 05 . View Article Online / Journal Homepage / Table of Contents for this issue cence. Signals were acquired using a strip-chart recorder (Fisher Scientific, Fair Lawn, NJ). A 1-5-pl interchangeable microdispenser (Drummond Scientific, Broomall, PA) was utilised to apply 2-p1 samples on 6.4 mm diameter filter-paper discs. As shown in Fig. l(a) and ( b ) the versatile luminescence sampling system used in this study consists of a circular copper disc (108 mm diameter and 4.8 mm thick) on which 20 equally spaced concentric circular depressions had already been made (7.9 mm diameter and 1.6 mm depth). Twenty copper rings (6.4 mm inside diameter) were inserted into the depressions to hold the paper discs firmly in the right position for RTP observation. To the bottom of the copper disc a smaller diameter concentric hollow copper cylinder was welded to facilitate the conduction of a cold stream from liquid nitrogen to the copper disc and to the sample for low-temperature study. A specially fabricated Dewar flask was used to contain the liquid nitrogen. All the circular depressions on the copper disc were numbered and 20 corresponding much smaller diameter depressions on the rim of the copper disc were drilled to match a plunger set screw for the purpose of reproducibly positioning each sample for RTP measurements. The plunger set screw was positioned beside the sampling spot, which was nine depressions from the RTP observation spot as shown in Fig. l(b). A laboratory-built chopper [Fig. l(c)] was employed to screen fluorescence signals from phosphorescence signals. It has the same diameter as that of the sampling copper disc and was made to have a duty factor of 0.35, i.e., 35% of the chopper cycle spent on exciting the sample and another 35% on observing the emission of analyte, each followed by a delay of 15% of the cycle. A phosphoroscope controller and motor (SLM Instruments, Urbana Champaign, IL) were used to rotate the chopper at any desired speed. A chopper speed of approximately 16000 duty cycles min-1 was used which enabled the RTP observation of compounds with lifetimes ranging from 0.6 to 3 ms. An 11.1 x 15.9 mm front surface plane mirror and a 25 mm focal length concave front surface mirror (Edmund Scientific, Barrington, NJ) were positioned above the chopper to permit optical alignment of both excitation and emission radiations on to one sample spot and on to the photomultiplier tube (PMT), respectively. Reagents The analytical reference standard pesticide samples were kindly provided by the Environmental Protection Agency (EPA) and were used without further purification. Table 1 lists these pesticides. Potassium iodide, sodium bromide and sodium chloride (Fisher Scientific, Fair Lawn, NJ), lead acetate trihydrate (Mallinckrodt Chemical Works, New York, NY) and silver nitrate (J&S Scientific, Crystal Lake, IL) were of certified ACS, analytical-reagent and ACS crystal grades, respectively. MCB liquid-chromatographic grade acetonitrile (EM Industries, Gibbstown, NJ) was used as the solvent for the preparation of pesticide solutions. The heavy-atom solutions were prepared in water de-mineralised by a Nanopure Barnstead exchanger (Sybron). Ion-exchange filterpapers. DE-81 and P-81 (Whatman Chemical Separations, Clifton, NJ), were punched to give 6.4 mm paper discs and were used as received. Procedure A 2-pl sample solution and a 2-pl heavy-atom solution were delivered on to a paper disc that was located in one depression in the copper disc near the plunger set screw. If it was the only sample to be analysed, the sampling disc was rotated clockwise passing nine depressions to locate the sampled depression at the observation spot for recording RTP intensity. However, if more than two samples were available for analysis, they could be applied on to sample discs one by one at the sampling spot and RTP intensities were measured sequentially at the observation spot. All the sampling spots on the disc were continuously purged by a de-humidified nitrogen stream. Neither sample heating by infrared radiation nor an oven was needed to observe RTP as reported earlier.9 RTP signals were measured when the plateau time9 was reached for each sample. Results and Discussion Luminescence Sampling System The system worked very well for RTP measurements, although the reproducibility among different depressions was not very satisfactory. A relative standard deviation of 12-21 \"/A was obtained for RTP intensities when 140 pg ml-1 of p-aminobenzoic acid was added simultaneously to paper discs in different depressions. This may be due to slight differences in depression size and position. The fluorescence spectrum of 100 pg ml- 1 of biphenyl solution contained in a small copper cup (approximately 0.2 ml solution volume) has been observed with this system as well as the low-temperature phosphorescence spectrum of 120 pg ml-1 of p-aminobenzoic acid. Further investigations of this sampling system for obtaining low and room-temperature luminescence spectra are in progress. Analytical Figures of Merit of Pesticides Six out of 14 selected pesticides phosphoresced at room temperature as shown in Table 1. All six phosphorescent pesticides have limits of detection of 0.4-6 ng when DE-81 and iodide ion were used as the substrate and heavy atom, respectively. However, naphthaleneacetic acid (NAA) is the only pesticide that phosphoresced on the P-81 cationic exchanger with a good limit of detection. The rise, plateau and fall times and fall rates were measured as previously described.' The results show that these parameters are dependent upon the analyte. This fact partly explains the irreproducibility of the observed RTP signals at different times between different runs. However, as the fall rates of the pesticides studied are very small, as shown in Table 1, it is not that critical if RTP is observed within a certain period of time past the plateau time. The linear dynamic ranges of these pesticides, as listed in Table 1, show that the linear dynamic range values are two orders of magnitude or greater. The concentrations of sample solutions were in the range 1-100 pg ml-1, except for NAA. which was 0.1-100 pg ml-1. Sample volumes from 2 to 14 pl for each concentration of an analyte were applied to the substrates to obtain sample amounts from 2 to 1000 ng o r more for the linear dynamic range graphs. Amongst the 14 pesticides, bentazon, azinphos ethyl and propanil gave weak RTP signals, which may be enhanced by the use of an appropriate substrate and heavy-atom species and concentration. Low-temperature paper substrate phosphorescence reported by McCall and Winefordner27 may be used to study these pesticides without using any quartz apparatus if this luminescence sampling system is employed. Substrate Evaluation As shown in Table 2, the blank background signals of P-81 are much larger than those of the DE-81 paper substrate. An Pu bl is he d on 0 1 Ja nu ar y 19 84 . D ow nl oa de d by M em or ia l U ni ve rs ity o f N ew fo un dl an d on 1 7/ 09 /2 01 3 19 :0 1: 05 . Table 1. Analytical figures of merit of certain pesticides Compound\" . . Phenothiazine . 1-Naphthol . Warfarin . . . Asulam . . . Carbaryl . . . . . . . Structure H . . . p OH oH H C O C H ~ O H II I O-CC-N-CH~ b . . . LOD\u00a7I Heavy ng Rise Plateau Fall rate LDR kex./Aen,,-t atom$ (pg mi-') time1 time1 (fall tirne)l slope (range)ll 3341524 3341532 3251477 2801418 293/510 CH2COOH 300/507 I I - I- I I- I- 3.2 3.2-7.6 0.2Y0 1.03(2720ng) (7.6- 12.4) 12 12-7 3 - 0.98 (2 240) 11.5 11.5-22.5 0.17% 1.01 (>260) (22.5-25) 9.6 9.6-13.1 0.2% 0.9 (>50) (13.1-15.9) 9.3 9.3-29.5 0.09% 0.96 (2 200) (29.5-40.5) 6.9 6.9-13.5 0.2% 0.97 (b 200) ( 13.5-29) 13 13-16 0.07% 0.83 ( 3 240) ( 16-45) * No or low RTP signal observed for azinphos ethyl, bendiocarb, bentazon, captofol, carboxin, ethylon, folpet and propanil. t Wavelengths in nanometres. $ Concentrations used: I- (1 M ) and Pb2+ (1 M). Substrates used: DE-81 (I-) and P-81 (Pb*+). 9 Limit of determination. Signal to noise ratio = 3 and sample volume = 2 1.21 used for calculation. 1 See reference 9 for details. All values in minutes. 11 Linear dynamic range (LDR) is calculated by use of log(RP1) vs. log(abso1ute amount in ng). The linear regression programme in a TI-55 calculator was used to carry out the calculation. Ranges of LDR begin with the LODs to the amount shown in parentheses. ~ ~~~~ - inter-heavy atom background intensity comparison on P-81 gives Pb2f > Ag+ 3 no heavy atom and on DE-81 C1- > Br> no heavy atom > I-. Table 1 shows that NAA is the only phosphorescent pesticide on P-81 substrate. Although 1-naphtho1 and carbaryl have the same naphthalene main frame structure as NAA, their functional groups should play a very important role in the inducement of RTP. The P-81 results reported here are the first to demonstrate RTP enhancement by a cationic exchange paper. Its enhancement of the room-temperature phosphorescence intensities of cationic analytes and of analytes using cationic heavy atoms warrants a further study. Mixture Analysis Using Heavy Atom and Substrate Effects Table 3 shows the heavy-atom enhancement factors for the pesticides under investigation. There was no enhancement for NAA but low enhancement was observed for 1-naphthol (1 .O) and carbaryl (1.9) when C1- was used as the heavy atom. However, strong enhancement was observed for these pesti- Pu bl is he d on 0 1 Ja nu ar y 19 84 . D ow nl oa de d by M em or ia l U ni ve rs ity o f N ew fo un dl an d on 1 7/ 09 /2 01 3 19 :0 1: 05 . Table 3. Enhancement factors of several heavy atoms on DE-81 Intra-compound\" Inter-compound* Concentra- Enhancement factor Enhancement factor tion/ Compound pg ml-' I- Br- C1 I - Br-- C 1 ~ Carbaryl . . . . . . . . . . 100 21.5 6.1 1 41 .o 11.5 1.9 Naphthaleneacetic acid . . . . 120 4.1 1 .O (Negative 200.2 48.1 '1 -Naphthol . . . . . . . . 120 23.3 5.8 1 23.7 5.8 1 .0 Phenothiazine . . . . . . . . 120 1 .Y 1.5 1 79.0 65.0 42.0 - intensity ) Warfsrii: . . . . . . . . . . 130 2.4 2.1 1 43.4 27.2 13.0 A S U ~ ~ I I I . . . . . . . . . . 110 12.9 2.8 1 31 .0 6.6 2.4 * Concentrations of heavy atoms were 1 M for I- and Br- and 2 M \u20acor C1 . Intra-compound enhancement factors were calculated for and within each compound using the lowest phosphorescence intensity among three heavy atoms as unity; inter-compound enhancement factors were calculated for and among all compounds and heavy atoms using phosphorescence intensity of 1-naphtholiC1- as unity. la) 450 500 550 Wavelengthinrn 600 Fig. 2. Spectra of (1) mixture A; (2) phenothiazine; (37 1-naphthol: and 41 Spectra of mixtures A and B and their ure Components. (II r P 3 w n t hl:ank (h\\ Enc-rtr:i nf ( 1 ) miatiirp R . ( 7 ) n h p n n t h i ~ 7 i n r . !?) warfarin; (4) 1-naphthol; and ( 5 ) reagent blank. Substrate. DE-81; and heavy atom. I - cides using I- . These results suggest that compounds with a naphthalene main frame structure will present high and low RTP intensities if I- and C1- are employed as heavy atoms, respectively. Although 1-naphthol and phenothiazine have the same excitation wavelengths and very similar emission wavelengths, the huge difference in RTP enhancement by C1and Br- can be used to determine phenothiazine selectively. The spectra of I-naphthol and phenothiazine (both 60 pg ml-I) and their synthetic mixture A, using Br- as the heavy atom, are shown in Fig. 2(u) and show the above effect. This effect is also evident in the spectra shown in Fig. 2(b) for a mixture B consisting of 40 pg ml-1 of phenothiazine, 40 pg ml-1 of 1-naphthol and 43 1.18 ml-1 of warfarin and for the pure components at the same concentrations using C1- as the heavy atom. The total disappearance of the 1-naphthol signal helps in analysis of the other two components. It is also worthwhile pointing out that the summation of the RTP intensities of the three components matches that of the mixture intensity. Based on this observation it should be feasible to carry out quantitative analysis of the mixture using simultaneous equations. Quantitative analysis of mixtures of various numbers of components is now under investigation by the use of this approach in this laboratory. To use this approach for mixture analysis the possibility of spectra shifting in position or intensity as recently reported by Seybold et ~ 1 . 2 8 for fluorescence should be ruled out. The RTP enhancement of NAA on P-81 has also been used to determine NAA in a six-component mixture C, and the spectra obtained are shown in Fig. 3. The concentrations of the components are NAA 20 pg ml-1, phenothiazine 20 pg ml-1, 1-naphthol 20 pg ml-1, warfarin 21.7 pg ml-1, asulam 18.3 pg ml-1 and carbaryl 16.7 pg ml-1. The concentration of pure NAA in Fig. 3 is 120 pg ml-l. Conclusions Heavy atoms and substrates can be employed for the qualitative analysis of mixtures using the selectivity they impose on different analytes. Various solid substrates and heavy atoms are available for this purpose. Quantitative analysis of the mixture, however, will also be feasible when the reproducibility of the sampling system has been improved. It is also desirable and essential to study the relationship between compound structure and RTP signal enhancement by heavy atoms and substrates. Based on such information, it may be possible to predict whether an analyte will phosphoresce using different heavy atoms and substrates. The versatile luminescence sampling system reported here will facilitate the continuous observation of RTP signals of analytes on paper disc, powder, particle and inorganic compound plate7 substrates. Despite the fact that measurements of RTP signals should be made within the plateau times of the analytes, the analysis time will be shortened as this Pu bl is he d on 0 1 Ja nu ar y 19 84 . D ow nl oa de d by M em or ia l U ni ve rs ity o f N ew fo un dl an d on 1 7/ 09 /2 01 3 19 :0 1: 05 . sampling system does not have to be removed and relocated during sampling and measurement processes. It seems feasible to identify an analyte based on its rise, plateau and fall times and fall rate because different values have been obtained for different analytes. The phosphorescence intensity of an analyte should be acquired during the plateau time in order to obtain more reproducible data for quantitative analysis. The authors thank Dr. J . D. Winefordner and co-workers at the University of Florida for leading us into this study and their constructive suggestions. The authors also thank EPA for providing analytical reference standard pesticides for this study. The present work was supported by the Grants-in-Aid Program for the Faculty of Virginia Commonwealth University. 1. 2. 3. 4. 5 . 6. 7. 8. 9." + ] + }, + { + "image_filename": "designv11_2_0000400_jsvi.2001.3570-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000400_jsvi.2001.3570-Figure6-1.png", + "caption": "Figure 6. Simpli\"ed model of the rotor: (a) location of the disk, (b) bearing sti!ness.", + "texts": [ + " It is easy to show that the unbalance response will be obtained as Md u (t)N\"Re(Mz 0 N e*Xt ), (52) where Mz 0 N is a constant vector with complex elements, de\"ned as the solution of the algebraic system ([K]!X2[M]#iX[C])Mz 0 N\"M 0 are chosen such that k1 = k01 + supx 2<( sinx1)g=(x1l 2)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000853_s0010-938x(03)00098-2-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000853_s0010-938x(03)00098-2-Figure2-1.png", + "caption": "Fig. 2. Schematic illustration of the designed structure.", + "texts": [ + " Argon as the shielding gas was used to protect the welding zone from oxidation at high temperature. Pulse width of 4, 7 and 12 ms were adopted, respectively. Welding speeds were between 160 and 260 mm/min. The reflectible characteristic of the laser beam makes it possible to deflect its traveling direction and realize welding of the inner wall of sleeve. Laser beam is a high energy density power and can produce deep penetration. So it can penetrate the sleeve and weld it with the tube. The designed welding equipment is illustrated in Fig. 1. Fig. 2 shows the designed structure. In the structure, the sleeve is concave so that it is easier to be deformed in the axial direction. The C-ring test specimens were prepared under ASTM G 38-73 code [13]. The dimension of C-ring machined from the tube was as follows; Outer diameter of 22.2 mm, thickness of 2.4 mm, width of 19 mm as shown in Fig. 3. Two holes were drilled to compress the C-ring by bolt and nut. The procedure for corrosion test is important because corrosion of heat exchanger tubes occurs mainly as stress corrosion caused by many factors" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000036_bf02481128-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000036_bf02481128-Figure1-1.png", + "caption": "Fig. 1 Neuro-musculo-skeletal model", + "texts": [ + " Based on this concept, we structured a neuro-musculo-skele ta l model closely approxi- These models can be expressed as a total of 64 nonlinear, first-order differential equations: 28 equations of motion for the musculo-skeletal system, and 36 equations for the nervous system. A walking movement can be obtained numeri: cally by calculating these equations. The shape of the body and the pattern of movement of this model are evolved by an evolutionary algorithm. mating the actual body structure of humans, as illustrated in Fig. 1 (see Yamazaki et a l . 7 for details). The shape of the human body was modeled as two, two-dimensional models: 10 rigid links representing the feet, calves, thighs, pelvis, upper torso including the head, and upper extremities in the sagittal plane, and two rigid links representing the pelvis and the upper torso in the horizontal plane in order to reproduce rotation at the waist. The principal 26 muscles involved in movement in the shoulder, waist, and lower extremities were also modeled. Each joint is driven by the moment due to muscular tension, and is also affected by the nonlinear viscous and elastic moment representing soft tissues such as ligaments" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001063_s0963-8695(03)00046-x-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001063_s0963-8695(03)00046-x-Figure8-1.png", + "caption": "Fig. 8. Mapping of the Barkhausen noise level on the loading zones of 90,343 bearing inner rings after engine operation.", + "texts": [ + " This homogeneity means that both the pre-stress treatments prior to engine operation and the load distribution on the inner ring during engine operation were homogeneous. Figs. 8 and 9 represent the mappings of inner rings 90,343 and A244 ,respectively. The level of BN, and consequently the stress level, is neither homogeneous nor uniform in the transverse direction of the raceways of these two rings. This lack of homogeneity and uniformity probably comes from a heterogeneous distribution of the loads on these inner rings during engine operation. On mapping in Fig. 8, the load must have been located essentially at the top of raceway, between 10 and 13 mm, whereas mapping in Fig. 9 shows the load situated between 2 and 5 mm. This second load, however, must have been less important than the previous one, given that the Barkhausen level is higher. Clearly, the loads on the ring introduce compressive stress, which has the effect of reducing the level of BN. These mappings allowed us to discover a significant asymmetry in the surface stress distribution of the loading zone, which explains the difference between the localized X-ray diffraction measurements and the Barkhausen estimations presented in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001152_tcst.2002.806455-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001152_tcst.2002.806455-Figure3-1.png", + "caption": "Fig. 3. Backlash model.", + "texts": [ + " In fact, introducing the reference variable and the tracking errors , , , the following sliding surface can be considered: Defining and on the basis of quantities , analogous to (12) and (13), a theorem similar to Theorem III.1 can be proved. In this section, it is considered the plant (1) having a backlash nonlinearity in the actuator and dead-zones in sensors. The following model of backlash [21], [23], equivalent to (4), will be used for design in the following. Define as the set of states of the backlash model, i.e., the set of all the points in or between the lines of slope (see Fig. 3). For any point at any time define two functions : and : (30a) (30b) The characteristic of backlash can be defined as follows: for any state at any time and for any input monotone over the output is given by (31) according to whether is monotonically increasing or decreasing, respectively. Therefore, for any initial state, at any time and for piecewise continuous input , the backlash output is uniquely determined. Define the following quantities: (32) Under Assumption II.2, a minimum value for and a maximum value for can be found in the time interval " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000469_2000-gt-0354-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000469_2000-gt-0354-Figure2-1.png", + "caption": "Figure 2. Typical bearing cross section.", + "texts": [ + " This platform consists of a Clark 1M6 compressor, that has been de-staged by removing four of the six stages, direct driven by a 130 Hp, 15000 rpm, variable speed motor. Past platforms have used lubrication fluids such as water, water/glycol, and currently Chevron light turbine oil (GST ISO 32). Another compressor platform will be completed in 2000 that will use water as the lubricant. The fluid control bearing is an active externally pressurized (hybrid hydrostatic) bearing that uses fluid forces to compensate for rotor related forces. It consist of a one or two part bearing, Fig. 2, which supports the rotor loads, position sensing eddy current transducers, high speed electrohydraulic valves, and a controller, Fig. 3. The bearing is a four pocket design that has adequate pocket areas 1 Copyright \u00a9 2000 by ASME rms of Use: http://www.asme.org/about-asme/terms-of-use Dow to perform active and static load support, and enough default surface area to allow for fault conditions. The position sensors are standard Bently Nevada eddy current displacement probes that measure both the static and dynamic position of the rotor relative to the stator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003350_tcst.2005.859639-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003350_tcst.2005.859639-Figure1-1.png", + "caption": "Fig. 1. Shape-change actuator arrays on an aircraft wing [7].", + "texts": [ + " In this section, we give an introduction of morphing aircraft and actuators. Then, we present a nominal feedback control design as well as its implementation with morphing actuators, and develop a new model of morphing actuator failures. Morphing aircraft use small shape-change effectors (called \u201cmorphing actuators\u201d) in large numbers to fulfill flight control tasks without flap. A representative of morphing aircraft is the innovative control effector (ICE) aircraft [7], whose wing span is depicted in Fig. 1. The distributed arrays of shape-change devices were chosen to compose the effector suite for the ICE configuration. The effector suite under study includes four arrays on each wing: three on the upper surface and one on the lower surface. There are totally 156 individual devices, 78 per wing on the entire suite of shape-change actuator arrays. The upper-surface leading-edge (ULE) array consists of 10 devices, the lower-surface trailing-edge (LTE) array and upper-surface trailing-edge (UTE) array both consist of 22 devices, and the upper-surface wingtip (UTip) array consists of 24 devices" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001769_tmag.2003.810533-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001769_tmag.2003.810533-Figure7-1.png", + "caption": "Fig. 7. Segmented stator.", + "texts": [ + " 6 illustrates the measured roundness errors for each tooth, averaged over the axial length of the stator core. We see that the second-order spatial deformation of the stator core is dominant and the maximum roundness error is about 20 m. Substituting the values of shown in Fig. 6 into (8) and calculating the cogging torque waveform, we find that the peak-to-peak amplitude of the superposed cogging torque is about 0.028 Nm. This roughly agrees with the measured one illustrated in Fig. 3. Next we investigate a brushless PM motor with an Nd\u2013Fe\u2013B ring PM rotor. It is again a 10-pole, 12-slot motor. Fig. 7 depicts the fabrication process of the segmented stator of the second test motor. The back yoke consists of small laminated pieces which are stacked like bricks, and if the core configuration in the cross sections , , , and is rotated by rad with respect to the motor axis, it becomes identical to that in the cross sections , , , and . Fig. 8 shows the stator and rotor for the test motor ( mm, mm). The whole stator core is tightened together firmly by an aluminum frame. The rotor has a radially oriented sintered Nd\u2013Fe\u2013B ring PM with T, whose magnetization distribution is unknown", + " 11(b), the measured magnetic flux densities agree very well with those computed from the optimal . According to , we see that about 70% of the pole-pitch is fully magnetized and the rest of it is roughly half-magnetized. The predicted Hall sensor position is also reasonable. The amplitudes of air-gap magnetic field harmonics computed with the FEA using the minimization result are as follows: T, T, T, and T. From these, we have T and T for the ring PM rotor. Fig. 12 shows profiles of the measured roundness errors in the first two cross sections and , shown in Fig. 7, of the second test motor. We note that both profiles have rad rotational symmetry and that if either of them is rotated by rad, then they are almost identical to each other. For other pairs of adjacent cross sections and where , pairs of roundness errors similar to those shown in Fig. 12 are also obtained. These distinctive features of the roundness errors can be inferred as resulting from a circumferentially uneven compressive force, possibly having rad rotational symmetry, due to the thermal stress in the aluminum frame, whose cross section has the same symmetry as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002712_tie.2004.825370-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002712_tie.2004.825370-Figure2-1.png", + "caption": "Fig. 2. Input and output variables of the induction motor.", + "texts": [ + " If the vector control is fulfilled such that -axes rotor flux can be zero, and -axis rotor flux can be constant, the electromagnetic torque is controlled only by -axis stator current from (9), and we have (14) (15) (16) (17) Substituting (14)\u2013(16) into (3) and (11)\u2013(13) yields (18) (19) (20) (21) where is the time constant of the rotor. III. PROPOSED CONTROL SCHEME The proposed sensorless control scheme is based on the current estimation without the flux and speed estimations. An induction motor may be considered as a multivariable input/output system as shown in Fig. 2. In this system the input variables are the stator voltages and are modulated through the electrical and mechanical parameters, and the output variables are the stator currents and rotor speed. The voltages and currents in Fig. 2 are the quantities in the stationary reference frame fixed to the stator. The voltage equations in the stationary reference frame are (22) where is the differential operator. Fig. 3 shows a model where the input and output variables are newly established. The subscript denotes the variable of the model, and is the command rotor speed of the model. From the induction motor of Fig. 2 and the model of Fig. 3, the following inference is possible. If both the stator currents of the motor and model are forced to be the same in the case where both the stator voltages are the same, the motor speed becomes the same as the model speed which is the speed command. In other words, if and in the case of and , then . Substituting into the reference frame with the synchronously rotating speed yields the following. If and in the case of and , then . The above relations may be mathematically described in terms of the quantities of the synchronously rotating reference frame described in Section II" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003592_physreve.75.031701-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003592_physreve.75.031701-Figure2-1.png", + "caption": "FIG. 2. The fiber geometry used in our stability analysis. The fiber has length L, outer radius R, and inner cutoff radius rc, where the smectic properties are assumed to break down. This model shows the layered structure consisting of concentric smectic layers which are essential for fiber stability.", + "texts": [ + " Regarding their fiber stability, our experiments showed that SmAP materials do not form stable fibers; SmCP can form both films and bundle of fibers, whereas the B7 materials form single and bundles of fibers, but they do not form freestanding films. Throughout our model, we assume a very simple smectic structure consisting of concentric cylindrical layers running through the entire length of the fiber L and from the outer radius R of the fiber to some defect core radius rc . This very simple model is shown in Fig. 2, and although not noted in the figure, the cylindrical coordinate system that we will be working in is as follows: r\u0302 pointing radial from the fiber center, z\u0302 pointing along the fiber long axis, and \u0302 being mutually perpendicular to r\u0302 and z\u0302 such that r\u0302 \u0302= z\u0302. With this coordinate system, we assume that the smectic layer normals lie along the radial coordinate r\u0302. Although the geometry is simple, we allow the formation of the general double-tilted SmCG phase characterized by nonzero polar and azimuthal angles and , respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003569_ijvd.2007.012304-Figure19-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003569_ijvd.2007.012304-Figure19-1.png", + "caption": "Figure 19 Mesh angle between sleeve and clutch gear", + "texts": [ + " The mesh module, which was constructed for simulating the possibilities of mesh processes between the sleeve and the clutch gear, simulates the synchroniser after the sleeve moves until arriving x = 0 to the end of shifting. The module will change the angle between the sleeve and the clutch gear, which is y in Figure 9, for analysing different mesh situation; here assumes the probability of all these angles are equal, which is random in reality. m , which is the mesh angle between the sleeve and the clutch gear defined in Figure 19, sets for simulating different possibility in this module. The angle will be set from 80 to 90\u00b0 on simulation because the angle between splines on sleeve is 10\u00b0. For simulating mesh module, m was set from 80\u00b0 to 90\u00b0 with an interval of 0.25\u00b0 and the calculation interval for mesh module is 0.00001 sec. Figure 20 shows the movements of the sleeve in different mesh angles, which bring out different shifting times. These curves show that the sleeve moves in different ways at different mesh angles. Certain mesh angles lead into the forward and backward movements of the sleeve, but the sleeve only moves forward at some mesh angles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001773_tra.2003.814497-Figure17-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001773_tra.2003.814497-Figure17-1.png", + "caption": "Fig. 17. A mixed-variable formulation.", + "texts": [ + " The compatibility equation is used to represent the relation between the side step and the direction field across the grain boundaries in a certain discretized form. The sweeping time must be expressed with such discrete variables. And then, we use various techniques in mathematical programming to solve this mixed-variable type of optimization problem. In this case, we use only the fastest sweep principle to reduce the number of independent variables. Other principles are not invoked directly. Of course, the problem is computation intensive, and we will be satisfied with certain improvement in the performance. Fig. 17 shows the proposed search space for a planar surface, and it also shows well the discrete version of compatibility. 3) Approaching From Continuous Vector Fields: We may even search for a continuous vector field, ignoring the discontinuity of the optimal solution hoping that a continuous vector field could approach the solution within a certain resolution (in finitely many steps). In this case, finding the (best) continuum boundaries with a given vector field emerges as an auxiliary problem. The algorithms for extracting the vector field topology and vector field modeling are related closely to this problem, but not directly [78]\u2013[80]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000733_70.795797-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000733_70.795797-Figure7-1.png", + "caption": "Fig. 7. Basis vectors of internal force subspace. (a) First column vector. (b) Second column vector. (c) Third column vector.", + "texts": [ + " It will be useful, however, for 2-D grasping in a plane. An example is shown in Fig. 6. (a) (b) A minimal dimensional representation of the internal force for this case is given by e12 0 d23e e21 e23 (d12 + d23)e 0 e32 d12e k12 k23 k (8) where d12 is the distance between C1 and C2; d23 is that between C2 and C3; e is the unit vector on the horizontal plane and normal to the straight line L, and k is a real number. The column vectors of the matrix in (8) are a set of basis vectors of the internal force subspace (see Fig. 7). Note that, although the first two basis vectors can be interpreted as the axial forces of the virtual truss, the last one cannot. Actually the last vector involves the three contact points and plays an important role in grasping. A method to express the last column vector by axial forces of members is to consider a fictitious contact point CF 4 that does not lie on line L, and add a joint and three line members to the original truss model as shown in Fig. 8. This will be called the augmented virtual truss", + " Since the four points are not collinear, there exists a set of nonzero real numbers fq1; q2; q3g such that e41q1 + e42q2 + e43q3 = 0: (9) On the other hand, the constraint at the fictitious contact point CF 4 is that the contact force at this point is zero e41k41 + e42k42 + e43k43 = 0: (10) Using this augmented truss model, we can show that a representation of the internal force is given by e12 0 e14q1 e21 e23 e24q2 0 e32 e34q3 k12 k23 k14=q1 (11) for any position of CF 4 as long as CF 4 is not on line L. The basis vector corresponding to the third column vector is shown in Fig. 9. Note that Fig. 7(c) corresponds to the case where CF 4 is taken at the infinity point on the straight line normal to line L. We next consider the case of four-fingered hands. Under the condition that the four contact points are not coplanar, the truss model given by Fig. 10 is rigid and statically determinate. This implies that the set of all unit axial forces constitutes a basis of internal force space. Hence the internal force can be represented by f I =Ek (12) E = e12 e13 e14 0 0 0 e21 0 0 e23 e24 0 0 e31 0 e32 0 e34 0 0 e41 0 e42 e43 (13) k = [k12 k13 k14 k23 k24 k34] T : (14) Ponce et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure1.21-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure1.21-1.png", + "caption": "Fig. 1.21. Fatigue of a structural member at the notch root", + "texts": [ + "20, this method counts each stress-strain hysteresis loop consecutively, and is reputed to be the most rational counting method in analyzing fatigue failures. (C) Crack initiation life and crack growth life Fatigue fracture of metal progresses through the process of crack initiation and its growth (propagation). When the crack growth process of machine components or structure members can be checked at periodical inspections, the crack initiation may be allowed. Of course, there can be many structures where any crack initiation is never permitted. The methods of estimating crack initiation life from a notch root and growth life are described. Figure 1.21 gives a schematic illustration of fatigue process starting from a notch root of a component. Even if repeated stress might be within elastic stress range in nominal stress, it can be sometimes realized that a plastic zone due to stress concentration can be actually formed around the notch root, where plastic strain occurs repeatedly. Then, the fa- 1.2 Functions and Qualities for Springs and Spring Material Selection 35 tigue crack initiation life at the notch root can be regarded as the low cycle fatigue life of plain specimens with no notches" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000552_308-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000552_308-Figure8-1.png", + "caption": "Figure 8. Revolution and subsequent oscillation of a pendulum with friction (Q = 20) excited from the equilibrium position with an initial angular velocity of = 2.3347\u03c90.", + "texts": [ + " The exact value of is slightly greater since the motion towards the inverted position occurs in the phase plane close to the separatrix but always outside it, with the angular velocity of a slightly greater magnitude. Consequently, the work of the frictional force during this motion is a little larger than the calculated value. For example, with \u03d50 = 0 and the quality Q = 20, the above estimate yields = \u00b12.098\u03c90, but a more precise value of determined experimentally by trial and error is \u00b12.101\u03c90. Figure 8 shows graphs of \u03d5(t) and \u03d5\u0307(t) and the phase trajectory for a similar case in which the initial angular velocity is chosen exactly to let the pendulum reach the inverted position after one revolution. The free oscillation and revolution of a rigid pendulum have been investigated on the basis of a simple theoretical approach, aided by a computerized experimental exploration with the help of the software package [1]. These simulations provide a good background for the study of more complicated nonlinear systems like a pendulum whose length is periodically changed, or a pendulum with the suspension point driven periodically in the vertical direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001467_978-94-015-8192-9_14-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001467_978-94-015-8192-9_14-Figure1-1.png", + "caption": "Fig. 1. Planar and Spherical Double-Triangular Parallel Manipulators", + "texts": [ + " The kinematics of sev eral planar parallel manipulators was investigated by Gosselin and Angeles (1990), Hunt (1983) and Gosselin and Sefrioui (1991). Spherical parallel manipulators constitute an important type in that they find applications in robotic wrists and other devices used to orient rigid bodies. The kinematics of a few spherical parallel manipulators was investigated by Gosselin and Angeles (1989, 1990), Craver (1989) and Gosselin et a1. (1992a, 1992b). In this paper we introduce first a new class of parallel manipulators in two versions, planar and spherical, as shown in Fig. 1. Similar to the double tetrahedron mechanism, which was investigated by Tarnai and Makai (1988, 1989a, 1989b) and Zsombor-Murray and Hyder (1992), these two manipula tors consist of two bounded rigid bodies whose bounding edges are in con tact. The geometric model of a planar 3-dof double-triangular (DT) device consists of two triangles. These triangles move with respect to each other such that each side of the moving triangle intersects a corresponding side of the fixed triangle at a designated point defined over that fixed side", + " Moreover, a second spherical triangle, labeled QIQ2Q3, likewise referred to as Q, is defined. Furthermore, the side P2P3 of P, arbitrarily regarded as the FT, intersects the arc Q2Q3 of Q, regarded as the MT, at point R 1 \u2022 We denote by R2 and R3 the other intersection points, that are defined correspondingly. Moreover Ri, for i = 1,2,3, cannot lie outside its corresponding vertices. Thus, feasible or admissible motions maintain Ri within edges Qi+l Qi-l and Pi+1Pi-l, for i = 1,2,3. Thus, the motion of triangle Q can be described through the arc lengths Pi of Fig. 1b, or actuator coordinates, for i = 1,2,3. Likewise, the Cartesian coordinates of the moving triangle Q are the set of variables defining its orientation. Note that the Cartesian coordinates of the three vertices of Q can be determined once its orientation is given. Similar to the direct kinematic problem of the planar mechanism, the same problem, as pertaining to the spherical mechanism, may be formulated as: Given the actuator coordinates Pi, for i = -I, 2, 3, find the Cartesian coordi nates of the vertices of triangle Q", + " The real negative solutions lead to the same configurations of the positive ones with the exception that the sides of the triangle n, d, e and f, are replaced by another triangle with the same vertices RI R2R3 , but different sides, namely, 27r - d, 27r - e and 27r - f. Then, the negative solutions are discarded. The upper bound for the number of real positive solutions of a polynomial is given by Descartes theorem, namely, The number of real positive solutions of a polynomial is given by the number of change of signs of the coefficients ko, kt, ... , kn minus 2m, where m~ o. The maximum number of changes of sign in the foregoing polynomial is eight. Therefore, the problem leads to a maximum of eight real positive solutions and, as a result, triangle Q of Fig. 1b admits up to eight different orientations, for the specified values of PI, P2 and P3. 3.2. EXAMPLE Consider the spherical triangles P and Q given as: QIQ2 = 60\u00b0 PI P2 = 70\u00b0 Q2Q3 = 70\u00b0 P2P3 = 58.6\u00b0 Q3QI = 50\u00b0 P3PI = 81.5\u00b0 and three points, RI, R2 and R3 , located by the three values PI = 10\u00b0, P2 = 49.5\u00b0 and P3 = 40\u00b0. These values correspond to the angles D2, E2 ~nd F2 given below: D2 = 43.4745\u00b0, E2 = 37.9120\u00b0, F2 = 106.7287\u00b0 Equation (32) is solved for Xl. The solutions are shown in Table 1. For this particular problem, we were able to find two real positive solutions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001167_demped.2003.1234568-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001167_demped.2003.1234568-Figure2-1.png", + "caption": "Figure 2. Dimensions and frequencies related to the characteristic Fault frequencies.", + "texts": [ + " The frequencies at which these components occur are predictable and depend on which surface of the bearing contains the fault; therefore, there is one characteristic fault frequency associated with each of the four parts of the bearing 121. The majority of the bearing-related condition monitoring schemes focus on these four Characteristic fault frequencies. These frequencies are: FIw = inner race fault frequency, FoW = outer race fault frequency, Fcr = cage fault frequency, and F ~ F = ball fault frequency. A thorough derivation of these frequencies is presented in [3]. The four characteristic fault frequencies are defined in (1)- (4) and illustrated in Fig. 2 where FR is the speed of the rotor, N E is the number of balls, DE is the ball diameter, and Dp is the ball pitch diameter. The angle 6 i s the ball contact angle; this is the angle between the centerline of the bearing and XRHL, which indicates the direction of the force that the rolling elements exert on the outer race. (3) D, cos(@) 2 The characteristic fault frequencies are the result of the absolute motion (vibration) of the machine. The stator current is not affected by the absolute motion of the machine, but rather by a relative motion between the stator and rotor (i " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000204_a:1007939823675-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000204_a:1007939823675-Figure5-1.png", + "caption": "Figure 5. A planar mobile manipulator system with two-link manipulator.", + "texts": [ + " Equation (37) together with Equation (32) constitute (2n \u2212 m) first-order nonlinear differential kinematic equations with n unknowns for qi and (n\u2212m) unknowns for he,i. Because the differential equations involved are basically of the same form as obtained in the previous section, the motion trajectory set and the commutation configurations can be obtained through the same procedure as described in Subsection 3.2. In this section a series of simulations are performed for a planar mobile manipulator system with a two-link planar manipulator mounted on a platform as shown in Figure 5. The end effector of the mobile manipulator moves in the (x, y) plane. The kinematic equation of the mobile manipulator is given by Xe = x+ d cos(\u03d5) + l1 cos(\u03d5+ \u03b81) + l2 cos(\u03d5+ \u03b81 + \u03b82) (38) Ye = y + d sin(\u03d5) + l1 sin(\u03d5+ \u03b81) + l2 sin(\u03d5+ \u03b81 + \u03b82) where l1 and l2 represents the length of each link, and d represents the distance from the center of the platform to the base frame of the manipulator. In the simulation, we set l1 = 0.5 m, l2 = 0.3 m, d = 0.25 m. JINT1344.tex; 6/02/1997; 12:18; v.5; p.12 From Equation (38), the Jacobian matrix is given by J = [ 1 0 \u2212ds\u03d5 \u2212 l1s\u03d51 \u2212 l2s\u03d512 \u2212l1s\u03d51 \u2212 l2s\u03d512 \u2212l2s\u03d512 0 1 \u2212dc\u03d5 \u2212 l1c\u03d51 \u2212 l2c\u03d512 \u2212l1c\u03d51 \u2212 l2c\u03d512 \u2212l2c\u03d512 ] (39) where the variables with subscripts are defined as s\u03d5 = sin(\u03d5), s\u03d51 = sin(\u03d5+ \u03b81), s\u03d512 = sin(\u03d5+ \u03b81 + \u03b82), c\u03d5 = cos(\u03d5), c\u03d51 = cos(\u03d5+ \u03b81), c\u03d512 = cos(\u03d5+ \u03b81 + \u03b82)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000762_tac.2000.880989-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000762_tac.2000.880989-Figure1-1.png", + "caption": "Fig. 1. Robot with trailers.", + "texts": [ + "railers, based on differential flatness and significantly more efficienct than former methods. Index Terms\u2014Differential flatness, nonholonomic path planning, obstacles, robot, trailer. I. INTRODUCTION The system considered in this paper is composed of a mobile platform with two driving wheels and a number of trailers, each trailer being hooked up on top of the wheel axis of the previous one (Fig. 1). This is typically a nonholonomic system [1], [4]. It has been proven small-time locally controllable [2]. This paper presents an effective steering method that accounts for small-time controllability, providing paths the length of which tends to zero when the goal configuration tends toward the initial configuration. Accounting for small-time controllability is a critical issue for nonholonomic motion planning in the presence of obstacles [3]. Several steering methods have been investigated for then-trailer mobile robot system being considered", + " In Section IV,we giveexperimental results dealing with obstacle avoidance and which are applied to the mobile robot Hilare pulling a trailer (Fig. 2). Manuscript received January 4, 1999; revised June 30, 1999. Recommended by Associate Editor, O. Egeland.This work was supported in part by ALCATELTELECOM. The authors are with LAAS-CNRS, 7 avenue du Colonel Roche, 31077 Toulouse, France (e-mail: florent@laas.fr; jpl@laas.fr). Publisher Item Identifier S 0018-9286(00)02154-1. II. FLATNESS PLANNING AND TOPOLOGICAL PROPERTY The system we consider (Fig. 1) is composed of a two driving wheel mobile robot towing n trailers. Pk; k denote the center and orientation of trailer k, which is connected to trailer k 1 at Pk 1. We assume that the angle between two consecutive trailers 0018\u20139286/00$10.00 \u00a9 2000 IEEE is bounded by k+1 k < =2 and denote by C the part of the configuration space satisfying these inequalities. The differential flatness of the system states that along a path, the configuration can be reconstructed using only the path Cn. of Pn in the plane" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002988_bf01244839-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002988_bf01244839-Figure5-1.png", + "caption": "Fig. 5. Wall-jet cell arrangements employing a commercial electrode body (Philips IS-560). 1 ISE; 2 ion-selective membrane; 3 reference electrode; 4 bore for the continuously flowing junction: 5 jet; 6 outlet", + "texts": [ + " The BME-44 electrode was tested both in a commercial clinical analyser (Horiba Sera 210 Na+/K + Ionanalyzer) and in a home-made flow-injection system optimized for biological applications. Horiba Ltd., Kyoto, Japan, is the first company distributing potassium analysers incorporating a BME-44 membrane in a specially designed, low-volume flow-through cell. The flow-injection manifold consisted of a peristaltic pump (LKB 12000 Varioperpex, Sweden), a pneumatic loop injector with a 50-/ll loop (Labor MIM OE-320, Hungary) and a small effective volume macro wall-jet cell [6] (Fig. 5). The dispersion tube was a coiled 2 m length of Teflon tube (bore 0.5 ram). The carrier solution, 1 or 10 mM KCl in 1 mM MgC12 and 25 mM TRIS (pH 8), had a flow-rate of 1.7 ml/min. EMF measurements were made with a digital pH meter (Radelkis OP-211/1) and the signal was recorded by an Omniseribe D 5000 x- t recorder. E. Lindner et al. Synthesis of the lonophore 2.2'-Bis [3,4-( 15-crown-5 )-2-nitrophenylcarbamoxymethyl] tetradecane (BME-44) [8] NO2 HOCH 2_CI_CH20H J NO2 + ~ NHCOOCH2 C(CH3)C12H26 ~,~ 3 \" v ~ NCO C12 H25 12 [ II III chloride was allowed to react at room temperature for 2 h" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001463_70.585907-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001463_70.585907-Figure7-1.png", + "caption": "Fig. 7. The range of depends on object shapes.", + "texts": [ + " \u2022 for a vH -eF type of PC, F TH = F Te Ttrans(0; y) Trot( ) H T 1 v 0 < y < le \u2022 for an eH-eF type of PC, F TH = F Te Ttrans(0; y) Trot( ) H T 1 e 0 < y < le + le \u2022 for an eH-vF type of PC F TH = F Tv Trot( ) Ttrans(0; y) H T 1 e le < y < 0 where Ttrans( ; ) and Trot( ) denote 3 3 homogeneous transformation matrices for translation and rotation, respectively, and and y are variables. These constraints show that although there are uncertainties in the locations of H and F , if a PC is formed between H and F , the relative location FTH has only one or two degrees of freedom. Note that the overlap constraints are the constraints on the ranges of y\u2019s. Whereas, the constraints on the ranges of \u2019s are the nonpenetration constraints, which are difficult to formulate in general terms because they depend on specific shapes of H and F (see Fig. 7 for examples). The nonpenetration constraints are handled in the second step of the two-step approach presented in Section III. Before we present the constraints and derivation in detail, let us describe how we approach the derivation and define the kinds of constraints to be expected. 1) General Analysis: Clearly, the coexistence of two PC\u2019s require the right-hand sides (RHS) of their two corresponding equality constraints to be equal, which provide a new 3 3 matrix equation E in terms of the free variables in the equality constraints of the individual PC\u2019s (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000755_robot.1996.509174-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000755_robot.1996.509174-Figure6-1.png", + "caption": "Fig. 6 Rolling contact", + "texts": [ + "1), each finger does not slide on the object surface. Note that the assumption (3.1) is the key difference from section 2. We use the same coordinate frames C, and C i defined in section 2. A spring along the axis y, is required 3.2. Compression of virtual springs We will derive the potential enerb? of the grasp system. So, the compression 6,, and 6, due to the object displacement will be investigated. By assumptions (3. I ) and (3.2), the positions of the object and the i-th finger move as shown in Fig. 6 when the infinitesimal translation (x, , y, ) and rotation <, occur. The following equations are obtained from geometric constraints. ii, +r , +6,, = x , + ( R I + r , ) c o s a , , a,,, = y , + ( R ! + r , ) s i n a , , rial = / ? , (y a sequencr 0 1 I)-II tr iri tsformat.ions delini Iig tlie k i i i ei i i ii t i c niutlrl :\n'1: - ll,.42 .... 4,,, ( 1 )\nThe goal of kinenlatic calibrittion is to identify the gronietric pararneters s J , a, and t i J , and also the non-geonirt.ric joint itiigle ofiset parameters #yff ( the joiut. angle is presuiiietl to 1 3 r relatctl t o the sensor reading its: tl; -: 0, -1 By\") . All of t,he uiiknowri kineniatic p i t r i i n i e t ~ * r ~ i t r c I)litcc.tl into vectors: 2 -. (si, s a , . . . ) ' I ' etc. ancl - p . ( ~ $ f , ~ l ' , ~ l ' , f i l ' ) \" .\n88CH2531-2/88/0000-0627$1.00 @ 1988 IEEE 627", + "of the endpoint coincides w i t h the base coortlinntes. Further, the endpoint location computed by the iiiodel, T,, is assumed to cliffer from the base coordinates by only a small amount. Thus, let the computed position bc. ( d . ~ . , , c/gc ,112. ) T . Similarly, let the calculated orientation R, ( that is, the upper left 3 x 3 niatrix 01 T,) be represented by infinitesiinal xyz Ei i ler rotations:\n1 I -ay' dz, 1 1 -32, By, Ra(Bz,)R,(dy,)R,(B-,) 2 dzc 1 -L).cc ( 2 )\nThus, the modeled endpoint location, evaluated a t the 1111 joint configuration e , may be represented as a six vector < 7. (dz,, dy,, dz,, BE,, By,, B z ~ ) ~ , n i i d the six kinematic loop closure equations given by:\n- o = L@ t B ,, A , & , E ) + I L Z ( 3 ) The error term 111' has been acltlr*tl to indicate that there is inodeling and rneasurenient noise.\n3 Iterative identification I n order t o solve for the kineiti.ttic parameters the equations ( 3 ) are linearized and iteratively ideiitifecl.\n3.1 Differential kinematics A t the i th joint configuration f the first differential of ( 3 ) is:\nwhere Ag' = 0-& and A s = ?-so etc. By denoting the combined Jacobian:\n( 5 )\nA&' = C ' A c p + ~ \" (6)\nequation (4 ) may be expressed more concisely as\n3.1.1 J a c o b i a n ca l cu la t ion Kach of the matrices in (4) are Jacobians with respect to the particular paranieters. For example, a&/@ is the familiar Jacobian which relates infinitesimal joint inovenients to end effector inovenients. Although the derivation of the Jacobians niay be performed in a variety of ways, the following procedure[6][7] reveals that the coluniiis of the Jacobian niay be interpreted as screw coordznates.\nImagine the w d effector variation AL' to he u i instantaneous screw displacenient composed of linear and angular velocity coinponents. The coinbinetl variation in all the paranieters is presumed to caiise this rntl point variation. Specifically, a variation of the D - l l paraiiirtrr sJ along the local link z axis, ~ f - ~ , cause6 a contribution to the end effector linear velocity of A S , Z : - ~ . The parameter vaiiatiori A(kJ about the local link z axis, x',, causes a contributiori to the endpoint's angular velocity of ( A a J ) x f - w,,, , arid a linear velocify contribution of w,, x b:+], where bJ+i is it vector froni the j l h coordinate system to the endpoint (Figure 2). Ttie 19~ and a, parameters are treated analogously. In total, the endpoint translation due to all of the parameter variations is given by: c;'=,z',., x biA0, + Z ~ - ~ A A , f X : x bl+,Aa, + x',Au,, and angular variation given by: Cy I zI, rAO, + x i n u , . Comparing itiese t o (4) i t is seen that the colunins of each of the four Jacobians are\nand\n3.2 Data collection and parameter estimation A wries trf 11 configurations of the irctual iiieclianism provides n se1.s 0 1 joint angle nieasiirenieiits ff, a n d rt equations of the forin ( 6 ) . ('oinpactly, t.he equations iiiay be written\nwhere\nAn estimate of the paranleter errors i b provided by ~ i i i ~ i i ~ n i ~ ~ i i g L S = ( A A - CF)' ( A 1 ('5) which yields\nAy - (C''C)-lC'TAJ ( 1 1 )\nFinally, the guc'ss at the pdr;tnieters i a updated as f - y,, t b.2, and the iteration continurs until A x + 0.\n4 Identifiability There inay be situations in which the paraiiieters are riot determined uniquely by the kinematic equations collected during nioveinent ol the nircli~rnisni. All sources of parameter ambiguity may be linked l o the r u i k ol'the niatrix C (provided that the first differential suficiently approxiniates the kinematics). If the columns of C are linearly tlepentient then the corresponding kineniatic parameters inay vary arbitrarily (these variations only satisfying the linear dependerice). 1)rprntlerice of the colunins of the niatrix C' causes C7'(' to becoiiie singular and the algorlthin f i l s . More 1111- portantly, il the r'irik degeneracy occurs when C' is evaliiated at the actual paranieters of the niechanisrn then the paratneters will be unitlentifial)lc.\nNow, acrordiiig t o definition (IO) the colunins of C' are a concatenation of the screw coordinates ( 7 ) and (8) for all configurations of the inechanism. Therefore, the columns of C' will be linearly dependent and thus the mechanisin unidtiitificille if arid only i f there is U constant linear relutiori ainoriy t h e a c i t u i coordmates for all coiifiyurafions of tht i n r ~ h a n i ~ i ~ ~ . T h i \\ condillon can be made niore useful by inspectlug the forin 01 the D-\u20ac1 screw coordinates; sprcitically, it can be shown that thf irect~sary and sufjicieizt condrtioir for tdeirtrficatton /hat tlicrr c s i a f rro constairf lincur relation aiiioriy tht local link s u r d 2 m t s ; that L A :\n\"r, L,xi t c,z; = 0v,,,1 ,,I 7 L, - c, - 0 (1')\nJ 1\nThe soiircrs 01 singularities are now eiiuineraiecl: (1) P a r a m e t e r s t h a t e n t e r l inear ly: A first source of paranieter aitibiguity beconies apparent by writing out the kincmatic closiirr qua t ions (3) (tor revolute nrariil)iilniors) to explicitly show i tit, linear dependence of the Irngt t i p.tr.rineters 181.\n\"f C 5 , z ; , t u,x; - 11 ( 1 3 ) J - 1\n('learly, equation (13) violatrs (onhiion ( 12). The naturnl w l u - t i o n to the problem is to define one n o i i Lero link length a5 unity; this particular parameter tletrriinnes the units of length. (2) I n h e r e n t s ingular i t ies i n t h e inechanism: Certain iiiec t i - anisrns have particular ayninirt Ties which allow the kineniat ics to be described in less ttinii tour p,irnitirtrrs per joint. I t i s t l i l l i c ult to provide a general rulv lor wlirn thib will happen, but 1 1 I > usii nlly restricted i o i i i ~ ~ ~ l i ~ t i i i ~ i i ~ ~ ( 1 1 i i iol)i11tj ( J I I ~ . 45 ,I \\ < r k S I I I I ~ I < , exdiiiple coii6iilrr irli i ig to < , t I i l j r d e cl 1 1)OI: I ) I u i ' t r i i l . r i i i i ) t i l ~ t t o i constrained bo t l i n i i t Iorii is 't lour I m r IiiikaKc I1 i l l c loui L t r" + ] + }, + { + "image_filename": "designv11_2_0003899_acc.2006.1657381-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003899_acc.2006.1657381-Figure1-1.png", + "caption": "Fig. 1. A conceptual interferometric imaging configuration using multiple spacecraft in formation. Spacecraft separations are of the order of ten of meters to kilometers for imaging planets in other solar systems.", + "texts": [ + " See [18], [25], [26] for earlier work on decentralized estimation problems for spacecraft formations In the formation flying problem we consider N spacecraft, each using an estimation-based controller to perform its component of a formation-wide control objective. The spacecraft are not assumed to be physically coupled or tethered and the only coupling in the problem arises from the performance objective. To motivate this problem further we briefly outline the nature of the control required for formation-based interferometers. Figure 1 illustrates a conceptual interferometric imaging formation. The formation is oriented to point towards a image target and each spacecraft acts as a collector reflecting light to a central combiner spacecraft. If the optical path lengths are held fixed (to within the order of nanometers) an interference pattern is generated between any two optical beams and can be measured. The amplitude and phase of this pattern is essentially a sample of the spatial Fourier transform of the image. Reconstruction involves an inverse Fourier transform of these measurements and the ultimate resolution depends on the spacecraft separation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001667_1.1504092-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001667_1.1504092-Figure1-1.png", + "caption": "Fig. 1 Schematic of the cam follower experimental test rig. The two follower configuration gives 2 cycles per cam revolution.", + "texts": [ + " Copyright \u00a9 2Journal of Tribology rom: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= an eccentrically mounted circular cam-follower mechanism. A summarization of the construction for an experimental rig to compare the model data is included as well. The error-differences between the numerical and analytical models are also discussed. A cam-follower test rig was developed to experimentally quantify the coupled evolution of wear and load in the mechanism. The rig\u2019s overall construction can be seen in Fig. 1, while the contact geometry can be seen in Fig. 2. The cam was CNC milled from a block of polytetrafluoroethylene ~PTFE!. The circular cam measured 38.1 mm in radius, 9.5 mm thick, and had a 6.35 mm eccentricity. The follower counterface wear surface was made of 17-7 PH stainless steel and had an initial average roughness of Ra52.1 micrometers. The follower shafts were made of stainless steel and slid on solid-lubricated PTFE bushings. Two 17 N/mm compression springs located behind the follower face provided the necessary normal force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000436_978-94-009-1718-7_9-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000436_978-94-009-1718-7_9-Figure2-1.png", + "caption": "Figure 2. (a) Kinematic Scheme of Motion Platform Limbs", + "texts": [ + " Description of the Device and Notation In our model, prismatic and spherical joints are replaced by ball screws and universal joints. An active ball screw in conjunction with a passive universal joint on a ball nut performs the same kinematic function as a passive spherical joint and an active prismatic pair working together. Three brushless D.C. motors are used as the driving devices and the ball screws are used to transform rotating motions to translating motions. These features can be seen from the CAD model and photograph in Figure 1. A schematic drawing of the driving simulator is shown in Figure 2{a). The device is fixed to the base by three passive revolute joints denoted by 1, 2, and 3 at the vertices of a base triangle with equilateral side length a. The joint axes directions Ul, U2, and U3, lie in the plane ofthe base triangle and are normal to the medians of the triangle. The motion platform is connected to the ball screws by three universal joints denoted by 4, 5, and 6,which form the vertices of an upper triangle with the same geometry as the base triangle. Each ball screw can only move in the plane normal to the respective base joint axis as shown in Figure 2{b). The lengths of the ball screws, denoted by rl, r2, and r3, are measured from the revolute joint to the universal joint in each case. The tilt angles of the links are denoted by 10 the flow factor is slowly increasing. When using B.C.A the flow factor in creases and approaches the results from B.C.B. Figure 13 shows the shear flow factors calculated for alh values 2.5, 3.3, 5 and 10 using both B.C.C and B.C.D. As for the pressure flow case the two results approach each other as the redno number increases. JULY 1997, Vol. 1 1 9 / 5 5 1 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 08/11/2013 Terms of Use: http://asme.org/terms In Figs. 10 and 11, pressure charts for the sliding case are shown. At some places the spacing between the two surfaces is zero or near zero, and at these places we get extremely high pressure spikes. Usually these pressure spikes will not influence the average values much, but for some cases they do. As de scribed earlier we calculate the average pressure gradient for a subarea by calculating the average pressure at the front and end boundary and then divide by the length. If one of the pressure spikes is situated on the front or end boundary, the average pressure on this boundary will be too high or too low. This large pressure will result in incorrect flow values for the smooth case. This is especially a problem when the subarea gets small. For a/h = 0.4 and redno = 30 we have only used 8 of the surfaces in the simulations since the calculated flow factors for two of the surfaces were obviously wrong. One of the surfaces had a shear flow factor equal -3 .2 while the other values were between -0.38 and \u20140.79. This large deviation was caused by a large negative pressure gradient more than 10 times the average gradient. For cr/h = 0.3 and redno = 30 we used 9 of the 10 surfaces. The other flow factors are based on results from all 10 surfaces. Figures 14 and 15 present the flow factors together with those found by Patir and Cheng (1978, 1979). Our flow factors indicate that the influence of the isotropic roughnesses on the flow is less than predicted by Patir and Cheng (1978, 1979) for small h/cr values, and slightly larger for high values. T0nder (1980) presented results that differed a lot compared to Patir and Cheng's results. T0nder's results indicated that the isotopic surface increases the pressure flow compared to the smooth case, while Patir and Cheng and our results indicate a decrease. Teale and Lebeck (1980) got results lying between T0nder's and Patir and Cheng's results. See Cheng (1984) or Hu and Zheng (1989) for a comparison between the various results. pressure prof i le roijgnness p induced ' \" pressure The values in Figs. 14 and 15 are taken from Figs. 12 and 13 at redno = 20. The average of the two boundary condition values has been used. In Fig. 13 the shear flow factors are negative while in Fig. 15 they are positive. When the smooth surface is moving and the rough surface is stationary, we get a decrease in the calcu lated flow compared to the smooth case. The stationary roughness valleys restrict the flow. For the opposite situation (smooth stationary and rough moving) the flow will increase since additional fluid is carried out by the moving roughness valleys. The decrease and the increase have the same magnitude when we use the same rough surface. In our case we have used a stationary rough surface, and then the flow factors are nega tive. It is, however, common to present the flow factors as positive values as for a rough, moving surface. Figure 16 shows the calculated pressure flow factors for all the 10 surfaces at h/a = 2.5. The average of these 10 values is shown in Fig. 12." + ] + }, + { + "image_filename": "designv11_2_0002043_ip-cta:20050904-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002043_ip-cta:20050904-Figure1-1.png", + "caption": "Fig. 1 Scheme of delta wing a Plan view b End view c Side view", + "texts": [ + " All the weights of the RNN are tuned based on the Lyapunov function to achieve favourable identification performance. And, by the L2 control design technique, the effects of the approximation error on the tracking performance can be attenuated to arbitrary specified level. The proposed NNIAC design method is applied for a wing rock motion control. Simulation results demonstrate that the developed NNIAC system can achieve favourable tracking performance without knowledge of the system dynamic function. The delta wing of an aircraft is represented schematically in Fig. 1. This delta wing has one degree of freedom, and the dynamical system includes the wing (a flat uniform plate) q IEE, 2005 IEE Proceedings online no. 20050904 doi: 10.1049/ip-cta:20050904 C.-F. Hsu is with the Department of Electrical and Control Engineering, National Chiao-Tung University, Hsinchu 300, Taiwan, Republic of China C.-M. Lin and T.-Y. Chen are with the Department of Electrical Engineering, Yuan-Ze University, Chung-Li, Tao-Yuan 320, Taiwan, Republic of China Paper first received 7th October 2002 and in revised form 20th May 2004 IEE Proc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000054_s0165-0114(96)00167-4-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000054_s0165-0114(96)00167-4-Figure1-1.png", + "caption": "Fig. 1. Membership functions of the input fuzzy variable sl. Fig. 2. Membership functions of the output fuzzy variable u~f.", + "texts": [], + "surrounding_texts": [ + "where Mio(X~) is a posit ive function. ~:i is a posit ive constant , p is a posit ive integer, sets Aia. A~ are given as following:\nZ,a = [ X i i l l X , - X,oll,,.~., < I], (3)\nA,-- {X, l l l g i - X,oll~,..., ~< 1 + ~/i I1. (4)\n\u2022 \" ~ \" is a set of strictly positive weights, Xio ~ R \" ' is a fixed point, g'i is a posit ive constant Here wi = i . . i j j j=l represent ing the width of the transi t ion region. IIXillp..w, is a weighted pi-norm, which is defined as\nI ( - -p . - l l lp\nj = l \\ iV ( i f .J\nIf Pl = 7=, then\n,xill .w, = ma ( \".Ix\"l, ... Ixim, I \\ 14'il Wimi f\nIf Pi = 2, wij = 1.j = 1 . . . . , m . then II X i tip ..... will denote Euclidean no rm I IX,II.f.~, {x;) is an app rox ima t ion of the fuzzy basis function p;j(Xi), which is defined as in [12], on .4i to f i(Xi) by\nNi f i A , t X i } = ~ OiJPij(Xi), (5)\nj= l\nwhere Ni is the n u m b e r of rules in the ith fuzzy subsystem, O~j denotes the peak value of the no rma l fuzzy set cor responding to j th rule in the consequence, j = 1 . . . . . N . i = 1 . . . . . N.\n3. Design of a decentralized adaptive fuzzy controller\nWithout loss of generality, the control gain bi is assumed to be a posit ive Constant. Fo r the subsys tem Pi define a switching function as follows:\nSi(t) = Cil ell q- ci2ei2 + \"\" \"Jr oil\" i - l le i (mi- I) Jr\" ei\" , , {6)\n. .~\",-~ ~ , . , - n and the coefficients q l . q : , , where ell = Xi l - - -~id, ei2 = .~il - - -~id . . . . ,elm~ \"~\" \" i l - - a id , . . . C i (mi_ l ) ~mi- -2 are the coefficients of the Hurwi tz ian po lynomia l 2 \" ' - 1 + q \" , _ ~ + \"- + c;1.\nDifferentiat ing si(t) with respect to t, we have\n\" i - 1\nSi(t) \"= ~,, ci jei t j+ 1} + blui( t ) + d i ( X , t) - - f i (Xi ) - x~'~(t). (7) j = l\nAdopt ing the following control lag,:\n( ) tti(t} \"~ -- kidSi,,(t) -- [~i-'(t}u*(t) + h i - l ( / ) I r l i ( t }Mio (X i ) -b ~ dlik(t)l lX~ I k u,r(t) k = O j = l\n+ (1 -- mi(t))ui~(t), (8)\nwhere kid > O, [9 i- 1 (t) is the est imate of b~- 1 at t time. uiy(t) is de termined by the following fuzzy rules. T a k e\n- \"q\"'}(t). (9) u*(t) = ~, coeio+ , ~ .,ia j = l Ni ui~(t) = ~ ~i j ( t )P l j (X i )+ r.ia(t)uif(t), (10)\nj = l", + "mi(t) = at I Ix , - X~oL, .~ , - 1\nsi~ (t) = sdt) - \u00a2 : a t ( s i ( t ) / 4)i),\ni f X i ~ Aid,\ni f X i ~ Ai ~ A~d,\ni f X i e A c ,\n(11)\n(12)\nm~(t) is a modula t ion function, 0 ~< m~(t) <<, 1, V t ~ O. In addition, ~i:(t) is an estimate of Oq/b~ at time t, and ~d(t) is an estimate of e~/b~ at time t. Saturat ion function sat(),) is defined as: sat()') = y, if lYl ~< 1; sat(y) = sgn(y) , if lYl > 1.4,; > 0 is the width of the boundary .\nAdopting the adapta t ion laws as follow:\nx \u2022 ij = - ( 1 -m~(t))rlilsi~(t)pij(Xi), j = 1 . . . . . N i, i = 1 . . . . , N ,\n~id ---- (1 -- mi(t))rh2rSi~(t)l, i = 1 . . . . . N ,\nijk = rlllXjllklsi~(t)l,~jk(O) >t O, i,j = 1 . . . . ,N, k = 0, 1 . . . . . p,\n':\" 1 ( ( ~ N ) ) b\u00a3 = u * ( t ) - ~ ~jk(t)llXjlp + mi ( t )M i o (X i ) uiy(t) si~(t), i = 1 . . . . . N, k=Oj=l\nwhere ~/~1 > O, t/i2 > 0 and 1/> 0 are strictly positive constants which determine the adapta t ion rate. The fuzzy control rules which determine U i f ( t ) a r e defined as follow:\nRji: if si is ,4~i, then uif is B- j i ( j = - 2 , - 1 , 0 , 1,2),\ninput: s~ is -4i, ou tput ui: is /~i, (i = 1, ... ,N) ,\nwhere the membership functions of the fuzzy sets -4i~ a n d / ~ are shown in Figs. 1 and 2, respectively. The fuzzy relation is defined corresponding to the ith rule as follows:\n~j~ = ~ j i x ~_ j , ,\ni.e.\n(13)\n(14)\n(15)\n(16)\n~ji(Si, Uif ) : .~ji(Si)\" B - j i ( t l i f ), (17)\nwhere x stands for the cartesian p roduc t , - denotes the produc t operat ion, ~ji(sl), /~_~i(u~f) denote the membership functions of the fuzzy sets ,4ji and/~_j~, respectively. The whole fuzzy relation corresponding", + "to all fuzzy control rules is defined as follows:\n2\n= L) G , j = - 2\ni.e.\n2\nRi(si 'uif) = V [Aj i ( s i )e - j i (u i f ) ] , (18) j = - 2\nwhere V is the max operation. Adopting the max-product compositional rule of inference and the method of the singleton fuzzification [11], it is easy to get the membership function of the output fuzzy set/~; as\n2\nni(lliY )~-\" V [Aji(s i )n-Ji(uiy )]. (19) j = -2\nUsing the method of the center of gravity defuzzification [2], the crisp control action of /~ is calculated by\n3;2/2 Uif ei (uif ) dulf uil = f 3/2 (20)\nJ - 3/2 Bi(ui\u00a3} duif\nFrom Figs. 1, 2 and (19), (20), we obtain\ntlif =\n2Z 3 + 9 z \"2, + 7 Z i + 3\n6z~ 2 + 9zi + 6\n2z 3 + 3z \"2, - 2zi\n6z 2 + 3zi + 3 '\n2zi 3 - - 3z .2, - 2Z i\n6Z \"2, - - 3 Z i + 3 '\n2Z 3 -- 9Z 2 + 7 Z i - - 3\n6z~ - 9zi + 6\nzi <~ - 1 ,\n, - 1 < z;~< - 0 . 5 ,\n-0 .5 < zi ~< O,\n0 < z~ 6 0.5,\n, 0.5 < zi ~< I,\nzi > i ,\n(i = l , ... ,N), (21)\nwhere zi = s i / ~ i . From (21), we have ui f ( t ) = - sgn(si( t ) ) , if [sd t> ~ .\n4. Stabi l i ty analys i s\nSubstituting (8) into (7), we obtain\n) ~i(t) = -- kidbisia(t) + (1 - b i ~ i - t ( t ) ) u * ( t ) + bibl-t (t) ao~( t ) l IX j l l ~ + m i ( t ) M i o ( X i ) u i f ( t ) k j = t\n- j i (X i ) + bi(1 - mi(t))uio(t) + d i ( X , t ) . (22)" + ] + }, + { + "image_filename": "designv11_2_0000556_s0003-2670(00)01031-x-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000556_s0003-2670(00)01031-x-Figure1-1.png", + "caption": "Fig. 1. Absorption spectra of ternary complexes of titanium(IV), vanadium(V) and molybdenum(VI) with hydrogen peroxide (10 mmol l\u22121) and 5-Br-PADAP: a \u2014 Ti(IV) system (20% MeOH); b \u2014 Ti(IV) system (60% MeOH), Ti(IV) (5 mmol l\u22121), 5-Br-PADAP (30 mmol l\u22121); c \u2014 Mo(VI) system, Mo(VI) (5 mmol l\u22121), 5-Br-PADAP (50 mmol l\u22121) and d \u2014 V(V) system, V(V) (10 mmol l\u22121), 5-Br-PADAP (20 mmol l\u22121).", + "texts": [ + " Binary Ti(IV)-(5-Br-PADAP) complex was formed in acidic medium (when hydrolysis of titanium(IV) ions was negligible [48]), for pH below 2.5. The reaction needed at least 20 min to be completed. Under such conditions the system was stable; its absorption maximum was situated at 605 nm. Ternary titanium(IV) systems were formed and were stable in a wide range of pH: 4.0\u20138.0 (maximum absorbances were measured within pH range 4.0\u20136.0). Under optimum conditions two different ternary complexes of titanium with H2O2 and 5-Br-PADAP were formed (Fig. 1), depending on methanol concentration in solution. For its concentrations below 40% prevailed the species absorbing at 540 nm (\u03b5(H2O2)=2.0\u00d7104 l mol\u22121 cm\u22121), for those above 50% the form absorbing at 580 nm (\u03b5(H2O2)=2.7\u00d7104 l mol\u22121 cm\u22121). The species could be chromatographically separated. Fig. 2 presents 3D chromatograms (absorbance versus time and wavelength) of the samples containing 20 and 60% of methanol, respectively. In the first case two bad separated peaks were observed: the first peak (k\u2032=0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003166_s00170-005-0296-2-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003166_s00170-005-0296-2-Figure3-1.png", + "caption": "Fig. 3 Model transformation of meshing gears (a) to the equivalent model of two cylinders for the meshing point B (b)", + "texts": [ + " Finally, the initial cracks that form when a surface is severely loaded have a tendency to intersect at the pitch line on the driver, while on the driven member they do not. Secondly, the pinion, being smaller, has obviously more cycles of operation than the gear. The slope of the fatigue curve makes the part with the most cycles the most apt to fail [8]. Basic parameters, influencing contact fatigue life of spur gears can be summarized as hertzianpressure on the tooth flank and sliding conditions alongside the engagement line. Pressure on the tooth flank can be estimated with classical Hertzian theory using an equivalent contact model (Fig. 3), and can be expressed analytically by [6], \u03c3H \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E 2 b \u03c0 1 \u03bd2\u00f0 \u00de FN R* ; s (2) where \u03c3H is Hertzian pressure, E is Young\u2019s elastic modulus, b is the gear width, \u03bd is Poisson\u2019s ratio, FN is the normal force on the tooth flank and R* is the equivalent radius curvature (Fig. 3). Sliding alongside engagement line is due to a difference between tangential components of velocity in the particular gear contact points (Fig. 2a). As a rule, the maximum value of tangential velocity difference occurs when the root of the teeth (dedendum) and the top of the counter-teeth (addendum) are meshing. Wear is usually given as a numerical value (parameter) and depends on the specific sliding coefficient \u03c8 (Fig. 2b). However, additional, and also very important parameters are: temperature on the tooth flank, thickness of the oil film in the EHD lubrication regime, residual stresses in the area near the top of the gear tooth flank surface, local geometry of the tooth flank, roughness of the contacting profile etc", + " Nevertheless, one of the main difficulties in numerical modelling of contact fatigue at spur gears seems to be the detailed determination of operational loading and/or strain\u2013 stress cycles of the meshing gears. Since the loading cycles are very important for the determination of fatigue life and directly influence the computational procedure of the initiation damage definition, they must be precisely determined. For this purpose, the following equivalent numerical contact model is introduced. 2.2 Equivalent numerical model For computational determination of fatigue crack initiation at gear teeth flanks, an equivalent contact model (Hertzian theory) [10, 15, 17, 19, 24] is used (Fig. 3). The equivalent cylinders have the same radii, as the curvature radii of gear flanks at the observed point (the inner point of single teeth pair engagement\u2014point B). According to Hertzian theory [19], the distribution of normal contact pressure in the contact area can be determined by p x\u00f0 \u00de \u00bc 2FN \u03c0a ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x2 a2 ; r (3) where FN is the normal contact force per unit width, a is half length of the contact area, which can be determined from [19] a \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4FNR \u03c0E ; r (4) where E* and R* are the equivalent Young\u2019s elastic modulus and the equivalent radius, respectively, defined as [19] 1 E \u00bc 1 \u03bd21 E1 \u00fe 1 \u03bd22 E2 ; (5) 1 R \u00bc 1 R1 \u00fe 1 R2 ; (6) where E1, R1, \u03bd1 and E2, R2, \u03bd2 are the Young modulus, the curvature radii and Poisson ratio of the contacting cylinders (see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000034_s0020-7403(00)00038-2-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000034_s0020-7403(00)00038-2-Figure2-1.png", + "caption": "Fig. 2. Free-body diagram of the strut having length l due to the stress p 2 in the X 1 direction.", + "texts": [ + " Thus, the total strain energy; in a strut of length 2\u00b8 due to bending moment M(x), axial load R, and shear load < is given by ;\"2; b #2; a #2; s \"P L 0 M2(x) EI(x) dx#P L 0 R2 EA(x) dx#P L 0 k<2 GA(x) dx. (2) 2.1. Ewective elastic constants for a hexagonal model of a columnar structure 2.1.1. In-plane ewective Young's modulus The remote stress p 1 along the X 1 direction produces a force P on the strut of length l. The force P is resolved into axial P cos h and transverse P sin h components as shown in Fig. 2. Substituting in Eq. (2) for R\"P cos h, <\"P sin h and M(x)\"1000 A/m colloidal chains are dominant. Typically, the pyramids occurred in formation as seen in Figure 6. The domain wall is located at the base of the pyramids, and E\u22062 ) - \u00b50\u00f82\u03c0a3H2 24 Nb(Nb - 1) (11) HDW ) Msw 2\u03c0 r r2 (6) E\u22a51 ) - 2\u00b50\u00f8a2MsHw 3 \u2211 i)0 N 2i + 1 1 + (2i + 1)2 (7) E\u22a52 ) - \u00b50\u00f82\u03c0a3H2 9 (N - 1) (8) E\u22061 ) - 2\u00b50\u00f8a2MsHw 3 \u2211 i)0 NB 1 + ix3 1 + (1 + ix3)2 (NB - i) (9) N ) \u2211 i)1 NB i ) NB(NB + 1) 2 (10) the centers of the closest beads are positioned a distance x \u2248 a from the domain wall" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002329_21.7484-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002329_21.7484-Figure6-1.png", + "caption": "Fig. 6. Swept volume of hand.", + "texts": [ + " Checking the interference between this hemisphere and the enlarged obstacles, the angle range of with possible collisions is calculated. The angle range of 8, with possible collisions is calculated by checking the interference between the perpendicular plane and enlarged objects, for each quantized angle of 8, in this range. The PFS is the complement of these obstacles in the joint angle space. The FFS can be described as follows. The swept volume of the hand within all possible orientations is approximated by a sphere (Fig. 6) with a radius of R ( R = 19.3 cm). Although the actual swept volume cannot occupy all the space within this sphere because of the robot arm geometry limitation on joint angles, there is no significant difference since a part of the main boom is also included in the sphere. The hand in every possible orientation does not collide with obstacles if there is no interference between this sphere and the obstacles. Enlarging all obstacles by the radius R, the hand can be regarded as a point on the tip of the main boom" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000858_1.1564571-Figure9-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000858_1.1564571-Figure9-1.png", + "caption": "Fig. 9 Experimental gear test rig at NASA GRC", + "texts": [ + "org/ on 08/22/20 For the WVD, the analysis was presented both for the lateral vibration signal and the torsional vibration. Figure 7 is part of the wavelet analysis for the lateral vibration signal, and Fig. 8 shows an analogous wavelet analysis for the torsional vibration. Just as for the previous case, the magnitude of the wavelet coefficients corresponds precisely to the degree of damage. 4.2 Analysis of Experimental Data. The second case of study is based on the experimental data obtained from the Spiral Bevel Gear Test Rig @19#, located at NASA Glenn Research Center, shown in Fig. 9. The primary purpose of this rig is to study the effects of gear tooth design, gear materials, and lubrication types on the fatigue strength of aircraft quality gears @5#. Vibration data from accelerometers mounted on the pinion shaft bearing housing was captured using a multi-channel Analog-to-digital converter in a PC. An optical device was used to provide timing and triggering of the vibration signal. The vibration signals obtained were time averaged 10 times according to the timing mark. The gear system used was composed of a 12-tooth test pinion and the 36-tooth gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001223_cbo9781139878326.006-Figure4.28-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001223_cbo9781139878326.006-Figure4.28-1.png", + "caption": "Figure 4.28 Modes of elastic buckling, (a) mode 1; (b) mode 2.", + "texts": [ + " The small photograph shows, for comparison, the buckling mode in uniaxial compression. https:/www.cambridge.org/core/terms. https://doi.org/10.1017/CBO9781139878326.006 Downloaded from https:/www.cambridge.org/core. UCL, Institute of Education, on 19 Apr 2017 at 12:27:34, subject to the Cambridge Core terms of use, available at 138 The mechanics of honeycombs with them). Here we find the combinations of biaxial stress which give each mode. We begin by isolating the representative unit for each mode which, if repeated (with reflection), builds up the entire pattern (Fig. 4.28). We first calculate the axial loads and moments acting on each member when remote stresses ox and ) (74) The theoretical expressions for the parameters of the two asymptotes may be of value for the fitting of parameters to experimental data. 8. Experimental technique The EMF has been measured on the following cell Ag|AgCl electrolyte \"var CA membrane electrolyte -fix AgCl|Ag Here \"electrolyte\" denotes an aqueous solution of pure HC1, NaCl, KC1 and CaCl2, respectively, and \"CA-membrane\" indicates a homogeneous celluloseacetate membrane" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002146_tmag.2004.838746-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002146_tmag.2004.838746-Figure2-1.png", + "caption": "Fig. 2. Schematic diagram of post-assembly magnetization.", + "texts": [ + " The magnetomotive force (MMF) is given by (1) where is the turns of the magnetizing coil, is the magnetizing pulse current, is the magnetization field strength of each flux path part, and is the length of each flux path part. Because of the air flux path, the MMF equation turns to be (2) where is the flux density of each flux path part, and is the permeability of air. Since is very small, the total needed MMF would be a quite large value. For practical motors, since the stator and rotor have the same number of poles, the stator winding can be used as the magnetizing coil for post-assembly magnetization of the permanent 0018-9464/$20.00 \u00a9 2005 IEEE magnet on the rotor. The magnetizing flux path is shown in Fig. 2. As we can see, the flux passes through iron core and air gap. This gives the equation of MMF as (3) where is the turns of the stator winding, is the current in the stator winding, is the flux density in the air gap, is the length of flux path in the air gap, is the flux density in the iron core, is the length of the flux path in the iron core, and is the permeability of iron core. Because is very small, and although is comparatively large, is far larger than the magnetizing MMF of the post-assembly magnetization keeps at a smaller value when compared with that of the component magnetization" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000757_robot.1993.292242-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000757_robot.1993.292242-Figure1-1.png", + "caption": "Figure 1. A Planar Tracked Vehicle Moving Along a Specified Path", + "texts": [ + " In the context of this paper, motion planning consists of computing the track forces required to follow the specified path at desired speeds. This work can be later used to compute the optimal vehicle motions (path and speeds) between given end points on a general terrain, following the approach presented in [8]. 2. Dynamic Model We consider a rigid planar vehicle moving on a horizontal plane. A coordinate frame defined by the unit vectors ex and ey is attached at the mass center parallel to the vehicle major axes, as shown in Figure 1. The position of the vehicle is specified by the location of its mass center, x, and by the rotation 8 of the vehicle frame relative to the inertial frame. The vehicle is moving at some velocity, vc= a. tangent to the path, and rotating at some angular velocity w = - . The angle a between vc and ex is called the slip angle. The slip angle is positive for a clockwise turn, negative for a counter clockwise turn, and zero for straight line motions. The external forces acting on the vehicle consist of the gravity force, mg, the normal force R, the lateral friction force F, and the longitudinal thrust Q, as shown in Figure 1. The thrust Q is the sum of the longitudinal thrust forces developed by the right and left tracks: Steering is accomplished by controlling the moment MQ created by the track forces where dx de dt Q = Q R + Q L (1) MQ = AQb (2) 796 1050-4729l93 $3.00 0 1993 IEEE and b is the distance between the tracks. The moment MQ around the mass center must overcome the friction moment, Mf, due to the skidding of the tracks. The equations of motion of the vehicle expressed in the body fixed frame are then Q = m g * e x (4) F = m % * e (3 y" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003251_s0022-0728(83)80113-2-Figure14-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003251_s0022-0728(83)80113-2-Figure14-1.png", + "caption": "Fig. 14. (a) Structure and dlmens]ons (,~) of methy lene b lue catxon [31 (32)], (b) an t i -para l le l o r ien ta t ion of MB p e r m a n e n t d ipoles m a d lmer [11,32,33]", + "texts": [ + " The transient is most likely to be connected to: (1) adsorpt ion-desorpt ion of nitrate ion at the interface of mercury/organic film; (2) a conformational change of LMB molecules in the adsorbed film [37] strongly affecting the kinetics of the reoxidatlon process, which is coupled to the phase transition, as demonstrated by a change in the anodlc transients in Fig. 1 l, and the reoxidation chronocoulograms in Fig. 13. 25 I J I I E 1 = - 5 5 0 o 50 (.) :L CI 88 E 2 / m V F~g. 13 Effect of molecu la r r ea r rangement on the charge t ransfer m 1 0 - 4 M MB solut ion, 0 1 M K C I + 1 M K N O 3. Reoxadatxon ch ronocou lograms for t 2 = 40 ms, 1 ms and 200 /~s at E 2, af ter 4 s reduc t ion at E 1 = - 5 5 0 mV. G E N E R A L D I S C U S S I O N Some properties of MB monomers and dimers, and their basic orientations in adsorbed layers are shown in Fig. 14, and Table 1. Our results show that the extent of adsorption above the monolayer coverage is determined by the presence of anions at the interface (Fig. 4), the hydration of anions playing an important role. It could be concluded that the tendency of MB dimers towards a stacking interaction [13,23] in aqueous phase and the adsorption at the mercury/aqueous solution interface increase in the sequence F - << NO 3- < C1- << C10 4 . In chloride and nitrate solutions the amount adsorbed approaches that for a bilayer film and slightly increases at less negative potentials (Fig", + " 4) with a 89 knee cannot be fitted with the B.E.T. model for a multilayer formation, but more probably it reflects a competitive adsorption of monomers and dimers (that are in equilibrium in the aqueous phase [11,12]), as soon as the first monolayer approaches completion. In the absence of a charge-transfer process we found no evidence that a reorientation or phase transition occurs in the MB film up to 1 0 - 3 M MB in solution. It is reasonable to assume that MB molecules in adjacent layers are paired in an anti-parallel position (Fig. 14b), the relative onentanon being consistent with that suggested from nmr and optical studies of the dimerlc molecules in solution [11,13,14]. It is then quite logical that the presence of anions in the absorbed film is more important for adsorption of dimers, since the hydrophobic parts of cations are oriented face to face, and polar positive charges towards the solution. The results at the mercury/aqueous electrolyte solution interface suggest that the effect of anions on MB adsorption at other interfaces might be equally important, and its understanding could contribute to clarification of the conflicting views on the applicability of MB adsorption to surface area determination [32,34,35]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000755_robot.1996.509174-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000755_robot.1996.509174-Figure2-1.png", + "caption": "Fig. 2 A g a s p with frictionless point contact", + "texts": [ + " Moreover, we analyze the condition on the finger's stiffness to stabilize the grasp with friction. The stability analysis is greatly simplified by using potential energy of the grasp system and is of practical use. 2. Stability of frictionless grasps 2.1. Modeling of grasps In this section, we discuss the grasp stability considering the curvature of an object and fingers when the fingers slide on the object surface without friction. Because of frictionless, each finger force is along the inward normal of object at contact point. We define coordinate frames shown in Fig. 2. The origin of the object coordinate frame CO is fixed at arbitrary position on the object. The object is approximated by a circle at the contact point as shown in Fig. 2. The origin of the contact-point coordinate frame C i is fixed at the center of curvature, and the axis xi of C, is along outward normal of object at contact point. The relative position of the origin of C, with respect to CO is denoted by p i , the relative orientation of C, with respect to CO is denoted by B, . The radius of curvature of the object and the finger at i-th contact point is defined by R, and r, , respectively. If the object has convex arc at the i-th contact point as shown in Fig. 3(a), we have R, > 0 . If the object has concave arc as shown in Fig. 3(b), we have R, < 0. The radius r, is defined in a similar way. In order to simplify the discssion, we make following assumptions. (2 1) Each finger is in a frictionless point contact with the object and has a. virtual spring shown in Fig. 2. (2 2) The shapes of an object and each finger are known, and can be approximated by circles of the curvature, respectively. (2.3) The grasping system is in an equilibrium state initially, and contact points and contact forces are known. (2.4) Two dimensional grasp. By setting virtual springs as assumption (2. I ) , we can derive potential cnerjg of the grasp system. Since the shape of the object is rcprcsented by the circles of curvature up to second order exactly, the second-order pa.rtial derivatives of the potential function is exactly derived according to assumption (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002678_ip-c:19850022-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002678_ip-c:19850022-Figure4-1.png", + "caption": "Fig. 4 Load angle variation with power factor angle, at 100% and 50% rated load", + "texts": [], + "surrounding_texts": [ + "the other, giving rise to cross-axis reactances. These have also been described by Dougherty and Minnich [8] in a slightly different form. The inclusion of these terms in machine general equations has also been proposed by Brown et al. [9], but their significance in generator performance remains to be explored.\n2 Calculation of steady-state operating points\nThe finite-element method has been described in detail elsewhere [4]. In the method used here, first-order triangular elements are used to represent a pole pitch of the machine, field current and load angle being determined for specified terminal voltage, current and power factor. Two slightly different methods have been described [3, 4], both requiring a small number of Newton-Raphson iterations to converge both iron permeabilities and terminal conditions. The method used here is more akin to that of Reference [3]. The iron magnetisation curves are represented by analytic approximations [10]. The accuracy in the representation in the airgap adjacent to the teeth, and in the edges of the teeth, is crucial, and must allow for fringing flux. The success of the calculation may be judged by the accuracy with which the saturation curves are produced: these are shown in Figs. 1 and 2 for a 500 MW generator\nfinite-element calculated points\nfor d and g-axes (stator-excited on the g-axis), and are compared with measured values obtained by the CEGB at Eggborough in 1975. The short-circuit curve may also be obtained by calculation [11]; but as the iron is virtually\n102\nunsaturated in that condition, agreement with measured values does not represent a good criterion for accuracy of representation. The mesh used here (obtained interactively) had 1786 nodes and 3490 elements. After renumbering, the total half-matrix bandwidth (including the leading diagonal) was reduced to 85 136. Each iteration, involving a modified Gaussian elimination of the banded matrix, took 4.3 s on an IBM 3033 computer. About four iterations were required for each load point, at a direct cost of about \u00a32 per point, using the lowest level of priority.\nSteady-state field current and load angle are shown in Figs. 3 and 4, plotted to a base of power factor angle, for\no o o o CEGB test points\nfinite-element calculated points\n100% and 50% power load, at the voltages near rated voltage for which load points were measured. In the past, such curves have been plotted to a base of power factor [4]: that introduces a double-bend near unity power factor, which has been avoided here. Also shown in Figs. 3 and 4 are the measured load points obtained by the CEGB: it will be seen that the agreement is good, although calculated field current is higher by 2-3%. The measured values of load angle, with accuracy limited by the techniques of nine years ago, show some scatter.\n3 Effective axis reactances\nThe following equations, derived from the steady-state phasor diagram, give the effective axis reactances corresponding to each load point:\nxd\nxq-\nif\ncos 3 + ifxa\n\u2014 i sin (3 + 4>)\nvt sin 3\ni cos (3 + 4>)\nIEE PROCEEDINGS, Vol. 132, Pt.\n(1)\n(2)\nC, No. 3, MAY 1985", + "These equations are in per-unit quantities, as defined in Section 10. The system used takes stator rated current as 1 per unit, and per-unit field current as the current which produces the same fundamental airgap MMF as the stator carrying three-phase currents of 1 per unit.\no o o o CEGB test points finite-element calculated points\nfl-axis contribution to xd\nA A A xd obtained by Smith et al. [7]\nA A A\n2.3\n2.2\n2.1\n2.0\n1.9\n1.8\nd 1.7\nu c o t> X o >\n0.5\n0.4\n0.3\n0.2\n0.1\nxd variation with load angle at 50% rated load\nxd derived from finite-element excitation calculations xd derived from CEGB tests xd obtained from basic reactances, using eqn. 12 <7-axis contribution to xd xd obtained by Smith et al. [7]\n\\ \\\n\\ \\\n0 10 20 30 40 50 60 70 80 90 load angle,deg\nFig. 7 xq variation with load angle at 100% rated load xq derived from finite-element excitation calculations o o o o xq derived from CEGB tests + + + xq obtained from basic reactances, using eqn. 11\nfield current contribution to xq (negative) d-axis contribution to xq\nA A A x obtained by Smith et al. [7]\n1EE PROCEEDINGS, Vol. 132, Pt. C, No. 3, MAY 1985 103", + "Figs. 5-8 show values of xd and xq corresponding to the load points of Figs. 3 and 4. The values from the calculated\n2.3\n2.2\n2.1\n2.0\n1.9\n1.8\n1.7\no\n0.5\n0M\n0.3\n0.2\n0.1\n-Xq=2.16\n\\\n\\\n10 20 30 40 50 60 load angle, deg 70 80 90\nFig. 8 xq variation with load angle at 50% rated load xq derived from finite-element excitation calculations o o o o xq derived from CEGB tests + + + xq obtained from basic reactances, using eqn. 11\nfield current contribution to xq (negative) rf-axis contribution to x^\nA A A xq obtained by Smith et al. [7]\nload points lie on smooth curves, about which the measured values are scattered. Calculated values range from 2.79 to 1.87 (xd), and 2.03 to 1.75 (xq). A broadly similar variation for xq is quoted in Reference [5], and for xq and xd by Fuchs in the same reference.\nxd at 50% load rises to xdu, the unsaturated value, at high load angles. Values measured from the stator on no load, xd = 2.6 and xq = 2.16, are clearly poor approx-\nimations for those prevailing under load conditions, being about 15% higher than the values at rated load. Values obtained by Smith et al. [7] are of the right order.\nFig. 9 shows measured and calculated values of (xd \u2014 xq). This quantity does not remain constant, as was assumed by Shackshaft and Henser [1].\nri. a>* u 0 D CJ\n*-\n0.8\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n-\n-\n-\nX\nX x o c\nx x X \u00b0\no\no\no x , x /\n/ /\n1 1 1 1 1\n1 1\n1\n1\n/\n0 10 20 30 40 50 60 70 80 90 load angle, deg\nFig. 9 (xd \u2014 xq) as a function of load angle o o o o.derived from CEGB test; 100% load\nderived from finite-element calculations; 100% load x x x derived from CEGB test; 50% load derived from finite-element calculations; 50% load\n4 Basic reactances\nIn the iterative finite-element determination of each load point, each element is given an appropriate permeability corresponding to its flux density under load. Fig. 10 shows\nFig. 10 Flux distribution in generator cross-section at 100% load and 0.966 power factor lagging\n0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 >2.0(T) Fig. 11 Flux density levels in generator cross-section corresponding to Fig. 10 Intermediate contours are at 0.25 T\n104 IEE PROCEEDINGS, Vol. 132, Pt. C, No. 3, MAY 1985" + ] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure2.27-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure2.27-1.png", + "caption": "Fig. 2.27. Rotating coil type eddy current flaw detector", + "texts": [ + " The leakage magnetic flux detection is the method of detecting the flux leaked from the defect directly, by a magnetic sensor instead of magnetic particles, as shown in Fig. 2.25 [2]. The eddy current flaw detection is the method of catching the defect by the eddy current disturbance when the alternating magnetic field is applied to the product. There is the through type method using circumferential through-type coil, where the bar can pass through the fixed coil and the rotating eddy probe coil method, where the detection coil rotates around the bar with high-speed, as shown in Fig. 2.26 and Fig. 2.27. The internal defects can be represented as pipe, segregation and nonmetallic inclusion inside of steel bar. The inspection can be normally conducted with the ultrasonic flaw detector. 2.1 Steel Material 71 The ultrasonic flaw detection is the method of catching internal defects by the change of the ultrasonic wave from transmitting to receiving, when the ultrasonic is applied to the bar through the search unit, as shown in Fig. 2.28. A wire rod product is coiled to a ring shape. The coiled wire rod can be inspected after cutting off each one sample from both ends" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003108_978-3-662-09771-7-Figure30-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003108_978-3-662-09771-7-Figure30-1.png", + "caption": "Fig. 30. Diagram of the relative position and orientations of one feature with respect to another.", + "texts": [ + " The distance of the feature from the centroid is the magnitude of the central vector. The relative orientation of the feature is the smallest counter-clockwise angle from the central vector to one of the feature's axes of symmetry (see Fig. 29). The relative position and orientation of one feature with respect to another is RECOGNISING AND LOCATING PART/ALLY VISIBLE OBJECTS 6 7 Fig. 31. Relative orientations of the corners of a rectangle. defined in terms of the three factors, D, 01, and 02, illustrated in Fig. 30. The LFF system determines the symmetries of a two-dimensional object in three steps: (I) formation of groups of similar features that are equidistant from the centroid of gravity of the object; (2) computation of the symmetries of the individual groups; (3) computation of the object's symmetries in terms ofthose of the groups. Features are defined to be similar for the purposes of group formation if they are the same type, are equidistant from the object's centroid, and share the same orientation relative to their central vectors", + " The program builds a description for each non-duplicate feature. It does this by partitioning all features of the object, whether they have been marked as duplicates or not, into groups- and then computing the rotational symmetries of the groups. Features are grouped together if they are equidistant from the focus feature, are at the same orientation with respect to vectors from the focus feature, and if the focus feature is at the same orientation with respect to vectors from the features to be grouped (see Fig. 30 for these relative angles). If two features are grouped together, they cannot be distinguished by their relative positions or orientations with respect to the focus feature. Looked at another way, if two features are in the same group, the structural unit composed of the focus feature and one of those features is identical to the structure formed by the focus feature and the other non-focus feature. Fig. 33 illustrates the grouping offeatures around a hole in the hinge part. Nearby feature selection" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000214_(asce)0733-9399(1999)125:12(1365)-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000214_(asce)0733-9399(1999)125:12(1365)-Figure1-1.png", + "caption": "FIG. 1. Cross Section of Arbitrary Shell of Revolution with Variable Thickness in Meridional Direction f and Positive Gaussian Curvature, and Curvilinear Coordinate System (f, z, u)", + "texts": [ + ", Kyongbook 780-712, South Korea. Note. Associate Editor: Mark Hanson. Discussion open until May 1, 2000. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on January 23, 1998. This paper is part of the Journal of Engineering Mechanics, Vol. 125, No. 12, December, 1999. qASCE, ISSN 0733-9399/99/0012-1365\u20131371/ $8.00 1 $.50 per page. Paper No. 17617. J. Eng. Mech. 1999. Fig. 1 shows the cross section of an arbitrary shell of revolution with thickness h varying in the meridional direction f. The shell is generated by rotating the section about the y-axis. Its curvature is described by the curvature of its middle surface (shown as the dashed curve in Fig. 1). A typical point P in the shell is positioned by giving its meridional and circumferential angles, f and u, respectively, and by the distance z measured along the normal to the midsurface. Thus, the shell surfaces are located at z = 6h/2. The ends of the shell (top and bottom) are determined by ft and fb, where the thicknesses are ht and hb, respectively. The meridian line that generates the shell midsurface when rotated is depicted in Fig. 2. This generating curve may be prescribed either by a single equation r = r(y) (1) JOURNAL OF ENGINEERING MECHANICS / DECEMBER 1999 / 1365 125:1365-1371", + " The principal curvatures of the middle surface are x1 = 1/r1 and x2 = 1/r2. The Gaussian curvature is k = x1x2. Although Figs. 1 and 2 depict a shell having positive k, shells with negative k (e.g., hyperboloidal), or both positive and negative k (e.g., toroidal) may be analyzed. To analyze the free vibrations of the thick shell of revolution, the kinetic energy T and strain energy V will be developed in terms of displacement components uf, uz, and uu, taken positive in the directions of increasing f, z, and u (Fig. 1). The kinetic energy is simply 125:1365-1371. D ow nl oa de d fr om a sc el ib ra ry .o rg b y N ew Y or k U ni ve rs ity o n 05 /1 0/ 15 . C op yr ig ht A SC E . F or p er so na l u se o nl y; a ll ri gh ts r es er ve d. 1 2 2 2T = r(u\u0307 1 u\u0307 1 u\u0307 ) r r df dz du (5)f z z zE u2 V where r = mass density; the overdots denote time derivatives; and the integration is carried out over the domain V of the shell. The radii rz and rz needed for the volume element are r (f, z) = [r (f) 1 z]sin f; r (f, z) = r (f) 1 z (6a,b)z 2 z 1 The strain energy of deformation is expressed in terms of the stresses fij and strains \u03b5ij as 1 V = (s \u03b5 1 s \u03b5 1 s \u03b5 1 2s \u03b5 1 2s \u03b5zz zz z zE ff ff uu uu f f fu fu2 V 1 2s \u03b5 )r r df dz duz z z zu u (7) The well-known stress-strain equations of isotropic, linear elasticity are s = l\u03b5 1 2G\u03b5 (8)ij ij where l = En/(1 1 n)(1 2 2n) and G = E/2(1 1 n) = Lame\u0301 parameters, expressed in terms of Young\u2019s modulus E, and Poisson\u2019s ratio n; and \u03b5 [ \u03b5ff 1 \u03b5zz 1 \u03b5uu", + " The 3D results of Table 2, which are for thick shells, are in accord with this trend. It is also interesting to note in Table 2 that, although the three shells all have the same ratio of mean thickness to length (hm /L = 0.25), a decrease of the thickness ratio from 1 to 0 typically results in increased frequencies. The one exception to this among the first five modes is Mode 1. LINEARLY VARYING THICKNESS As a second example, one involving meridional curvature, a spherical shell segment having linearly varying thickness is used. This is well represented by Fig. 1, with r2 = a, which is the spherical radius (a constant). A convergence study is presented in Table 3 for the first five frequencies of n = 1 modes for a shell having ht /hb = 1/3, ft = 307, fb = 907, and ht /a = 0.1 (Fig. 1), with n = 0.3. The convergence rate is seen to be approximately the same as that for the conical shell (Table 1), requiring frequency determinants of order 96\u2013150 for four-digit convergence of the first five frequencies. Again, one observes that a thick (2D) shell theory, as represented by TZ = 2, yields frequencies that are 1370 / JOURNAL OF ENGINEERING MECHANICS / DECEMBER 1999 J. Eng. Mech. 199 FIG. 4. Cross Sections of Spherical Shell Segments Corresponding to Table 4 (hm /a = 0.2, ft = 30&, ft = 90&) significantly different than those from 3D analysis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003666_0278364907080737-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003666_0278364907080737-Figure2-1.png", + "caption": "Fig. 2. Simply connected configuration space introduced by Cowan et al. (a) The beacons are represented by the gray circles named b1 b2 b3 . (b) Configuration space plotted in the image projection space.", + "texts": [ + " The resulting camera map incorporates (a transformed copy of) the full relative pose and its gradient will be used to generate a servo controller that forces convergence to (some arbitrarily small specified neighborhood of) any desired visible pose along \u201csafe\u201d transients guaranteed to maintain the view along the way. For the purposes of this paper, it is sufficient to identify a beacon with the location of its centroid projected onto the plane. Given three such centroids, without any loss of generality, we define their composed landmark parameter space 2 1 by fixing the world frame so that the second beacon is at the origin and the remaining beacons lie along lines going through the origin that define congruent angles: : 1 2 2 1 1 0 2 0 0 (see figure 2(a)). The coordinates of each beacon bi in the world frame are: b1 b2 b3 1 R e2 0 2 RT e2 (1) where R [cos sin sin cos ] is the standard 2 2 rotation matrix and e2 is the canonical base vector [0 1]T . We define the camera map to be a transformation that relates the pose (position and orientation) of the robot in the world 3. We assume that the camera is fixed to the robot\u2019s frame. frame (SE 2 ) to the pinhole projection of the beacons in the camera\u2019s image plane. For convenience, we treat the camera image plane as (a subset of) the unit sphere, 2, and drop the azimuthal component, thereby projecting all pinhole camera readings onto the great circle, 1 2, corresponding to bearing in the horizontal plane", + " In this manner, a beacon\u2019s pinhole image is parameterized by the angle of the ray that connects it to the camera center when projected onto the horizontal plane. We denote by this image projection space\u2014the triple of angles of each of the beacons in a landmark. Note that, although a physical camera has a flat image plane, we prefer to work with a ray\u2019s angle computed by the transformation i arctan i 2, where i is the i th angle and i is the coordinate measured by the camera in meters (after pre-processing using a lens calibration model), as illustrated in figure 2(a). Because subsequent computations involving robot pose associated with the camera map are most easily expressed in polar coordinates, we find it expedient to introduce a new space4, 2 , diffeomorphic to the robot configuration space with coordinates r (see figure 2(a)), where 2 is the 2-dimensional torus. To reconstruct the pose of the robot in the world frame, with coordinates x y , a composition of changes of coordinates is implemented. We denote the change of coordinates from the intermediate space to the image projection space by intermediate camera map cci : , cci : arctan 1 arctan 2 arctan 3 (2) where the terms i : 2, defined by i : R R bi r R e2 (3) are vectors that go through beacons bi for a given configuration and the function arctan is assumed to take into account which quadrant its argument is in", + " The following formula gives a rough idea of how to compute the parameter d approximately, given the distance between beacons 1 and 3, denoted by db, and the robot\u2019s maximum distance away from the beacons, denoted by dmax , both with units in meters: d 2 arcsin db 2dmax By construction explodes at the obstacles and is zero at the goal. The resulting navigation function : [0 1] is the squashed version of , with constant shaping scalar 0: : (8) In the world frame the navigation function is the composition q : q (9) and the gradient is the pullback: q DcT q q . Let I be the convex hull generated by the planes defined by the terms in the denominator of , i.e. M 1 0, 1 2 0, etc, illustrated in figure 2(b). The robot\u2019s configuration space is defined by: : c 1 I (10) The physical implementation of the algorithms presented in this paper was carried out on the hexapod robot RHex, whose horizontal plane behavior is known from empirical experience to be roughly modeled as a quasi-static unicycle. Therefore we recall the equations of motion of the unicycle, extensively studied in the literature (Zenkov et al. 2002), with q x y : x sin u1 y cos u1 u2 (11) The nonholonomic constraint is A q q 0 , where A q cos sin 0 (12) Notice that the nonholonomic constraints of the unicycle preclude the direct use of the navigation function gradient vector field", + " Lens correction: the standard Heikkil\u00e4 and Silven (1997) lens model is used. The lens correction map includes all the intrinsic camera parameters, including focal length, and returns \u201cnormalized\u201d points, with units in meters, projected into a plane 1 meter away from the robot\u2019s camera. Calibration is performed at startup using a flat checkerboard surface. 3. Image stabilization: The centroid information provided by the image processing library follows a postprocessing roll correction. Since it assumed that the beacons project into a line, following figure 2(a), roll correction is accomplished by fitting a line to the 2D centroid of the 3 blobs (chosen by size and class) and attaching a frame to it. The beacon coordinates are defined in relation to that frame. The following simplified expression is used in the experimental implementation, where Xi Yi are the centroids of the three beacons in the image plane after Heikkil\u00e4\u2019s lens correction map: i Xi Yi 1 2 (57) i arctan i 2 (58) with, : . Xi . Yi 3 . Xi Yi . Xi 2 3 . X2 i (59) In the simulations developed in Section 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003597_bf02844206-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003597_bf02844206-Figure5-1.png", + "caption": "Figure 5 Over-trace of blade displacement from several views including (a) oblique frontal, (b) oblique sagittal, (c) transverse, and (d) sagittal plane. Axes are marked X, Y and Z as indicated, arrows indicate the direction to the goal and (a) and (b) represent TC and HC, respectively.", + "texts": [ + " 5a and b appear to confirm earlier observations that the path of the stick from the top of the backswing to initial ground contact (TC) is primarily pendular in nature (Polano, 2003; Woo, 2004), similar to a golf swing (Mason et al., 1992; Neal, 1983; Whittaker, 1999). However, once the toe makes contact with the ground, the blade\u2019s movement path shifts dramatically in all directions. The blade\u2019s sagittal (YZ) plane movement demonstrates a primarily linear (or translational) movement path (Figs 5c and d) and it shifts away from the base of support in the X direction (Fig. 5a), thus confirming earlier observations (Woo, 2004) and further suggesting that an important transition phase between the primarily rotational acceleration of the stick in downswing and the primarily linear acceleration of the stick during loading exists. Figs. 5a, b and d also demonstrate that during this phase (from TC to HC) there is a clear tendency to load the blade from toe to heel in a \u2018rocker\u2019-like fashion. It appears that this \u2018rocker phase\u2019 is at least partially a function of the stick\u2019s geometry (particularly the lie angle)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002209_s00170-005-2602-4-Figure18-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002209_s00170-005-2602-4-Figure18-1.png", + "caption": "Fig. 18. Profile error", + "texts": [ + " \u03b22 = 90\u25e6) 8.2 Effect of a profile error on the dynamic response Profile errors result in imperfections on the geometry of the teeth. It is characterized by a shape deviation between the real profile and the theoretical profile of the tooth. A profile error constitutes a source of important excitation in gearboxes. For similar teeth profiles error, these excitations are periodic of fundamental frequency equal to the mesh frequency corresponding to the wheel affected by this error. As it is presented in Fig. 18, the defect of profile error is introduced by the addition of a displacement type term ep(t) to the tooth deflection on the line of action. This error is supposed identical on all teeth for the wheel (12). We can assimilate its variation by: ep(t) = \u221e\u2211 n=1 ep12 sin (2\u03c0n fe1t) (33) where ep12 and fe1 represent respectively the profile error value and the first mesh frequency. The profile error leads to a new external excitation expressed by: { Fep(t) } = k1(t) \u2202\u03b41(t) \u2202qi ep12(t). (34) The profile error with amplitude ep12 = 100 \u00b5m will amplify the amplitude of the linear displacements on the three bearings" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000611_jsvi.2002.5111-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000611_jsvi.2002.5111-Figure1-1.png", + "caption": "Figure 1. A simple rotor system geared by bevel gears and their virtual cylindrical gears of bevel gears.", + "texts": [ + " Firstly, the dynamic model is developed to suit the perpendicularly spiral bevel-geared rotor-bearing system, and then the mechanism of coupled vibrations of the system is analyzed in theory. Finally, we analyze the dynamic characteristics of the system in some cases. Bevel gear teeth are higher element kinematic pairs, with constrained motion, that engage with slide contact. The tooth surface of a bevel gear is formed by a family of spherical involute curves for straight bevels [9]. Therefore, the inherent generalized displacements between a pair of bevel gears are complex. Figure 1(a) shows a rotor system geared by a bevel gear pair, whose transmission can be simplified by a virtual cylindrical gear pair shown in Figure 1(b). In this analysis, the major assumptions, such as neglecting the errors and deformations of gear teeth, are the same as in reference [8], so that the following relationship between two gears is also satisfied: xe1 sin a\u00fe ye1 cos a\u00fe rb1y1 \u00bc xe2 sin a\u00fe ye2 cos a\u00fe rb2y2; \u00f01\u00de where a is the pressure angle of the gear, and rb1 and rb2 are the radii of base circles of the two virtual cylindrical gears. As shown in Figure 2(a), the straight bevel motion described in the co-ordinate frame oxeiyeizei can be determined from xei yei zei 8>< >: 9>= >; \u00bc cos di 0 sin di 0 1 0 sin di 0 cos di 2 64 3 75 x0 i y0 i z0i 8>< >: 9>= >;; \u00f02\u00de where di \u00bc d1; d2 (i \u00bc 1; 2) are the pitch cone angles and xi; yi; zi (i \u00bc 1; 2) are the co-ordinates of the two gear centers", + "q\u00fe \u00f0G\u00fe C\u00de\u2019q\u00fe Kq \u00bc Q; \u00f08\u00de where M; G; C and K are the generalized mass, gyroscopic, damping and generalized stiffness matrices, and Q and q are the generalized force and displacement vectors respectively. In general, Q is composed of unbalanced forces, exciting torque, etc. in geared rotor dynamics. Although the presented model is developed for the spiral bevel-geared rotor-bearing system, it can also be used in the corresponding system geared by zero1, straight bevel gears, For the hypoid geared system, a further co-ordinate transform between gear and pinion may be needed. In order to clarify the mechanism of coupled vibration of the bevel-geared system, we consider the system as shown in Figure 1(a), which is composed of two same massless rotors and spiral bevel gears. The rotors are supported by rigid bearings. Ignoring the motion in the x direction (horizontal), constraint equation (7) is haply of the following form: y1 \u00fe z1 \u00fe rby1 \u00bc y2 \u00fe z2 \u00fe rby2: \u00f09\u00de Although the above equation is not precise, it implies the relationship among the lateral, axial and torsional direction. In this way, a system of 5 degrees of freedom can be obtained while neglecting the gyroscopic effect and damping forces (or moments)", + " The consequences indicate that it can evoke considerable responses in the lateral and axial directions besides its own direction, therefore the traditional criteria for the control of vibration of the system are facing a challenge in the spiral bevel-geared rotor system. In order to illustrate the modelling procedure of a spiral bevel-geared rotor system, a simple example is given here. The system is composed of two rigid bevel gears, and two massless rotors, which are supported on rigid bearings as shown in Figure 1(a). The coordinate systems oixiyizi (i \u00bc 1; 2) refer to rotor 1 and rotor 2, respectively, where oixizi (i \u00bc 1; 2) are the horizontal planes. For the system, equation (5) can be written as y2 \u00bc \u00bdd1y1 \u00fe \u00f0a1x1 \u00fe b1y1 \u00fe c1z1\u00de \u00f0a2x2 \u00fe b2y2 \u00fe c2z2\u00de =d2: \u00f0A1\u00de Kinetic energy: The total kinetic energy of the system is the summation of the translational and rotational kinetic energies of rigid disks, gears and rotors as below. After neglecting the terms of higher order, the kinetic energy can be approximated as T X2 i\u00bc1 1 2 mi\u00f0 \u2019x2 i \u00fe \u2019y2 i \u00fe \u2019z2i \u00de \u00fe 1 2 Jz i \u00f0Oi \u00fe \u2019yi\u00de2 \u00fe 1 2 Jd i \u00f0 \u2019j2 i \u00fe \u2019c 2 i \u00de Jz i Oji \u2019ci ; \u00f0A2\u00de where mi (i \u00bc 1; 2) is the mass of the ith gear, J j i (i \u00bc 1; 2; j \u00bc d; z) the diametrical and polar moments of inertia, xi; yi; zi; ji; ci and yi (i \u00bc 1; 2) the translational displacements of the gear center and the tilting angles, and torsional angle of the ith gear respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001747_s0022-0728(01)00644-1-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001747_s0022-0728(01)00644-1-Figure2-1.png", + "caption": "Fig. 2. Cyclic voltammograms for 2.0 M cobaltoxime I complex on Pt disk electrode (3 mm diameter) in an acetonitrile solution containing 0.1 M TBAP at scan rates: (1) 25; (2) 50; (3) 75; (4) 100 mV s\u22121.", + "texts": [ + " In acetate buffer solutions of pH 4.0, the modified electrodes exhibited well shaped cyclic voltammograms corresponding to the reversible transformation of the surface deposited cobaloxime complexes. The electrochemical experiments were carried out at a thermostated temperature 25 0.1 \u00b0C. 3.1. Electrochemical properties of cobaloxime complexes in acetonitrile solution The cyclic voltammograms of a cobaloxime I+acetonitrile solution at various scan rates on the surface of a Pt disk electrode are shown in Fig. 2. This complex exhibits two well defined reversible voltammetric responses corresponding to the Co(III)/Co(II) and Co(II)/Co(I) couples, as was reported earlier for some other complexes [36]. The respective formal potentials of the two couples are about \u2212100 and \u2212750 mV versus Ag/AgCl/0.1 M TBAPF6 in acetonitrile. The plots of peak currents versus (scan rate)1/2 for both anodic and cathodic peaks are linear for sweep rates of 25\u20132000 mV s\u22121 (not shown). For both couples, the ratios of anodic to cathodic peak currents are unity and the separation between the cathodic and anodic peak oxyphenylporphyrin chloride [25], phthalocyanine and naphthalocyanine [26\u201328], anthraquinone polymers [29,30], polynaphthoquinone [31], poly-(o-phenyldiamine) [32] and 1,4-naphthoquinone derivatives [33]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002537_09544097jrrt67-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002537_09544097jrrt67-Figure7-1.png", + "caption": "Fig. 7 Central pivot for Y25 Bogies (all dimensions in mm)", + "texts": [ + " Table 3 shows the results for a vertical load of 18.9 KN. To model primary suspension force elements, the Kolsch method [16] has been used, explained in equation (6), in which the valuem denotes sharpness of diagram (Fig. 6) in the transition areas between stick and slip motions. Figure 6 shows force displacement in the vertical direction with m \u00bc 10. C0 \u00bc Ch Cg _K \u00bc C0 _X 1 0:5 sign( _XK )\u00fe 1 2K FD m F \u00bc CgX \u00fe K (6) The bogie frame is connected to the carbody through a central pivot and side bearers [17]. Figure 7 shows the central pivot that is a spherical joint. The bogie frame has angular motions about the joint centre with respect to the carbody. Contact surfaces and their relative motions generate dry friction in the central pivot. Researches and tests by Nielsen [18] show that the moments in the central pivot have maximum value, which can be evaluated as in equation (7). These values are in the slip mode, and in the stick mode the angular stiffness is about Table 1 Mass, moment of inertia, and centre of mass for the Y25-freight truck Y25 assembly Centre of mass (m) Moment of inertia (kg m2) Mass [kg] Ixx Iyy Izz One unit Wheelset with axle box hwh \u00bc 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003392_acc.1994.735092-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003392_acc.1994.735092-Figure1-1.png", + "caption": "Figure 1: Spacecraft coordinate frames", + "texts": [ + " In addition, if W is persistently exciting, the estimated parameters asymptotically converge to the true parameters. The adaptive control laws are applied to the problem of attitude control and momentum management of the Space Station assuming that there are uncertainties in the inertia matrix of the spacecraft. 5.1. Equations of Motion of Spacecraft The nonlinear spacecraft model includes the spacecraft attitude kinematics, rotational dynamics, and CMG momentums. The coordinate systems of interest are the local-vertical, local-horizontal (LVLH) axes and the body axes (see Fig. 1). The Euler angle se uence associated with this s stem is pitch, yaw, an\\ roll around.YB, Z,, and d, res ectively. The XL - ZL plane is the instantaneous o s i t plane. It is assumed that the spacecraft is in a circular orbit with orbital angular velocity n. In the sequel, (61, 62,6'3) are the roll, pitch, and yaw Euler angles of the bod with respect to LVLH, w is the absolute an ular ve3bcity vector in the body axes, U is the C&G control torque in the body axes, h is the CMG momentum in the body axes, and I is the spacecraft inertia matrix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003560_joe.2007.893688-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003560_joe.2007.893688-Figure2-1.png", + "caption": "Fig. 2. Cross-sectional view of ROSS showing removable motor frame with dual motors attached to the underside of HDPE hull cover.", + "texts": [], + "surrounding_texts": [ + "1) Hydrostatic Considerations: ROSS was designed to be positively buoyant, with principal buoyancy contributions from the battery bin and the electronics casing providing a total buoyancy of 108 kg to offset the total dead weight in air of 95.5 kg. For the purpose of locating the positions of the center of buoyancy (CB) and the center of gravity (CG) of the complete structure, the origin of the reference axes was located at the nose tip. Computations on AutoCAD\u2122 show that the separation between CB and CG in the vertical plane is about 51 mm with CG coordinates (Xg, Zg) at (1112, 24) mm and CB coordinates (Xb, Zb) at (1210, 27) mm. The hydrostatic restoring moment prevents ROSS from rolling over under most conditions. As a safety measure, two slim line empty PVC floats were secured to the sides of the main hull to reduce roll and pitch to within 1 . This was not used in all our tests, but if integrated with the main hull, it results in a highly stable platform. 2) Towing Resistance, Propulsion, and Endurance: At a typical forward speed of 1.4 m/s, which was captured from GPS field data, and an associated Reynolds\u2019 number , the towing resistance (or axial drag) of ROSS can be estimated from to be 40 N where 1000 kg/m is the density of seawater and is the drag coefficient of the hull taken to be a finite cylinder with fineness ratio 5. The hull is attached to a motor frame which presents an additional estimated drag of 8 N, resulting in an approximate total towing resistance of 48 N and a towing power equal to 66 W. The vehicle is propelled by two Tecnadyne 520 brushless dc motors each capable of a maximum forward thrust of 70 N at 940 r/min in water. In practice, input power of 304 W was supplied to the thrusters from a bank of lithium polymer batteries at a working current of 1.4 A per thruster. This gives a total propulsion system efficiency . The endurance of ROSS is approximately 7 h assuming that the 12-Ah bank of batteries is derated by 20%, and that the thrusters require an average current drain of 1.4 A. The hotel payloads on ROSS, which include navigational and communications hardware, chlorophyll, altimeter sensors, and control electronics, have a current drain of 1.5 A from a separate bank with a similar discharge rate of 0.1 C (C-rate). The specifications of the experimental ROSS craft are summarized in Table I. III. In Situ CALIBRATION OF CHLOROPHYLL SENSOR A low-cost miniature submersible fluorometer (MiniTracker II, Chelsea Instruments, U.K.) was used in experiments to measure in situ chlorophyll concentrations along the mission tracks followed by ROSS. The fluorometer has a concentration range from 0.03 to 100 mg/m which varies linearly with output voltage in the range 0 to 4 V dc . It uses a high-intensity blue (430 nm) light-emitting diode (LED) source as the excitation source and receives fluorescence from chlorophyll cells at a center wavelength of 685 nm. The in situ sensor is mounted below the nose volume on ROSS, thus avoiding spurious signals arising from air bubbles released from the turbulent wake of the propeller motors which are located further down in the aft section. The motion of the craft causes seawater to flow past an open cowled enclosure on the sensor endcap. This arrangement emulates a dark chamber and does not require seawater to be pumped through it. The recommended method of calibrating chlorophyll sensors is by the in vivo chlorophyll method. The reason for this is because the calibration graph depends on the plankton species in seawater. For this determination, a Perspex box was filled with 3 L of freshly filtered seawater whose concentration was measured previously by the standard method using a Turner Design fluorometer [see (1)]. Measurements of the sensor output were made over a longer 15-s interval for different seawater samples, including a blank sample using distilled water. The in vivo graph shows a slope of 5.084 mg/m /V with a fitted linear regression line to measured chlorophyll concentration of in situ water samples in Fig. 4. We took adequate care in suspending the sensor inside the Perspex box of seawater, and in lining the sides of the box with black paper so as to cut down on possible spurious reflection and fluorescence from Perspex. The calibration equation used in converting sensor volts to chlorophyll is Chl sensor volts" + ] + }, + { + "image_filename": "designv11_2_0002319_0141-0296(88)90015-6-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002319_0141-0296(88)90015-6-Figure2-1.png", + "caption": "Figure 2 Basic two bars system", + "texts": [], + "surrounding_texts": [ + "Cable network analysis by a nonlinear programming technique J. P. Coyette and P. Guisset\nDynamic Engineering S.A., Ambachtenlaan, 21, B3030 Heverlee, Belgium (Received November 1986; revised August 1987)\nStatic cable network analysis is an highly geometrically nonlinear problem which can be solved by direct minimization of total potential energy. Theoretical and practical aspects related to extensible (elastic) cable analysis are presented. A finite element approach supports evaluation of potential energy. The nonlinear problem is solved through an optimization code (MINOS). Great flexibility results from the various constraints (linear or nonlinear, equality or inequality) which can be imposed. Applications are presented including special boundary conditions such as unilateral contact without friction. Extension to dynamic analysis is also provided whereas basic information about the software developed is given.\nKeywords: cable analysis, geometric nonlinearities, energy minimization, nonlinear optimization\nBecause of their flexibility, cables offer interesting possibilities for shaping attractive three-dimensional forms. The main difficulty encountered in cable structure analysis is related to the lack of flexural rigidity which leads to large displacements. The geometric nonlinearities arise because the deformation of the structure must cause sufficient strain in the cables to produce the required changes of tension in order to satisfy the static equilibrium.\nDue to unavailability of analytical solutions (except for simple cases), structural analysis of cable structures implies generally the use of numerical methods. A classical approach in this field is the (stiffness) displacement method which leads to set up equilibrium equations in terms of displacements. Such-an approach is quite satisfactory but often get to troubles especially when the initial shape is far from the solution to be obtained.\nA better solution can be achieved in this case by resorting to the basic energy concepts underlying the stiffness approach. The theorem of minimum total potential energy is very attractive in this context, especially when its use is based on a powerful nonlinear optimization code.\nA finite element approach supports the evaluation of this energy function (the objective function of the minimization process). Various constraints can be considered, enabling for example the treatment of unilateral contact without friction.\nAfter determination of the static solution, a dynamic\nanalysis can be easily performed by direct integration of the motion equation in the time domain, using the Newmark scheme.\nBasic concepts\nIn order to simplify the analysis, the following hypotheses are taken into account:\n\u2022 cables are perfectly flexible and possess only axial stiffness \u2022 material is linear elastic \u2022 only small strains are involved\nThe determination of the equilibrium position is based on the theorem of stationary potential energy:'\n~ = 0 (1)\nwhere\n= U + V (2)\nis the total potential energy, the sum of the strain energy U and the potential energy of the external loads I/. In order to equilibrate the cable system under the action of static loading, the total potential energy must be minimum:\nStable ,~ n minimum (3)\nequilibrium\n0141-0296/88/01041-06/$03.00 \u00a9 1988 Butterworth & Co (Publishers) Ltd Eng. Struct. 1 988, Vol. 10, January 41", + "Strain energy\nStrain energy can be evaluated from\ng = ~ EAe. 2 ds (4)\nwhere EA is the axial rigidity of a cable, \u00a2 is the axial strain, ds is the infinitesimal element along a cable and S denotes all the cables of the structure.\nWith reference to Figure 1, axial strain is calculated from\ndp - ds dp - - 1 (5)\nds ds\nwhere dp is the actual (strained) length of an initial (unstrained) element of length ds.\ndp = ((dx) 2 + (dy) 2 + (dz)2) \u00bd (6)\nSo, (5) becomes\n((dx V (dq (azVV c. = + + \u2022 - 1 (7)\n\\ \\ d s ) \\as/ \\ ~ ) )\nExternal potential\nThe external potential is defined according to\nV = V. + V F (8)\nwhere Vg is the potential related to dead loads and V F the potential of concentra ted loads. Grav i ty forces are assumed to act in the opposi te direction to the z-axis. So, Vg is given by:\nGeometric configuration of an infinitesimal cable element\nwhere\nALl = L1 -- L (12) AL2 = L2 - L\nare the elongat ions of bars 1 and 2. If small displacements are considered, e longat ions are related to displacements variables (u, v) by\nALl = u cosa + v sine (13) AL2 = - u cose + v sine\nSo, relation (11) becomes\nEA n = 2L- (u cose + v sine) 2\nEA + 2 L - ( - u cose + v sine) 2 - Pv (14)\nThe minimizat ion process leads to the linear equat ions\nOK 2EA - - 0 o r - - c o s 2 e u = 0 ~3u L\n(OK 2EA - - 0 or - - s i n : e v = P ~v L\n(15)\nand the solution appears to be\nPL u = 0, v = (16)\n2EAsine\nThe n energy function (14) is illustrated in Figure 3 for the part icular case considered (Lx = 0.80 m, Ly = 0.60 m, E = 2 x 1 0 S k N m -2, A = 5 x 1 0 - g i n 2 , P = 5 0 k N ) . T h e solution point S given by (16) can be identified on the n surface.\nIf large displacements are tolerated, e longat ions of the two members have to be formulated as\nALl = ((Lx + u) 2 + (Ly + v ) 2 ) 1/2 - L (17) AL2 = ((Lx + u) 2 + (Ly + / ) ) 2 ) 1 / 2 _ L\nand the corresponding n energy function takes the form\nEA n = ~ L (((L ~ + u) 2 + (Ly + v ) 2 ) 1/2 - - L ) 2\nEA + 2L- (((Lx - u) 2 + (Ly + V)2) 1/2 __ L ) 2 (18)\n- - P v\nThe minimizat ion process of this (non-quadrat ic) func-\n42 Eng. Struct. 1988, Vol. 10, January", + "tion leads to two nonlinear equations which have to be solved by an iterative method.\nAgain an illustration of g energy is provided in Figure 4 for the previously considered case. The two stable equilibrium configurations S and S' (Figure 5) can be identified on this surface. Of course, configuration S' has to be discarded here in the context of cable structures.\nFinite element diseretization\nThe purpose of FE discretization is two-fold: firstly to compute numerically the potential energy function, and then to achieve the minimization of that function, nodal coordinates being the decision variables of the problem.\nEnergy function evaluation\nReplacing the continuous cable by connected finite elements, the energy function can be written as\n7~ = ~ 7~ e -~- V F ( 1 9 ) e\nwhere % is the element contribution to the objective function:\n1~ e = U e + Va, e ( 2 0 )\nIn this expresson, Ue is the element strain energy and Vg,\u00a2 is the element gravity loads potential. Introducing, the normalized local coordinate defined through the relation (Figure 6)\nEng. Struct . 1988, Vol. 10, Janua ry 43" + ] + }, + { + "image_filename": "designv11_2_0000755_robot.1996.509174-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000755_robot.1996.509174-Figure3-1.png", + "caption": "Fig. 3 Compression due to object displacement", + "texts": [ + " 2. The origin of the contact-point coordinate frame C i is fixed at the center of curvature, and the axis xi of C, is along outward normal of object at contact point. The relative position of the origin of C, with respect to CO is denoted by p i , the relative orientation of C, with respect to CO is denoted by B, . The radius of curvature of the object and the finger at i-th contact point is defined by R, and r, , respectively. If the object has convex arc at the i-th contact point as shown in Fig. 3(a), we have R, > 0 . If the object has concave arc as shown in Fig. 3(b), we have R, < 0. The radius r, is defined in a similar way. In order to simplify the discssion, we make following assumptions. (2 1) Each finger is in a frictionless point contact with the object and has a. virtual spring shown in Fig. 2. (2 2) The shapes of an object and each finger are known, and can be approximated by circles of the curvature, respectively. (2.3) The grasping system is in an equilibrium state initially, and contact points and contact forces are known. (2.4) Two dimensional grasp", + " (A , - a , ) +(B , -b,> = ( R , + \u2018 ; I 2 . By substituting Eq. (2) into Eq. (3), the compression 6, is given by (3 1 2 2 6, = .Yj - (RI + 5 ) k 4- . 6; =x, - ( R , + r , ) + J W . ( 5 ) (4) Considering the physical constraint, we have Equation ( 5 ) denotes the relationship between the displacement (xi, y,,<;) with respect to C, and the compression 6, at the virtual spring k, . In the same way, when either the object or the i-th finger has concave arc around the i-th contact point as shown in Fig. 3(b), (c), the compression 6; is given by 6, =x, -(I?, + r , ) - J ( I ? , + r , ) 2 - y 1 2 . (6) 2.2.2. Object Coordinate Frame We investigate the relationship between the displacement at the origin of CO and the compression 6 , . When infinitesimal translation (x, y) and rotation < occur at the origin of C, due to extemal disturbance, the displacement at p , , which is the position of the origin of X i , is represented by ( - Y , Y ) ~ + (Rot(47 - f 2 ) p I , (7) where I , is a 2 x 2 identity matrix, and Rot(*) is a rotation matrix represented by COS(*) -sin(*) sin(-) COS(*) By transforming the displacement (x,y,<) in C, into the displacement ( x l , in C l , we have < I = < Using 7\u2019 PI = P , ( C O S ( Q ; - $,),sin(@, - 4,)) > we have x, = x c o s Q , +ysinB; + p i { c o s ( < - + i ) - c o ~ ~ i ) , y , = -xsin6\u2019, + ycosQ, + p i {sin(<- 4;) + sin+,} " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003614_10402000701739271-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003614_10402000701739271-Figure2-1.png", + "caption": "Fig. 2\u2014Visual comparison of thrust washer wear under different loading conditions.", + "texts": [ + " The frictional torque is recorded from the power output of the motor, since with increasing frictional torque the power needed to run the motor at a constant speed increases as well. The temperatures are recorded using thermocouples embedded near the bearing surface. The experimental results from Jackson and Green (2), (3) show that the thrust washer bearing is prone to severe and sudden distress at high loads and speeds. These are similar to the trends predicted in Salomon (29) and Bollani (30) and are shown in the progression of the washer distress in Fig. 2. By visual inspection D ow nl oa de d by [ G eo rg ia T ec h L ib ra ry ] at 1 0: 38 1 1 N ov em be r 20 14 Fig. 3\u2014Example of finite element predicted deformation of a three-dimensional thrust washer surface (all lengths are in meters). it is seen that at high speeds the wear types change from abrasive to scuffing. The scuffing depicted in Fig. 2 is so severe that the washer at the highest load and speed has adhered to or welded to the contacting part behind it. While at a low load (260.9 N) and speed (1300 rpm) the washer wears very little, indicating that there is then probably a full film of lubrication separating the surfaces. These points of severe distress are characterized by large and sudden increases in the bearing temperature and friction. The bearing, if not unloaded and shut down immediately, can also melt and weld together at this state" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000771_j.1460-2687.1999.00011.x-Figure7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000771_j.1460-2687.1999.00011.x-Figure7-1.png", + "caption": "Figure 7 Model used to evaluate the effect of the forearm when a ball impacts at a distance b from the racquet centre of mass. The racquet is pivoted at the wrist and the forearm is pivoted at the elbow.", + "texts": [ + " As shown by Casolo and Ruggieri (1991), the effective mass of the forearm is less than the actual mass since the racquet applies an impulsive force to the end rather than the centre of the arm, the other end of the arm being pivoted at the elbow. Furthermore, the arm is not rigidly attached to the handle, due to the \u00afexibility of the wrist. Consequently, the effect of the hand and the arm cannot be simulated correctly simply by adding a \u00aexed mass to the end of a freely suspended racquet. The dynamics of the situation can be modelled as shown in the following Section. A simple model of the effect of the arm on racquet dynamics, consistent with the above observations, is shown in Fig. 7. The racquet is approximated as a beam of mass M and length L connected by a pivot joint to the forearm, which is represented as a beam of mass MF and length LF. It can be assumed that the other end of the forearm is pivoted about the elbow, but it is assumed for simplicity that the elbow does not translate during the impact. The impact of a ball on the racquet can be represented by an impulsive force, F, applied at a distance b from the racquet CM, the CM being located a distance h from the end of the handle", + " The equations of motion are then F FR MdV=dt 1 Fb\u00ff FRh Icmdx=dt 2 and FRLF IFdxF=dt 3 where V is the velocity of the CM of the racquet, I is the moment of inertia of the racquet about its CM, IF is the moment of inertia of the forearm about the elbow, x is the angular velocity of the racquet and xF is the angular velocity of the forearm. The velocity of the pivot joint at the wrist is given by 70 Sports Engineering (1998) 1, 63\u00b178 \u00b7 \u00d3 1998 Blackwell Science Ltd VP LFxF hx\u00ff V 4 In these equations, it is assumed that x is measured in an anticlockwise sense (as in Fig. 7) and that xF is measured in a clockwise sense as appropriate for an impact near the tip of the racquet (as in Fig. 8). Similarly, V is taken as positive when the racquet moves downwards in Fig. 7 and VP is taken as positive when the pivot joint moves upwards. Since the racquet exerts a force on the forearm at the pivot joint, an effective mass of the forearm, ME, can be de\u00aened by the relation FR MEdVP/ dt MELFdxF/dt, So from eqn 3, ME IF=L2 F. For example, if the forearm is approximated as a uniform beam, then IF MFL2 F=3 so ME MF=3. Equations (1)\u00b1(4) can be combined to show that dV/dt x dx/dt where x Icm MEh h b Mb ME h b 5 Now consider a point on the racquet located a distance x to the right of the CM where the racquet velocity is V ) xx" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002694_isatp.2005.1511447-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002694_isatp.2005.1511447-Figure4-1.png", + "caption": "Figure 4: (a) Schematic representation and (b) picture of the prototype.", + "texts": [ + " The values of the contact angles can be controlled using appropriate coatings on the surfaces in contact with the liquid. Moreover if the objects to be handled are not flat their curvature radius has to be taken into account in the evaluation of the capillary force. An experimental set up was conceived and a demonstration prototype actualized. It is provided of 2 d.o.f. (vertical and horizontal translation) and an elastic membrane, with radius (Rg) equal to 0.8 mm, was fixed to its bottom tip (figure 4a). A hydraulic actuation system controlled the shape of the membrane and, in particular, realized the transition between the flat and the hemispherical configuration. The elastic membrane is mechanically fixed to the tip of a micro-syringe filled with an uncompressible liquid (water); in this way the curvature of the membrane is controlled by the displacement of the plunger, actuated by a micro-comparator. When the plunger is pushed inside the syringe, the liquid induces a uniform stress on the membrane, which is thus deformed maintaining a constant curvature radius" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002866_j.jsv.2003.10.034-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002866_j.jsv.2003.10.034-Figure1-1.png", + "caption": "Fig. 1. Geometry of a spinning shaft subjected to a moving mass.", + "texts": [ + " Then, the shaft deformation expressed in terms of either an inertia frame [8,10] or a co-ordinate system fixed to the rotating shaft [16] can be determined by using the modal analysis or the assumed mode method or the integral transformation method. The present work formulates a rotating shaft subjected to a moving mass through the energy method and quantifies the differences in vibration responses between a rotating shaft subjected to a moving mass and that subjected to a moving force. In addition, the influences of the inertia effect induced by the moving mass on the whirl speed are also investigated. Consider a uniform shaft of length L lying in the x\u2013z plane and rotating at a constant angular velocity O as shown in Fig. 1. A concentrated mass M moves with a constant speed vm along the shaft but does not rotate with the shaft. The moving mass is assumed to remain in contact with the shaft during the motion. The shaft has a cross-sectional area A, second moment of area I, crosssectional shape factor k, Young\u2019s modulus E, shear modulus G and density r: The deformed beam is described by the transverse translations V \u00f0x; t\u00de and W \u00f0x; t\u00de in the y and z directions and small rotations B\u00f0x; t\u00de and G\u00f0x; t\u00de about the y- and z-axis, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000183_3-540-45501-9_4-Figure14-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000183_3-540-45501-9_4-Figure14-1.png", + "caption": "Fig. 14 Direct impact on collinear system with interface springs that represent the local elastic stiffness at each point of contact.", + "texts": [ + " Contact Problems for Elasto-Plastic Impact in Multi-Body Systems 223 6.1 Example: Collinear Impact In Row Of Identical Spheres We consider an axially aligned row of many identical spheres which are initially in diametrical contact but not compressed. The jth element or sphere in the row has mass M, diameter D and an axial displacement uj. The local compressive stiffness of each contact region is denoted by k, while in extension the stiffness vanishes. Between the contacts each body is assumed to be rigid. This onedimensional system is illustrated in Fig. 14. Wave Propagation In Linear Coaxial Periodic System As long as the contact forces remain compressive, a typical element of this periodic system has an equation of motion 2 2 0 0 1 12 ( )j j j ju u u u\u03c9 \u03c9 \u2212 ++ = +!! , 2 0 /k M\u03c9 = . (49) For a wave of slowly varying amplitude the displacement uj varies according to ( ) ( )i x t i jD t ju Ue Ue\u03ba \u03c9 \u03ba \u03c9\u2212 \u2212= = , where the wave-number \u03ba is related to the wave-length \u03bb by \u03ba = 2\u03c0 / \u03bb and 1i= \u2212 . By substituting this solution into (49) a dispersion relation is obtained, 224 W" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002016_0094-5765(91)90103-c-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002016_0094-5765(91)90103-c-Figure2-1.png", + "caption": "Figure 2. One of the layouts for a test sheet for Fitts' reciprocal", + "texts": [ + " Each sheet consisted of both horizontal and vertical target strips, one set in the top half of the sheet and the other in the bottom half. The strips had widths of 2.5, 6.4 or 15.2 mm, and separations of 51, 89 or 178 mm between the mid points of the strips. The 9 combinations of width and separation were repeated twice, once with the horizontal pattern on top and once with the vertical pattern on top: this was to control for possible differences in difficulty in the upper and lower locations. An example of a typical configuration is shown in Fig.2. The order of performing horizontal or vertical tapping was written on the sheets, and was reversed in half the sheets to give a balanced design for combinations of g levels and test orders. tapping task. In this exanple the upper (horizontal) pair of bars is used for vertical tapping movements, and the lower (vertical) pair for horizontal movements. The an~plitude of movement is controlled by the separation of the bars, and the precision by the width of the bars. The subject switched on the cassette recorder at the appropriate place to start the Fitts' test" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001619_1.1633265-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001619_1.1633265-Figure2-1.png", + "caption": "FIG. 2. Schematic showing particles of mass m impacting right parallelepipeds whose sections are ~a! rectangular and ~b! regular n-sided polygons ~shown here for n56), with incident and reflected angles c and c8 as given in the text. Each body rotates about its z-axis of symmetry, the angles b locating radii r1 and r are measured positive from a, and the polygon has side length a and fixed \u2018\u2018radius\u2019\u2019 R.", + "texts": [ + " by N and integrating over the cylinder surface exposed to the oncoming particles gives Fx5mn0E 0 LE 0 p @2v2R sin 2f sin f 1atR2vv sin2 f#dfdz5 p 2 mn0atR2Lvv , ~6! Fy52mn0E 0 LE 0 p @2v2R sin3 f 1atRvv sin f cos f#dfdz52 8 3 mn0RLv2. ~7! Denoting M5mn0pR2L the mass of gas particles displaced by the cylinder and A52RL its frontal area, the total force on the cylinder is F5 1 2Matvvi2 4 3Amn0v2j. ~8! Like the sphere, the cylinder experiences a steady inverse Magnus force, a steady drag force and zero lift. Bodies of noncircular section will now be considered. Depicted in Fig. 2~a! is a right parallelepiped of length L and rectangular section a3b undergoing uniform rotation v about the z-axis placed at the centroid of the section. The counter-clockwise positive angle a5vt is measured from the x-axis. With an eye on forthcoming generalizations, we donote the right and left exposed faces by subscripts 1 and 2, respectively. Then coordinates r1 and b, measured positive from a, locate points on the right face whose lower and upper corners are at b252tan21(a/b) and b15tan21(a/b), This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 157.211.3.15 On: Thu, 15 Jan 2015 18:42:44 respectively. From Fig. 2~a!, expressions for radial r1 and horizontal x1 positions on this exposed surface, and the factors k1 and k18 for respective projections of momentum imparted to the body along the x- and y-axes, are given by r15 b 2 cos b , x15r1 cos~a1b!, k15sin~a1b!, k1852cos~a1b!. With this notation the particle m in Fig. 2~a! strikes the right (i51) face with incidence angle c5p/22a and deflects through angle c85tan21@(cos a2g cos b)/(sin a2g sin b)#, where g5atvr1 /v . The number of collisions per unit time impacting area element dx1dz is N5n0vdx1dz and the momentum changes imparted to this surface are DPx52mv sin 2a1atmr1vk1 , ~9a! DPy52mv~12cos 2a!1atmr1vk18 . ~9b! Multiplying ~9a! and ~9b! by N and integrating over the exposed i51 ~right! surface yields ~F1!x5 mn0b 2 sin aE b1 b2E 0 LFv2 sin 2a cos2 b 2atvvb sin~a1b", + " face yields the force components (F2)x and (F2)y and summation of results gives the total force F5@mn0v2L~b cos a2a sin a!sin 2a1 1 2Matvv#i 22mn0v2L~a sin3 a1b cos3 a!j, ~12! where M5mn0abL is the mass of the gas displaced by the parallelepiped. Note that setting L5b5a in ~12! gives the result for a perfect cube. The limit b\u21920 for a flat plate Fplate522mn0aLv2 sin2 a~cos ai1sin aj! ~13! gives no Magnus force, though there are unsteady lift and drag components. Finally, we take the general case of a right parallelepiped rotating about the centroid of its n-sided regular polygon section of side a, as depicted in Fig. 2~b!. For brevity, only the Magnus force will be computed. The number of surfaces exposed to the particle stream depends on whether n is even or odd. For n even, there are I5n/2 exposed surfaces except for those discrete times when (n22)/2 sides are instantaneously exposed. For n odd, the number of exposed sides is given by I5 n11 2 , S 2k p n ,a,~2k11 ! p n D ; I5 n21 2 , S ~2k11 ! p n L q i q } C o s 0 +{( q p )iq L i d +(*> } i n 0 l' ( Rd + Ld ) i y 1 + to q i x 1 = Ld)(idCos0 - i qS i 0 q 0 + i q C o s 0 (5) (6) ( i iq dire t ( ' ( ( el yl yl' y 1 - ( Rd + pLd ) i y 1 - <*> q i 1 (pLd p q+ L ) i d - ca 0 } S i n 0 i n 9 e,K = - Lq)i to ( d-Lq)id-co 0 st -x2 coordinate axis at r fro th - th n ax v t o iy th -q axis components as shown n e e . s (9 a (10 y i d\" (9) (10) os( 0+71/2) - i n( 0 7t i n( 0 + " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000012_s0021-9673(99)00177-6-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000012_s0021-9673(99)00177-6-Figure3-1.png", + "caption": "Fig. 3. Schematic diagram of the oxidative / reductive pyrolysis furnace of another non-flame SCD. Reprinted with permission from Ref. [76].", + "texts": [ + " More hydrothe reducing environment in the upper part of the gen-rich flow-rates are employed in this burner than flame and is subsequently transferred into the ozone in the flame version. When the combustion products reaction chamber by means of a sampling probe. One leave the hot zone, they are in a very reductive advantage of the flame SCD is that both the FID and environment, which facilitates the formation of the chemiluminescent sulfur species. No simultaneous zones, as employed in a different version of the SCD FID signal is available from the standard configura- [75]. A schematic drawing of this configuration is tion of the flameless SCD. shown in Fig. 3. In this case, oxidation of the column An FID adapter has been devised to allow the effluent takes place inside the inner ceramic tube at introduction of the flame gas from the FID to the the lower part of the furnace and the subsequent flameless SCD burner, thus providing simultaneous reduction takes place in the outer ceramic tube at the FID/SCD detection. The drawback of this configura- upper part. tion is the loss of sensitivity by an order of mag- In any of the above configurations, the oxygen (or nitude due to the fact that only about 10% of the air) and hydrogen flow-rates are very critical in flame gas is transferred into the burner" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000034_s0020-7403(00)00038-2-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000034_s0020-7403(00)00038-2-Figure1-1.png", + "caption": "Fig. 1. Hexagonal model of rod-like columnar structure and unit cell.", + "texts": [ + " [17] and Gibson and Ashby [18], the present model produces transverse isotropy for regular hexagonal columnar structure and, when applied to a square honeycomb, it produces a Poisson's ratio which is admissible for this structure. This investigation illustrates that the e!ective elastic properties of cellular materials are dependent not only on the relative density but also on the strut morphology. A summary of the theoretical works for cellular materials presented by various authors is given in Table 1. The all-embracing nature of the present study is evident. We consider a hexagonal model of columnar structure with non-uniform strut morphology as shown in Fig. 1. Although bending deformation of struts is a dominant mode for the in-plane properties, axial and shear deformations become increasingly important as the relative density of the cellular material increases. In this paper, a theoretical model is developed which accounts for bending, axial and shear deformations of the struts. The honeycomb model of Gibson et al. [1] and Gibson and Ashby [3,18] is extended to the hexagonal model of rod-like columnar structure with non-uniform strut morphology. The present analysis is limited to linear elastic behaviour and small displacements", + " An exact expression of strain energy due to shear loading requires the exact shear stress distribution across the beam section which is often di$cult to obtain. Fortunately, in practical problems, the shear strain energy is often small compared to bending strain energy. Hence, for practical problems, the need for exact values of shear strain energy is not critical. Consequently, for this study, we used an approximation of the shear strain energy as that presented by Boresi et al. [19]. A hexagonal model of rod-like columnar structure with horizontal struts of lengths l and h and vertical struts of length ll is shown in Fig. 1. The dash}dotted rectangular block of this \"gure is a unit cell from which, by successive re#ections and translations, the whole structure can be constructed. The top face of the cell is a rectangle of sides h#l sin h and 2l cos h. The height of the block is ll as shown in Fig. 1. The spatially periodic nature of the cell morphology requires that the individual struts deform anti-symmetrically about their mid-spans. So, there is no resultant moment across the strut section at the mid-span (x\"0). Thus, the strain energies tending to de#ect the struts can be determined from the strain energy equations for cantilever beams of length of l/2, h/2 and ll/2 subjected to bending, axial, and shear loading, and vice versa. For a cantilever beam of length \u00b8 with slowly varying cross section, the strain energies due to bending moment M(x), axial force R, and shear force < are given by ; b \"P L 0 M2(x) 2EI(x) dx, ; a \"P L 0 R2 2EA(x) dx and ; s \"P L 0 k<2 2GA(x) dx, (1) where E, G, and l are Young's modulus, shear modulus, and Poisson's ratio of material, respectively, k is a shear correction coe$cient which depends on the strut cross section [19,20] (k+1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000149_jsvi.1997.1220-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000149_jsvi.1997.1220-Figure1-1.png", + "caption": "Figure 1. The model of a catenary\u2013vertical cable system.", + "texts": [ + " These equations are solved in succession by using the solvability conditions that make the expansion (10) uniform. The longitudinal dynamics of hoisting cable systems can be described by a differential equation of the type given by equation (1), and analyzed as discussed above. The dynamic model of a hoisting cable system with periodic excitation is presented in what follows. Hamilton\u2019s principle is applied to derive the equation of motion, with the cable damping mechanism represented by an equivalent viscous damping model. The model of a hoisting cable system is represented in Figure 1. In this model, the cable is divided into a horizontal catenary of length OC=Lc passing over a sheave of radius R, and of mass moment of inertia I, and into a vertical rope with a mass M, representing the conveyance with payload, attached to its bottom end. The end O1 of the cable is moving with a prescribed winding velocity v(t) due to the cable being coiled onto a rotating cylindrical drum, so that the entire system translates axially, with the mass M being constrained in a lateral direction. The section l=OO1 represents a varying length of this part of the cable that is already coiled onto the winder drum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002901_bf00927180-Figure18-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002901_bf00927180-Figure18-1.png", + "caption": "Fig. 18. Geometric explanation of the angular compensation at the level of the central hexagon angles and at that of triangles forming the 6-pointed star. 1 and 2 indicates the hypothetical displacement of linkers.", + "texts": [], + "surrounding_texts": [ + "Fine structure of Cienkowskya mereshkovskyi and particularly organization of the arrays of Mt's which stiffen the axopods suggest three areas of interest (1) those related to Mt-pattern formation with reference to different hypotheses of nucleation, (2) those concerning the MTOC and (3) those concerning taxonomic relationships with the other heliozoa." + ] + }, + { + "image_filename": "designv11_2_0003668_robot.2007.363142-Figure9-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003668_robot.2007.363142-Figure9-1.png", + "caption": "Fig. 9. Control block diagram with PI-controller", + "texts": [ + " |s| = 1), then the robot will be unable to follow the path with accuracy and will skid. The lateral efforts F\u0302l are estimated with the lateral contact model and a measure of the kinematic state of the vehicle. Several slip control methods exist in the literature, including nonlinear and gain-scheduled PID, sliding mode [8], fuzzy logic [9], or Lyapunov synthesis [10]. Simple slip control strategies have been used for several mobile robots in rough terrain ([11], [12]). Like these authors, we implement a simple PI-controller (Fig. 9). A derivative gain is inappropriate since the slip rate is a discontinuous function. Each independent electric motor is controlled in torque (namely in current). Numerical simulations of a one-wheel vehicle have been led in a dynamical multibody modeling software [13]. An extension to this software has been developed to implement the terramechanic contact model. The step response of the controller is depicted on Fig. 10 (s\u2217 = 0.8, Kp = Ki = 100). After a short period where s is not continuous (at t = 0+, v = 0 and \u03c9 > 0, see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003608_j.apacoust.2006.04.012-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003608_j.apacoust.2006.04.012-Figure2-1.png", + "caption": "Fig. 2. Diagram of the model used.", + "texts": [ + " The objective is to assess the validity of a very simplified model of the rattle phenomenon to estimate the sensitivity of a simplified gearbox. We have to show the limitations of such a model and underline the parameters the most important on rattle noise. For Pfeiffer [30], rattle in a real gearbox is a cascade process. Such phenomenon is difficult to analyse since interaction between gears have to be taken into account for the resolution of dynamical equations. The model used is a Kelvin\u2013Voigt model (Fig. 2), usually used to analyse the backlash crossing phenomenon between gears [36,37]. It is a simple model with two degrees of freedom (Fig. 2). It is made of a driving gear and an unloaded gear, whose motion are linked during contact phases, or are independent during free-flight phases, when the unloaded gear moves within backlash. Some modifications have been made (i.e. works of Azar and Crossley [32]) in order to avoid numerical discontinuity problems. We have introduced a nonlinear parameter in the expression of the damping during impact. The angular position of the driving gear (primary shaft of the gearbox) is given by the angle h1, the position of the unloaded gear is given by the angle h2 ( _hi is the angular velocity in rad/s and \u20achi is the angular acceleration in rad/s2)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000414_37.710879-FigureI-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000414_37.710879-FigureI-1.png", + "caption": "Fig. I . SMART 3s robot.", + "texts": [], + "surrounding_texts": [ + "Impact Modeling and Control for Industrial Manipulators\nG. Ferretti, G. Magnani, A. Zavala Rio\nor arobotic manipulator, the impact of the end-effector on the F environment occurs in the transition from unconstrained (free) motion to constrained motion. Contact force at impact is difficult to control and oscillatory behavior (or, worse still, instability) can easily occur. Several kinds of models have been proposed to explain impact-force behavior. For instance, in [ 171 a rigid, six-degree-of-freedom (d.0.f.) model of the manipulator is assumed for a geared PUMA 560 arm; in [13] a sixth-order model is derived for a direct-drive manipulator (CMU DD arm 11) in single-joint operations, accounting for the arm, sensor, and environment compliances and whose dominant dynamics is due to the environment. In [ 191 a sixth-order model that takes into account the joint compliance inherent in reduction gears and the sensor and environment dynamics is adopted for a prototype single-joint geared arm.\nIn this article. the impact-force behavior is experimentally studied on a six-d.0.f. commercial manipulator interacting with a very hard granite surface. The arm was manufactured with standard components and is representative of current industrial products. It is shown that the elastic-joint robot model proposed by Spong [ 161 completely explains frequency and damping of impact-force oscillations, so that oscillations can be totally ascribed to joint compliance, while links behave as rigid bodies. The initial part of the impact transient is also affected by Coulomb friction in the joints, which contributes to the dissipation of the kinetic energy of the arm at impact.\nSeveral control strategies have been proposed in the literature for impact and force control. A nonlinear feedback control law was proposed in [ 171 to decouple and linearize the system, so that the motion of the manipulator and the contact force can be controlled independently along each unconstrained (motion) and constrained (force) direction. In [ 191 an integral gain control was used for permanent (bounceless) contact and throughout transition, but bounces took place. In [13] a discontinuous explicit force control was implemented to avoid bounces, which led to a proportional positive gain (smaller than unity) for the transient phase of impact and to an integral gain for tracking the force setpoint once a bounceless contact had been established. In fact, [ 131 highlights that integral control, widely recognized (see, e.g., [8], [lo], [14], [19]) as the most suitable choice for permanent contact, is not suitable for the transition phase as bounce and instability might occur because of integrator wind-up [2].\nThis article shows, through analysis and experiments, how to effectively employ integral control even in the transition phase,\nmaintaining contact with the environment without bounce despite the potential problems of integrator wind-up. We begin by describing the experimental setup and how the manipulator model is derived. We then report the experimental results and model validation (by comparison of simulation and experimental results) and discuss the open-loop permanent contact and impact. We also give an analysis of the wind-up prolblem of integral control, propose methods to avoid or counteract it, and report bounceless experimental controlled impacts.\nThe Experimental Setup The experimental environment (Fig. 1) is based on the SMART 3 s robot, a six-axis industrial robot (manufactured by COMAU), equipped with an open version of the standard controller C3G 9000 [4]. In this version the controller can exchange data with an extemal PC that runs user-defined control algorithms. There are several operating modes. In om, the controller action can be completely excluded, allowing motor-current setpoints to be directly commanded by the user's algorithms from the PC at a sampling frequency of 1 kHz (and with a communica-\nG. Ferretti and G. Magnani are with the Dipartimento di Elettronica e Iilformazione. Politecnico di Milano, Piazza Leonmdo da Mizci 32, 20133,Miluno. Italy. Cferretti,mugiiuni}~elet.polimi.it. A. Zavalu Rio (mv209@mel.go.jp), is with the Mechanical Engineering Laboratory, Robotics Department. Mechanisms Division, Ministry of International Trude and Industry. Nurniki 1-2, Tsukuba, Ibaraki. 305. Japan.\nAugust 1998 0272- 1708/98/$10.0001998IEEE 65", + "tion delay of two ms; i.e., twice the sampling interval). At this sampling frequency the PC acquires force-sensor and motor-resolver measurements. A six-axis wrist-force sensor from AT1 was adopted, with a resolution of 0.1 N.\nIn order to reduce the dynamic complexity of the system being studied and to facilitate the analysis of the experimental data and the validation of the model, all motors but the fifth were mechanically braked in suitable positions, so that impact was due only to the movements of the fifth joint, which therefore also controls the impact. However, it must be emphasized that the dynamic effects of joint compliance (which greatly affect industrial robots) are not eliminated by locking the motor coordinate as the brakes act on the back of the motor shaft, and the joint itself is not locked.\nSystem Modeling The general model of a compliant joint robot in contact with a\nsurface is the following:\nM(q)q+c(q,q)+g(q)-PTTr T t = -K(Pq -qm)-D(Pq - q m )\nJ m S m + D m q m + + ~f = (1)\nwhere q and q, are the link and the motor coordinate vectors, respectively; M( 4) is the robot inertia matrix; c( g , ir) and g( (1, are the vectors of Coriolis and centrifugal terms and the vector of\ngravitational terms, respectively; P = diag(pt) is the matrix of transmission ratios; T,, zr, zf, and T~ are the motor torque vector, the transmitted torque vector, the friction torque vector, and the joint torque vector due to the external force, respectively; and K =diag(k,), D = diag(di), J, = diag(jmi), and D, = diag(d,,) are the matrices of the joint stiffness, damping coefficient, motor inertia, and the motor damping coefficient, respectively.\nFor analysis purposes, the model in Equation 1 was linearized in the impact configuration (Fig. 2). In this configuration the contact force is affected by the torque delivered by the fifth motor and by the compliance of joint 2, while it is not influenced by joints 1,3,4, and 6 (in the configuration of Fig. 2, the moment of the contact force withrespect to the axis ofjoint 3 is zero). Therefore, a three-d.0.f. mechanical system can be considered: two degrees of freedom are associated with the motor and the link coordinate of joint 5 , and a third is associated with the link coordinate of joint 2. The system can be described by the mass-spring-damper system shown in Fig. 3 and by the following linear equations:\nm22(q)642 + %s(q)64s + g 2 2 ( q Y % 2 + gzS(q)6qs -Pz6T,z = 6T,*\n6212 = -k ,P2h - d2P2642\n6% = -ks(P5%5 -6qm,)-ds(P,~4s -64,J jmS6ims + dm,69,, + 6 ~ , , +6~~~ = 6zmS\nm S Z ( q ) 6 i Z + m S S ( q ) 6 i S + 8 5 2 ( q h 2 + g5S(q)6q5 - P 5 6 T c 5 =\u201ce5\n(2)\nwhere q denotes the joint coordinates of the impact configuration depicted in Fig. 2.\ni.e., the torques exerted about axes 2 and 5 by the contact force, are determined by the characteristics of the contact, as illustrated in Fig. 4. Since contact is made between a rounded metal tool fixed on the force sensor and a granite surface lying on the floor (see Fig. 2), the compliance of the environment is negligible with\nThe variations of the equivalent joint torques, 6~~~ and\nrespect to the force-sensor compliances. As a consequence, no motion of the contact point is allowed normal to the surface, while the deflection of the force sensor, 6q,, is algebraically related to the variations of the joint angles, 6q and 6q :\nwhere the constants a, and a, are computed by linearizing the constraint relationship imposed by the rigid contact.\nIn turn, the deflection of the force sensor is algebraically related to the amplitude of the contact force through the torsional stiffness, k,:\nIEEE Control Systems 66" + ] + }, + { + "image_filename": "designv11_2_0002513_j.elecom.2005.10.024-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002513_j.elecom.2005.10.024-Figure1-1.png", + "caption": "Fig. 1. Schematic drawings showing the construction of the twin-electrode thin-layer cell (TETLC).", + "texts": [ + "7 mol L 1 sodium iodide was used for the gold layer etching. An Autolab PGSTAT 30 (Eco Chemie) bipotentiostat with data acquisition software made available by the manufacturer (GPES 4.8 version) was used for electrochemical measurements. Experiments were done in the proposed electrolytic cell, a homemade Ag/AgCl (saturated KCl) electrode [35] and a platinum wire being used as reference and auxiliary electrodes, respectively. The fabrication process of the micro-device denominated twin-electrode thin-layer cell (TETLC) is based on the following steps (Fig. 1): (a) the image of the twinelectrode and the toner masks (spacers) are drawn in 1:1 scale using a CorelDraw 7.0 software (Corel, Ottawa, Canada); (b) these images are then printed using an HP LaserJet 1200 series on a waxed paper of the type used as support (base material) for self adhesive labels; (c) the toner masks with the twin-electrode images are heat-transferred at 100 C/1.5 min (Thermal press: HT 2020, Ferragini, Sa\u0303o Carlos, SP, Brazil) onto two different gold surfaces obtained from a recordable compact disc (Mitsui Gold Standard); (d) the toner-free gold areas are etched by exposure to an iodide/iodine solution for 10 s; (e) the toner is then removed with the help of a cotton swab soaked with acetonitrile (Fig. 1(a) and (d)); (f) by using a drill, two orifices (solution inlet and outlet) with 0.8 mm of diameter are made in the CD polycarbonate slice where the top electrode is situated; (g) two toner masks are heat-transferred (Fig. 1(b) and (c)) (100 C/1.5 min) to the CD slice containing the orifices; (h) a second piece of polycarbonate was heat-sealed on top of the toner layer by heating the \u2018\u2018sandwich\u2019\u2019 to 120 C for 2.5 min (Fig. 1(e)). Each toner mask generates a micro-channel with a thickness of 6 lm [36] and since, two toner masks were used to prepare the electrochemical cell, the unprinted areas generated microchannels with a depth of approximately 12 lm.Wepreferred to use two toner masks because of problems associated with uncompensated solution resistance in devices with thinner micro-channels; (i) finally, amicro-tip and a plastic reservoir (500 lL) are glued (epoxy glue) in the inlet and outlet sides, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002817_tie.2006.874278-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002817_tie.2006.874278-Figure8-1.png", + "caption": "Fig. 8. Prototype motor and encoder. (a) Stator. (b) Rotor. (c) Encoder.", + "texts": [ + " For switching angle control, a 2-channel 10-bit D/A converter is used. The calculated switching-on angle as digital data is output to a channel of the D/A converter as analog data, then the switching-off angle is output to the other channel of the D/A converter. The absolute control resolution is obtained by the resolution of the D/A converter as \u03b8resolution = \u03b2r \u00b7 Vmax 2n+1 \u00b7 (Vmax \u2212 Vmin) (10) where n denotes the bit numbers of the D/A converter. In this paper, the absolute resolution of switching angle is about 0.01\u25e6. Fig. 8 shows a photograph of the prototype motor and encoder. The tested motor has 12 stator poles and 8 rotor poles. Three photosensors are equipped in the encoder with the phase interval to produce analog position signals. Fig. 9 shows the experimental waveforms of the sensor signal, command signals of switching on and off, and the switching angle of a phase. In Fig. 9, the switching-on and switching-off signals are determined by the combination of sensor signal and two switching commands. Fig. 10 shows the sensor signal, switching-on reference, switching signal, and phase current" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002768_bfb0040159-Figure2.8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002768_bfb0040159-Figure2.8-1.png", + "caption": "Figure 2.8 MERGE example: (a) components before merging; (b) resulting object.", + "texts": [ + " This task is performed by the M E R G E algorithm, which realizes the complete range of set operat ions on arbi t rary polyhedra. The algori thm takes two polyhedra, described by lists of points, lines, and surfaces, and yields a new polyhedron which is either the union, intersection, or difference of its arguments (see Figure 2.7 for definitions of these operations). As the procedural representa t ions are interpreted, successive appl icat ions of the MERGE algorithm are used to build up quite complex shapes, as i l lustrated in Figure 2.8. The MERGE algorithm can also be invoked directly in GDP, allowing the World Model to be altered and subsequently re-merged. Systems that do not have this operat ion are unable to generate explicit forms of composite objects. Without explicit representa t ion of the objects at higher nodes of the tree, it is relat ively difficult to perform operat ions that depend on the volume propert ies of the composite object , for example robot path planning or even finding the volume of an object , without putt ing strong constraints on the structure of the tree" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001105_taes.2003.1238739-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001105_taes.2003.1238739-Figure3-1.png", + "caption": "Fig. 3. Two angles of TVC in body coordinate.", + "texts": [ + ": DESIGN OF OPTIMAL MIDCOURSE GUIDANCE SLIDING-MODE CONTROL FOR MISSILES WITH TVC 825 The motion of a missile can be described in two parts as follows: Translation: _vM = aM + gM , _rM = vM (1) Rotating: J _! = _J! ! (J!) + T\u0304b + d: (2) All the variables are defined in the nomenclature listing. Assume that the nozzle is located at the center of the tail of the missile, and the distance between the nozzle center and the missile\u2019s center of gravity is l. Furthermore, we also assume that the missile is equipped with a number of sidejets or thrusters on the surface near the center of gravity that will produce a pure rolling moment whose direction is aligned with the vehicle axis Xb, referred to Fig. 3. Thus, the vector Lb, defined as the relative displacement from the missile\u2019s center of gravity to the center of the nozzle, satisfies Lb = l. Note that J is the moment of inertial matrix of the missile body with respect to the body coordinate frame as shown in Fig. 2 and hence is a 3 3 symmetric matrix. Generally speaking, for various practical reasons the rocket engines deployed on the missile body cannot vary with any flexibility the magnitude of the thrust force. Therefore, for simplicity we assume here that the missile can only gain constant thrust force during the flight. After referring to Fig. 2 and Fig. 3, the force and torque exerted on the missile can be respectively expressed in the body coordinate frame as F\u0304b =N cosdp cosdy cosdp sindy sindp (3) and T\u0304b = Lb F\u0304b +Mb = lN Mbx=lN sindp cosdp sindy (4) where N is the magnitude of thrust, dp and dy are respectively the pitch angle and yaw angle of the propellant, and Mb = [Mbx 0 0] T is the aforementioned variable moment in the axial direction of the missile. Let the rotation matrix Bb denote the transformation from the body coordinate frame to the inertial coordinate frame" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000456_jsvi.1998.1587-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000456_jsvi.1998.1587-Figure2-1.png", + "caption": "Figure 2. Single-degree-of-freedom model of a pair of spur gears.", + "texts": [ + " The radii R1 and R2 correspond to the radii of the base circles of the gears 1 and 2, respectively. The transmission error, defined as the difference between the actual and ideal positions of the driven gear, is expressed as a linear displacement along the line of action. The sign convention used for the transmission error is positive behind the ideal position of the driven gear. Analyzing gears with low contact ratio o (i.e., 1Q oQ 2), the non-linear equation of motion for the dynamic transmission error x can be written as (Figure 2): mx\u0308+ cx\u0307+ f1(x, t)+ f2(x, t)=W0, (1) where x=R1u1 \u2212R2u2, (2) u1 and u2 being the angular displacements of the two gears; the equivalent mass of inertia m of the system is: m= I1I2/(I1R2 2 + I2R2 1 ); (3) W0 is the static load given by W0 =T1/R1 =T2/R2, (4) T1 and T2 being the driving and driven torques, respectively; fj (x, t) are the elastic forces of the meshing tooth pair j, for j=1, 2 fj (x, t)=6kj (t)[x\u2212 ej (t)] 0 when x\u2212 ej (t)q 0 when x\u2212 ej (t)E 0. (5) Obviously, equation (1) can be easily extended to high contact ratio gears" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002209_s00170-005-2602-4-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002209_s00170-005-2602-4-Figure3-1.png", + "caption": "Fig. 3. Parameters of variation of the mesh phasing", + "texts": [ + " Mesh frequencies fei on the two gearmeshes contacts are related by the following relation [16]: fe2 = Z22 Z21 fe1 (2) where Z21 and Z22 represent the numbers of teeth of the two wheels (21) and (22). The term pi represents \u201cthe initial angular phasing\u201d of two mesh stiffness. We can take p1 = 0 then the phasing between the two initial angular of the gears contacts will be equal to p2 [3]. This mesh phasing, noted by h, depends on the numbers of teeth and on the wheels locations in the gearbox; it is expressed by the relation: h = p2 \u2212 p1 = \u03c8Z 2\u03c0 . (3) Z designates the number of the tooth of the intermediate wheel represented in bold line (Fig. 3). \u03a8 represents the angle that the second line of the centers makes in relation to the first line. Figures 3b and c represent a particular case of wheels location (\u03c8 = \u03c0). On Fig. 3b for an even number of teeth (Z = 2p, p: integer), the mesh phasing h = 0 and the two stiffness are in phase. On Fig. 3c for an odd number of teeth (Z = 2p+ 1, p: integer), the two stiffness are lagged of one half-period. In most gearboxes, especially for those having a reduced sizes, wheels axis are in the same plane between the two parts of the gearbox (Fig. 4) that permits an easy wheels assembly [17]. In this work, we tried to optimize the conception of the twostage gear system while varying \u03b22. We defined a fixed reference frame (O, X0, Y0) to the model as represented on Fig. 5. \u03b1i are the pressure angles of two gearmesh contact" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001112_s026357479700074x-Figure11-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001112_s026357479700074x-Figure11-1.png", + "caption": "Fig . 11 . A model of the three-link manipulator arm .", + "texts": [ + " The average error for the testing session was 0 . 7% for the first joint and 0 . 1% for the second joint . Figure 10 shows the graph of both the actual and desired output for the two joints for second orientation . The second orientation of the arm needs more neurons for the training stage because of the wide distribution of the output data . The network was found to need more training either by increasing the number of hidden neurons or iterations when the data or patterns are widely distributed . Figure 11 shows the three-link manipulator arm for which the link parameters are shown in Table IV . Again the link lengths are taken to be 1 as above , to simplify the calculations . The arm can move around in three-dimensional workspace . Again , an artificial neural network , with three inputs and outputs , and a single hidden layer was used for the training session . The path that was used to train the neural network is the trajectory of the end ef fector in three-dimensional workspace as Fig . 8 . A graph of the training session for second orientation of the two-link arm " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001863_oceans.1997.624110-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001863_oceans.1997.624110-Figure2-1.png", + "caption": "Figure 2 : Body-fixed ({ B}) and earth-fixed ({U}) reference frames.", + "texts": [ + " 3 Vehicle Modeling This section describes briefly the dynamic model of the ensemble that consists of Sirene and the associated laboratory. See [l] for complete details. In what follows, to simplify the presentation, the ensemble will be referred to simply as the vehicle. 3.1 General equations of motion Following standard practice, the kinematic and dynamic equations of motion of the vehicle can be developed using a global coordinate frame { U } and a body-fixed coordinate frame { B } , as depicted in Figure 2. The following notation is required ([6]): 111 = [z, y, 21' - position of the origin of {B} measured in {U}. 7 2 = [$,Q,$]' - angles of roll ($), pitch ( e ) , and yaw (4) that parametrize locally the orientation of { B } with respect to { U } . v1 = [U, U, wIT - linear velocity of the origin of { B } relative to { U } , expressed in { B } (i.e., body-fixed linear velocity). v2 = Lp,q,rIT - angular velocity of {B} relative to { U } , expressed in { B } (i.e., body-fixed angular velocity). With this notation, the kinematics and dynamics of the vehicle can be written in compact form as Kin em at i cs [ ; ] = [ 3 ( 7 d 0 0 Q ( l l z ) ] [ zi ] e $ = J ( q ) v (l) Dynamics 'distance between the center of buoyancy arid the center of mass" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001043_s0029-8018(03)00016-7-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001043_s0029-8018(03)00016-7-Figure5-1.png", + "caption": "Fig. 5. A 2280 tons coring vessel with five azimuth thrusters.", + "texts": [ + " (1)\u2013(6) regard an optimum control law of the thruster system, and Eqs. (10)\u2013(15) are used in the present optimum control design for a dynamic positioning system. In this section, we present a simulation results for positioning of a coring vessel (Displacement = 2280 tons, LBP = 80 m, Beam = 12 m, Draft = 1 m) in which the present optimum control for the thruster system of a DP system was installed. The coring vessel was simulated with five azimuth thrusters, and the distance between each thruster as shown Fig. 5. The thrusters were bi-directional. In the simulation a given task was accomplished in an unknown offshore marine environment. The vessel was moved by the various environmental forces. The vessel had to maintain within \u00b13.0 m of a certain position located in the reference position of the working sets, the motion path of the coring vessel during positioning as shown in Fig. 6. Therefore, the longitudinal resultant thrust, lateral resultant thrust and moment commands were obtained by the control system of the DP system shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure2.26-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure2.26-1.png", + "caption": "Fig. 2.26. Through type eddy current flaw detector", + "texts": [ + " The leakage magnetic flux detection is the method of detecting the flux leaked from the defect directly, by a magnetic sensor instead of magnetic particles, as shown in Fig. 2.25 [2]. The eddy current flaw detection is the method of catching the defect by the eddy current disturbance when the alternating magnetic field is applied to the product. There is the through type method using circumferential through-type coil, where the bar can pass through the fixed coil and the rotating eddy probe coil method, where the detection coil rotates around the bar with high-speed, as shown in Fig. 2.26 and Fig. 2.27. The internal defects can be represented as pipe, segregation and nonmetallic inclusion inside of steel bar. The inspection can be normally conducted with the ultrasonic flaw detector. 2.1 Steel Material 71 The ultrasonic flaw detection is the method of catching internal defects by the change of the ultrasonic wave from transmitting to receiving, when the ultrasonic is applied to the bar through the search unit, as shown in Fig. 2.28. A wire rod product is coiled to a ring shape. The coiled wire rod can be inspected after cutting off each one sample from both ends" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003070_j.physe.2004.04.024-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003070_j.physe.2004.04.024-Figure1-1.png", + "caption": "Fig. 1. Formation of free-standing several-ML thick bent bifilms and 2ML-thick InAs and GaAs layers with naturally mismatched lattice co in an InAs/GaAs bifilm MBE-grown on an InP substrate; (c) bending substrate during selective etching of the underlying AlAs sacrificial la", + "texts": [ + " Conceptually, we have a molecular technology that deals with artificial 2Dmolecules (molecular MLs). Since molecular MLs are extremely precise, the new method enables obtaining precise nanoobjects. Below, we give a brief overview of an extended version of the d. method and report some new results on nanostructuring,\u2014in the fields where substantial progress has been currently made. The method for fabricating nanotubes from strained heterostructures using stress-driven processes [6,7] is schematically illustrated by Fig. 1. The diameter D of self-formed tubes depends on the thickness d of the starting heterofilm and on the elastic stress in it. This diameter can therefore be precisely predetermined in the MBE process in the range between several hundreds of micrometers to two nanometers [7]. Fig. 2 exemplifies scanning electron microscopy (SEM) and HRTEM images of first InGaAs/GaAs nanotubes [7]. SiGe/Si micro- and nanotubes were for the first time obtained in Refs. [9,10]. Thin initial InGaAs/GaAs bifilms roll in hollow cylinders with continuous single-crystal wall" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000530_s0045-7825(02)00308-0-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000530_s0045-7825(02)00308-0-Figure1-1.png", + "caption": "Fig. 1. The multilayer triangular TRIC element; coordinate systems.", + "texts": [ + " Then, the total natural tangent stiffness matrix is computed by adding together the tangent stiffness matrix of each layer. A number of benchmark test examples are examined exhibiting highly nonlinear behaviour in order to test and verify the proposed elasto-plastic large displacement formulation of TRIC shell element. Efficiency and accuracy of the proposed element is demonstrated by a set of numerical examples taken from the literature. For the multilayered composite triangular shell element the following coordinate systems shown in Fig. 1 are adopted. The natural coordinate system which has the three axes parallel to the sides of the triangle. The local elemental coordinate system, placed at the triangle\u2019s centroid, and the global Cartesian coordinate system where global equilibrium refers to. Finally, for each ply of the triangle, a material coordinate system 1, 2, 3 is defined with axis 1 being parallel to the direction of the fibers. The use of these different coordinate systems makes TRIC a suitable element in modeling multilayer anisotropic shell structures that can degenerate, as special case, to a sandwich or single-layer configuration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003402_j.conengprac.2005.12.003-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003402_j.conengprac.2005.12.003-Figure2-1.png", + "caption": "Fig. 2. The components arranged in their final position in the chassis.", + "texts": [ + "6 times lower than expected, indicating high hydrogen losses or lower stored H2 volume. The chassis was designed and laser cut out of 0:2500 thick plexiglass. Several layers were stacked and fused with methylene chloride solvent to support the weight of the FC and electronics and prevent excessive bending. The FC stack was placed in the front of the vehicle to allow unobstructed air flow. To accommodate the rear-wheel drive and achieve a good weight balance the electric drive and the hydrogen tank was placed with all the electronics in the rear, as shown in Fig. 2. Two supports were manufactured so that the bottle could slide in and out easily for refilling. Finally, the roof of the bus could be removed to allow for easy access to the components. The track was designed as a figure-eight manufactured of plywood and plaster. The middle of the track was grooved to guide the front steering mechanism of the bus, which was a simple hinge attached to the front pivoting axle of the toy bus. Having specified the FC power (voltage and current) and ensuring adequate hydrogen supply the powertrain was designed as follows" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003047_iros.2006.282270-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003047_iros.2006.282270-Figure1-1.png", + "caption": "Fig. 1 A mobile manipulator manipulating a heavy object may go unstable.", + "texts": [ + " INTRODUCTION In a mobile robotic system, whether wheeled or freeflying in space, dynamic forces affect the motion of the base and the manipulators, based on the action and reaction principle. The kinematics, dynamics and control of such systems have been described in previous works, [1-3]. One of the most important problems caused by base movement, when the system undergoes a fast maneuver or tries to climb a slopped terrain, is the instability problem or tipping-over. For instance this phenomenon can happen when such a mobile robotic system manipulates a heavy object as shown in Fig. 1. Therefore, to perform path and trajectory planning in controlling such systems, an instantaneous dynamic stability measure is required. The planning can also be done off-line using a simulation routine. Then, based on a proper stability margin criterion, any critical and hazardous work conditions 1- Associate Professor 2- PhD Candidate 1-4244-0259-X/06/$20.00 C)2006 IEEE can be determined to avoid in real work conditions and provide safety of the system and its operator. Besides, such a stability measure can be used in autonomous or unmanned vehicles and teleoperated mobile manipulators operating in unknown environment", + " Considering the procedure of computing three measures including MHS measure, Energy-Equilibrium Plane and Force-Angle leads to a comparison between these metrics, in terms of the required computational operations, as depicted in Table I. Notice that for all measures the coordinates of support polygon vertices are considered as inputs. The number of these points is assumed to be 'n'. Also, for all measures the wrench exerted on the mobile base by the manipulator arm(s) is assumed to be available, and hence computations of these forces/torques are not taken into account. The required computational effort for the considered system as a benchmark depicted in Fig. 1 reveals the efficiency of the MHS over the two other measures. Note that 'N' in Table I indicates the number of dof of manipulator arm. Note that by computation of a closed-form solution for c.m. height in terms of joint angles the computational burden can still be decreased for MHS computation. In this section, the proposed MHS is briefly described for uneven terrains. Recall that for the case of rigid suspension (e.g. our benchmark system) the movement on a rough terrain is meaningless. On the other hand, when there is a wheeled mobile-field robotic system in hostile environments the use of some kind of suspension/wheel compliance module is inevitable like the one which has been proposed by Sujan and Dubowsky [19], and also by Abo-Shanab and Sepehri [17]", + " Since, the proposed MHS measure is based on the contact points between the base and ground, by considering the virtual structure and the applied forces/torques (except the forced exerted to the tires) we can compute the applied moments about different edges of support pattern. Hence, the NMFS metric becomes applicable. Note that since the pure rotation has been considered as instability, and the rotation of the system will be caused due to the moments, we believe that the definition of instability by a moment-based metric is absolutely expected. Next, the MHS measure is applied on the system shown in Fig. 1 during various maneuvers, and compared to other measures which were introduced previously. V. CASE STUDIES AND DiscusSIONS To compare the MHS measure with the main introduced measures, three cases for movement of the system are considered and analyzed. As shown in Fig. 1, the system consists of a relatively heavy mobile base and a 6 degree-offreedom manipulator arm with the configuration of PUMA 560. Table II expresses the complete specifications of the mobile manipulator. The D. H. parameters of the manipulator are expressed in Table III. The mass moments of inertia about different edges of vehicle are as follows: I, 186.7091l(kg.M2) I, 686.7091l(kg.M2) Note that the base is considered as a square so that IV3 = IV and IV, =J,. It is assumed that the mobile base moves on a flat terrain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002489_rob.4620060409-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002489_rob.4620060409-Figure1-1.png", + "caption": "Figure 1. Four-link robot in horizontal plane (reaction surface applies for Simulation 3 and Simulation 4).", + "texts": [ + " Overview of Computer Simulation Study The Cartesian-space position/force control scheme for redundant robots given in (4)-(8), (24)-(26) is now applied to a direct-drive four-link planar robot in a series of four computer simulation examples. The results presented here are samples selected from a comprehensive computer simulation study that was carried out to test the performance of the proposed controller. Note that the results given here are selected because they are typical of the larger study, and not because they represent the best performance obtainable with the proposed control law. Consider the four-link robot in a horizontal plane shown in Figure 1. The robot parameters are link lengths I , = 12 = 13 = 14 = 1 .O m, link masses ml = m2 = m3 = m4 = 10.0 kg, and joint viscous friction coefficients cI = c2 = c3 = c4 = 40.0 Nt . m s; the link inertias are modeled by thin uniform rods. In the simulation examples presented here, two of the simulations involve endeffector position control and two involve end-effector position/force control. For the position control simulations the robot dynamic model that relates joint torques T E R4 and joint angles B E R4 is given by T = H(e)e+vcc(e, e)+vr(e) (324 while for the position/force control simulations the robot dynamic model is T= H(e)e+v,,(e, e )+v , (e )+JTP (3%) I n the dynamic models (32) the inertia matrix H = [h i j ] E R4x4, Coriolis and centrifugal torque vector V, = [ u i ] E R4 and viscous friction torque vector Note that the gravity vector is orthogonal to the plane of motion of the robot, so that no gravity torques appear in (32). It must be emphasized that the dynamic model (32)-(33) is used only to simulate the robot behavior and is not used in the control law formulation. The forward kinematics y = f ( 0 ) and Jacobian matrix J for the robot shown in Figure 1 are For the two position/force control simulations a frictionless reaction surface is placed in the robot workspace as shown in Fig. 1. This reaction surface is located parallel to the x axis at z = 0.0, and has a stiffness of lo4 Ntlm. In these simulations the base frame is chosen as the constraint frame, so that the position subspace and force subspace are each of dimension one and correspond to the x and z axes, respectively. The position subspace Jacobian 442 Journal of Robotic Systems -1 989 Jp E RIx4 and force subspace Jacobian Jf E RIx4 then correspond to the first and second rows of J in (33, respectively. The end-effectorlenvironment contact force P E R is computed as follows: 0 if z > 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000972_s0165-0114(99)00111-6-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000972_s0165-0114(99)00111-6-Figure1-1.png", + "caption": "Fig. 1. The membership functions of the input variable S of IF-part.", + "texts": [], + "surrounding_texts": [ + "As the authors [3,16] pointed out that the fuzzy control rules are the principal factor to determine the performance of a fuzzy controller. In this section, we 2rst construct the FSMC, and then show how to develop an adaptive FSMC controller for obtaining the equivalent control through rules adaptation. Then, we construct the hitting control to guarantee system\u2019s stability. Now, the rule base of FSMC is constructed as (i; j)th rule: IF S is Ai and S\u0307 is Bj THEN u\u0302eq is uk ; (9) where i\u2208 I = {\u2212 n;\u2212 n+ 1; : : : ;\u22121; 0; 1; : : : ; n\u2212 1; n}; (10) j\u2208 J = {\u2212m;\u2212m+ 1; : : : ;\u22121; 0; 1; : : : ; m\u2212 1; m}; (11) k \u2208K = {\u2212l;\u2212l+ 1; : : : ;\u22121; 0; 1; : : : ; l\u2212 1; l}: (12) In this study, the triangular-typed and singletons are, respectively, used to de2ne the membership functions of IF-part and THEN-part, which are shown in Figs. 1\u20133. The membership functions of IF-part and THEN-part are arranged as having the same width and boundary in the universe of discourse [a\u2212n; an]; [b\u2212m; bm] and [\u2212U;U ], respectively. The rule is de2ned in the following analytic form [16]: k = \u3008\u2212 i \u2212 (1 \u2212 )j\u3009; \u2208 [0; 1]; (13) where \u3008x\u3009 is an operation that takes an integer which is the nearest to x and is a rule regulating factor. Obviously, by properly adjusting , the value of k will be changed by (13), that indirectly determine which uk should be taken into account. So the controller is expected to provide diMerent control actions corresponding to diMerent . According to (12), it is easily found that (13) is constrained by \u2212 l6 i + (1 \u2212 )j6l: (14) Considering the extreme case, i= n and j=m, the following condition shows that should be satis2ed: 6 l\u2212 m n\u2212 m : (15) It also shows that l= n\u00bfm to satisfy the condition \u2208 [0; 1]. De2ne each membership function of THEN-part as uk = klD; (16) where D=U=l; kl is the modi2ed function of k and is represented as kl = \u2212 i \u2212 (1 \u2212 )j: (17) 162 J.-Y. Chen / Fuzzy Sets and Systems 120 (2001) 159\u2013168 Without loss of generality, consider the case of ai6S6ai+1 and bj6S\u03076bj+1, thus there are four rules are 2red (i; j); (i; j + 1); (i + 1; j); (i + 1; j + 1): (18) Therefore, we can get the crisp output through defuzzi2cation strategy u\u0302eq = Z W ; (19) where Z =w1u1 + w2u2 + w3u3 + w4u4 =w1[\u2212 i \u2212 (1 \u2212 )j]D +w2[\u2212 (i + 1)\u2212 (1 \u2212 )j]D +w3[\u2212 i \u2212 (1 \u2212 )(j + 1)]D +w4[\u2212 (i + 1) \u2212 (1 \u2212 )(1 + j)]D = [w1( (\u2212 i + j) \u2212 j) + w2( (\u2212 i + j \u2212 1) \u2212 j) +w3( (\u2212 i + j \u2212 1) \u2212 (j + 1)) +w4( (\u2212 i + j) \u2212 (j + 1))]D; (20) W =w1 + w2 + w3 + w4 (21) and w1 = min[#Ai(S); #Bj (S\u0307)]; w2 = min[#Ai+1(S); #Bj (S\u0307)]; (22) J.-Y. Chen / Fuzzy Sets and Systems 120 (2001) 159\u2013168 163 w3 = min[#Ai(S); #Bj+1(S\u0307)]; w4 = min[#Ai+1(S); #Bj+1(S\u0307)]: (23) The main task of this section is to derive an adaptive law to adjust the regulating factor such that the estimated equivalent control u\u0302eq can be optimally approximated to the equivalent control of the SMC under the situations of unknown functions f and g. To design the regulating factor , we transfer differential equation (1) to a vector form. Let the sliding mode coeHcient be = [ 1; 2; : : : ; n\u22121; 1]T such that the Hurwitz polynomial $(p) =pn + n\u22121pn\u22121 + \u00b7 \u00b7 \u00b7+ 1 has all its roots in the open left-half of the complex plane. The variable p denotes the Laplace variable. We now de2ne the auxiliary input as ueq = \u2212 g\u22121(f \u2212 Tme \u2212 r(n)) (24) and substituting (24) and (8) into Eq. (1), after some manipulations, we have e(n) = \u2212 Tme + g[\u2212 u\u0302eq + ueq \u2212 uh] (25) or equivalently, it can be written in the following vector form: e\u0307=Ae + bc[\u2212 u\u0302eq + ueq \u2212 uh]; (26) where A = 0 1 0 0 \u00b7 \u00b7 \u00b7 0 0 0 0 1 0 \u00b7 \u00b7 \u00b7 0 0 ... ... ... ... . . . ... ... 0 0 0 0 \u00b7 \u00b7 \u00b7 0 1 0 \u2212 1 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u2212 n\u22121 ; bc = 0 0 ... 0 g : (27) Suppose there exists a optimal regulating factor \u2217 which is constant such that the u\u0302eq has minimum approximation error '= u\u0302\u2217eq \u2212 ueq : Then from (19)\u2013(21), we have u\u0302eq \u2212 u\u0302\u2217eq = 1 W ( \u2212 \u2217)(; (28) where (= [w1(\u2212 i + j) + w2(\u2212 i + j \u2212 1) +w3(\u2212 i + j \u2212 1) + w4(\u2212 i + j)]D: (29) De2ne a Lyapunov function candidate V as V = 1 2 S2 + g 2* +2; (30) where +\u2261 \u2212 \u2217 and * is a positive constant. Using (4), (5), (8) and (26), we have V\u0307 = SS\u0307 + g * ++\u0307 = S TAe + gS(u\u0302\u2217eq \u2212 u\u0302eq) \u2212 gS'\u2212 gSuh + g * ++\u0307 = S TAe \u2212 g * + [ *S( W \u2212 \u0307 ] \u2212 gS'\u2212 gSuh : (31) If we choose the adaptive law as \u0307= *S( W (32) then Eq. (31) becomes V\u03076S TAe \u2212 gS'; (33) where we use the fact that the uh has the same sign with Sg (refer Eq. (37)). Up to now, we have been deducing the factor according to (32). In order to complete the FSMC controller design, the hitting control should be taken into account to ensure state trajectory moves toward the sliding surface as well as to guarantee the stability of the control system. Achieving this goal, a Lyapunov function candidate is given as V = 1 2 S 2: (34) Then diMerentiate V with respect to time. Based on the stability of sliding mode control [11], we have" + ] + }, + { + "image_filename": "designv11_2_0003950_978-1-4020-4535-6_26-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003950_978-1-4020-4535-6_26-Figure4-1.png", + "caption": "Figure 4. Top: magnetic structure and winding arrangement of the analyzed and constructed concentrated coil PM motor. Bottom: disposition conventions of coils and PMs.", + "texts": [ + "65 mm: with these values, hm = 3 mm is suited to gain an acceptable no-load magnetization (in fact, with \u03b5 \u2248 0.15, it follows: \u03b7PM \u2248 0.75; Bt = 1.32 T; tooth flux \u03d5t0 = 0.761 mWb); FEM simulations [14] confirmed (7) (\u03d5tanalytical = 1.012 \u00d7 \u03d5tFEM). Fig. 3 shows the designed rotor during the construction process: the PMs are glued on the steel surface, inserted in suited slots for their correct and accurate positioning. As the stator yoke, also the rotor yoke results definitely oversized (in fact, it was designed for a four pole motor). The complete cross section of the machine is represented in Fig. 4, that shows also the adopted winding disposition (in it, a layer displacement Nts = Nccph/2 = 3 has been adopted). The FEM evaluated distribution [14] of the no-load flux density amplitude in the toothed zone (at half stator tooth height) is shown in Fig. 5; the following remarks are valid: the FEM peak value Bt confirms the analytical result; the peripheral amplitude distribution of |Bt0| appears substantially sinusoidal, thanks to the gradual displacement among PMs and teeth within each cycle", + " of winding parallel paths, equal to Nc, or sub-multiple of it (here a = 1 has been chosen); tu = average turn length; As = slot cross section; \u03b1cu = slot filling factor; e = \u201cper tooth\u201d equivalent permeance. While R1 is simple to be evaluated, L1 can be analytically evaluated only with some approximation; on the other hand, it can be obtained with energy calculations by a magnetostatic FEM simulation, substituting the PMs with passive objects, with the same permeability of the PMs. For the machine of Table 2, Fig. 4, the values of Table 3 have been obtained. The choice of Ntuc is a key design issue, greatly affecting the performances. In the following, just the Joule losses will be taken into account, neglecting the core P c and mechanical losses P m, that can be considered separately. To evaluate the influence of Ntuc, the phasor diagram of Fig. 6 must be considered, analyzing the machine operation under sinusoidal feeding, at voltage V. It is useful to define the quantities \u03c1E and Ik as follows: \u03c1E = E V = \u03c9 \u00b7 0 V = \u03c9 \u00b7 01 V \u00b7 Ntuc (13) Ik = V Z = V\u221a R2 + (X)2 = V N2 tuc \u00b7 \u221a R2 1 + (\u03c9 \u00b7 L1)2 : (14) they represent the e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001860_iros.1997.649021-Figure11-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001860_iros.1997.649021-Figure11-1.png", + "caption": "Figure 11: Quality results for Objl", + "texts": [], + "surrounding_texts": [ + "125\nM. Muller. Enttoicklung von Grezfstrategien f u r Precision-Grasps mit der DLR-Dreifingerhand. Diplomarbeit, Imtitut fur Robotik und Systemdynamik, DLR Olberpfaffenhofen, 1997.\nV.-D. Nguyen. Constructing force-closure grasps. Int. Journal of Robotics Research, 7(3):3 - 16, June 1988.\nJ. Pertin-Troccaz;. Grasping: A state of the art. In 0. et al. Khatib, editor, Robotics Review, vol-\nume 1, pages 71 - 89. MIT Press, Cambridge, MA, 1989.\nN. Pollard. Parallel methods for synthesizing whole-hand grasps from generalized prototypes.", + "126\n0 3 5\n0.25 Wor.toi100 e bestof100 +\nw C f P l O l 1 0 0 0 best01100 + - 02 L L 0 15 7\n0 1\nt\na\n02 y\n\"0.1 I I 0 100 2M) 3w 400 5W 6W 700 800 800 1000\n[8] N. Pollard. Synthesizing grasps from generalized prototypes. In Proceedings of the 1996 IEEE International Conference on Robotics and Automation, pages 2124 -2130, Minneapolis, Minnesota, April 1996. IEEE.\n[9] IC. B. Shimoga. Robot grasp synthesis: A sur-\n.\", I 0 1w 2M) 3w 400 6M) Boo 700 B[K) sw 1m _ .\n[lo] A. Sudsang and J. Ponce. New techniques for computing four-finger force-closure grasps of polyhedral objects. In Proceedings of the 1995 IEEE International Conference on Robotics and Automation, pages 1355 - 1360, Nagoya, Japan, May 1995. IEEE.\n[I11 Homepage of the DLR multisensory articulated hand. http://www.op.dlr.de/FF-DRRS/MECHATRONICS/DFG/index.html, 1997.\n[12] \"home page for qhull\" (convex hull algorithm). http: //www.geom.umn.edu/software/qhull/, 1995.\nI131 Telemanipulation demonstration: deliver a soft ball to a human being. http://www.op.dlr.de/FFDR-RS/STAFF/eckhardhub/telerobotics.html, 1.996." + ] + }, + { + "image_filename": "designv11_2_0000062_s0043-1648(98)00402-5-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000062_s0043-1648(98)00402-5-Figure1-1.png", + "caption": "Fig. 1. The modified four-ball rolling bench test at Bournemouth.", + "texts": [ + " The failure modes of these balls were characterised. This paper is also an attempt to predict the crack propagation phase by the boundary element methods and to compare the predictions with experimental results. This work not only concentrates on the Hertz contact stress, but also on the influence of traction and lubricant pressure. A suitable growth mechanism of ring cracks is proposed. The rolling contact fatigue tests were performed using a \u017d .modified rolling lower balls four-ball machine as shown in Fig. 1. This machine was employed as it correctly models ball bearing motions and precisely defines the contact load. It consists of an assembly that simulates an angular contact rolling element bearing. The stationary steel cup represents a bearing outer-race, three lower balls represent the rolling elements within a bearing-race and the upper ball represents the inner-race. The assembly was \u017d .Fig. 3. Pressing defect image on HIP silicon nitride balls post-test . loaded via a piston below the steel cup, from a lever-arm load" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000400_jsvi.2001.3570-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000400_jsvi.2001.3570-Figure4-1.png", + "caption": "Figure 4. Euler's angles.", + "texts": [ + " The rotating system Oxyz has the y-axis coincidental with the >-axis of the \"xed system, and x- and z-axis parallel with the principal axes x@ and z@ of the shaft cross-section (if the angular de#ections are neglected). The \"nite element procedure for rotors with symmetric shaft, developed by Nelson and McVaugh [14], will be considered. Modi\"cations will be made to accommodate the e!ect of shaft asymmetry. The shaft model includes the e!ect of rotary inertia and the gyroscopic e!ect. Shear of the cross-section and internal damping will be neglected. 4. KINEMATICS We consider (Figure 4) two frames with the origin at the center of the shaft cross-section, CX>Z, having the axes parallel with the axes of the \"xed frame OX>Z, and Cx@y@z@, whose axes are the principal directions of inertia of the cross-section. The link between the two frames is made through the set of Euler's angles u, h and t. To bring the shaft cross-section from its unde#ected position to the current one, three rotations are to be applied successively: one of angle t about the Z-axis, one of angle h about the new axis x, denoted as x 1 , and one of angle u about the new axis z, denoted as z 2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002619_j.robot.2004.07.010-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002619_j.robot.2004.07.010-Figure4-1.png", + "caption": "Fig. 4. A view of linear tracked mobile PUMA manipulator.", + "texts": [ + " , m} \u2264 \u03b52 (46)\u2223\u2223\u2223mk+1 L \u2212mkL \u2223\u2223\u2223 \u2264 \u03b53 (47) where \u03b51, \u03b52, \u03b53 are predefined small positive constants. If the termination conditions are satisfied then, the updated trajectory is the optimal and corresponding value of mL is the maximum allowable load, which can be carried by the mobile manipulator. Otherwise the program jumps to Step 2. Also, satisfying termination criterion means that linearization errors are eliminated or significantly reduced. A spatial three-jointed PUMA robot mounted on a linear tracked base is considered as shown in Fig. 4. For simplicity the compliance on links and joints is ignored. As a result, the generalized coordinates related to joint and link flexibility qj\u03b5Rn, qf \u03b5R n\u2211 i=1 nmi and their derivatives must be omitted from kinematic and dynamic equations. Suppose that initially the load is at a point with coordinates {xe = 0.50m, ye = 0.20m, ze = 0.30m)i and it must reach to final point with coordinates {xe = 1.30m, ye = 0.40m, ze = 0.30m)f at T = 2.4 s. The base motion coordinate xb is limited between 0m and 2m and joint limits of the manipulator are such that the first joint is free, second joint \u22122 /3 \u2264 \u03b81 \u2264 2 /3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001773_tra.2003.814497-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001773_tra.2003.814497-Figure8-1.png", + "caption": "Fig. 8. Jump conditions along a grain boundary. (a) Continuity jump condition. (b) Coverage jump condition.", + "texts": [ + " This section is simply for mathematical rigor and completeness, which clarifies the subtleties alluded to in the differential version of our problem. The essence of the idea has already been explained in the previous section. We introduce basic concepts with a simple example. We then generalize and provide formal definitions. Continuity Jump Condition: For a given direction field and a side step function, a grain is a simply connected open set in the designed surface , at every point of which the compatibility equation (6) holds.7 Consider the two neighboring grains, and , separated by the \u201cborder line\u201d , as shown in Fig. 8(a). Let a unit tangent vector of the borderline be denoted by . Of course, we assume that the boundary curve is at least piecewise smooth. We resolve the ambiguity in the sign of the vector by setting where is the unit tangent vector of the surface streamlines. This is equivalent to where , , is the Jacobian matrix of the parameterization , was defined in (2), and is the counterclockwise 90 rotation matrix. 7We introduce the notion of grains abruptly here, just for convenience. The formal definition is given in the next subsection. We say that the continuity is satisfied between the two grains if the side step function, defined in the combined region , satisfies the following condition for a given direction field: if a sweeping path in and a sweeping path in are \u201cconnected\u201d at a point in the border line (for example, at the point in Fig. 8), the shifting procedure, (4), in both grains generates the next sweeping paths that meet at a common point on the border (for example, at the point in the figure). In equation form, the condition is expressed by (11) Note that the subscriptions indicate the domains of the limit processes where . This condition is referred to as the continuity jump condition. We can also make a \u201cflux argument\u201d to reach the same conclusion. Coverage Jump Condition: We now ask what the value of the side step and the direction angle at a point on the borderline should be. We consider a flat surface and a parallel velocity vector field in each grain. In addition, we tentatively assume that the value of the side step on the border is just as shown in Fig. 8(b), one of the two limit values approaching from both grains. We now consider sweeping along a middle streamline with a disk of diameter . There are two cases shown in Fig. 8(b). In the first case, when the streamline is deflected through line which is orthogonal to the boundary, it is observed that the swept area properly covers regions between the two sweeping paths. However, in the second case, when the streamline is reflected by line , it is observed that a gap appears near the boundary. With some plane geometry, we can find the necessary size of the disk to fill this gap. We generalize this observation and require the following condition for proper coverage of the surface: (12) where the symbols are as defined in (11)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001548_978-1-4615-3910-0_13-Figure13-2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001548_978-1-4615-3910-0_13-Figure13-2-1.png", + "caption": "Figure 13-2 Representative stress-strain hysteresis loop for a material undergoing low cycle fatigue.", + "texts": [], + "surrounding_texts": [ + "This section is devoted to describing the most popular empirical models available, along with their applicability to SMT fatigue life prediction." + ] + }, + { + "image_filename": "designv11_2_0002115_1.1609483-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002115_1.1609483-Figure4-1.png", + "caption": "Fig. 4 Deformed debris shape \u201esaucer shape debris\u2026: \u201ea\u2026 perspective view; \u201eb\u2026 side view; and \u201ec\u2026 top view", + "texts": [ + " Coulomb friction was used to model the contact between the mating surfaces and the contact between the mating surfaces and debris. The cylinders were pressed together by applied loads to obtain the desired Hertzian contact pressure. FEA Debris Aspect Ratio Formulas. The FE results were used to develop simple models describing the debris deformation in heavily loaded rolling/sliding contacts. Debris aspect ratio is defined as the ratio of the deformed height of the debris divided by its width and is given by Ad5 lz 2rd (1) Figure 4 depicts the side, perspective and top view of a deformed debris. Debris aspect ratio in the inlet ~which is a strong function of its position!, and in the contact zones are described respectively by Ad50.02md 0.004S W Ed8dd 2D 20.0261S Y d Td D 0.0173 e20.827X 25.0,X,22.3 (2) Ad50.2md 0.300S W Ed8dd 2D 20.0891S Y d Td D 0.341 22.3 =\nAdditional suffixes\nb = base value for per-unit system o = open-circuit conditions sc = short-circuit conditions u = unsaturated value\nNote: Currents, voltages and reactances are represented by lower-case letters as above when in per-unit. Upper-case symbols indicate values in amperes, volts and ohms.\nd- and g-axis currents produce magnetomotive forces on their respective axes.\nPaper 3788C, (PI), received 4th June 1984\nDr. Macdonald is with the Department of Electrical Engineering, Imperial College of Science & Technology, London, SW7 2BT, United Kingdom, and Mr. Reece and Dr. Turner are with the Stafford Laboratory, GEC Engineering Research Centre, PO Box 30, Lichfield Road, Stafford, ST17 4LN, United Kingdom\nThe accurate calculation of the reactances of synchronous machines has received much attention in the last 10 years. It has been recognised that the iron paths are often heavily saturated, and that steady-state reactances are functions of operating voltage, load and power factor. Attempts have been made to deduce general relationships from measurements on load, and from machine dimensions using finiteelement or finite-difference methods. Discrete reluctance models have also been suggested.\nPower systems engineers are particularly concerned to have good values of generator steady-state load angles, so that any subsequent calculation of transient stability may commence from an accurately known, base condition. Shackshaft and Henser [1] suggested an empirical approach, based on measurements giving a cosinusoidal variation of effective reactance with internal load angle. Sugiyama et al. [2] suggest that xq/xd = 0.84, and that reactances can be considered to fall with voltage behind Potier reactance or effective total excitation current.\nThe use of finite-element methods to represent a twodimensional cross-section of the machine, with accurate delineation of the geometry of the airgap, slots and teeth, and variation of iron permeability from element to element, has made the calculation of generator steady-state performance possible, and each load point has its corresponding reactances. A number of programs have been written to obtain the load angle and field current corresponding to a particular voltage and load [3,4]. Demerdash and Hamilton [5] present a similar approach, and give a useful list of references to work published in North America. Being two-dimensional, these programs require allowances to be made for stator end-leakage reactance obtained with other programs [6], and for fringing at the ends of the core. More approximate representations have been made, on the grounds that the use of finiteelements is too expensive [7], but it will be shown below that the direct computing cost of the finite-element model is small.\nDetailed examination of generator performance with the finite-element method as described below has shown that the use of axis reactances alone is possible, but, under saturated conditions, the windings on one axis produce flux on\nIEE PROCEEDINGS, Vol. 132, Pt. C, No. 3, MAY 1985 101", + "the other, giving rise to cross-axis reactances. These have also been described by Dougherty and Minnich [8] in a slightly different form. The inclusion of these terms in machine general equations has also been proposed by Brown et al. [9], but their significance in generator performance remains to be explored.\n2 Calculation of steady-state operating points\nThe finite-element method has been described in detail elsewhere [4]. In the method used here, first-order triangular elements are used to represent a pole pitch of the machine, field current and load angle being determined for specified terminal voltage, current and power factor. Two slightly different methods have been described [3, 4], both requiring a small number of Newton-Raphson iterations to converge both iron permeabilities and terminal conditions. The method used here is more akin to that of Reference [3]. The iron magnetisation curves are represented by analytic approximations [10]. The accuracy in the representation in the airgap adjacent to the teeth, and in the edges of the teeth, is crucial, and must allow for fringing flux. The success of the calculation may be judged by the accuracy with which the saturation curves are produced: these are shown in Figs. 1 and 2 for a 500 MW generator\nfinite-element calculated points\nfor d and g-axes (stator-excited on the g-axis), and are compared with measured values obtained by the CEGB at Eggborough in 1975. The short-circuit curve may also be obtained by calculation [11]; but as the iron is virtually\n102\nunsaturated in that condition, agreement with measured values does not represent a good criterion for accuracy of representation. The mesh used here (obtained interactively) had 1786 nodes and 3490 elements. After renumbering, the total half-matrix bandwidth (including the leading diagonal) was reduced to 85 136. Each iteration, involving a modified Gaussian elimination of the banded matrix, took 4.3 s on an IBM 3033 computer. About four iterations were required for each load point, at a direct cost of about \u00a32 per point, using the lowest level of priority.\nSteady-state field current and load angle are shown in Figs. 3 and 4, plotted to a base of power factor angle, for\no o o o CEGB test points\nfinite-element calculated points\n100% and 50% power load, at the voltages near rated voltage for which load points were measured. In the past, such curves have been plotted to a base of power factor [4]: that introduces a double-bend near unity power factor, which has been avoided here. Also shown in Figs. 3 and 4 are the measured load points obtained by the CEGB: it will be seen that the agreement is good, although calculated field current is higher by 2-3%. The measured values of load angle, with accuracy limited by the techniques of nine years ago, show some scatter.\n3 Effective axis reactances\nThe following equations, derived from the steady-state phasor diagram, give the effective axis reactances corresponding to each load point:\nxd\nxq-\nif\ncos 3 + ifxa\n\u2014 i sin (3 + 4>)\nvt sin 3\ni cos (3 + 4>)\nIEE PROCEEDINGS, Vol. 132, Pt.\n(1)\n(2)\nC, No. 3, MAY 1985", + "These equations are in per-unit quantities, as defined in Section 10. The system used takes stator rated current as 1 per unit, and per-unit field current as the current which produces the same fundamental airgap MMF as the stator carrying three-phase currents of 1 per unit.\no o o o CEGB test points finite-element calculated points\nfl-axis contribution to xd\nA A A xd obtained by Smith et al. [7]\nA A A\n2.3\n2.2\n2.1\n2.0\n1.9\n1.8\nd 1.7\nu c o t> X o >\n0.5\n0.4\n0.3\n0.2\n0.1\nxd variation with load angle at 50% rated load\nxd derived from finite-element excitation calculations xd derived from CEGB tests xd obtained from basic reactances, using eqn. 12 <7-axis contribution to xd xd obtained by Smith et al. [7]\n\\ \\\n\\ \\\n0 10 20 30 40 50 60 70 80 90 load angle,deg\nFig. 7 xq variation with load angle at 100% rated load xq derived from finite-element excitation calculations o o o o xq derived from CEGB tests + + + xq obtained from basic reactances, using eqn. 11\nfield current contribution to xq (negative) d-axis contribution to xq\nA A A x obtained by Smith et al. [7]\n1EE PROCEEDINGS, Vol. 132, Pt. C, No. 3, MAY 1985 103" + ] + }, + { + "image_filename": "designv11_2_0001991_s0263574700007712-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001991_s0263574700007712-Figure3-1.png", + "caption": "Fig. 3. The kinematic structure of the two robot arms,", + "texts": [ + " A* = C C \" 5 if \"^TB 0 if 2B (17) l if - \u2014 ^ : Finally, the minimum distance function between a line segment and a point is given by d(LSuPT2) = h(k*) (18) 140 Collision-free motion 3. Point l.o Point Two points are expressed by Then, the distance between two points is expressed by d(PTu PTZ) - HQuh) = lltfn -P21U (20) m. PROBLEM FORMULATION In this section we establish a framework for a collision-free motion planning scheme of two articulated robot arms in a common work space. The kinematic structure of two robot arms is shown in Figure 3. We use the homogeneous coordinates and the DenavitHartenberg representation13 to describe robot kinematics. where q0) = (q\\\u00b0, q$\\ qf)' is the joint variables pf the /th robot arm (1 = 1, 2) T^ = the 4 x 4 homogeneous transformation matrix which represents the /til robot arm base coordinate system with respect to the reference gQQrd.}nate system (1 = 1,2) Pol \u2022 (Xo/> y>o}, z{o), 1)' is the 4 x 1 augmented position vector Of the origin of the j the link coordinate system of the ;'tj) robot arm, with respect to the /th robot arm base g$#rdjnate system (1 = 1, 2; ) Pi0 = (XP' yV> ZT< 1)' i s t n e 4 x " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001486_cdc.1994.410906-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001486_cdc.1994.410906-Figure1-1.png", + "caption": "Figure 1 : The carlike robot.", + "texts": [], + "surrounding_texts": [ + "Take another local Lie-Backlund submersion onto an open subset of R x R: . Assume the existence of a local Lie-Backlund isomorphism ip , which leaves fixed any element of R x Rz, and such that J p = OPip. Fibers at the same point of 6, and 6, have the same dimension, since they are exchanged by 1,. The counterpart of (1) isdXi/dt = A(t ,X , U , . . . , dGiui/dtGi), = I , . . . , n, where X = (Zl , . . . , in) are local coordinates on a fiber of e,. The xi\u2019s and the i i \u2019 s are related by\n(3) x; = T,( t , X, ii, . . . ,dFi i /dtF) , X; = .I;.(t, X , U , . . . , dYu/d tY) .\n2.5. Example. Consider the \u201cclassic\u201d dynamics (e$ [22,291)\ndx - = F ( x , U ) dt (4)\nwhere u = (U,, . . . , U,) E R\u201c is the control, the state x belongs to an n-dimensional C\u201c-manifold X, F : X x R\u201d\u2019 + T X is CO\u201d. It corresponds to the diffiety D with local coordinates (t, X I , .. . , x,, ujui) I i = 1, . . . , n; vi 2 0) and Cartan field $ + E:=, Fa& +\nlocal coordinates x I , . . . , x, of X . The canonical LieBacklund submersion D +. R x Rz, ( t , x,, u~\u201d\u2019) H ( t , u ~ \u2019 \u201d \u2019 ) is of finite type; its fiber is the state-space X. 2.6. Remark. (l) , (2) and (3), which differ from the usual differential geometric setting [22, 291, are analogous to the formulas obtained via differential fields [ 12,13, 141. They were confirmed in various practical situations (cJ [ 15, 211). The lowering of the order of input derivatives in (1) via (3) was solved in [8]. 2.7. A system S is said to be time-invariant if, and only if, it can be written S = R x Sr& where W is the time axis and Sred the associated reduced system. Appropriate charts permit to recover (l), (2) and (3) where t is absent. 2.8. Remark. A diffiety is often understood as the set of solutions of a differential equation. Our formalism appears then to be an extension of Willems\u2019behavioral approach [43]. 2.9. Remark. We refer to [ 17,181 for an interpretation of the strong accessibility property via the Vinogradov variational complex (cf [30, 44]), which is intrinsic, i.e., independent of any state-variable representation and time scaling (see 3.1).\n3 Feedbacks\n3.1. \u2019 h o systems S and S\u2019 are said to be orbitally equivalent at points p E S and p\u2019 E S\u2019 if, and only if,\nthere exists a Lie-Backlund isomorphism x between open neighborhoods of p and p\u2019, such that p\u2019 = x p . The mapping x is called an endogenousfeedback (cJ [16,26]). Notice that the time t is transformed by such an equivalence like any other variable: It leads to time scalings, which have been discussed in the introduction. Derivation with respect to two different times in a given system is nothing else than picking up two different Cartan fields in the Cartan distribution. 3.2. Remark. The previous definition is equivalent to saying that the two differential algebras, with respect to appropriate Cartan fields, of C\u201d-functions in neighborhoods of p and p\u2019 (see 2.1) are isomorphic (compare with [23]). 3.3. Assume that S = R x Sred and S\u2019 = R x S:ed are time-invariant (see 2.7). They are said to be differentially equivalent at q E Sred and q\u2019 E s:ed if, and only if, Sred and Sied are orbitally equivalent at q and 4\u2019. The time is, now, left fixed. 3.4. To (4) corresponds the (Kalman) input-state Jiltration [7] 3 = (F,, I v = 0, f l , f 2 , . . .} of the differential algebra, with respect to 5, of Cm-functions, where\n0, if u 5 -2 functions of x , if v = -1 functions of ( x , U, . . . , d\u2019u/dt\u201d), if U 5 0\nA static state feedback between two dynamics of type (4) is an endogenous feedback, which furthermore preserves the input-state filtration [715. The extension to quasi-static state feedbacks [7] is immediate. 3.5. The systems S and S\u2019 are orbitally dynamically equivalent at p E S and p\u2019 E S\u2019 if, and only if, there exists a Lie-Backlund correspondence between open neighborhoods of p and p\u2019. This correspondence, which is called an exogenous feedback, is the most general dynamic feedback.\n4 Flatness\n4.1. A system S (resp. a time-invariant system S = W x S r t d ) is said to be orbitally (resp. di$erentially) f i t at a point p E S (resp. q E Sred) if, and only if, there exists a topological (resp. differential) equivalence between p (resp. q ) and a point of a differential affine space W x R; (resp. a reduced differential affine space Wz). The set w = ( w , , . . . , w,)\n%ee also an unpublished manuscript by B. Jakubczyk.\n34 1", + "in 1.4 is called a linearizing, orfit, output.6 4.2. S (resp. S = R x Srrd ) is said to be orbitally (resp. diferentially) linearizable by exogenous feedback if, and only if, at a point p E S (resp. q E Srcd), there exists a local Lie-Backlund submersion from a differential affine space (resp. a reduced differential affine space) onto an open neighborhood of p (resp.\n4.3. Again, considerations on filtrations permit to demonstrate that any dynamic feedback-linearizable system is flat. Theorem. Any system, which is orbitally (resp. differentially) linearizable by exogenous feedback at a point, is orbitally (resp. differential1y)jat at this point.\n4).\n5 Stabilization via time scaling\n5.1. Consider the well known carlike robot:\nC\u201d-function [0, TI 3 t H s ( t ) E [0, L ] , such that s(0) = 0, s ( T ) = L and S(0) = S(T) = 0. The smooth open loop control\nsteers the car from the configuration (xc(0), yc (0) ,ec (01, (pc (0)) , with uc(0) = 0, to M L ) , yc(L) , M L ) , (pc(L)) , with uc(T) = 0. 5.3. Singularity is being removed by taking derivatives not with respect to time, but to the arc length s of C, which plays the r6le of a \u201cnew\u201d time. Set ui = u i i ( t ) , i = 1 ,2 where the vi\u2019s arenew control variables. Using\nd d ds dt the rule - = i(t)--, ( 5 ) becomes\ndx dY de t a n q - = u1 case, - = ut sine, - = ul -, 3 = v2 . ds ds ds 1 ds\n(6) If the system is close to the reference trajectory defined by C, then ut % l . Flatness yields the dynamic feedback\nThe 2 x 2 decoupling matrix of the system (6)-(7) between the input w = ( w l , w 2 ) and the output (x, y ) follows from the relations\nI . tanp ,\nX = u1 case, y = u I s i n e , 8 = uI-. 4 = uz ( 5 ) 2 = wl s ine , (y ;y i~w2 1 2cose - ( ~ I ) \u2019 s i n ~ m e ) c l r y I 2 ~ j ~ > c o s 0 t a r i q\nwhere (x, y , O , $ ) is the configration state, U = +({ I I \u2018\n(U], u z ) is the control and 1 is the length of the car. Differential flatness is easily checked [16]: (x, y ) is a Itsdeterminant A C which is # OaroundC, shows\nthe regularity. The reader may verify that this inverse singular, since the corresponding tangent linear sysdoes not exist at t = T if the derivatives are expressed tem is uncontrollable. According to Brockett [3], ( 5 ) with respect to time.\nlinear stabilizing feedback\nlinearizing output. Any steady state may be seen as\ncannot be stabilized by a smooth state feedback. As - d\u2019, . -\nIcos2(p\u2019\nd \u2019 x - = yields the shown by Coron [GI, a time-varying one must be used. 5*4. Setting 5.2. Take, as in [16], a smooth curve C defined by the\nR2 (s is the arc length, K ( S ) the oriented curvature of C, O,(S\u2019) the angle ofthe oriented tangent to C, &(s) = tan-\u2019(lK(s))). Consider, for T > 0, an increasing -\nbraic counterpart and several applications. See [31] for a related d2d, h d , ds ds\n- (A + iik + a) (% - %(\u2019(\u2018))) - (.r--r\u2019(\u2019y\u2018\u2018)) dl:l2d, ) U = $ ( s ( r ) ) - (2 + + *) (2 - $ ( S ( t ) ) )\n- (A + I + I)(e - h( s ( f ) ) ) - (F &d?) ( Y \u2018See [18] for more details and [16] for the differential alge-\ndifferential geometric formalization, and [28] for the utilization of exterior algebra. See [38] for another approach of dynamic feedback linearization. ( d 1 7 d27 d 3 ) corresponds to the tracking poles with respect to the \u201dtime\u201d s: %, i = 1 , 2 and z = x, y are", + "given by References\n5.5. Pulling back the preceeding feedback to the time t of course yields a time-varying smooth feedback. The error e ( t ) satisfies 11 e ( t ) 11 Mle-M2S(t) , where MI, M2 are strictly positive constants. For the backward motions displayed on figure 2, one has 1 = 1. m, d , = 113.5, d2 = 113, d3 = 1 / 2 5 Notice that after a distance 1 1. m, e ( T ) 0. Such asymptotic stabilization stategy is interesting when the length L of the reference trajectory C is much larger than the car length 1: we have here L / 1 > 3. 5.6. Remark. See [20] for more details, another example and a general stabilization theorem concerning driftless flat systems. Robustness follows from [l].\nConclusion\nTime scalings and, even, controlling the clock (cf. [ 181) will play a most important r6le in forthcoming publications for dealing with non-flat systems and providing a general framework for model reduction. Other applications of this new differential geometry are also in preparation, to nonholonomic mechanics for instance (see, e.g., [W).\n[I] M.K. BENNANI, Commande non lin6aire de vChicules sur roues avec remorques, Rapp. Option Aurnmatique, B o l e Polytechnique, Palaiseau, 1994.\n[2] A.M. BLOCH, N.H. MCCLAMROCH and M. REYHANOGLU, Control and stabilization of nonholonomic dynamic systems, IEEE \u2018IA.C.37, 1992, pp. 1746-1757.\n[lo] S. DIOP. Elimination in control theory, Mark Conrr: Sign. Syst., 4, 1991. pp. 17-32.\n[Ill ibid. Differential-algebraic decision methods and some applications to system theory. Theorer. Compur. Sci., 98. 1992. pp. 137- 161.\n[12] M. FLIESS, Automatique et corps diff6rentiels. Forum Mark, 1, 1989. pp. 227-238.\n[13] ibid. Generalized controller canonical forms for Linear and nonliear dynamics, IEEE i7A.C.. 35, 1990. pp. 994- 1001.\n[I41 M. FLIES and S.T. GLAD, An algebraic approach to linear and nonlinear conbol, in Essays on Co~rol: Perspectives in fhe Theory and irs Applications, HL. Trentelman and J.C. Willems, Fds, Birkh;iuser, Boston, 1993. pp. 223-267.\n[IS] M. FLIESS and M. HASLER, Questioning the classic state space description Via the circuit examples, in Realiznrion and Modelling in System Theory(MTN3\u201989, vol. I), M.A. Kashoek, J.H. van Schuppen, and A.C.M. Ran, Eds, BirlrNLuser, Boston, 1990, pp. 1-12.\n[16] M. FLIESS, J. LEVINE, PH. MARTIN and P. R~UCHON, Flatness and defect of nonlinear systems: introductory theory and applications, Inter J . Conk 1995.\n[I 71 ibid. Towards a new differential geometric setting in nonlinear control, Proc. Inremar. Geomerncal Con$. Moscow. May 1993, to appear.\n[I81 ibid. Linhisation par bouclage dynamique et transformations de Lie-BkMund, C.R. Acad. Sci. Pans, 1317, 1993, pp. 981-986.\n[19] ibid. Sur la ghdt r ie locale des fibrations de Lie-BLklund, in preparation." + ] + }, + { + "image_filename": "designv11_2_0000272_1.1395624-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000272_1.1395624-Figure3-1.png", + "caption": "FIG. 3. Spiral wave tip movement during stationary drift ~thick line!. Superimposed is the core of a freely rotating spiral ~thin line!. Parameters are the same as in case B in Fig. 2.", + "texts": [ + " Our numerical results face us with a paradox: on the one hand, general collision arguments tell us that nonzero drift velocities cannot be observed for T f /Ts>1; on the other hand, we clearly observe nonzero drift velocities for T f /Ts >1. The core of our argument to resolve the paradox is that the trajectory of the spiral wave tip after the collision results in an effectively larger spiral wave period Ts ! . To understand this we will look in the following paragraph into the actual dynamics of the spiral wave trajectory after the collision. As Fig. 3 shows, there are mainly four phases for moderately sparse spirals, an initial collision phase ~phase 1 in Fig. 3!, a noncurling phase due to a strong \u2018\u2018dense\u2019\u2019 interaction of the broken front with the refractory tail of the spiral ~phase 2 in Fig. 3!, then a transitory curling phase ~phase 3 in Fig. 3! and a forth phase where the spiral wave tip eventually has relaxed onto the core of a freely rotating spiral ~phase 4 in Fig. 3!. During the noncurling phase 2 the newly created broken end and the next wave train are almost moving without changing their distance due to the refractoriness and, hence, the tip velocity is c f . Despite the transitory nature of phase 3 where the spiral has not yet relaxed on the stationary core, the numerics show that its velocity has already reached the stationary velocity cs . This is the two-dimensional analog of the observation in one dimension that arbitrary initial conditions very quickly assume the stationary velocity although their shape has not taken the stationary shape", + " This is due to the fact that the velocity is determined by diffusion and hence only the foremost part of the front does matter. It is this transitory phase 3 which has been neglected so far and which allows for nonzero drift velocities for T8.1 ~in Ref. 5 only phase 4 has been considered, and in Ref. 4 only the noncurling phase 2 has been considered under the assumption of equal growing and front velocities!. During phase 3 the tip moves on a quasi-circle with a radius larger than the radius of the freely rotating spiral, as can be seen in Fig. 3. This effectively introduces a larger spiral wave period Ts !.Ts to keep the velocity cs constant. This explains the seemingly paradoxical nonzero drift velocities for T85T f /Ts>1 since the results in Fig. 2 are depicted versus the spiral wave period of the freely rotating spiral Ts . Studying the dependence of the drift velocity on the initial conditions in terms of position of the spiral wave tip on the core of the freely rotating spiral, we found the plausible result that the actual values of the drift velocities do not depend on the initial conditions, but that the maximal T8 >1 exhibiting nonzero drift velocities does depend on the initial conditions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002880_iros.2005.1545420-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002880_iros.2005.1545420-Figure4-1.png", + "caption": "Fig. 4. Experimental setup", + "texts": [ + " A 6-DOF force sensor (ATI Nano43 F/T transducer) is integrated at the end-effector. The operator holds a tool mounted at the end-effector. The robot responds to the applied force, allowing the operator to have direct control over the robot motion. We illustrate our virtual fixture implementation using two sample tasks and report the results. The first sample task is to guide the tool tip following a 2D b-spline curve in a plane while keeping the tool perpendicular to the plane. The experimental setup is shown in Fig. 4. We drew a set of line segments on a flat plastic plate, assumed to be a plane, and attached OPTOTRAK R\u00a9 (Northern Digital Inc., Waterloo, Ontario, Canada ) LEDs to the plate. We defined a target coordinate frame for the plane with origin, x and y axis on the plane and z axis pointing along the normal direction of the plane. We used a digitizer to gather sample points on the line segments in the target coordinate frame. Then we generated a 5th degree b-spline curve in the target coordinate frame by interpolating these sample points" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002880_iros.2005.1545420-Figure5-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002880_iros.2005.1545420-Figure5-1.png", + "caption": "Fig. 5. Geometric relation for two sample tasks (a) Follow a curve with a fixed tool orientation with respect to the curve (b) Rotate around an axis with a fixed angle.", + "texts": [ + " Using the method discussed in II-B.3, we set Ht and ht using n = 8 in (10). The constraints for the tool tip frame are HtJt(q)\u2206 q \u2265 ht (19) where Jt(q) is the Jacobian matrix that maps the tool tip frame to the joint space. Tool shaft frame: We create a second b-spline curve c2 by translating the given b-spline c1 by [ 0 0 100mm ]t in the target coordinate frame. We maintain the tool shaft perpendicular to the plane by constraining the origin of the tool shaft frame to move along c2. As shown in Fig. 5(a), we translate Pc1 by [ 0 0 100mm ]t in target coordinate frame to obtain Pc2. The reference direction is set as l\u0302c2 = l\u0302c1. Using the method discussed in II-B.3, we set Hs and hs using n = 8 in (10). The constraints for the tool shaft frame are HsJs( q)\u2206 q \u2265 hs (20) where Js( q) is the Jacobian matrix that maps the tool shaft frame to the joint space. We combine two constraints together to generate the virtual fixture for the task. We require our tip motion proportional to the user\u2019s force input f , then we set our optimization problem as arg min\u2206 q \u2225\u2225\u2225Wt(Jt( q)\u2206 q \u2212 k f) \u2225\u2225\u2225 , s", + " The aim is to guide the tool tip to pivot on a point other than the SHR mechanical RCM while rotating the tool shaft around a given direction with a fixed angle. In the experiment, we set the given direction as la = [0\u22120.2 1]t, the fixed angle as \u03b3 = 15deg, the pivot point Pt as [0 0\u221210]t with respect to the mechanical RCM. Instead of constraining two frames, we only constrain on the tool tip frame in this sample task. For each computational loop, the tool tip position xpt and the tool orientation l\u0302t are obtained from the robot encoders and its kinematics. For the rotational component, we constrain the tool to rotate along an axis. As shown in Fig. 5(b), the rotational axis \u03c9\u0302d can be calculated as d\u03021 = l\u0302t\u00d7 la \u2016l\u0302t\u00d7 la\u2016 ; d\u03022 = d\u03021\u00d7 la \u2016d\u03021\u00d7 la\u2016 ; R = [ d\u03022 la \u2016 la\u2016 \u2212d\u03021 ] ; \u03c9\u0302d = R \u00b7 [cos \u03b3 sin \u03b3 0 ]t (22) The signed error \u03b4r can be computed as \u03b4r = l\u0302t \u00d7 l\u0302a \u2016l\u0302t \u00d7 l\u0302a\u2016 \u00b7 sin \u03b3 \u2212 l\u0302t \u00d7 l\u0302a (23) Following the method described in II-B.4, we set Hr and hr using n = 8 in (13). For the translational component, we constrain the tool tip on Pt. Following the method described in II-B.1, we set Hp and hp using n\u00d7m = 4\u00d7 4 in (4). We require the tool rotational motion proportional to the user\u2019s torque input \u03c4 , then we set the optimization problem as arg min\u2206 q \u2016Wt(Jt( q)\u2206 q \u2212 k \u03c4)\u2016, s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002099_robot.1988.12102-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002099_robot.1988.12102-Figure1-1.png", + "caption": "Figure 1: Two robots handling a rigid body object. . .", + "texts": [ + " The organization of the paper is as follows. In Section 2, a problem formulation is presented along with the definition of \"supporting orientation\". In Section 3, a solution approach is proposed by ernploying the conuol techniques for redundant manipulators. In Section 4, a numerical example is presented to show the utility and power of our proposed method, where two PUMA 560 manipulators are considered. The paper concludes with Section 5. Consider two rohots each with n joints canying a rigid object as shown in Fig. 1, which is too large and tm long for a single robot to handle. The task given to the two robots is to move the object from one location to another along a prescribed path, while not exceeding joint limits and/or avoiding obstacles. Under the smoothness assumption mentioned earlier. the problem is to determine the joint trajectorieb of two robots iis well as the trajectory of the follower's gripping position to accomplish the task. Let (CO, y\", z\") . (zi,, y!, z k ) , and ( x i ) y;, 2 ; ) be the coordinate frames of object, end effectors of the leader and the follower, respectively (see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003047_iros.2006.282270-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003047_iros.2006.282270-Figure4-1.png", + "caption": "Fig. 4 A virtual structure for movement of platform on rugged terrain where each wheel will be on a different height.", + "texts": [ + " On the other hand, when there is a wheeled mobile-field robotic system in hostile environments the use of some kind of suspension/wheel compliance module is inevitable like the one which has been proposed by Sujan and Dubowsky [19], and also by Abo-Shanab and Sepehri [17]. Such a system is depicted in Fig. 3.. and can be still handled by MHS measure. To this end, it is just sufficient to prescribe the coordinates of support polygon vertices as inputs to our proposed algorithm. To be more rigorous, in the presence of flexible suspension the chassis is considered as a point of concentration and the distorting force should also be considered. In Fig. 4 a virtual structure has been considered for a platform on rough terrain where each tire has a different height when compared with others. Since, the proposed MHS measure is based on the contact points between the base and ground, by considering the virtual structure and the applied forces/torques (except the forced exerted to the tires) we can compute the applied moments about different edges of support pattern. Hence, the NMFS metric becomes applicable. Note that since the pure rotation has been considered as instability, and the rotation of the system will be caused due to the moments, we believe that the definition of instability by a moment-based metric is absolutely expected" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002116_ccece.1998.682564-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002116_ccece.1998.682564-Figure1-1.png", + "caption": "Figure 1: Inverted pendulum on a cart", + "texts": [], + "surrounding_texts": [ + "114\nsults demonstrate the effectiveness of the controller in the balancing and tracking problem, while we point out limitations in performance for the convergence of the parameter estimate towards its true value. These limitations arise mainly form the lack of precision of our homemade benchmark components.\nIn section 2 we give the equations describing the system dynamics. In section 3, we propose a control law to regulate the rod angle. An adaptation law and a cfl are also given. This triplet deals with the angle stabilization with no concern for the cart motion. In section 4, the controller is augmented with a MRAC module. In section 5 we give some experimental results.\n2 Problem formulation\nF = mg sin 6' cos 6'+ (.g sin 6 - u ) ( M + m sin2 8)\n~-\ncos 6'\nwhere u is the part of the control law to be designed, and the state representation\n21 = 5, 2 2 = i) 2 3 = 8, x4 = e results in\nU 2 4 = y4 + - 1\nConsider an inverted pendulum (with uncer- where tain but constant rod length) on cart moving in constrained translation (F'IG.1). The design goal is to stabilize the pendulum in its vertical unstable equilibrium position. This system is commonly treated as a 4-state ( 6 ' , 6 , x ) k ) space model, where x is the cart position, and 8 is the rod angle. From the Lagrangian, the general equations of motion are ml sin(x3)x! $92 = gtan(x3) + + sin2(23) and m sin(x3) cos(z3)xj M + m sin2( x3) $94 = -\n( M + m ) ~ + m ~ 8 cos 8 - mzj2 sin 8 = F ZcosB+l$-gsinB = o 3 Angle stabilization\nWhere F is the force acting on the cart, m and M are the masses of the rod and cart respectively, g is the gravitational acceleration and I is one-half of the length of the rod. To simplify the state-space representation (to apply the integrator backstepping algorithm)) we try to take as input the angular acceleration of the rod (rather than the force F ) . Since the parameter I is unknown, only partial transformation (which does not depend upon I ) is possible. Choosing the feedback control law In this section we use the backstepping algorithm to develop a control law to regulate the rod angle without regard for the cart motion. The angle will converge to its desired value from a wide set of initial conditions. The rod length is assumed to be unknown. The controller has thus not only to guarantee the stability and the regulation of the tracking error, but also the convergence of the unknown parameter estimate towards its true constant value. Since this parameter does not appear linearly in the system equations, the adaptive", + "115\nt would render the derivakive of the augmented cf I\n1 1 V ( 5 3 , 5 4 ) = + $\nnegative definite. Since 1 is unknown, we employ the certainty-equivalence form of ( 5 ) , in which I is replaced by an estimate 1\n1 u = -1 (k3 + k4)J4 + (1 - k:)& - esp + $94 ^I The final control function of Lyapunov\nallows the choice of an adaptation dynamics\n[ 1 backstepping procedure needs a slight modification to apply. In the first step, we define ; = -,,t4 (k3 + k4)t4 + (1 - k:)t3 - dsp + $94 the error variable\n($3 = x 3 - os, where y is the adaptation gain. With this choice, the derivative of the Lyapunov function ( 6 ) became negative, which implies that the closed-loop sub-system is globally asymptotically stable (GAS). with the cfl 1 2 W 3 ) = $3 we obtain our first virtual control\n54d = 4 3 t 3 + os, 4 Control of cart position Where k3 > 0 is a design parameter, and O, is the signal to be tracked by the angle X3. The two remaining uncontrolled state equaWe define our second error variable tions (cart position)\nJ4 = 24 - 24d\n= 2 4 + k3t3 - os,\nThe subsystem (3)-(4) can be rewritten in the (J3, 54)-space as\n53 = 4 3 5 3 + 54 64 = - k i t 3 + k354 - 0, + ~4 + - I U\nIf I were known, the control\n(1 - @ t 3 - esp + va] ( 5 )\nz1 = 2 2\nI .. x 2 = g tan(O,,) -\ncoS(Os,) Os,\nare the zero dynamics (of the closed-loop system. They can be modeled by a doubleintegration with a gain kp\nAn indirect MRA controller is used to compensate this part. Due to the errors convergence dynamics in the inner loop, the gain is", + "116\ntime varying. To compensate this variation, the MRAC uses a recursive least squares algorithm to identify the* gain. The reference model is given by\n1 H ( s ) =\n(1 + 43 and the obtained controller is\n1 + 37s G, =\nk,72(3 + 7 s )\n5 Experimental results In this section, the controller designs of section 3 and section 4 are implemented and evaluated on an experimental test-bed. A laboratory-scale version of the nonlinear benchmark has been constructed. The control force F is provided by a 12V DC motor. To avoid the damaging of the motor, a saturation element is inserted in the controller to limit the voltage command. Both rod angular position and cart position are sensed by potentiometers. To estimate the cart velocity and the rod angular velocity, we apply a finite difference scheme.\nThe figure 2 shows the position tracking performances, while the figure 3 gives the angle deviation from its vertical position (during the cart travel). We notice that the controller shows a good robustness despite its lack of performance in ensuring the convergence of the unknown parameter I towards its true constant value. This limitation is caused by the actuator saturation and the high level of noise introduced by the lack of precision of the components used to build the test-bed.\nReferences [l] I. Kanellakopoulos, P. V. KokotoviC, and\nA. S. Morse. Systematic Design of Adaptive Controllers for Feedback Linearizable\nSystems. IEEE Transactions On Automatic Control, vol. 36, NO. 11, pages 1241-1253, 1991.\n[a] M. KrstiC, I. Kanellakopoulos, and P. KokotoviC. Nonlinear and Adptive Control D esign. W iley -1nt er science Publication, 1995." + ] + }, + { + "image_filename": "designv11_2_0003873_0094-114x(81)90056-2-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003873_0094-114x(81)90056-2-Figure3-1.png", + "caption": "Figure 3. I", + "texts": [ + " Hence ~\" of (20) is negligibly small. As a result (17) approximates the equation of a circle of infinite radius. In this case, it can be seen from (18) and (19) that the two tetrahedra ABCD and AtBjC1DI are infinitely apart, with A,D, being parallel to AD. As a increases, the two tetrahedra approach each other rapidly and 0 decreases. The throat of the hyperboloid reduces from an infinite circle to a finite ellipse which then diminishes in size while the hyperboloic section in the X - Z plane elongates. Figure 3 depicts parts of the X-Y and X - Z sections of the hyperboloid of a Bennett linkage as a varies from 10 \u00b0 to aMAX. k~ of this linkage is 1.2 times ks and the skew angle between IA and Ic (or 18 and ID) is 90 \u00b0. When a = aMAX, i.e. when a = b, it can be derived from (18) that 0 = aMAX/2, (in the case of Fig. 3 aMAX = 67.56 \u00b0) and from (19) that t = - c12. In other words both Y and Z perpendicularly bisect the line LM of Fig. I as well as bisecting the angle between BC and AD. Therefore the two principal axes of the hyperboloid coincide respectively with the joins of the mid-points of the two pairs of opposite sides, AB and GD, AC and BD, of the tetrahedron ABCD (see section 1). Under this condition, the two tetrahedra ABCD and A~BICTD~ align themselves in such a way that AB, BD, CD, CA, BC and AD coincide respectively with C~D,, B,D~, A,B,, C~A~, A~D, and B~GI", + " From (7) and (8) we have a > b >> c. Therefore ~ and ~\" of (20) are much larger than s r. This results in a very elongated central elliptical section and a very compressed X - Z section of the hyperboloid. Figure 4 depicts parts of the X - Y and X - Z sections of the hyperboloid as sin-~X/(kdk2) varies from 30o-90 \u00b0. k, and k2 of the Bennett linkage involved are such that kl = 2kz. Apart from the fact that there is little change in the length of the minor axis OY, the pattern is very similar to that of Fig. 3. To see how the pattern of the hyperboloid varies regarding different link lengths we fix the skew angle between IA and ic and then vary kl with respect to k2. When kl = k2, i.e. when the four links of the mechanism have equal lengths, it can be seen from (I) and (2) that a is always equal to 90 \u00b0. The hinge axes IA and la then intersect respectively with ID and Ic at the points, say, F and E (Fig. 5) on the line of symmetry, x. Therefore, in this case the regulus of this particular form of hyperboloid degenerates into a pair of planar pencils whose poles are respectively E and F" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003073_j.matcom.2006.07.003-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003073_j.matcom.2006.07.003-Figure1-1.png", + "caption": "Fig. 1. (a) Schematic of a linear guide system and (b) geometry of the rolling ball in contact with rail and carriage.", + "texts": [ + " The rolling track was also simulated in a realistic way by incorporating the finite element analysis with the surface-surface contact model. As a validation, relevant experimental modal tests were carried out on linear guideways with different preloads. Finally, comparisons and discussions on the results obtained from numerical predictions and experimental measurements were made and suggestions for further studies on the factors affecting the vibrations characteristics of rolling guides were supplied at the end of this report. The linear guideway system is essentially designed with a Gothic arc groove, as shown in Fig. 1, which enables the rolling ball to contact with carriage and rail simultaneously and can be considered as a Hertzian contact mode here. According to the Hertzian elastic contact deformation theory, there is a nonlinear relationship between the local deformation at the contact point and the applied load acted on the contact components. For a linear guideway, the deformation of the raceway groove will increase with the applied load on the ball and enable the contact stiffness of the rolling interface to rise in a nonlinear way. Such a variation in contact stiffness may affect the dynamic behavior of this mechanism to a different extent. Therefore, in order to obtain correct vibration characteristics of a guideway, the contact stiffness must be suitably defined, see Johnson [6] and Goldsmith [2] Fig. 1 shows the geometry of the ball in contact with the groove of carriage and rail at the contact angle of \u03b2, forming a two-point contact state. When a compression force F is applied, the contact boundary of contacting objects will deform a small amount of \u03b1 and form an area contact of the shape of an ellipse with the major axis 2a and minor axis 2b. The relationship between local contact force F and elastic deformation \u03b1 can be written as follows: F = kh\u03b1 3/2 (1) kh = 4 3 qk (\u03b41 + \u03b42) \u221a A+ B (2) \u03b4i = 1 \u2212 \u03bc2 i \u03c0Ei (3) a = qa 3 \u221a 3F (\u03b41 + \u03b42) 4(A+ B) (4) b = qb 3 \u221a 3F (\u03b41 + \u03b42) 4(A+ B) (5) where \u03b1 is the elastic deformation of the contact area, \u03b4i the material properties of Hertz\u2019s contact theory, E the Young\u2019s modulus,\u03bc the Poisson\u2019s ratio of material, a the semi-major and b is the semi-minor of the contact ellipse" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002397_j.arcontrol.2004.01.011-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002397_j.arcontrol.2004.01.011-Figure3-1.png", + "caption": "Fig. 3. Kite and lines seen from the top, and visualization of the lateral angle \u03c8.", + "texts": [ + " Fig. 2), we therefore assume that el = we/\u2016we\u2016. The transversal axis of the kite can be described by a perpendicular unit vector et that is pointing from the right to the left wing tip (as seen from the kite pilot, in upright kite orientation). The orientation of et can be controlled, but it has to be orthogonal to el (cf. Fig. 2), et \u00b7 el = 0. (3) However, the projection of et onto the lines\u2019 axis (which is given by the vector er) is determined from the length difference l of the two lines, see Fig. 3. If the distance between the two lines\u2019 fixing points on the kite is d, then the vector from the right to the left fixing point is d \u00b7 et , and the projection of this vector onto the lines\u2019 axis should equal l (being positive if the left wing tip is farther away from the pilot), i.e., l = d et \u00b7 er. Let us define the lateral angle \u03c8 to be \u03c8 = arcsin( l/d). For simplicity, we assume that we control this angle \u03c8 directly. It determines the orientation of et which has to satisfy: et \u00b7 er = l d = sin (\u03c8)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002493_j.engfailanal.2005.07.019-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002493_j.engfailanal.2005.07.019-Figure3-1.png", + "caption": "Fig. 3. The picture of the undamaged differential pinion analysed in the study.", + "texts": [ + " On a smooth road, the movement comes to both wheels evenly. The inner wheel should turn less and the outer wheel should turn more to do the turning without lateral slipping and being flung. Differential, which is generally placed in the middle part of the rear bridge, consists of pinion gear, mirror gear, differential box, two axle gear and two pinion spider gears. A schematic illustration of a differential is given in Fig. 1. The technical drawing of the fractured pinion shaft is also given in Fig. 2. Fig. 3 shows the photograph of the fractured pinion shaft and the fracture section is indicated. In differentials, mirror and pinion gear are made to get used to each other during manufacturing and the same serial number is given. Both of them are changed on condition that there are any problems. In these systems, the common damage is the wear of gears [2\u20134]. In this study, the pinion shaft of the differential of a minibus has been inspected. The minibus is a diesel vehicle driven at the rear axle and has a passenger capacity of 15 people" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000034_s0020-7403(00)00038-2-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000034_s0020-7403(00)00038-2-Figure4-1.png", + "caption": "Fig. 4. Free-body diagrams of the struts equivalent for length h and l due to the shear stress q 12 .", + "texts": [ + " (28) For a 2D regular honeycomb (h\"l, h\"303, ll\"b) with tapered strut morphology, when k\"0, this reduces to lH 12 \"lH 21 \" Nl!Ml Nl#3Ml , (29) which is the same as that given by Warren and Kraynik [2]. For bending compliance only, Eq. (29) reduces to (lH 12 ) b \"(lH 21 ) b \"1 which is the same as that given by Gibson and Ashby [3,18]. 2.1.3. In-plane ewective shear modulus A remote shear stress q 12 produces a force F 1 on the h strut, and both forces F 1 /2 and F 2 on the l struts as shown in Fig. 4. The forces F 1 and F 2 are written in terms of the remote shear stress q 12 as F 1 \"2q 12 lll cos h and F 2 \"q 12 ll (h#l sin h). (30) The e!ective shear deformation comprised three factors. These are (i) the bending and shear deformation of the h strut, (ii) the rigid-body rotation of the h strut due to the bending and shear deformation of the l struts, and (iii) the axial deformation of the l struts. For<\"F 1 , Eqs. (19) and (30) give the deformation component due to bending and shear deformation of the h strut: (d h ) bs \"23.0.co;2-x-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001046_(sici)1097-0207(19960315)39:5<763::aid-nme879>3.0.co;2-x-Figure2-1.png", + "caption": "Figure 2. Tip deflections for a fast maneuver (m)", + "texts": [ + " To account for the non-linear geometric effect on the axial displacement obtained with this model, one can update uo in the postprocessing stage of the simulation using the foreshortening uf. This axial displacement can be calculated using the well-known second-order approximation, which for a planar beam takes the form: Thus, the axial deflection at the tip plotted for Model I1 is in fact uo - uf. 782 I. SHARF The results for a slow maneuver, displayed in Figure 1, show that all three models produce approximately the same displacements. Solutions for the fast maneuver are plotted in Figure 2 for Models I1 and 111. In this case, Model I produces physically unrealistic results because of the lack of the non-linear stiffness terms which ensure the stiffening of the beam. The deflections calculated with Model 111 are in good agreement with those of Hanagud and Sarkar29 for a similar prescribed-angle maneuver. At a first glance, the results of Figure 2 point to significant differences between the two stiffened models. However, further investigations reported in Reference 30 uncovered that the non-linear beam element used in Model 111 possesses poor convergence characteristics. This is illustrated in Figure 3, where we present the deflections calculated with Model I11 for the beam discretized with four elements. Also are shown the responses obtained with Model I1 and a two-element discretization of the beam. The bending deflection for the latter is in close correspondence with that reported by Hsiao et a1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003569_ijvd.2007.012304-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003569_ijvd.2007.012304-Figure1-1.png", + "caption": "Figure 1 A disassembled strutless double-cone synchroniser", + "texts": [ + " The results of the study could pave the way for improving the performance of shifting and synchronisation, such as shift time, synchroniser durability and operational comfort, since the simulation model can assist researchers in understanding the synchronisation as well as the influence of abrasion on synchronisers. In this study, the simulation model will focus on the strutless double-cone synchroniser, which is used on one available sedan shifting from first to second gear ratio. A strutless double-cone synchroniser consists of seven components, such as sleeve, hub, annular spring, outer ring, cone, inner ring and clutch gear as shown in Figure 1. The simulation model will be built on commercially available software, ADAMSTM, for analysing mechanical dynamics. In this simulation model, all components are assumed to be solid and rotational freedom around the rotational axis except for the hub and sleeve. Since the input and output shaft transfers power through the transmission gear and hub, respectively, the transmission gear connects on the ground with a revolutionary joint, whereas the hub is fixed on the ground because the reflected inertia from the whole vehicle is much higher than that reflected from transmission gearbox" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001859_robot.1996.503850-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001859_robot.1996.503850-Figure4-1.png", + "caption": "Figure 4: The Euler representation of the composite mass moment", + "texts": [ + " Similarly for other vectors. As will be seen, the z-component of tribute to joint torque. does not con- Eext we extract pertinent developments from [ll]. The composite mass moment 2; about joint i considers all links from i to the most distal link n to form one rigid body; hence it is configuration-dependent. Express %, in the modified link i coordinates with the Euler notation: xi sqi c G i - ai = Ri sqa s& (2) [ R i C r ) i 1 where Ri is the vector length and qi and & are two angles that define the vector direction (Figure 4) . The composite mass moment a; influences joint gravity torque ri through: ri = Zi-1. (a; x g) = (i-lg x i-1zi-l) .R,(O;)\"R; (3) where Ri = R,(Oi)R,(ai) defines the standard DH rotation matrix for joint i, and the gravity vector i-lg is expressed in link i - 1 coordinates and is presumed known. Expanding (3) , (4) 7; = Ai sin(6; + ai) where we define Equation (4) reveals the sinusoidal relation for joint i between its gravity torque and joint position, assuming other joints are fixed. Experimentally we rotate joint i in steps for its full range while keeping other joints stationary", + " Joint i torque and position sensors are sampled for each step, to obt,ain data pairs [q, Oil on a sinusoidal curve. Ordinary least squares then fits the data pairs [q, Oil to (4). Parameters Ai and are extracted from the sinusoidal curve fitting. Since gravity is known, we can then find Risq i from Ai and from @pi to obtain the 2, y components of i R i in (2). Consequently, define the identifiable x,y component ' A f i of i R i : Ri srli CFi i J v i = [ Ri s ~ i s l i ] (6) The z component, defined as i T i such that i?& = i f l i + i7; (Figure 4), cannot be found at this point and does not influence joint i torque because it is parallel to the rotation axis. However, it may influence more proximal joint torques. Expression (3) can be simplified as: (7) ~ - (i-1 g x ' - ' z ~ - I ) . Rz(Oi) i f i i which emphasizes the need to know the normal component ' A f i of the composite mass moment i*i; there is no need to identify the z component iTi. 3 Gravity Torque Model This section develops a recursive procedure to calculate i f i i . This procedure is equivalent to specialization of previous research on the identifiable combinations of all inertial parameters [9, 10, 121 to just the gravity components, but we present our own derivation for greater clarity in this particular context" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002756_s0960-0779(04)00429-1-Figure3-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002756_s0960-0779(04)00429-1-Figure3-1.png", + "caption": "Fig. 3. Element of beam.", + "texts": [ + " To gain a flavour of the quantitative advantages of moving away from a linear approximation, not to mention the qualitative advantages, we can look at the difference in percentage error incurred for the linear case and the third order approximation from the Taylor expansion for the sine function, which is used essentially to describe the deflection of a typical element of the cantilever beam from horizontal, see Fig. 2. Even the analysis which considers the third order Taylor expansion enhances the accuracy of the angle calculation (see Fig. 2), hence more precise approximations of the beam deflection and consequently the overall stiffness are needed, and one of such approaches is given below. Consider an infinitesimal section of one of the beams with forces R and R + dR, and moments as shown in Fig. 3, where u, v, and s are the horizontal, vertical, and natural co-ordinates of the beam section, / is the inclination angle of the beam section. R has only a vertical component as the length of the beams must be conserved and rotation at the end of the beams is prevented. Therefore taking moments about the left-hand side of the element, we have \u00f0M \u00fe dM\u00de M \u00fe Rdu \u00bc 0; \u00f01\u00de after some manipulation we obtain X M L F0(t) = cos\u03c9t EI Fig. 1. A simple beam system. /00 \u00fe R EI cos / \u00bc 0; \u00f02\u00de where ( 0) represents differentiation with respect to s, and assuming d/ ds \u00bc M EI, where E is Young s modulus and I is second moment of inertia", + "12), leads to / \u00bc sx0 qs2 2 \u00fe e qx4 0 10x2 0f 4 6x0f 5 \u00fe f6 : \u00f0A:13\u00de For s = L and / = 0, the quantity x0 is approximately equal to x0 \u00bc qL 2 : \u00f0A:14\u00de Using this approximation in the terms of (A.13) which are multiplied by small parameter e, substituting (A.12) and neglecting terms smaller than e and evaluating at s = L we have the more accurate solution that x0 \u00bc qL 2 \u00f01 16e\u00de: \u00f0A:15\u00de Substituting (A.15) into the term in (A.13) which is not multiplied by e, substituting (A.14) in the terms multiplied by e and using (A.12) to substitute for f and neglecting terms smaller than e gives us / \u00bc qls 2 qs2 2 \u00fe e 40qs4 L2 48qs5 L3 \u00fe 16qs6 L4 8qls : \u00f0A:16\u00de It can be seen from Fig. 3 and (A.2) that dv ds \u00bc sin / / /3 6 ; \u00f0A:17\u00de therefore using (A.16) and (A.17) and neglecting terms smaller than e we have dv ds \u00bc qls 2 qs2 2 1 48 q3L3s3 \u00fe 1 16 q3L2s4 1 16 q3Ls5 \u00fe 1 48 q3s6 \u00fe e 40qs4 L2 48qs5 L3 \u00fe 16qs6 L4 8qls : \u00f0A:18\u00de Using (A.14) and (A.10) to substitute for e provides dv ds \u00bc qls 2 qs2 2 1 480 q3L5s 1 48 q3L3s3 \u00fe 7 96 q3L2s4 3 40 q3Ls5 \u00fe 1 40 q3s6 \u00f0A:19\u00de and integrating gives v \u00bc qls2 4 qs3 6 1 960 q3L5s2 1 192 q3L3s4 \u00fe 7 480 q3L2s5 3 80 q3Ls6 \u00fe 1 280 q3s7 \u00fe C1: \u00f0A:20\u00de For s = 0, v = 0, thus it can be seen that the constant of integration is zero, and so evaluating at L and taking the first two terms of the equation for x = vjs=L yields x \u00bc qL3 12 1 1680 q3L7: \u00f0A:21\u00de Using the first term to approximate the smaller term we have q \u00bc 12 x L3 1 36x2 35L2 : \u00f0A:22\u00de Which is, approximating with a binomial expansion and remembering q \u00bc R EI R \u00bc 12 EI L3 x\u00fe 432 35 EI L5 x3: \u00f0A:23\u00de The stiffness of the beam, k, is defined as dR/dv which leads to k\u00f0x\u00de \u00bc 12 EI L3 \u00fe 1296 35 EI L5 x2: \u00f0A:24\u00de [1] Lurie AI" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003692_978-3-540-73812-1-Figure2.225-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003692_978-3-540-73812-1-Figure2.225-1.png", + "caption": "Fig. 2.225. Installation of specimen and loading method [9]", + "texts": [ + " On the other hand, the spring deflection limit (Kb value), which is a surface bending stress 266 2 Metallic Material for Springs when a constant permanent deformation occurs at the loading point in deflecting and unloading a plate, is standardized in JIS H3130 (Japan) and DIN 1777 (Germany). The measuring method of Kb value, which falls into repeatedly deflecting method and moment method, is designated in JIS H3130. The moment method can be suitable for measuring material with high strength and large deflection material such as copper beryllium. Figure 2.225 [9] shows how to apply the load in the moment method. It depends upon the applications that either 0.2% proof stress or Kb value should be used. For example, it should be safe to use 0.2% proof stress for the parts with complicated bending like connectors or when stress can be applied on the sheared surface with stamping. In the U.S., the research and development of connectors has been popular, so in ASTM, only 2% proof stress is standardized. In case of no bending and no plating process like some switches or relays, it becomes possible to draw out the capability of material by using Kb value" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003583_j.mechmachtheory.2007.05.008-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003583_j.mechmachtheory.2007.05.008-Figure8-1.png", + "caption": "Fig. 8. The geometrically limited region, contact line, blowhole area, and cross-section area for the rotors.", + "texts": [ + " Because the design parameters of mating rotor profiles are coupled together with complicated mathematical equations, therefore, improving the profiles is difficult. In addition, the rotor profiles are limited to several known curve types. However, since 0094-114X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2007.05.008 * Corresponding author. E-mail address: imezhf@ccu.edu.tw (Z.-H. Fong). Nomenclature Ab blowhole area Ao1 cross-sectional area of single male groove (Fig. 8) Ao2 cross-sectional area of single female groove (Fig. 8) At total cross-sectional area of rotors (= Ao1 + Ao2) Bi coefficients of cubic-spline segment, i = 1\u20134 C center distance between rotors Fopt penalized objective function Lc length of contact line per lobe LD ratio of length to diameter of male rotor N point number of contact line Nf normal vector in fixed coordinate system Sf Oi original point of coordinate system Si, i \u00bc 1; 2; f (Of: pitch point) P penalty function Pi indicated power of compressor Qr real displacement of compressor Si\u00f0xi; yi; zi\u00de coordinate system i, where i \u00bc 1; 2; f ; c (1: male rotor; 2: female rotor; f: fixed; c: contact line) Tf average female torque Tm average male torque Vr sliding velocity d\u00f0j\u00dex;i horizontal displacement of ith point in jth section d\u00f0j\u00dey;i vertical displacement of ith point in jth section f objective function f1 meshing equation f \u00f0i\u00deuc undercut condition, i \u00bc 1; 2 (1: male rotor; 2: female rotor) gi inequality constraint, i = 1\u20135 m12 ratio of rotation speed = x1/x2 n\u00f0j\u00dep point number in jth section ni\u00f0nx;i; ny;i\u00de unit normal vector in coordinate system Si, i \u00bc 1; 2; f p(j) coefficient used to adjust jth section curvature for d\u00f0j\u00dex;i pT pitch of male rotor q(j) coefficient used to adjust jth section curvature for d\u00f0j\u00dey;i ro1; ro2 outer radius of rotor rp1; rp2 pitch radius of rotor ri position vector in coordinate system Si, i \u00bc 1; 2; f s\u00f0j\u00dei boundary variable in horizontal direction, i \u00bc 1; 2 (1: start; 2: end) t; t\u00f0j\u00dei normalized curve parameter of ith point in jth section u curve parameter of the sealing line u\u00f0j\u00dei distance between ith and (i + 1)th points in jth section umax upper range of cubic-spline segment umin lower range of cubic-spline segment uuc undercut parameter v\u00f0j\u00dei boundary variable in vertical direction, i \u00bc 1; 2 (1: start; 2: end) w design variables zi number of lobes, i \u00bc 1; 2 (1: male rotor; 2: female rotor) db(db,x,db,y) displacement of control point b dd(dd,x,dd,y) displacement of control point d di displacement of control point, i \u00bc a; c k lead angle of rotor all modern screw rotors are finished by a CNC grinding machine, adhering to such limitation in rotor profile design is pointless", + " (17), fx0f\u00f0u\u00de; y0f\u00f0u\u00deg is the tangent vector of the sealing line, the superscript T is the transpose symbol of the tangent vector and fxf\u00f0u\u00de rp1; yf\u00f0u\u00deg is a position vector on the sealing line that points to the center of the male rotor. The undercut may occur when the vector fxf\u00f0u\u00de rp1; yf\u00f0u\u00deg is perpendicular to the tangent vector fx0f\u00f0u\u00de; y 0f\u00f0u\u00deg. The undercut parameter uuc for the male or female rotor can thus be obtained by solving Eqs. (17) and (18), respectively. As shown in the left of Fig. 7, interference may occur between the male and female rotor lobes when the included angle of single lobe hT exceed a pitch angle on the pitch circle as shown in Fig. 8: hT 6 2p z1 \u00f019\u00de In addition, the geometric limit for the sealing line should be considered. The sealing line should be located inside the overlapped region of two rotors as indicated in Fig. 8. Therefore, the following geometrical constraints should be considered for sections II and III: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 c1 \u00fe y2 c1 q 6 ro1 \u00f020\u00de where fxc1; yc1g is a coordinate of the sealing line in S1 and ro1 is the outer radius of the male rotor. For sections I and IV, fxc2; yc2g is a coordinate of the sealing line in S2 and rp2 is the pitch radius of the female rotor so the geometric limit can be represented as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 c2 \u00fe y2 c2 q 6 rp2 \u00f021\u00de Constraints from Eqs. (15)\u2013(21) are important for a varied rotor profile. The capacity and displacement of the compressor depend on the leakage and geometrical cavity volume of the two rotors. Thus, contact line length, blowhole area, total cross-sectional area of rotors, and ratio of indicated power to real displacement are the most common indexes used to estimate compressor performance. As shown in Fig. 8, the total cross-section area of the single male and female rotor grooves\u2014which directly affects the volumetric capacity of the screw compressor\u2014is defined as At = Ao1 + Ao2. The coordinates of the contact line of the rotor fxc; yc; zcg can be calculated as follows: xc \u00bc xf yc \u00bc yf zc \u00bc pT/1 \u00bc \u00f0rp1 tan k\u00de/1 8>< >: \u00f022\u00de where pT is the pitch of the male rotor and k is the lead angle of the rotor. The length of the contact line Lc can be calculated numerically by summing up the distance between points on the instant contact line, as shown in the following equation: Lc \u00bc XN 1 i\u00bc1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xc;i\u00fe1 xc;i\u00de2 \u00fe \u00f0yc;i\u00fe1 yc;i\u00de 2 \u00fe \u00f0zc;i\u00fe1 zc;i\u00de2 q \u00f023\u00de where N is the point number of the contact line. As shown in Fig. 8, the blowhole is a space-curved triangular surface formed by the apex of contact line and the cusp of the housing [3,5,6]. Calculation of the parametric analysis is based on a set of point data for the sealing line given 5/6 rotors with a center distance of 98.0 mm; male and female rotor outer diameters of 138.507 mm and 109.76 mm, respectively; a length to male rotor diameter ratio of 1.619, and a male rotor wrap angle of 298.622 . The results were obtained for an oil-flooded air compressor at 3850 rpm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001758_pesw.2000.849955-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001758_pesw.2000.849955-Figure1-1.png", + "caption": "Fig 1 PMciple ofradial fopce production", + "texts": [ + " The relationships of radial forces, toque component amwts, currents and voltagw in the radial force windings are calculated The prototype inset-ype PM machine was designed and coI1sII1Icted. The machine panmeters of ladial force genemtion have been estimated from the relationshp between induced voltages and the rotor displacements. A new control method of beanngless motors under loaded conditions is realized by using the measured machine parameters. The effectiveness of the proposed method is verified in experiments. In addition, the load test of inset-tyPe PM bearingless motor is reported. motors Ld is smaller than Lq [15]. II. MATHEMATICAL ANALYSIS Fig.1 shows the principle of radial force production in an insettype bearingless PM motor. The 4-pole excitation fluxes Y,,, are producsd by the permanent magnet mounted on the surhce of the mtor. Toque can be produced by the interactions between Y,,, and 4-pole winding N,,. The fluxes in phase with Y,,, can be produced by 4-ple winding Nd. Additional 2-pole rssdial force windiugs N, and Ny are wound m the stator slots together with conventid 4-pole motor winding Nd and N,. The radial forces can be produced by the unbalanced flux d a i l y in the air-gaps caused by the interactions W e e n Y,,,and the fluxes generated by 2-pole windings N, and N,,. If N, winding current is positive, 2-pole fluxes Yxl and Yfl are produced as shown in Fig. 1. Therefore, the flux density is increased in the &-gap 2 but deg-eased in the air-gap 1. Radial force F, is generated towards the negative direction in the x-axis. Similarly, the Ny winding current produks the ydireCtion radial forces. The inductance mairk of the inset PM motor is written as follows [6]: 0-7803-5935-6/00/$10.00 (c) 2000 IEEE 202 where Yb Yq Ym and Yy are the flu linkages Of NQ N,,, N, and instantaneous values of currents in Nb Nq, N, and Ny windings, Ny win- respectively. The currents h, 4, i, and i," + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003364_iros.2006.282077-Figure8-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003364_iros.2006.282077-Figure8-1.png", + "caption": "Fig. 8 Leg projection difference illustration.", + "texts": [], + "surrounding_texts": [ + "The aforementioned approach was applied on the planar bipedal walking robot, illustrated in Fig. 2, with the geometrical and inertial properties as shown in Table 1. All the links are modelled based on uniform mass distribution. This is to consider the sensitivity for the real-implementation. Fifth-order TFS i.e. with n=5, are used for the trajectories described in (6) and (7). To pursue a human-like walking with straight knee occurring at stance leg, we set cl=O. Table 2 shows the parameter set for GA initialization and the coefficients for the objective and penalty functions. The proposed approach was applied to the two walking examples shown in Table 3. The chromosome solutions in the format of [Ai, Bi, Ci, Ch, Ck, t1, t2], x1 and x2, are obtained for the two examples, respectively. xl = [0.277 -0.087 0.022 -0.008 -0.000 -0.397 -0.118 -0.024 -0.017 -0.006 0.457 0.200 -0.038 -0.077 -0.046 -0.036 0.000 0.050 0.44] x2= [0.238 -0.057 0.012 -0.004 0.0003 -0.356 -0.043 0.042 0.004 -0.003 0.469 0.074 -0.050 0.008 -0.017 -0.021 0.000 0.065 0.47] For the above two examples, Ch= 4.28 rad/s and c9h 4.15 rad/s, respectively. The value of Cmax used for the GA is 1400 and the fitness function values of the two solutions are 1287 and 1309, respectively, indicating good optimization outcomes. Furthermore, the effect of the 5th order coefficient is relatively small compared with the 1St order coefficient. Therefore, 5th order TFS is sufficient. A. Example 1 For the gait generated for Example 1, Fig. 4 shows the ZMP trajectory for one walking cycle. Fig. 5 shows the position of the centroid of the trunk versus time. In both figures the reference coordinate frame is OXYZ. Fig. 4 shows that the ZMP trajectory is always within the footprint, even though the specified step length is not small and the speed is not slow. From Fig. 5, it can be seen that a regular walking speed of 0.45 m/s has also been achieved. Fig. 6 to Fig. 9 further illustrate the motion obtained. From Fig. 7, which shows the difference of the vertical length projections,f andf, of the left and right legs, respectively, the instant of leg strike is observed at td-0.44s. This is equal to t2 in the solution x1 given earlier. From the resulted motion data, the leg strike velocity is vx=0.15m/s, v =-0.2m/s. This value has been confirmed to be acceptable by the results of subsequent dynamic simulations. The actual step length of 0.32m is also very close to the target step length. 00 a-) * ) N Time (s) Fig. 4 ZMP Trajectory. 0 0Co 5t a) 0 a-)*E) 0 7_1 *) a) a) a) Time (s) Fig. 6 Joints' trajectories. B. Example 2 Similarly, the solution x2 is applied. Fig. 10 shows the generated joints' trajectories. From the motion data, the ZMP trajectory is constrained within [-0.06m 0.06m] which is even tighter than that in Example 1. The leg strike velocity is vx=0.12m/s and v =-0.224m/s. The step length is 0.27m and the walking speed is kept around 0.36m/s. The first leg strike instant is td=0.47s, which is equal to t2 in the GA solution. The resulting walking pattern is shown in Fig. 11. C. General comments The results obtained for the two examples confirm that the proposed approach can be used to synthesise reliable trajectories for stable human-like walking gaits. This approach can also be used to generate gaits for walking on slopes and stairs [13]. C~ a) 0 a) 0 a) a) a) Time (s) Fig. 10 Joints' trajectories" + ] + }, + { + "image_filename": "designv11_2_0000236_s0890-6955(00)00081-x-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000236_s0890-6955(00)00081-x-Figure4-1.png", + "caption": "Fig. 4. The simplified 11-DOF system (a), and a diagram of the spindle displacement (b).", + "texts": [ + " output matrix C(Q) depends upon the selection of output signals and the direct transmission matrix D(Q) is usually zero. Further discussion of all matrices in the developed SV model can be found in [11,12,44]. Eqs. (7) and (8) define the structure of a class of scalable models [60]. When the dimension of x(Q,t) is fixed, one specific model structure is defined. For example, the system shown in Fig. 2 has 22 generalized coordinates (assuming a flexible tool\u2013spindle interface). If this system is simplified by eliminating the workpiece and tool [compare Fig. 4(a)], the number of generalized coordinates reduces to eleven, namely: six translations of the shaft and housing, and five respective rotations6 [compare Eq. (12)]. This specific system is distinguished by its unique values of elements in the m, c(\u00b7) and k(\u00b7) matrices which are linked to the physical system properties through Eqs. (3)\u2013(5). Other salient features of the SV model are [43,44]: 1. Convenient \u2018mapping\u2019 between actual parameters and their representations in the model, 2. Accuracy and scalability of the model accomplished by on-line estimation (tuning) of the unknown parameters, 3", + " Once this relationship is established, using vibration sensors placed on the housing facilitates on-line estimation of the instantaneous preload in shop-floor conditions. The class of analytical models developed above facilitates application of several methods for preload estimation [12,42]. One of these methods, simple and fast, is based upon the premise that some modal properties of the spindle assembly, such as the resonance frequencies and damping ratios, are well correlated with the preload but little sensitive to other properties of the machine tool whose changes are difficult to measure. For the sake of clarity a simplified 11-DOF system shown in Fig. 4(a) is considered henceforth7. Mechanical interface between the housing and a motionless base consists of four three-dimensional EDEs [12]. A rudimentary model of the front and rear bearings comprises two EDEs to represent radial stiffnesses (compare Fig. 2), and a third EDE not shown in the figure, which represents the axial stiffness [11]. This simple model, convenient in the initial phase of analysis, does not account for the bearing moments due to the shaft rotation about the X and Y axes, and neglects the dynamics of rolling elements8", + " 8 Results obtained with comprehensive bearing models are discussed, for example, in [11,16,17,39,62]. u(t)5[Fx(t),Fy(t),Fz(t)]T, (11) global generalized coordinates associated with the shaft and housing gg5[xs(\u00b7),ys(\u00b7),zs(\u00b7),js(\u00b7),fs(\u00b7),xh(\u00b7),yh(\u00b7),zh(\u00b7),jh(\u00b7),fh(\u00b7),yh(\u00b7)]T, (12) and state variables obtained from gg according to Eq. (9). Symbol \u2018(\u00b7)\u2019 denotes arguments of the generalized coordinates and state variables, namely \u2018[Q(Fp), t]\u2019. Potential output signals of interest include displacements of the spindle shaft and housing at points A, A*, B and B* shown in Fig. 4, which are designated dA(\u00b7),d\u2217 A(\u00b7),dB(\u00b7),d \u2217 B(\u00b7), and corresponding accelerations designated aA(\u00b7),a\u2217 A(\u00b7),aB(\u00b7),a\u2217 B(\u00b7). Application of the method delineated in Section 2 yields a model featured by eleven vibration modes with natural frequencies fi, and damping ratios zi, (i=1,2,...11). They are readily calculated from the eigenvalues, li, of the A[Q(Fp)] matrix as fi[Q(Fp)]5 1 2p \u00ce(Re{li})2+(Im{li})2 (13) zi[Q(Fp)]5 |Re{li}| \u00ce(Re{li})2+(Im{li})2 (14) The obtained values of fi[Q(Fp)] and zi[Q(Fp)] are potentially applicable for the preload estimation", + " Based on the results, a list of candidate modal properties for consideration is established. In the next step, different sensor types (e.g. accelerometers, displacement sensors) and their locations are examined. The analysis indicates which sensors and locations are favorable for the estimation of the chosen modal properties. This is illustrated by way of the following example pertaining to the spindle dealt with in Section 4. First, a proximity sensor measuring the displacement dA(t) of the spindle shaft10 in the X direction (Fig. 4, point A) in response to u(t)=Fx(t) is considered. The observation matrix, C(Q), accounts for an impact on the measured output signal of two generalized shaft coordinates: (1) translational motion along the X axis, and (2) rotational motion about the Y axis. Other matrices in the SV model are not affected by the selection of sensors. A scalar transfer function of the system obtained according to Eq. (15) is represented by the Bode plots shown in Fig. 5. The graphs represent three preloads: nominal (gray solid line), 120% (dashed) and 140% (solid)", + " Next, to avoid difficulties of measuring angular accelerations of the shaft, a feasibility of the preload estimation based on the housing vibrations is investigated. If a single torsional accelerometer attached to the housing is used, the observation matrix becomes C2(Q) = [01\u00d74 1 01\u00d717] and a new transfer function is obtained. Its magnitude plot shown in Fig. 6 indicates 10 Practical implementation of the measurement is not considered here since only the model is investigated. clean and strong resonances in the frequency range of interest. Alternatively, two linear accelerometers placed at points A* and B* shown in Fig. 4 can be used. Suitable accelerometers are widely available and inexpensive, such as ADLX202 [63] priced below $20. The above brief example expanded into rigorous mathematical analysis allows to study the impact of other physical properties, such as stiffnesses of the housing-base fixture, and further enhancements of the proposed algorithm that improve its accuracy and robustness. A small size, medium speed spindle characterized in Table 1 was tested. An initial preload level of the front bearings was adjusted by applying suitable shims", + " After installation of each new set of shims the actual stiffness was experimentally evaluated by two independent methods to assure (1) accurate estimation, (2) assessment of the system\u2019s linearity, and (3) validation of sensors and the employed analytical model. First, the static stiffness was calculated from the relative displacement between the shaft and housing caused by a known constant force. In the second method, described below, the dynamic stiffnesses of bearings and housing-base fasteners were estimated independently by using displacement sensors and accelerometers. The displacements between the points {A, A*} and {B,B*} on the shaft and housing (Fig. 4) in response to a known harmonic excitation have been measured. Example displacements dA(t) and dB(t) together with the excitation force Fx(t) are plotted in Fig. 7 versus time, for a minimum preload case (no shims). The effective stiffnesses of the front and rear bearings are evaluated 11 as [12]: kf5E t H(lbr\u2212lbf)[dsr(t)(lbf\u2212lsf)+dsf(t)(lbf\u2212lsr)] Fh(t)lbr(lsf\u2212lsr) J; kr5E t H(lbf\u2212lbr)[dsr(t)(lbr\u2212lsf)+dsf(t)(lbr\u2212lsr)] Fh(t)lbf(lsf\u2212lsr) J (17) where E t{} is the expectation operator, Fh (t) is a sufficiently strong force (|Fh(t)|.Fmin), and the meaning of other symbols is defined in Fig. 4(b). The obtained values represent stiffnesses of the respective bearings connected \u2018in series\u2019 with the joint stiffnesses of interfaces with the shaft and housing [6]. As expected, these joint stiffnesses change after each disassembly\u2013assembly of the spindle required to replace the shims. A strong impact of these stiffnesses, documented by the data12 shown in Fig. 8, necessitates accurate in-process assessment of the resultant bearing stiffnesses in the validation of the proposed preload monitoring method", + " Experimental estimation of these stiffnesses [43] has not been carried out in this research due to its complexity. It is a subject of an ongoing work. Fig. 9 shows representative periodograms [69] of signals involved in the estimation of the natural frequencies and damping ratios. These signals are: input force Fx(t) applied to the spindle, displacements of the spindle, dA(t), and displacements of the housing d\u2217 A(t). These signals are measured in the X direction at a moderate preload (13 \u00b5m shims). Accelerometers are mounted inside of the spindle [11,12,41] and on the housing (points {A,A*} in Fig. 4). The periodograms obtained under continuous white noise excitation force Fx(t) indicate resonance peaks near 250, 350 and 500 Hz. The highest resonance is difficult to distinguish in the displacement signal of the housing. However, this resonance can be easily found in periodograms of the housing acceleration (not shown). To avoid shortcomings of methods commonly used in the experimental estimation of modal parameters [26,33], a parametric estimation technique involving ARMAX class of \u2018gray box\u2019 models was employed in this research [70]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000771_j.1460-2687.1999.00011.x-Figure9-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000771_j.1460-2687.1999.00011.x-Figure9-1.png", + "caption": "Figure 9 The force acting on the hand was measured at three points b, c and d, for four impact positions on the strings, as labelled. The distance from the Centre to the COP was 5 cm.", + "texts": [ + "29 m, so the axis of rotation is shifted to a point 4 cm from the end of the handle. Both calculations are consistent with the observed results. This value of ME is consistent with an approximate estimate of the mass of the forearm, about 1.8 kg, but x does not depend strongly on ME when ME is larger than the mass of the racquet. For the same racquet parameters, the centre of percussion (COP) is located at b 0.14 m, assuming that the axis of rotation coincides with the end of the handle. This locates the COP 5 cm from the centre of the strings, as illustrated in Fig. 9. According to the above theoretical model, the reaction force FR acting on the end of the forearm should be zero for an impact at the centre of percussion. Previously, it has been assumed that for an impact at the COP, the reaction force on the hand would be zero (Brody 1979, 1981). One might expect that the force on the hand should be essentially the same as the force on the forearm. However, the measurements presented in the Figure 8 Schematic diagram comparing the motion of a free and a hand-held racquet when a ball is dropped near the tip or throat of the racquet, showing the racquet position before the impact (thin line) and after the impact (thick line)", + " Recent measurements of the hand forces by Hatze (1998) are consistent with the results described below, but Hatze concluded that the COP was of limited signi\u00aecance since the forces on different parts of the hand vary with time. In order to measure the forces on the hand, a small piezo was located on the handle, underneath the hand, as described in the section on Experimental Techniques. The impulsive forces acting on the hand were measured at three different points under the hand, and for four different impact points on the strings, as indicated in Fig. 9. The racquet was held \u00aermly by the right hand in a stationary position with the strings in the horizontal plane, and a tennis ball was dropped onto the strings from a height of 20 cm. The results of this experiment are shown in Fig. 10. Absolute values of the force were not calibrated, but the relative magnitudes can be compared with the 150 mV positive signal recorded when the handle was gripped \u00aermly by the hand (or \u00b1 150 mV when the grip was released). The grip waveform decayed to zero with a time constant of 70 ms, representing the discharge time constant of the 7 nF piezo through the 10 MW voltage probe" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000686_bf01607864-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000686_bf01607864-Figure6-1.png", + "caption": "Fig. 6. Surface grinding operation.", + "texts": [ + " The following design example illustrates a design problem, highlighting tolerance selection, using the proposed methodology. The initial phase, comprising steps 1 through 3, is implemented in the following subsections. 6.1. The Design Problem and the Tolerance Sub-Problem The design problem considered for study is established in Section 2.2. The tolerance problem is the gear transmission. The performance parameter is transmission error, given by Eq. (1). 6.2. Establish Precision: The Gringing Operation Surface grinding is the manufacturing operation studied (Fig. 6). Here a grinding wheel is mounted on an horizontal spindle, and the workpiece is clamped 110 R.S. Srinivasan et aL on a reciprocating table, typically using a magnetic chuck [11]. A suitable depth of cut is set, and as the table reciprocates beneath the grinding wheel, material is removed by abrasive action. Transverse motion is obtained by cross feed as shown in Fig. 6. The grinding wheel can be considered as an agglomeration of multiple cutting edges, with each abrasive grain acting like a single point tool. However, the geometry of the cutting tools is inconsistent, due to the random orientations of the individual grains. Therefore the grinding process has a predominant random component. Deterministic effects due to vibration are also present [11]. The effects of premature deformation of the workpiece, ahead of the cutting region, are also cited in the same reference" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001612_ac0156013-Figure4-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001612_ac0156013-Figure4-1.png", + "caption": "Figure 4. (a) Scheme of the optical system: 1, blue LED; 2, 8, filters; 3, 5, 7, lenses; 4, dichroic mirror; 6, sensing fiber (diameter 105 \u00b5m); 9, photon counter. (b) Zoom into the sensing region: 10, INOX tube; 11, PTFE tube; 12, polypropylene capillary. (c) Cross section of the polypropylene capillary with the optical fiber incorporated into its lumen, drawn to scale. The wall of the polypropylene fiber (thickness 200 \u00b5m) serves as support for the permeation liquid membrane. The arrows indicate the radial diffusion of the analyte into the lumen.", + "texts": [ + " The blue LED was obtained from Oshino (Tokyo, Japan), and the filters and dichroic mirror (set XF 115) were from Omega Optical Inc. (Brattleboro, VT). The optical fiber (105/125 A) was bought from CeramOptech (Bonn, Germany), and the photomultiplier H7421-50 came from Hamamatsu Photonics (Schu\u0308pfen, Switzerland). The timer/counter board CTM-05/A was purchased from Keithley Instruments S. A. (Du\u0308bendorf, Switzerland). The polypropylene hollow fiber Accurel ppq 3/2 was supplied by Membrana GmbH (Wuppertal, Germany) and the peristaltic pump by Omnilab (Mettmenstetten, Switzerland). A scheme of the optical system is given in Figure 4. All bulk optical elements were mounted on an aluminum plate (dimensions 42 cm \u00d7 28 cm \u00d7 1 cm). The light of the blue LED (\u03bbmax ) 460 nm, fwhm ) 70 nm, 3.1 V) was passed through an excitation filter (\u03bbmax ) 475 nm, fwhm ) 40 nm) and coupled into a multimode optical fiber (length 1 m, NA 0.22) via a dichroic mirror. The output power at the opposite distal end of the optical fiber at 475 nm was 15 nW. At this end, the fiber was introduced into the tubing via a 5-cm-long INOX tube (inner diameter 250 \u00b5m, corresponding to the outer diameter of the fiber-optic acrylic jacket)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000712_bf02844160-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000712_bf02844160-Figure6-1.png", + "caption": "Figure 6 Rebound off the backboard. Figure 7 Illustrative rebound off the backboard.", + "texts": [ + " Then if, for example, the ball curves to the basket from the right side of the backboard the ball centre trajectory may be represented as in Figures 6a and 6b. [Observe that, even though the ball comes off the backboard, the ball centre comes away from the backboard from a plane approximately one ball radius (12.125 cm) in front of the backboard.] The optimal trajectory for minimum ball speed (and hence least energy) may be obtained using an analysis similar to that of the free throw and the direct shot. Specifically, let the ball centre have coordinates (xT, yT, zT) when the ball is at the backboard (see Figure 6). Then from Eqns. (25) and (26) we see that the optimal bounce angle \u03b8\u2032T (relative to the positive \u039e-axis in the \u039e-Z plane) and the optimal (minimum) bounce speed VT min are: tan 2\u03b8\u2032T = \u2013\u2206\u03be/\u2206z = \u2013(xT 2 + yT 2)1\u20442/zT (28) and V 2 T min = = (29) where \u2206\u03be and \u2206z are distance increments in the \u039e and Z directions defined by comparison of the equations and Figure 6. To illustrate the application of these expressions, consider a layup shot where the player shoots the ball toward a corner T of a white box outline, typically painted on the backboard. Specifically, let T (the target point) have coordinates (0.260, \u20130.305, 0.457) m [or (0.852, \u20131.0, 1.5) ft]. Then, from Eqns. (28) and (29), \u03b8\u2032\u03a4 and VT min are seen to be: \u03b8\u2032\u03a4 = 159.39 deg and VT min= 1.216 m/s (30) (3.99 ft/sec) V \u2032 = Vx\u2032nx + Vy\u2032ny+ Vz\u2032nz g(xT 2 + yT 2) \u2013(xT 2 + yT 2)1\u20442 + zT(1 + sin 2\u03b8b) g(\u2206\u03be)2 \u2206\u03bes sin 2\u03b8b \u2013 \u2206z(1 + cos 2\u03b8b) 54 Sports Engineering (2003) 6, 49\u201364 \u00a9 2003 isea = \u20130.738 nx + 0.866 ny + 0.428 nz m/s = \u20132.42 nx + 2.84 ny + 1.404 nz ft/sec (31) where nx, ny and nz are unit vectors parallel to the X, Y and Z axes (see Figure 6). Once the ball centre rebound speed and direction are known, we can determine the corresponding speed and direction just prior to backboard impact by using the rebound equations developed in the Appendix. Specifically, for a rebound speed V \u2032 at an angle \u03b8\u2032\u03a4 relative to the horizontal toward the basket (see Figure 7) and directed at an angle \u03b2\u2032 toward the basket (see Figure 6), the X, Y and Z components of the rebound velocity are: v\u2032x = \u2013V \u2032 cos \u03b8\u2032\u03a4 sin \u03b2\u2032 v\u2032y = V \u2032 cos \u03b8\u2032\u03a4 cos \u03b2\u2032 v\u2032z = V \u2032 sin \u03b8\u2032\u03a4 (32) Then, from Eqns. (A8), the pre-impact velocity components are vx = \u2013v\u2032x/e vy = (5v\u2032y + 2r\u03c9z)/3 vz = (5v\u2032z + 2r\u03c9y)/3 (33) The pre-impact ball centre speed V and inclination angle \u03b8T relative to the horizontal are then: V = (vx 2 + vy 2 + vz 2)1\u20442 and \u03b8T = tan\u20131 [vz/(vx 2 + vy 2)1\u20442] (34) Finally, the approach angle \u03b2 in the X-Y plane (see Figure 6) is \u03b2 = sin\u20131 [vx/(vx 2 + vy 2)1\u20442] (35) Continuing the illustration example, if there is no ball spin just prior to impact, at target point T (0.260, \u20130.305, 0.457) m of the backboard, the impact ball centre velocity components are: vx = 0.802 m/s = 2.63 ft/sec vy = 1.44 m/s = 4.73 ft/sec vz = 0.713 m/s = 2.34 ft/sec (36) where we have used a coefficient of restitution e of 0.92. Correspondingly, the pre-impact ball centre speed and direction angles are then: V = 1.797 m/s = 5.896 ft/sec \u03b8T = 23" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002768_bfb0040159-Figure2.7-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002768_bfb0040159-Figure2.7-1.png", + "caption": "Figure 2.7 MERGE operations: (a) union; (b)intersection; (c) and (d) difference.", + "texts": [ + " Except for the case of aggregates, the next step is to create a polyhedral representation of the CALL \u2022 Z Y I TRAN XYZ (DIST); /*Translate position cursor*/ CALL I IROT (ANGLE); /*Rotate position cursor*/ CALL I IMIRROR /*Reflect position cursor about axis*/ 95 non-primitive part or sub-part . To do this, it is necessary to combine the polyhedral representations of the sub-par ts according to their specified polar i ty ( \" H O L E \" or \"SOLID\"). This task is performed by the M E R G E algorithm, which realizes the complete range of set operat ions on arbi t rary polyhedra. The algori thm takes two polyhedra, described by lists of points, lines, and surfaces, and yields a new polyhedron which is either the union, intersection, or difference of its arguments (see Figure 2.7 for definitions of these operations). As the procedural representa t ions are interpreted, successive appl icat ions of the MERGE algorithm are used to build up quite complex shapes, as i l lustrated in Figure 2.8. The MERGE algorithm can also be invoked directly in GDP, allowing the World Model to be altered and subsequently re-merged. Systems that do not have this operat ion are unable to generate explicit forms of composite objects. Without explicit representa t ion of the objects at higher nodes of the tree, it is relat ively difficult to perform operat ions that depend on the volume propert ies of the composite object , for example robot path planning or even finding the volume of an object , without putt ing strong constraints on the structure of the tree" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002752_0-387-33015-1-Figure6.6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002752_0-387-33015-1-Figure6.6-1.png", + "caption": "Figure 6.6. Electrostatic \"sponge\" encapsulation scheme employing charged matrix in polyelectrolyte shell.", + "texts": [ + " McSHANE The diffusion-loaded capsules and emulsion-based systems have advantages in stability and ease of use, but are limited in concentrations that can be achieved. This may be a more critical limitation for enzyme-based systems, in which high enzyme concentrations are required to maintain diffusion-limited behavior and extend operating lifetimes when enzymatic activity is lost with time. Another possibility that has been studied is the use of charged matrix within a polyelectrolyte capsule, where the matrix serves to electrostatically adsorb high concentrations of oppositely-charged molecules from the surrounding solution. This is illustrated in (Figure 6.6), and demonstrated for anionic alginate matrix for attraction of cationic dextran (amino-dextran) in (Figure 6.7). The nature of the effect is clearly seen in the uptake of significant dextran-amino (SOOkDa), while smaller anionic dextran (77kDa) was excluded from the same particles. These examples constitute only a limited view of many possibilities for microcapsule-based sensor construction; they show promise for building stable systems with entrapped glucose-sensing chemistry and therefore provide sufficient basis for discussion of the different sensing systems that can be achieved using them" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002789_amr.6-8.303-Figure9-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002789_amr.6-8.303-Figure9-1.png", + "caption": "Fig. 9. Complex mould insert with no conventional possibility for integrating a cooling system which is geometrical optimized for the casting process", + "texts": [ + " Applying the metal foil LOM technology, the production of such parts is done in an automated procedure nearly not needing any manpower which is therefore more economic. Further on complex cooling systems in moulds can be realised by the metal foil LOM technology. A lot of mould inserts \u2013 which can include cavities \u2013 and especially sliders and cores often can not be fitted with a suitable cooling system because its manufacture is impossible with mechanical processes because no accessibility exists (Fig. 8, Fig. 9). Such parts are very common in mould making and show another potential of application of the metal foil LOM technology. Complex cooling systems can be realised by applying an additive procedure, which can produce metallic parts, and expensive erosion processes can be replaced. The technology of Laminated Object Manufacturing (LOM) is characterised by the generation of contours out of foil or plate which are joined afterwards. For the realisation of metal foil LOM technology a two step process is necessary" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001540_.2001.980230-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001540_.2001.980230-Figure1-1.png", + "caption": "Fig. 1. An interpretation of $td and A.", + "texts": [ + " Moreover, the helmsman will choose the magnitude of $ dependent on the distance from the straightline, i.e. dependent on y. We therefore want the ship angle to be a function of y, for instance we could choose $d = -ky, where k is a constant parameter. However, we do not want theshiptowhirlroundifthedeviationyislarge. Wewantthe ship course to stay within certain bounds, typically [- ;, 51, and we therefore choose $d = - arctan(y/4) (15) The control parameter 4 can be interpreted as the distance ahead of the ship along the x-axis, i.e. the straight-line trajectory, that the ship should aim at, see Figure 1. For instance 4 could be chosen equal to two boat\u2019s length, corresponding to an usual choice in Line of sight algorithms. We could however choose $d equal to any function -aY(y) satisfying YqJ(Y) > 0 (16) (17) ay(0) = 0 x l i U, : y 4 [-- -1 2 \u2019 2 Kinematically, i.e. neglecting the sway velocity assuming U = 0, we see from (11) that this choice of Qd will control y to zero, since U > 0 and sin(-uy(y))y < 0 Vy # 0. Due to the ship dynamics however, U will in general be nonzero. We will in the following show that designing a control law for -rr based on the idea of making 11 converge to $d = - arctan(y/4) , will indeed make the ship track the desired trajectory, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0002151_0957-4158(92)90038-p-Figure6-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0002151_0957-4158(92)90038-p-Figure6-1.png", + "caption": "Fig. 6. Electromagnetic actuator ETH-190/50/1 consisting of the magnet, the power amplifiers, the ferromagnetic laminated sleeve on the rotor, and sensors. The main specifications are given in Table 2a, the frequency response is shown in Fig. 9.", + "texts": [ + " There are intentions to upscale this liquid phase epitaxy process for generating semiconductors of the highest quality. In collaboration with a Swiss company, we built a magnetically supported milling spindle, which currently is launched as a prototype. The cutting power is about 35 kW, the rotation speed is up to 40,000 rpm, and the cutting speed for aluminium is up to 6000 m sec. This high-speed milling offers advantages with respect to the milling process and production costs. An extensive description is given in [7]. The design objective for the actuator shown in Fig. 6 was to generate high forces within a large frequency range that can be used to control rotor vibrations. The magnet has eight poles and can generate forces independently in two mutually orthogonal directions. This actuator is used firstly to generate test forces acting on a rotor for identification purposes and then to work as an active damper or as a bearing [8]. The rotor itself is 2.3 m long, 100 m m in diameter and supported in two oil bearings. These bearings are known to cause coupling effects between the lateral motions of the shaft" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001255_0003-2670(92)80099-s-Figure2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001255_0003-2670(92)80099-s-Figure2-1.png", + "caption": "Fig. 2. Effect of the carrier, CHIC and immobilization time on activity of lysine oxidase-catalase co-immobilized on collagen membrane. A = Specific activity of lysine oxidase; a = activated collagen membrane with CHIC; b = activated collagen membrane without CHIC; c = native collagen membrane with CHIC; d = native collagen membrane without CHIC.", + "texts": [], + "surrounding_texts": [ + "Biosensors for the determination of L-lysine were prepared according to methods described E. Vrbovd et al. ~Anal. Chim. Acta 270 (1992) 131-136 previously [22,23,25]. Lysine oxidase and catalase were covalently co-immobilized either on a nylon net activated by partial hydrolysis with hydrochloric acid or on a native and activated collagen membrane. The effect of CHIC and the duration of immobilization on the enzyme activity is shown in Figs. 1 and 2. The maximum activity of lysine oxidase co-immobilized on the net was reached after 2 days (468 IU ml-1 enzyme); in contrast, the activity on the protein carrier after the same period was very low in three cases (18 IU ml- a on average) and the maximum activity was reached after 4 days (320 IU ml-1 on average). No significant differences between a modified and a native (original) collagen membrane were found. T h e presence of CHIC had, in agreement with previous work [22], a mild stabilizing effect (Fig. 3). The biosensors prepared were characterized by the effect of pH on the activity of enzymes (Fig. 4). The optimum pH was 7.5; 90-100% of the enzyme activity was retained over a relatively wide range of pH (6.5-9.6). The shapes of the pH curves were not influenced by the type of carrier applied and were shifted toward the acid range compared with the pH optimum of the free enzyme (8.0-9.0). Measurements of the effect of temperature on the enzyme electrode signal showed the same maximum value of activity for both enzyme conjugates (at 45\u00b0C, Fig. 5). From the calibration graphs (rate of oxygen consumption in the reaction mixture), the linear range of the biosensor with respect to the substrate concentration (e-lysine) was found in the extend over two orders of magnitude (Fig. 6) with a lower limit of determination of 6.7 x 10 - 6 M in the reaction vessel, i.e., 1 x 10 - 4 M in the in-" + ] + }, + { + "image_filename": "designv11_2_0001779_robot.1997.614329-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001779_robot.1997.614329-Figure1-1.png", + "caption": "Figure 1 : The inertial (fixed) frame and the moving frame attached to the rigid body.", + "texts": [ + "and the Cartesian stiffness matrix. In Section 4, we show that various definitions of the Cartesian stiffness matrices in the literature correspond to different choices of the affine connection in the task space. A numerical example taken from [a] is presented in Section 5 to illustrate this fact. Section 6 contains some concluding remarks. 2 Geometry and kinematics Consider a rigid body moving in free space. Assume any inertial reference frame {F} fixed in space and a frame {M} fixed to the body as shown in Figure 1. At each instance, the configuration (position and orientation) of the rigid body can be described by a homogeneous transformation matrix corresponding to the displacement from frame {F} to frame {M}. These transformations form a Lie group SE(3) , the special Euclidean group in three-dimensions [5]. On a Lie group, the tangent space at the group identity has the structure of a Lie algebra. The Lie algebra of SE(3) is denoted by se(3) and is given by: A 3 x 3 skew-symmetric matrix C2 can be uniquely identified with a vector w E IR3 so that for an arbitrary vector z E IR3, Ox = w x 2, where x is the cross product in IR3", + "3 If the connection used to compute the Cartesian stifj'ness matrie is symmetric, the Cartesian stiffness matrix itself is symmetric. Assume we have a non-redundant manipulator. Let q = {SI,. . . , qe}T be the vector of joint coordinates and assume that the robot does not have a singularity at q = { q y , . . . , q g } T . Choose an end-effector frame {M} which is fixed to the last link of the manipulator and set the inertial reference frame {F} to be the position of the end-effector frame at q = { q y , . . . , qg}T (see Fig. 1). Point q = { q y , . . . , therefore corresponds to the identity element of SE(3) and in some neighborhood U , SE(3) is (locally) parameterized by the joint coordinates. At every point A E U , we can choose the so called coordinate basis for the tangent space, which is given by E; = & (.). Since any other vector field can be expressed as a linear combination of Ei's, we can define the affine connection by setting: Note that for the coordinate basis all the Lie brackets vanish. We therefore have: V E , E ~ = 0 , i , j = l , " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0000528_0301-679x(94)90004-3-Figure1-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0000528_0301-679x(94)90004-3-Figure1-1.png", + "caption": "Fig 1 Geometry of misaligned journal bearings", + "texts": [ + " Then, integrating the pressure over the bearing surface, the forces and moments acting on the journal are calculated. The equilibrium position of the journal is then determined using a two-dimensional Newton-Raphson iteration method. Finally, the linear and non-linear bearing stiffness and damping coefficients are evaluated by means of the small perturbation technique. Analysis Reynolds equation Let us consider a journal on a rigid solid full bearing with geometric characteristics as shown in Fig 1, with laminar flow of the considered as incompressible oil film and constant viscosity of the lubricant. Neglecting body forces, and the variation in pressure across the film thickness, and assuming a no-slip condition at the Newtonian fluid/solid interface, the Reynolds equation takes the form h3 ) -- V. I ~ V P = V - [ h U ] - V (1) 244 1994 VOLUME 27 NUMBER 4 where Ix is the lubricant viscosity, P(0, z) is the unknown pressure distribution and h = h(0, z) is the oil film thickness, given by the following expressions for aligned and misaligned journals, respectively: h(0, z) = c + eo cos0 (2) h(0, z) = c + eo cos0 + z [Oy cos(0 + ~o) + 0~, sin(0 + dpo)] (3) where % and 0y are the misalignment angles (Fig 1). In equation (1) when the bearing is not moving 2U = Ui + VJ. For steady-state bearing operation the velocities have the values V = 0 and U = or and for dynamic loading V and U are given by V = 2 cos(0 + ~o) + P sin(0 + ~0o) + Z[~y COS(0 + ~00) + I~x sin(0 + q~o)] (4) U = or - 3c sin(0 + ~o) + P cos(0 + ~o) + z[-(~y sin(0 + ~o) + t~x cos(0 + ~0o)] (5) where 2 and 3~ are the velocities of the journal centre as shown in Fig 2. For an aligned bearing the rotational velocities 0x and 6y are equal to zero" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0001505_cdc.1996.572715-Figure3.2-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0001505_cdc.1996.572715-Figure3.2-1.png", + "caption": "Figure 3.2: Both real and reference unicycles", + "texts": [ + " Thus, replacing the expressions of A(q) , S(q), M and K ( q , q ) into (2.2), we obtain the resulting unicycle's singular perturbation model : ( : ) = g o ( ~ , r ] , ~ , \u20ac ) + g 1 ~ 1 + 9 2 ~ 2 (3.4) cb where U = ( ~ 1 , ~ 2 ) ~ is the torque vector, go = Now, we complete model (3.4) by taking into account the reference trajectory's dynamics, in the same manner as Samson did in [12] in the case of pure rolling without slipping conditions. However, before doing so, we introduce the following definition of the reference trajectory (see also figure 3.2). Definition 3.1 We call reference trajectory, denoted 7;1\", the application : T : [ to , +CO) + R3 t c+ (vz ,r( t ) , vy,t.(t), ve,r(t)) where vx,, and vy,, are the components of Vir (velocity of N, with respect to the inertial frame k o and expressed in the frame attached to the plateform of the reference unicycle, denoted Rz) and Vg,r = 10,. Remark 3.1 Notice that the position ( z r , v , ) T of a point M, (see jgure 3.2) and the orientation 0, of the reference unicycle WMR result from the time integmtion of 7;\" and the knowledge of the initial conditions Remark 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv11_2_0003048_imtc.2004.1351399-FigureI-1.png", + "original_path": "designv11-2/openalex_figure/designv11_2_0003048_imtc.2004.1351399-FigureI-1.png", + "caption": "Fig. I . Rolling clcmcnl bcaring pamclry", + "texts": [], + "surrounding_texts": [ + "IMTC 2004 - Ins1rumenl;ltion and Measurerncnl Technology Conference Carno, Italy. IX-20 May 2004\nNeural Network Based Motor Bearing Fault Detection\nLevent Eren I, Adem Karahoca ', Michael J . Devaney3 'Department o f Electrical and Electronics Engineering\n'Department of Computer Engineering University of Bahcesehir Bahcesehir, Istanbul 34538, TURKEY\nUniversity of Missouri - Columbia Columbia, MO 6521 I , USA\n'Department of Electrical and Computer Engineering\nAb.vfrad ~ Bearing ,farrlt.s ore the higgesl single rnrrse of nrolor ,failr~rez The hwring d