[
    {
        "image_filename": "designv11_31_0003925_014233129101300503-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003925_014233129101300503-Figure1-1.png",
        "caption": "Fig 1 illustrates the axis system used in submarine dynamic investigations. In this paper we are concerned only with depth and pitch control.",
        "texts": [
            " Both input signals contain noise at wave frequencies which cause nugatory motions of the hydroplanes. Previous work, (Daniel and Richards, 1983), with LQG (Linear, Quadratic, Gaussian) controller designs showed that notch filters, designed to track the predominant wave frequency, could be used to reduce the hydroplane activity at periscope depth. This technique has now been applied successfully to an H-infinity controller. In general, the depth control of a submarine is effected by means of bow and stern hydroplanes as also illustrated in Fig 1. These are fitted in pairs, port and starboard. The bow hydroplanes are usually all moving low-aspect-ratio hydrofoils with both port and starboard fixed to one shaft and moved by a single actuator. The stern hydroplanes are usually much larger and fixed to the hull. They have rear flaps to provide lift, and again both port and starboard flaps are fixed to the same shaft and are moved by a single actuator. The maximum usable plane angle is around 20 degrees. To run straight and level when submerged, a submarine must be neutrally buoyant with the centre of gravity vertically below the centre of buoyancy - ie, there must be no pitch moment on the boat"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002569_1.2828770-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002569_1.2828770-Figure8-1.png",
        "caption": "Fig. 8 Influence of minimum oil film thickness on EHD lubrication char acteristics",
        "texts": [
            " The influence of the gear tooth number is great too: the EHD load carrying capacity is almost propor tional to the gear tooth number, and also, a reduction in the power losses and a slight increase in the flash temperature occur for bigger gear tooth numbers. The worm thread num ber and the worm diameter (in case of constant gear face width) have but a relatively slight influence on all the EHD lubrication characteristics. Furthermore, the influence of some operating characteristics on EHD lubrication has been investigated. The minimum oil film thickness (Fig. 8), especially for its lower values, has a very strong effect on all the EHD lubrication characteristics. By reducing the minimum oil film thickness a strong increase in the EHD load carrying capacity and a sharp drop in the power losses occur. But the minimum oil film thickness is limited: in order to ensure full EHD lubrication a ratio of minimum oil film thickness to composite surface roughness of the order of two to three is believed to be necessary. The influence of the worm speed on EHD load carrying capacity and power losses is much more moderate, but there is a strong increase in the oil and flash temperatures due to the higher shear ratio in the oil film"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003165_10402009608983615-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003165_10402009608983615-Figure4-1.png",
        "caption": "Fig. 4--Mean expansion vs. accommodation 0 b s e ~ e d for each month.",
        "texts": [
            " However, it is interesting to see that the significant weather changes from August (hot summer) to October (cool fall) and to December (frigid winter) did not seem to affect the bearing condition. It may be due to the fact that the actual ambient tetnperature inside the plant did not vary as much as the temperature outside the plant. T o show the general trend of the bearing condition, Table 1 is compiled for the mean, maximum, and minimum expansion and accommodation observed during each month for the collected data. T h e means are plotted in Fig. 4. From Fig. 4, one can clearly see that the mean thermal loads for October and December are approxitnately the same D ow nl oa de d by [ \"Q ue en 's U ni ve rs ity L ib ra ri es , K in gs to n\" ] at 2 0: 54 0 9 M ar ch 2 01 5 Bearing Condition Monitoring for Preventive Mainten:uice in a PI-oduction Environment 94 1 and that the meiun thermal loacl fhr A u g ~ ~ s t is signilicantly higher. 11 is concciv;~l~lc that the interference f i t insiclc of the bearing was rcducctl d ~ l c to the break-in in the c;~rly months of sel-\\vicc, resulting in lower bearing preload"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002954_(sici)1521-4109(199804)10:4<236::aid-elan236>3.0.co;2-s-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002954_(sici)1521-4109(199804)10:4<236::aid-elan236>3.0.co;2-s-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms. A) 0.05 M sodium phosphate buffer (pH 7.2), td \u00bc 60 s; B) (A) plus 50 mM 6MP, td \u00bc 0 s; C) (B) after 60 s deposition at 0.1 V. Numbers on curves refer to the number of repetitive cycles.",
        "texts": [
            " For constant potential electrolysis measurements, a silver wire (2 mm diameter) was used as working electrode, and the solution was deaerated with nitrogen gas throughout electrolysis. All experiments were run at room temperature. Electroanalysis 1998, 10, No. 4 q WILEY-VCH Verlag GmbH, D-69469 Weinheim, 1998 1040-0397/98/0404-0236 $ 17.50\u00fe.50/0 In pH 7.2 sodium phosphate buffer, 6MP can exhibit a cathodic peak at about \u20131.0 V and a small anodic peak at about \u20130.18 V at a silver electrode. But both peaks are rather small and ill-defined, particularly at a concentration less than 50 mM. There are no discernible peaks on the repetitive CVs (Fig. 1B); however, an accumulation process can significantly improve the situation (Fig. 1C). By using cathodic-stripping voltammetry a discernible peak was obtained for 6MP even at the 0.1- to 0.01-mM level. Since the cathodic peak is more sensitive, this peak was used for the determination of 6MP. The 6MP peak height changes with scan rate over the range examined and is linearly related to it, which is typical of a surfacereactant-controlled electrode process (Fig. 2). Furthermore, the peak shifts to more negative potentials with increasing scan rate. There is about a 136-mV shift in peak potential when the scan rate changes from 10 to 100 mV/s, which implies a 1-e reduction of the depolarizer (assuming the electron-transfer coefficient, a, is 0.5) [19, 20]. Constant potential electrolysis was carried out at potentials corresponding to the cathodic or anodic peaks (as shown in Fig. 1). A 1.5-h electrolysis of a 1mM 6MP solution at the cathodic peak potential did not lead to a visible change in either the CVs or in the capillary electropherograms. Likewise electrolysis at the anodic peak produced no visible change, partly because of blocking by the adsorption film. Since no change occurred with both anodic and cathodic electrolysis, the anodic wave cannot be ascribed to the oxidation of 6MP to bis(6-purinyl)-disulfide or purine-6-sulfinic acid [14] and the cathodic peak cannot be attributed to the reduction of 6MP or its oxidation products formed at more positive potentials",
            " Thiopurines like 2-mercaptopurine (2MP), 2-thioxanthine (2TX), 6-thioxanthine (6TX), 2-amino- 6-mercaptopurine (2AMP), and 6-mercaptopurine riboside (6MPR) also exhibited CVs somewhat similar to that of 6MP at a silver electrode. But other purine derivatives such as 6-hydroxypurine, purine, xanthine, guanine, adenine, uric acid, or 2-amino-6-methylmercaptopurine (2AMMP), which lack the \u2013SH group, do not exhibit any pronounced current peaks at the silver electrode under these conditions. Therefore the peaks caused by thiopurines are mainly due to the \u2013SH group. Since 6MP did not show similar current signals at a Au, Pt, or Cu electrode under the conditions listed for Figure 1, the current signals are related to the characteristics of the silver electrode. It is worth noting that when the potential sweeps to about \u20130.8 V (i.e., before the cathodic peak) and then reverses, the anodic peak does not appear; when the potential sweeps from about \u20130.3 V (i.e., after the anodic peak) the cathodic peak does not appear. Therefore both the anodic and cathodic peaks are related although there is a large seperation between them. A part of this separation may be due to uncompensated IR-drop",
            " With increasing deposition time the 6MP peak tends to move closer to the hydrogen evolution wave giving poor separation between the two on stripping CVs. If one continues to cycle following the first stripping CV, a peak at about \u20130.75 V can be observed on the 2nd cycle (Fig. 3). This peak is well defined, it is linear with 6MP concentration, and its height is dependent on deposition potential and time. However, this new peak decreases rapidly with repeated cycling and following several additional full cycles approaches the response of no accumulation; this suggests the decomposition of deposits. As can be seen in Figure 1, the peaks for 6MP are rather broad and small, partly due to the slow charge-transfer and slow adsorption-deposition rates. To improve the situation surfactants were added to the media to promote the electrochemical process. Among these cetyltrimethylammonium bromide (CTAB) was found to be ideal for this purpose. In the presence of CTAB the stripping peak acquired a rather sharp shape and the peak height increased correspondently (Fig. 4). The ideal CTAB concentration for 5 mM 6MP was found to be 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003584_b978-0-7506-0119-1.50006-0-Figure1.2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003584_b978-0-7506-0119-1.50006-0-Figure1.2-1.png",
        "caption": "Figure 1.2 Methods of generating cylinders",
        "texts": [
            " It is convenient that only these shapes are used because, except when numerical techniques are used, it is difficult to control accurately the simultaneous movement of the tool or work in more than two directions. The movements are controlled by the standard constructional features of the machine. Chapter 3 gives details of movement actuating mechanisms and slideways. Generat ion of cy l inders A cylinder is composed of a circle and a straight line. There are four techniques of producing cylindrical forms, as shown in Figures 1.2a-d. In Figure 1.2a the tool rotates and moves axially. This technique is suitable when the tool is small relative to the work; drilling is the most common example. Vertical boring machines also use this technique. The fact that the drill and boring tool produce internal cylinders does not change the principle involved. In Figure 1.2b the work rotates and moves axially. This technique is suitable when the work is small relative to the tool; cylindrical grinding is an example of this technique. Sliding head automatics also use this technique for small-diameter work. In Figure 1.2c the work rotates and the tool moves axially. Turning on lathes is an example of this technique. In Figure 1.2d the tool rotates and the work moves axially. This technique is suitable when the cylindrical form is required on a workpiece which would be difficult to rotate, such as the bearing housings on a lathe headstock. Horizontal boring machines can use this technique. In these four methods it is comparatively easy to control the rotational movements using spindles rotating in bearings. The translational straight line movements are achieved using carriages guided by slideways. The roundness of the forms produced will be dependent on the precision of the rotation of the spindles in the bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003776_s0301-679x(03)00046-x-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003776_s0301-679x(03)00046-x-Figure1-1.png",
        "caption": "Fig. 1. Schematics of cold rolling.",
        "texts": [
            " [11] examined the effect of the elastic deformation of the workpiece on the film thickness when extruding billets and found it insignificant, that finding was for hydrostatic extrusion with a single component lubricant and might not transfer to cold rolling with mixtures. Distinction in behavior between components of a binary mixture is induced by the differences between the gradient fields for partial pressure [12]. The latter will be augmented if elastic deformation of the workpiece and the roller is taken into account. As elastic deformation results from solid\u2013fluid interaction, the solution of the problem will be iterative: for this, we apply Newton\u2019s method and a parametric continuation scheme [6], to promote convergence. Fig. 1 is a schematic representation of the various zones in metal rolling. The original and the final thickness of the strip are represented by t0 and t2, respectively, R is the roller radius and the reduction ratio is g = (t0 t2) / t0. For x1 R, where x1 is the location of the downstream boundary of the inlet zone, we have x 1 = \u221aRt1g and the film shape can be represented locally by h(x) h1 x2 x2 1 2R 2p E\u2019 p(s)ln x1 s x s 2 ds. (7) Here E\u2019 is the contact modulus of roller and workpiece, and the last term on the right hand side represents elastic deformation of the bounding surfaces due to the pressure, p(x), of the lubricant",
            " Component interaction (diffusive body force), p, is calculated from [14, 15] p mD r2 (v(1) v(2)) (11a) where mD 40mwater(mr 1) fC\u0302 (16 19mr)(3 2mr) , (11b) Here mr = moil /mwater, C\u0302 = R2 d /We is the so-called surface tension group, Rd and We are droplet Reynolds number and droplet Weber number, respectively, and r is the equivalent radius of the dispersed component. The surface velocity of the strip, U(x), is no longer constant, contrary to the case of visco-plastic theory, but is given by U(x) U0t0 / t(x). (12) The local value of the workpiece thickness, t(x), can be calculated with the help of de(x), the local deformation of the strip (Fig. 1) as t(x) t0 2de(x) (13) de(x) h(x) h0 (x0 x)2 2R . (14) In obtaining (13) and (14), we made two assumptions, viz., x1 R and de(x0) = 0, where x0 x1. As de(x) occurs only in the velocity term and as the latter is only a weak parameter of the problem, we rate these assumptions acceptable. To non-dimensionalize Eq. (8) we introduce the following dimensionless quantities x\u0304 x x1 , h\u0304 1 t\u030421 h R , p\u0304 p s , d\u0304e deR (t0g)2 (15a) a\u0304 as , r\u0304 1 t\u03042 1 r R , g t0 t2 t0 (15b) V\u0304 6(Ur Us) m Rt7/2 1 s , \u0304 s , t\u0304 tg R (15c) 1 There are, of course, more accurate relationships than Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002394_1.2830592-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002394_1.2830592-Figure2-1.png",
        "caption": "Fig. 2 Schematic of an FIVIR seal test rig",
        "texts": [
            " As suggested by Metcalfe (1981), and theoretically proven by Green (1989), the FMR seal is a better design than the flexibly mounted stator (FMS) seal (Green and Etsion, 1985) for high performance applications. While it is worth noting that FMS and FMR seals are about equally used in various industries, no experimental investigation of the dynamic response of the FMR seal has been reported. To simulate physically the steady-state response of an FMR seal and to assess the theoretical results an experimental pro gram was carried out, where features of the test rig (Fig. 2) and methods of data analysis were discussed in detail in Lee and Green (1994a), and in whole in Lee (1992). Obstacles in the rig performance have been identified and eliminated (Lee and Green, 1994b). Since in the test rig the FMR seal was mounted on a shaft, its dynamic behavior was expected to be somewhat influenced by the shaft dynamics. The analytical results (Green, 1989), however, were obtained assuming that the shaft is perfectly rigid. Therefore, before comparisons be tween the experimental and theoretical results can be made, the effect of the shaft dynamics on the seal response had to be known",
            "5198 kg rotor produced a polar mo ment of inertia, 7\u0302 = 4.1619x10\"\" kg\u00abm ,\u0302 and a transverse moment of inertia, 7, = 2.8032 x 10 \" kg\u00abm .\u0302 The outer radius was ro = 20.32 mm, and the radius ratio was 7?, = 0.8. The rotor geometry rendered a balance ratio of 0.5 assuming flat faces 158 / Vol. 117, JANUARY 1995 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use and unpressurized rotor chamber (see Fig. 2). The water vis cosity, II, was 0.8935 mPa-s at 25\u00b0C. The transmissibilities of Eq. (1) are in the angular mode. Therefore, only the angular rotordynamic coefficients are needed here. The support stiffness and damping coefficients as derived by Lee and Green (1994a) are 1)4 Z>/=12xM^( l - i? f )7?, - ' \u201eG\u201e (A2) A\", = 5.346-t146.1c A 36.36- fo) ?1.4 [N\u00bbm/rad] where p is the pressure differential across the seahng dam, J?m = (l +Ri)/2, is the dimensionless seal mean radius, and \u00a3\u201e = (1-\u00ab,)/?\u201e ' 36"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure6-1.png",
        "caption": "Fig. 6. Typical Engine Mounting Elements",
        "texts": [
            " Damping is, however, of advantage in limiting movement when going through resonance and when the engine is set in motion by shock forces. A damper which will only react to the large amplitudes of vibration produced by these conditions would, therefore, solve this problem but a cheap and reliable form of this type of damper has not yet been found. Proc Znstn Mech Engrs (A.D.) SELECTION OF MOUNTING UNITS When anti-vibration mountings were first introduced, simple rubber washers were fitted under the engine feet in the manner shown in Fig. 6a. The engine itself could then no longer serve as a structural member of the chassis, but this disadvantage was well offset by the vibration insulation obtained which in the light of modern comfort still left much to be desired. There was, however, in those early days a chassis of definite mass which, as already explained, gave better insulation than the modem rather light and flexible vehicle structure. The design shown in Fig. 6a was soon superseded by the system shown in Fig. 6b where all metallic contact between engine and chassis had been eliminated. The second type of fitting is now used only on special purpose vehicles such as dumpers and tractors where comfort of the operator depends more on seat design than on absence of vibration. The main purpose of the mounting is then to allow twisting of the chassis without imposing large stresses on the engine block. Rubber bushes on trunnions (Fig. 6c) preferably arranged in a three-point mounting system with the axes of the bushes in different directions, are also employed for the same purpose. When engine mounting theory had been further developed rubber bushes or bush type elements arranged around the longitudinal principal axis were fitted, and many designs of this type are still in use (Smith 1947). The floating power arrangement was the first suspension system to take notice of the inclination of the longitudinal principal axis of inertia and arranged for the mountings to act about this axis. A high point front engine mounting on or near the principal axis was at first considered essential but this feature has obvious disadvantages in construction and fitting, and was later eliminated by modified forms of suspension systems based on the 'floating power'. With oil engines in particular, the need for large deflections with close buffering for shock loads and torque reaction made the steel spring more attractive than the rubber mounting. A diagrammatic arrangement is shown in Fig. 6d. The advantages of the steel spring are (1) close control of spring rate, (2) maintenance of properties under all climatic operating conditions and for long periods of time, and (3) not affected by oil. On the other hand this type of steel spring also results in difficulties due to: (a) The spring rate at right angles to its axis is low and cannot be easily controlled. Separate control linkages or guides must therefore be used. (b) High frequency noise can be transmitted through the spring and, therefore, rubber washers must be fitted at the ends of the steel spring",
            " Section through bonded-rubber sandwich with integral overload stops. construction often necessitates mountings with large deflections to overcome periods of noise and vibration in the engine running range. With progress in rubber compounding and bonding of rubber to metal it is now possible to obtain quite large deflections, so eliminating one of the advantages claimed for steel springs. For minimum spring rate in one plane with stiffness in a perpendicular direction, rubber in shear is employed as shown in Fig. 6e. Natural rubber compounds are used almost entirely for their better overall mechanical properties over a fairly wide temperature range. Synthetic rubbers may be used in special instances for oil resistance or high-temperature conditions, but it is always advisable to select mounting positions where there is little danger of excessive oil contamination and where temperatures would not normally exceed 70\u00b0C. Natural rubber can then be used with low creep, low permanent set, little variation in properties from -20\" to +7O\"C, high tensile strength, etc",
            " It is, however, essential that the suspension be not critical to changes in natural frequency of about 10 per cent. Buffers to limit engine movement under shock loads and due to torque reaction must usually form part of a suspension system. Even with steel spring mountings, rubber stops are employed for this purpose. By using bonded-rubber NO 1 1957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub.comDownloaded from SUSPENSION OF INTERNAL-COMBUSTION ENGINES IN VEHICLES 23 mountings it is possible to incorporate buffering in the mounting units as shown in Fig. 6 f, i, and 1. Other advantages of the rubber spring are first, the possibility of changing the stiffness in the ratio of 1 to 4 by using rubber compounds of varying hardness. Secondly, the design of the rubber element can be varied so that any desired stiffness ratio is obtained for the various directions (Fig. 6g, ti, and i). In order to utilize rubber to its best advantage, that is, obtain the maximum strain energy with heavy loads and large deflections, it should be stressed in a combination of compression and shear (Horovitz 1957). This effect is achieved in the designs shown in Fig. 6g, h, and i. The mounting in Fig. 6g consists in essence of two sandwiches in a vee, and separate mountings are often fitted into an assembly to give the same sort of properties. In one horizontal direction the stiffness is very low while at 90\" to the low stiffness direction, the horizontal stiffness is high. The mounting would normally be arranged to give control of movement in the high stiffness direction, insulation mainly in the lowest stiflhess direction where the rubber is in shear and to carry load vertically for maximum insulation by large deflection but combined with high load capacity. In Fig. 6h a heavier unit of similar construction is shown, but here partial compression is applied to the rubber for loading in all directions. The same applies in the case of conical mounting, Fig. 6i. The unit shown in Fig. 6j also illustrates rubber in compression and shear but here, and in the case of the eccentric bush shown next, the same section of rubber is not loaded in the two senses simultaneously. The eccentric bush is of particular interest as it will give a larger deflection than a normal concentric bush and has the advantages of economy and simplicity in fitting. Fig. 61 shows a recent development of an improved form of rubber and steel spring which, apart from engine mounting application, has also found application as a vehicle suspension unit (Moulton and Turner 1956-57)",
            " From all accounts this mounting arrangement works very satisfactorily and similar systems have been adopted for other cars on the European continent. The number of parts required for each mounting assembly is rather large but, on the other hand, a large equivalent static Proc Insrn Mech Engrs (A.D.) deflection (a in.) can be obtained by a low spring rate. Damping is provided by the rubber sleeve surrounding the helical spring, and horizontal movement is checked by the central rubber-covered sleeve. The mounting element shown in Fig. 6 could well provide a neater solution from the standpoint of parts per mounting assembly. Quite apart from the large deflection, this mounting arrangement is of interest as a centre-of-percussion mounting. A vertical shock load acting through the chassis on the rear mounting will not produce any reaction at the front mountings, and vice versa. In order to achieve this control of engine movement under vertical shock loads the spacing between the front mounting, rear mounting, and centre-of-gravity of the power unit must be in a certain relationship fixed by the inertia of the power unit about a transverse axis",
            " NO I 1957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub.comDownloaded from SUSPENSION OF INTERNAL-COMBUSTION ENGINES IN VEHICLES 35 Substituting for d from equation (27) and em C sin-. cos (a-p) = - sin B 2mS C 2m2S cos (a-p) e sin a. sin B - = or and therefore C In tenns of heights 1 and h this reduces to KR = 7 = 2mZS(1+ cot a cot /?) . . (30) KR = 2S(rz--Ih) . . . . (31) where r is the radius of the mountings from the intersection of their compression axes. Effect of Znterleaf on Properties of V-system In the arrangement shown in Fig. 6 two cases were considered for the compression stiffness of the mountings. In both cases Angle between compression axes was taken as 2 x 30\u201d. Height of intersection of mounting axes 19.25 in. (1) Soft mounting, that is, without interleaf & = 4 from equation (21) Kv = 2S($+3) = 6.5s from equation (22) KH = 2S($+l) = 3.5s from equation (24) 1 = - 19.25 X 2 = 11 in. from equation (31) KR = 2q494.3 - 11 x 19.5) =565S 3.5 (2) Hard mounting, that is, with one interleaf k = 8 Kv = 12.5s KH = 5.5s I = 7 in"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure3.16-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure3.16-1.png",
        "caption": "Fig. 3.16",
        "texts": [],
        "surrounding_texts": [
            "3.3 Full-Bridge DC-DC Converters 135\n\u2022 first K'1 and K 2 are closed (state 3):\nu' = - U; i = - I'\n\u2022 then K'1 and K2 are closed (state 4):\nu' = 0; i = 0\nOn the operational diagram common to all full-bridge choppers, the polar ities which can be attributed to u' and i are shown. The branches of the v-i characteristics on which the four switches must operate are then indicated. It can be seen that\nK 1 and K2 must be controlled turn-on/turn-off devices, K 2 and K'1 can be simple antiparallel-connected diodes.\nThis gives the circuit configuration.\nThe controlled semiconductor device TC 1 makes the reversal possible (u' and i change polarity during the periods when they are not zero, i.e. the mean values, U' and I, change polarity). The controlled device TC2 takes charge of the variations in the ratios I U '/U I or II I I'l.\nIf TC2 is conducting for a. T during each cyle T,\nu I I u = I I I' = a.,\n- u I I u = - I I I' = 1 - a.,\nif U' and I are positive,\nif U' and I are negative.\nIt can be seen that the commutations TC 1-D'1 and TC2 - D 2 must be forced and commutations D'1-TC 1 and D 2-TC2 are natural.\n3.3.3.2 Chopper Connecting a Voltage-Reversible Voltage source to a Current- and Voltage-Reversible Current Source (Fig. 3.17)\nSince the voltage source is not current-reversible, its current i is positive when the converter connects the two sources and zero when it disconnects them. Equating input and output instantaneous powers gives:\nI i u =-U.\nI'\nIf I' is positive, u' equals + U or zero. If I' is negative, u' equals - U or zero.\n- For a positive I', K 1 and, alternately, K 2 and K2 are closed:",
            "136 3 DC-DC Converter Circuits: An Overview\n\u2022 When K 1 and K~ are closed,\n(state 1 or 1')\nif U is positive, vK; = U > 0; vK 2 = U > 0 (state 1)\nif U is negative, vK; = U < 0; vK 2 = U < 0. (state 1')",
            "3.3 Full-Bridge DC-DC Converters 137\ni\n(>0;=0)\niK1\nU VK1l K1 I' ---(>0;<0) (>0; <0)\nVK 1~ K' 1\nin\nK1\n(1 '1 ',2,2') (3,3',4,4')\n(3') VK1 ( 1 ') VK2\n~ (3)\n~ ( 1 ) (4,4') (2,2')\nK; iK'1\nK~ iK'2\n(3,3') ~ ( 1 '1 ') ~VK'2 VK'1\n(1 ',2',4') 0 (1,2,4) (2',3',4') 0 (2,3,4)\nt ..\nt .. T1 ------11------ ------{~----- T 2"
        ]
    },
    {
        "image_filename": "designv11_31_0002213_1.1707468-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002213_1.1707468-Figure2-1.png",
        "caption": "FIG. 2.",
        "texts": [
            " 1, in which the triangle ABC is considered as infinitely small: If D is different from zero, and C is equal to zero, there is a finite shear flow along the edge of regression, and more generally, the shear flow has the value: ii12=n12-limit [~n2(A2-Al)]' (14) >'2=1.1 P From the results established above, the condi tions of statically determined equilibrium of the membrane can be deduced. Case I. The membrane does not include its edge of regression. 549 [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: 136.165.238.131 On: Sat, 20 Dec 2014 06:42:07 CIA). The membrane is limited by two generators and two lines of curvature (Fig. 2). If two conditions are imposed at each genera tor, these two conditions give two relations between the unknown functions C(>\\l) and DC>\\l)\u00b7 Thus the arbit~ary functions are determined. More exactly, if the shear is not given, C(AI) appears through a differential equation of first degree and it is necessary to give the shear along one generator, or a general resultant of shear along one of the two limiting curves, thus giving the possibility of determining the arbitrary constant which appears in C(Ai)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure17-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure17-1.png",
        "caption": "Fig. 17. (a) The perceived shape of the space CFNS(ti) generated by the robot R6: (b) The simplified traffic patterns L4; L6; L7; L6; L1 generated by R6:",
        "texts": [],
        "surrounding_texts": [
            "Since the major goal of the traffic language is to assist an autonomous robot to represent and understand the traffic priorities of the other moving objects in the same navigation space avoiding collisions, it is necessary that the synthesis of traffic priority patterns to be defined semantically. Notation: a) (commutative) with b) (associative) with and Definition: The length of a perceived pattern is defined as the number of corridors which compose the pattern. Corollary: Two perceived patterns (generated by the same or different robot, at the same time for two different moving objects) with the same length are not necessarily identical in shape. Definition: The synthesis # (semantically) of two traffic patterns determines the order of the robots priorities one against the other. Proposition: (commutative) Proof: Let assume that three robots are moving in the same navigation space, as shown in Fig. 10. The robot is the main one and are the secondary robots. For this particular case, and Thus, the pattern produces the relationship between the robots\u2019 priorities. The pattern provides the priority relationship Thus, the synthesis provides the relationship (1) among the robots\u2019 priorities. Now, the synthesis provides (2). These two relationships are identical, which means that Following this process easily it can be proved the general case Proposition: (associative) Proof: Similar to commutative. Notation: (identity traffic pattern) for every Corollary: In a free navigation space with secondary moving robots there is a possibility of existence of the following traffic pattern configurations. 1) There is a maximum of two patterns with . 2) There is a maximum of one pattern with or . 3) There are patterns such that where Corollary: In a free navigation space FNS if there are the traffic patterns and the there is not the pattern where the sequence of the values for the indexes are and or and or and Traffic Complexity Table II presents the traffic complexity of moving robots in a CFNS under two different assumptions. \u2022 In the first assumption, called individual, a robot views all the other moving robots, generates all the traffic patterns from its own position and calculates all the possible traffic priorities of the other robots against its own priority. \u2022 In the second assumption, called global, every robot views all the other moving robots, generates all the traffic patterns and calculates all the possible traffic priorities for all the moving robots including itself. V. ILLUSTRATIVE EXAMPLES In this section, two illustrative examples for traffic cases are provided and solved by using the KYKLOFORIA language. In the first example, the traffic case includes six moving robots in a free navigation space shown in Fig. 11. Figs. 12\u201317 provide the shape of the free navigation spaces observed TABLE III SIMULATED RESULTS FOR FIG. 18 by each moving robot and the traffic patterns generated by each of them in their own free space. In the Fig. 18, the velocities of the moving robots are considered the same, thus the traffic priority relationships generated by the traffic language are given in Table III. Each moving robot knows the traffic priority relationships in the same free space. Thus, the robot makes use of its own which is higher than and goes out of the narrow corridor. At a time min, covers a distance of 4.5 m. The robot has to wait of a period of 0.6 min, and then it proceeds into the open corridor by covering a distance of 1.4 m in 0.485 min. Initially, covers a distance of 1.3 m in 0.325 min, then it slows down and waits for 0.55 min before it proceeds into the narrow corridor following the robot and covering a distance of 0.9 m in 0.23 min. The robot using its own higher priority over covers a distance of 4.5 m. The robot waits for 0.75 min and then proceeds forward by covering a distance of 1.5 m. Finally, the robot covers a distance of 4 m in 1.125 min because it spends some time to change its direction. Note that, and TABLE IV SIMULATED RESULTS FOR FIG. 19 (a) (b) Fig. 14. (a) The perceived shape of the space CFNS(ti) generated by the robot R3: (b) The simplified traffic patterns L1; L7; L2; L6 generated by R3: change their directions (as shown in Fig. 9) avoiding a possible collision. In the case that the velocities of the robots are considered different, then Table IV shows the traffic priority relationships and the robots traffic paths and locations are given in Fig. 19. In particular, present a traffic behavior similar to the previous case with the same velocities, by using the Table IV. covers a distance of 4.9 m with m/min. covers a distance of 1.4 m with m/min. covers a distance of 1.3 m with m/min and a distance of 0.6 m with m/min. waits until passes the intersection point and then covers a distance of 1 m with m/min. covers a distance of 4.8 m with m/min. Finally, covers a distance of 2.5 m with m/min. The second example explains the use of the language for the improvement of the traffic schedule of a particular robot under the assumption that the local traffic flow in a certain region is almost the same every time that the robot enters that region. In this case, the robot enters the region from left to right at time and spends min crossing it. At that time, there are three other moving robots crossing the same region from different directions (see Fig. 20). The traffic flow extracted by the robot in that region, is represented by the following language words: The symbol & represents the synthesis operator between words for the formulation of the traffic flow extracted by a robot traveling through a region where In this particular case there is no delays during the traveling. Fig. 21 shows the same region, at a different time where the robot enters the region from the right to the left in order to cross it by following the reverse path of Fig. 20. At this time there are four other moving robots and a fifth one is coming to the same region. The traffic flow extracted by the robot is represented by the following words: where In this particular case there are delays due to conflicts between the robots directions and traffic priorities. More specifically, the robot has to wait until and pass first and then it continues its own path. This mean that the robot knows the time required to cross the region, and in the latter case it took more time, At this point the robot analyzes the traffic flow perceived by itself and modifies its traffic path for a future cross of the same region under a traffic flow similar to More specifically, it follows the next algorithmic steps: 1) Check each word , for patterns . 2) Search for possible patterns , to replace in a word . 3) Replace the first with an in . 4) Rearrange the word into a new one , which includes the affects on the other patterns due to replacement ( instead of ). 5) If the new word includes less number of patterns then use it in the new , else go to 2 to replace the next with an in . 6) If the new overall traveling time is less than the original then proceed else no changes Thus, Fig. 22 shows the new modified traffic path. The new traffic flow extracted by is represented by the following words: where Thus, the new traffic flow includes less conflicts and no significant delays for the robot"
        ]
    },
    {
        "image_filename": "designv11_31_0003427_s0263574700019743-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003427_s0263574700019743-Figure5-1.png",
        "caption": "Fig. 5. New optimal search directions with two active constraints: a (5,.*, (n2, Art22))5*0; b (St,t, (/i21 A/J2 2)) = 0.",
        "texts": [
            " The new search direction S2k is obtained by projection of Suk onto the plane containing x2k. Let n2i be the normal to this plane (Figure 4). S2k is given by the following relation: $2.* = (5,.* - (n2u Sltk)n2i)/\\\\Si,k - (n2U 5,.*>n2,|| (29) Case 2: two active constraints The point x2k is on an edge. Let n2l and n22 be the gradients of the two active constraints. We can express Si.* as: ot2 \u2022 n22 , /\\n22) (30) where (A) designates a cross product. If a3 y4 0, the search direction S2Jc is a unit vector along either n2l A/I2 2 or - n n AH,2 (Figure 5a). Otherwise, Si,k is projected onto the plane of which the normal corresponds to the largest value otj (Figure 5b). S2.* = (5,.* - (n2t, Shk)n2j)/\\\\SUk - (n2j, Sx,k)n2j\\\\ (31) Case 3: three or more active constraints. The point x2M is a vertex of O2. To determine S2ik, we consider the search direction SIJt and the active edges e2j of the object 2 (Figures 6a to 6c). We project Suk onto each active edge: ft = <*,.*, \u00ab?/> (32) Then, the new search direction S2,k is given by a unit vector along the edge which corresponds to the largest value Pj. ,e2i)e2j\\\\ (33) 7. NUMERICAL RESULTS An extensive set of numerical examples in 3D space with various shapes of objects (Figure 7) have been applied to test the contribution of the new optimal search directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003672_a:1023048802627-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003672_a:1023048802627-Figure1-1.png",
        "caption": "Figure 1. The kinematics scheme of 2-R robotic manipulator and local improvement of robot end-effector pose accuracy.",
        "texts": [
            " When the robot performs given technological operations, it is important to use different parts of the robot working space (Veryha et al., 2000). In some cases, it is allowed to change the location of the working point at some value due to the repositioning of the working objects (Hrman et al., 1999; Yurkevich, 2000). This slight change of the end-effector working position allows performing local optimization of the end-effector pose accuracy by using robot joint error mutual compensation. For the kinematics scheme of 2-R robotic manipulator, shown in Figure 1 (x0y0 \u2013 base robot coordinate system, x1y1 and x2y2, accordingly, the Cartesian coordinate systems of first and second links), elementary end-effector Cartesian errors x and y can be defined in the base coordinate system as: x = \u2212( l1 sin q1 + l2 sin(q1 + q2) ) q1 \u2212 l2 sin(q1 + q2) q2, y = ( l1 cos q1 + l2 cos(q1 + q2) ) q1 + l2 cos(q1 + q2) q2, (1) where q1 and q2 are joint coordinates, q1 and q2 are elementary joint errors of the first and second joints, l1 and l2 are, accordingly, lengths of the first and second manipulator link",
            " In practice, Equation (2) does not allow reaching joint error maximum compensation, because joint errors q1 and q2 will change with the change of the location of the working point in q2opt. Average values of joint error q1 and q2 will be the same only for similar trajectories in the given area of the robot working space (Kieffer et al., 1997; Veryha and Kourtch, 2000). In order to improve robot end-effector pose accuracy L based on (2), the method of improving robot end-effector pose accuracy using joint error maximum mutual compensation was developed. One should move the given initial working point Pinitial (see Figure 1), in the direction of the joint coordinate q2opt. This will change the working point Pinitial into the point Pfinal, at which the average values of joint errors will not change at more than 1 percent (Kieffer et al., 1997). This will lead to an improvement of the end-effector pose accuracy L when performing the given technological operation. Similarly, the improvement of the end-effector pose accuracy in the given working points can be performed for other types of robots. As an example, one can consider the allowed change adist = 10 mm of the working point Pinitial (see Figure 2). It is supposed that a given technological operation must be performed in point Pinitial with Cartesian coordinates x = \u2212288.053 mm and y = 529.429 mm, joint coordinates q1 = 1.77 rad and q2 = 0.79 rad (see Figure 1) by the 2-R robotic manipulator. Based on the presented experimental results, the end-effector positioning accuracy was L = 1.9 mm in the point Pinitial. The joint error values q1 = 2.29 \u00d7 10\u22126 rad and q2 = 2.11 \u00d7 10\u22126 rad were found in the point Pinitial based on the manipulator kinematics model. Using Equation (3), the optimal value of the joint coordinate q2opt = 3.147 rad was found for the given conditions. According to the previous discussions, the value of the initial joint coordinate q2 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003419_s0389-4304(96)00049-5-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003419_s0389-4304(96)00049-5-Figure1-1.png",
        "caption": "Fig. 1. Belt layout and measurement location.",
        "texts": [
            " However, analysis of the phenomena during actual engine operation is significant for the effective usage of the belt unit testing machine which can be easily handled. This study observes the generating mechanism of transverse vibration as the cause of the meshing order noise which is one of the timing belt noises. The results of this study prove that the suppression of the excitation force is effective for reducing the transverse vibration. 2. Experimental method An in-line four-cylinder engine was employed. Figure 1 shows the belt layout and measurement locations. The timing belt drives a water pump and an oil pump as well as a valve train. The transverse vibration was measured using a laser velocimeter and a displacement transducer from the back face of the belt. Between the crank pulley and the idler, the measurement location was set at a distance of one fourth of the belt span from the crank pulley to measure the first mode of the vibration, with the second mode also considered. The tight side tension was measured by strain gauges placed on the idler support and the effective tension was measured by gauges placed on the crank pulley"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003052_980220-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003052_980220-Figure2-1.png",
        "caption": "Figure 2. Biaxial truck model structure together with assumed coordinate systems. Suspension and tyre-road contact forces and moments",
        "texts": [
            " This paper presents two of them, that can be effectively run on PCs. Most of the attention was focused on showing results of experimental verification of simulation models. VEHICLE MODEL STRUCTURES The physical model of the car [7, 8, 9, 11, 12, 13] is based on the structure of a biaxial vehicle with independent front wheels and dependent rear wheels (Fig. 1). It consists of 8 mass-elements treated as rigid bodies (body, rear axle beam, two front unsuspended masses, four rotating wheels). The biaxial truck model [9, 10, 13] (Fig. 2) has a similar structure, but the front suspension is dependent. It consists of 7 rigid mass elements bodies (body, front and rear axle beams, four rotating wheels). Vehicle motion is described in fixed coordinate system Oxyz connected with the road and in many local systems connected with the model bodies (Fig. 1 and 2). Both models have 14 dof (degrees of freedom): 3 co-ordinates of vehicle body centre of gravity O1 position in fixed system Oxyz ( ), 3 angular co-ordinates of body position (yaw , pitch \u03d51 and roll \u03d11), 4 co-ordinates of unsprung masses relative motion (car: ; truck: ), 4 angular coordinates of wheels\u2019 rotation (\u03d55, \u03d56, \u03d57, \u03d58)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003718_iros.1999.812833-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003718_iros.1999.812833-Figure4-1.png",
        "caption": "Figure 4: Detection of the flat wall and extraction of DWV (Detected \u2018Wall Vector). The calculated ERPs are grouped by the discontinuity and fitted into lines. DWV is extracted referring to two end ERP points, Rs, Re-",
        "texts": [
            "J denoting the direction of the ultrasonic reflection can be calculated using this geometrical constnaintr- Thm we cap determine the position of two ERPs B1 ad\u2018 RZ &erring to this 4. WhZe the rob8 is t radmg, a new range data is manredl by the uttEasonic sensor whenever the robot proceedb a certain length. The above mentioned process for the calculation of ERP is repeated when a pair of new range data is obtained. In order to detect a flat wall, position continuity of ERP is checked and they are grouped (see Figure 4). If the distance between two ERPs is short enough, these ERPs are considered to belong to the same wall and are grouped in the same cluster. If the distance is longer than a threshold length, namely when a discontinuity is found, these ERPs are clustered to the different groups. This grouping process continues until a discontinuity is found. If the number of ERP in the clus- d 4 ter exceeds a defined maximum number, the grouping process also stops in order to use obtained data properly. Then, the number of ERP in the cluster is counted and if it is over a threshold the verification process will be done"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003622_978-1-4471-0765-1-Figure23-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003622_978-1-4471-0765-1-Figure23-1.png",
        "caption": "Figure 23. Structure of the tactile sensor made of electrically conductive fabric",
        "texts": [
            " Transition in terms of three kinds of DOFs for both translational and rotational ones is also indicated . Due to the geometric constraints between arms for the screwdriver and for the LRF, the screwdriver and the bolt could not be observed at once. Thus, the LRF observed only the bolt because the positional uncer tainty of the bolt was much larger than that of the screwdriver. Edges e') , and e'2 of the bolt were observed. Figure 22 shows a successful operation of putting a screwdriver on a bolt. 318 Figure 23 shows the verification result of the pre dicted success probability with the actual success ratio. The predicted success probability coincides with the actual success ratio. probability of success J.( __ predicted success probabiJity \u2022 actual success ratio +-_-40.-0~_-20-.()~-().O~-2-0.\"C\"() ~4(:':).:-() <t> (deg.) Figure 23. Comparison of the two success probabilities in the screwdriver-bolt operation. The angle Ij> indicates the relative angle between the direction of the slot and the viewing direction of the range finder. In each viewing angle, the same operation was repeated 50 times to obtain the snccess ratio. 6.5 Gear Mating A gear-mating operation, shown in Figure 24, belongs to group (e) in Figure 9. In this operation, a priori knowledge about how gears are mated is nec essary because there are many potential matches between gear teeth",
            " In model and vision based robots, it is hard for the robot to know whether the robot interacts with the ob jects. The robot sitting on a chair actually does 506 not know whether the robot body is touching the chair or not. It should have tactile sensors dis tributed on the body to know this at least. In order to give large number of distributed tactile sensors to a robot, we have developed a sensor suit from an electrically conductive fabric. The electrically conductive fabric (ECF) is electrically plated cloth. The structure of the tactile sensor is shown in Figure 23. It has six layers. The top and bottom layers covers the sensing element and the wiring layer. The sensing element is a switch made of three layers. The layer 5 is a cloth of ECF. The layer 4 has reticulate structure and works as a spacer between the layer 4 and 6. The layer 4 has distributed segments of ECF. Each ECF segment is connected to the video multiplexer by electri cal conductive string (ECS). The layer 2 is non electrical conductive cloth. As wiring is achieved by sewing on the non ECF cloth with an ECS, it is easy to build complexed wiring using multiple layered wiring with other non ECF cloths "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure7-1.png",
        "caption": "Fig. 7. Diagrammatic V-arrangement of Mounting",
        "texts": [
            " In some cases this V-arrangement is used only at one end of the engine, in others it is used both at front and rear with rubber-bushed links or other fittings to control foreand-aft movement. On Diesel engines V-arrangements both of mountings and of rubber-bushed links are frequently employed. It is therefore essential to have a clear understanding of the properties of a V-arrangement of mounting. The principle was first applied correctly in aircraft where it was referred to as \u2018dynafocal\u2019 since all mounting axes met in one point. As shown in Fig. 7 two mountings fitted with their compression axes meeting in one point are equivalent to two mountings fitted in an orthodox manner in a higher plane, as indicated. The point of action of the V-mountings is always below the point of intersection of the compression axes, the amount of correction depending on the ratio of compression to shear stiffness of the mounting elements. If the mountings are placed fairly low down, it is not always possible to ensure that their point of action lies on the longitudinal principal axis of the engine unless interleaved mountings are used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003144_0957-4158(93)90059-b-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003144_0957-4158(93)90059-b-Figure3-1.png",
        "caption": "Fig. 3. Servomechanism with asymmetrical loading.",
        "texts": [
            " ) > O, note that an equivalent state-variable description for x~ = q and x2 = 0 is 3\u00a2 1 = X 2 (2) f\u00a22 = f ( X l , X2) + g(Xl , X2) u, (3) where and f (X l , X2) -- -V(Xx, m ( x l , x2) 1 g ( x l , x2) - m(xl, x2) Clearly, g ( - , . ) > 0 since m ( . , . ) > 0 . Many practical servomechanisms are described by this particular structure of differential equations [16, 17]\u2022 For such systems, the function m ( . , .) typically models an equivalent mass function so that the condition m ( . , \u2022 ) > 0 is satisfied. As examples, the servomechanism with asymmetrical loading shown in Fig. 3 has dynamics of the form given by (1); likewise, position control systems which utilize limited rotation pancake D.C. motors [16] (which offer the advantages of small form factor, high torque and brushless operation without requiring high-speed switching inverters and electronic commutation) as actuators also result in dynamics of the type described by (1). For the dynamical system described above, if the functions f and g are known exactly, then for a suitable choice of aim and azm, the control law 1 U ( t ) - - [ - - a l m X l - - a 2 m X 2 - - f(xa, x2) + r], (4) g(xl, x2) will yield a stable closed-loop system for trajectory following"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002645_1.2889688-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002645_1.2889688-Figure1-1.png",
        "caption": "Fig. 1 A general rotor-bearing system",
        "texts": [],
        "surrounding_texts": [
            "Consider a flexible rotor system consisting of D disks and"
        ]
    },
    {
        "image_filename": "designv11_31_0003583_978-94-011-5870-1_20-Figure19.10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003583_978-94-011-5870-1_20-Figure19.10-1.png",
        "caption": "FIGURE 19.10 Example of deformation partitioning which includes viscosity, for the 45\u00b0 limb-dip chevron fold in Figure 19.7(a): equal-thickness multilayer (tz = 0.5) and V = 10. (a) Mohr diagram (reciprocal stretch versus rotation) of partitioned simple shear in layers 1 and 2, with principal axes shown by triangles. (b) The resulting strain ellipses for the two layers. Compare with Figure 19.7(d).",
        "texts": [
            " Conse quently, the incompetent layers accommodate the rest of the deformation, dictated by the bulk shortening. No rheology or viscosity entered into the relationships above. It will become apparent from the next section, which includes layer viscosity, that the relationships derived by this geometric modelling may provide a good approximation when the competent:incompe tent viscosity ratio is high (2:: 50). The geometrical model of deformation parti tioning (Figure 19.7) can he modified to allow for deformation in both competent and incom petent layers. Figure 19.10 maintains the same geometric principles as before, that the com bined shear strain of the layer pairs fulfils the 'similar fold' requirement (equation 19.3 and Figure 19.7): $ = a and 'Y = tan a. However, when both layers are treated as deformable, with shear strains 'Y1 = tan $1 in layer 1 (thick ness proportion t1) and 'Yz = tan $z in layer 2 (thickness proportion tz), and taking t1 + tz = 1, 'Y1t1 + 'Yztz = 'YB = tan a. (19.14) Now introducing the viscosity ratio for the two layers, 1J./lJ.z = V, and assuming that both layers have a constant (Newtonian) viscosity during finite deformation, the rule for strain refraction across contrasting layers (Treagus, 1983) states that the ratio of layer-parallel shear strain is equal to the inverse viscosity ratio",
            " The strain refraction from layer 1 to layer 2 is a special case (simple shear) of the more general strain refraction given in Treagus (1983, 1988). Solutions to these algebraic expressions can thus be illus trated on the Mohr diagrams for A' vs. 'Y' (see Treagus, op. cit.). Alternatively, the polar Mohr diagram for reciprocal stretch vs. rotation solu tion proves a convenient method of construc tion for deformation partitioning, as already used the geometric model (Figure 19.7(c)). This will be developed below (Figure 19.10). Modelling deformation partitioning in folds Layer viscosity ratio measured as a ratio to the bulk viscosity V;::: 50 cannot be used, it is necessary to deter mine the ratio of layer viscosities, J-L1 and J-L2' as ratios of the 'bulk viscosity' J-LB. A bilaminate multilayer comprising alternating layers (Figure 19.7(a)) has a bulk anisotropy (Biot, 1965, p. nomenclature is given by (19.20) J-LBt = J-L1J-Li[t1J-L1 + t2J-L2] = 1/[(tiJ-L1) + (tiJ-L2)]\u00b7 (19.21) J-LBn is the bulk viscosity under layer-parallel normal stress, and J-LBn is the 'transverse' or shear viscosity, under layer-parallel shear stress",
            " Mohr representation of deformation partitioning with viscosity, on fold limbs The partitioned simple shear in inverse propor tion to the layer viscosity, given in equations (19.18) and (19.19), can be written as a factor of the bulk shear strain, 'YB (here = tan a): 'Y/'YB = 1/[1 + t2(V - 1)] (19.26) 'Yi'YB = v/[1 + t2(V - 1)]. (19.27) These are, of course, reciprocal expressions to the viscosity ratios in (19.22) and (19.23). The geometric model (Figure 19.7) assumes that 'YB = tan a, and so the amounts of simple shear in layers 1 and 2 can now be simply deduced. Figure 19.10 provides a Mohr dia gram solution of the simple shear partitioning, comparable to the geometric modelling in Fig ure 19.7, but now taking V = 10. Layer 1 strain Changes from active to pallive folding: fold 'flattening' and partitioned 'flattening' cannot here be taken as approximately zero. Calculations above showed that for a t2 = 0.5 multilayer (equal thickness layers), the viscosity ratios (to the bulk) for layers 1 and 2 were 5.5 and 0.55, respectively. This means (also equa tions (19.26) and (19.27)) that 'V1 = 0.18tan a, and 'V2 = 1.82tan a. This is shown in Figure 19.10(a) for a = 45\u00b0, and the Mohr circles for layers 1 and 2 drawn accordingly. The resulting strains (Figure 19.10(b)) are: layer 1, 51 = 1.08, 53 = 0.92 and e = 40\u00b0 (~= 50\u00b0), and layer 2, 51 = 2.28, 53 = 0.44 and e = 22\u00b0 (~ = 68\u00b0). The latter are not greatly different from the end member geometric model (Figure 19.7(d)), where for layer 2, 51 = 2.4, 53 = 0.41 and ~ = 67.5\u00b0. General model for deformation partitioning in buckle fold limbs A comparison of the algebraic treatments, with or without the viscosity considerations, sug gests that the simple end-member geometric model may serve as a good approximation for folding deformation in bilaminate multilayers",
            " If 'homogeneous flattening' cannot be accepted, is there a form of 'flattening' that might operate as a late stage of folding or fold modification, but which is partitioned? The next section will consider modelling of parti tioned flattening of folds, according to the prin ciples of deformation partitioning in folds considered earlier, and obeying the strain refraction principles in Treagus (1983, 1988). Partitioned flattening is treated according to the same principles as the deformation partitioning controlled by viscosity treated earlier (Figure 19.10). In that case, the bulk shear strain (-YB) parallel to layering was set at tan (x, according to the model of bulk similar folding. This was then partitioned in bilaminate multilayers in the competent and incompetent layers, as different amounts of simple shear, according to equa tions (19.26) and (19.27). In the present case, however, there will be two components of the deformation (Figure 19.11) (Treagus, 1983, 1988), which together will make up the vari able deformation from layer to layer: (a) A layer-parallel stretch component will homogeneously affect all the layers",
            "34) This bulk layer-parallel shear strain can be considered as a simple shear component which is then partitioned unequally among the compe tent and incompetent layers in the bilaminate, in inverse proportion to the viscosity. This is identical to the model introduced earlier for deformation partitioning in folding which included viscosity. Restating expressions (19.26) and (19.27) for 'Yl and 'Y2 in terms of their ratio to 'YB: 'Y/'YB = 1/[1 + t2(V - 1)] 'Yi'YB = V/[l + t2(V - 1)]. (19.35) (19.36) These proportions of layer-parallel simple shear were fully discussed and illustrated earlier (e.g. Figure 19.10). As before, where V ~ 50, 'Y/'YB = 0 'Yi'YB = I/t2 (19.37) (19.38) and the partitioning can be considered simply in terms of the incompetent thickness propor tion (e.g. Figure 19.7), as for the geometric modelling earlier. It will be apparent from the examples given below that the sense of this layer-parallel shear component is the same as the sense of simple shear for buckling-related deformation: i.e. dextral on left-dipping limbs and sinistral on right-dipping limbs (see Figure 19.7). Combining the strain components: partitioned flattening The effects of an equal component of layer parallel stretching (pure shear) and different components of layer-parallel simple shear across layers combine to make different defor mations in competent and incompetent layers (Figure 19",
            " This analogous case to the high-contrast sys tem, but with V = 10, is show in Figures 19.15(b) and 19.16(b) (see also Figure 19.6, curve 10). The deformation partitioning curves, 1 and 2, for this example, involve noncoaxial strain superposition in the competent as well as the incompetent layers. The three folding stages are distinguished as before. Stage 1 is considered as a homogeneous layer-parallel shortening of S3 = 0.78, up to ex = 10\u00b0. Stage 2 of active buckling from 10\u00b0 to 45\u00b0 involves some deformation in the compe tent layers according to Figure 19.10 (This is the model that includes viscosity terms.) This deformation has been added to Stage 1 to pro duce curve 1 in Figure 19.15(b) by Mohr con structions. Curve 2 is close to curve 2 in Figure 19.15(a). For Stage 3, the curves are again compared for buckling-related partitioning and parti tioned flattening. For competent layers (Figure 19.15(b), curve 1), the two curves are less distinct than for the previous example (V = 50), because of the combined effects of a greater initial shortening, weak buckle-related straining (simple shear) and the noncoaxiality of the superposition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002512_0954407971526362-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002512_0954407971526362-Figure3-1.png",
        "caption": "Fig. 3 (a) A tight side and (b) a slack side partially meshed tooth",
        "texts": [
            " Keywords: power transmission, timing belts, failure analysis, tooth root cracking NOTATION Fi land friction force at fully meshed pitch i F, N tooth friction and normal contact load Kt fully meshed belt tooth stiffness Kp tooth stiffness in the partial meshing model Kb belt cord stiffness Nf number of fully meshed teeth Pb unstretched belt pitch length Pp pulley pitch measured at the cord line Qi circumferential tooth load at fully meshed pitch i Rp, dRp pulley radius and pitch line differential Rc radius at the cord line TG cord tension at G (see Fig. 3a) Ti, T 9i belt cord tensions at pitch i Ts slack side tension Tt tight side tension \u00e3 friction angle \u00e8a geometric angle of wrap \u00e8e,f angular extent of land contacts in partially meshed tooth model \u00e8g angular extent of a fully meshed tooth\u00b1groove contact \u00e8h,i,j,k hinge angles in partially meshed tooth model \u00e8l angular extent of a fully meshed land contact \u00e8n,i pulley surface outward normal direction in partial meshing model \u00e8p angular extent of one pitch on pulley \u00e8r angular variable in partially meshed tooth model (see Fig. 3) \u00e8s angular position of slack side partially meshing groove \u00e8t angular position of tight side partially meshing groove \u00e8u,v tooth seating angles in the tight and slack sides (see Fig. 3) \u00ebi tooth deflection at fully meshed pitch i \u00ec belt=pulley sliding friction coefficient Timing belts, originally developed with trapezoidal tooth forms for synchronous motion transmission, are now developed with curvilinear tooth forms to the stage that their torque transmitting capacity matches that of vee belts of the same size (1). Their service life may be limited by wearing away of the protective fabric that covers the rubber teeth and belt land regions, or by failure of the fabric at the tooth roots, or by other mechanisms such as separation of the fabric cover from the belt or failure of the tensile loadcarrying cords or by cracking of the back cover (2\u00b14)",
            " If Ti and \u00ebi are given, the system of equations (3) to (9) enables Ti 1 and \u00ebi 1 to be calculated for given belt properties Kb, Kt and \u00ec, pulley radius Rp and pitch line differential dRp, and pitch difference (Pp \u00ff Pb). In the context of this paper, repeated application of equations (3) to (9) enable \u00eb and T9 at the last full mesh tooth Nf to be calculated from \u00eb1 and T1 at the first full meshed tooth. Values of \u00eb1 and T1, and \u00eb and T 9 at the last full mesh tooth act as boundary conditions to the partial meshing analysis. Figure 3a represents an approximation to the geometry of a partially meshed tooth at the tight side. A part FG of the cord in the belt land, subtending an angle \u00e8f at the pulley centre, is wrapped round the pulley. The part GH is assumed to be straight, in the direction of the tangent to the pulley at G. The back of the belt tooth, HI, is also assumed to be straight. It is further assumed, as an approximation, Proc Instn Mech Engrs Vol 211 Part D D04395 # IMechE 1997 that there is a frictionless hinge at H, so that the direction of HI can differ from that of GH by \u00e8h. Similarly a hinge at I allows the direction of HI to differ from that of Tt by \u00e8i. With these simplifying assumptions of the cord path, and knowledge of the pulley groove and belt tooth profiles, the interference between the belt tooth and pulley groove can be calculated. Figure 3a also shows an element dNi and dFi of the distributed contact force between the belt tooth and pulley groove. If it is assumed that this is proportional to the interference, three equilibrium equations (two force and one moment) can be developed from the geometry equations. Similarly, three equilibrium equations can be set up for the slack side (Fig. 3b), involving hinge angles \u00e8j and \u00e8k. The following paragraphs show how six equilibrium equations can be set up for the six unknowns \u00eb1, T1, \u00e8h, \u00e8i, \u00e8j and \u00e8k, and solved to determine the belt path and loadings. It is chosen to describe the pulley groove and belt tooth profiles in an x\u00ffy coordinate system with origin at the intersection of the centre line of the partially meshing pulley groove and the pulley pitch circle of radius Rc, as illustrated in Fig. 3a and b. y is the outward radial direction and x the circumferential direction as shown. This choice is made because the belt tooth centre Ot on the cord line should settle close to the origin of this coordinate system in a fully meshed state. First of all the position of Ot on the tight side is determined by following the path of the belt cord from the point G: xOt \u00ffRc sin \u00e8r lGH cos \u00e8r lHI 2 cos (\u00e8r \u00ff \u00e8h) (10) yOt Rc(cos \u00e8r \u00ff 1) lGH sin \u00e8r lHI 2 sin (\u00e8r \u00ff \u00e8h) where, from loop equations \u00e8r \u00e8p \u00ff \u00e8g 2 \u00ff \u00e8f (11) \u00e8f \u00e8p \u00ff \u00e8t \u00ff \u00e8g 2 \u00ff \u00e8i \u00ff \u00e8h and the lengths lGH and lHI take into account the stretching of the cord as described in Appendix 1",
            " Inputs to the calculation are the operating conditions of tight and slack side belt tension (obtained from the transmitted torque and total belt tension), the angle of wrap on the pulley and the number of teeth on the pulley; belt geometry conditions of belt pitch length, the difference between the pulley and belt pitch measured at the cord line and the pitch line differential (measured between the cord line and the pulley surface) and the groove and tooth profiles; and the belt stiffness and friction properties. It is further specified whether the calculation is to be for a driving or driven pulley: in the full mesh part of the contact this is needed to fix the direction of the land friction forces [equations (4) and (9), \u00e4 1)]; in the partial mesh regions, it determines whether the instantaneous views, for D04395 # IMechE 1997 Proc Instn Mech Engrs Vol 211 Part D example in Fig. 3, are to be regarded as views of teeth entering or leaving contact. Figure 3 represents driven pulley contacts if the pulley is imagined as rotating clockwise and driving pulley contacts if anti-clockwise. The calculation proceeds by selecting an initial value \u00e8t of the pulley angular position, developing the six tooth equilibrium equations (Section 2.3) and solving for the six unknowns using a minimization of residuals technique, the Powell optimization routine to be found in the National Algorithm (NAG) library (9). The method requires an initial guess: Tl is initially taken to be Tt and the other five variables are set to zero",
            " This procedure of following the pulley rotation is not only efficient with respect to choosing the initial guess, it is essential for determining the size and direction of the contact friction forces [\u00e4Fi in equation (13)]. The direction of motion of each element on the belt tooth surface is tracked, regarding the tooth as a rigid body: that is to say motion associated with the tooth contact deformation is neglected. The direction is calculated from the motion of the tooth centre plus rotation about the centre and requires the position of the tooth centre and the tooth angular orientation from the previous increment to be known. At each pulley contact element, (xp, yp)i in Fig. 3, the direction of motion of the belt tooth relative to the pulley normal, \u00e3 i , is obtained. It is interpreted as a friction angle: in equation (13) \u00ec i tan \u00e3 i if tan \u00e3 i < \u00ec (15) \u00ec i \u00ec if tan \u00e3 i > \u00ec and the direction of the friction force opposes the projection on to the contact plane of the direction of motion. Meshing and unmeshing calculations for driving and driven pulleys have been carried out for curvilinear toothed belts with the profile known as HTD1y (10) and are reported in Section 4",
            " A more comprehensive account of these experiments will be published on another occasion. Figure 7 presents the entry and exit tooth loads calculated from the partial meshing model for the same conditions as in Fig. 6, taking Kp to be 90 N=mm2 (a sensitivity analysis varying Kp from 90 to 180 N=mm2 showed small variations of loads with Kp, but not large enough to consider further). Force is plotted against pulley rotation. The origin for pulley rotation has been shifted from the theoretical measures \u00e8t and \u00e8s (Fig. 3) to match the experimental pulley rotation positions when Fx and Fy 0. The theoretical force variations are qualitatively like the experiments: the tangential Fx is greater than Fy at driving and driven entry; Fy is greater than Fx at driving exit; Fy falls to zero more rapidly than Fx at driven exit. The trends in rates of change of forces with pulley rotation are also qualitatively similar between theory and experiment: at driver entry and driven exit the ratios of Fx to Fy change with pulley rotation",
            " It only allows one pitch at entry and one at exit to be in partial mesh. This does not occur experimentally. Experiments show that it can take up to two pitches of rotation to seat a belt tooth and even more in some low-tension driven entry conditions. However, with this exception, the characteristics of relative force variation predicted theoretically are sufficiently in line with experiment to encourage further consideration of theoretical predictions. Figure 8 shows, for the same conditions as Fig. 7, the hinge angle variations \u00e8h, \u00e8i, \u00e8j, and \u00e8k (Fig. 3) with pulley rotation. In this case rotation is described by the angular values of \u00e8t and \u00e8s. At driver entry, \u00e8h is initially greater than \u00e8i but a cross-over occurs as meshing develops. At driven exit, \u00e8h and \u00e8i have a large difference and \u00e8i is even negative for a portion of the unmeshing cycle, as a result of friction forces holding the belt tooth in the pulley groove. At driver exit and driven entry \u00e8j and \u00e8k are much closer in their values than are \u00e8h and \u00e8i at driver entry and driven exit",
            " A reduction of 0:05 in \u00d8 results in a ten-fold increase in life when tooth root cracking is the cause of failure. Although the partial meshing analysis has given a unifying measure of root strain, its predictions of force build-up during partial meshing do not agree quantitatively Proc Instn Mech Engrs Vol 211 Part D D04395 # IMechE 1997 with experiments, although qualititive patterns of variation can be seen (Fig. 7). The assumption of a belt tooth that maintains a straight back during meshing and is joined to the belt lands by frictionless hinges (Fig. 3) is obviously an over-simplification. It is also an over-constraint to insist that at entry and exit to a pulley only one tooth can be in partial mesh. For all these reasons, work is continuing both to improve the model, relaxing some of its constraints, and to develop alternative, finite element models of partial meshing, against which to calibrate the improvements. Previous work (6) had concluded that the stiffer a tooth, the better, as far as resistance to tooth root cracking is concerned. The present work confirms this (Fig",
            " H. C., Coutsoucos, A., Dalgarno, K. W., Day, A. J. and Parker, I. K. Life prediction of automotive timing belts. Proceedings of International Conference on Motion and Power Transmission, 1991, pp. 376\u00b1381 (Japanese Society of Mechanical Engineers, Tokyo). 8 Johnson, K. L. Contact Mechanics, 1st edition, 1985, Sec. 4.3 (Cambridge University Press, Cambridge). 9 National Algorithm Library (NAG) routine C05NBF. APPENDIX 1 Belt cord stretching in partial meshing The cord tension in the belt land (Fig. 3a) varies from the value T1 at F to a value TG at G and is then constant over the length GH. An adaptation of the full mesh modelling [equations (3) and (4)], gives TG as TG T1 exp (\u00e4\u00ec\u00e8f ) (19) A further adaptation [equation (9)] gives the stretch of the belt land dl as dl Pp Pb Kb \u00e8l \u00ff \u00e8f \u00e8p TG TG\u00e4 \u00ec\u00e8p [1\u00ff exp (\u00ff\u00e4\u00ec\u00e8f )] ( ) (20) If the unstretched belt land length is l, and recognizing that the loading of the first tooth in full mesh causes the partially meshed land to be out of register with the pulley land by \u00eb1, D04395 # IMechE 1997 Proc Instn Mech Engrs Vol 211 Part D lGH l dl \u00ff \u00eb l \u00ff Rc\u00e8f (21) The cord tension above the tooth varies from TG at H to the tight side tension Tt at I",
            " In adapting the full mesh equations as above, there is an implicit assumption, in locating the position of the hinge H, that there is no backlash of the belt tooth in the pulley groove. APPENDIX 2 Partial meshing belt tooth=pulley groove geometry relations In this work, the pulley groove and belt tooth profiles are defined numerically by the coordinate data sets (x9p, y9p)i, (x9b, y9b)i, i 1 to n, referred to the coordinate systems Ox9p, Oy9p; Ox9b, Oy9b as illustrated in Fig. 16. The transformation to the coordinate system Ox, Oy (Fig. 3) is achieved as follows for the tight side, with similar expressions for the slack side (\u00e8v replacing \u00e8u): xp,i x9p,i yp,i y9p,i \u00ff dRp xb,i xOt x9b,i cos \u00e8u \u00ff (y9b,i \u00ff dRp) sin \u00e8u yb,i yOt x9b,i sin \u00e8u (y9b,i \u00ff dRp) cos \u00e8u The profiles are regarded as n\u00ff 1 linear segments, joining points i and i 1, i 1 to n\u00ff 1. A tooth=pulley interference assessment is carried out for every pulley surface segment. The normal to the pulley segment is constructed, passing through the point [(xp,i xp,i 1)=2, (yp,i yp,i 1)=2)], with gradient \u00ff(xp,i 1 \u00ff xp,i)= (yp,i 1 \u00ff yp,i)"
        ],
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    },
    {
        "image_filename": "designv11_31_0002406_s0378-4371(99)00282-4-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002406_s0378-4371(99)00282-4-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic of a test sphere (diameter ) in a structure of random thin rods. (b) Excluded volume Vex (2) of the sphere and one rod. Note that Vex is independent of the rod orientation.",
        "texts": [
            " The orientationally averaged excluded volume of two randomly oriented spherocylinders with respective diameters ; D and lengths \u2018; L is given by Onsager [6]: Vex = ( =6)( + D)3 + ( =4)( + D)2(\u2018 + L) + ( =4)( + D)\u2018L : (1) If one spherocylinder is a sphere (\u2018 = 0) and the other spherocylinder is a thin rod with a diameter D. , the excluded volume reduces to: Vex = ( =4) 2L+ ( =6) 3 for D /1 : (2) Note that the excluded volume in Eq. (2) is a spherocylinder formed by translation of the sphere with diameter over the length L of the thin rod (see Fig. 1). When the sphere centre is located inside the excluded volume, the thin rod intersects the sphere. The number Ns of such intersections experienced by a test sphere is therefore: Ns = Vex = ( =4) 2L(1 + (23 ) =L) ; (3) where is the average rod number density. Eq. (3) neglects all contact correlations: the intersections (or contacts) of rods with the sphere are taken to be statistically independent. Such random contacts will probably only occur for very thin, high-aspect ratio rods. Two limiting cases are the number of intersections or contacts for very long rods Ns = ( =4) 2L for L /1 (4) and the number of contacts for very short rods: Ns = ( =6) 3 for L ",
            " For a static isotropic thin-rod collection the assumption of random contacts has been made [3,4] in analogy with Onsager\u2019s second virial approximation [6] for thermal rods. One argument is that the surface fraction of contact area vanishes for L=D\u2192 \u221e, so contact areas reduce to point contacts. Whether such point contacts are indeed uncorrelated however, has not been rigorously proven yet. It should be noted that the experimentally observed [3,4,11] invariance in Eq. (20) strongly suggests that contact correlations for thin rods are weak, otherwise higher-order terms would be noticeble in experiments [3,4]. For such thin rods, intersections with a sphere as in Fig. 1A would be weakly correlated as well. The density of random, rigid thin rods which cage a sphere in three dimensions can be obtained from the rod\u2013sphere excluded volume, in combination with a numerical analysis of the contact distribution on the sphere. One prediction is that the caging density of bres is proportional to the square of the bre diameter. The essential assumption of random sphere- bre contacts in our approach is probably only strictly justi ed in the limit of in nite rod aspect ratio"
        ],
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    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure7-1.png",
        "caption": "Fig. 7. (a) Representation of the projected pattern PrP (ti) by Rm using the distances dqk calculated by Rm from the triangles like (ABC). (b) Generation of the projected pattern PrP (ti) using corridors C10; C20; C30; C40, in particular, using the distances dqk = [(dlm)2 +(drm)2 2(dlm) (drm) cos(x)]1=2: (c) Shows the generation of PPk and PrPk and (d) shows the generation of Lk.",
        "texts": [
            " Note that at the left side of the perceived robot, is the first corridor of and at the right side of the same perceived robot, is the last corridor of It is also important for each robot to have the ability of detecting, perceiving the shape, defining the directions and calculating the velocities of other moving objects in the same navigation space [5]. Generation of Traffic Priority Patterns The generation of traffic priority patterns requires the synthesis of the appropriate perceived patterns with main goals the isolation of two moving robots only in the same free subspace generated by a set of corridors. More specifically, a traffic priority pattern is generated by the synthesis of a perceived pattern and its corresponding projected pattern (see Fig. 7). The perceived pattern is the one generated by the main robot (as shown in Fig. 6), and the projected pattern is the one generated also by the main robot but it represents a view of the possible perceived pattern from the secondary robot\u2019s position. The pattern is not necessarily identical to the actual perceived pattern by the robot because of the CFN constraints [5]. The generation of the pattern is a product of the distances produced by triangles like (ABC). The synthesis of the and patterns is where denotes the composition of the two patterns expressed as the union of the corridors, which compose the perceived and projected patterns"
        ],
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    },
    {
        "image_filename": "designv11_31_0003840_jsvi.2002.5051-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003840_jsvi.2002.5051-Figure10-1.png",
        "caption": "Figure 10. Impacting surfaces meshed into sub-areas.",
        "texts": [
            " by locking the degree of freedom y1 using a grub screw fitted at the small end. The elements in each matrix were obtained by curve fitting of the experimental frequency response curves measured in each sub-system. After some impacts with low squeeze velocities, it was observed that the residual oil film stiffness can be neglected (Ko 0). Clearly, in this case no simple equation (as that for the first rig) could be derived to calculate the impact force. Instead, the lower half of the piston skirt surface was divided into small elements (Figure 10). By knowing the top and bottom skirt displacements and the profiles of the piston skirt and cylinder wall, the time history of the piston/cylinder clearance h(t) was determined. These time histories were used to solve the finite difference form of Reynolds\u2019 equation in cylindrical co-ordinates, giving as a result the impact force time history (FRe) in each section of the mesh. The connecting rod was connected to the crank-shaft with very reduced lateral clearance to prevent the piston moving sideways during the impact"
        ],
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    {
        "image_filename": "designv11_31_0003815_s0020-7225(99)00089-0-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003815_s0020-7225(99)00089-0-Figure1-1.png",
        "caption": "Fig. 1. Deformation of a micro-stretch particle.",
        "texts": [
            " Micro-stretch continuum can model polymeric liquid crystals with small linear chains or side chains and hydrophilic liquid crystal groups, liquid crystals with \u00afexible \u00aebers, spring-like suspensions, anisotropic \u00afuids and bubbly \u00afuids. A material particle P of these liquid crystals, in the natural state, at time t 0, is identi\u00aeed by its position vector X (or its material coordinates XK , K 1; 2; 3) and an orientation vector N (or by its components NK , in material coordinates) attached to P. The motion carries P to a spatial position x (or in spatial coordinates to xk, k 1; 2; 3) and N to a spatial orientation n (or nk, in spatial coordinates), at time t, Fig. 1: xk xk X; t ; nk vkK X; t NK ; 2:1 where and henceforth repeated indices denote summation over the range 1, 2, 3. I assume that x(X, t) and v X; t possess continuous partial derivatives with respect to XK and t, and det xk;K > 0 2:2 so that inverses of (2.1) are given uniquely by XK XK x; t ; NK XKk x; t nk: 2:3 I denote partial derivatives with respect to XK and xk by capital and minuscule letters following a comma, e.g., xk;K oxk oXK ; XK;k oXK oxk The two-point tensors vkK and xKk satisfy orthogonality relations vX Xv 1; det v 1= det X 1: 2:4 For convenience, I introduce v by vkK j vkK ; XKk 1 j vkK ; 2:5 where v is orthonormal, i"
        ],
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    {
        "image_filename": "designv11_31_0003168_s0261-3069(99)00070-9-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003168_s0261-3069(99)00070-9-Figure4-1.png",
        "caption": "Fig. 4. The use of laser cut tabs to support tooling islands.",
        "texts": [
            " The advantage of building horizontally is that the \u017dwaste from the cavity can be used to make the core if .a laser or similar is used for processing . Problem areas occur when islands or up stands are required. There are several potential solutions to this. \u017d .1. The use of tooling inserts as islands see Fig. 2 . 2. Locate from dowels; dowel holes can be cut into \u017d .the required laminates see Fig. 3 but require enough space to be used. 3. Secure the islands to the edge of the tool by using \u017d .tabs see Fig. 4 . The tabs are added to the CAD model and automatically cut during the laser process to add support to the island. This method automatically supports islands in the tool because any up stands are automatically supported within the vertical laminate, as demonstrated in Fig. 5. \u017d .From the candidate joining methods Table 2 several could be ruled out fairly quickly. v Mechanical fastening } unsuitable where cooling or heating channels are required. Problems with distortion at elevated temperatures"
        ],
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    },
    {
        "image_filename": "designv11_31_0003534_ccece.1994.405657-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003534_ccece.1994.405657-Figure2-1.png",
        "caption": "Figure 2. Voltage-limit ellipse and torque in the (id-iq) plane",
        "texts": [
            " 2-z - vs -t / U q ud = R, 1,) - w x 4 i , and i, =id i- ji U, =R,i,,+w,&i, +w,@\" It is clear from these equations that if we consider the i, = 0 strategy, the magnitude of the terminal voltage V, increases with increase in either the rotor speed or the q-axis current. Saturation of the current regulator occurs. at high speed. when for a given torque the motor terminal voltage V, approaches the maximum voltage VDU. Combining the equations (31). one can have an expression connecting id. io and V__ ils (31) I f w, and Vmu are given. this equation represents an ellipse in the ( I < - iq) plane as shown in figure 2 In this plane. the torque equation given by (4). are a hyperbolas Let us assume that we want to impose the q-axis current to obtain a torque given by the point A. Since this point is outside the ellipse. the system cannot reach it. The resulting current vector is then forced to diverge from the q-axis and reach point B, in order to remain within the ellipse boundaries [4]. The d-axis current becomes then negative. Moreover. when the PMSM operates in the fluxweakening repon. the q-axis inductance (Lq) IS not constan1 but varies depending on the q-axis current and the control performances are then automatically affectedt51"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002651_1.2889691-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002651_1.2889691-Figure1-1.png",
        "caption": "Fig. 1 A gear-pair system with a squeeze film damper",
        "texts": [
            " This is done by using Floquet's theory in conjunction with Hsu's method in evaluating the appropriate monodromy matrices. Then, numerical results are presented, illustrating the effect of gear mass unbalance on the stability of the system responses. These results are verified and comple mented by results from numerical integration of the equations of motion. Emphasis is placed on analyzing irregular response of the system, arising within forcing frequency ranges where the periodic response is unstable. Analysis Outline The model of the system examined is shown in Fig. 1. The interaction of gear-a with gear-b is modeled by an appropriate set of springs and dampers. The gears are supported by a bearing or by a connection to a shaft and their motion includes lateral and torsional components. The driving gear-a is supported by an SFD without centering spring. For this system, the equations of motion can be written in the classical matrix form: where Mq -t- Cq + ATq = f\u201e\u201e(t) + f\u201e,(q, q) q ( 0 = {u\"u\"ugu'^UyUo] (1) while M, C and K are the mass, damping and stiffness matrix of the system, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002322_tt.3020060106-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002322_tt.3020060106-Figure2-1.png",
        "caption": "Figure 2 Fresh discs",
        "texts": [],
        "surrounding_texts": [
            "A GL-4 pass level oil was formulated with 2.75 wt.% additive B, as per the recommendations of the manufacturer. This oil, as expected, could accept a load of 80 kg without any scuffing. The metal transfer in terms of weight loss or gain of the discs was also small up to this load level. Beyond this, a sudden large change was noticed, both in scuffing and in disc weight loss. A repeat run at the fail level confirmed this finding. The results are given in Table 4 (see p. 75). Similarly, the same additive was used to obtain an oil at GL-5 level. Here also at failure, sudden scuffing and metal transfer occurred. This was at a load of 140-160 kg with a clear pass up to 120 kg (see Table 5, p. 75). This gives an indication that there is a distinct transition between evaluating oils at GL-4 and at GL-5 level, and that it appears possible that one can use this method for GL5 oils as well. Further work is required to establish this. Tribotest journal 6-1, September 1999. (6) 73 lSSN 1354-4063 $8.00 + $8.00 74 Bisht and Singhal To demonstrate further the discriminating ability of this test procedure, additive B was blended at an intermediate level of 4.4 wt.%, which is a treatment level midway between a GL-4 and a GL-5 level oil. The results are given in Table 6. It is seen from this that the failure load is at about 120 kg, i.e., midway between the two oils previously evaluated. This has given further confidence in the ability of the test method to discriminate between these oil quality levels. Tribotest journal 6-2, September 1999. (61 74 ISSN 2354-4063 $8.00 + $8.00"
        ]
    },
    {
        "image_filename": "designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure1-1.png",
        "caption": "Figure 1. Helical symmetric constraint relationship: (a) 3D view; (b) top view",
        "texts": [
            " Contract grant sponsor: Overseas Research Scholarship, U.K. Contract grant sponsor: Bridon International Ltd, Doncaster, U.K. components are generally thin and long, and thus the proper use of helical symmetry can reduce the model size signi\u00aecantly.1,2, To make use of general helical symmetry, a basic sector must be chosen to have `helical matching edges', which means that there exist corresponding nodes on each edge, geometrically rotated by a sector angle ys and o set by a sector length zs (see Figure 1). To ensure the helically symmetric nature, if a sector angle increment dys and a sector length increment dzs are imposed, the `helical matching edges' must remain as `helical matching edges' after deformation. For general helical symmetry, the deformation relationship between the corresponding nodes n(r, y, z) and n0 r; y ys; z zs can be expressed as: Dr0 Dr 1 Dy0 Dy dys 2 u 0 z uz dzs 3 where Dr, Dy, uz and Dr 0;Dy0; u0z are the displacement components of node n and its corresponding node n0 in the cylindrical co-ordinate system, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003470_1.367166-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003470_1.367166-Figure4-1.png",
        "caption": "FIG. 4. A schematic diagram of the sample configurations for ~a! solid and ~b! liquid Cd0.96Zn0.04Te ~all dimensions in mm!.",
        "texts": [
            " The subsequent precompounded ingot was then grown from the melt using a commercial 17-zone VB growth furnace and \u2018\u2018mined\u2019\u2019 into samples that measured 1031035 mm3 in size. The samples were designed so that the thickness ~5 mm was oriented in either the ^100&, ^110&, or ^111& directions. One surface was lapped and the other chemical-mechanical polished to provide a reflective surface for the laser interferometer. They were inserted in 10 mm i.d. square quartz ampoules with quartz plugs ~to fill in the free volume! and sealed under 1026 Torr with a very small free volume to inhibit the vaporization of Cd during subsequent heating @Fig. 4~a!#. Ingots for liquid state measurements were prepared in the same manner, except that the polycrystalline ingot ~;350 g! was contained in a 30 mm i.d. quartz ampoule @Fig. 4~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: 129.120.242.61 On: Sat, 29 Nov 2014 12:55:07 Heating was accomplished in a programmable tubular furnace. The furnace was equipped with a temperature controller that was able to maintain the temperature to within 1 \u00b0C. The Cd0.96Zn0.04Te samples were supported by a Al2O3 support assembly. The laser source and receiver gained access into the furnace through small ~;4 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure10-1.png",
        "caption": "Fig. 10. Petrol Engine Suspension on Steel Springs",
        "texts": [
            " Mountings arranged with equal spacing from the principal axis are the better solution, as the same units in the same rubber can be employed and torque reaction will, in any case, always act with the same force (but in opposite directions) on the mountings, independent of the relative distances of the mountings from the aankshaft centre-line. A link fitted with bushes is used for fore-and-aft location on this underfloor engine, while excessive movement under shock load is prevented by buffers fitted to the chassis with an arm from the engine, which is not shown. The method of fitting adaptor brackets to each pair of mountings allows easy and quick fitting and removal of the engine complete with mountings. A very interesting application of steel springs to passenger car engine mounting is shown in Fig. 10. The main mountings are fitted only just in front of the plane containing the centre of gravity, so that there is hardly any load on the rear mounting. From all accounts this mounting arrangement works very satisfactorily and similar systems have been adopted for other cars on the European continent. The number of parts required for each mounting assembly is rather large but, on the other hand, a large equivalent static Proc Insrn Mech Engrs (A.D.) deflection (a in.) can be obtained by a low spring rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003607_026635119100600305-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003607_026635119100600305-Figure6-1.png",
        "caption": "Fig. 6.",
        "texts": [
            "316 Example: Fixing for silhouette ~; = 15\u00b0 and increasing successively the dimension ofeach sec tor, keeping e constant, the result will be ~; = l3\u00b030',~; = 9\u00b0 and ~~ = 7\u00b030' from the direct read ing of its angles. Then for a folding angle a = 30\u00b0, it will be: (Fig. 7) Analytically: tan ~; sin a = 0.535 For silhouettes supported on a horizontal plane - whose angular variation is 180\u00b0 - those of 6 sec tors are the most adequate, because they offer a good margin to make corrections and they can produce different types of profiles. Example: for a great raise silhouette the charac teristic central angle ~ should be greater than the others. If~; + ~; + ~; = 45\u00b0;~; = 22\u00b0,~; = 13\u00b0, and ~; = 10\u00b0 can be fixed (Fig. 6). The polygonal responds to an eliptic curvature whose successive centres are in the intersection of the perpendiculars to the concave edges drawn from each vertix -C'C\", 0'0\", F'F\", etc. On taking the silhouette to 8 sectors for the same angular variation of 180\u00b0 even if it approaches more to the envelope curve, its capacity of varia tion and the degree of rigidity will be also percep tively diminished, for, having rigidity directly proportional to the characteristic angle B, when ~ diminishes, the rigidity also diminishes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002403_1.2818522-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002403_1.2818522-Figure2-1.png",
        "caption": "Fig. 2 The inclined prop effect",
        "texts": [
            " The problem is discretised by defining a number of nodes along the length of the bristles and approximating all the forces on the bristle to point forces acting at the nodes. From the linear nature of the problem it follows that the principle of superposition may be used. For bristle bending in the orthogonal plane, in addition to the aerodynamic forces, frictional effects between contacting bristle rows, at the backing ring and at the shaft interface are also considered. A mechanism termed the inclined prop effect (Fig. 2), can, in addition to the aerodynamic forces, be responsible for Nomenclature A, B = viscous and inertial resistance tensors a, b = viscous and inertial resistance coefficients c = normal bristle deflection at the tip dr = build clearance D = shaft diameter e = unit vector E = modulus of elasticity F\\ = resistance force per unit volume / = moment of inertial / = bristle length k = coefficient of expansion for rotor M = bending moment p = static pressure p,, = downstream pressure p, = pressure ratio (pjp,,) p\u201e = upstream pressure P = inclined prop force r = radial co-ordinate R = axial reaction force at the backing ring edge S\u201e = tip force normal to bristle Sr = shaft reaction normal to surface of shaft t = torque T = friction force H = mean velocity vector x \u2014 distance along bristle length (from tip) y = normal bristle deflection z = axial co-ordinate a = coefficient of friction between the shaft and the bristle tips j3 = axial deflection of bristle at backing ring (see Fig. 2.) Sr = radial expansion of the rotor <p = bristle lay angle (0 degree for ra dial alignment) A = cohesion (friction) factor ju, = viscosity d = tangential co-ordinate p = density w = shaft rotation speed Subscripts e = effective j , i = bristle row j , location x = x, n = direction normal to the bristles in the r \u2014 9 plane s = direction aligned with the bristles in the r - 9 plane t = turbulent z = axial direction Journal of Engineering for Gas Turbines and Power OCTOBER 1999, Vol. 121 / 657 Downloaded From: http://gasturbinespower"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003758_0301-679x(89)90148-5-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003758_0301-679x(89)90148-5-Figure1-1.png",
        "caption": "Fig 1 Experimental apparatus.\" 1, rotor; 2, bearing housing; 3, tilting pad; 4, guide bar,\" 5, bearing housing of ball bearing; 6, ball bearing; 7, air bellows; 8, oil film",
        "texts": [
            " If the purpose of the experiment, however, is only to prove the fact that a destabilizing factor in tilting pad bearings exists, which leads to instability of the system or oil whirl (not oil whipping), then the experimental conditions can be relaxed. In this paper, the small-eccentricity condition of tilting pad bearings relies not upon the high-speed rotation of the rotor but upon the adjustment of the static load of the tilting pad bearing. For brevity, only the important details are reviewed here. As shown in Fig 1, the test rig is of inverse arrangement. A rigid rotor is supported symmetrically by a pair of high-quality ball bearings (75 mm in diameter) mounted in bearing housings. Through a flexible coupling and an accelerator, the rotor is connected to a dc motor which is steplessly adjustable. The tilting pad bearing to be tested is raised by eight guide bars of diameter of 6 mm and suspended at the centre of the rotor. Using a set of air bellows, the static load and the eccentricity of the tilting pad bearing can be adjusted over a large range"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002709_s0020-7683(98)00150-4-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002709_s0020-7683(98)00150-4-Figure1-1.png",
        "caption": "Fig[ 1[ The four cases of limiting boundary condition at the end of a member[",
        "texts": [],
        "surrounding_texts": [
            "Using a technique similar to that of Hete nyi \"0835# and taking an element dx of the pile in Fig[ 0 it may be seen that\\ for moment equilibrium\\ dM dx \u2212P\"x# dy dy \u2212Q\"x# 9 \"0# where P\"x# is the axial compressive force which is dependent on x\\ the distance along the pile\\ and Q\"x# is the shear force at a point x along the pile[ These variables can be written as M \u2212EI d1y dx1 \\ P\"x# P9\u2212fx and dQ dx k\"x#y \"1\u00d03# where EI is the ~exural rigidity of the pile member and is constant along its length in the present analysis\\ P9 is the force in the pile at the top of the pile \"x 9#\\ f is the friction per unit length of pile and k\"x# is the modulus of subgrade reaction[ f is assumed to be constant and k\"x# is assumed to vary linearly with x\\ the distance below the top of the pile\\ so that k\"x# k9\u00a6cx \"4# where k9 and c are constants for the foundation[ kl is de_ned as the maximum value of the sti}ness parameter which exists at the base of the pile at x l \"Fig[ 0#[ The non!dimensional parameters m and l are introduced such that m Pl P9 \\ l 0 kll 3 EI 1 0:1 \"5# where Pl is the load in the pile at the bottom of the pile \"x l#[ m represents the proportion of the buckling load which is supported at the base of the pile and l is the non!dimensional soil!sti}ness parameter[ In this way\\ piles completely supported by friction will have m 9 and end!bearing piles with no friction will have m 0[ It follows that f P9\u2212Pl l \"0\u2212m# l P9 \"6# Di}erentiating \"0# with respect to x and then substituting the variables from \"1#\u00d0\"4#\\ the following is produced EI d3y dx3 \u00a6\"P9\u2212fx# d1y dx1 \u2212f dy dx \u00a6\"k9\u00a6cx#y 9 \"7# If the variable j 0 k9\u00a6cl EI 1 0:3 \"x\u2212l# a\"x\u2212l# \"8# is introduced\\ then x j a \u00a6l \"09# It follows that dy dx a dy dj \"00# and\\ generally\\ dny dxn an dny djn \"01# The governing equation with respect to j can now be formed as d3y dj3 \u00a62 P9\u2212 fj a \u2212fl a1EI 3 d1y dj1 \u2212 f a2EI dy dj \u00a62 k9\u00a6 cj a \u00a6cl a3EI 3 y 9 \"02# Now\\ let P9 a1EI P9 z\"klEI# b \"03# Hence f EIa2 \"0\u2212m#b l9[4 \"04# and fl a1EI \"0\u2212m#P9 a1EI \"0\u2212m#b \"05# Also\\ let k9\u00a6 cj a \u00a6cl a3EI kl a3EI \u00a6 cj a4EI 0\u00a6gj \"06# where\\ g c akl \"07# and let G\"j# mb\u2212 \"0\u2212m#bj l9[4 \"08# Hence\\ the dimensionless governing equation becomes d3y dj3 \u00a6G\"j# d1y dj1 \u2212 \"0\u2212m#b l9[4 dy dj \u00a6\"0\u00a6gj#y 9 \"19# This is a fourth!order di}erential equation with variable coe.cients[ An exact solution is not available and\\ therefore\\ a power!series solution will be assumed[ The solution is of the form y s n 9 anj n \"10# and by substituting it into \"19#\\ the following recurrence relationship between the coe.cients an is produced an \u2212 mb\"n\u22121#;an\u22121 n; \u00a6 \"0\u2212m#\"n\u22122#b\"n\u22121#;an\u22122 l9[4n; \u2212 \"n\u22123#;an\u22123 n; \u2212 g\"n\u22123#;an\u22124 n; \"11# For any value of the parameter n\\ an may be written in terms of the _rst four terms in the series \"a9\\ a0\\ a1 and a2#[ Therefore\\ an is a linear function of a9\\ a0\\ a1 and a2\\ and so the general solution to the di}erential equation is y s 2 i 9 AiYi \"12# where Yi ji\u00a6 s n 3 anj n \"13# and for n \u00b3 3\\ an 0 if n i and an 9 if n i[ A9\u00d0A2 represent the four constants of integration[ To obtain a buckling load of the pile and the corresponding mode shape\\ the boundary conditions at the ends of the member must be speci_ed[ If rotation is fully allowed\\ an expression for the bending moment at the pile end\"s# must be obtained[ When displacement in the y!direction is fully allowed\\ an expression for the shear force is required[ The expressions for zero displacement\\ slope\\ bending moment and shear force with respect to the coordinate x are\\ respectively\\ y 9\\ dy dx 9\\ d1y dx1 9 and 0 d2y dx2 \u00a6 P EI dy dx1 9 \"14\u00d017# but\\ with respect to the coordinate j\\ they are\\ y 9\\ dy dj 9\\ d1y dj1 9 and d2y dj2 \u00a6G\"j# dy dj 9 \"18\u00d021# The speci_cation of the boundary conditions at the two ends of the pile yields four homogeneous equations\\ which can be expressed in a matrix equation\\ \u00f0M\u0141A 9 \"22# where M is formed using the following half!matrices to de_ne all four possible instances of limiting boundary conditions \"Fig[ 1#\\ with one half!matrix being evaluated at x 9 and one at x l^ \u00f0Mfixed\u0141 $ Y9\"x# Y0\"x# Y1\"x# Y2\"x# Y?9\"x# Y?0\"x# Y?1\"x# Y?2\"x#% \"23# \u00f0Mpinned\u0141 $ Y9\"x# Y0\"x# Y1\"x# Y2\"x# Y\u00fd9\"x# Y\u00fd0\"x# Y\u00fd1\"x# Y\u00fd2\"x#% \"24# \u00f0Mfree\u0141 $ Y\u00fd9\"x# Y\u00fd0\"x# Y\u00fd1\"x# Y\u00fd2\"x# Y\u00fd9\"x#\u00a6G\"j#Y?9\"x# Y\u00fd0\"x#\u00a6G\"j#Y?0\"x# Y\u00fd1\"x#\u00a6G\"j#Y?1\"x# Y\u00fd2\"x#\u00a6G\"j#Y?2\"x#% \"25# \u00f0Mno rotation\u0141 $ Y?9\"x# Y?0\"x# Y?1\"x# Y?2\"x# Y\u00fd9\"x#\u00a6G\"j#Y?9\"x# Y\u00fd0\"x#\u00a6G\"j#Y?0\"x# Y\u00fd1\"x#\u00a6G\"j#Y?1\"x# Y\u00fd2\"x#\u00a6G\"j#Y?2\"x#% \"26# and A K H H H H k A9 A0 A1 A2 L G G G G l \"27# The condition =M= 9 gives the eigenvalues corresponding to the buckling load of the pile[ A modi_ed sign count algorithm is used to _nd the eigenvalues which are expressed in terms of j \"West and Pavlovic \\ 0882#[ Hence\\ the values of the constants of integration A9\u00d0A2 relative to each other are obtained for a particular eigenvalue and the buckling mode shape is calculated[ \"A note should be made regarding computations as l : 9] clearly\\ for l 9 there is a singularity because then a 9 which leads to l : ^ however\\ the present algorithm works well for very small but _nite l \" for example\\ l \u00bc 9[9990#[# It is now convenient to introduce the following non!dimensional parameters\\ where the buckling force will be denoted as Pcrit] F k9 kl \\ u Pcrit PE \"28\\39# where PE is the Euler buckling load of a simply supported beam with no elastic supports along its span and is given by PE p1EI:l1[ u is the dimensionless buckling force as de_ned in Hete nyi \"0835#[ It would be expected that\\ for the _rst buckling mode of an end!bearing simply supported pile\\ u tends to one as the sti}ness of the supporting medium tends to zero\\ while for a pile which is built!in at both supports\\ u tends to four[ These results are predicted by simple Euler theory[ For the case of friction piles these limits no longer exist\\ but by using m 0\\ an end!bearing pile can be modelled in order to verify the proposed method[ Note that\\ if the applied load on top of the pile was eccentric \"or the pile was not vertical#\\ then this could be analysed by modelling the eccentric loading as a moment and:or shear force at x 9[ This could be accommodated by the vector in eqn \"22# no longer being a zero vector[ While this would not alter the problem of the determination of the limiting eigenvalues \"which is the principal object of the present work#\\ there would be no proper bifurcation point but a steady increase in de~ection which would rapidly tend to large values as the critical load was approached["
        ]
    },
    {
        "image_filename": "designv11_31_0002870_elan.1140050508-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002870_elan.1140050508-Figure1-1.png",
        "caption": "FIGURE 1. CVs of the carbon paste electrodes: (a and b) the plain carbon paste electrodes and (c and d) the CMEs. Electrodes were exDosed for 5 min to (a and c) 0.1 M KCI blank solution and (b and d) 1 x ion one. (Scan rate: 100 rnV/s.) M Cu(l)",
        "texts": [
            " A continuous stream of nitrogen gas was passed through the solution while measurements were being taken. Chemical accumulation of Cu(1) was carried out in a buffered preconcentration solution containing Cu(1) ion. The CME depositing the Cu(1) ion via complex formation was removed from the preconcentration solution, washed with distilled water thoroughly, and transferred to the separate measuring cell. After this, the stripping voltammograms were obtained in one having only 0.1 M KCI solution. RESULTS AND mscussroN Cu(I,l Ion Deposition and Electrochemical Behauior of the CMEs. In Figure 1, cyclic voltammograms for two plain carbon paste elecrrodes (a and b) and for two diddcontaining carbon paste electrodes (c and d) are shown, respectively. Where (a) and (c) are CVs from a blank solution without dipping an electrode in the solution having a test ion. (b) and (d) are CVs obtained after dipping an electrode in Cu(1) ion solution. There were no significant differences in the CVs between (a) and (c) over the potential range of +0.8 to -0.8 V (vs. SCE). The only difference was that the background current of the CMEs (Figure lc) was higher than that of the unmodified plain carbon paste electrode (Figure la)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002835_s0389-4304(99)00037-5-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002835_s0389-4304(99)00037-5-Figure2-1.png",
        "caption": "Fig. 2. Model of the delivery truck.",
        "texts": [
            " But even with these types of systems only points which are left of the envelope curve can be reached. The area in the lower left quarter of the diagram can, however, only be reached by the use of active systems. Such a system improves driving comfort and safety, it is true, but a disadvantage is the increased requirement of energy and the increased fuel consumption. The model of a delivery truck has been created with the simulation tool SIMPACK (`SImulation of Multibody Systems PACKagea). The model of the vehicle is represented in Fig. 2. The model consists of di!erent rigid bodies which are connected by joints and constraints. Driving torque and steering movements will be transferred to the model by forces and moments that are reacting to the di!erential or the steering wheel. All co-ordinates of the suspension and the steering system as well as all spring-, damperand stabiliser bar-values were chosen on the base of a real delivery truck. The weight distribution was also adapted from this vehicle. In general, four di!erent suspension systems can be distinguished (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002295_pime_proc_1995_209_154_02-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002295_pime_proc_1995_209_154_02-Figure2-1.png",
        "caption": "Fig. 2 Details of the FE mesh of the blade root and disc sector",
        "texts": [
            " The total number of degrees of freedom is over 30000 and 8-node and 20-node solid elements as well as 16-node transition elements (from 20-node to 8-node solid elements) are employed. The 20-node elements are applied in the highest stressed regions of the attachment (minimum neck sections of the root and disc as well as contact surfaces of hooks). For other less-stressed parts of the attachment, 8-node elements are applied. One layer of the transition 16-node elements is utilized in order to join 8-node and 20-node regions together. The elements are put into 11 layers parallel to the attachment disc mid-plane. The FE mesh details are shown in Fig. 2 for the attachment blade root and disc sector. The mesh is symmetrical with respect to the attachment vertical axis; however, the mesh details are shown only on one side of both attachment parts. The layout of %node, 16-node transition and 20-node elements within a pair of root and disc hooks are illustrated in Fig. 3. Note that the mesh density has been chosen to be assigned for long, multiple and expensive calculations. Moreover, the aim of these calculations is not simply a technological analysis of the actual stress of a real object itself (it may need even more dense division into finite elements)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003570_37.856182-Figure12-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003570_37.856182-Figure12-1.png",
        "caption": "Figure 12. State-space diagram: x1 versus x2 for negative values of Kc.",
        "texts": [
            " The first is composed of the equilibrium points that have| |x d1 1< (the inner points of the band). These equilibrium points have neutral stability independent of the value of the parameter Kc. The stability of the extreme points of the band changes, however, depending on the value of the parameter Kc. Thus, for negative values of Kc these equilibrium points are unstable. It is also known that there are no limit cycles for these values of Kc. The system behavior under these conditions is shown in Fig. 12 in a qualitative diagram of states, where states x 1 versus x 2 are depicted. On the other hand, the extreme equilibrium points are stable for positive values of the parameter Kc, but the system behavior varies depending on the magnitude of this parameter. In particular, as discussed in a previous section, no limit cycles exist if the value of Kc is small. The system behavior under these conditions is depicted in a state diagram in Fig. 13. The fact that a change in the stability of some equilibrium points has been produced, varying the parameter Kc, is a first change in the phase portrait, which occurs when the value of Kc becomes zero",
            " 15(b)], the band of equilibrium points re- 98 IEEE Control Systems Magazine August 2000 mains stable and the amplitude of its attraction basin is infinite, since there are no limit cycles surrounding it (phase portrait of Fig. 13). Finally, when Kc reaches a negative value [Fig. 15(a)], the extreme equilibrium points of the band become unstable. This implies that if a small disturbance causes the system to evolve toward the outside of the zone| |x d1 1\u2264 , the state variables will evolve away indefinitely from their equilibrium values (recall Fig. 12). It is worth noting how the conventional saddle-node bifurcation of Fig. 1 has been transformed into a more complex one, in this case due to the dead zone. It is very interesting to note that in the saddle-node bifurcation of periodic orbits, two limit cycles are born when Kc varies from the one of part b to that of part d in Fig. 15. The emergence of these limit cycles has two main differences with respect to the better-known Hopf bifurcation: 1) the limit cycles emerge with amplitude different from zero, and 2) the stability of the equilibrium point does not change"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002471_1.5058663-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002471_1.5058663-Figure1-1.png",
        "caption": "Fig . 1 . Illustration of screw feed powder feeding for laser cladding/alloying process.",
        "texts": [],
        "surrounding_texts": [
            "Powder feeder is used widely for laser surface treatment such as cladding and alloying. The stability of\npowder feeding is directly affecting the processing quality. This paper investigates the use of a pressure\nsensor for the continuous monitoring of powder flowrate and the incorporation of closed loop servo-control\nsystem for the on-line feedback control of powder flowrate. The stability of the powder feeding has been\nfound much improved by the new feeding system especially during warm up period (about 30 minutes). The\nmeasurement of of powder particle velocity and establishment of a dynamic model of the powder feeding\nprocess are also presented.\n1. INTRODUCTION\nPowder feeding has found many advantages over other techniques (e.g. preplaced powder process, wire feeding process) in laser cladding and alloying processes because of the increased efficiency and controllability. In these processes the stability of the powder feeder directly affects the processing quality such as unifonnity of clad/alloying thickness and dilution/surface layer composition. In most of current practice powder feeders are open loop operated without flowrate sensing. Off-line weighting (over 0.5 to lmin flow ) are often used for the determination of flowrate. For screw feeders (Fig. l), the mass flowrate is set according to the assumed fixed linear relationship between the motor speed and mass flowrate and precalibration is used before processing to determine this relationship for each materials and particle sizes. This may not be very reliable, since it assumes the prefixed relationship is not changing during processing. Fig. 2a shows an experimental result from such a feeder of the feedrate as a function of the motor speed (weight method was used in this test). Although a linear relationship exits, the actual magnitude of the . powder flowrate can be different for the same motor speed setting. This is further confirmed by an experiment shown in Fig . 2b where the powder flowrate was measured by weighing when the motor speed and gas supply settings were kept constant. A warm up time of about 30 minutes is shown. These experiments may not represent the instabilities for all powder feeders, but at least they demonstrated that open loop powder feeding could result in changes of powder flowrate even if the control settings are kept constant due to variations in the volume density of powders with time and levels of powder in the hopper. The consequence of this is the variation of clad/alloying composition due to dilution as well as the variation of clad/alloying track geometries. Therefore it is necessary for in -process monitoring and closed loop control especially when multiple hopper/feed is used for in-situ variable composition cladding and alloying. This paper presents the use of a pressure\nICALEO (1993)/965",
            "sensor for continuous powder flowrate sensing and closed loop control system for the control of powder flowrate on a screw feed pneumatically conveyed powder feeders.\n2. IN-PROCESS CONTINUOUS POWDER FLOWRA TE SENSING\nThe on-line powder flowrate sensing was achieved by using a compact pressure sensor attached to the powder pick-up as illustrated in Fig.3. The sensor can be placed anywhere\nbetween the gas flowmeter and powder delivery tube.\nFig.3. powder flowrate sensing arrangement.\nPm. Vm :m.ass flown.te\nThe sensing element of the pressure sensor is a 0. 1 \" square silicon chip with integral\nsensing diaphragm and four piezoresistors arranged in a bridge. When pressure is applied to\n966/ICALEO (1993)",
            "the diaphragm it causes it to flex, changing the resistance, which results in an output voltage\nproportional to the pressure when an excitation voltage is applied to the device. The\nsensitivity of the sensor is 6.67mV/p.s.i with lOV power supply. The response time of the\nsensor is 1ms. The sensor signal is further amplified and filtered followed by the following\nalgorithms using hardware electronics:\n(1)\nwhere V m is the final electrical voltage signal representing powder flow rate, M> 1 is the pressure detected when there is powder flow, M>0 is the pressure detected when there is no powder flow ( taken in by a memory circuit before powder delivery), \ufffd is the sensor\nsensitivity (from pressure signal to electrical signal including amplification) of the system.\nOne of the conditions for the sensing system is that a constant gas flow is supplied to the\nconveying tube through a flow meter orifice. This can be realised by ensuring that:\n(2)\nwhere P q is the up stream pressure and P d is . the pressure on the down stream side of the\nflowmeter. Under this condition the gas flow rate is not significantly affected by variations\nin the down stream pressure.\nThe basic principle of the flowrate sensing is that the gas will do work to deliver and\naccelerate the powders from the entrance of the delivery tube to the exit of the tube. Since\nthe gas pressure at the exit of the tube is atmospheric, the energy required is then generated\nby the gas pressure difference between the two points. Higher flowrate therefore requires higher pressure to deliver. If there is a height difference between the two points then the\ngravitational force should also assist or resist the mass delivery depending on which end is\nhigher. The quantitative analysis of this can be made by a energy balance of the gas at both\nends of the tube:\n(3)\nwhere M>1 is the gas pressure difference between the entrance and the exit of the powder\nconveying tube, Pg is the gas density, g is the gravitational acceleration, M1 is the attitude differences between the exit and entrance ends of the feed tube, L1 is the powder feed tube length, Cr is a friction factor, Ugm is the average (mean) gas velocity in the tube, Cd is drag coefficient, and Ugs is relative velocity between the gas and solid particles. The first term on the right hand side of this equation is the pressure drop due to elevation; the second term,\nthe friction; and the third term acceleration.\nWhen the gas flow is laminar (which is true when gas velocity is below 8m/s and gas tube diameter of less than 8mm) Cd = 14/Re and\u00b7Cr = 1 6/Re, where Re is the Reynolds number. Therefore Cr > Cd. Also since Ugm>Ugs\u2022 and L1 >> D1, the second term (the friction term)\nICALEO (1993)/967"
        ]
    },
    {
        "image_filename": "designv11_31_0003053_s0167-8922(98)80098-9-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003053_s0167-8922(98)80098-9-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the FMR noncontacting mechanical seal",
        "texts": [
            " The objective of this research is to develop techniques to detect and monitor contact between the rotor and the stator in a FMR noncontacting mechanical seal test rig in real-time. The instantaneous dynamic response of the rotor is measured using proximity probes. Decisions arc made based on a geometrical contact criterion, rotor angular response orbit analysis, or spectrum ana-lysis as derived from the proximity probe signals. 2.1. The test rig A seal test rig was built to study the dynamic behavior of a FMR noncontacting mechanical face seal [4]. The schematic of the noncontacting FMR mechanical face seal test rig is shown in Fig. 1. The rotor is flexibly mounted on a rotating shaft through an elastomcr O-ring. This allows the rotor to track the stator misalignment and move axially. A carbon graphite ring is mounted on the rotor through an elastomer O-ring. A groove is made at the rotor where the bottom of the carbon graphite ring touches the rotor face. The stator is fixed in the housing. The stator and the carbon graphite ring form the seal interface. The sl~fi is screwed into a spindle that is connected through two wafer-spring couplings to a motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002421_6.1995-1442-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002421_6.1995-1442-Figure5-1.png",
        "caption": "Figure 5: S l ider c r ank m o d e l",
        "texts": [
            " The same nomenclature t o the revolute hinge formulation is used. The sliding motion can be written as follows pareqt node Figure 4: Slide hinge geometry where p is the sliding distance (Fig.4). Variational form of Eq.13 is given as Simple mathematical manipulation gives the following vector form relation. Consequently the following relation is established between nodal variables and the independent degree of freedom. 4 Computat ional examples 4.1 Slider crank The model slider crank is shown in Fig.5. As shown in Fig.5, both slider and crank are composed of five elements connected with a weld hinge. Slider and crank are connected by a revolute hinge and the tip of the slider has a cylindrical hinge, which impose both rotational and sliding constraint. The tip of the crank is connected to a fixed point with a revolute hinge. At the nominal configuration, each revolute axis is oriented in the out-of-plane direction. The stiffness of both the slider and crank is 1277136000Kgmm2. Lengths of the slider and crank are 113mm and 70mm, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002616_0020-7403(96)00057-4-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002616_0020-7403(96)00057-4-Figure4-1.png",
        "caption": "Fig. 4. Transformation of a CWR process into a rod reducing process.",
        "texts": [
            " These solutions have been obtained on the basis of various engineering methods of analysis, such as energy methods and the upper-bound method. In Ref. [10] the author made an attempt to use the slab method to determine qm, but the verification revealed that the results obtained through this method were too small. The analysis carried out here assumes that the mean unit pressure in the CWR process is equal to the pressure in the reduction (extrusion) process of a round bar from a substitute diameter dz to the diameter d (equal to the diameter of the product after rolling) (see Fig. 4). Thus we have the notion of the substitute reduction of a portion 6~ = d J d . T h e energy method Because of the axial symmetry, the process of reduction through a conical die (Fig. 5) can be considered in the cylindrical co-ordinates {r, z, v). The work performed by the external force Qo over the distance Azt is given by: 2 2 dz - d . W z = Q o A z l = qm sin :~z~ ~ ZXZl. (2) But the total work of plastic deformation, assuming that the Haar-Karman 's postulate of equality of two principal stresses is fulfilled, can be described by the following expression: W p = T a o l n (Aza-AZ2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure2-1.png",
        "caption": "Figure 2. Geometric model for circular bar problem: (a) extraction of basic sector; (b) characteristic geometric elements on the basic sector",
        "texts": [
            " A commercial \u00aenite element analysis programme (ANSYS) was used throughout. The elements used for the structural discretization are brick elements de\u00aened by eight nodes having three degrees of freedom on each, i.e. translations in the x, y and z directions. The material properties are assumed as follows: Young's modulus, E 188 GPa Poisson's ratio, 0.3 To verify the algorithm and its implementation, the problem of a circular bar subjected to tension and twisting is analysed \u00aerst. A helical portion of a slice of the bar is chosen as the basic sector as shown in Figure 2. F and M are the induced axial force and moment generated as a result of applying the prescribed axial displacement or twist, respectively. The radius R 1 mm and the angle ac 608 is used. The slice thickness zs is 0.1R. Three models with helical angles a of 458, 608 and 758, respectively, were analysed. Figure 3 shows the \u00aenite element mesh of the model, with only 12 brick elements being used. Only one element division along the axial direction is needed to include helical e ects, due to the accurate boundary conditions. The corresponding nodes in the helically symmetric corresponding cross-sections A and A0 shown in Figure 2(b) satisfy the general helical symmetric relationship. The four radial edge lines L1 , L 0 1, L2 and L02 are initially straight and perpendicular to the symmetric axis. They should remain straight and perpendicular to the symmetric axis after deformation. The corresponding nodes on the sets of corresponding lines (L1 , L 0 1 and (L2 , L 0 2 should retain the same radial deformation pattern. The angle ac will remain unchanged on both top and bottom cross-sections after deformation. Table I summarizes all the boundary conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure6-1.png",
        "caption": "Figure 6. Characteristic geometric elements on the basic sector of wire rope strand",
        "texts": [
            " In this Figure F andM are again the induced axial force and moment of the strand, respectively. Figure 5 shows a typical \u00aenite element mesh of the model. Since the stresses vary rapidly in the vicinity of the local contact region, a much \u00aener mesh was used therein (shown in the detailed view). Contact between the core wire and the helical wires has been simulated using contact elements, which can simulate general surface-to-surface contact with coulomb friction sliding. The friction coe cient was set as 0.115. Figure 6 shows all the constrained nodal location on the arti\u00aecial boundaries. The boundary conditions are the same as in the previous example (cf. Table I). The two extreme cases of either \u00aexed end (G 0) or free end (twist moment M 0) were analysed. A strand axial strain of 0.004 was applied in increments of 0.001 in the analysis. The Copyright # 1999 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng, 15, 435\u00b1443 (1999) results have been compared to those obtained using Costello's theory,3 and the experimental data reported by Utting and Jones4,5 in Table III"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002458_bfb0032164-Figure2.1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002458_bfb0032164-Figure2.1-1.png",
        "caption": "Fig. 2.1. Inverted pendulum on a cart",
        "texts": [
            " , rn], ri E N, we define the sets 79(r) = {A = diag(51I~x,...,Snlr~), 15/E R } , B ( r ) = { B = d i a g ( B 1 , . . . , B n ) , [ B, E P J ' \u00d7 r ' } , S ( r ) = { S E B ( r ) l S i > O , i = l , . . . , n } . (1.3) Finally, the symbol Co{v1,.. . ,VL} denotes the polytope with vertices vl, \u2022 .., VL, and for P > 0 and a positive scalar )~, Sp A denotes the ellipsoid ERA = {X [ xT p x <_ )~}. 2. T h e i n v e r t e d p e n d u l u m e x a m p l e The inverted pendulum is built on a cart moving in translation without constraint (see figure 2.1). Our goal is to stabilize the it in the vertical position, with an uncertain but constant weight m. In fig.2.1, ~ is the position of the cart, 0 is the angle position of the pendulum with the vertical axis, u is the control input acting on the cart translation and w is the disturbance. We seek to control the angle and the translation position, 0 and ( . The nonlinear dynamic equations of the system are: [tacos 2 0 - 4 (M + rn)]0 [mcos 2 0 - ] ( M + m)]~ c] = ] r = mcosOsinOd 2 - ~ ( M + re )s in0 cos ou(t) + = m g s i n O c o s O - 4 m l d 2 s i n O - ~u(t) (2.1) We assume that the mass m is constant and unknown-but-bounded: m E [m 0 - Am , m0 -t- Am], where too, A m are given"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003931_jsvi.1999.2484-Figure13-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003931_jsvi.1999.2484-Figure13-1.png",
        "caption": "Figure 13. (a) Con\"guration of the typical belt tensioner, (b) schematic diagram of the two-belt span modelled as axially moving beams passing through a tensioner.",
        "texts": [
            " Substituting the solution into equations (34)} (41) and equation (11), the vibrational power #ow through the axially moving belt can be obtained from equation (19). 2.4.2. \u00b9ensioner condition The reduction of the vibrational power #ow through belt}pulley systems is of interest in many practical \"elds because of the concomitant vibration and noise problems in pulleys, tensioners, and their structural support systems. The tensioner sustaining the appropriate tension in the belt}pulley system also transfers the vibration power. The physical condition of the belt}pulley system with a tensioner as depicted in Figure 13(a) will be called the tensioner condition. In Figure 13(b), a schematic diagram is illustrated for the theoretical modelling of vibration power transmission in the belt}pulley system with a tensioner. The boundary conditions speci\"ed for the tensioner are as follows: w 1 (0, t)\"w 0 ( jqu p t), L2w 1 Lx2 K x1/0 \"0, w 1 (l 1 , t)\"w 2 (0, t), (42}44) L2w 1 Lx2 K x1/l1 \"0, L2w 2 Lx2 K x2/0 \"0, (45, 46) EI L3w 1 Lx3 K x1/l1 !EI L3w 2 Lx3 K x2/0 \"m L2w 1 Lt2 K x1/l1 #c 2 Lw 1 Lt K x1/l1 #k s2 w 1 (l 1 , t), (47) L2w 2 Lx2 K x2/l2 \"0, w 2 (l 2 , t)\"w 0 ( jqu p t)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure22-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure22-1.png",
        "caption": "Fig. 22. Representation of a traffic flow for six moving robots with resolved main conflicts.",
        "texts": [
            " This mean that the robot knows the time required to cross the region, and in the latter case it took more time, At this point the robot analyzes the traffic flow perceived by itself and modifies its traffic path for a future cross of the same region under a traffic flow similar to More specifically, it follows the next algorithmic steps: 1) Check each word , for patterns . 2) Search for possible patterns , to replace in a word . 3) Replace the first with an in . 4) Rearrange the word into a new one , which includes the affects on the other patterns due to replacement ( instead of ). 5) If the new word includes less number of patterns then use it in the new , else go to 2 to replace the next with an in . 6) If the new overall traveling time is less than the original then proceed else no changes Thus, Fig. 22 shows the new modified traffic path. The new traffic flow extracted by is represented by the following words: where Thus, the new traffic flow includes less conflicts and no significant delays for the robot In this paper, the formal modeling of a generic traffic priority language was presented. The traffic priority language is a useful methodology for autonomous robots avoiding collision in unknown navigation space. The development of the traffic language (written in C) was based on the good representation of the current free navigation space of each robot, the detection of other moving objects (robots) in the same space and the development of the simple traffic priority patterns for each robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002860_s004070050024-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002860_s004070050024-Figure4-1.png",
        "caption": "Figure 4",
        "texts": [
            " I shall call the central spherical region, whose cross-section is the circular unshaded region in Figure 3, the core and refer to the surrounding part, whose cross-section is the shaded lunules, as the external region. Newton takes the earth to be uniformly dense and so the amount of matter in any region is proportional to its volume. For the reason given above, the tidal forces in the spherical core cancel in pairs and so produce no net effect. However, because of the tilt of the axis NS to AC, there are particles in the external region to the left of 5 and above the plane of the ecliptic, such as P1 in Figure 4, that have no corresponding particle on the right. The corresponding forces, such as f1, give a net force to the left on the part of the earth above the ecliptic. Similarly, forces such as f2 give a net force to the right on the part of the earth below the ecliptic. The effect of these forces is to produce a turning effect, or torque, tending to turn the earth about an axis through C, perpendicular to the plane of the paper, bringing NS in line with AC. Below, I shall refer to this axis as Cperp",
            " He was therefore not able to deduce correctly the angular motion of the earth about its centre of mass under the torque produced by the external forces. Because Newton did not have the ideas of rigid body dynamics needed to explain correctly the movement of the earth\u2019s rotation axis, it is of interest to consider what his method actually was, and to see where it goes astray in the light of later ideas. Newton appears to have thought of the precession as a motion produced primarily in the external part of the earth (shaded in Figure 4), and that this motion was then modified by having to be \u201cshared\u201d with the spherical core to which it was rigidly attached. His first step is to suppose all the \u201cparticles\u201d making up the external part of the earth redistributed so as to form a uniform spherical ring about the equator, as shown in Figure 5. As we noted above, he shows, in Lemma 2, that this will increase the \u201ctotal force or power\u201d of the tidal forces to turn the earth about the axis Cperp (BB\u2032 in Figure 5) by the factor 5/2. He then imagines the spherical core removed so that the spinning ring is in orbit on its own"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003843_02678298908026435-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003843_02678298908026435-Figure9-1.png",
        "caption": "Figure 9. Schematic diffraction pattern and structure for Sc phase.",
        "texts": [
            " The pattern of IIIa (see figure 8 (a) ) is that of a S$ phase for which the layers tend to be oriented parallel to the direction of stretch, but the mesogenic cores are oriented locally along the helix. Due to the cylindrical symmetry around the helix axis the wide angle diffuse reflection is nearly uniform. The pattern given by the fibre of polymer IIIb (figure 8 (b)) is typical of a S,* phase with the mesogenic cores oriented along a single direction (the direction of stretch) as inferred from the wide angle diffuse crescent (see figure 9) [S]. The smectic layers are distributed on a cone. The intersection of this cone with the Ewald sphere consists of the two lines on which the small angle reflections are located. The fact that the mesogenic cores are oriented along a single direction means that we have untwisted the helix of the S$ structure. The two polymers (IIIa and IIIb) do not differ in the symmetry of their phases (both are SE) but rather by their viscoelastic properties. The small angle reflections correspond to Bragg spacings of 45 A for the layers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003928_0301-679x(91)90060-m-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003928_0301-679x(91)90060-m-Figure1-1.png",
        "caption": "Fig 1 Theoretical diagram showing the contact between ideally smooth elastic and hard rough bodies",
        "texts": [
            " Later, a paper 7 appeared which reported the results of investigation of the contact of an elastic body, whose surface in two mutually perpendicular directions was described by periodic functions, with a smooth surface of a counter body. In this case the relative position of bulges and hollows follows a regular pattern. The model we present below describes an arbitrary position of asperities. In what follows the authors use this model for analysing the running-in of rough surfaces. Consider the contact interaction of a system of punches with an elastic half-space (Fig 1). The system of punches is characterized by: \u2022 the total number N \u2022 the shape of the contact surface of an individual punch fi(P) (it is assumed that each punch is a body of revolution with axis perpendicular to the nondeformed surface of the half-space, and p is the distance to the axis of revolution of a punch) \u2022 the distance l 0 between the axes of symmetry of the ith and jth punch \u2022 the height distribution of punches hi. The region of contact of the system of punches with the elastic half-space is a set of sub-regions ~oi (i = 1, 2 ",
            " IN' _ _ _ 2 ~2 Qj arcsin )~i 3'r j = I 1.4_i (4 ) It will be noted that in the case of the system of cylindrical punches with flat bases of radii ai penetrating into the elastic half-space, the contact regions are specified and t ip) = 0. It then follows from Eq (4) that N 1 - - 1 , ' 2 gi Qi (1-v2)+ Z Qi arcsin a-i (5) 2asE ~raiE J ~. lsj I ( j ~ i ) The condition of contact of the ith punch with the elastic half-space is of the form: ~i = hi -- \")1 (6) where ~ is the approach of bodies under load (Fig 1). Forming the relations (5) and (6) for each punch of the system, we get 2N equations for determining the values of 5i and Qi (i = 1,2 . . . . . N). When studying the contact interaction of the system of smooth axially symmetrical punches with the elastic half-space with a view to determining the unknown radii as of the subregions coi, one should add to Eqs (4) and (6) the relations N f\",f '(p)dp 1 - v 2 ~ , Qj ~i = - a , + ~ E ( 7 ) jo \\a~-p- iv-s lii \\ ]-(a,/l#) 2 which were obtained by analogy with Ref 8 such that the pressure at the boundary of contact regions cos is zero",
            " \\V*] \" \" where w* is the linear wear of the ith punch in the centre of its own contact area, Q* and V* are certain characteristic values of the load and the slip rate, and Kw is a coefficient that is equal to the linear wear rate at Qi = Q*, Vi = V*. From the contact condition of the ith punch of the system with the elastic half-space it follows that ai(t) = h i - w * ( t ) - y ( t ) (12) where 8~(t) is the depth of penetration of the ith punch at an arbitrary time; hi is the initial height distribution of punches; and y(t) is the approach of bodies under load (7 = y(0):~0) (Fig 1). The relations (11) and (12) together with (5), which are written for each punch of the system at an arbitrary time, and the equilibrium condition (8), are a set of equations for studying the wear kinetics of the interrelated punches, located at an arbitrary distance l 0 from each other. This set of equations can be rewritten in the form: N gti(t) + E Boglj(t) = - \"~,(t) - Biq?(t) j - I N 1 - - 1) 2 qi(t) - 2 a i s l E Q ( t ) (13) i = l TRIBOLOGY INTERNATIONAL where 1 - v 2 2 a qi(t) - 2aHEQ~(t)' Bii = (1-8o) arcsin_ \"IT lij = K w 2a, E ]\u00b0 _ \\V*J [(1-v2)Q*J y l ( t ) - - At a given initial height distribution of punches hi the initial values of qi(O) are known from Eqs (5) and (12) at t=0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.58-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.58-1.png",
        "caption": "Fig. 2.58",
        "texts": [
            " It is thus the basic device for converters operating in natural commutation. 72 2 Switching Power Semiconductor Devices In order to use it in forced-commutation converters, an extra turn-off circuit must be added (see Chap. 5) or a controlled turn-off thyristor used in its place. This is the GTO thyristor which will be studied in the last part of this chapter. This difficulty in turn-off has led to the thyristor being replaced by transis tors in low- and medium-power equipments. 2.4.1 Description and Operation 2.4.1.1 Description As shown in Fig. 2.58a, the thyristor is a semiconductor device with four alternately P and N doped layers. Metallization is used to obtain the three terminals - anode A, cathode K and gate G. Theoretically, there are two types of thyristor: \u2022 N type or anode gate thyristors, in which the gate is connected to the N layer next to the anode: \u2022 P type or cathode gate thyristors, in which the gate is connected to the Player next to the cathode. In practice, only the second type, corresponding to Fig. 2.58a, is found. Figure 2.58b gives the circuit symbol for the thyristor and indicates the voltage and current conventions. The thickness and doping of each layer are different and affect the thyristor properties: \u2022 the N 2 layer (cathode layer) is very thin and highly doped; \u2022 the P 2 control layer is thicker and less highly doped. Together with N 2 , it forms the cathode junction JK; \u2022 the N 1 layer (blocking layer) is the thickest and the less doped. It gives to thyristor its blocking possibility; together with P 2 it forms the control junction lc; \u2022 the P 1 anode layer has similar characteristics to those of P 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002735_0094-114x(92)90062-m-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002735_0094-114x(92)90062-m-Figure3-1.png",
        "caption": "Fig. 3",
        "texts": [
            "7 x 10 j kll/m 3 Considering forces acting on all finks, equation (35) may be rewritten in the following form: 5 1\"~,~06, + E P,~)+ T~ ~ = 0, (36) ka*m where l'~, '~ is some component of the six-dimensional input torque T, ~. Equation (36) is in unified form. If r = I and n = 3, 2, I, respectively, formulas (17), (18) and (19) can be gained. This shows that the number of virtual input parameters and supplementary equations is the same. The nth supplementary equation in the rth branch is obtained by the relation that the virtual local equivalent moments of_E~ and Et(k >~ n) for ~ ) equal the virtual equivalent moment of all forces acting on the mechanism for ~ ) . A 4 d.f. five-loop spatial mechanism is shown in Fig. 3. The central link is connected to the frame by six branches. There are two links in AG, BH, CH, D! branches and one link in EI, FG branches. Around the central circular link three spherical pairs locate in (7, H, ! as three points. The kinematic pairs at six points A, B, C, D, E, F are Hooke joints. Four revolute pairs are coaxial and upward. According to the idea of hypothetic mechanisms we add one link and one pair in El and FG branches, respectively. The original mechanism becomes a six-d.f, hypothetic mechanism for which the six links in the basic plane O--XY are input links"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure7-1.png",
        "caption": "FIGURE 7, Cross section of a portion of the journal-bearing oil film showing the action of the squeeze film.",
        "texts": [
            "I6 These studies show that two new elements are introduced into the picture of the converging wedge discussed above. First, referring to FIGURE 6 , if the load increases in magnitude, the shaft will increase its eccentricity ratio 7 , and, probably, its direction, in order to reach the equilibrium position predicted by the curves of FIGURES 4 or 5, which is characteristic of the higher load. This radial motion will result in the oil in the film ahead being squeezed and forced to flow around the shaft (FIGURE 7). Because of its viscosity, the oil will offer a resistance to the shaft's motion, just as the liquid in a hydraulic damping mechanism resists the motion of the piston. This resistance is proportional to the radial velocity Burwell: Full Fluid Lubrication 767 4 of the shaft and will contribute appreciably to the load support of the oil film, so long as the radial motion continues. Therefore, it cannot last indefinitely under a constantly increasing load, but will be most effective in supporting reciprocating loads, such as the load piston pins experience"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure5-1.png",
        "caption": "Fig. 5. Equivalent closed-loop kinematic chains: (a) RRPP; (b) RRRA; (c) ARPP; (d) ARRA.",
        "texts": [
            " If kinematic chains that are equivalent with arc-railslider joint are sought out, more closed-loop kinematic chains with a virtual continuous axis can be constructed by replacing arc-railslider joint with the equivalent kinematic chains. Actually, there only need seeking out equivalent kinematic chains whose output link have a point with the trajectory of circular-arc. Among the four-bar kinematic chains, the required equivalent kinematic chains can be found out, such as PRRP [44] (Fig. 2), RRPP [45] (Fig. 5a), RRRA [45] (Fig. 5b), ARPP (Fig. 5c), ARRA (Fig. 5d) and RRRR [46], noting that RRRA, ARRA and RRRR are all arranged to parallelogram. Based on the constraint screw-based synthesis method, replacing the arc-rail-slider joints in the A R R Az z z z1 2 3 4 with the equivalent kinematic chains obtained in Section 3.2, closed-loop kinematic chains with a virtual continuous axis can be constructed. Taking RRRA for example to explain the synthesis procedure in detail. Replacing the two arc-rail-slider joints in A R R Az z z z1 2 3 4 with two same RRRA chains can obtain the 2\u2212RRRAR closed-loop kinematic chain, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003277_elan.1140040906-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003277_elan.1140040906-Figure1-1.png",
        "caption": "FIGURE 1. Structure of the cylindrical microelectrode: (a) cylindrical platinum electrode with 2 Fm diameter; (b) silver-coated platinum wire; (c) epoxy resin; (d) silver paste; (e) glass capillary tube; (f) cable leading.",
        "texts": [
            " Silver was removed by immersion in nitric acid prior to enzyme immobilization. Instrumentations The determination of glucose was carried out as reported previously [26]. In brief, a homemade potentiostat was utilized and the data obtained was recorded with a chart recorder (Riken Denshi, SPjSV). A two-electrode configuration was constructed and a silver/silver chloride electrode was employed as the counter electrode. Electrode Preparation The structure of a platinum microelectrode of 2-pm diameter is illustrated in Figure 1. A silver-coated platinum wire was first connected to a cable and was put into a capillary glass tube fabricated with a capillary puller (Narishige). Subsequently, the inside of the glass tube was filled with epoxy resin. After the resin had hardened, the protective silver was removed by immersion in nitric acid. To insulate the exposed silver on the crosssection, the tip of the capillary tube was coated with epoxy resin. This resulted in a cylindrical platinum microelectrode of 2 pm in diameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure5-1.png",
        "caption": "Figure 5. Dynamic modes Ti, T2 and T3 of a beam",
        "texts": [
            " This condition is fulfilled because small deformations are assumed. Therefore, it is demonstrated that amplitudes of static modes do not increase the number of variables of the problem. 2.2. Dynamic modes Dynamic modes are introduced to better represent the deformed configurations of a flexible body. These are internal modes whose deformation do not affect the natural co-ordinates that define the body. They are obtained as the vibration modes of the body with fixed boundaries (these boundaries are the natural co-ordinates). Figure 5 shows mode Tl , first bending mode in local plane (5, j ) , Y2, first bending mode in local plane ( j , 2) (notice that the beam has null slope at both ends to respect the boundaries), and Y3, second bending mode in the same plane. There are a finite number of static modes (five in the example) but there are an infinite number of dynamic modes. However, only a few of them should be considered; namely, those that are expected to be excited during the motion. Sometimes, acceptable accuracy will be obtained with only static modes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003718_iros.1999.812833-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003718_iros.1999.812833-Figure6-1.png",
        "caption": "Figure 6: Relation between the robot's position and the landmark in the environment.",
        "texts": [
            " Here, we use the same technique for the position estimation of APCS. In our system, not only position PA but also the error covariances CpA are always estimated, and occasionally corrected by using landmarks. PA and CpA are expressed as follows: P A = (i:) (1) ) (2) 2 u z A u x A y A u Z A e A ' P A = u z A Y A uYA u Y A e A ( u Z A e A u Y A e A 2 2 Here, we explain the method for the position correction using the detected flat wall mentioned above section. The illustration of the relation between the robot's position and the landmark is shown in Figure 6. The robot could get the information about not only the distance r between the robot's position and the landmark but also the angle < which shows the direction of the landmark from the robot's orientation. Therefore, if we express the position of the flat wall as a line ax + by + c = 0 in the x-y coordinate, the direction of this line is perpendicular to> the normal line of the flat wall that was detected by using ultrasonic sensor, so the following constraint can be made. bcos(6A + <) - asin(6A + <) = 0 (3) The distance from the robot to the landmark is r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003882_00423118708969172-Figure11-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003882_00423118708969172-Figure11-1.png",
        "caption": "Fig. 11.- Slip velocity iir and slip vector of wheel-at rcnd level. Rolling speed V; of wheel and speed vector V of wheel centre. Assumed total force vector F",
        "texts": [
            " 5 D ow nl oa de d by [ U ni ve rs ity o f W at er lo o] a t 0 9: 10 2 4 O ct ob er 2 01 5 The wheel is assumed to remain in an upfight position. Horizontal forces are produced by side and fore and aft slip components of the slip vector of the wheel. The slip vector o is defined as Vs/vr. The vector Vs represents the velocity of a material point attached to the wheel body momentarily ' located in the contact centre at (or slightly below) road level. The quantity V represents the speed of rolling of the wheel. This is the forward velocity of the wheel centre relative to the material point mentioned above (Fig.11). For a freely rolling wheel with o = = 0, the rolling speed equals the speed of travel (Vr = V ) . In case the wheel is locked Vr = 0 and thus - VS = V and o -C -. With this definition of slip employed, the force vs slip characteristics become identical for the longitudinal and the lateral aopect. This is true if the model exhibits equal elastic fields and frictional properties in lateral and longitudinal direction. This, for example, appears to be the case with a model showing one or more rows of cylindrical elastic studs embedded in a rigid wheel body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure10-1.png",
        "caption": "FIGURE 10. Schematic diagram of hydrostatically supported bearing (Fuller: Machine Design).",
        "texts": [
            " In situations where very thin oil films are possible, however, this load support might become very appreciable. Thin oil films occur in certain areas of rubbing surfaces which have become closely aligned through \u201crunning-in.\u201d Hydrostatic Lubrication. The mechanisms discussed above have required relative motion of the two surfaces, either tangentially, or toward and away from each other. If no motion of either kind exists, complete separation of the surfaces may be achieved in the manner shown schematically in FIGURE 10. Oil under high pressure is pumped continuously into a recessed region in one of the two surfaces. It flows out through the narrow clearance or sealing space around the edges. If the surfaces are carefully and smoothly finished and well aligned, this clearance can be kept so small that the flow rate is not unreasonably large. The only requirement is that the surfaces do not touch. The oil is collected in a sump below the bearing and returned to the pump. A very good description of the principle and its applications is given in a series of articles by The friction is entirely viscous in nature, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003993_fld.1650060704-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003993_fld.1650060704-Figure5-1.png",
        "caption": "Figure 5. Peak pressure distributions for varying inclination: shaft speed = 40,OOO Rev min-','e = 0.65, inlet temperature = 40\" C",
        "texts": [],
        "surrounding_texts": [
            "One of the main objectives of this investigation (as stated earlier) is to provide a method for predicting temperature variations in a high-speed misaligned lubricant film and its consequent effect on the load-carrying capacity and power loss. To achieve this, the previously developed model has been applied to a journal bearing that had a bush of length and radius 36.8 mm with a clearance ratio ( R , - R , ) / R , of 0004. The lubricant used was Shell Tellus 27 which has a density of 860 kg/m3 and a specific heat of 2000 J/kgK, which were assumed to be constant. The temperature dependence of the lubricant viscosity is obtained by assigning values of M = - 3.878 and B = 9.85 in the Walther equation (9). For this set of numerical experiments MISALIGNED HYDRODYNAMIC JOURNAL BEARINGS 45 1 the bearing shaft was assigned a rotational speed of 40,000 rev min- ' with a centre-line eccentricity ratio of 0-65. The overall distortions of the lubricant film pressure and temperature fields are depicted pictorially in Figures 4(a), (b) and (c) for shaft inclinations of 0, 0.001 and 0.002 radians, respectively. Generally, for a shaft that is constrained to misalign in the direction of the applied load, the peak pressure does not move in a streamwise direction, although increasing misalignment reduces slightly the extent of the cavitated region (or area of subzero pressure). However, the temperature increases continuously along the streamwise length of the film with the most rapid increases associated with the largest pressure gradients in the film. 452 J. 0. MEDWELL AND D. T. GETHIN The axial variations of pressure and temperature, where the maximum values of these quantities occur, are shown in Figures 5 and 6. The circumferential positions at which peak pressures and temperatures are generated do not coincide for the cases considered here. Generally the maximum pressure is located at a position some 60 per cent of the arc length (/3) from the main supply inlet. However, the maximum temperatures, because of the continued heat dissipation in the lubricant film, occur near to the onset of cavitation. The results for the misalignment displayed in Figures 4(a), (b) and (c) are limited by the eccentricity ratio. To avoid surface contact between the shaft and bush when considering higher values of misalignment, the eccentricity ratio has to be reduced. This has the initial consequence of reducing the length of the cavitated zone in the partial arc film, permitting a fuller film to be established. However, the increased misalignment reduces further the minimum value of the lubricant film thickness while moving its position nearer to the upstream location. This enables cooler lubricant to flow into the regions downstream of the minimum clearance location. The cumulative effect of this is shown in Figure 7, where lines of constant lubricant temperature have been drawn to provide an isotherm map, thus showing that a distinctive 'hot spot' has been generated. Some global performances for a misaligned bearing are shown in Figures 8 and 9 for an eccentricity ratio of 0.65. The isothermal solution, which is based on a constant lubricant temperature equal to that of inlet (i.e. 40\" C), as expected, predicts far greater load and power losses than the full thermohydrodynamic solution. A further numerical experiment was carried out where the power loss computed using the thermohydrodynamic solution is used in a simple MISALIGNED HYDRODYNAMIC JOURNAL BEARINGS 453 454 J. 0. MEDWELL AND D. T. GETHIN THERMOHYOROOYNAMIC ISOTHERMAL (BULK TEMPERATURE) ISOTHERMAL (INLET TEMPERATURE) -0- THERMOHYOROOYNAMIC a-0 THERMOHYORODYNAMIC ISOTHERMAL (BULK TEMPERATURE) ISOTHERMAL (INLET TEMPERATURE) 0 THERMOHYOROOYNAMIC a=O MISALIGNED HYDRODYNAMIC JOURNAL BEARINGS 455 energy balance, together with the predicted lubricant flow, to estimate the bulk lubricant temperature. This is equivalent to the sump temperature that would be monitored in situations where a bearing is likely to be highly stressed. If this temperature is used in the isothermal procedure, then the load and power loss characteristics compare closely with the thermohydrodynamic solution. The results of the aligned case are also included in the Figures where it can be seen that for a fixed eccentricity ratio, misalignment has significantly increased the load-carrying capacity only of the bearing. This is a consequence of the high peak pressures generated by misalignment, which more than offset the reduction in lubricant viscosity brought about by the accompanying increased temperatures. However, it should be pointed out that the increase in load carrying capacity is based on the midplane eccentricity ratio and is not in conflict, therefore, with the conclusions of other workers'V6 since their contention of a reduction in load carrying capacity is based on minimum film thickness. In reality, the journal would position itself within the bush so as to react to the applied loading exactly. Finally the maximum and bulk lubricant temperature variations with speed for a misalignment of 0.002 radians and an eccentricity of 0-65 are shown in Figure 10. It can be seen that although the bulk temperatures exhibit modest rises over the inlet lubricant temperature, the maximum temperatures generated are dangerously high and would certainly be a limiting parameter in such a bearing operation."
        ]
    },
    {
        "image_filename": "designv11_31_0002937_pl00014419-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002937_pl00014419-Figure9-1.png",
        "caption": "Fig. 9. A downward force on object i results in a horizontal force on object r + j . The external gravity force acting on object r + j has no effect, as long as gravity points exactly downward.",
        "texts": [
            " The modification is made in two steps. Let Qext be an external force acting downward on each object with strength proportional to an object\u2019s mass. In the assemblies of Theorem 5.1, contact occurred between object i and object r + j if ai \u2208 Aj . We modify the constraints on objects r + 1 through r + s so that each object can now move only horizontally. The fixels are positioned so that selecting fixel j prevents object r + j from moving to the left. Contact between objects i and r + j is modified as shown in Figure 9. In order for object i to move downward, object r + j must move to the left. Clearly, selecting fixel j prevents object i from moving downward. Note however that if fixel j is unselected, the external force acting on object r + j induces no motion of object r + j . This modification does not change the fact that it is NP-hard to pick a minimal fixel set yielding directional equilibrium. This first modification overcomes the objection that the external force chosen for the previous proof was somewhat unnatural"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003299_jsvi.1996.0908-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003299_jsvi.1996.0908-Figure5-1.png",
        "caption": "Figure 5. The similarity transformation.",
        "texts": [
            " After this transformaion, process A\u2013D, B\u2013G and C\u2013E are non-parallel, and one requires an additional transformation of these processes, namely a similarity transformation in the direction of the U-axis. Its initial point coincides with the projection of the initial point of the process on the U-axis. Its coefficient is inversely proportional to the segment a(U), i.e., the change in U between the initial point of the process and the point where the process intersects the U-axis. In the new co-ordinates, U*a = =U\u2212Ua =/a(Ua) (or U*b , U*c ); F**, 0022\u2013460X/97/250903+05 $25.00/0/sv960908 7 1997 Academic Press Limited Masing\u2019s principle is fulfilled (Figure 5). One can also see in Figure 2 that triangles CMN and BPQ are similar, H(U)/a(U)= constant, and it is sufficient to know only the function H(U) for the transformation in the U-axis direction. Next L(U) and H(U) will be found for a real vibration isolator. For the system shown in Figure 2, L(U) and H(U) are the half-sum and half-difference of loading and unloading processes during sliding in the friction element. The ends of the hysteresis loop are not used for the definition of L(U) and H(U). One can approximately find the length of these sections using Masing\u2019s principle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002309_s11666-999-0001-3-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002309_s11666-999-0001-3-Figure6-1.png",
        "caption": "Fig. 6 (a) to (c) Valve seat cladding with Al-Si-Cu-Ni powder (CO2 laser power 6.8 kW, processing speed 0.6 m/min). (d) Piston-ring groove processing with Al-Si-Ni-Cu powder (Nd:YAG laser power 2.7 kW, processing speed 0.65 m/min). 1, oversized groove; 2, filled by laser cladding; 3, final machining",
        "texts": [
            " The laser coating process is especially suitable for aluminum because any precleaning such as etching of the aluminum surface layer is not necessary. The inner cladding of a hypereutectical AlSi layer (thickness: ~2 mm) on an aluminum pipe (AlSi10 cast) is depicted in Fig. 5(a). The enlargement (Fig. 5b) shows explicitly the axial overlapping of the adjacent coating tracks (\u03b4 ~45%) and the homogeneous structure of the layer. After final processing of such pipes by milling or honing they can be typically used as liners. Figure 6 shows other industrial applications. Wear resistant layers have been applied to aluminum substrates as valve seats (Fig. 6a-c) and to piston-ring grooves (Fig. 6d). In the latter case, the individual steps are described in detail. After machining an oversized groove (1), it was filled by laser cladding (2). The final piston ring groove was machined (3) to produce the final geometry required. The same approach can also be applied to pistons made of magnesium, but this requires the use of slightly modified working parameters. Besides aluminum and magnesium, there are also other base materials that can be finished by laser power technology. Figure 7 shows a nozzle made of continuous cast copper, which has been partially clad with a nickel-base alloy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003570_37.856182-Figure11-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003570_37.856182-Figure11-1.png",
        "caption": "Figure 11. Nyquist plot of L s( ): (a) Kc < 0; (b) Kc >0 and small; (c) Kc >0 and large.",
        "texts": [
            " It is easy to see that, in contrast to the continuous set of equilibrium points, the stability of the extreme points depends on the value of Kc. As will be explained in more detail in the next section, here we can distinguish three cases, depending on the value of the controller constant: 1. Negative values of Kc (positive feedback): In this case, given a value of A, it can be considered that the Nyquist plot of L s( ) encircles the point \u22121/ ( )N A , provided that a sufficiently small radius is selected to surround the pole s =0 [Fig. 11(a)]. Therefore, the extreme equilibrium points are unstable. This case, however, is unrealistic from a control engineering viewpoint. It is included only for the sake of mathematical completeness. 2. Small and positive values of Kc: In this case, there is no intersection between the \u22121/ ( )N A locus and the L j( )\u03c9 locus [Fig. 11(b)]. Thus, the extreme equilibrium points are stable under these conditions. 3. Large and positive values of Kc: In this case, there are two intersection points between the \u22121/ ( )N A locus and the L j( )\u03c9 locus [Fig. 11(c)]. As will be seen in the next section, this implies the existence of two limit cycles, the first of them unstable and the second one stable. Since the nearest limit cycle to the equilibrium point is unstable, we can conclude that the extreme equilibrium points are also stable under these conditions. The crossing points between \u22121/ ( )N A and the Nyquist plot of L s( ) are sought to predict limit cycles. As stated earlier, \u22121/ ( )N A is real and negative (Fig. 7), which implies that the intercepts between the open-loop transfer function and the negative real axis must be studied. Taking into account that Kc is a real constant, the intersection points between this function and the real negative axis have the form L jw K G j K Kc c( ) ( )180 180= =\u2212\u03c9 , where K K K= + =1 2 1 2 1 2 \u03c4 \u03c4 \u03c4 \u03c4 constant. According to the above expression, and since \u22121/ ( )N A has a negative maximum, no limit cycle exists for low values of Kc [see Fig. 11(b)]. If the value of Kc increases, it reaches a threshold (K Kc min / .= \u2248\u03b3 0 8087) where \u03b3 is the absolute value of the negative maximum of \u22121/ ( )N A at which the transfer function intersects \u22121/ ( )N A . At this point, two limit cycles August 2000 IEEE Control Systems Magazine 97 appear, one of them unstable and the other one stable. It must be emphasized that the frequency at which L j( )\u03c9 intersects the real axis is constant and has a value of \u03c9180 14 91= . rad/s. This will be the frequency of oscillation of all the limit cycles that may appear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002616_0020-7403(96)00057-4-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002616_0020-7403(96)00057-4-Figure6-1.png",
        "caption": "Fig. 6. Analysis of a rod reducing process using the upper bound method.",
        "texts": [
            " (4) d~ 8 sin a cos From the balance of the input energy (2) and the dissipated energy Eqns (3)-(4) we can obtain the dependence of the mean unit pressure in non-dimensional form: cr~ = sin~.(6~ - I) ln6z + - ~ ' m k \" 4 ~, (5) \"v\" 3 ~/:3- cos c~- sin 2~ ~ The upper bound method This solution is based on the assumption that the plastic deformation area is described by the so called spherical velocity field, described by Avitzur [11]. The material is assumed to deform plastically in the sub-area \"B\" which is in the form of a spherical sector bounded by the surfaces r -- rl and r = r 2 and by the die cone surface, see Fig. 6(a). To obtain the solution, one transforms the system by adding velocity Vo to each of its zones. Following the transformation, the reduction of a rod [Fig. 6(a)] is converted into the system presented in Fig. 6(b), characterizing a drawing process. The drawing stress qc of round bars determined by the upper bound method, in non-dimensional form, is expressed by [11]: a0 ,,//33 \\ s i n 2c~ + m ' c t g a ' l n d + where f(~) is determined by: 2~ - sin c~ L ] 2sin 2 ~ + 2ink , (6) 1 x / ~ - c o s ~ / ' l + l l c o s 2 ~ + _ _ I n - - - - , . f(~) = 2 ~/11 w/ l l cos~. + ~/1 + 11 cos2~ Considering the external force balance of the formed object one can obtain the equation: d 2 d 2 _ d 2 q c ' 7 C ' 4 - = qm ' rc 4 (7) (8) 238 Zb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002333_s0045-7825(98)00367-3-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002333_s0045-7825(98)00367-3-Figure4-1.png",
        "caption": "Fig. 4. Coordinate systems S,, Sp and S~ applied for the design of Root's blowers.",
        "texts": [
            " [1(0(05), 05) - E] = 0 (52) The singularity point of the envelope is determined by the equations tip = p ( O, 05) 0, 05) = 0 (53) g,(O, 05) = 0 The singularity point is indeed the point of regression if ~l=lf\u00b0Ll~\u00b0go ge, (54) where go = O/O0[gt(O, 05)], g,~ = O/005[gt(O, 05)]. The proposed approach enables to simplify the singularity equation using it in form of Eq. (44), and simplify as well the determination of go and g~b. The developed theory is illustrated with the example of Root's blowers (Fig. 3). The ratio of angular velocities of the rotors of the blower is one and the centrodes are two circles of the same radius r (Fig. 4). Movable and fixed coordinate systems S r, Sp and Sj are shown in Fig. 4. The generating curve ~7 r is a circular arc of radius p and is represented in S r as (Fig. 5) r(O) = ( - p sin O)i r + (a + p cos O)j, (55) The tangent and the normal to v r are represented as T r = r o = [ - p c o s O - p s i n 0 0] v (56) N r = T r \u00d7 k , = [ - p s i n O p c o s 0 0] T (57) Applying Eq. (17), we obtain the following equation of meshing Our goal is to determine the singularities of a curve Xp that is conjugated to the circular arc Xr. To solve this problem, we consider the segment of line of action that corresponds to the meshing of curves Xr and "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002295_pime_proc_1995_209_154_02-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002295_pime_proc_1995_209_154_02-Figure1-1.png",
        "caption": "Fig. 1 An overall schematic of the attachment geometry and loading",
        "texts": [
            " The aim is to find an answer to the question of what the differences are between stress values of a frictional contact problem of unknown geometry of contact and the stress values of frictionless simplifications of the problem (with either unknown or assumed stable geometry of contact). Due to the qualitative character of the research the applied friction Q IMechE 1995 model assumes a constant and uniform friction coefficient. 3.1 An example of the turbine blade attachment A real axial entry curved fir-tree blade attachment with four pairs of root and disc hooks on each side of the attachment is chosen for the research (Fig. 1). The geometry and material data obtained from the designer are the following. The attachment curvature radius r is 0.125 m and a shift of the curvature centre from the disk middle plane b is 0.025 m. The attachment is loaded with the blade (of length L equal to 0.39 m) of the first stage of the low-pressure part of a 200 MW steam turbine. The blade rotating at an angular velocity w = 3.1415 x 10' s-l (3000 r/min) produces a centrifugal force F, equal to 109.146 kN acting on the root platform of the height g = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002512_0954407971526362-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002512_0954407971526362-Figure2-1.png",
        "caption": "Fig. 2 (a) Forces on and (b) compatibility of meshing of a fully meshed belt pitch",
        "texts": [
            " It also constrains meshing and unmeshing to occur within one pitch of pulley rotation. This restriction, the better the higher the belt tension and the smaller the pulley diameter, is discussed in Section 5. The fully meshed modelling has been published before (5) but is summarized here for convenience of later use. By convention, as in Fig. 1, the fully meshed belt pitches are labelled 1 to Nf , from the tight to the slack side; and the land associated with a particular tooth is anti-clockwise from the tooth. Figure 2a is a detail of the forces on the general pitch i. It shows the belt cord tension changing from Ti at the boundary with pitch (i\u00ff 1) to Ti 1, with an intermediate value T9i at the junction between the tooth and land. It also shows the circumferential component Qi of the tooth\u00b1groove contact load and the land friction force Fi. Circumferential force equilibrium gives T 9i Ti \u00ff Qi and Ti 1 T 9i \u00ff Fi (3) and the capstan formula (assuming that there is sliding between the belt and pulley land) gives Fi T 9i[1\u00ff exp (\u00ff\u00e4\u00ec\u00e81)] (4) where \u00ec is the land sliding friction coefficient and \u00e4 1 depending on the direction of sliding, explained later. Figure 2b concerns the compatibility of the stretching and displacement of the belt pitch within the pulley pitch. It places a belt pitch, of initial length Pb at the cord line but stretched by tension to Pb dPb, on to the pulley pitch, of length Pp at the cord line. It shows a displacement \u00ebi at one end, that gives rise to the tooth loading Qi, and a possibly different displacement \u00ebi 1 at the other end. Compatibility of meshing requires \u00ebi 1 \u00ebi (Pp \u00ff Pb) \u00ff (dPb)i (5) where, for a pulley of cord line radius Rc (Rc Rp the pitch line differential dRp) Pp Rc\u00e8p (6) The belt tooth is supposed to be linearly elastic, so that a tooth stiffness Kt is defined by Qi Kt\u00ebi (7) The cord is also assumed linearly elastic, so that a uniform tension T is related to the stretch of one pitch by T Kb dPb (8) In fact (Fig. 2a) a belt pitch is not under uniform tension. If tension is assumed to vary linearly from Ti to T 9i over the D04395 # IMechE 1997 Proc Instn Mech Engrs Vol 211 Part D tooth and then as required by the capstan formula over the land it can be shown that (4, 5) (dPb)i Pp Pb Kb \u00e8g \u00e8p (Ti T 9i) 2 T 9i\u00e4 \u00ec\u00e8p [1\u00ff exp (\u00ff\u00e4\u00ec\u00e8l)] ( ) (9) where \u00e4 1 on a driven pulley and \u00ff1 on a driving pulley, if T > Kb(Pp \u00ff Pb); and has the opposite sign otherwise. If Ti and \u00ebi are given, the system of equations (3) to (9) enables Ti 1 and \u00ebi 1 to be calculated for given belt properties Kb, Kt and \u00ec, pulley radius Rp and pitch line differential dRp, and pitch difference (Pp \u00ff Pb)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003607_026635119100600305-Figure11-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003607_026635119100600305-Figure11-1.png",
        "caption": "Fig. 11.",
        "texts": [
            " 10). Such distances X indicate the number of sectors conforming the plane pattern and are those that regulate the greater or smaller raise as they differ more or less between them. The angle 8' should be, besides, even multiple of 360\u00b0 to obtain an integer number of circular sectors. Stated in this way, each horizontal projection corresponds to only one silhouette and in its resolution, it is necessary to work alternatively on the two planes which pass one through 0IC and the other through 01A. (Fig. 11). This silhouette is taken as auxiliary to determine some angles or edges that find in true magnitude on it. As a is variable, each sector adopts a different folded angle, identifying itself according to the following criteria: For the sector OC: a j = folding angle in OCA and OCB a; = folding angle in OAM and OBN For the sector OF: a2 = folding angle in OFD and OFE a; = folding angle in OMD and ONE For the sector 0IF: a3 = folding angle in 0IFD and 0IFE a; = folding angle in 0IDMI and OIEM j a; = a;, and a2 = a3 but it is necessary to differen tiate them for the process of calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002874_s026357470001835x-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002874_s026357470001835x-Figure3-1.png",
        "caption": "Fig. 3. The Integrated Motion Inc. manipulator.",
        "texts": [
            " In Figure 2d, the time warp obtained with m = 5 is plotted; as anticipated, the virtual time is now allowed to recover the real time leading to a shorter duration of motion (2 s). The maximum tracking error along the trajectory is 6.89e-4 m. A real-time kinematic control scheme based on the proposed technique has been implemented on the Direct Drive Manipulator Research and Development Package11 by Integrated Motions Incorporated. Although mechanically simplified - it is a two-degree-of-freedom planar robot (Figure 3) - this manipulator is a good test bed for motion control algorithms due to the open architecture of the control system. A block diagram of the hardware architecture of the system is shown in Figure 4. The user interface, the trajectory generation and the inverse kinematics take place on a 80486-based host computer, while the servo control runs on a TMS320C30 DSP-based board. The open modular structure of the software architecture allowed to replace the original routines with custom software. A PD independent joint controller has been implemented on the DSP board, whereas the feedbackcorrection pseudoinverse algorithm with time warp has been implemented on the host computer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002292_s0141-9331(99)00045-9-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002292_s0141-9331(99)00045-9-Figure6-1.png",
        "caption": "Fig. 6. Motion of link 2 following motion of link 1.",
        "texts": [
            " The actuator used for the first joint was a 12 V DC motor, with a maximum power of 3.7 W, connected to the link with a speed reducer with a ratio of 160:1 and to a rotational potentiometer, used as a position transducer for the first link. 2. To exploit the motor power to the utmost the structure of An extra weight was added to the tip of the second link to increase the sensitivity of the second link to the motion of the first link and to facilitate the escape from singular configurations (link 2 closed on link 1, u2 p). As an example in Fig. 6 it can be observed that after a clockwise torque applied to the first joint, this joint will rotate clockwise, while the second joint will rotate counter-clockwise. The mass on the tip amplifies this effect, thus increasing the controllability of the robot. The control circuit is made up of an electronic board that acquires the angular positions of the two links, processes them on the basis of the reference positions and gives the output the PWM control signal for the DC motor, causing a different torque for the joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003850_s0924-0136(03)00286-3-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003850_s0924-0136(03)00286-3-Figure4-1.png",
        "caption": "Fig. 4. A 3D circle defined as the intersection of a sphere and a plane.",
        "texts": [
            " Based on these information, the CNC computer performs the space curve interpolation, issuing in each program-iteration the selected stepping command to the driving motors of the machine axes. This process is repeated until the programmed terminal point is reached. The algorithm was implemented and tested in both its versions, implicit and parametric. Two representative examples, one for each version, were selected to demonstrate the effectiveness of the proposed method. Example 1. Consider a plane intersecting the surface of a sphere centered at the origin, as shown in Fig. 4. The goal is the interpolation ability of the full circle or any segment of the circle which is defined as the intersection curve of the two surfaces. The surface of the sphere (with radius r) is implicitly defined by the equation f = x2 + y2 + z2 \u2212 r2 = 0 (24) and the equation of the plane passing through the origin is g = Ax + By + Cz = 0 (25) which may be derived from three points in space. Let these points be, the start and end points Ps(xs, ys, zs) and Pe(xe, ye, ze) of the desired circular arc and those of the sphere center c(xc, yc, zc)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002868_s0301-679x(99)00041-9-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002868_s0301-679x(99)00041-9-Figure1-1.png",
        "caption": "Fig. 1. Physical model and surface geometry. (a) Physical model; (b) surface geometry of body 2.",
        "texts": [
            " Nomenclature a hminpressure\u2013viscosity coefficient, Pa21 minimum film thickness, m b h0temperature\u2013viscosity coefficient, K 21 reference parameter for dimensionless film g thickness, h0=a2/Rxratio of radii of curvature, g =Ry/Rx h k1, k2viscosity of lubricant, Pa s thermal conductivites of bodies 1 and 2, W h\u0304 m21 K21dimensionless viscosity of lubricant, h\u0304=h/h0 h0 keinlet viscosity of lubricant, Pa s ellipticity parameter, ke=b/a n1, n2 kfPoisson\u2019s ratios of bodies 1 and 2 thermal conductivity of lubricant, W m21 r K 21density of lubricant, kg m23 r\u0304 lWdimensionless density of lubricant, r\u0304=r/r0 half width of the ring flat zone, m r0 Pinlet density of lubricant, kg m23 dimensionless pressure, P=p/pH r1, r2 pdensities of bodies 1 and 2, kg m23 pressure, Pa a pHsemiminor axis of the Hertzian contact maximum Hertzian pressure, Pa, ellipse, m pH=3w/(2pab) b Rx, Rysemimajor axis of the Hertzian contact radii in x and y directions of body 1, m ellipse, m rW relative half width of the ring flat zone, c1, c2 rw=lw/bspecific heats of bodies 1 and 2, J kg21 K 21 S slide/roll ratio, S=(u12u2)/uR cf T\u0304specific heat of lubricant, J kg21 K 21 dimensionless temperature, T\u0304=T/T0 d1, d2 Tdimensionless thickness of the temperature temperature, K calculation domains of bodies 1 and 2, T0 inlet temperature, K d1=d 91/a, d2=d 92/a U, V dimensionless velocities in x direction and d 91,d 92 y direction, U=u/uR, V=v/uRthickness of the temperature calculation domains of bodies 1 and 2, m u, v velocities in x direction and in y direction, E m s21equivalent elastic modulus, 2/E=(12 U1, U2 dimensionless velocities at the surfaces ofv2 1)/E1+(12v2 2)/E2, Pa bodies 1 and 2 in x direction,E1, E2 elastic moduli of bodies 1 and 2, Pa U1=u1/uR, U2=u2/uRG material parameter, G=aE u1, u2 velocities at the surfaces of bodies 1 and 2H dimensionless film thickness, H=h/h0 in x direction, m s21H* dimensionless film thickness, H*=105\u00d7h/Rx uR entrainment velocity, m/s, uR=(u1+u2)/2H00 dimensionless constant UR dimensionless entrainment velocity,H*ave dimensionless average film thickness, UR=uR\u00b7h0/(E\u00b7Rx)H*ave=105\u00d7have/Rx W dimensionless load, W=w/(E\u00b7R2 x)H*cen dimensionless central film thickness, w load, NH*cen=105\u00d7hcen/Rx x, y, z, z1, z2 coordinates, mH*min dimensionless minimum film thickness, X, Y, Z, Z1, Z2 dimensionless coordinates,H*min=105\u00d7hcen/Rx X=x/a, Y=y/a, Z=z/h, Z1=z1/a, Z2=z2/ah film thickness, m xin, xout, yout coordinates of the boundaries, mhave average film thickness within Herzian Xin, Xout, Yout dimensionless coordinates of thecontact ellipse, m boundarieshcen central film thickness, m The physical model mentioned above is shown in Fig. 1(a), body 2 has a ring flat zone. The two surfaces in the contact region only have velocities u1 and u2 in the direction of the minor axis of the Hertzian contact ellipse, which is the common situation in engineering. Details of the geometry of body 2 are illustrated in Fig. 1(b). Based on the work of Yang and Wen [7], the dimensionless Reynolds equation associated with Newtonian EHL point contact problems under thermal and steady state conditions can be written as: \u2202 \u2202XSe\u2202P \u2202XD1 \u2202 \u2202YSe\u2202P \u2202YD5 \u2202 \u2202X (r\u0304*H) (1) where e5SrhDeH3/l, l512uRh0R2 x/(a3pH), r\u0304*5r\u03049eh\u0304e(U22U1) 1r\u0304eU1, SrhDe512Sh\u0304er\u03049e h\u03049e 2r\u03040eD, r\u03049e5E1 0 Fr\u0304EZ 0 1 h\u0304 dZ9GdZ, r\u03040 e 5E1 0 Fr\u0304EZ 0 Z 9 h\u0304 dZ9GdZ, 1 h\u0304e 5E1 0 1 h\u0304 dZ, 1 h\u03049e 5E1 0 Z h\u0304 dZ,r\u0304e5E1 0 r\u0304dZ. In solving Eq. (1), the boundary and cavitation conditions must be satisfied, their dimensionless forms are HP(Xin, Y)=P(Xout, Y)=P(X, \u00b1Yout)=0 P(X, Y)$0(Xin,X,Xout, \u2212Yout,Y,Yout) All parameters are defined in the Nomenclature",
            " Their dimensionless boundary conditions are: T\u0304(X, Y, Z1)|X=Xin =1, T\u0304(X, Y, Z2)|X=Xin =1 T\u0304(X, Y, Z1)|Z1=\u2212d1 =1, T\u0304(X, Y, Z2)|Z2=d2 =1 At the solid\u2013liquid interfaces, the heat flux continuity should be satisfied, i.e.: 5CMA\u00b7 1 H \u2202T\u0304 \u2202Z | Z=0 = \u2202T\u0304 \u2202Z1| Z1=0 CMB\u00b7 1 H \u2202T\u0304 \u2202Z | Z=1 = \u2202T\u0304 \u2202Z2| Z2=0 (4) where CMA=kf a/(k1h0), CMB=kf a/(k2h0). Defining a dimensionless coefficient rW to represent the relative half width of the flat zone in body 2 rW5lW/b (5) Assuming that lW\u00bfRy, it can be obtained that hW=(brW)2/(2Ry) from Fig. 1(b). Within the flat zone, the dimensionless film thickness equation can be written as: H(X, Y)5H001 X2 2 kR (6) 1 2j p2EE P(X9, Y9) \u00ce(X\u2212X9)2+(Y\u2212Y9)2 dX9 dY91HW where j5p(11g)/(4F2g ), F25E p 2 0 [12(12k \u22122 e )sin2 x] 1 2 dx, kR5Rx /(Rx2hW), HW5hW/h0 Out of the flat zone, the dimensionless film thickness still has its conventional form as H(X, Y)5H001 X 2 2 1 Y 2 2g (7) 1 2j p2EE P(X9, Y9) \u00ce(X\u2212X9)2+(Y\u2212Y9)2 dX9 dY9 The applied normal load must be supported by the generated hydrodynamic pressure in the calculation domain, so the dimensionless form of the force balanced equation is EEP dX dY5 2 3 pke (8) The lubricant viscosity\u2013pressure\u2013temperature relationship proposed by Roelands et al",
            "8ke, but in the cases of light loads or high speeds, the computation domain is enlarged in X and Y directions to avoid \u2018numerical starvation\u2019. In the present multigrid solver for Reynolds equation, 4 levels are employed, the finest grid consists of 129 nodes in the X direction and 49 nodes in the Y direction and is also used for the solution of three-dimensional energy equations with 21 nodes in the Z direction within film and 12 nodes in the Z1 and Z2 directions within bodies 1 and 2, respectively. It should be pointed out that \u2202H/\u2202Y concerned with Eqs. (1) and (2) is discontinuous mathematically at both edges of the flat zone in Fig. 1(b). In the present algor- ithm, the central difference is employed for the term \u2202H/\u2202Y inside the calculation domain to avoid this discontinuity. This treatment implies that both edges are approximated by the discretization grid, an mathematical edge does not exist, the practical model in the calculation is an approximation of it. Numerical computation tests show that the above algorithm is effective and robust for thermal EHL problems in a wide range of operating conditions. In most cases, it takes less than 10 min of CPU time to obtain an convergent solution in a Pentium/133 computer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003885_3.20369-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003885_3.20369-Figure4-1.png",
        "caption": "Fig. 4 Stability boundaries for case 2 with five times minimumcontrol-energy gains.",
        "texts": [
            ") Eigenvalues for the closed-loop system and saturated rudder or aileron are given in Table 4. The eigenvalues for MCE and high-gain cases in Tables J and 4 show that the high-feedback-gain system is relatively more stable even with saturated rudder or ailerons. Intuitively, the size of the stability region should also increase with increased system stability. The validity of this intuition is illustrated in this example. The saturation and stability boundaries in normal-mode and physical coordinates are shown in Fig. 4. By comparison to Figi 3a, the size of the stability region is seen to be increased; however, the stability boundary in Fig. 4 passes through the saturated-aileron region, and so the stability region depends on the aileron saturation limits. Consider the case when elements in the control weighting matrices for the rudder and aileron are not the same. High (low) control weighting on rudder and low (high) control weighting on aileron result in low (high) feedback gains for the rudder and high (low) feedback gains for the aileron, respectively. Although not MCE, high values of control weightings ensure that there is negligible alteration of stable modes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003160_s0093-6413(00)00104-x-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003160_s0093-6413(00)00104-x-Figure10-1.png",
        "caption": "Fig. 10 Construction details of Free to Roll rig assembly",
        "texts": [
            " The term sets for roll angle(error, e) and roll rate(rate of change of error, ce) consist of negative big (NB), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM) and positive big (PB). The control input is also made to have the same term sets. The membership functions of this forty-nine rules based FLC are presented in the next section. 4. E x p e r i m e n t a l S e t u p and Results: The experimental set up consists of a delta wing rig mounted in the wind tunnel. The rig is free to roll with the delta wing of 80\" sweep back mounted on its shaft. The construction details are shown in Fig. 10. It consists of a U shaped metallic structure whose two ends are hinged to the vertical walls of the tunnel test section. The model is mounted on this structure by a nut and bolt attachment present at its base. The structure with the model mounted on it, is coupled to a rack and pinion arrangement with the help of which the angle of attack can be varied from 0 \u00b0 to 45 \u00b0. For variation of the side slip angle a slot is provided at the lower end of the U shaped structure along which the nut and bolt attachment can be moved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002326_1.483175-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002326_1.483175-Figure14-1.png",
        "caption": "Fig. 14 Effect of non-optimized parameters on dimensional instability",
        "texts": [
            "8 Validation of Optimum Parameters on Actual Components of Jet Engine. The predicted optimum parameters for the tolerance range of 10 to 20 microns were validated for practical application on compressor disc. By using these optimized v, f, d, a, and r the 400 (10.02, 0.00) mm locating diameter was machined. Immediately after machining dimensions were checked, it was found to be 400 (10.010, 0.00) mm. After 360 hours, the same dimension was 400 (10.015, 0.00), which is within the acceptable tolerance band. Figure 14 and Fig. 15 show the effect of nonoptimized and optimized parameters on dimensional changes. The results prove the validity of this optimization technique and the parameters for the practical applications. The following conclusions emerged form the present study: om: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/28/20 1 Investigations on plastic deformation characteristics of Inconel 718 concludes that shear localized chips of Inconel 718 very similar with titanium Ti-6Al-4V alloy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002983_026635119200700412-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002983_026635119200700412-Figure3-1.png",
        "caption": "Fig. 3. Dome geometry.",
        "texts": [
            " The circular non-hollow section is considered in the present study. In calculating the stiffness matrix and the internal member resistant forces, Gauss point integration is used. The Gauss points are 15 (in circumferential direction of the section) x 5 (in radial direction of the section) x 5 (in direction of member axis). The stress-strain relationship is assumed to be bi-linear as shown in Fig. 2. The strain on any Gauss point of a cross section depends on this relationship. 2.3 Analytical Model o cry --_. -e:y E=2\u00b706xl05 MPa Et =2.0&103 MPa __------- -cry Figure 3 shows the shape and the member arrangement of a rigidly jointed single layer reticulated dome. As for the boundary condition, the nodes of the outer ring are pin-roller supported and can move horizontally in every direction on the horizontal plane. The dimensions of the domes are shown in Table 1,where R is the radius, h is the height of a unit dome, L is the member length and Xis the slenderness ratio of a member. The diameter of the cross section of a member is constant (=24 mm) and a halfopen angle of a unit dome is 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002321_jsvi.1999.2384-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002321_jsvi.1999.2384-Figure8-1.png",
        "caption": "Figure 8. Numerical model 3.",
        "texts": [
            "ect and bearing anisotropy in the rotor-bearing system cause separation of two natural frequencies. Since the proposed method, unlike the FEM, does not require re-meshing the system model every time the length ratio is changed, the aforementioned calculation can be readily performed along with varying only the element lengths of the model. The present example deals with the multi-stepped rotor-bearing system exempli\"ed in reference [6] in order to show the applicability of the proposed method to general rotor-bearing systems. Figure 8 is the cross-sectional drawing along the longitudinal axis of the shaft. The speci\"cations of the rotor-bearing system are described in Table 3. In this case, 14 uniform elements are taken to model the multi-stepped shaft. Two di!erent bearing sets are considered: one is TABLE 1 Comparisons of eignevalues computed by the proposed method and the FEM (eigenvalues j k \"p k #ju k , rad/s) p k /u k FEM FEM FEM Proposed method Mode 4 elements 8 elements 12 elements 1 element 1st B* !0)00746/206)54 !0)00746/206)49 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003622_978-1-4471-0765-1-Figure24-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003622_978-1-4471-0765-1-Figure24-1.png",
        "caption": "Figure 24. Structure of the sensor suit for a 35 axes humanoid",
        "texts": [
            " probability of success J.( __ predicted success probabiJity \u2022 actual success ratio +-_-40.-0~_-20-.()~-().O~-2-0.\"C\"() ~4(:':).:-() <t> (deg.) Figure 23. Comparison of the two success probabilities in the screwdriver-bolt operation. The angle Ij> indicates the relative angle between the direction of the slot and the viewing direction of the range finder. In each viewing angle, the same operation was repeated 50 times to obtain the snccess ratio. 6.5 Gear Mating A gear-mating operation, shown in Figure 24, belongs to group (e) in Figure 9. In this operation, a priori knowledge about how gears are mated is nec essary because there are many potential matches between gear teeth. First, two virtual edges eland e'l are generated; one edge is placed on the center of the nearest tooth to the line connecting two gear centers; another edge is placed on the center of the nearest gap to the line. Then, the orientation of the inserted gear is adjusted so that these two virtual edges are aligned. The position of a virtual edge is calculated from the position of the edges on the tooth (or gap) on which the virtual edge is set (see Figure 24). Assum ing that the shape of the tooth is almost rectangular, the virtual edge is obtained by fitting a line of the center points of pairs of edge points. Figure 25 shows a successful gear-mating opera tion. Figure 26 shows the comparison of the pre dicted success probability with the actual success ratio. The predicted success probability is consistent with the actual success ratio. 7 Summary 7.1 Conclusions We have described a method of systematically gener ating visual sensing strategies for a skill library"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure7-1.png",
        "caption": "Figure 7. Robot modeling in natural co-ordinates",
        "texts": [
            " Its properties are: L1 = 0.3 m, Lz = 4 m, L3 = 5 m, L4 = 0.5 m, E = 6895e07 N/m2, p = 2699 Kg/m3, inner and outer radius of bodies 2 and 3, ri = 0.04 m, I , = 0.05 m. Besides, there is a lumped mass of 200 Kg just in the middle of the last body in the kinematic chain, representing a load. As it can be seen, bodies 2 and 3 are much longer than the others, and they have tubular sections. Hence, they are modeled as flexible bodies, while bodies 1 and 4 are considered as rigid. The robot has been modeled as shown in Figure 7, where point 1 and the y-component of unit vector 3 are fixed. Angle-relative co-ordinates have been defined to make easier the kinematic guidance. Fixed unit vectors 10 and 11 have been introduced only to measure angles, that have been defined as follows: O1 between unit vectors 10 and 3; Oz between unit vectors 11 and 2; O3 between the vector with origin at point 2 and end at point 1, and unit vector 5; O4 between the vector with origin at point 3 and end at point 2, and unit vector 8. For both flexible bodies, static modes of bending and torsion are considered, and the axial one is neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003520_pat.1993.220040212-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003520_pat.1993.220040212-Figure1-1.png",
        "caption": "FIGURE 1. Schematic view (side and top) of thin layer cell for potentio-absorptometry.",
        "texts": [
            " The thin layer cell was then set in the plastic cell with Pt and Ag electrodes, and the plastic cell was sealed by the rubber cap. The PEO solution rose in the thin layer cell by capillary phenomenon, and the electrode reaction under potential was analyzed spectroscopically. For PEOs with average molecular weight of more than 400, PEO-Hb was dissolved in distilled water and cast onto the IT0 electrode with a micro-syringe. A dried PEO-Hb cast IT0 electrode was then attached with a glass plate to prepare the thin layer cell. This was then soaked in the PEO oligomers containing KC1 as the supporting electrolyte (see Fig. 1). PEO-Hb was also cast onto the IT0 electrode. The dried PEO-Hb cast electrode was further covered with PMEO containing KCl. Another IT0 glass electrode (as a counter electrode) was attached instead of a glass plate as shown in Fig. 1. Polished silver wire (@=0.5 mm) was soaked in the PMEO layer as a Electron Transfer Reaction of PEO-modified Hemoglobin / 135 n 8 100- W >r 0 c Q) .- 80- r 0) c 0 0 .- c g 60- K s A Q 0 0 0 0 0 0 A 0 A B 0 0 A I -1.0 -0.8 -0.6 The cell temperature was kept constant by circulating thermostated water into the cell holder. The reduction of PEO-Hb was carried out by applying a negative potential, -0.5 - -1.2 V (vs. Ag). A potentiostat (Nikko Keisoku Co., NPOT-2501) was used for potentio-absorptometry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002857_0890-6955(95)00052-6-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002857_0890-6955(95)00052-6-Figure1-1.png",
        "caption": "Fig. 1. A three-phase four-pole induction motor.",
        "texts": [
            " Then, monitoring of drill fracture by the stator current of the induction spindle motor system is proposed and tDepartment of Mechanical Manufacture Engineering, National Yunlin Polytechnic Institute, Yunlin, Taiwan, 63208, R.O.C. ~Department of Mechanical Engineering, National Taiwan Institute of Technology, Taipei, Taiwan, 10672, R.O.C. 729 730 H.S. Liu et al. supported with experimental results. Finally, the paper concludes with a summary of the present work. In general, a three-phase induction motor consists of two main components: a stationary stator and a revolving rotor. The rotor is separated from the stator by a small air gap. As shown in Fig. 1, a three-phase (a, b, c) set of voltages is applied to the stator and then a three-phase set of currents (Ia, Ib, and Ic) is flowing. These currents produce a rotating magnetic field with four alternate N-S poles. Therefore, the motor in Fig. 1 is called a three-phase four-pole induction motor. The rotation speed of the magnetic field which is also called the synchronous speed ns (rpm) can be expressed as: 120f ns = - - (1) P where f is the frequency of stator in hertz and p is the number of poles per phase. In reality, the rotor rotation speed, i.e. the rotation speed of an induction motor, is always slightly less than the synchronous speed ns. The slip s expressed as a percent of the synchronous speed is defined as the difference between the synchronous speed ns and rotor speed n, that is: ns - n - - - ( 2 ) S n s Figure 2 illustrates how electrical energy is converted into mechanical energy in an induction motor",
            " A series of experiments were carried out on a CNC machining center (Yeong Chin YCM-VMC60A) using a 12 mm x 140 mm (diameter x length) twist drill for the machining of $45C steel plates. A three-phase four-pole induction spindle motor (Mitsubishi SJ7.5K-A) was installed in the machining center with a gear ratio of five between the 734 H . S . Liu et al. motor and spindle. Then, the rotor speed n is equal to five times the spindle speed. For an induction motor, the stator currents (Ia, Ib, and Ic) (Fig. 1) have the same peak-to-peak amplitude but are displaced in time by a phase angle of 120 \u00b0. Therefore, only one of the stator current signals was measured by a current-to-voltage (C/V) sensor (LEM Module LA 50-P) and recorded on a PC workstation through a data acquisition board (DT2828) with a sampling rate of 1000 Hz. The instantaneous stator Monitoring Drill Fracture from Current Measurement 735 current signal is an a.c. signal with a frequency of stator f [equation (1)]. In the experiments, the amplitude of the instantaneous stator current was chosen as the sensing signal for monitoring tool fracture"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002900_20.141296-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002900_20.141296-Figure4-1.png",
        "caption": "Fig. 4. Very long cylinder excited by two horizontal wires in parallel to the axis of the cylinder. Wire\u2019s current is sinusoidal.",
        "texts": [
            " It seems that a good choice in this case is the eddy current permeability of a semi-infinite plate magnetized in parallel to its surface (Fig. 3(b)). The thickness of the semi-infinite plate is chosen equal to the diameter of the cylinder. The eddy current average magnetization of the cylinder magnetized by ac fields in perpendicular to its axis will be (according to expression (23)): p, singh ab 1 + 1 -~ ab cosh ab Using the expression (24) of the eddy current average magnetization, the force exerted on a very long conductive cylinder of p, = 1 by two horizontal wires parallel to the axis of the cylinder (Fig. 4) can be evaluated. The wires current excitation is sinusoidal. This particular arrangement is used because results obtained according to the present method can be compared with experimental and theoretical results reported previously in the literature [ W . The force exerted on a diamagnetic object is [9], [ 111 + F = p, V(GV)G, (25) where Vis the volume. Similarly to expression (25) of the forces exerted on a diamagnetic material the eddy current force exerted on a conductive body by ac magnetic fields can be obtained as: (26) + + FBc = p, V Real (MFtvCelageV)& For the arrangement shown in Fig. 4, the force component exerted on the conductive cylinder of p, = 1 in the y direction will be (see expressions (24) and (26)): (27) dHy dy sinh ab - ab cosh ab sinh ab + ab cosh ab F E e = 2p,VH - Real where Hy is the rms value of the y-axis applied field component. Fig. 5 compares results obtained according to the RABINOVICl AND KAPLAN: EFFECTIVE MAGNETIZATION AND FORCES DUE TO EDDY CURRENTS I 867 3 0 z - 1 d E 0 0.4 0.8 1.2 1.6 2.0 YIR Fig. 5 . Results regarding the vertical component of the eddy current forces for the two dimensional arrangement shown in Fig. 4. An aluminum cylinder of 1 cm radius and 50 cm length, is suspended, when its center is on an axis passing midway between the two conductors spaced 2 cm centers and carrying a 20 A (rms value) and 400 Hz current. Results are obtained according to the present method ( X ) and also were experimentally (0) and theoretically evaluated [ 101. present method (expression (27)) with experimentally and directly evaluated results shown in reference [ l o ] . It is seen that the fit is fairly good, and as a result also the evaluation of the eddy current magnetization (expression (24)) should be valuable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002641_s0389-4304(99)00049-1-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002641_s0389-4304(99)00049-1-Figure5-1.png",
        "caption": "Fig. 5. Statical measurement of gravity center height.",
        "texts": [
            " Then this model can be written as a form of continuous-time domain through the transformation from z- to s-domain. Therefore through the comparison of this model with kinetic model (Eq. (2)), the height of gravity center is estimated in the form below: hs\"F(e 2 ) \" K Ms< (2/<)K f K r l2!<M(K f l f !K r l r ) K f /e 2 !2K r M2K r l r a r !K f l f (a f #a r )N . (8) 3.4. Measurement of static gravity center height Firstly, the height of gravity center is measured statically by inclining the vehicle as shown in Fig. 5, which is the method based on Japanese Security Guarantee standard. Here a middle-sized truck is loaded under two conditions. One is lower #at concrete load and the other is higher load status, and both the gravity center height measurement and the gravity center height measurement in unloaded condition are taken as true values. According to these conditions, the steering angle, roll rate and vehicle velocity during actual running are measured. The roll rate is easily a!ected by the cant or undulation of the road surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003850_s0924-0136(03)00286-3-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003850_s0924-0136(03)00286-3-Figure2-1.png",
        "caption": "Fig. 2. Motion generation along the intersection curve of two parametrically defined surfaces.",
        "texts": [
            " Starting from a given point K0, lying on the intersection curve of the two surfaces, step selection process is repeated at each generated point K1, K2, . . . , until a given final point Kn, also lying on the intersection curve, is reached (Fig. 1). For a parametric formulation of the step selection problem, let one first assume that for a current point P0(x0, y0, z0) lying on the intersection curve of surfaces S1, S2, the corresponding point of the generated path is P(x, y, z) with the distance PP0 not exceeding the predefined step size (Fig. 2). Let one also assume P1(x1, y1, z1), P2(x2, y2, z2) the points at which the normals N1, N2 from P meet the surfaces. Step selection requires the computation of the tangent vector t\u0304 which in this case may be expressed as the cross product t\u0304 = N\u03041 \u00d7 N\u03042 (10) The parametric representation of points P1, P2 lying on surfaces S1, S2, respectively, is given by the position vectors P\u03041 =   x1(u1, v1) y1(u1, v1) z1(u1, v1)   , P\u03042 =   x2(u2, v2) y2(u2, v2) z2(u2, v2)   (11) where (u1, v1) and (u2, v2) are the independent parametric coordinates of the two surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.2-1.png",
        "caption": "Fig. 2.2",
        "texts": [
            "2 Diode Steady-State Characteristics The P-N junction diode is made up of a two-layer silicon wafer. The P-type is connected to anode A, and theN-type to cathode K. Figure 2.1 shows its circuit symbol and indicates the conventional signs for current i and voltage v. junction 20 2 Switching Power Semiconductor Devices k, Boltzman constant, T, absolute temperature on Kelvin scale. In fact, the current deviates from this theoretical value when v increases; but, at the beginning of the characteristics, it has effectively an exponential form (Fig. 2.2). If the temperature rises, thermal ionization produces more carriers and the saturation current I, increases, but the coefficient q/kT is smaller. Figure 2.2a shows the beginning of the curve i(v) for two values of temperature T. \u2022 In the case of the current, a diode can be characterised by the mean value of the forward current it can sustain. This value is expressed as 10 or h or hAv (averaged forward current). The following are also indicated: \u2022 maximum admissible value for a repetitive current peak hM or JFPM (peak forward current), \u2022 maximum admissible value for a non-repetitive current peak hsM (surge non-repetitive forward current). For power diodes the direct voltage drop for the nominal value of the current h is normally between 1.3 and 1.5 V. These characteristics - and all the others - are defined for a given junction temperature Ti and case temperature Tease\u00b7 2.1.2.2 On-State Losses For the normal values of the forward current, the diode voltage drop can be shown by a straight line segment characterized by a threshold voltage V0 and a resistance r (Fig. 2.2b): v = V0 + ri. 2.1 Diodes 21 For given values of u and i, the instantaneous power in the diode is Taking the mean value over a cycle T, the ON-state losses are obtained: P = _!_ J P dt = _!_ [ Vo J i dt + r J i 2 dt] To T o o P = Voimoy + r(/ms \u00b7 (2.2) When the temperature rises, V0 decreases but r increases. 1.1.2.3 The Surge Factor: Remarks In order to calculate protections, a surge factor I 2 t is defined. This integral quantity is defined in the case of a sinusoidal half-wave of the forward current, of peak value IFsM and of duration T, normally taken equal to 10 ms (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002761_1.568457-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002761_1.568457-Figure4-1.png",
        "caption": "Fig. 4 Test-seal assembly drawing",
        "texts": [
            " during excitation. They are also used to statically align the test item with respect to the rotor. For the present investigation, the test-bearing assembly was replaced with the test-seal assembly illustrated in Fig. 3. Highpressure water is injected radially at the center of the assembly with two diametrically opposed locations. The water splits and exits axially across twin test seals whose geometries were defined in Fig. 1. Exit orifice seals are used at each end to hold a slight back pressure. Figure 4 presents an assembly drawing of the test rom: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 05/20/2 seals and housing. The design of Fig. 4 allows interchangeable test seal elements. Figure 5 illustrates the static and dynamic loading arrangement for testing hydrostatic bearings. The hydrostatic bearings have high stiffnesses, and a static load is applied from a pneumatic cylinder to yield specified static eccentricity ratios out to 0.5. Zonic hydraulic shaker heads are used to provide dynamic excitation alternately in the direction of the static load and perpendicular to it. For the present tests, the seals are comparatively weak, and the hydraulic heads are used for both static positioning and excitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002213_1.1707468-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002213_1.1707468-Figure8-1.png",
        "caption": "FIG. 8.",
        "texts": [
            " (A2-AI)2 (A2-AI)3 A2- AI (19) >'1 is the arc along the edge of regression, while A2 - >'1 is the radius of geodesic curvature rl of the curves >'1 (see Fig. 1). Thus it can be written: C(AI) C' (AI) pC(AI) D(AI) \u2022 n12 =--; n2 =--+--+--. (20) rl2 ' r12 r13 rl I t appears that n12 is given by the relation of shear in tapered panels, the apex of the panel being at the edge of regression. In order to examine n2, consider, instead of the flow, the total force acting between two generators sepa rated by an angle da. rlda is the distance between the two generators at any point. Thus, the force is (noting that pda=dAI) (see Fig. 8) C' (AI)dAI C(AI)dAI dF2=n2rlda =D(AI)da+ + . , rl rl2 (21) The factor D(AI) \u00b7da corresponds to a direct load applied along the membrane between two gener ators. The factor dC(AI): rl is due to the variation 552 of shear from one side of the considered clement of membrane to the other. The factor C(AI)dAI: r12 is due to the variation of position of the apex along the generators (as compared with a cone, in which case the apex has a definite position). Assuming that the generators are limited by the radii rl', rl\", with no end loads, then: F l2 , total shear force which is transmitted along the generator, is given by dC(AI) rl\" +rl' --= -F12 \" ,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002907_3516.662865-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002907_3516.662865-Figure14-1.png",
        "caption": "Fig. 14. Resonant beam accelerometer design. The seismic mass (m) is suspended on four support beams (sb) and four resonating beams (rb).",
        "texts": [
            " This opens the way for machining sophisticated sensor structures, as is required for the SmartPen described in Section II. Research, therefore, currently concentrates on the machining of sensor structures. Fig. 13 shows a first example obtained by EDM-based silicon micromachining. The proposed structure is an acceleration sensor, as described in [28]. For this sensor, the suspension system of the mass was machined with EDM. The aim of the second example is to machine a resonant beam accelerometer structure, as shown in Fig. 14. This accelerometer consists of a seismic mass ( ) suspended on eight beams, four suspension beams ( ) and four resonant beams ( ). The sensing principle is based on a shift in resonance frequency of the resonant beams induced by the acceleration forces. A major problem is the machining of a monolithic sensor structure in silicon. To be able to manufacture this sensor by EDM, a test structure with only two beams was attempted. Fig. 15 shows the resulting double beam structure. The parallelism between the top and bottom surfaces of the beam that can be obtained by this technique is about 1:300"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002622_jctb.280610309-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002622_jctb.280610309-Figure2-1.png",
        "caption": "Fig. 2. Apparatus used for membrane testing: ( 1 ) clamp assembly, (2) fill plug '0' ring, (3) pressure relief valve, (4) fi l l plug, ( 5 ) pressure fitting, ( 6 ) tubing, (7) '0' ring, (8) barrel, (9) stirring rod, (10) spin bar, ( 1 1 ) base, (12) hose nozzle,",
        "texts": [
            "\u2019\u2019 which comprised three stages: -preparation of a polymer solution in dimethyl- formamide (in the case of PAN-spinning solution, the solvent was 50% (w/w) aqueous NaCNS; -casting of a film, 0.2 mm thick, of this solution; -immersion of the film in water (gelling). The membranes were formed on a glass plate, making use of an applicator with a gap 0.2 mm high. The were subsequently rinsed in water for 12 h to remove solvent traces. Table 2 presents the composition of casting solutions and the conditions for preparation of the membranes. Before the enzymes were immobilised, the membranes has been tested with deionised water in the apparatus shown in Fig. 2 to determine the dependence of the volumetric flux (J,) on the membrane pressure (AP) within the range 0.5 x lo5 to 3.0 x lo5 Pa at a temperature of 298 K. In the case of the membranes tested, the relationship describing the function J, = f (AP) was determined. The form of the function, depending on the kind of membrane, was J , = A, .AP (1) or J, = B,.(AP)\u2019 (2) 234 M . Bodzek, J . Bohdziewicz, M . Kowalska DM F-dimethylformamide. Conditions-Casting thickness: 0.2 mm; gelling agent: water; temperature of membrane preparation: 293-298 K; gelling time; 900 s; temperature of membrane gelling :293-298 K",
            " Kowalska to the formula: and the ultrafiltration retention coefficient ( R ) defined by the equation: The volume permeate flux (J,) was calculated based on the measured time of the ultrafiltration process. 3 RESULTS AND DISCUSSION lmmobilisation properties-ultrafiltration pressure: l.105 Pa; membrane diameter: 76 mm; membrane area: 38.5 cm\u2019; time: till all enzymes have been immobilised. surface. The membrane with an enzyme gel layer may be used in an enzymatic reactor to carry out biochemical reactions. Immobilisation was carried out in an ultrafiltration device (Nuclepore type s-76-400) with a volume of 400 cm3 and a membrane diameter of 76 mm (surface area 38.5 cm2 )(Fig. 2). Immobilisation was achieved under a pressure of 1 x lo5 Pa. An aqueous solution of the enzyme (concentration of 30-40 pg cm-\u2019) was used for immobilisation. A 100 cm3 volume of protein solution was filtered and 90cm3 of permeate recovered. This operation was repeated until all enzyme had been adsorbed. The activity of the enzyme in the immobilisation sooution and the protein content in the permeate were determined. Table 4 presents the amount of enzyme adsorbed on the respective kinds of membranes as well as the initial activity of the solution used for immobilisation, calculated by means of the formula:\u201d.\u2019 (4) 2.4 Ultrafiltration of model phenol wastewaters with membrane-immobilised enzymes Attempts to purify model wastewaters using the membrane-immobilised enzymes were performed in an ultrafiltration device operated in a dead-end mode (Fig. 2). For the experiments, 500 cm3 of phenol wastewaters were ultrafiltered, with a two-fold volume reduction factor, i.e. the volume of the permeate was 50% that of the feed. The effect of pressure (within the range 0.5 x lo5 to 3.0 x lo5 Pa) and the phenol concentration (within the range 1 to 8 mmol dmP3) upon the phenol removal efficiency from the wastewaters was determined. The phenol concentration was determined colorirnetrically in the respective ultrafiltration streams.\u201d The degree of b i o d e g r a d a t i o n of phenol ( B d ) was calculated according Figures 5 and 6 show the dependence of the permeate flux on the pressure exerted on the enzyme-membranes, with a phenol concentration of 4 mmol dmW3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002213_1.1707468-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002213_1.1707468-Figure4-1.png",
        "caption": "FIG. 4.",
        "texts": [
            " The condi tions in IA and IB are not essentially changed, the only modification consists in the fact that the end shear and normal flow are not the quantities nl2 and n2, but combinations of nl, nl2, and n2. The shear qo' and normal flow no' along JOURNAL OF APPLIED PHYSICS [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: 136.165.238.131 On: Sat, 20 Dec 2014 06:42:07 the edge (Fig. 4) will be: no' =nl cos2 w+n2 sin2 w+2n12 sin w cos w, qo' = enJ -n2) sin w cos w (15) +n12(sin2 w-cos2 w) (positive signs as shown on Fig. 4). The shear and normal flow can be replaced by the flow along the generators and the \"general ized\" shear conjugate to the direction of the edge and the generators. Calling these flows n' and q' we find (Fig. 5) : no' n' =--=nl cos w cot w sin w (16) +n2 sin w+2n12 cos w, q' =qo' +no' cot w =nl2+nl cot w. In this manner it is found that, provided it is made use of conj ugate flow along the edge, the con jugate shear is not a function of 112; thus it does not contain C' and D, and the results obtained under IA and IB remain unchanged, as the knowledge of q is equivalent to the knowledge of n12 (nl is determined in all cases: nl = - ZR')"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003168_s0261-3069(99)00070-9-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003168_s0261-3069(99)00070-9-Figure3-1.png",
        "caption": "Fig. 3. The use of dowels to locate tooling islands.",
        "texts": [
            " Generally, for shallow components, a horizontal build is preferred on the grounds of minimum build time; where deep cavities are required, a vertical build could be quicker. Both strategies are demonstrated in Fig. 1. The advantage of building horizontally is that the \u017dwaste from the cavity can be used to make the core if .a laser or similar is used for processing . Problem areas occur when islands or up stands are required. There are several potential solutions to this. \u017d .1. The use of tooling inserts as islands see Fig. 2 . 2. Locate from dowels; dowel holes can be cut into \u017d .the required laminates see Fig. 3 but require enough space to be used. 3. Secure the islands to the edge of the tool by using \u017d .tabs see Fig. 4 . The tabs are added to the CAD model and automatically cut during the laser process to add support to the island. This method automatically supports islands in the tool because any up stands are automatically supported within the vertical laminate, as demonstrated in Fig. 5. \u017d .From the candidate joining methods Table 2 several could be ruled out fairly quickly. v Mechanical fastening } unsuitable where cooling or heating channels are required"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003144_0957-4158(93)90059-b-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003144_0957-4158(93)90059-b-Figure7-1.png",
        "caption": "Fig. 7. Mechanical arrangement for experiments.",
        "texts": [],
        "surrounding_texts": [
            "The design of the proposed parallel direct adaptive neural network controller has been discussed above. In this section, we consider the application of the proposed strategy for the real-time control of a pilot scale D.C. motor-based positioning system with an asymmetrical load. In the following, the experimental set-up used is first described, and the hardware architecture used for implementing the complete control system is also discussed. Finally, the results of real-time experiments in applying the parallel direct adaptive neural network controller are presented which provide experimental verification of the effectiveness of the strategy. 3.1. Experimental set-up The experimental set-up for the real-time experiments is shown schematically in Figs 6 and 7. The actual apparatus is also shown in the photograph in Fig. 8. This pilot scale position control system has a D.C. motor as an actuator which is driven by a voltage input in the range + 5 V. In the apparatus, the angular velocity of the output shaft is measured using a tachogenerator, and the angular position is measured using a continuous rotation potent iometer . The output shaft also has an asymmetrical load attached to it in the manner shown in Fig. 6. The complete controller algorithm is implemented on the microcomputer, and the program code is written in the C programming language. The controller algorithm receives position commands and generates the signals as specified by (6)-(12). Position signals and velocity signals are read in real-time from a potentiometer and tachometer, respectively. A sampling interval of 45 ms is used. In addition, the software that we developed provides facilities for monitoring the position signals of the control system in real-time. 3.2. Controller design and test conditions In this section, we investigate the performance of the proposed parallel direct adaptive neural network controller strategy in the experimental set-up described above, and compare it with a control system designed using adaptive linear state-feedback control techniques. For the real-time experiments, the set-up of the parallel direct adaptive neural network controller is as shown in Fig. 5; the control system based on adaptive linear state-feedback techniques is shown in Fig. 9. Detailed discussions of adaptive linear state-feedback control techniques can be found in standard texts like [10] and [1l] and are omitted here. Different loading conditions were evaluated in the real-time experiments for position control. The mechanical arrangement shown in Fig. 6 was set up, and the test conditions used are shown in Table 1. These real-time experiments essentially test the ability of the overall control system to respond to a change in position command when different asymmetrical loads are attached. The results of the real-time experiments investigating positioning performance are shown in Fig. 10a-c for the proposed parallel direct adaptive neural network controller. Results of tests under identical experimental conditions for a system based on adaptive linear statefeedback control techniques are shown in Fig. l l a - c for comparison. As mentioned earlier, our developed software provides facilities for real-time monitoring of the position and other relevant signals. In each of Figs 10a-c and l l a -c , there are two frames of signals shown, an upper frame and a lower frame. x-axis: 6.4s/d iv -axis: 57 dog/ally (top frame), 2-5 vohsddlv (bottom f rame) op Frz.me : Position Bottom Frame: I~put Voltage x -ax i s : 6.4s/d iv ~-~i~: 57 d , \u00a2 ~ ~mp ~me). 25 ~oJt~di~ Coonom ~.m~) op Frame :Posltmn ]],ottom Frame: Input Voltage x-axis: 6.4s/div /r.~is: 57 d ~ (~p f,~c), 2-s vo]~,ti,, Coo.ore ~ 0 op Frame : Posit*on Bottom Frame: Input Voltage x-axis: 6.4s/div -axi$: 57 deg/dlv (top frame), 2-5 vollMdiv (bottom frame) op Frimc : Position Bottom Frame: Input Voltage x- ~Jdx: 6.4rddiv ~l-ixis: 57 deg/div (top frame), 2.5 volts/div Coortom frame) op Frame : Position Bottom Frame: Input Voltage In all cases, the upper frame shows the position reference command signal qref(t) (which is the critically damped periodic signal) and the actual position response q(t) of the system; the lower flame shows the input signal u(t) generated by the appropriate controller under study. From the figures, it can be seen that the proposed parallel direct adaptive neural network controller effectively adapted to the different loading conditions within 12 s in each test, and achieved an asymptotic closed-loop positioning performance that is invariant under the different loading conditions. After the initial adaptation phase, fast positioning response was achieved, and the tracking of the position reference signal is quickly attained. For the adaptive linear state-feedback design, positioning performance attained was acceptable under low loading conditions; however, as the loading increased, the performance deteriorates and becomes quite unacceptable. In particular, under Test Conditions B and C, the state-feedback controller was not able to achieve satisfactory tracking of the position command signal. The following additional remarks may be made. (a) Position control of nonlinear servomechanisms. In the early period of development in adaptive control [10, 11], it was sometimes hoped that adaptive methods could be developed for linear control strategies, and then by virtue of adaptation, could be made applicable to nonlinear systems as the nonlinear dynamics could (it was hoped) be modelled as linearized equivalents with time-varying parameters. The real-time results for the adaptive linear state-feedback controller shown in Fig. l l a - c clearly debunks the hope that this may in general be possible. For this servomechanism with asymmetrical loading, the adaptive linear controller provided quite satisfactory performance under low loading conditions (Fig. 11a, small nonlinearities), but begins to deteriorate fairly rapidly for larger loading conditions (Fig. 11b and c, heavy nonlinear dynamics). This stems from the fact that the adaptive linear controller was not designed to handle systems with nonlinear dynamics. In contrast, the proposed parallel direct adaptive neural network controller was designed from the outset for control of the class of nonlinear servomechanisms with dynamics described by (1). Its efficacy in position control for the servomechanism with asymmetrical loading (which fits into this class of nonlinear systems) is clearly demonstrated in the excellent closed-loop responses shown in Fig. 10a-c. (b) Adaptation to different loading conditions. The ability to provide good closedloop control for nonlinear servomechanisms, discussed already, is an important feature of the proposed parallel direct adaptive neural network controller. In addition to that, it should be noted that the real-time experiments also tested the ability of the proposed adaptive neural network controller to handle changes in loading conditions. The results of Fig. 10a-c show that the proposed adaptation mechanism responded well and maintained good closed-loop responses under the different loading conditions. The results above thus demonstrates that the proposed parallel direct adaptive neural network controller provides an effective control strategy for servo systems with nonlinear dynamics which cannot be handled by linear controllers, and they also provide experimental verification of the analytical results of Sections 2.2-2.3."
        ]
    },
    {
        "image_filename": "designv11_31_0002857_0890-6955(95)00052-6-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002857_0890-6955(95)00052-6-Figure10-1.png",
        "caption": "Fig. 10. (a) Demodulated stator current with tool fracture; (b) photograph of the fractured drill (spindle speed = 1000 rpm; feedrate = 200 mm/min; drill diameter = 12 ram; work material: $45C).",
        "texts": [
            " It is deafly shown that drill fracture can be detected by setting a threshold on the demodulated stator current signal in Fig. 7(c). The three-dimensional (3D) demodulated current signal in this drilling test is shown in Fig. 9. The demodulated stator current signal without drill fracture from the first cycle to the ninth cycle is demonstrated. Catastrophic drill fracture suddenly occurred in the tenth drilling cycle. In the following cuts, cutting parameters in drilling operations were changed to verify 738 H.S. Liu et al. the feasibility of monitoring drill fracture by the demodulated stator current signal. Figure 10 shows the experimental result for the other drilling test using a spindle speed of 1000 rpm and a feed of 200 mm/min. The demodulated stator current signal and the photograph of the fractured drill are shown in Figs 10(a) and (b), respectively. Drill fracture was clearly detected at 12.2 sec [Fig. 10(a)]. Figure 11 shows the experimental result for another drilling test using a spindle speed of 1200 rpm and a feed of 220 mm/min. A similar result for the detection of tool fracture from the demodulated stator current signal is illustrated. In this paper, an inexpensive and reliable technique for the detection of drill fracture in drilling operations has been developed. The stator current of three-phase induction motors is used to monitor the variations of motor torque due to drill fracture. It is found that the stator current is not so sensitive to the motor torque variations because of the limited bandwidth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002780_s0927-0256(98)00103-7-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002780_s0927-0256(98)00103-7-Figure7-1.png",
        "caption": "Fig. 7. Microstructure of the rectangular plate-like particle dispersed system (N1 5, N2 2) at strain 1000.",
        "texts": [
            " Namely, the \u00afexible particle dispersed system behaves as a viscoelastic \u00afuid. Elastic property is caused by the deformation of particles. Simulations were carried out to investigate the transient behavior of the plate-like particle dispersed system by using a periodic cell. The simulation systems reported here are 5 vol% suspension, containing rigid square plate-like particles (N1 N2 3) and rigid rectangular plate-like particles (N1 5, N2 2). Both systems are composed of 100 plate-like particles, so total number of spheres is 900 and 1000, respectively. Fig. 7 represents the microstructure of a rectangular plate-like particle dispersed system at strain 1000. Because this particle has the nature of both plate and rod, this system shows the mixed orientation of both systems. Hence, the planar orientation and furthermore the orientation of the major axis of particle in the shear direction (the x axis) is observed. The orientation of major axis is similar to the case of rod-like particle dispersed systems. The transient microstructure is understood by Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002333_s0045-7825(98)00367-3-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002333_s0045-7825(98)00367-3-Figure5-1.png",
        "caption": "Fig. 5. Generating profile 27,. Fig. 6. Line of action and centrodes of Root's blowers.",
        "texts": [
            " The proposed approach enables to simplify the singularity equation using it in form of Eq. (44), and simplify as well the determination of go and g~b. The developed theory is illustrated with the example of Root's blowers (Fig. 3). The ratio of angular velocities of the rotors of the blower is one and the centrodes are two circles of the same radius r (Fig. 4). Movable and fixed coordinate systems S r, Sp and Sj are shown in Fig. 4. The generating curve ~7 r is a circular arc of radius p and is represented in S r as (Fig. 5) r(O) = ( - p sin O)i r + (a + p cos O)j, (55) The tangent and the normal to v r are represented as T r = r o = [ - p c o s O - p s i n 0 0] v (56) N r = T r \u00d7 k , = [ - p s i n O p c o s 0 0] T (57) Applying Eq. (17), we obtain the following equation of meshing Our goal is to determine the singularities of a curve Xp that is conjugated to the circular arc Xr. To solve this problem, we consider the segment of line of action that corresponds to the meshing of curves Xr and .Sp. The tangent to such a segment of the line of action is obtained as (see Eq",
            " The singularity equation is determined as (see Eq. (44)) gl(O, Cb) = x~T,I + YIT~.I - 2rTvl = sin ~b[p + 2a cos 0 - 2r cos(0 - ~b)] - p cos 0 sin(0 - \u00a2~) = 0 (61) Parameters 0 o and ~b 0 of a point that is the candidate for the singularity point can be obtained by solving equation gl = 0 and f = 0. The singularity point is also the point of regression if inequality (54) is satisfied. The investigation of existence of a singularity point must be accomplished considering as the input parameter the ratio p / a of design parameters p and a (Fig. 5). The envelope (generated curve ~p) (Fig. 7(a)) is derived using the algorithm represented in Section 2. Our investigation has been performed for the design parameters (p-= 0.713r, a = 0.96r). It was proven that two singularity points occur in the neighborhood of point M determined by (0 o = 84.8 \u00b0, ~b o = 11.9 \u00b0) and (0 o = 99.2 \u00b0, ~b o = 27.8\u00b0). These two points are simultaneously points of regression and the piece of envelope ~o has the shape of a 'swallow tail'. Such a piece of the envelope is represented to an enlarged scale in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003022_978-1-4471-1501-4_1-Figure1.1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003022_978-1-4471-1501-4_1-Figure1.1-1.png",
        "caption": "Figure 1.1: Schematic of an open-chain robot manipulator with base frame and end-effector frame.",
        "texts": [
            " Joints can essentially be of two types: revolute and pris matic; complex joints can be decomposed into these simple joints. Revolute joints are usually preferred to prismatic joints in view of their compactness and reliability. One end of the chain is connected to the base link, whereas an end effector is connected to the other end. The basic structure of a manipulator is the open kinematic chain which occurs when there is only one sequence of links connecting the two ends of the chain. Alternatively, a manipulator contains a closed kinematic chain when a sequence of links forms a loop. In Fig. 1.1, an open-chain robot manipulator is illustrated with conventional representation of revolute and prismatic joints. Direct kinematics of a manipulator consists of determining the mapping between the joint variables and the end-effector position and orientation with respect to some reference frame. From classical rigid body mechanics, the direct kinematics equation can be expressed in terms of the (4 x 4) homogeneous transformation matrix 'T.CO) = C (1.1) o where q is the (n x 1) vector of joint variables, bpe is the (3 x 1) vector of end-effector position and b Re = (bne b Se bae ) is the (3 x 3) rotation matrix of the end-effector frame e with respect to the base frame b (Fig. 1.1); the superscript preceding the quantity denotes the frame in which that is expressed. Notice that the matrix b Re is orthogonal, and its columns bne , bse , bae are the unit vectors of the end-effector frame axes X e, Ye, Ze. Denavit-Hartenberg notation An effective procedure for computing the direct kinematics function for a general robot manipulator is based on the so-called modified Denavit Hartenberg notation. According to this notation, a coordinate frame is attached to each link of the chain and the overall transformation matrix from link 0 to link n is derived by composition of transformations between consecutive frames"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure9-1.png",
        "caption": "FIGURE 9. Section through the oil film of a parallel surface slider bearing.",
        "texts": [
            " An interesting mechanism which would produce a pressure in the film between relatively moving parallel surfaces, in instances where the forces of inertia are absent, has recently been proposed by Fogg.% The theory has since been solved quantitatively by Cameron and Wood* and by Cope.?* The theory is that the lubricant, in being drawn between parallel surfaces in relative motion, undergoes a rise in temperature due to friction. The friction causes a slight positive expansion. The larger volume must then flow out across an exit section CD, which is no larger than the entrance section A B (FIGURE 9). A relative constriction of the flow results. In contrast to the original mechanism of pressure development described in the first section of this paper, where a constant volume of liquid was required to flow through a smaller space, in this instance, a larger volume of liquid is required to flow through an identical space. A pressure develops in the film in order to balance flow into, and out of, the clearance space in both cases. Quantitatively, the analysis is much the same as the analysis outlined originally by Reynolds, but the mass flow, rather than the volume flow, is conserved in each infinitesimal volume of the clearance space, and this is the more fundamental condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003022_978-1-4471-1501-4_1-Figure1.4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003022_978-1-4471-1501-4_1-Figure1.4-1.png",
        "caption": "Figure 1.4: Characterization of link i for Newton-Euler formulation.",
        "texts": [
            " The linear velocity of the origin of link frame i is given by (1.72) whereas the angular velocity of link i is given by (I. 73) Notice that eqs. (1.72) and (1.73), when referred to frame i, are in general more efficient than (1.58) for computing link velocity. Differentiation of (1. 72) and (1.73) respectively gives Pi = Pi-l + Wi-l X Pi-l,i + Wi-l X (Wi-l X Pi-l,i) + ~i(ijiai + 2Wi-l x qiai) (1.74) and Wi = Wi-l + (i(ijiai + Wi-l x qiai). (1.75) Furthermore, the acceleration of the center of mass of link i is given by (1.76) With reference to Fig. 1.4, the Newton equation gives a balance offorces acting on link i in the form of (1. 77) where 'Yi denotes the force exerted from link i - 1 on link i at the origin of link frame i. Substituting (1.76) in (1. 77) gives (1.78) The effect of mig will be introduced automatically by taking Po = -g. The Euler equation gives a balance of moments acting on link i (referred to the center of mass) in the form of (1. 79) where ii is the inertia tensor of link i with respect to its center of mass. Applying Steiner's theorem, the inertia tensor with respect to the origin of link frame i is given by \u2022 T Ii = Ii + miS (ri)S(ri), (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002557_s0893-6080(97)00043-9-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002557_s0893-6080(97)00043-9-Figure3-1.png",
        "caption": "FIGURE 3. Architecture of the PDA neurocontroller. The discretizing neurons have spatially tuned filters that input the sensory information, The neighbouring (or geometrical) connections connect discretizing neurons that represent neighboring discretization points. Neighbouring connections are utilized for spreading activation. Interneurons measure the sustained spreading activities and perform associative learning with the control neurons. Interneurons which reside at discretizing neurons corresponding to the actual state of the plant activate their connections to control neurons which sum up the incoming activities and output the result.",
        "texts": [
            " The basis of the neurocontroller is a path planning algorithm that uses harmonic functions to encode the collision free trajectories (Connolly & Grupen, 1993; Keymeulen & Decuyper, 1992; Lei, 1990; Morasso et al., 1993; Tarassenko & Blake, 1991). We have extended this algorithm to include the learning of an approximate inverse dynamics control of the plant to be controlled (Fomin et al., 1994; Szepesvfiri and Lrrincz, submitted). Now, we briefly describe the working of this neurocontroller. Let us first consider the path planning part of the neurocontroller (see Figure 3). Sensory neurons provide the input to the network. They may be thought of as discretizing the state space of the plant. Another layer of neurons, the spatially tuned neurons of the geometry discretizing layer develop a problem dependent discretization of the state space: the weights of these neurons are developed in a self-organizing process (a winner-takesall mechanism). The path planning problem is given in terms of discretization point occupancies. Any discretization point, called spatially tuned neuron, can be occupied by an obstacle, the plant, or the target",
            " This eases the learning problem since it suffices to know a mapping that is proportional to the inverse dynamics mapping. Such a proportional mapping is called the position-direction to action (PDA) mapping. It has been shown in Fomin et al. (1994) and Szepesv~iri and L6rincz (submitted) that the realization and learning of PDA mapping can be solved by simple Hebbian learning and by extending the path planning architecture with two additional neuronal layers. To this end we have equipped the path planner neural net with interneurons and control (command) neurons (see Figure 3). Control neurons should emit the control signal that moves the plant along the gradient. Interneurons are situated at lateral connections (to each connection there correspond two directives and thus two interneurons) and are connected to the control command neurons by adaptive connections. Equivalently, interneurons can be considered to store control commands. The working mechanism of the neurocontroller is as follows: an interneuron is enabled to \"f ire\" only if it is in the neighbourhood of the plant's state represented on the discretization layer",
            " The angle between the horizontal line and the trajectory of the plant reflects the relation between the magnitude of 9 In this case the path p lanning a lgor i thm was turned of f and the interneuron activities were directly preset to their desired values. the perturbation vector b and the speed vector vwE. The trajectory of the plant that used the compensation mechanism starts at the same angle but quickly curves back and relaxes at the desired west to east (horizontal) direction. This shows that the plant with the compensation mechanism is able to track asymptotically the desired speed field. This property becomes more apparent if one considers the features of compensation in the upper light part of Figure 3. This figure shows the absolute value of the angle between the horizontal direction and the actual speed (dashed line) and the Euclidean length of the compensatory vector, w (solid line). At the edges of the state space the estimation of the gradient and thus also the estimation of the correct control command are effected by the break of symmetry. The figure shows that the direction of motion approximates the desired direction, and the length of the compensatory vector fluctuates around a constant value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003748_s0378-5173(01)00683-4-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003748_s0378-5173(01)00683-4-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the flow injection system used for bismuth(III) determination. The central bar of the manual injector\u2013commutator shows the injection position after commutation. P, peristaltic pump; S, sample or reference solutions; L, sample loop (250 l); C, carrier solution, 0.5 mol l\u22121 EDTA (pH 8), flowing at 4.4 ml min\u22121; G, earthed stainlesssteel tube; TISE, tubular ion-selective electrode; RE, Ag/AgCl reference electrode; R, record and W, waste.",
        "texts": [
            "30 g of PVC in 10 ml of tetrahydrofurane (THF) followed by the addition of o-nitrophenyl octyl ether (NPOE) and the ion pair [Aliquat 336][Bi(EDTA)] such as: (a) 1% (w/w) ion pair, 69% (w/w) NPOE and 30% (w/w) PVC; (b) 2% (w/w) ion pair, 68% (w/w) NPOE and 30% (w/w) PVC; (c) 5% (w/w) ion pair, 65% (w/w) NPOE and 30% (w/w) PVC; (d) 10% (w/w) ion pair, 60% (w/w) NPOE and 30% (w/w) PVC. These solutions were deposited 3\u20134 times directly in hole walls using a dropper. The utilization of o-nitrophenyl octyl ether as mediator solvent resulted in improved selectivity and fast response times relative to the previously used dibutylphthalate (Montenegro et al., 1993; Teixeira et al., 1997). 2.4. Flow injection system The tubular electrode was inserted into a flow injection system schematically shown in Fig. 1. The 0.5 mol l\u22121 EDTA solution was used as the carrier (C) at a flow rate of 4.4 ml min\u22121. In order to stabilize the baseline, a concentration of 10\u22127 mol l\u22121 bismuth(III) was added to carrier solution. A bismuth(III) sample or reference in 0.5 mol l\u22121 EDTA solution contained in the sample loop (L, 250 l) was injected and transported by the carrier stream after the baseline had reached a steady-state value. The analytical path was 40 cm and the entire flow injection system was maintained at 25\u00b0C, and the potential differences between the tubular and reference electrodes were measured in the pH/ion meter",
            " After that, the samples were dissolved in 0.5 mol l\u22121 EDTA solution and were transferred to a 100-ml volumetric flask and this volume completed with the same solution. The percentage content of bismuth 5% (w/w) ion pair; 65% (w/w) NPOE and 30% (w/w) PVC, indicating that the tubular electrode preferentially responds to the anionic [Bi(EDTA)]\u2212 species, in pH 8. The effect of pH in the range 3\u201311 on the potentiometric response of a 1.0\u00d710\u22123 mol l\u22121 bismuth(III) solution under the conditions specified in the legend of Fig. 1 was investigated. The pH of these solutions was adjusted by the addition of 2 mol l\u22121 HCl or 2 mol l\u22121 NaOH solutions. The results obtained show that there are no significant variations in the potential in the pH ranging from 3 to 11. 3.2. Flow injection parameters and tubular electrode characteristics Preliminary studies were carried out to establish the best flow injection parameters and tubular electrode characteristics. The effect of varying sample loop length from 15 to 150 cm (75\u2013750 l) for [Bi(EDTA)]\u2212 solution ranging from 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure4-1.png",
        "caption": "Fig. 4. Disturbing Forces and Their Components on a Four-cylinder Engine",
        "texts": [
            " Generally, the remaining force or couple acting with the frequency of the engine speed is small enough to be disregarded. If it is found on tests of engine suspensions that vibrations with a frequency equal to the rotational speed are present throughout the running range, then some extraordinary unbalance must be sought. Seconday Out-of-Balance Force. On the four-cylinder engine under consideration, the secondary force F acts at right angles to the crankshaft centre-line halfway between cylinders 2 and 3, with a frequency of two vibrations per engine revolution. In Fig. 4 this force is shown resolved into : ( 1 ) A small component force dong OZ which is not usually troublesome. (2) A large component along OY which is almost vertical. To obtain insulation sufficient vertical deflection must be provided by the mountings. (3) A couple about the transverse axis OX due to the offset a of the secondary force from the principal axis OX through the centre of gravity. This couple is often ignored but can cause trouble at moderate engine speeds. Higher Order Out-of-Balance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002403_1.2818522-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002403_1.2818522-Figure3-1.png",
        "caption": "Fig. 3 Engine seal test facility",
        "texts": [
            " The torque produced by the seal on the shaft is the sum over all the bristle rows of the product of normal shaft reaction, coefficient of friction, shaft radius, and number of bristles per row: t = X aSrD/2 Apparatus Design, instrumentation calibration and operation of the engine seal test facility is described in detail in Wood and Jones (1997). A brief description is given here. Interference seal clearance seal bristle bore (mm) 327 328 backing ring diameter (mm) 329 330 rotor diameter (mm) 328 327 The working section is shown in Fig. 3. Two test seals are employed in a back to back configuration in order to minimize axial loading of the shaft and bearing assembly. The shaft is driven by a 100 kW air turbine. Approximate geometries for the test seals are given in Table 1. The parasitic aerodynamic, air turbine and bearing torques are calibrated; this allows the torque produced by the seals to be inferred from the observed acceleration of the rotor. A video system is used to observe and record the behavior of the seals. Cameras are coupled to two endoscopes which focus on a 5 cm circumference on the upstream side of the seal and a 1 cm circumference on the downstream side"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002873_s0924-0136(97)00078-2-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002873_s0924-0136(97)00078-2-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustrations of the solutions proposed.",
        "texts": [
            " When the element is compressed flow occurs in both the longitudinal and lateral directions. Three different flow patterns have been proposed and evaluated: a simple homogeneous deformation pattern, SODIREC; a nonhomogeneous triangular flow pattern, SODITRI; and a pattern incorporating a parabolic function in the lateral direction, SODIPAR. The analysis for all of these solutions in both one-step compression with fixed penetration and tool widths are investigated and then extended into incremental compression with various penetration levels, tool widths and friction levels. Fig. 1 shows possible patterns of deformation for one increment. 3. Homogeneous pattern of deformation One of the analyses presented for the investigation of deformation patterns in open-die forging has been performed assuming a homogeneous parallel flow of the material. The idea here is simply to represent the material flow by a parallel velocity field in which the deformed cross-section remains rectangular. For predicting the forging load and metal flow in both the lateral and the axial directions,, a kinematically-admissible velocity field distribution was constructed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003654_bf00542566-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003654_bf00542566-Figure4-1.png",
        "caption": "Fig. 4. A spring under axial force",
        "texts": [
            " We start with the determination of compression rigidity of a column. For a highly compressible spring the changes of geometrical parameters are considerable and the non-linear precritical state should be connected with the actual compression rigidity of the equivalent column. We assume that the actual rigidity is described by E A = (EA)o ffc (3.1) where (EA)o is the initial rigidity in the unloaded state, and #c the modification function due to geometrical non-linearity. First of all we determine the initial compression rigidity (EA)o. Figure 4 shows the decomposition of generalized internal forces in a wire cross-section: bending moment Mb, twisting moment Mr, normal force N and shear force T are Mb = PRo sin ao, N ---- P sin s0, (3.2) Mt ~- PRo cos ~0, T --~ P cos s0. M N Making use of Castigliano's principle we calculate the deflection under force P (regarded here as small, determined by linear elasticity) 2 r c n 0 ( Rg sin ~ c% R] cos ~o sin2 ~o @ ~---~w] dqb / = PRo \\/Y2 os + aJo + cos 0 (3.3) where EJw, GJow, EAw, y~GAw are bending, twisting, tension and shearing rigidities of the wire, respect ively, no is the original n u m b e r of coils, and ~o is the shearing fac tor for a circular crosssection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003654_bf00542566-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003654_bf00542566-Figure6-1.png",
        "caption": "Fig. 6. Element of a spring under shear force",
        "texts": [
            " I ts effect will be discussed later. The shearing compliance should be introduced also for the compressed spring with actual length H, pitch angle a and number of coils n. The compressed spring is loaded by a shear force Q. We are interested in displacement due to shearing, completely omitting deflection connected with bending of the spring as a whole. Therefore, in any cross-section, we take only the appropriate par t M~ of the total moment, namely M~ = QR sin ~ (3.21) which causes bending and torsion of the spring wire, Fig. 6, M~ = Ms cos ~, M t = Ms sin ~. (3.22) Similar to the previous case we consider only an element of the spring with wire length ds and referring to it an element of the compressed column dx. Making use of Castigliano's theorem we can write d~ =- QR2(1 q- ~ sin2 ~) sin 2 \u00a2 ds. (3.23) EJw On the other hand, the angle of shear deformation ) /of the column element under force Q and tha t found from Fig. 6 are equal: d/ Z = CaQ - - dx\" (3.24) Introducing (3.23) into (3.24) we have R 2 (1 + ~ sin 2 o\u00a2) sin~ \u00a2, (3.25) C 8 - - - - EJw sin o~ and Cs = C~(\u00a2, ~x, R , d, E, v) is the local shearing compliance of the compressed equivalent column. The mean value of C~ can be written as follows: ~b0-k2r:n 0 ~ = 1 f 2nn C a d\u00a2 = 03(\u00a20 , n, R, d, ~x, E , v) = 1/(GA)column. (3.26) \u00a2o The mean values 0b and 0s depend on ~0 and n but if 2n is an integer they are independent of them. Then the critical loading found for such compliances is an average to both critical forces for the actual helical spring",
            "28) we dropped the index column to simplity the notation. I t turned out that \u00a20 and n have very small influence on the bending rigidity E J of the column. For v ---- 0 we get no influence at all (#b ---- 1) and for v ~ 0 /~ is just slightly different from unity. Finally, for the sake of simplicity, we took with good accuracy ttb = 1. The influence of \u00a20 and n on the shearing rigidity GA is much greater. According to (3.21) individual parts of the coil have various effects on the displacement. The regions closer to \u00a2 ---- ~:/2 and 3~/2 (Fig. 6) give larger and regions closer to the force Q smaller contribution to the global shearing displacement whose increment is given by (3.23). The beginning of the spring does not have to start with angle q~0 ---- 0 and that possible starting angular coordinate has influence on the value of the integral in (3.26) and finally on/~(n, \u00a20). Assuming the most unfavorable situtation (minimalization of GA with respect to $0), it means the pessimistic solution, we obtained the estimation 1 -- 0.3576/n, /~ ---- max 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003656_a:1016321525162-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003656_a:1016321525162-Figure3-1.png",
        "caption": "Figure 3. Details of the model for plane (a) and 3D (b) analyses.",
        "texts": [
            " The planar model includes the bearing sections and a surrounding region of air, which dimension is 20 times greater than the height of the bearings. The mesh employs 8-nodes elements characterized by magnetic vector potential formulation [12]. Only one degree of freedom per node is considered in the present analysis, namely the axial component of the magnetic vector potential. The final mesh has been filled with approximately 6500 elements and 20 000 nodes. Such a great number of elements is due to the very accurate definition of the region immediately surrounding the rings (Figure 3(a)), which is important in force calculations. When the radial displacement e is considered, a 3D solid mesh has to be defined. Since the plane containing the axes of the rings is a plane of symmetry for the geometry, a model of only half volume can be adopted. Even in this case both rings and air are included in the mesh. In order to limit the number of elements, the volume of air is not as big as in the plane case and special \u2018infinite\u2019 elements have been added for surrounding the bodies. The solid model has been defined by 10-node tetrahedral elements characterized by one degree of freedom per node, the scalar magnetic potential [12]. The mesh is obtained with approximately 100 000 elements and 140 000 nodes, with the same care to the region around the bearing underlined for the plane analysis. A detail of the inner ring mesh is shown in Figure 3(b). The calculation of forces in Ansys is obtained by a special macro which applies both the Maxwell Stress Tensor and the Virtual Work methods [13]. The same analyses made by means of the FE method have been carried out by defining a numerical evaluation of magnetostatic integral equations. This approach is more general with respect to the equivalent current method, since the magnetization M in the rings is not supposed to be uniform but it changes because the interaction of the two magnets is considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.7-1.png",
        "caption": "Fig. 9.7. Determination of the stiffness ofa mechanism",
        "texts": [
            " Analogously the reduced flexibility is defined: (9.12) In the same way a reduced angular stiffness of an elastic element with respect to some axis is defined. In order to determine the angular stiffness of an elastic element (Fig. 9.6) with respect to axis D we apply a moment M to link BD, and let the link tum through on angle !:J.a. From the relationship M!:J.a + F!:J.O =0 wefmd From here we obtain the reduced stiffness CD: (9.13) Let us consider a mechanism with two elastic elements arranged in series (Fig. 9.7). In this case we have where 0\\ and O2 are deformations of the elastic elements. Defming the total dis placement of point K in the direction Kx, we obtain Ax = (ax I 001 )!:J.81 + (ax I 882 )!:J.82 = p(cJI (ax I 881 f + c2\"1 (ox I 882 )2 ). Hence, (9.14) Thus, the reduced stiffness of two elastic elements arranged in series is equal to the sum of the reduced stiffnesses of the individual elements. Let the angle rp be the output coordinate of the considered mechanism. We will call outlet stiffness crp the ratio of the moment M' applied at the output to the displacement I1rp of the output link of the mechanism, provided the input is fixed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002701_s0043-1648(98)00254-3-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002701_s0043-1648(98)00254-3-Figure1-1.png",
        "caption": "Fig. 1. Sketch of construction.",
        "texts": [
            " Based on viscous adsorption theory 8 , the w xdistribution of fluid density is not the same across the thickness of the film 9,10 , that is, density varies with the distance from surface to calculating point. When these changes are connected with the change of viscosity on the surface layer, the w xaverage viscosity of the surface layer is produced 11,12 . To obtain the viscosity model, the calculating method is adopted to bearing property analysis for low speed, heavy-load and micro-machines in study. The parameters of the study, adsorbent thickness d , d , and viscosity of surface layer m , m , will determine the lubricant\u2019s characteristics.1 2 1 2 As shown in Fig. 1, three parameters are introduced. They are inseparable adsorption layer viscosity m and m ,1 2 thickness of adsorption layer d and d , and conventional viscosity m . Because the thickness of adsorption layer is very1 2 0 ) Corresponding author. 0043-1648r98r$ - see front matter q 1998 Elsevier Science S.A. All rights reserved. \u017d .PII: S0043-1648 98 00254-3 small, and the surface effect acts only at small region apart from surface, therefore, a uniform calculating viscosity is assumed in every range",
            " E u E u2 3 zshyd : u su m sm2 2 3 0 2E z E z\u00a2zsh: u s03 Because thickness of adsorption layers are very smaller than the one of oil film, adsorption property between metal and oil may be considered as the same. Then, let m sm sm, d sd sd , velocity is as follows:1 2 1 2 1 E p z\u00b0 u s z zyh y UqU\u017d .1 2m E x D 1 E p z zyh d dyh m mU d m\u017d . \u017d .~u s q 1y y zqUy 1y U 4\u017d .2 \u017e / \u017e /2 E x m m m m D D m0 0 0 0 1 E p U u s z zyh y zyh\u017d . \u017d .3\u00a2 2m E x D \u017d . \u017d . \u017d 4.where Ds hm r m q2d 1y mrm0 0 Based on the continuity of flow, one can gain the following relationships for the model shown in Fig. 1, at stability, Newtonian fluid and infinite: 31 h 1 1 2 2q sy q2d 3h y6hdq4d y\u017d .x \u017e /12 m m m0 0 E p mU U 2 2 2= q h q4d y4d h q 2d yd h qU hyd\u017d . \u017d . \u017d . E x 2m D D0 3E q 1 E h 1 1 E p E mUx 2 2 2 2sy q2d 3h y6hdq4d y q h q4d y4d h\u017d . \u017d .\u00bd 5\u017e /E x 12 E x m m m E x E x 2m D0 0 0 U 2q 2d yd h qU hyd s0\u017d . \u017d . D Let m) smrm . Reynolds equation is derived as follows:0 E 1 E p 3 2 2h q2d 3h y6hdq4d y1\u017d . )\u00bd 5\u017e /E x m E x )E m 2 2 2 2s6Um h q4d y4d h q 2d yd h q2 hyd 5\u017d . \u017d . \u017d . \u017d .0 E x D D We introduce the following dimensionless parameters 6m UL0 ) ) )ps p hsh h dsd hb b2hb xsx )L msm)m 6\u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002924_70.744609-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002924_70.744609-Figure2-1.png",
        "caption": "Fig. 2. A passive joint and the saw.",
        "texts": [
            " Assume that and denote the numbers of joints, links, DOF of each joint, and the maximum DOF of each link (six for spatial motion and three for planar or spherical motion), respectively. Then, according to the mobility equation, given by [31] (1) the mobility of our two-arm system is three where the two arms are rigidly grasping a saw. Since it is not enough to control three positional variables and one force variable, we deliberately insert a passive revolute joint at the end of the SCARA robot such that the direction of the axis is parallel to the axis of the saw coordinate system, as shown in Fig. 2, to increase the mobility of the system up to four. In our experiment, we demonstrate that the additional passive joint plays an important role. The kinematics of general closed-chain systems such as multiple arms or dual arms is divided into two layers [11]. The first layer describes the internal relationship between the independent joint set and the dependent joint set. The kinematic relationship is obtained by relating higher-order kinematic constraint equations among the multiple chains. The second layer deals with relationship between the endeffector motion coordinates and the independent set of actuator coordinates",
            " Let is defined as the first-term of (37). Substitute (37) into (38) to obtain (39) or (40) where (41) Now, the choice of (42) provides the minimum norm solution and the constraint equation (38). Here, denotes the pseudo-inverse solution of There will be many different choices of possible in (38). In our experimental work, we utilize the internal loading to eliminate unwanted pitch motion which can be created by moment-unbalancing along the (or pitch) direction during the sawing task (refer to Fig. 2). Now, we derive a force relationship between the mini-mum actuator coordinates and moment vector at the contact position. From (12), the angular velocity vector of the saw is obtained as (43) where denotes the matrix of dimension of 3 4, which is formed by collecting fourth, fifth, and sixth row vectors of Now, from the duality relation between the force and velocity vectors, we have (44) where denotes the moment vector at the contact point. Assuming that is not singular, the moment vector is given as (45) Now, since we desire the moment about the y-axis to be kept zero regardless of the sawing motion, we decide and as (46) where denotes the second row of and is a scalar",
            " Therefore, the magnitude of the vertical force will be decided according to the strength and the roughness of the material to be sawn. In our experimentation, we consider two different vertical forces (i.e., 5 and 10 Newton). The motion of the saw is controlled to have periodic motion in the -direction. We also considered two different sawing speeds (i.e., 0.1 and 0.2 m/s). Initially, we perform sawing task with the blade type (a) of Fig. 7 under the conditions of 0.1 m/s sawing speed and 5 N vertical force. Fig. 8 shows the roll motion (rotational motion about the -axis of Fig. 2) when the additional passive joint is not included. This roll motion is not desirable since it keeps the saw from following a straight-line motion. On the other hand, Fig. 9 shows that the unwanted roll motion can be eliminated by including a passive joint to the system. A small perturbation is observed at each moment that the motion of the saw is reversed. This may be due to the backlash existing in the two-arm system. Also, an internal load control to suppress an unwanted pitch motion (rotational motion about the -axis of Fig. 2) have been considered. Without consideration of the internal load control algorithm derived in the Section IV, a periodic pitch motion occurs in the sawing task, as shown in Fig. 10. By using the internal load control algorithm, the pitch motion can be notably reduced as shown in Fig. 11. The remaining pitch motion of Fig. 11 may be caused by the dynamic motion of the saw. Also, Figs. 12 and 13 demonstrate the force and velocity responses for our proposed control scheme. The rise time for both responses is about 1 s and the transient responses look stable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002213_1.1707468-Figure15-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002213_1.1707468-Figure15-1.png",
        "caption": "FIG. 15.",
        "texts": [
            " Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 136.165.238.131 On: Sat, 20 Dec 2014 06:42:07 frames. Special precautions must be taken for the distribution of the axial forces along a frame which is not parallel to the axis of the surface, and the method is simple only in the case when such a frame is an end frame, on which applied forces are known. (1) Projection on a Plane Perpendicular to the Frames The procedure is essentially the same as between two parallel frames.' the difference between Fig. 15 and Fig. 13 residing in the fact that the two load lines giving the values of the loads perpendicular to the frames are not parallel. Thus, it is necessary to draw two directions of sets of lines defining the loads at the two frames, respectively parallel to the two frames. The force polygon is drawn starting at the intersection of the two first lines, defining the origins of loads A' and A\", respectively, and it must end at the intersection of the two last lines, which gives a control of the equilibrium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure4.53-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure4.53-1.png",
        "caption": "Fig. 4.53",
        "texts": [
            " \u2022 For the braking with energy recovery to be stable in the case of a series machine, a control loop must be introduced. Equation (4.91) gives the condi tion which the peak current value in the machine must verify in order to the chopper being able to control the current. When the rotation speed becomes too high or the voltage supply falls to a value too low, it may be impossible to satisfy condition (4.91). In this case, the stability can be restored by series-connecting a resistance R' with the machine (Fig. 4.53). This produces mixed braking since the power delivered by the machine is partly dissipated in copper losses and partly recovered by the supply. Bibliography The main use of choppers feeding RL E loads lies in variable-speed drives with DC motors. The majority of publications concerning choppers deal with such drives. - In the books [1-5] dealing with speed variation of DC motors, equal attention is given to equipment with a rectifier powered by an AC supply and to equipment with a chopper powered by a DC supply"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003549_1.2831295-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003549_1.2831295-Figure8-1.png",
        "caption": "Fig. 8 The solution of </>(X, Y) for seal S,{a) without a tangential seal surface displacement, Ps = 0, (b) with a tangential seal surface displace ment, Pa = 1",
        "texts": [],
        "surrounding_texts": [
            "Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use displacement is absent the dimensionless numbers Pg and P, of Table 7 are not relevant. Figures 8(a) and 9(a) present the numerically obtained dis tribution of <^(X, Y) and F{X, Y) of seal S belonging to the general film thickness equation without a tangential seal surface displacement Eq. (10) and the two-dimensional roughness ge ometry Eq. (13). Comparable figures can be obtained in the case of seal R. It appears that the maximum of the envelope of the hydrodynamic pressure distribution in the axial (Y) direction is located more to the oil than to the air side of the seal, both in case of seal R and seal S. Despite flow interaction between the individual pressure distributions of the asperities, the pressure level be tween the asperities drops to values equal to the pressure level at the two axial boundaries. This indicates that there is hardly any cooperation present between the various asperities in gener ating the axial pressure distribution. Table 8 shows some numerical results of practical importance for seal R and S. The net axial fluid flow appears to be directed to the air side of the seal in both cases of seal R and seal S. This is in contrast with experimental observations of fully flooded radial lip seals. Besides this, the order of magnitude of the computed net axial oil flow is too low by a factor of about 100 to 650. The average hydrodynamic pressure generated is too low by a factor of about 5 to 6 compared to values observed experimen tally. The same applies to the shaft friction torque which is too low by a factor of 3 to 7. Now the results of the same seal roughness structure but with a tangential seal surface displacement included, are shown. Figures 8(^) and 9(b) present the numerically obtained dis tribution of (^(X, Y) and F(X, Y) of seal S belonging to the general film thickness equation with a tangential seal surface displacement Eq. (14) and the two-dimensional roughness ge ometry Eq. (13) using Ps = 1. Comparable figures can be obtained in the case of seal R. Since the pressure between the various asperities reaches levels beyond the pressure level at the two axial boundaries it appears that the various asperities 272 / Vol. 118, APRIL 1996 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Table 7 bers Numerical input data of the dimensionless num-"
        ]
    },
    {
        "image_filename": "designv11_31_0003224_70.704227-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003224_70.704227-Figure10-1.png",
        "caption": "Fig. 10. (a) Linear motion from p0 to p1, as described in the text. (b) Joint velocities resulting from executing this motion with a constant value of _s = 0.404, corresponding to a translational velocity of 250 mm/s. (c) Joint velocities resulting from executing this motion using a trapezoidal velocity profile for _ . The profile was generated using _ = 0.404 and = 0.808, corresponding (in the region where s) to translational velocity and acceleration values of 250 mm/s and 500 mm/s2. The value of d was 0.2.",
        "texts": [
            " However, near the singularity, these separated solutions are still fairly close together, implying that it is possible to \u201cjump\u201d between them with only a minor deviation in the path. This is usually what damped-least-square techniques do when applied near self-motion singularities: the resulting motion passes through the singularity, closely approximating the solution that would be followed if the singularity lay exactly on the path. The results of this paper are now applied to an example where the regional 3R structure of the PUMA (i.e., joints to ) is made to follow a linear path into a combined elbowshoulder singularity with multiplicity 4 [Fig. 10(a)]. The initial and final path points are and with the corresponding joint values given by and The path itself is parameterized by and given by (18) with the singularity occurring at 1. Motion along the path is specified via . At the singularity, however, a nonzero value of will result in unbounded values for [Fig. 10(b)]. To handle this, we reparameterize within a certain distance of the singularity, according to if if (19) as shown in Fig. 11. For , and are identical, while for 1 , takes the general form (20) This is identical to (3), except for the extra scaling and offset factors ( and ) that provide continuity with at 1. Although the singularity has multiplicity 4, we can use 2 because the PUMA is a quadratic manipulator (Section IV-A). Motion along the reparameterized path can be specified via , and as long as is twice differentiable, and will be well-behaved [this will also be true of higher time derivatives if is made smoother at the junction point ]. Near the singularity, is directly proportional to , and inversely proportional to . The exact relationship between , , and depends on the first-order terms of the Puiseux series expansions for , but for this example a reasonable value of 0.2 was simply determined empirically. Fig. 10(c) shows the joint velocities which result from making follow a simple trapezoidal velocity profile. The actual motion in Fig. 10(c) is computed as follows. At each time : 1) is calculated from its velocity profile; 2) equation (19) is inverted to find ; 3) the current path point is determined from (18); 4) the joint values are then calculated using the PUMA inverse kinematics. The Denavit\u2013Hartenburg parameters used for the PUMA (as per the coordinates of [34]) were 431.8, 149.09, 20.32, and 433.07. For nonredundant manipulators, we have shown that a piecewise analytic path can always be desingularized at any singularity having a finite root multiplicity "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure8-1.png",
        "caption": "Fig. 8. 2-DoF RPM with actuators: (a) R U \u0399\u0399 SSP /2\u2212RRRA \u2212 / PU; (b) Actuators locked; (c) S R U \u0399\u0399 S2\u2212 P \u2212RRRA \u2212 /2\u2212 PU.",
        "texts": [
            " So, S2 m is a continuous axis of the moving platform, but not a virtual continuous axis. According to Section 5.1, the continuous rotation of the moving platform around S1 m can be driven by actuating the side-link, connecting-link or arc-slider of the 1st or 2nd limb. Aiming to motion simulation for large-scale heavy-weight apparatus, this paper adds a SPR actuating limb between the connecting-link of the 1st limb and the base. The continuous rotation of the moving platform around S2 m is driven by actuating the prismatic pair of the SPU limb, as shown in Fig. 8a. According to the input selection principle [47], firstly, lock the actuators at an arbitrary pose of the moving platform. Then, because the reciprocal product of two screws is irrelevant with the coordinate system selection, the coordinate system o x y z\u2212L L L L shown in Fig. 8b is established. oL is located at the intersection point of the two VSLs. xL is parallel with the line connecting the hinge points of the two universal pairs in the first and 2nd limbs. And zL is perpendicular with the plane spanned by the two VSLs. The constraint screws contributed by the 2nd equivalent limb is the same as Eq. (23). The kinematic pair screws of the 1st equivalent limb with locked actuator are b a bS S= (0, 0, 1 ; , , 0), = (1, 0, 0 ; 0, 0, \u2212 )11 m 12 m (25) And its corresponding constraint screws group is a b a bS S S S= (0, 0, 0 ; 0, 1, 0), = (0, 1, 0 ; 0, 0, \u2212 ), = (0, 0, 1 ; , , 0), = (1, 0, 0 ; 0, 0, \u2212 )21 r 22 r 23 r 24 r (26) The SPU limb turns into a SU limb after locking the actuated prismatic joint",
            " It can be represented in the frame o{ }L as l m n p q rS S= Ad = ( , , ; , , )o 31 r g 31 r 31 31 31 31 31 31L\u2032 (29) where Adg is the adjoint representation [48] of the homogenous configuration matrix of frame o{ }L\u2032 with respect to frame o{ }L . The rank of the constraint screws group constituted by Eqs. (23), (26) and (29) is equal to six, i.e. the moving platform cannot move anymore. So, the input selection is reasonable. The rationality of other schemes of inputs selection can be verified by the same method. Generally, redundant actuation limbs are often applied to ensure inputs symmetry and reduce the power of the actuators. A type of redundant actuation configuration is shown in Fig. 8c. The configuration shown in Fig. 8c is taken for instance to establish its kinematics model. Establish the fixed right-handed coordinate system O XYZ\u2212 . Let the origin O locate at the intersection point of the two VSLs, the axis of X be parallel with S2 m and the axis of Z be along S1 m . Establish the moving right-handed coordinate system o xyz\u2212 . Let the origin o locate at the center of the line connecting the hinge points of the two universal joints in the 1st and 2nd limbs. Let the axis of x be along S2 m . And let the axis of z be parallel with S1 m . Moreover o is right aboveO at the initial pose. The configuration S R U \u0399\u0399 S2\u2212 P \u2212RRRA \u2212 /2\u2212 PU shown in Fig. 8c can be equivalent with S U4\u2212 P /RR shown in Fig. 9 according to kinematic equivalent. According to the above analysis, EOE\u2032 constitutes an isosceles triangle. Let the angles between OE , AH and the axis of X be \u03b8 and \u03bb respectively at the initial pose. Assuming the moving platform rotates \u03b3 degrees around S1 m and \u03b1 degrees around S2 m . Then, l \u03c6 \u03b3AB AH AB AH= + \u2212 2 cos( + )1 2 2 2 (30) l RMN ON Oo oM= = \u2212 \u2212 o O 2 (31) l \u03c6 \u03b3A B A H A B A H\u2032 = \u2032 \u2032 + \u2032 \u2032 \u2212 2 \u2032 \u2032 \u2032 \u2032 cos( \u2212 )2 1 2 2 (32) l RM N ON Oo oM\u2032 = \u2032 \u2032 = \u2032 \u2212 \u2212 \u2032o O 2 (33) where, \u03c6 \u03b8 \u03bb= + and Ro O is the rotation matrix of frame o{ } with respect to frame O{ }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003820_i2003-00116-1-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003820_i2003-00116-1-Figure1-1.png",
        "caption": "Fig. 1 \u2013 A viscous sphere rolling on a hard plane (dFI is the inertia force per unit volume).",
        "texts": [
            " Through the analysis of a rolling sphere, it is found that the deformation during the rolling process not only produces a rolling frictional torque (according to BP [6], the rolling frictional torque is caused by the viscous deformation of a rolling body), but also an inertial force, which is caused by the change of accelerations (or centrifugal accelerations during rotation) due to deformation. For unit mass dm in a rolling sphere, the inertia force caused by rotation is aIdm = R\u03c92dm, (1) where aI = R\u03c92 is the acceleration caused by rotation, dm is the unit mass, R is the radius of the sphere and \u03c9 is the rolling speed. When there is no deformation, the inertias of all points inside a rolling sphere are balanced (see fig. 1, dFI left and dFI right are equal and in opposite direction), while as there is deformation (\u2206R = 0), the aI in the deformed volume will deviate, and the deviation is \u2206aI = \u2206 ( R\u03c92 ) = \u2206R\u03c92 + 2R\u03c9\u2206\u03c9. (2) This deviation is the source of inertial normal force (which is caused by the unbalance of inertial forces in the normal direction). The inertias of a rolling sphere are unbalanced due to the changes of accelerations that produce an inertial force FI in the normal direction (see fig. 1). For a sphere as shown in fig. 1 (the center of the contact circle is x0 = 0, y0 = 0, z0 = 0), \u2206aI of the point at the bottom of the deformed volume (x = 0, y = 0, z = \u2212h) is \u2206aI = \u2206R\u03c92 = \u2212h\u03c92, (3) where h is the deformation height. \u2206aI of the front and back edges x = x+ = a or x = x\u2212 = \u2212a (y = 0, z = 0) are \u2206aI = 2R\u03c9\u2206\u03c9 = \u22124h\u03c92, (4) where a is the radius of the contact circle. From the above it is seen that \u2206aI is negative for the deformed volume. Hence, the induced inertial force is in the same direction as the normal compression force caused by elastic deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003771_s0967-0661(01)00094-6-Figure19-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003771_s0967-0661(01)00094-6-Figure19-1.png",
        "caption": "Fig. 19. Intercept scenario with maneuverable target.",
        "texts": [
            " Taking as baseline the 2DOF model given by Eq. (21), several items were added in the simulation such as effect of gravity, mass and mass distribution variation due to fuel consumption, a first order inner loop dynamics on the angle of attack, and a first order actuator model for the engine dynamics. Vm \u00bc 1 m FAxW mg sin g\u00fe Th cos a ; \u2019g \u00bc 1 mVm FAzW mg cos g\u00fe Th sin a ; \u2019XE \u00bc Vm cos g; \u2019ZE \u00bc Vm sin g: \u00f021\u00de A performance test is shown by an off-boresight maneuver against a maneuverable target as shown in Fig. 19. The initial engagement has a heading error of 1801, with a target having a higher initial velocity, and generating an acceleration of the order of 10 g\u2019s. Time histories with missile and target trajectories, missile velocity, commanded and actual angle of attack, missile acceleration, and turn rate are given in Fig. 20. From the figures, it can be seen that a velocity reduction of the missile during the turn reversal is followed by an acceleration, once the intercept cone has been acquired. The presence of the variable structure component in commanded angle of attack is also evident, in the phases of flight where uncertainty is present"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003224_70.704227-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003224_70.704227-Figure5-1.png",
        "caption": "Fig. 5. Hypothetical situation in which Gj(zj ; s) has a repeated root of multiplicity = 4 at s0. The four (possibly complex) solution branches which converge at s0 are diagramed in the top figure. The dotted line in the bottom figure shows a circular contour, defined by s = s0+ ei , surrounding s0 in the complex s plane. If we start at s0+ and follow the analytic continuation of a branch jp around the contour, the resulting value may switch to another branch jq after one full circuit. In general, circuits about the contour, for some , may be required before the analytic continuation returns to jp.",
        "texts": [
            " Then, in the vicinity of , any branch connected with this root can be expressed by (16) where C, , , is one of the th roots of unity, and is of principal value. A proof of this for the case where the coefficients of are polynomials of finite degree is given in [27, vol. 3, sec. 45]. This is generalized in [28] to the case where the are analytic functions. Similar results are described in [29, p. 89]. A sketch of the proof in [28] is as follows. Taking to be complex, consider a small circular contour in the plane around , parameterized by an angle , and described by for some (Fig. 5). At any point on this contour, the solution branches of are distinct, with of them converging at as . Let be a converging branch. Starting at (i.e., 0), let denote the value obtained by following the analytic continuation of along the contour. At 0 we have . After one circuit of the contour, may jump to a different branch , such that . However, after circuits of the contour, for some , must return to the original branch . If we define the auxiliary variable by , then each of the branches connected by the contour can be locally expressed by one single-valued function "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002714_1.555369-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002714_1.555369-Figure6-1.png",
        "caption": "Fig. 6 Tested spherical contact slider system",
        "texts": [],
        "surrounding_texts": [
            "3.1 Theoretical Derivation of a Perfect Contact Sliding Condition. When the slider is in contact with the disk, the motion of the slider is governed by Eq. (3) and the system becomes linear. Thus, the response of the slider spacing to random surface waviness can be obtained by the principle of superposition as follows: h~t! 5 z~t! 2 zd ~t! 5 O k51 ` $Hs ~ fk !A~ fk ! sin ~2pfk t 1 fk !% 2 d (7) where A( f k) is the amplitude of the frequency component at f k, while f k is the phase. H s( f k) is the frequency response function of the slider spacing and is given by Hs ~ fk ! 5 S fk fr D 2 \u00ceH 1 2 S fk fr D 2J 2 1 S 2zc fk fr D 2 (8) where f r is the contact resonance frequency which is given by =k c/m/(2p) (suspension stiffness k is negligible as compared with k c). The variation of the spacing corresponds to the first term of the right-hand side in Eq. (7). Thus, standard deviation s s of the spacing variation is obtained from the Parseval formula and orthogonality of the trigonometric function in the form ss 5 \u00ce1 2 O k51 ` @$Hs ~ fk !% 2 z $A~ fk !% 2# (9) Because the histogram of the spacing variation is close to Gaussian as seen in Figs. 2 and 3, the probability of 99.7% of the spacing values is confined within 63s s. Therefore, the perfect contact sliding condition will be given by 3ss , d (10) Slider load condition for contact sliding thus becomes 3kcss , F (11) If the spectrum of surface waviness, the contact resonance frequency and the contact damping ratio are specified, the relationship between contact stiffness and slider load, which makes the slider come in contact with the disk, is given by Eqs. (9) and (11). If the slider parameter values and b are specified, on the other hand, the critical standard deviation s of surface waviness can be determined from condition (11). 3.2 Comparison Between Analytical Results and Computer Simulation. Since condition (11) is not a sufficient condition but only a necessary one for perfect contact sliding, the critical value of s in condition (11) was compared with that of a numerical simulation for a slider with initial disturbance of ten nanometer height. As stated above, the topological characteristics of surface waviness can be defined by standard deviation s, and roll-off parameter b or p. In calculation of the critical value of s, Journal of Tribology From: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= the frequency components of surface waviness were taken into account from 15.625 kHz, which corresponds to wavelength of 0.96 mm, because the standard deviation s of surface waviness is specified by means of the sample length of 0.96 mm. Because the fundamental period T 0 in random surface generation is 2.048 ms (fundamental frequency is 488.3 Hz), the lowest frequency component of 15.625 kHz is 32nd order and can be denoted by f 32. By using the waviness amplitude at f 32 as a reference amplitude, the amplitude at frequency f k is written as A~ fk ! 5 $A~ f32 !%S f32 fk D b (12) From the Perseval formula, the standard deviation s of the surface waviness is given by s 5 \u00ce1 2 O k532 2048 F $A~ f32 !% 2S f32 fk D 2bG (13) Therefore, the amplitude spectrum of surface waviness at frequency f k can be expressed in terms of s and b, as follows: A~ fk ! 5 \u00ce2s \u00ceO k532 2048 S f32 fk D 2b S f32 fk D b (14) Substitution of Eq. (14) into Eq. (9) yields ss 5 s \u00ce 1 O k532 2048 ~ f32 /fk ! 2b O k532 2048 F $Hs ~ fk !% 2bS f32 fk D 2bG (15) From condition (11) and Eq. (15), the standard deviation of surface waviness which satisfies perfect contact sliding is given by s , F 3kc \u00ce O k532 2048 S f32 fk D 2b O k532 2048 F $H~ fk !% 2S f32 fk D 2bG (16) For the parameter values in Table 1, the boundary value of s (the right hand side value in condition (16)) was calculated by taking all the frequency components from 15.625 kHz (k 5 32) to 1 MHz (k 5 2048) at every 488.3 Hz. In the numerical simulation, the maximum spacing in quasi-steady state was examined by changing the s value for four cases of p or b values. Note that the surface waviness by midpoint displacement method has a statistically constant amplitude in the frequency range between 15.625 kHz and 31.25 kHz, and that the surface waviness by the Fourier filtering method has uniform roll-off characteristics of b for the entire frequency range. Figure 4 shows a comparison between the analytical boundary value of s and the maximum spacing h max that was numerically calculated based on the Fourier filtering method (solid lines) and midpoint displacement method (dashed lines). Values of h max are mean values of 16 samples. The negative spacing indicates that the slider is always in contact with the disk. Symbol D indicates the analytical boundary values of s for the cases where b 5 1.0 ( p 5 1.0), b 5 1.25 ( p 5 1.5), b 5 1.5 ( p 5 2.0) and b 5 1.75 ( p 5 2.5) from the left side, respectively. Because the numerically calculated s values at which h max curves cross the zero spacing line coincide with the corresponding analytical values (D) within 0.1 nanometer, it is proved that the analytical necessary condition of a perfect contact sliding can predict the numerical simulation results. JANUARY 2000, Vol. 122 / 241 /data/journals/jotre9/28685/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded 3.3 Experimental Verification of a Perfect Contact Condition. In order to experimentally verify the analytical results, an experimental apparatus was prepared for measuring contact vibrations of a spherical contact slider sliding on a rotating hard disk. An experimental disk spindle and spherical contact slider are schematically illustrated in Figs. 5 and 6, respectively. A 95 mm (3.5 in.) commercially available aluminum disk was driven by an air-bearing spindle motor. The thin film disk was mechanically textured with an average roughness Ra of 7 nm, coated with 15 nm of carbon and lubricated with 2 nm of perfluorinated polyether. The contact slider system has a glass ball with a diameter of 1.0 mm at the tip of a suspension beam which is 8 mm long, 0.5 mm wide and 0.05 mm thick. Damping tapes are put on both sides of the beam to suppress the elastic vibration of the beam. Free vibration of the lowest mode of the slider and suspension system had a natural frequency of 324 Hz and a damping ratio of 0.107. The effective mass of the slider is 2.06 mg. The suspension stiffness is 8.54 N/m. The effective contact damping ratio between the spherical slider and test disk was identified as 0.1 through a collision experiment (Ono and Maruyama, 1998). The slider was sliding at a 25 mm radius position on the disk at a rotational speed 242 / Vol. 122, JANUARY 2000 From: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= of 3600 rpm. The vibrations of the contact slider at the back side of the slider and disk surface displacement were measured by LDV with a 100 Hz high-pass filter. The detected signals were processed by a FFT analyzer. Figure 7 shows the measured amplitude spectrum of the surface of the disk that was used in the experiment. The recorded data length is 8 ms and the frequency bandwidth is 100 kHz with a spectrum resolution of 125 Hz, which will be appropriate because the contact resonance of the spherical contact slider is about 60 kHz at most in the range of the slider load tested. For calculation of the critical slider load to realize the contact sliding condition, the measured frequency spectrum is represented by two continuous lines (a and b) which have three roll-off characteristics. The discretized spectrum amplitudes at every 125 Hz up to 200 kHz along these two lines were used to calculate the critical slider load. The effective linear contact stiffness that yields the same elastic potential energy as a nonlinear Hertzian contact at the static equilibrium condition was calculated by using the Hertzian spherical contact formula. The Young\u2019s modulus and Poisson\u2019s ratio of the slider were assumed to be E 1 5 385 GPa and n1 5 0.3, respectively. Those of the disk were assumed as E 2 5 70.4 GPa and n2 5 0.3. By using the effective contact stiffness, slider mass, effective damping ratio and the frequency characteristics of the disk in Fig. 7, standard deviation s s of the slider vibration was calculated as a function of slider load F from Eq. (9). Figure 8 shows 3 s s and static penetration depth d as functions of slider load F for two different fitted lines of a and b in Fig. 7. It is noted from this figure that the critical slider load for a perfect contact condition is between 1.12 mN for line a, and 1.40 mN for line b. Since the spacing cannot be measured directly, it is difficult to distinguish the boundary between contact vibration and bouncing one from time domain data. Therefore, we show the frequency spectrum of the slider vibrations for various values of slider load in Fig. 9. The symbol of \u00b9 represents the resonance frequency of contact vibration calculated from the equivalent contact stiffness of the spherical slider. As stated in previous paper (Ono, Takahashi and Iida, 1999), apparent resonance peak shift to a smaller frequency when the slider is bouncing. Thus the boundary between contact sliding and bouncing can be estimated by examining a slider load below which the peak frequency begins to decrease from the triangle point. In order to clearly show the beginning of decrease in peak frequency from the calculated contact resonance, we show the theoretically calculated contact resonance frequency and the peak frequencies of slider vibrations in the experiment in Fig. 10. We note from this figure that there remain some discrepancy between Transactions of the ASME /data/journals/jotre9/28685/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Download theoretical and experimental values of the contact resonance frequency although the reason of this is not clear. However, it is obvious that the experimental peak frequency tends to decrease below the slider load of 1.5 mN. This experimental critical slider load of 1.5 mN is fairly close to the theoretical value of 1.4 mN. Therefore it can be said that the theoretical results were verified experimentally. 3.4 Frequency Range of the Surface Waviness Necessary for Calculation of a Perfect Contact Condition. In order to examine the frequency range that should be taken into account for calculation of a perfect contact sliding condition, the standard deviations of the slider vibrations are calculated by changing the lower and higher frequency ranges from the contact resonance. In this calculation, slider parameters in Table 1 are used. Thus, the contact resonance of the slider is 276 kHz. As a model of surface waviness, the fundamental frequency (rotational speed) is assumed to be f 0 5 100 Hz, while the amplitude at f 0 5 100 Hz is assumed as A( f 0) 5 1 mm. As one example of frequency characteristics of surface waviness, uniform roll-off characteristics of b 5 1.5 are assumed from f 0 5 100 Hz to 1 MHz. Figure 11 shows the standard deviation of slider vibration s s as a function of lower cut-off frequency, taking Journal of Tribology ed From: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/ the upper cut-off frequency as a parameter. When all frequency components from 100 Hz to 1 MHz at every 100 Hz are taken into account, the standard deviation s s is 0.983 nm, which can be considered as the truest value. When the lower cut-off frequency is 150 kHz and the higher one is 500 kHz, s s becomes 0.958 nm which is 97.4% of the truest value. Thus, it can be said from Fig. 11 that a sufficiently precise value of s s is obtained by considering all frequency components within a range from half to twice the contact resonance frequency. As seen in Fig. 7, the real surface of a disk does not have uniform roll-off characteristics. Therefore, Fig. 12 shows the calculated standard deviation of slider vibrations for another surface waviness where b is 2.0 below 10 kHz, 0.5 from 10 kHz to 100 kHz and 1.0 from 100 kHz to 1 MHz. The contact resonance frequency is located in the frequency range where b 5 1.0. As seen in Fig. 12, it is noted that a sufficiently precise value of s s can be calculated if all components in a frequency range from half to twice the contact resonance frequency are taken into account. In statistical analysis of the vibrations of a contact slider that is sliding on a real surface of disk, it is desirable to measure the surface displacement with a recording time of one revolution. In addition, the maximum frequency in the surface displacement data should be more than twice the contact resonance. Therefore, in the experiment described above, the maximum frequency was chosen to be 100 kHz, while the fundamental frequency was desired to be JANUARY 2000, Vol. 122 / 243 data/journals/jotre9/28685/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloade 60 Hz. However, since the recorded data length of the FFT analyzer used in the experiment was limited to 1600, the recording time was chosen to be 8 ms (125 Hz fundamental frequency), which corresponded to about a half of one revolution. This limitation can be allowed because the slider vibrations were steady, and disk waviness has nearly periodical characteristics within the recording time (leakage error can be negligible). Although the spectrum resolution should be equal to the fundamental frequency for prediction of slider vibrations, the frequency components smaller than the lower cut-off frequency can be disregarded. When the surface waviness amplitude is specified in terms of standard deviation s, the sample length to measure the s value should be chosen to be equal to the wavelength of the cut-off frequency in spatial domain."
        ]
    },
    {
        "image_filename": "designv11_31_0003584_b978-0-7506-0119-1.50006-0-Figure1.4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003584_b978-0-7506-0119-1.50006-0-Figure1.4-1.png",
        "caption": "Figure 1.4 Forming operations",
        "texts": [
            " It is now more economical to use numerical control for this type of work. The shape of the work produced is dependent on the movements, which are controlled by the numerical information input to the control unit of the machine. There is no need to produce templates or patterns: when a firm has copying machine tools, numerically controlled machines can produce the templates required more economically than by traditional methods. Forming With this principle, the shape of the tool is the reflected shape of the work. Examples of forming are shown in Figures 1.4a-d. Figure 1.4a shows an angle end mill. To produce this form on a numerically controlled machine, a standard end mill would probably be used with the spindle head being rotated under numerical control to the required angle; the flat section at the base of the angle would be produced as a separate operation. Figure 1.4b shows a form tool producing the end faces on a nut. Figure 1.4c shows a vee groove being formed; this could be an operation carried out on a numerically controlled machine. Figure 1.4d shows two form tools for producing a ball joint. The nut and the ball joint are likely to be required in extremely large quantities, and would justify the cost of producing the form tools required. Machine tools have to be very rigid to use the forming principle for producing components, and generally the form has a maximum length of the order of 50 mm. Components can be produced more quickly when using the forming principle than when using the other principles, because the only movement required at feed rate is the movement of the tool to the depth of the form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002420_1999-01-0743-Figure11-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002420_1999-01-0743-Figure11-1.png",
        "caption": "Figure 11. Wheel Forces after Throttle Off from Steady State Cornering with Visco-Lok Center LSD and Visco-Lok Hang-on",
        "texts": [
            " All of the engine braking torque is carried by the rear wheels (as in a rear-wheel drive vehicle) which causes a significant reduction in the capacity for lateral grip of the rear wheels. This causes the vehicle to oversteer (figure 10). The engine braking torque is transmitted to both axles in the transfer case and \"hang-on\" with Visco-Lok configurations. Thus the braking torque at the rear axle is reduced by the portion transferred to the front axle. This reduces the slip at the rear axle making more lateral grip available here while at the front axle the lateral grip is reduced as this axle carries some of the engine braking torque (figure 11). The distribution of the engine braking torque in the VT-P configuration can be optimized by variation of the ViscoLok characteristic (cut-in, preload) so that this variant has a good handling performance similar to the transfer case configuration. 6 Braking with ABS from steady state cornering \u2013 The reaction of the vehicle to braking while cornering is virtually identical for all the tested configurations. The relative yaw angle is approximately zero (figure 12) indicating that all the configurations show neutral steering behavior"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003515_20.908385-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003515_20.908385-Figure3-1.png",
        "caption": "Fig. 3. Transmission of NRRO.",
        "texts": [
            " The first and the second vibration modes are the rocking and the axial modes respectively that are mainly affected by the flexibility of base plate. The third and the fifth modes are the disk mode with one and two nodal diameters, and the fourth mode is the disk mode with the umbrella shape. It shows that mode splits are observed in rocking mode and the disk modes 0018\u20139464/00$10.00 \u00a9 2000 IEEE with nodal diameters, which split their frequencies into the forward and the backward frequencies as the rotor rotates. NRRO is mainly caused by the defects of ball bearings, and transmitted to the disk through the spindle system as shown in Fig. 3 [1], [4], [5]. NRRO may be reduced if damping material is appropriately inserted in the transmission path to isolate or to absorb NRRO. In order to maximize the reduction of the NRRO, it should be inserted in the place that the strain energy is concentrated. Finite element analysis shows that strain energy is highly concentrated on the contact area between the hub and the inner race of the upper bearing or the contact area between the bearing spacer and the outer races of ball bearing, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002484_(sici)1097-4563(199701)14:1<1::aid-rob1>3.0.co;2-x-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002484_(sici)1097-4563(199701)14:1<1::aid-rob1>3.0.co;2-x-Figure1-1.png",
        "caption": "Figure 1. Force system acting on a quadruped walking vehicle with four feet on the ground.",
        "texts": [
            "15 ized with stride length l (Appendix: Definition 8), the x-coordinate of the support point of any leg i for aThe necessary condition to avoid optimal solu- tion discontinuities discussed in this section are satis- forward/backward periodic gait can be conveniently calculated from16fied in the following sections. xi 5 ci 2 G(t 2 wi) (2) where, ci is the x-coordinate of the initial support position of leg i (Appendix: Definition 9), wi is theA vehicle-fixed reference frame is used here. The xaxis is in the direction of progression. The z-axis is motion phase of leg i, G(t 2 wi) is a periodic function of real variable t 2 wi and it is defined as follows16:vertically upward when the body of the vehicle is level. The y-axis completes a right-handed, orthogonal set (Fig. 1). G(t 2 wi) 5 t 2 wi 1 KT (3) For simplification, we assume that the support surfaces are parallel to each other and the vehicle where K is an integer that satisfies the condition 0 # t 2 wi 1 KT , T.body is parallel to the support surfaces, so \u2018\u2018vertical\u2019\u2019 in this article means normal to the support surfaces, The y-coordinate of the support point of a leg for a forward/backward gait is a constant. In other case,and \u2018\u2018horizontal\u2019\u2019 means parallel to the support surfaces. for example, for crab and turning gaits, the computa- tion of the support point positions of legs is alsoThe force system acting on the vehicle is shown in Figure 1. The force/moment quasi-static equilibrium quite simple. Using the principle of convex combination, weequation of the vehicle can be written as: need to know the time t1 i at which the leg i is placed and the time t2 i at which the leg i is lifted. We defineAF 1 B 5 O (1) t1 1 5 0 in a locomotion cycle, then w1 5 0. Since the time here is normalized to the locomotion cycle timewhere, when there are four support points, F 5 T, the value of t1 i in a locomotion cycle is equal to F2(t2 4 ) F3(t2 4 )] can be solved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003763_s11661-003-0196-8-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003763_s11661-003-0196-8-Figure1-1.png",
        "caption": "Fig. 1\u2014(a) through (e) Surface refinement of castings with the use of concentrated heat flux. ( f ) Cross section of surface-refined element using the GTAW surfacing method.",
        "texts": [
            " Presently, a laser, electron beam, or electric-arc plasma are used as a heat source for the realization of rapid crystallization of surface-layer areas. In the recent period of time, gas tungsten arc welding (GTAW) has enjoyed more and more interest. Such factors as the low price of equipment and easy availability, as well as the lack of special requirements for the preparation of a heated surface, speak for its application. Surface hardening of individual workpieces may be accomplished by various heat-flux path configurations (Figure 1). In the case of their overlapping, cementite precipitates become partially decomposed. Precipitates of cementite, martensite, residual austenite, and graphite occur in those areas. Both areas exhibit comparable values of hardness (Figure 2). The GTAW method has already achieved a high degree of perfection and has been finding wide application in recent years both for joining and postcasting treatments of cast machine and equipment parts. This method is particularly interesting in technological and economic respects"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003311_2.838-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003311_2.838-Figure1-1.png",
        "caption": "Fig. 1 Coupled rotor/fuselage dynamic system.",
        "texts": [
            "The ACSR scheme is based on the idea that in a linear system one can superimposetwo independentresponsessuch that the total response is minimized. When applying this scheme to the helicopter vibration reduction problem, the fuselage is excited by controlled forcing inputs at selected locations so that the combined response of the fuselage, due to both the rotor loads and the applied excitations, is minimized. The schematic representationof such a coupled rotor/active control/fuselage dynamic system and its associated control system for vibration reduction is depicted in Figs. 1 and 2. In Fig. 1, a four-bladed coupled rotor/ exible fuselage model with four actuators for vibration suppression is shown. The ACSR platform is shown as the rectangular structure (plate 1) at the top of the fuselage. The actuators, depicted by the heavy (dark) vertical lines in Fig. 1, extend between points p1 \u2013p2, p3\u2013p4, p5\u2013p6, p7 \u2013p8 , respectively, and are connected to the four corners of the ACSR platform. The schematic control loop governing the ACSR system is shown in Fig. 2. Preliminarytestsof theACSR systemhaveproducedverypromising results for the control of vibration in helicopters.7 \u00a1 9 In the tests, the selection of sensors and actuatorswas based on results obtained from extensive ground shake tests. The major advantages of the ACSR system are 1) one can select locations for preferential reductionof vibratory motion, 2) reducedpower requirements,and 3) minimal airworthiness requirements",
            " To determine the fuselage mass and stiffness matrices, the elastic fuselage is modeled as a threedimensionalstructure.A collectionof elements (i.e., an element library) is used to generate the structural dynamic model of the fuselage. The elements used in the model consist of linear Euler\u2013Bernoulli beams and nonstructuralmass elements. To achieve a realistic structural dynamic model for the helicopter fuselage, it is important to account for the concentrated masses as shown by the open circles in Fig. 1. These nonstructural masses, such as fuel tanks, engine, transmission,payloads, etc., are modeled using a consistently derived nite element model.31 Numerical results indicate that if concentratedmasses are not properly accounted for in the fuselage model, the salient features of the rst few modes corresponding to those present in an actual helicopter cannot be captured.32 At each node, the nonstructuralmass element is capable of three translational,as well as three rotational, degrees of freedom",
            " The generalized coordinates describing the fuselage elastic motion are expressed as qe = U \u00bb (19) In the model, the fuselage dynamics are represented by a truncated set of eight natural modes of free vibration. This representation reduces the number of degrees of freedom associatedwith the fuselage exibilitywhile retainingthe dominantcomponentsof fuselage deformation. An ACSR platform combined with its actuators is an important ingredient that has to be incorporatedinto the coupled rotor/ exible fuselage model, as shown in Fig. 1. In this study, the rotor system is mounted to a rigid rectangular plate connected to the fuselage. The engine and gear-box are assumed to be mounted to this rigid platform. Four actuators, represented by the heavy, dark vertical lines in Fig. 1, are connectedbetweenthe fourcornersof theplatform and separate locations within the fuselage. The corners of this plate are denoted p2 , p4, p6 , and p8 . The actuators are aligned vertically and are connected to the bottom of the fuselage cabin at points p1, p3, p5, and p7 . The locations of the actuator attachment points is somewhat arbitrary.The primary requirement is that there is relative motion between the actuator endpoints in the fuselage modes to be controlledby the ACSR system. The vertical alignment used in this study was chosen primarily to reduce the vertical accelerations in the fuselage cabin",
            " (34) corresponds to the oscillatory part of the hub loads and acceleration vectors given by FH = F0 + FNbC cos(Nb w ) + FNb S sin(Nb w ) MH = M0 + MNbC cos(Nb w ) + MNb S sin(Nb w ) ab = a0 + aNbC cos(Nb w ) + aNb S sin(Nb w ) (35) In this section, the results for a coupled rotor/ exible fuselage model are presented for a four-bladed helicopter. The rst eight fuselage free vibration modes and the comparison of the vibratory hub loadsfor the hub xed and hub free cases are also presented.The helicopter parameters are chosen to model approximately an MBB BO-105 helicopter operating at a weight coef cient of Cw =0.005, with soft-in-plane hingeless rotor blades. The three-dimensional fuselage is modeled by beam elements combined with nonstructural masses, as depicted in Fig. 1. For the soft-in-plane rotor, the basic data used in the computation, togetherwith the uncoupledrotatingnaturalfrequenciesfor the blade modes, are given in Table 1. The chosen airfoil is the NACA 0012. All calculationswere carried out using seven modes for each blade: three ap, two lag, and two torsional modes. Six harmonics were used in generating the blade responses.The data for the nite element representationof the fuselage are also provided in Table 1. The exible fuselage dynamics are represented by a truncated set of eight natural modes of free vibration, so as to reduce the number Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.16-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.16-1.png",
        "caption": "Fig. 9.16. To the determination of the natural frequencies of an elastic mechanism",
        "texts": [
            " As a result, the elements of the flexibility matrix are represented in the following form: exx = cjl(OxM /oql)2 + c2\"1 (OxM /oq2f +C31(OxM /oq3)2, exy = cjl(OxM /oql )(OyM /oql)+ c2\"I(OxM /oq2)(OyM /oq2)+ C31(OxM /oq3)(OyM /oq31 eyy = cjl(OyM /oqlf +c2\"I(OyM /oq2f +C31(OyM /oq3f, exz = cjl (Ox M /oql )(OZ M /oql)+ ci.1 (OxM /oq2)(OZ M joq2)+ C31(OxM /oq3)(az M joQ3), e yz = cjl(OyM joQI)(OZM joqd+ ci.I(OyM joQ2)(OZM joq2)+ C31(OyM /oq3)(OZM /oq31 ezz = cjl(OZM joqlf + c2\"I(OZM /oq2)2 +C31(OZM /oq3f. The flexibility matrix of type (9.34) is symmetric. That is why, eyx = exy ' 9.4. Determine the natural frequencies of the slider-crank mechanism in the equilibrium position shown in Fig. 9.16. The inertia moment of crank 1 with respect to the rotation axis 0 is J, the mass of slider 3 is m, the mass of the connecting rod 2 is negligibly small. Elastic elements are: the transmission connecting the braked rotor of the motor with the crank and the connecting rod which can deform in longitudinal direction. The stiffness of the transmission, reduced to the rotation angle of the crank, is cl> the stiffness of the connecting rod is c2' The radius of the crank is a, the length of the connecting rod is L"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003049_bfb0032596-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003049_bfb0032596-Figure4-1.png",
        "caption": "Figure 4 shows a vertical cut through the spreading layer:",
        "texts": [],
        "surrounding_texts": [
            "Several features of the presented algorithm faciliate a neuronal implementation. The work space is spatially discret, and every point in space may be represented by a neuron. The parallism of neural networks can be exploited because computation and communication is only local. The state of a point in the work space or a neuron depends only on its former state and the states of the immediate neighbors. A neuron only needs to exchange discret information: active or not. However, a neuron should have some notion of time, in order to remember wether it has been activated as member of a wave or a path. So, we choose spiking neurons as model neurons with dynamic behavior for our neuronal implementation. 3.1 Spiking Neurons Spiking neurons are basically complex integrate-and-fire neurons [1] [2]. A general model for a spiking neuron is shown in figure 3: The neurons communicate via spikes only. Incoming spikes x(t)e {0, 1 } are weighted and induce a time-varying potential at a synapse which changes according to an impulse response function h(t) on a time scale much longer than a single spike. A spiking neuron may have several synapses with different impulse response functions. The time course of h(t) models a postsynaptic potential and equips the neuron with a short term memory. This function may be composed of a sharp rise with a following exponential decay or it may be a solely decaying function. The combination function g accumulates various potentials by means of addition, subtraction and/or multiplication. This yields the membrane potential. The output function f finally compares the membrane potential with a firing threshold to determine whether to emit a spike y(t)e {0, 1 } to the connected neurons or not. The weights of a connection may be changed according to a appropriate learning rule. We choose Hebbian-learning, in which the weights between co-activated neurons are strengthened. A neuron is called to be target-learning-active when the membrane potential is actually greater than a learning threshold. A neuron is source-learningactive when it emits a spike. The weights are decayed when only the target or only the source neuron is learning-active. By this way we are able to learn a directed connection from a source to a target neuron when both neurons are simultanously learning-active. For our simulations we used a simulator for spike-processing neural networks with graphical user interface, called SimSPiNN [8], which we have developped because available neuro-simulators are not well suited for the simulation of spike-processing neural networks. In [9] and [10] we survey the relevant features that an efficient implementation of spike-processing neural networks should regard. For real-time simulation of very large-scale networks (N>I00 000) we are currently developping a hardware accelerator, called NESPINN [ 11 ]. 3.2 Neuronal Implementation of the Radar Path Planner To implement the radar pathfinder using our neuron model, we need only two processing layers: 9 the spreading layer implementing the spreading rule and 9 the path layer implementing the path rule. Each point in the workspace has one corresponding neuron in the spreading layer and one in the path layer. 1361 Each neuron is connected to its horizontal and vertical neighbors by an exitatory connection and to itself by an inhibitory connection. All connection have a delay value of 1 time step. When a neuron is active, i.e. when it spikes, it passes this spike to its horizontal and vertical neighbors. So, in the next time step each neighbor neuron becomes active if it is not currently self-inhibited. This way a wave fl'ont of active neurons spreads trough the spreading layer. The self-inhibition of the neurons is needed to prevent the wave from moving backward. Each spreading neuron has an inhibitory obstacle-point-inpm (O), by witch it is inhibited if it is part of an obstacle, and an exitatory target-point-input (T), by witch it can be activated periodically to create a wave Each neuron in the spreading layer has a corresponding neuron in the path layer to which it is connected be an exitatory connection (P). Each neuron in tile path layer is connected to each of its eight neighbors with three connections, one permanent and two learning ones. In addition each neuron has three inputs. Figure shows the inputs and the connections to tile left neighbors of a neuron in the path layer. Figure 6 is used ~o explain how the path layer works: An oriented connection is to be learned from tile starting point S to the first point P of Ule path. To learn this connection, the corresponding neuron of S (neuron S) in the path layer must be source-learning active and simultaneously neuron P must be target- learning active. Figure a shows the initial situation when no connection is learned yet. S gets a source-learning activation by a continual signal at its input start_in. The source actiwltion leads also to a spike activation, so the neuron spikes continuously, passing a source-learning inhibition over the permanent connection s inhib to P. Neuron P is not spiking, so the connection s inhib from P to S has no effect yet. The wave fi'ont in the spreading layer has reached P, so neuron P gets a spike from its corresponding neuron in the spreading layer via its input spreading_in. This spike makes P target-learning active. Thus the learning connections source activ and target inhib from S to P are created. Via soure_activ P gets a permanent sourcelearning and spiking activation form the continuously spiking S. Via targetinhib a further target-learning activation of P is prevented. Via the permanent connection s inhib from P to S the source-learning activation of S is canceled. So now, neuron P is source-learning active and continuously spiking. This is the same situation that we had before with neuron S. If the next wave front in the spreading layer reaches a neighbor Q of P, a path is built from P to Q. The input target in is used to stop the building of the path at the neuron corresponding to the target point. moving obstacle In this paper we have presented a new path planning algorithm, the radar path planner. This path planner is capable of planning paths in unknown, partially known, and changing environments. A path is build in the following way: In regular intervals the target point sends out a wave front traversing the work space with constant speed. The neighbor point of the starting point that is first reached by the wave front must be part of an optimal path. This neighbor point becomes now the new starting point and the procedure is repeated until the target point is reached. When the source point, the target point or an obstacle moves a new optimal path is dynamically build. The path is cut and rebuild when an obstacle moves into the path. When a path becomes sub-optimal by a moving target point or obstacle, a new optimal path is found by path length limitation and cutting noise. Furthermore we have presented an efficient implementation of the path planner with spiking neurons. The features of the presented algorithm faciliate a neuronal implementation. We choose spiking neurons as model neurons with dynamic behavior for our neuronal implementation."
        ]
    },
    {
        "image_filename": "designv11_31_0002569_1.2828770-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002569_1.2828770-Figure1-1.png",
        "caption": "Fig. 1 Worm grinding by a wheel of bicircuiar profile",
        "texts": [
            " Also, the influence of design and operating parameters of the new type of worm gear ing on EHD load carrying capacity of the oil film, on energy losses, and on the flash temperature of the worm thread and gear teeth has been investigated. Contributed by the Power Transmission and Gearing Committee for publication in tlie JOURNAL OF MECHANICAI, DESIGN. Manuscript received Nov. 1995; revised Aug. 1996. Associate Technical Editor: M. Savage. Theoretical Background Geometry and Kinematics of tlie New Type of Worm Gearing Worm and Gear Tooth Surfaces. The worm is ground by a grinding wheel whose profile consists of two circular arcs (Fig. 1). The ground worm surface points are defined by equations M\u201e ,.(SW) 0 (1) where matrix M.g\u201e\u201e performs the coordinate transformation from the coordinate system Kg,, (attached to the grinding wheel) to the system K\u201e (attached to the worm, Fig. 1). The setting angle of the grinding wheel axis, T\u201e,J,, is equal to the worm lead angle, Wou- In equations (1) r\u0302 jfj\"' is the position vector and n*,f\"'' the normal vector of the grinding wheel surface; vj,?,!'''\"'' is the relative velocity vector of the grinding wheel to the worm. To insure the correct mating of the worm and the gear, the gear teeth should be processed by a hob whose generator surface corresponds to the worm surface. But, because the teeth in the hob are relieved, the diameter of the new hob should be slightly larger than the worm diameter to provide tool life",
            ") '\" = 0 0 (2) where matrix Mg\u201e,, provides the coordinate transformation from the coordinate system Kg\u201e (attached to the grinding wheel) to the system K,, (attached to the hob), matrix M^g performs the coordinate transformations from the coordinate system Kk to the system Kg (attached to the gear), and Vgt7'''* is the relative velocity vector of the grinding wheel to the hob. The difference in matrices Mj,\u201e,, and M, and in velocities v (SW,/0 and is only in the center distances: for worm grinding the Journal of Mechanical Design IVIARCH 1997, Vol, 1 1 9 / 1 0 1 Copyright \u00a9 1997 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/31/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use center distance is a\u201eg (Fig. 1); in \"grinding\" the generator surface of the hob, the center distance is C/,, slightly bigger than a\u201eg because of the oversized hob. The last of equations (2) describes mathematically the gener ation of gear teeth by the hob, where ni*' is the normal vector of the hob generator surface, and vj,'\"'^' is the relative velocity vector of the hob to the gear. Tooth Contact. Theoretically, line contact exists between the worm thread and the gear teeth. The instantaneous contact line on the gear tooth surface, for a prescribed value of the rotational angle of the worm, is defined by the following equa tions ri\u00ab' = M\u201e,r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002536_1.402765-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002536_1.402765-Figure2-1.png",
        "caption": "FIG. 2. Lines of constant phase passing through peaks of the sinusoidal undulation expansion function, Eq. (17).",
        "texts": [
            " (15) and (17), each undulation error expansion function \u2022PCm =\u2022\u2022Pyk (Y)\u2022Pzt (Z) is completely characterized by the y- and z-direction wave numbers/\u2022k and vt, respectively, or equivalently, by the y- and z-direction wavelengths A\u2022 = p\u0153 1 and At = vU 1. In order to further utilize the foregoing results, it will be convenient o use two alternative parameters, uniquely determined by/\u2022 and vt and the gear mesh geometry, to characterize each undulation expansion function OCm (y,z) and its corresponding mesh transfer function \u2022 (g). Figure 2 illustrates in the y,z Cartesian tooth coordinates the lines of constant phase passing through the peaks of the generic expansion function \u2022PCm (y,z) defined by Eqs. ( 15 ) and (17). In addition to dealing directly with the axial wave number tt\u2022 -- A ff 1, it will be convenient from here on to deal also with the axial wavelength A\u2022 normalized by the axial pitch Aa, which is the spacing between the lines of contact of adjacent mating teeth measured in the plane of contact in the direction parallel with the gear axes. The axial pitch Aa is illustrated in Fig. 2 of Ref. 9, and is defined by Aa\u2022AA _ A A c -- L tan \u20220 tan \u2022p (47) according to Fig. 2 of Ref. 9, and Eqs. (C4), ( A6 ), and (A4) of Ref. 8, where A and L are the same parameters used in the right-hand sides of Eqs. (34a) and (34b), A and A c are the base and circular pitches, respectively, and \u2022P0 and \u2022p are the base and pitch cylinder helix angles, respectively. Thus the new normalized wave number, introduced here as an alter- native to p k (or A\u2022 ), is qk \u2022Aa/'tk -- Aa/'\u2022k' (48) Furthermore, it is desirable to relate the slope of the lines of constant phase illustrated in Fig. 2, ..... , (49) to the slope of the tooth contact lines defined in this same y,z coordinate system. The slope of such a contact line is illustrated in Fig. 4 of Ref. 8. From the upper portion of Fig. 4 of Ref. 8, one may observe that this slope is dz D \u2022 - ,4 ' (50) Thus, using Eqs. (49) and (50), we can relate the two slopes by their ratio, P\u2022t '\u2022 D /A D vt D Aa ...... vt, (51) \u2022'tf\u2022 At-t\u2022, Aq\u2022, according to the definition (48). The slope parameter may be regarded as an alternative to the wave number vt",
            " The conditions (94a) and (94b) for negligible attenuation arising from multiple tooth contact can be understood readily with the aid of Fig. 5 which applies to the case ! \u2022 = 0. When Eqs. (94a) and (94b) are satisfied for the case l \u2022 -- 0, the spacing and slopes of the lines of the same constant phase of sinusoidal undulation errors on consecutive teeth coin- cide, perfectly, with the spa\u2022-ng and slopes of the instantaneous lines of tooth contact of consecutive tooth pairs. When this concurrence occurs, every point on every line of tooth contact experiences exactly the same phase of the sinusoidal undulation error illustrated in Fig. 2 at each rotational position of the gear pair. Thus, as the gears rotate, the resulting transmission error is a perfect single frequency sinusoid with amplitude 2lc l, according to Eqs. (12) and (68), since no attenuation from multiple tooth contact can take place when all tooth contact points experience, at each rotational position of the gear pair, exactly the same phase. The rotational harmonic number n of the resulting transmission error is given by Eq. (95) or, equivalently, by n = rN = mi in this case where l \u2022 = 0, according to Eq",
            " (55). To determine the tooth meshing harmonic Fourier series coefficients of the transmission error contribution aris- ing from such an undulation, in this case where a(k,1)\u2022 is given by Eq. (62), it is necessary, there\u2022fore, to investigate further only the mesh transfer function \u2022bat (p/A) appearing in Eq. (42). The general form of \u2022at (p/A) is given by Eq. (54). Here, we shall consider only the case where the slope of the lines of constant phase of the sinusoidal undulation error illustrated in Fig. 2 coincides with the slope of the lines of tooth contact illustrated in the upper portion of Fig. 4 of Ref. 8. According to Eq. (51), this important case is described bypat = 1, for which Eq. (103) is applicable. Evaluating Eq. (103) at g = p/A, according to Eq. (42), one obtains \u2022at (p/A) = Jo [rrQa (p - qa )]Jo [ rrQ, (p - qa )] - \u2022 {w(p-qa - n')jo(n'rrQa)jo(n'rrQ,) except n'---O Xjo [rrQa (p - qa -- n') ] Xjo [rrQt (p - qa -- n') ]}, (104) which we emphasize isapplicable only to the casepat = 1",
            " VI B 1 that, in the case of such grinding machines,for everyfixed position of the workpiece, and therefore the worktable, the locus of points of contact between the grinding wheel and the tooth being ground is identical with a line of contact between two meshing teeth. Thus, any undulation error arising from the screw drive that controls lateral worktable motions must be everywhere the same on each line of contact between meshing teeth. (The same is true for any undulation errors arising from the wormwheel drive.) From this fact, it follows that the lines of constant phase illustrated in Fig. 2 must be parallel to the lines of tooth contact; hence, p\u2022 = 1. Let us now turn to property (2) above. For fixed rotational and translational positions of the worktable, assume one line of contact has been ground as described in Sec. VI B 1 above. Now, assume that the grinding wheel is retracted and the worktable is moved in pure rotation exactly one tooth spacing interval (360/N) degrees, after which the grinding wheel is brought back onto position to grind an adjacent ooth on the workpiece at this fixed new worktable position",
            " y I [-zone of \u2022 T \\contact at s' = 0 ' 'T' \u2022 cL io\u2022(\u2022a\u2022f t Line of contact '\u20221 at s'= 0 \u2022 I I1\u2022-- - T -I-I-I-\u2022 I1\u2022' I F\u20222 I A I - I I s' I, , _ I , __ Path of I u \u20221 \u2022 contact\u2022j I I\". .as,cac the sinusoidal undulation illustrated there is related to the lead L' and number of teeth Nw on the wormwheel by L ' 2 \u2022rR b 2 \u2022rR Ak .... , (A2) Nw N\u2022 tan \u00bdb N\u2022 tan \u00bd where Eq. (A1) and the relation 8 Rb/tan \u00bdb = R/tan \u00bd (A3) have been used, where R and \u00bd are, respectively, the pitch cylinder radius and pitch cylinder helix angle. From Fig. 2 of Ref. 9 and Eq. (C4) of Ref. 8, we have A a -- AA/L -- A/tan \u00bdb, (A4) where A a is the axial pitch and A is the base pitch. Introducing Eqs. (A2) and (A4) into Eq. (95) gives n N\u2022A N\u2022 .... , (A5) N 2rrRb N since, by definition, we have A = 2rrRb/N. (A6) From Eq. (A5), it follows that n -- Nw; that is, the transmission error rotational harmonic number of the sinusoidal un- dulation arising from the worktable wormwheel (rotational) drive is equal to the number of teeth N\u2022 on the wormwheel. Equation (95) was used as a basis for obtaining the result n = N\u2022 here, whereas Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002905_pime_proc_1996_210_484_02-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002905_pime_proc_1996_210_484_02-Figure2-1.png",
        "caption": "Fig. 2 Schematic of thrust cones showing parameters and coordinate system used in the analysis with x, y, z a right-hand set",
        "texts": [
            " The major value of Simon's work is the treatment of thermal effects, which are significant at the very high surface speeds considered (up to 300 m/s). The work described in the present paper is concerned with a fundamental analysis of EHL effects in conical thrust rims of the type used in large marine reduction gears. The aim of the study is to obtain a better understanding of thrust cone operation and hence to provide improved techniques for their design. The following papers will deal with thrust cones of a 'crowned' geometry and with an overall method for the design of thrust cones. The two conical surfaces are shown schematically in Fig. 2. The cone angle 8 has a value of about 60\" in this figure to aid clarity. In a practical design the value of 8 is usually close to 90\". The centre distance is denoted b, and the edges of the cone tracks are defined by the constants k,, k 2 , k 3 , k,. The x, y axes lie in the tangent plane of the contact between the cones, as shown in Fig. la. The y axis coincides with the line of contact under zero load and the x axis passes through the points of intersection of the outer edges of the two conical tracks projected into the tangent plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003837_pime_proc_1990_204_094_02-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003837_pime_proc_1990_204_094_02-Figure1-1.png",
        "caption": "Fig. 1 Structure model of the bearing",
        "texts": [
            " The hydrodynamic pressures along the bearing edges are equal to the ambient value. 2. At the film rupture boundary, the Reynolds boundary conditions are considered, that is These boundary conditions are introduced into the numerical procedure for the solution of equation (6) by adopting Christopherson\u2019s method (7). That is, during the iterative process, all sub-ambient pressures are set to zero. To test the new method, a simple finite element structural model of a Ruston-Hornsby V6 Mk I11 connecting-rod bearing is generated as shown in Fig. 1. The bearing structure is represented by a circular ring with constraint on the top 84\u201d region of the outer surface. The connecting-rod is assumed to be rigid. Circumferentially, the bearing is divided into 60 uniform divisions. For the EHL analysis a relationship in the form of a compliance matrix [L] is required between the radial displacements at the nodes and the nodal pressures. This compliance matrix [L] is determined by a finite element method as follows. 0 IMechE 1990 The structural equation in the finite element analysis is {Fl = CKl(6) (10) where {F) is the column vector of nodal loads applied to the system, (6) is the column vector of nodal displacements and [g is the system stiffness matrix which can be assembled for the radial displacement of the nodes on the inner surface of the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002404_1.1833961-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002404_1.1833961-Figure1-1.png",
        "caption": "Figure 1 Schematic cross section of MC-EPS",
        "texts": [
            " With its natures of flexibility, bistability and wide viewing angle, the MC-EPD, we believe, is an ideal candidate for paper-like display media. Based on this conviction, we have pursued the development of microcapsule-type electrophoretic sheets (MCEPS) and means of writing images on them. In this paper, we discuss the structure of the MC-EPS and the principle of writing, and report an evaluation of an experimental prototype. ISSN0099-0966X/99/3001-0180-$1.00 + .00 (c) 1999 SID Structure of MC-EPS Princitde of Writing Figure 1 shows a schematic cross section of an MC-EPS that we consider here. It consists of a base film made of a flexible material such as plastic or paper, microcapsules enclosing an electrophoretic suspension uniformly coated on the base film with a binder, and a transparent protecting layer on the top. With such a simple structure, it can be manufactured inexpensively. In order to obtain the flexibility of the sheet, the binder is required to lhave some degree of softness. It is also necessary that at least one of the base film and the protecting layer be dielectric"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003632_artl.1994.2.1.101-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003632_artl.1994.2.1.101-Figure6-1.png",
        "caption": "Figure 6. (a) Behavioral strategies of the best individuals from generation I 16, Phase II. (b) Finite State Machine of the best Individuals from generation 116. Score = 0.26.",
        "texts": [
            " During this phase the robot only reacts to the environment with a simple stimulus response, and achieves a mean score only of 0.21 or so, depending on the starting state. Toward the end of phase I, in generation 107, the robot acquires a slightly more complex computational structure (Figure 5b); it acquires the ability to use its memory (in state 101), and some forward-backward movement toward the edges becomes evident, especially in the upper right (Figure 5a). This gives it a slightly greater score (about 0.22 from 0.21), and then quickly evolves to the computational structure and behavior shown in Figure 6. In Figure 6, achieved in generation 116, the memory unit is fully engaged and the computational structure is much richer. But some state transitions are still not possible (e.g., 000 directly to 011), and in spite of the richer computational ability, the behavioral repertoire is still similar to that of phase I, supplemented by occasional diagonal traverses of the grid. It had a similar score (0.26 vs. 0.22). In phase III (Figure 7) there are two more differences in the responses, (note the change in response to 01 input in the uppermost right of the figure and the upper-left to lower-right traversal in response to 01 input from state 000)",
            " From the figure it may be observed that the noiseless robot never turned right; it turned only left or else went straight ahead. So when noise was introduced they again went straight ahead or else turned left\u2014never right. Consequently, they did not exit from the white arena and touched additional new cells they might not otherwise have visited. During phase II, in contrast, the strategy was very fragile, being destroyed by lower noise rates. Note that phase II networks responded to the lack of illumination (i.e., black stimulus) in complex ways (see Figure 6a), so that they would sometimes get off the white arena onto the black, and were unable to return to the white arena after venturing out. In effect, the noise pushed them away from the arena. Phase III networks were capable of more complex behavior and could return to the white arena after venturing out into the black zone (see Figure 8). While they did sometimes leave, they could also return. As a result, their fitness values remained more or less constant. We compared the real robot's behavior to the simulated robot's behavior, by finding the noise level that resulted in scores most similar to those of the embodied robots"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002860_s004070050024-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002860_s004070050024-Figure2-1.png",
        "caption": "Figure 2",
        "texts": [
            " Note that f1 and f2 are difference forces that arise while the earth-moon system is orbiting the sun. Thus the moon at P1, since it is closer to the sun that it would be at A1, experiences a stronger attraction that it would at A1, and so a net force away from the plane 5. Similarly, at P2, it is further from the sun than it would be at A2, experiences a weaker attraction than it would at A2, and so, again, a net force away from 5. The results of Newton\u2019s analysis, in Prop 30, of the effects of this force, can be summarized with reference to Figure 2. The notation in Figure 2 is the same as that in Figure 1. PI is a perpendicular dropped from the position of the moon P on to the line TS, and I have labelled the angles T\u0302PI, P\u0302TN and S\u0302Tn as \u03b8 , \u03c6 and \u03c9 respectively. As a result of his analysis in Prop 30, Newton concludes that, at any instant, the line of nodes is rotating with an angular speed that is proportional to the product sin \u03b8 sin \u03c6 sin \u03c9. (I am using modern notation. Newton\u2019s notation is more archaic.) When the moon is at point A in Figure 2, and the line of nodes is along the line of quadratures Qq (both conditions are needed),then the angles \u03b8 , \u03c6 and \u03c9 are each 90 degrees, and the product takes its maximum value 1. In this situation, Newton also deduces, from the ratio of the deflecting force to the gravitational pull of the earth, and the angular speed of the moon in its orbit, that the angular speed of the line of nodes is 33s 10th 33iv 12v (33.1759 sec.) per hour backwards (east to west). He therefore has, using modern notation, the equivalent of the expression R = 33",
            " In other cases they are regressive, and by the excess of the regress above the progress, they are monthly transferred backwards.\u201d In expression (1), the angle \u03c9 changes relatively slowly and the most rapid change comes from the variation in \u03b8 and \u03c6 as the moon moves on its orbit. In Corollaries I and II of Prop. 30, Newton shows, using a geometrical method, that the mean value of R over a complete revolution of the moon is half the value it has when the moon is in syzygies, that is, when it is on the earth-sun line at A or B in Figure 2. When the moon is at point A, \u03b8 = 90\u25e6 and \u03c6 = 180\u25e6 \u2212 \u03c9 and equation (1) gives R = 33.1759 sin2 \u03c9. The mean value, Rm say, is therefore half this, that is Rm = 16.5879 sin2 \u03c9 (2) seconds of arc per hour. (Newton\u2019s expression for the constant is 16s 35th 16iv 36v.) Integration gives this same result if we make the same simplifying assumptions as Newton, namely, that the moon moves with uniform speed on its circular orbit, and that we can neglect the very small difference in the angle \u03b8 made by the inclination of the moon\u2019s orbit to the plane of the ecliptic",
            " We can consider the single moon as being acted on by two forces (the earth\u2019s gravity and the disturbing force) and we are interested only in the motion of its centre of mass. The second law is therefore sufficient. The solid ring is a rigid body with a set of varying forces acting around its circumference, and we need to know its rotational motion about the centre of mass. The second law is therefore not sufficient. A point to note is that it is only the mean motion of the nodes of the individual moons that Newton refers to in this argument. If we refer back to Figure 2, and his expression for the rate of movement of the nodes in seconds of arc per hour, namely, R = 33.1759 sin \u03b8 sin \u03c6 sin \u03c9 (1) we see, as we noted before, that this rate is variable and depends, through \u03b8 and \u03c6, on the position of the moon in its orbit. When sin \u03b8 or sin \u03c6 passes through zero the direction of movement reverses. Imagine now a ring of moons, initially spaced at equal intervals around the circumference of the circular orbit of Figure 2, and ignore (as Newton does) any interaction between them. Because these moons have different values for \u03b8 and \u03c6 we must imagine them as being on circular orbits whose nodes are moving at different rates \u2013 some, indeed, will be moving forward while others are moving backward. There will therefore be relative movement between them (slight, but in principle important) and they will not preserve their relative positions as if they were part of a rigid body. To get them to do so would require the introduction of forces between them, with which Newton\u2019s methods would not be capable of dealing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003953_xa96-8nv4-dbq1-2c8g-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003953_xa96-8nv4-dbq1-2c8g-Figure4-1.png",
        "caption": "Figure 4. Experimental assembly: acquisition data and X-Y-Z system with surface to be analyzed under the sensor.",
        "texts": [
            " Various profilometric 3-D instruments can be selected: optical instruments, scanning microscopy or stylus instruments. This last technique is used in our study. The three dimensional measurement system is made of three major components including the contact stylus, the instrument, which is in contact with the surface to be measured; a mechanical displacement unit moving along the orthogonal axes X-Y-Z. Such a device allows displacement of the sample in the X-Y plane. The Z-axis is the support of the stylus based measurement allowing its vertical setting (Figure 4). The measure of the zone to be analyzed consists of exploring a surface grid obtained by plotting a certain number of parallel profiles, which are one sampling step Dy apart. Each profile contains a number of points Zij (X, Y), point one sampling step Dx apart, (X,Y) being a discrete spatial point in the horizontal point. The sample has a circular form; the Y-axis linear move is replaced by a q-axis rotative move. The experimental assem- essee State University on June 12, 2015 at East Tennessee State University on June 12, 2015jim"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002907_3516.662865-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002907_3516.662865-Figure9-1.png",
        "caption": "Fig. 9. Photograph of the SMA-actuated microvalve.",
        "texts": [
            " The major difference compared to other SMA-based microvalves is that, in this design, the SMA is not contacting the drug, which is a substantial advantage for biocompatibility. Several prototypes were built to arrive at a concept with minimal dimensions, minimal number of parts, and minimal energy consumption. The reduction of parts is of extreme importance for both miniaturization and production (cost) reasons. For this purpose, classic hinged joints were avoided and replaced by elastic joints. Also, screwed clamps were replaced by technologies like gluing, melting, and soldering. Fig. 9 shows an image of the completed valve. This valve contains only three parts, a plastic body, a screw, and an SMA wire. The dimensions of the valve are 8.5 5 2 mm . These small dimensions allow one to integrate the valve on a PCB with the electronics, simplifying the electrical connections. As already stated, the pincher opens when the central joint is elastically deformed by a contraction of the SMA wire. Simple resistive heating induces this contraction of the SMA. When cooling the SMA, the pincher closes again by the elasticity of the joint, thus resulting in a normally closed design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003515_20.908385-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003515_20.908385-Figure1-1.png",
        "caption": "Fig. 1. Solid Model of a 2.5 HDD.",
        "texts": [
            " Based on the characterization of NRRO, it develops a new design of a spindle motor that can reduce NRRO effectively by inserting visco-elastic damping material in the transmission path of NRRO. Manuscript received February 12, 2000. This work was supported in part by Samsung Electromechanics Company. G. H. Jang is with the Department of Precision Mechanical Engineering, Hanyang University, Seoul 133-791, Korea (e-mail: ghjang@email.hanyang.ac.kr). Publisher Item Identifier S 0018-9464(00)08386-2. Dynamics of a spindle system is investigated through the finite element analysis and modal testing. Fig. 1 shows the solid model of a 2.5 HDD with 2 disks to perform finite element analysis. It consists of 29 600 elements, and the base plate is so complicated that it requires 24 300 solid elements. The ball bearing is an inner-race rotating type, and its stiffness and contact angle are determined by A. B. Jones\u2019 theory [6]. Modal testing is performed to validate the finite element model. Fig. 2 shows the frequency response function of a 2.5 HDD while the rotor speed is increased up to 90 Hz in 5 Hz increments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.1-1.png",
        "caption": "Fig. 9.1. Models of a rigid and of an elastic mechanism",
        "texts": [
            "1 Mechanisms with Elastic Links and Their Dynamic Models We will call mechanism with elastic links or simply elastic mechanism a dynamic model of a real mechanism obtained under the assumption that some constructive elements of its links and kinematic pairs are deformable. From this definition it follows that mechanisms with elastic links can be obtained from the corresponding rigid mechnisms, if in the latter some rigid constraints are replaced by deformable ones. Let us illustrate this with concrete examples. In Fig. 9.1a is shown a lever rocker mechanism with rigid links. Assuming that the connecting rod AB can be deformed in longitudinal direction, and introducing in the mechanism model the corresponding elastic element, we obtain a mechan ism with elastic links, whose model is shown in Fig. 9.lb. The assumption about the elasticity of joint A (along two mutually orthogonal directions), or of joint D (along the x -axis) leads to the models shown in Fig. 9.1 c,d. In Fig. 9.2a a model of a rigid mechanism is shown transmitting rotation from engine D to the actuating link - rotor R. Assuming that shaft 0-1, connecting the engine with gear 1 deforms (twists), we obtain the model of an elastic mechanism, shown in Fig. 9.2b. If one considers as deformable shafts 0-1 and 2-3 as well as the gears at the contact point of the teeth, one obtains a more complex model, shown in Fig. 9.2c. Finally, taking into account the deformability of the shaft supports, it is possible to complicate even further the model of the mechanism (Fig",
            " When replacing the rigid constraints by deformable elements we should take as a base the following assumptions: a) The introduced elements will be considered as one-dimensional, i.e. their de formation is determined by the assignment of one scalar parameter (longitu dinal tension or compression, twist angle etc.). Moreover, the real, stiff constraint can be replaced through one or several one-dimensional elements. So, in Figs. 9.1b and 9.1d the rigid constraint is replaced by one element and in Fig. 9.1 c the flexibility of the joint is reflected by the introduction of two one dimensional elements. b) It will be assumed that the considered mechanism, in principle, has to be rigid in order to realize a program motion, and that small deformations of the elastic elements lead to deviations of its motion from the program motion, i.e. to dynamic errors. Hence, we will not consider as elastic a mechanism, whose elastic elements serve for the realization of the functions of a rigid mechanism, e.g., for the force closure of the follower in the cam mechanism shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003477_6.1992-3715-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003477_6.1992-3715-Figure1-1.png",
        "caption": "Fig. 1 Schematic of Bristle Holder and Rotating Cam Used for High Amplitude WeadFatigue Tests",
        "texts": [
            " heattreatable alloys were heat-treated, etc). J Disolacements This test was designed to simulate high-cycle fatigue using a 0.040 inch radial shaft run-out at 1200\u00b0F. Fatigue test specimens were cut from actual (miniature) brush seals, and the runner material was uncoated Inconel 718. The test specimens accumulated in excess of fifteen million fatigue cycles. Scanning electron microscopy was utilized to characterize pre- and post-test fiber morphology, and specimen weight change was also monitored. Figure 1 shows the lobed-runner, and specimen geometry. Within the test fixture, the specimens were positioned such that the fibers were just contacting the smooth runner surface. This assured that the leading edge of each specimen would see the full 0.040 inch run-out condition as each lobe passed. After being loaded, the test fixture was placed in the rig, the shaft was activated (running speed 300 rpm), and the temperature ramp was started. The temperature for all tests was 1200\u00b0F. For the first nine million cycles, the specimens were evaluated after each million cycle increment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003223_0043-1354(94)90311-5-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003223_0043-1354(94)90311-5-Figure3-1.png",
        "caption": "Fig. 3. (a) Construction of microelectrode chamber. (b) Set-up of microelectrode chamber with microscope.",
        "texts": [
            " Biofilm growth occurs on the outside of the inner rotating cylinder and on the inside of the outer one. Four slides can be removed from the outer cylinder, allowing for measurements of biofilm properties (biofilm thickness etc.). With a rotational speed of 200 rpm and external recirculation of approx. 1 1/min, diffusion resistance in the hydraulic boundary layer is negligible (Jansen, 1983). A microelectrode chamber was constructed, in which any one of the four slides from the reactor could be placed. The chamber [Fig. 3(a)] is constructed from a transparent acrylic material with flexible rubber- and silicone packings which make the construction watertight and compensate for small differences in size of the different slides. There are two parts to the chamber: an upper part (the cover) and a lower part, in which the reactor slide is placed. The cover is fixed in a frame of stainless steel and a small circular hole in the middle allows for the passage of the microsensor. The lower part of the chamber is attached underneath the cover with two removable metal straps. Because the cover is longer than the slide-chamber this construction allows the slide to be moved relative to the microsensor, which is kept in a fixed set-up. The change in microsensor position is easily carried out within a few seconds without any loss of water. The chamber has been constructed with a small \"'window\" permitting the use of a stereo microscope for positioning the microelectrode tip at the surface of the biofilm [Fig. 3(b)]. However, it must be observed that this is only a practical help for the positioning; the exact location The electrode-measuring chamber is connected to the biofilm reactor through the external recirculation loop. A slide from the biofilm reactor is placed in the measuring chamber and oxygen profiles are measured under the same chemical conditions as found in the bulk liquid of the biofilm reactor. Hydraulic conditions are established in as similar a way as possible. Tracer experiments have shown that the combined set-up (reactor + measuring chamber) is ideally mixed (Larsen, 1992)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003654_bf00542566-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003654_bf00542566-Figure5-1.png",
        "caption": "Fig. 5. A spring under overall bending",
        "texts": [
            " They will be determined by a linear analysis, but in the deformed state, with R0, no and s0 replaced by R, n and s. Additionally, it is assumed that displacements caused by buckling are infinitely small and hence the changes of the geometrical parameters of a compressed spring can be neglected. We start with the bending compliance determining first of all its local form. The compressed spring is loaded at its end by a concentrated overall bending moment M* which causes torsion of the spring wire, Fig. 5, M t t = M * cos \u00a2 cos s (3.15) m o m e n t and double bending (Mo = M, + Mtb) M b = M*(sin 2 \u2022 + cos 2 \u00a2 sin ~)112. (3.16) Using the energy approach (Castigliano's theorem) we calculate the increment of the total angle of deflection of the spring element M* dO = (1 + v cos 2 ~ cos 4) ds (3.17) EJw where ds is the elementary length of the wire. Next we define the local bending compliance Cb demanding that the element dx of the compressed equivalent column under moment M* has the same angle of deflection, namely dO = Q M * dx "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000009_bf03184963-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000009_bf03184963-Figure1-1.png",
        "caption": "Fig. 1. Model of the vehicle.",
        "texts": [
            " Numerical calculations by de Pater 1) have shown that the lateral motion of a highly simplified model of a railway vehicle can converge to a purely periodic motion for certain values of three essential parameters. In the present paper a more analytic approach is used to determine the conditions of stability of such oscillations. In addition, this approach affords some further insight into certain details of the motions discussed. For the sake of completeness the model is described again briefly (see fig. 1). The vehicle consists of a rigid body on two axles, four wheels. If more than two axles are present, no trucks however, only the first and last will be considered. The axles and wheels have no other freedom with respect to the body than that of rotation. The wheels are cylindrical without flanges; each flange is repleced by a vertical roller with limits the lateral movement of the axle belonging to it. The distance between the axles is 2a. - 393 - The distance between the two rails is 20. The other variables are defined as follows: plane between the two rails, ip = angle between the longitudinal direction of the vehicle and that of the track, M = mass of the vehicle, k = coefficient of frictional glide (\"creep coefficient\"), g = acceleration of gravity, I = moment of inertia of the vehicle about its central vertical, Y = half the lateral play of an axle on the track"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.60-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.60-1.png",
        "caption": "Fig. 2.60",
        "texts": [
            " When the thyristor has become reverse-conducting, the holes in the P 1 layer invade the N 1 layer: therefore, the resistivity of the latter does not decrease as was the case during forward-bias avalanche. The reverse current increases under a reverse voltage which remains high: the thermal dissipation limits are reached very quickly. A negative voltage higher than its reverse-breakdown voltage VsR must therefore not be applied to the thyristor. 76 2 Switching Power Semiconductor Devices 2.4.2 Steady-State Characteristics 2.4.2.1 Output Current-Voltage Characteristics \u2022 Figure 2.60 gives the anode current iT variations as a function of the anode to-cathode voltage vT, for zero gate current. This characteristic comprises three distinct branches: - With negative voltage (OA). This characteristic has the same form as that of a PN junction. The thyristor is characterised by the tolerable maximum repetitive reverse voltage VRRM\u00b7 - With positive voltage and blocking state (OB). Voltage vT can reach V80 without the thyristor allowing a significant forward current to flow. When vT reaches v80 , the current becomes sufficiently strong to bring about the avalanche breakdown: the corresponding value is called the latching current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003000_ip-epa:19982170-Figure16-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003000_ip-epa:19982170-Figure16-1.png",
        "caption": "Fig. 16 em Computed 1ocaljTowfield through end winding in plane of wafi-",
        "texts": [
            " This prevents the development of radial flow, forcing the flow to turn axially as it passes through the \u2018fan\u2019. The majority of the circulation therefore takes place in the space above the wafters. The high positioning of the recirculation and the dominance of the wafters starve the bar end fan. This would have secondary effects like poor local cooling on the rotor and at the base of the end winding. IEE Proc -Electr Power Appl I V d 145, No 5, September 1998 425 tial component of the flow at the inlet to the winding causes a region of separation at the upstream edge of the inlet, Fig. 16. Losses are incurred because the separation reduces the effective flow area and results in increased velocities. If the channel is too short for reattachment to occur before the channel exit, the dynamic pressure head is effectively lost. There are also regions of separation inside and towards the rear of the winding. The windings remove the tangential momentum from the through-flow and flow leaves the rear of the winding in the form of relatively weak radial and axial jets. These jets and their impingement on the casing form two distinct vortices of different sizes at the rear of each block, Fig. 16. Further up the winding the smaller vortex moves outwards towards the casing, resulting in a weak counter-swirling flow. Fig.15 porosity = Flow Jield 100% in a radial plane through the wafters (computed) for The velocities generated by the \u2018fan\u2019 are predominantly tangential at around 85% of rotor tip speed, with a very small radial component, averaging only 5% of tip speed. Since the circulating flow rates are low, the tangential velocity is dominant throughout the entire flow field: there is a large volume of strongly swirling flow (average velocity around 60% of tip speed) surrounding the \u2018fan\u2019, and a region of much slower swirling flow (average velocity around 15% of wafter tip speed) behind the end winding, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002722_la9510386-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002722_la9510386-Figure1-1.png",
        "caption": "Figure 1. Sketch of a fluid particle attached to a solid surface. P1 and P2 are the pressures inside and outside the particle; r and \u03b8 are its curvature radius and contact angle.",
        "texts": [
            " Indeed, if a slow process of diffusion across the phase boundary is present, the transported component inside the fluid particle can be treated as an independent component in so far as its chemical potential is different from that in thesurrounding fluidphase. Sinceusually themechanical equilibrium is establishedmuch faster than the diffusive one, we may investigate the equilibrium shape of the attached fluidparticle irrespective of the lackof adiffusive equilibrium. For the sake of simplicity we will consider the attachmentof abubble ordroplet toa flatplate (negligiblegravity effects; Figure 1). The same system is investigated in the X Abstract published in Advance ACS Abstracts, November 1, 1996. (1) Eriksson, J. C.; Ljunggren, S. Langmuir 1995, 11, 2325. (2) Craig, V. S. J.; Ninham, B. W.; Pashley, R. M. J. Phys. Chem. 1993, 97, 10192. (3) Christenson, H. K.; Fang, J.; Israelachvili, J. N. Phys. Rev. B 1989, 39, 11750. (4) Ducker, W. A.; Xu, Z.; Israelachvili, J. N. Langmuir 1994, 10, 3279. (5) Shchukin,E.D.; Pertsov,A.V.; Amelina,E.A.ColloidChemistry; Moscow University Press: Moscow, 1982 (in Russian). (6) Adamson,A.W.PhysicalChemistry ofSurfaces;Wiley: NewYork, 1976. (7) Kirkwood, J. G.; Oppenheim, I. Chemical Thermodynamics; McGraw-Hill: New York, 1961. S0743-7463(95)01038-9 CCC: $12.00 \u00a9 1996 American Chemical Society article by Eriksson and Ljunggren1 (eqs 26-29). The approach can be further extended to describe bridging cavities. The variation of the grand thermodynamic potential of the system reads where \u2206p ) P1 - P2 (Figure 1) is the capillary pressure, \u03b3 andAl are the surface tension and the area of the liquid/ gas interface, As is the area of the solid/gas interface, \u2206\u03b3 ) \u03c91 - \u03c92 is the difference between the surface densities of the grand potential for the solid/fluid 1 and solid/fluid 2 interfaces, V is the volume of the attached particle of fluid 1, andNi and \u00b5i denote the number of molecules and the chemical potential of the i-th component (1 e i e k). Let us denote Then some geometrical considerations yield where r is the curvature radius of the fluid interface. Further we consider a process taking place at \u03b4\u00b5i ) 0 (i ) 1, ..., k). Then we substitute eqs 3 and 4 into eq 1 and in the resulting expression set the coefficientsmultiplying the independent variations, \u03b4r and \u03b4x, equal to zero to derive Finally, from eqs 5 and 6 one derives In this waywe establish that both the Laplace andYoung equations correspond to a local extremum of \u2126, i.e. to the equilibrium position of the attached fluid particle at the solid substrate (Figure 1). Our purpose below is to investigate under which conditions this equilibrium position is stable (\u2126 is minimum) or unstable (\u2126 is maximum). Let us first imagine a processwhich takes place at fixed chemical potentials of all components. Such a process canhappen if all componentspresent in thebubble/droplet are soluble in the surrounding outer liquid phase, and in addition, the process should be slow enough for the diffusion equilibrium between the inner and outer fluid phases to bepermanently present",
            " This is eq14,whichgives exactly the Young equation, which expresses the condition for the mechanical equilibrium, as can be rigorously proven by means of variational calculus (see ref 9, eq 1.46). The other sufficient condition, eq 15, simply expresses the fact that at constant radius, r, the parameter y (and the contact area, As ) \u03c0r2y) is maximum for x ) 0; this is a geometrical relation rather than a condition for the mechanical equilibrium. Hence, in agreement with Eriksson and Ljunggren,1 we conclude the following: For \u2206\u03b3/\u03b3 > 0 there is a stable position of the attached particle determined by the Young equation, eq 8, with an acute contact angle, 0 < \u03b8 < 90\u00b0, cf. Figure 1. For \u2206\u03b3/\u03b3 e 0 there is no stable position of the attached particle corresponding to the mechanical equilibrium in so far as the Young equation, eq 14, does not correspond toaminimumof thegrandpotential\u2126. This isanontrivial conclusion. Indeed, all configurations of attached fluid particleswith obtuse contact angles cannot be stable.Note that this conclusion holds only for fluid particles which do not contain an independent component. Second, let us imagine another process with a bubble/ droplet containing (at least) one component which is insoluble in the outer fluid",
            " Consequently, we may draw the curious conclusion that the configuration of such an attached bubble nucleus is mechanically stable (see eq 38), due to the fact that the nucleus is out of diffusive equilibrium. The role of the hydrophobic surface can be (at least) to decrease the work of nucleation (formation of the critical nucleus): as shown in ref 5 where whom and whet are the works of homogeneous and heterogeneous nucleation and f(\u03b8) is a factor accounting for the shape of the attached fluid particle (Figure 1). Note that f(\u03b8) monotonically decreases with the increase of \u03b8 (i.e. with the increase of the solid surface hydrophobicity in the case of bubbles). Finally we note that the existence of a negative line tension (neglected in theabove considerations) in all cases leads to the appearance of a local minimum in the \u2126 vs x curves (corresponding to a stable attachment) in close vicinity to the point x ) 1. Variational derivation of the Young equation with line tension can be found in ref 11; see also ref 12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003672_a:1023048802627-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003672_a:1023048802627-Figure3-1.png",
        "caption": "Figure 3. Kinematics scheme of 6-DOF PUMA robotic manipulator links forming the redundancy in the vertical plane.",
        "texts": [
            "9 \u00b5m in Pinitial shows that the end-effector positioning accuracy increased by 6.4% due to the better joint error compensation. A robotic manipulator is said to be redundant when it possesses more degrees of freedom than are necessary for the specified task, i.e., the dimension of its joint space is greater than the dimension of its task space. As an example of the conventional redundant industrial robot, one can consider 6-DOF PUMA type robot. The kinematics scheme of the 6-DOF PUMA robotic manipulator links forming the redundancy in the vertical plane is shown in Figure 3. The following symbols were used in Figure 3: 1, 2, 3 and 4 \u2013 first, second, third and forth links, 5 \u2013 end-effector, x0y0 \u2013 base robot coordinate system, x2y2, x3y3 and x4y4 \u2013 accordingly, the Cartesian coordinate systems of second, third and forth joints, q2, q3 and q4 \u2013 second, third and forth robot joint coordinates. The extra degrees of freedom in the joint space usually results in the existence of an infinite number of inverse kinematics solutions for the robotic manipulator. This can be used for calculating the best manipulator joint configuration that could provide joint error maximum compensation for a given working point in the robot working space",
            " The following recursive equations, based on incursion method and (5), were used to find the optimal joint configuration for redundant robotic manipulator: q2(i + 1) = ( x + q2l2 sin q2(i) + ( q2 + q3)l3 sin(q2(i) + q3(i))+ + ( q2 + q3 + q4)l4 sin(q2(i) + q3(i) + q4(i)))g1 + q2(i), q3(i + 1) = ( y \u2212 q2l2 cos q2(i) \u2212 ( q2 + q3)l3 cos(q2(i) + q3(i))\u2212 \u2212 ( q2 + q3 + q4)l4 cos(q2(i) + q3(i) + q4(i)))g2 + q3(i), (6) where i \u2013 iteration number, g1 and g2 \u2013 parameters defined as (Dubois and Resconi, 1995): g1 = t1(\u2202F1/\u2202q2)\u221a (1 + (\u2202F1/\u2202q2) 2)(1 + (\u2202F1/\u2202q2) 2 + (\u2202F2/\u2202q2) 2) , g2 = t2(\u2202F2/\u2202q3)\u221a (1 + (\u2202F2/\u2202q3)2)(1 + (\u2202F1/\u2202q3)2 + (\u2202F2/\u2202q3)2) , where t1 and t2 \u2013 convergence parameters, empirically found to be equal 70000 for the given recursive process, F1 and F2 are functions equal to the left sides, accordingly, of the first and second equations from (5), \u2202F1/\u2202q2, \u2202F1/\u2202q3, \u2202F2/\u2202q2 and \u2202F2/\u2202q3 are partial derivatives of functions F1 and F2. In order to verify the developed method of end-effector pose accuracy improvement using joint error maximum compensation for redundant robotic manipulators, the following computer simulations of 3-R redundant robotic manipulator with three links in the vertical plane forming the redundancy, similar to the one of PUMA type robotic manipulator (see Figure 3), were performed. It was supposed that the redundant robotic manipulator with link lengths l2 = 0.4 m, l3 = 0.25 m and l4 = 0.25 m came into the position with the Cartesian coordinates in the base system: x = 0.5881129 m and y = 0.0622528 m with the joint coordinates q2 = 0.5\u25e6, q3 = \u22122\u25e6 and q4 = 2\u25e6, average joint errors q2 = 0.0001\u25e6, q3 = \u22120.0001\u25e6 and q4 = 0.0001\u25e6 and the following end-effector pose accuracy L = 65.2 \u00b5m. Using the recursive incursion method, the following solution for the optimum redundant robot configuration with the maximum joint error compensation in the given working point was found with an assumption that joint error values did not change significantly (Kieffer et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure5.13-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure5.13-1.png",
        "caption": "Fig. 5.13",
        "texts": [
            " If the current ripple in the load cannot be ignored, the value of I' when T 1 is switched off will be considered. Times tP and tc are referred to the oscillation half-cycle, rr.y'LC, of resonant LC circuit. The commutation time has been computed for' equal to 0.7; it shows little variation as a function of I'. The increase D.U' in the average output voltage has been related to U and multiplied by ( Tjny'LC). 5.3 Series Commutation: Principle In presenting tum-off by series commutation, the diagram shown in Fig. 5.13 will be used. Capacitor C and auxiliary tum-off thyristor T 2 are added to main thyristor T 1 and free-wheeling diode D 2 \u2022 C can thus be directly series-connected with T 1 between the input and the output of the chopper. An inductor L' must be added to enable T 1 to let I' through during its ON-state period. Together with inductor L, the second auxiliary thyristor T~ enables C to be charged. A damping circuit comprising resistance R. and diode D. enables voltage uc to be brought down to zero at the end of commuta tion",
            " We have chosen to leave out the minor modifications (the permutations of two elements directly series-connected, for example) in order to concentrate on modifications which affect certain aspects of the operation. 5.5.1 Modification of the Type of Semiconductor Switch 5.5.1.1 Replacing a Diode by a Thyristor A diode can always be replaced by a thyristor as long as a suitable control is used for the thyristor. Starting with the circuit in Fig. 5.3, it is possible to obtain the three circuits in Fig. 5.17 (thyristors replacing diodes are drawn in black). Starting with the circuit in Fig. 5.7, it is possible to obtain that in Fig. 5.18. (The diagram in Fig. 5.13 has no diode in the turn-off circuit and thus the thyristor-diode replacement is irrelevant.) \u2022 In the case of the circuit using parallel commutation by capacitor, in which thyristor T 3 replaces diode 0 3 (Fig. 5.17b and 5.17c), the capacitor discharge auxiliary circuit can be either introduced or not, depending on whether T 3 is controlled at the same time as T 2 or not. This enables this circuit to be removed as soon as current I' has reached a value such that it is no longer necessary to shorten the commutation time (infinite value of 2 in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure4-1.png",
        "caption": "Figure 4. Static modes @., and @s dues to a unit vector",
        "texts": [
            " This means that points and unit vectors are indeed material points and directions of the body, and not merely fictitious mathematical entities. This is why, when altering their relative positions, deformation of the body appears. For every unit vector in excess, two static modes are obtained. They are the static deformation modes corresponding to a unit rotation of the vector around the two local axis \u2018more\u2019 3538 J . CUADRADO. J. CARDENAL AND J. GARCfA DE JAL6N perpendicular to it, keeping fixed the rest of the boundaries. Thus, continuing with the body in Figure 3, unit vector nl produces two modes in Figure 4. Static mode G4 corresponds to a torsional deformation around y-axis, while static mode corresponds to a bending deformation in the plane ( j , 2). We remark that the rotation of the beam at point rl around unit vector n1 is not detected by the variation of any co-ordinate. This rotation will be considered as an internal deformation of the beam, as it will be seen when studying the dynamic modes. The interest of using static modes is that their amplitudes qi(i = 1,. . . , Ns) can be expressed in terms of natural co-ordinates (points and unit vectors), so that they do not constitute new variables of the problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003687_isie.1999.801773-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003687_isie.1999.801773-Figure1-1.png",
        "caption": "Fig. 1. Model of a mobile manipulator",
        "texts": [
            " The position is controlled for the tangential direction and the force is controlled for the vertical one. Then we propose a controller to raise characteristics of response in work-space by control of the configuration and distribution of the joint torque. 11. A MODELING OF MOBILE MANIPULATOR In this paper, the mobile manipulator is composed of a mobile robot with a pair of independent driving wheels on a horizontal plane and a manipulator arm with 4 degree-of-freedom in a 3-dimensional space. Its model is shown in Fig.1. The configuration of the mobile manipulator can define as the following vectors. e, = [e, & l T , z = [zc yc 4C]T, ea = [e, . . . oslT rotational angles of the left wheel and the right one, respectively; position vector of Pc with respects to the world frame; heading angle of the mobile robot with respects to the world frame; rotational angles of the i-th joint of the arm (i = 1, . . . ,5); The position vector of PE in world coordinate frame is r = [z y z]*, and the driving joint vector is 8 = [e: @ZIT"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003565_20.582697-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003565_20.582697-Figure6-1.png",
        "caption": "Fig. 6. Vectors of B after Phase A has been switched off for 10 mechanical degrees.",
        "texts": [
            " We have also fixed the rotational speed of the rotor at 2000rpm. The model was solved as a nonlinear transient problem. At the end of each time step the position of the rotor mesh was updated before the start of the next time step. Fig. 5 shows how the rotor and stator mesh are not connected on the Lagrange sliding interface, Fig. 7 shows the current waveforms of the three phases as well as that of the DC-link current with rotor position. Table I compares the measured peak and rms current with that computed from the FE simulation. Fig. 6 shows the flux path 10 mechanical degree after the coils of the A phase were switched off and the B phase coils switched on. VI. CONCLUSION An efficient and robust scheme for use in dynamic simulation of electromagnetic devices with 3D finite elements 2013 has been described. The scheme can couple directly the finite element model of a device to its external circuits, thus allowing a complete simulation of the behaviour of the connected system. Moreover, it provides a sliding interface technique for the movement of moving parts within the model to be taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003052_980220-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003052_980220-Figure9-1.png",
        "caption": "Figure 9. Submodel II. Describes body and unspring masses vibrations (degrees of freedom: , \u03d51, \u03d11, , , , \u03d14) zO1 \u03b6 1 2Ol \u03b6 1 3Ol \u03b6 1 4O",
        "texts": [
            " They may be a result of real road measurements or the realisation of stationary gaussian random process describing real road according to ISO recommendations [28]. For some motion cases (mainly even road motion) it is possible to simplify and speed up model construction process. Division into partial models was applied [16]. The main model is divided into 3 type coupled sub-models. For example for car model they are: \u2022 submodel I (Fig. 8) which describes basic motion of the vehicle (degrees of freedom: , ), \u2022 submodel II (Fig. 9), which describes body and unsprung masses vibrations (degrees of freedom: , \u03d51, \u03d11, ), \u2022 submodels III (Fig. 10), which describes rotations of wheels (degrees of freedom: \u03d55, \u03d56, \u03d57, \u03d58). The submodel II generates current values of normal reactions of the road that are input values for the tyre model (mentioned above). Truck model is divided in analogical way. In this case submodel II has dependent front suspension. x yO O1 1 , \u03c81 zO1 \u03b6 \u03b6 \u03b6 \u03d1 1 1 1 4 2 3 4O O O' ', , , 5 EQUATIONS OF MOTION THE MAIN MODELS \u2013 The equations of motion were derived from Lagrange equations of 2nd kind"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003224_70.704227-Figure11-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003224_70.704227-Figure11-1.png",
        "caption": "Fig. 11. Reparameterization used in the PUMA example.",
        "texts": [
            ", joints to ) is made to follow a linear path into a combined elbowshoulder singularity with multiplicity 4 [Fig. 10(a)]. The initial and final path points are and with the corresponding joint values given by and The path itself is parameterized by and given by (18) with the singularity occurring at 1. Motion along the path is specified via . At the singularity, however, a nonzero value of will result in unbounded values for [Fig. 10(b)]. To handle this, we reparameterize within a certain distance of the singularity, according to if if (19) as shown in Fig. 11. For , and are identical, while for 1 , takes the general form (20) This is identical to (3), except for the extra scaling and offset factors ( and ) that provide continuity with at 1. Although the singularity has multiplicity 4, we can use 2 because the PUMA is a quadratic manipulator (Section IV-A). Motion along the reparameterized path can be specified via , and as long as is twice differentiable, and will be well-behaved [this will also be true of higher time derivatives if is made smoother at the junction point ]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003179_s0043-1648(98)00176-8-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003179_s0043-1648(98)00176-8-Figure3-1.png",
        "caption": "Fig. 3. The vi~o-elasti\u00a2 heha~ior of a material. (at Without the rolling motkm. (b) With the rolling nmtian.",
        "texts": [
            " Micro-slipping, plastic hysteresis and thermoelastic hysteresis also exist in the process of rolling\u2022 However, because the energy loss due to these phenomena is actually negligible, it can be suggested that the major conceres are the elastic hysteresis and adhesion components. \u00a5 rT / _ , \u00a2~_E___ x Fig. 2. llluslrdfion of the rolling-friclion n~yJel. Generally speaking, the material under the contact surface wil l produce elastic deformation as a result o f a load application. An immediately complete recovery oftbe deformation may be expected for perfectly elastic materials. However. in fact. due to visco-elastic behavior of materials as shown in Fig. 3. the major portion of the elasticity energy will not be fully recovered until the contact is completely removed. which will result in a higher pressure at the contact side than at the contact-removal side. The resultant can be expressed by a resistant torque. M.. and a horizontal resistant force. -VF'. as shown in Fig. 3b. The energy loss due to the resislant torque and force is the elastic hysteretic loss which is a function of the applied load. the material properties, the geometry of the comact elements, and the rolling velocity. Based on the Hertzian contact theory, the line contact load on a umt length at a position which is y distance away from the center of the contact may he expres.~d as follows: 2(2 p(y l = \"~--~] I - (y /b )2] t j2 {4) where b is the half width of the contact region: / 4 [ I - u ~ I - v ~ Q The vertical displacement of the surface at y is: B(y)=~,,,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002824_107754639800400502-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002824_107754639800400502-Figure1-1.png",
        "caption": "Figure 1. The comparison of linear (a) and nonlinear (b) analysis of slide bearings using stiffness ci, and damping dt,k coefficients of the lubricating film. The coefficients C\u00a1,k and d;,k are assumed as constant for the shaded areas. 1 = trajectory of the journal center during dynamic loading; 2 = circle of clearance; 3 = semicircle of static equilibrium.",
        "texts": [],
        "surrounding_texts": [
            "520\n1. THE THEORETICAL MODEL\nThe modeling of dynamics of real rotor lines and turbo-set supports is a very complex problem. We can distinguish some characteristic substructures, each of which is a separate module:\n~ slide bearings, ~ labyrinth seals, ~ rotor supports with bearing external fixings, ~ foundations, ~ rotor lines with disks, clutches, and other rotating elements.\nThe first three substructures have nonlinear characteristics. In particular, the characteristics of slide bearings are strongly nonlinear. These problems have been the subject of works (Ding and Krodkiewski, 1993; Hattori and Kawashima, 1991; Khonsari and Chang, 1993; Muszynska, Franklin, and Bentley, 1988; Pavelic and Amano, 1992; Russo and Russo, 1993; Subbiah and Rieger, 1988). Usually the authors of these works have assumed a simple model of slide bearings. The problems that are connected with the heat transfer in the bearing, especially during large displacements of the journal in the area of the oil gap, are neglected in the nonlinear analysis of these models.\nLet us now present the adopted nonlinear model of the rotor-bearing system beginning with the most difficult subsystem to be theoretically modeled-namely, the slide bearings.\nUsing the system of coordinates and denotations as in Figures 1 and 2, the hydrodynamic pressure distribution in the lubricating film can be described by the Reynolds equation in the form of\nat University of Newcastle on August 28, 2014jvc.sagepub.comDownloaded from",
            "521\nEquation (1) is integrated with boundary conditions as follows: zero-pressure gradient at the boundaries of the continuous noncavitating oil film and zero pressure at the bearing edges, that is,\nwhere ~ *, ~2* are coordinates that determine the position of the boundaries of the continuous lubricating film. These boundaries are variable in time, that is, 4* (t) and 42* (t). A physical explanation of the condition (2) is given in Figure 3.\nThe determination of the functions $g (t) and 42* (t) is a very complex problem. In a general case, these functions should be found from the equation of continuity in the cavitation zone, treating time t as an independent variable (the effect of the so-called prehistory). It is possible to show (Kicinski, 1986, 1989) that in the case of abundant bearing lubrication (which often occurs), the determination of the functions ~i , ~2 by means of equation (2) is appropriate.\nat University of Newcastle on August 28, 2014jvc.sagepub.comDownloaded from",
            "522\nat University of Newcastle on August 28, 2014jvc.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_31_0002707_0020-7403(94)00045-l-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002707_0020-7403(94)00045-l-Figure2-1.png",
        "caption": "Fig. 2. Nodal coordinates of the shaft element.",
        "texts": [
            " The equations of motion, including the effects of gyroscopic and rotary inertia in the inertial coordinates, can be obtained as follows [8]: I ~-~ J + ~z2LEI(z)~z2J + kL(z)x + k (z)y + cL(z); + =L(z, t) pA(z) ~f\u00a2 + az [J(z) azatj + Uz 2 + k~x(Z)X + kby(z)y + c~(z)2 + e~r(z)~9 =fy(z, t) (1) x l _ Linearized dynamic characteristics of bearings Zd ~l gb LIL-[ ] [ ] I O I t~ I ~3~ [ ] shaft [ ] z bearing 199 d i sk identification may not be feasible. This implies that the direct use of Eqn (1) for identification purposes is not practical. Since in practice the diameter of a shaft often changes stepwise along the axial direction, we propose an identification approach based on the finite element method. Let q~ be the nodal displacement vector of the ith element with eight degrees of freedom, four degrees of freedom of displacement in the x and y directions and four of rotation about the x and y coordinates (see Fig. 2). The term nodal derives from the fact that in finite 200 Juhn-Horng Chen and An-Chert Lee element terminology the boundary points are called nodal. Let tkx and Cr be the interpolation functions of the x and y coordinates, which are the lowest degree admissible polynomials, i.e. the cubic spline. In particular, we have q~ = [x~ Yi lOri loci xi+i Yi+i lOt(i+1) lOx(i+i)] t (2) Cx = [q~x~ 0 q~2~ 0 ~b3x 0 \u00a2 , ~ 0]' (3) \u00a2~ = [o 4 ~ o - ~ o ~ o - \u00a2 , ~ ] ' (4) x = \u00a2 t q~ y = \u00a2 ~ q~ [;]=r< L,~H q~ = ~btq~ ~b = [\u00a2x, q~y]s\u00d72 (5) where ])ix --~\" ely \u00a2 3 x = ~b3y in which 4 denotes the (Z -- Zi)/l"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003237_0020-7403(93)90037-u-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003237_0020-7403(93)90037-u-Figure1-1.png",
        "caption": "FIG. 1. Force equilibrium of a bearing.",
        "texts": [
            " A set of nonlinear algebraic equations is assembled from the transfer matrix relations to determine the steady-state responses. Two examples with cubic nonlinearity are given to demonstrate the proposed method and numerical algorithm. The nonlinear rotor-bearing system considered includes components of the linear shaft and the rigid disk supported by rolling bearings with the restoring force of power nonlinearity. For simplification, the damping forces of the bearing are assumed to be linear. Thus, the equations of the bearing forces as shown in Fig. 1 are expressed in the following: (1) Fy = KyxX + Kyr Y + K'yxXn + K',r Yn + CyxX + (Tyr Y = V~r + V~, where Kij are linear spring coefficients, Kit are nonlinear spring coefficients, and C u are linear damping coefficients. We designate the characteristic factors which have the magnitude of the same order as the disk eccentricity and the disk mass as e and m, respectively. Using the dimensionless representation, the restoring forces of Eqns(1) _ _ = _ _ _ + + x x e n - 1 x y e n - 1 Ke K e K - e K - - + K _ _ = _ \" ' Y Y e n - 1 Ke K e + - K - e + ~ e + K become: (2) Steady-state analysis by the transfer matrix method 481 where K = (K~x + K~y + Ky~ + K , ) ",
            "t, time into Eqn (1), and using the harmonic balance method [7], we obtain the bearing forces as below: F~ = AX--1 e-j~'t + A~e j~t + AX-~e -jp~\u00b0~ + A~e jp~'t = ~cos~ot + ~sin~ot + ~'\u00a2cospo~t + ~'~sinpwt (6) and Fy = BY_ 1 e -j~'t + B~ e j'~t + BY_j,e -jp~'r + Bge jp~'t = ~ccoscot + ~ssinogt + ('ccosp ~ot + ('ssinpcot where coefficients of Ay and By are nonlinear functions of the displacement coefficients CY (i = 1, - l, p, - p , and j = x, y), which can only be obtained when the coefficients Xci, X~i, Y\u00a2i and Y~i are known. From force equilibrium, as shown in Fig. 1, we have the relations between shear forces of two sides of the bearing in the following: Q~ = Q~ _ F r (7) Substituting Eqns (6), P = Pc1 cos~ot + Psi sino~t + Pcpcosp~ot + Pspsinpo~t and Q = Q\u00a21 cosmt + Q,, sin~ot + QcpcOSpCot + Q,psinp~ot into Eqn (7), the relations between the coefficients of forces at both sides of the bearing points can be obtained as follows: ( P o l ) , = ( P c 1 ) , - ~o , ( P , 1 ) ~ = ( P , 1 ) , - ~ , , (Pop)r = (Pop), - ~ , ( Q c l ) r = ( Q c l ) l - - ~\u00a2, ( P , , ) , = ( P , p ) , - ~',, (8) (Q ,1 ) , = (Q,1) , - ~ , , (Qcp)r = (Qcp), - ~ , (Q,p)r = (Qsp), - ~',"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002497_jaer.1996.0022-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002497_jaer.1996.0022-Figure3-1.png",
        "caption": "Fig . 3 . Bearing and pressure areas of a disc projected on to a y ertical plane ( A b 5 ABE ; A p 5 BCDE )",
        "texts": [],
        "surrounding_texts": [
            "The cultivating disc is a segment of a thin spherical\nshell and its critical dimensions are shown in Figs 1 to 5 . The principal parameters are the radius of the rear spherical surface , R 0 ( Fig . 1 ) the thickness of the disc material , t , and the radius of the circle of the sharpened edge in the circumferential plane of the disc , r ( Figs 1 and 5 ) . Other disc parameters can be deduced in terms of these dimensions . The tilt angle of the disc , a ( Figs 1 and 5 ) is defined as the angle which the circumferential plane makes with the vertical plane . The disc angle , b ( Fig . 2 ) is the angle which the circumferential plane makes with the horizontal direction of motion of the plough . The depth of disc soil working , d ( Fig . 1 ) is the vertical distance from\nRo\ne\na\nr\nc\nSoil level\nSoil l evel\nRs\nL\n\u03b2c\nd\nFig . 1 . Geometrical parameters of a disc tilted at an angle a to the y ertical plane ( upper : ele y ation ; lower : plan )\nthe soil surface to the lowest point of the circle which forms the circumferential edge of the disc ( Fig . 1 ) .\nFor any disc , the angles a and b and the working depth , d , are the factors which determine the areas of the front and rear surfaces of the disc which engage the soil and are of importance in relation to the magnitudes of the consequent forces acting on the disc .\nWhen a disc is working in soil the rear spherical surface will be in contact with soil if the disc angle is less than a critical angle , b c ( Fig . 1 ) . This angle is reached when the direction of motion is tangential to the circle of intersection of the soil surface with the rear surface of the disc , at the point where it intersects the chord of intersection . If the disc angle , b , is equal to or greater than this angle , there is no soil contact with the rear surface and the vertical and horizontal bearing areas are zero . Expressions for the calculation of b c are given in Section 3 . 1 .\nFor a particular disc angle , b , there is a critical depth , d c , for which the angle b is equal to the critical angle , up to which there is no soil contact with the",
            "rear surface of the disc . An equation for determining values of d c is given in Section 3 . 2 .\nThe bearing area is defined as the area of the rear convex surface of the disc engaged with soil and will exist when b , b c . Expressions for this area when projected on to a horizontal plane ( A b h ) (area AFB in Fig . 2 ) are given in Section 4 . 2 . 2 and on to a vertical plane , normal to the direction of motion ( A b ) (area ABE in Fig . 3 ) , in Section 4 . 2 . 1 .\nThe pressure area is defined as the area of the concave front surface of the disc engaged with the soil , which represents the area of soil cut by the disc . Expressions for this area projected on to a horizontal plane ( A p h ) (area AFBCD in Fig . 2 ) are given in Section 4 . 2 . 1 and on to a vertical plane , normal to the direction of motion ( A p ) (area BCDE in Fig . 3 ) , in Section 4 . 1 . 1 .\nWhen working in gangs there is generally some overlap of the areas of soil cut by adjacent discs . For a particular disc spacing there is a critical angle , b 0 , above which there will be overlap of the cut areas . There will also be a critical spacing , g c , for a particular disc angle , at less than which there will be partial overlap of the worked areas . Expressions for these critical values are given in Section 5 . 1 . The area of overlap between discs ( A o v ) (area BFG in Fig . 4 ) is\nderived in Section 5 . 1 and the uncut area ( A u ) (area CEF in Fig . 4 ) in Section 5 . 3 . The gang area ( A g ) (area BDEF in Fig . 4 ) , or the area cut by a single disc , is considered in Section 5 . 2 .\nThe disc may be sharpened externally or internally . The formulae derived in Sections 3 to 5 apply to an internally sharpened disc . The ef fect of external sharpening is discussed in Section 6 in relation to the width of the bevelled surface and to critical disc angle . Modifications required to the formulae for an externally sharpened disc are also discussed .\nIn practice , disc sizes are given in terms of the diameter of the circumferential or edge circle (2 r ) and their concavity ( c ) , which is the depth from the plane of the edge circle to the inner spherical surface . Disc sizes range from 500 to 900 mm edge circle diameter with concavities over a range from 75 to 165 mm . 10 , 11 The thickness of discs is usually between 5 and 9 mm , depending on disc size . In terms of the basic parameters of the disc , the concavity , c , is given by c 5 R o 2 ( R 2\no 2 r 2 ) 1/2 2 t for inside sharpening and by c 5 R o 2 h R o 2 t ) 2 2 r 2 j 1/2 2 2 t for outside sharpening . In the calculations presented in this paper , a shallow and a deep disc are considered , sharpened internally and of dimensions representative of a typical disc size , which is usually in a range 600 to 700 mm edge circle diameter . 1 2\nFor the shallow disc , R o 5 915 mm and r 5 315 mm ; for the deep disc R o 5 560 mm and r 5 305 mm . The disc thickness ( t ) was equal to 5 mm in both cases . The discs were , therefore , of approximately equal size but of dif fering concavities . For the shallow disc c 5 51 mm and for the deep disc c 5 85 mm , for inside sharpening .\nIn practice , for disc ploughs 1 2 the disc angle ( b ) ranges between 35 8 and 55 8 and is commonly in the range 40 8 to 45 8 . The tilt angle of the disc 1 2 ( a ) is normally in the range 15 8 to 25 8 . The spacing between discs ( g ) when working in a gang 1 2 is usually in the range 180 to 300 mm . In the calculations presented in this paper , the working depth of the discs 1 3 ( d ) was considered over a range from 60 to 180 mm .\nThe critical disc angle , b c , occurs when the disc angle , b , is such that the direction of motion is tangential to the rear spherical surface of the disc at the soil surface ( Figs 1 and 2 ) and is given by\nsin b c 5 L / R s (1)\nIn this expression L is half the length of the chord of",
            "the disc edge circle in the plane of the soil surface ( Fig . 5 ) and is given by\nL 5 h d (2 r cos a 2 d ) j 1/2 sec a (2)\nThe term , R s , is the radius of the circle of intersection of the soil surface ( Fig . 1 ) with the outer spherical surface of the disc and is given by\nR s 5 R o [1 2 h sin ( a 1 e ) 2 d / R o j 2 ] 1/2 (3)\nwhere the angle e ( Fig . 1 ) is given by\nsin e 5 r / R o\nThe variation of critical disc angle ( b c ) with tilt angle ( a ) was calculated from Eqns (1) to (3) and is shown in Fig . 6 for working depths of 60 and 180 mm , for the shallow and deep discs . In general , the ef fect of tilt angle was relatively small , particularly for the\nshallow discs . In practice , disc angle varies between 35 8 and 55 8 for plough discs and tilt angle between 15 8 and 20 8 , so that for typical settings ( a 5 20 8 and b 5 40 8 to 50 8 ) the critical angle is exceeded for both discs . The only case where the critical angle is not exceeded is for the deep disc at tilt angles greater than 20 8 at a disc angle of 35 8 , when working at a depth of 180 mm .\nThe critical tilt angle ( a c ) occurs when the tilt of the disc is equal to the angle made by the tangent to the rear spherical surface , in a diametral plane of this surface , at a point where it intersects the circumferential plane of the disc . When this angle is reached the"
        ]
    },
    {
        "image_filename": "designv11_31_0000047_j.proeng.2016.06.331-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000047_j.proeng.2016.06.331-Figure8-1.png",
        "caption": "Figure 8: Charpy samples of varying SoG (a) SoG<1o (b) 1o<SoG<3o (c) SoG>3o",
        "texts": [
            " Figure 7 is Figure 6 where the data have been classified in SoG classes as denoted by the legend in Figure 7. Recall that all wood used in major-league bats, must exhibit a SoG within \u00b13o. The data that are presented in Figure 7 do not show a clear relationship of increasing strain-to-failure with decreasing SoG. Thus, the results suggest that density has a much greater effect on the impact failure properties of the wood than SoG. Once the wood has begun to fracture, however, SoG plays a large role in the crack propagation of the wood. This phenomenon is highlighted in Figure 8 which shows three different failure modes of wood samples from each of the three classes of SoG that were examined using the Charpy test. Figure 8 shows the fracture response as a function of SoG. In Figure 8(a), the sample has not completely fractured through the width and the fracture surface is indicative of brash wood failure. In comparison, the sample in Figure 8(b) exhibits more splintering of the wood at the fracture site while also not completely splitting through the width. Figure 8(c) shows a high SoG specimen that split along the grain line during impact, thereby resulting in the formation of sharp edges on the fracture surface. This failure propagation behaviour is important to consider when discussing the issue of broken bats during gameplay as high SoG wood is more likely to fail in a multi-piece fashion. 3. Conclusions The following conclusions may be drawn from the results of the mechanical testing performed. MOE and MOR increase with increasing wood density for maple and ash wood species"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure20-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure20-1.png",
        "caption": "Fig. 20. Representation of a traffic flow for four moving robots without main conflicts.",
        "texts": [
            " Finally, covers a distance of 2.5 m with m/min. The second example explains the use of the language for the improvement of the traffic schedule of a particular robot under the assumption that the local traffic flow in a certain region is almost the same every time that the robot enters that region. In this case, the robot enters the region from left to right at time and spends min crossing it. At that time, there are three other moving robots crossing the same region from different directions (see Fig. 20). The traffic flow extracted by the robot in that region, is represented by the following language words: The symbol & represents the synthesis operator between words for the formulation of the traffic flow extracted by a robot traveling through a region where In this particular case there is no delays during the traveling. Fig. 21 shows the same region, at a different time where the robot enters the region from the right to the left in order to cross it by following the reverse path of Fig. 20. At this time there are four other moving robots and a fifth one is coming to the same region. The traffic flow extracted by the robot is represented by the following words: where In this particular case there are delays due to conflicts between the robots directions and traffic priorities. More specifically, the robot has to wait until and pass first and then it continues its own path. This mean that the robot knows the time required to cross the region, and in the latter case it took more time, At this point the robot analyzes the traffic flow perceived by itself and modifies its traffic path for a future cross of the same region under a traffic flow similar to More specifically, it follows the next algorithmic steps: 1) Check each word , for patterns "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002459_941761-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002459_941761-Figure1-1.png",
        "caption": "Fig. 1-a Premature Contact in a Spur Gear Set.",
        "texts": [
            " CALCULATION OF INITIAL SEPARATION SPUR GEARS - Fig (1-a) shows initial separation for a pair of involute spur gear teeth in the premature contact region. Fig (1 -b) shows separation in the postmature contact region. These figwes have been exaggerated for clarity and are not to scale. In Fig(1-a), point E is the SAP (start of active profile) of the pinion. 0 1 and 0 2 are the centers of the pinion and gear, respectively. Theoretically, point E is the first point of contact. At the instant point E comes in contact, the pinion makes an angle P and the gear makes an angle a with the line joining centers. From Fig (1-a), Fig. 1-b Postmature Contact in a Spur Gear Set. At a time interval dt before this mesh position, the pinion makes an angle (B,+P) and the gear makes an angle @,+a) with the line of centers. 8, = N, x 8, (7) At this position, the point E on the pinion is at E'. On the gear, the point E was at the tip and is now at position D'. In this position, the separation between the mating tooth pair is DID\". The tooth pair is in contact if the deflection is greater than D'D\". The gear tip makes an angle 8' with the line of centers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002641_s0389-4304(99)00049-1-Figure12-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002641_s0389-4304(99)00049-1-Figure12-1.png",
        "caption": "Fig. 12. E!ect of roll compensation.",
        "texts": [
            " The gravity center height is in accord with the trend of the loading status. The estimated gravity center height is applied to the vehicle model of Fig. 10. The model forecasts the rolling behavior as shown on the quadrant plane of Fig. 11 according to roll angle and roll rate. The rolling behaviors located in the \"rst and third quadrant tend to be divergent. This result of stability estimation shows the wheel brake acts appropriately and prevents rollover. An experimental result for rollover prevention is shown in Fig. 12. This is a measurement when the test vehicle is passing a J-turn. When the rollover behavior is over a certain threshold upon inspecting the gravity center height, the system makes each wheel brake work then reduce the rolling motion quickly. Through the comparison of transfer function coe$cients between the kinetic model and ARX estimation model coming from experimental data the gravity center height estimation is performed. As a result of our study, (1) vehicle gravity center height can be precisely estimated; and (2) the gravity center height can be decided according to the loading status e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002307_rob.4620120203-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002307_rob.4620120203-Figure1-1.png",
        "caption": "Figure 1. Closed-chain robotic system formed by dual manipulators and an object (I = inertial, 0 = object, B = base, C = contact coordinate frames).",
        "texts": [
            "' The upper-level coordinator collects all the necessary information and solves the inter-chain coordination problem, which is, in fact, the force distribution problem. The corresponding constrained, optimal solutions (which are the set-points of chain contact forces and input joint torques) decouple this large-scale system into j lower-level subsystems. Then, j local controllers may be assigned to solve the associated redundant manipulator problems in parallel. In this research, a dual-chain robotic system formed by two redundant manipulators grasping an object is adopted as an example mechanism (see Fig. 1). With the two-level hierarchical control scheme, the efficient Compact-Dual LP (linear programming) method' is applied to resolve the upper-level force distribution problem. And, the effective Compact QP (quadratic programming) methodI8 together with the computed torque method\" is used to solve the lower-level local redundant manipulator control problem. To demonstrate that all the control methods adopted here work well, a suitable simulation package should be developed such that the simulation problem of the closed-chain robotic system can be solved",
            " In the next section, the Friction Coefficients Inter-Chqin Coordination (Conatrained, Physical Joint Torque Limits Desired Motion of Dvnami d oLd Upper Level Coordination) er Level , / I ( . . . . ( \\ \\ , \u2019:?{ Intra-Chain I Intrs-Chain I Chain 1 Control # 1 Control $ j Figure Q. Two-level hierarchical control scheme for multiple-chain robotic systems. Compact-Dual LP method is used to solve the force distribution problem of a dual-chain robotic system. 3. SOLVING THE FORCE DISTRIBUTION DUAL LP METHOD PROBLEM USING THE COMPACT- For hard point contact with friction, only forces are transmitted from the chains to the object. From Figure 1, the force balance equations on the object may then be written as: (Because a dual-chain robotic system is considered here, j = 2 thereafter.) 2 O F 0 = k = l c (OD, * \u201cg,),, where OFo resultant force/moment vector applied to object expressed in the object coordinate frame (0), [6 x 11, (OD& partial spatial transform from the contact coordinate frame for chain k(Ck) to the object coordinate frame (0), [6 x 31, (\u2018g,), unknown contact force vector onto the object expressed in the contact coordinate frame (CJ, [3 x 11",
            " The simulation problem, on the contrary, is to find the accelerations (include joint accelerations, 8, and object accelerations) and contact forces/moments (h,) with the input joint torques (7) given. The simulation problem is also called the direct dynamics problem. In this article, the control problem has been studied in sections 3 and 4; while the simulation problem will be introduced in this section. The example mechanism for a closed-chain robotic system is formed by two planar redundant manipulators, each with 3 degrees of freedom (dof), grasping an object with hard point contact (see Fig. 1). The planned motion is a straight line simple harmonic motion with equal accelerations and velocities in 'i and '2 directions. To solve the simulation problem of this closed-chain robotic system, how many equations arise from the system and how many unknown variables needed to be solved must be known beforehand. From the descriptions for the simulation problem of a closed-chain robotic system, the unknown variables that must be solved in this system are the accelerations and the contact forces",
            " In the next subsection, the simulated contact forces for this system will be derived. 5.1. Formulating the Contact Forces In this subsection, the formulation of the simulated contact forces of a closed-chain robotic system will be derived.20 At first, the closed-chain dynamic equations for this system will be formulated. The dynamic equations of a manipulator has been expressed in Eq. (8). For two manipulators grasping an object and performing a straight line simple harmonic motion with hard point contact, as shown in Figure 1, the dynamic equations for manipulators 1 and 2, respectively, are: where (&)I ['f;, If;]', contact force vector without 'fl at Cl onto object with respect to inertial coordinate frame, 126 Journal of Robotic Systems-1995 \"f;, If$]', contact force vector without 'fs at C, onto object with respect to inertial coordinate frame, Jacobian matrix for linear velocity that relates the contact force components yf and 'f; to the joint torques, T,, Jacobian matrix for linear velocity which relates the contact force components 'f; and 'f$ to the joint torques, T,, The object dynamic equations may be obtained by applying the Newton-Euler equations in the inertial coordinate frame as: 'JT 9; 0 0 lo do * cos 4 - d o sin 4 or in compact form, H, * Zo + b, = ('E * 'g,-)l + ('E ",
            " Secondly, the geometrical constraints will be obtained. In this system, the c.g. of the object expressed in the inertial coordinate frame is ('xo, 'yo, '2,) and the planned trajectory is the planar simple harmonic motion in the I i - '2 plane. Therefore, the c.g. of the object will not change in the '9 direction and 'yo will be independent of the joint angles of each manipulator. Based on these facts, the geometrical constraint equations in this system will be derived as follows. Referring to Figure 1, the geometrical constraint equations from the origin of the inertial coordinate frame to c.g. through manipulator 1 are expressed as: and k0 - I, sin(Ol1) - 112 sin(&, + 612) - I,, sin(Bll + 012 + 813) + do cos 4 = 0, 3 c,(Z) = 0. (28) Also, the geometrical constraint equations for manipulator 2 are expressed as: and '2, - I,, sin(&,) - I , sin(02, + e,) - I , sin(02, + Bu + 6,) - do cos 4 = 0, * Cq(Z) = 0. (30) Cheng et al: Closed-Chain Dual Manipulator System 197 where is the distance from the origin of the inertial coordinate frame I to Bk in '9 direction, and l,,, I, I, Okl, dk2, Ok, are the link lengths and joint angles of manipulator k, k = 1, 2, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure9-1.png",
        "caption": "Fig. 9. Equivalent configuration S U4\u2212 P /RR .",
        "texts": [
            " Let the origin O locate at the intersection point of the two VSLs, the axis of X be parallel with S2 m and the axis of Z be along S1 m . Establish the moving right-handed coordinate system o xyz\u2212 . Let the origin o locate at the center of the line connecting the hinge points of the two universal joints in the 1st and 2nd limbs. Let the axis of x be along S2 m . And let the axis of z be parallel with S1 m . Moreover o is right aboveO at the initial pose. The configuration S R U \u0399\u0399 S2\u2212 P \u2212RRRA \u2212 /2\u2212 PU shown in Fig. 8c can be equivalent with S U4\u2212 P /RR shown in Fig. 9 according to kinematic equivalent. According to the above analysis, EOE\u2032 constitutes an isosceles triangle. Let the angles between OE , AH and the axis of X be \u03b8 and \u03bb respectively at the initial pose. Assuming the moving platform rotates \u03b3 degrees around S1 m and \u03b1 degrees around S2 m . Then, l \u03c6 \u03b3AB AH AB AH= + \u2212 2 cos( + )1 2 2 2 (30) l RMN ON Oo oM= = \u2212 \u2212 o O 2 (31) l \u03c6 \u03b3A B A H A B A H\u2032 = \u2032 \u2032 + \u2032 \u2032 \u2212 2 \u2032 \u2032 \u2032 \u2032 cos( \u2212 )2 1 2 2 (32) l RM N ON Oo oM\u2032 = \u2032 \u2032 = \u2032 \u2212 \u2212 \u2032o O 2 (33) where, \u03c6 \u03b8 \u03bb= + and Ro O is the rotation matrix of frame o{ } with respect to frame O{ }"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002860_s004070050024-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002860_s004070050024-Figure1-1.png",
        "caption": "Figure 1",
        "texts": [
            " (Indeed, it is only an assumption about the shape of the orbit that defines the nodes at an instant when the moon is not actually crossing the plane of the ecliptic.) In Prop. 30 he computes the rate of movement of the nodes on the assumption of a circular orbit and, in Prop. 31, he assumes his more complicated orbit of Prop. 28. The results do not differ greatly numerically, and it is his result for the circular orbit that he uses in his later treatment of the precession of the equinoxes, so I shall describe this. The Motion of the Nodes Assuming a Circular Orbit In Figure 1, T represents the earth and P1 and P2 the moon at two different places on its circular orbit. TS is the line from the earth to the sun, and Nn is the line of nodes which passes through T at the centre of the orbit. The lines TS and Nn are in the plane of the ecliptic, which we take to be the plane of the paper, and the plane of the moon\u2019s orbit is to be imagined as tilted to this plane by a rotation of about 5 degrees about the line Nn. The line Qq, called the line of quadratures, is a line in the plane of the ecliptic, passing through T, and perpendicular to the earth-sun line TS",
            " Qq is then the intersection of this plane with the plane of the ecliptic, and P1A1 and P2A2 are the perpendicular distances of P1 and P2, respectively, from 5. On the basis of his discussion in Prop.25, and the further assumption that the earthmoon distance is negligible compared to the earth-sun distance, Newton concludes, in Prop. 30, that the component of disturbing force that causes the moon to continually change the plane of its orbit, and thereby the movement of the nodes, is (a) Parallel to the earth-sun line TS, (b) Proportional to the distance of the moon from the plane 5 (the distances P1A1 and P2A2 in Figure 1), and (c) Always directed away from 5. In Figure 1, I have represented this force by f1 and f2, respectively, for positions P1 and P2 of the moon. f1 and f2 are thus respectively proportional to the distances P1A1 and P2A2, and directed away from the line Qq. Note that f1 and f2 are difference forces that arise while the earth-moon system is orbiting the sun. Thus the moon at P1, since it is closer to the sun that it would be at A1, experiences a stronger attraction that it would at A1, and so a net force away from the plane 5. Similarly, at P2, it is further from the sun than it would be at A2, experiences a weaker attraction than it would at A2, and so, again, a net force away from 5. The results of Newton\u2019s analysis, in Prop 30, of the effects of this force, can be summarized with reference to Figure 2. The notation in Figure 2 is the same as that in Figure 1. PI is a perpendicular dropped from the position of the moon P on to the line TS, and I have labelled the angles T\u0302PI, P\u0302TN and S\u0302Tn as \u03b8 , \u03c6 and \u03c9 respectively. As a result of his analysis in Prop 30, Newton concludes that, at any instant, the line of nodes is rotating with an angular speed that is proportional to the product sin \u03b8 sin \u03c6 sin \u03c9. (I am using modern notation. Newton\u2019s notation is more archaic.) When the moon is at point A in Figure 2, and the line of nodes is along the line of quadratures Qq (both conditions are needed),then the angles \u03b8 , \u03c6 and \u03c9 are each 90 degrees, and the product takes its maximum value 1",
            " As a result of the precession, the plane of the equator rotates about the normal AC, in a manner somewhat similar to the rotation of the plane of the moon\u2019s orbit. In this case, however, the motion is uniform (ignoring small irregularities Newton does not consider) compared to the non-uniform, reversing movement given by equation (1). Newton evidently wanted to use his quantitative results on the movement of the moon\u2019s nodes to get a value for the rate of precession of the equinoxes, that is, the rate of rotation of the axis NS about AC. He attributes both effects to the same cause \u2013 the difference forces, described above, and denoted by f1 and f2 in Figure 1. In this case, 3 de Revolutionibus, Book I, Chapter 11. the forces are acting, not on the moon moving freely in space, but on \u201cparticles\u201d in the body of the earth. (Newton here speaks of \u201cparticles\u201d in an unspecified sense. He does not, in this context, discuss their nature, or the forces they might exert on one another. He does, however, speculate on such matters in Query 31 at the end of the Optics.) I have indicated two of these forces in Figure 3 \u2013 here f1 acts on particle P1 and f2 on particle P2",
            " Although Newton has correctly identified a torque about the axis Cperp, due to tidal forces, as the cause of the precession of the axis NS about AC, it is by no means obvious how he imagines it as producing this effect. It is evident, from his subsequent steps, that he has no conception of the modern notion of a torque as producing a change of angular momentum and, indeed, no conception of angular momentum. He appears to be thinking of the torque as a kind of generalisation of the single tidal force acting on the moon (f1 and f2 in Figure 1) in his treatment of the movement of the nodes. The moon, however, is moving freely in space, and he has to consider only its translational motion, under the tidal force and the earth\u2019s gravity, and his second law (force equals mass times acceleration) is sufficient for this. The particles in the earth\u2019s body, on the other hand, on which the tidal forces act, are part of a rigid body, and he wishes to determine their rotational effect, for which his second law is not sufficient. The laws of rigid body motion, sometimes called Euler\u2019s laws of motion, can be stated in the following form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002319_0021-8928(95)00015-h-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002319_0021-8928(95)00015-h-Figure2-1.png",
        "caption": "Fig. 2.",
        "texts": [
            " We introduce the system of coordinates i , y, z as follows: ~ is the length of the arc along the distorted axis,~ is measured in the plane of bending from the axis along the perpendicular to the latter, and ~ is measured along the perpendicular to this plane. The averaged value of a variable is its integral over the section normal to the deformed axis, divided by the area of cross-section. Such averages are denoted by angular brackets. The earlier notation (with x, y, z subscripts) are kept for the physical vector and tensor components in the new system of coordinates; y -- u(x, t) is the equation of the displaced axis in the fixed two-dimensional Cartesian system of coordinates of the observer lying in the plane of the bend (Fig. 2). The procedure for obtaining equations presupposes that terms of order 8/L and u/L, small compared to unity, will be neglected. The averaging of the equilibrium equations and the moment equation obtained by multiplying the axial projection of the momentum equation by the )7 coordinate leads to the traditional relations N ' - p = 0 (3.1) Q = M' (3.2) M'\" + (Nu')\" = 0 (3.3) N = (o~y)S and Q = (o~s are the tensile and shear forces, respectively, and M = (o~)S is the bending moment acting over the cross-section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003244_(sici)1097-4563(199603)13:3<163::aid-rob4>3.0.co;2-q-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003244_(sici)1097-4563(199603)13:3<163::aid-rob4>3.0.co;2-q-Figure3-1.png",
        "caption": "Figure 3. Two types of collision. (a) Collision between an obstacle and the robot. (b) Collision between nonadjacent links.",
        "texts": [
            " If any cell is occupied by an obstacle, either entirely or partially, this cell and its eight adjacent cells are labeled a hazardous region. Hazardous regions are created to reduce the calculations needed for checking collision between links and obstacles, as explained in section 3. 1. Collision between a robot link and an obstacle. 2. Collision between two non-adjacent robot links (mechanical stops are usually added to each joint to ensure that adjacent links do not collide). Both types of collision are shown in Figure 3. The path planner must ensure that neither type of collision occurs for every proposed robot motion. Because both the robot and obstacles are represented by line segments (after obstacle expansion and robot shrinkage), a collision is equivalent to an intersection between two line segments.I7 Therefore, an intersection between a Iink and obstacIe edge or between two links constitutes a collision. Appendix A presents the equations of an intersec- 166 Journal of Robotic Systems-1996 tion between two parametric lines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002862_07)15:6<435::aid-cnm257>3.0.co;2-w-Figure4-1.png",
        "caption": "Figure 4. Extraction of basic sector for wire rope strand problem",
        "texts": [
            " Tension, shear, bending and twist deformations develop Copyright # 1999 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng, 15, 435\u00b1443 (1999) C o p y rig h t # 1 9 9 9 Jo h n W iley & S o n s, L td . C o m m u n . N u m er. M eth . E n g n g , 1 5 , 4 3 5 \u00b1 4 4 3 (1 9 9 9 ) 4 4 0 W . G . JIA N G A N D J. L . H E N S H A L L simultaneously, together with local contact deformation, when the strand is subjected to an axial load. Taking advantage of the helical symmetry of the strand, a segmental slice of 1/12 of the strand can be chosen as the basic sector (see Figure 4). The angle ac 308 and the slice thickness were chosen as 0.1 mm. In this Figure F andM are again the induced axial force and moment of the strand, respectively. Figure 5 shows a typical \u00aenite element mesh of the model. Since the stresses vary rapidly in the vicinity of the local contact region, a much \u00aener mesh was used therein (shown in the detailed view). Contact between the core wire and the helical wires has been simulated using contact elements, which can simulate general surface-to-surface contact with coulomb friction sliding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002290_951039-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002290_951039-Figure3-1.png",
        "caption": "Figure 3. Applied Force and Normal Load",
        "texts": [
            " Thus the roller follower rotates counterclockwise at an angular velocity (\u03c9f - d\u03c6/dt). The absolute tangential velocity (Vr) of the roller follower center is Vr = Vf + rf (\u03c9f - \u03c6) (10) Hence the relative angular velocity of the roller follower is obtained by rearranging equation 10: By substituting equations 2 and 9 in equation 11, we obtain The follower lever rotation angle (\u03a6) can be described as NORMAL LOAD (Wn) - The normal load between the cam and follower is a function of the contact geometry at each cam angle as shown in Figure 3. Pushrod force (Wp) has been calculated at each cam angle by the computer simulation and verified by experiment.(1),(5) The normal load (Wn) can be obtained by a steady state moment equilibrium since the friction at the lever pivot O is negligible compared to other forces: that is, where the angle (\u03bef) between the normal contact line and the lever axis (OO\u2019) was given by equations 7 and 8. The similarity analysis of the roller follower pin friction based on experimental data, which is shown Figure 4, is presented in this section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002333_s0045-7825(98)00367-3-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002333_s0045-7825(98)00367-3-Figure10-1.png",
        "caption": "Fig. 10. Pin tooth of the pinion.",
        "texts": [],
        "surrounding_texts": [
            "The developed theory is illustrated with the example of Root's blowers (Fig. 3). The ratio of angular velocities of the rotors of the blower is one and the centrodes are two circles of the same radius r (Fig. 4). Movable and fixed coordinate systems S r, Sp and Sj are shown in Fig. 4. The generating curve ~7 r is a circular arc of radius p and is represented in S r as (Fig. 5) r(O) = ( - p sin O)i r + (a + p cos O)j, (55) The tangent and the normal to v r are represented as T r = r o = [ - p c o s O - p s i n 0 0] v (56) N r = T r \u00d7 k , = [ - p s i n O p c o s 0 0] T (57) Applying Eq. (17), we obtain the following equation of meshing Our goal is to determine the singularities of a curve Xp that is conjugated to the circular arc Xr. To solve this problem, we consider the segment of line of action that corresponds to the meshing of curves Xr and .Sp. The tangent to such a segment of the line of action is obtained as (see Eq. (41)) [ c o s c o s ( 0 - - p c o s 0 c o s ( 0 - - a c o s 0 c o s ] T, = [ - r sin ~b cos(0 - ~b) - p cos 0 sin(0 - ~b) + a cos 0 sin ~b[ (60) L 0 J Parameters 0 and 4, in Eq. (60) are related by equation of meshing (58). The singularity equation is determined as (see Eq. (44)) gl(O, Cb) = x~T,I + YIT~.I - 2rTvl = sin ~b[p + 2a cos 0 - 2r cos(0 - ~b)] - p cos 0 sin(0 - \u00a2~) = 0 (61) Parameters 0 o and ~b 0 of a point that is the candidate for the singularity point can be obtained by solving equation gl = 0 and f = 0. The singularity point is also the point of regression if inequality (54) is satisfied. The investigation of existence of a singularity point must be accomplished considering as the input parameter the ratio p / a of design parameters p and a (Fig. 5). The envelope (generated curve ~p) (Fig. 7(a)) is derived using the algorithm represented in Section 2. Our investigation has been performed for the design parameters (p-= 0.713r, a = 0.96r). It was proven that two singularity points occur in the neighborhood of point M determined by (0 o = 84.8 \u00b0, ~b o = 11.9 \u00b0) and (0 o = 99.2 \u00b0, ~b o = 27.8\u00b0). These two points are simultaneously points of regression and the piece of envelope ~o has the shape of a 'swallow tail'. Such a piece of the envelope is represented to an enlarged scale in Fig. 7(b). Note: In the case of Root 's blowers, there is such a point of the line of action (point P in Fig. 9 where equation singularity (35) or (36) is satisfied. However, a singularity point of Xo is not generated at P because v(p) ~ . (r) and - (p) r ~=V. Eqs. (35) or (36) is satisfied just because vectors v~ IUtr are collinear. At point P of line of action, a regular point of ~p but not a singular point of ~ , is generated. The appearance of singularities is a herald of the oncoming undercutting. Fig. 8 shows that the extension of the length of the circular arc of curve 2f, is accompanied by undercutting of envelope .,Yp (in the 'swallow tail' part). Undercutting of envelope 2?p may be avoided by limitation of parameter 0 that must be in the range 0 <~ 0 < Oj~ m, where 0t~mcorresponds to the point of singularity of .Sp. Fig. 8 shows the family of circular arcs X~ and the envelope 2?p. Fig. 9 show a segment of line of action that corresponds to the meshing of X~ and Xp. The drawings illustrate that singularity points of ~p are generated at points M, and M e of line of action L where the normals to L pass through point Op of rotation of the driven rotor. The discussed approach for determination of singularities can be applied for a cycloidal gearing with a pin tooth (Fig, 10) of the pinion (driving gear). Examples of such a cycloidal gearing are: (i) the meshing of the pin tooth and the chamber in Wankel engine [9] (Fig. 11); and (ii) cycloidal gearing applied in pumps [3,6]. The ratio of angular velocities in such a case differs from one, and the gear centrodes may be in intemal and external tangency. Fig. 12 shows a family of circles Xr that are represented for the following conditions: (i) the ratio of angular velocities of mating rotors is one, the centrodes of the rotors are equal and are in external tangency; (ii) the ratio of design parameters is a/p = 1.35. The family of generating circles Xr has two envelopes designated as X~p ~ and X~ 2~ (Fig. 12). Envelope X~ 2~ is undercut in a small neighborhood of two points of singularities. Envelope X~p ~ is formed by two intersecting curves. Inside of the space that separates 27~p ~ and Ec2~ there is a zone of undercutting of X ~ ~ (Fig. 12). - - p"
        ]
    },
    {
        "image_filename": "designv11_31_0002211_1.1707606-Figure16-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002211_1.1707606-Figure16-1.png",
        "caption": "FIG. 16. Schematic diagram of apparatus for measuring hysteresis of tire cords.",
        "texts": [
            " After the cord had been put through several cycles, the loop ob tained from the observed data was essentially' closed. The areas within the loops correspond to the energy loss or hysteresis due to the imperfect elasticity of the cord. This phenomenon of elastic hysteresis, which has been reported upon for 398 textile fibers by a number of experimenters,21.23 was investigated by us for some of the tire cord samples herein described. The apparatus used for measuring hysteresis is schematically depicted in Fig. 16. A calibrated spring D served to give the necessary tension to the cord at various points In the cycle as the motor-driven eccentric E gradually increased the pull on the cord C and released it again. A two meter length of the cord was used and was fastened to the wire leaders by means of the stirrups T described earlier. Two pointers M on the wires passed in front of two 23-cm scales S in such a way that the position of the upper one gave the elongation of the spring, which could be converted to load; the difference be tween the positions of the two pointers permitted calculation of the elongation of the cord"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002900_20.141296-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002900_20.141296-Figure8-1.png",
        "caption": "Fig. 8 . Finite flat disc is magnetized by a large diameter coil. (a) Schematic representation of the experimental arrangement. 1: Waveform Generator Wavetek 132 VCG/Noise Generator. 2: Step-up coupling transformer 1 : 4. 3: Bipolar Operational Power SupplylAmplifier BOP 36-12M. 4: Excitation coil of 29 turns, 90 mm length, 125 mm diameter. 5: Force Transducer Gould UFI-Model 1030. 6: Waveform Generator Wavetek 164 Sweep Generator. 7: Precision ac Amplifier Brookdale Type 452. 8: Digital Voltmeter. Current supplying the excitation coil was of 20 App and of 1 kHz, 2 kHz, and 3 kHz, respectively. The force transducer was excited by a 1 0 0 Hz voltage. Aluminum discs were of 42-mm diameter and of thickness 0.7 mm, 1.6 mm, and 3 mm, respectively. (b) One-dimensional arrangment chosen for the evaluation of the effective eddy current permeability.",
        "texts": [
            " However, it seems that few experimental results, if at all, were reported about eddy current magnetization and forces of finite flate discs, whose demagnetization factor is very close to one. This section presents original experimental results regarding the eddy current forces exerted on flat discs of aluminum. The experimental results are compared with data obtained according to the present evaluation method of the effective magnetization due to eddy currents and in sequel of the eddy current forces. The experimental arrangement is shown in Fig. 8(a). The diameter of the excitation coil is about three times larger than that of the discs. As a result, the excitation magnetic field exerted on the aluminum discs can be considered as equal to that on the coil axis. To facilitate the measurements the discs are placed at the end of the excitation coil, where the eddy currents force will be maximum. The experimental results regarding the eddy current forces exerted on the aluminum discs of the same diameter but of different thicknesses (and as a result of different demagnetization factors) are shown in Table I",
            " The results obtained according to the present evaluation method (expressions (23), (26)) are also shown. The agreement between them is fairly good. The one dimensional effective eddy current permeability which is needed for magnetization evaluation in the presence of eddy currents (expression (23)) is that of an infinite cylinder magnetized in parallel to its axis and whose diameter is equal to that of the discs (expression (22)). The demagnetization factor is close to that of an oblate ellipsoid whose axes are aluminum discs diameter and thickness (Fig. 8(b)). From the results of Table I it is seen that the eddy current force on the body volume unit increases with the demagnetization factor, as was expected from expression (23). V. CONCLUSION The paper presents an approximate evaluation of eddy current magnetization effects in conductive objects, when the similarity with the diamagnetic phenomena is used. The usefulness of this approach is proved by comparing results about eddy current forces obtained through the present method with experimental results and theoretical results published in the literature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003993_fld.1650060704-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003993_fld.1650060704-Figure1-1.png",
        "caption": "Figure 1. Bearing notation",
        "texts": [],
        "surrounding_texts": [
            "INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 6,445-458 (1986)\nDepartment of Mechanical Engineering, University College of Swansea, Singleton Park, Swansea 5A2 8PP. U.K.\nThe analysis presented herein deals with the evaluation of pressure and temperature fields which are generated in thin fluid films of varying thickness. The particular problem of a misaligned journal bearing has been studied by solving simultaneously the Reynolds and energy equations, which also include the effects of viscous dissipation and the variation of fluid viscosity with temperature.\nThe method has been used to predict pressure and temperature fields as well as global performance parameters for a typical journal bearing operation.\nThere are a large number of practical flow problems which involve the movement of a thin fluid film between two surfaces in relative motion. If the surfaces are inclined then a pressure field is generated in the film and it is this capacity for supporting a load that forms the basis of hydrodynamic lubrication. A common engineering artefact which exploits this principle is the cylindrical bore journal bearing in which a loaded shaft (or journal) rotates in a metallic bush that is fed continuously by a lubricating fluid. Under ideal operating conditions the longitudinal axes of both shaft and bush are parallel, although displaced eccentrically. This gives rise to a thin converging fluid film (see Figure l(a)) which generates a pressure field and forms the load carrying portion of the bearing.\nOften journal bearings operate in a misaligned mode where the shaft and bush axes are inclined to each other, this occuring most commonly in the plane in which the shaft is loaded (i.e. in the direction indicated by Win Figure l(a), and is usually due to the flexure of the shaft). Consequently the resulting pressure and temperature fields in the lubricant film will be distorted, with the maximum pressure and temperature being significantly higher than in the aligned case. In many instances the latter quantity, which depends on the viscous dissipation in the lubricant film, is the limiting parameter on the range of bearing operation, and therefore the designer must have a method at his disposal for its estimation.\nAlthough many procedures exist for the calculation of bearing characteristics for aligned cases, little information is available for the \u2018off design\u2019 operation referred to above. Some work exists for isothermal ~ a s e s , l - ~ and recently further work4 has endeavoured to account for thermal effects by including dissipation due to shearing action in the thin films.\nWith the exception of the work described in Reference 4, the major shortcoming of most approaches is that they ignore the temperature dependency of the lubricant viscosity, and that\n\u2018Lecturers in Mechanical Engineering\n027 1-209 1/86/07044- 14$07.00 0 1986 by John Wiley & Sons, Ltd.\nReceived 18 January 1986 Revised 18 January 1986",
            "446 J. 0. MEDWELL AND D. T. GETHIN\nthey are addressed to a bearing which is supplied with lubricant at a point close to the maximum film thickness-a configuration which is not used extensively in practice since it may not allow birotational motion of the shaft. By adopting a single feed point, the analysis is simplified considerably, since it is unnecessary to update the film thickness profile during the mildly iterative (i.e. convergence in a few iterations) calculation as it is with a twin axial groove geometry for example (see Figure l(a)). Indeed it is the necessity to update the film profile which renders the solution strongly iterative in nature. This arises since the journal will assume a final position in the bearing which depends on the applied loading.\nThe present paper illustrates a method for analysing the behaviour of a bearing fed by two axial grooves, as well as linking the fluid properties of the film to local film temperature to give a complete thermohydrodynamic solution to the problem. This involves, basically, the simultaneous solution of the Reynolds and energy equations using finite difference methodology.",
            "MISALIGNED HYDRODYNAMIC JOURNAL BEARINGS 447\nBecause, in practice, misalignment in high load, high speed operation causes many bearing failures, the analysis employed here has been adapted for turbulent lubricant films.\nThe Reynolds equation for a steadily loaded journal bearing of finite width may be written as\n(1) ax where G , and G, are included to account for the augmented exchange or transport properties associated with turbulent motion.\nAn energy equation may be derived in which the variation of the mean temperature of the lubricant is described by a balance of the generated heat with that convected away in the film. Hence any cross-film or streamwise conduction effects are neglected, giving rise to the so-called adiabatic condition-a good approximation for thick films operating under turbulent conditions. The temperature of the lubricant film at any point (x , z ) can be represented by a mean value T,,, and appears in the energy equation in the following manner:\nUh(x, z) h3(X, z ) G , G,--\nq aZ aZ = - . r , U + - ax\nwhere\nUh(x , z ) 0.94 -- h(x, z)7c - 1 + 0.,,2( y) . ?U (3)\nThe domains over which equations (1)-(3) give a complete description of the physical occurences are shown in Figures l(a) and l(b), together with other relevant geometric data required for the solution of the aforementioned equations. First the local lubricant film thickness under the misaligned conditions must be expressed. This may be done either by assuming (as did Asanabe et d.') that the misalignment takes place along the diameter connecting the positions of maximum and minimum film thicknesses or, more realistically, along the load line. Hence\nX h ( x , z ) = ( R , - R , ) { ~ + E C O S (;I -- *)} - f f Z C O S K , (4)\nwhere the midplane eccentricity ratio E\n&=--------.\nR2 - R , To complete the statement of the problem, the boundary conditions of the oil-film distribution and the temperature fields must be described. For the solution of the Reynolds equation, the boundary conditions are\np = O at x = x l and x = x 2 ,\np = O at z = +--, p = O when p < O . L 2"
        ]
    },
    {
        "image_filename": "designv11_31_0003477_6.1992-3715-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003477_6.1992-3715-Figure2-1.png",
        "caption": "Fig. 2 Photograph of Ring Geometry Samples",
        "texts": [
            " All wear surfaces are characterized using ;canning electron microscopy, energy dispersive X:a7 spectroscopy, micrometerology, optical microscopy and hardness measuring techniques to ~ ~ e s s the operating wear mechanisms and potential iroperty/performance correlations. The ring-on-ring iamples are tested using a contact pressure of 2 PSI md temperatures up to 1200\u00b0F. Rotational speeds of 10,000, 20,000 and 30,000 RPM are employed for 30 ninutes each to achieve a total test time of 1.5 hours. A photograph of the ring geometry samples is ihown in Figure 2. The primary test rig used for brush seal material optimization is a high speedhigh temperature rig capable of shaft s eeds up to 60,OOO RPM offering a surface speed of ! 20 ftlsec for approximately 1 inch diameter tribological test pieces. Tests can be conducted at elevated temperatures, up to 1300\u00b0F with light surface contact pressures. The test rig, illustrated in Figure 3 is of unique design and provides very precise friction data on a real-time basis. The rig has a variable frequency AC drive converter to provide speed control of the direct drive shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003638_j.1559-3584.1992.tb02238.x-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003638_j.1559-3584.1992.tb02238.x-Figure9-1.png",
        "caption": "Figure 9.",
        "texts": [
            " Vertical thrusters would act primarily to counter the vehicle\u2019s slight positive buoyancy and maintain depth while the vehicle was moving too slowly to achieve depth keeping with the control surfaces. In order to meet the movement requirement, and noting that no currents would be present in the pool, i t was thought that the thrusters would have to produce at least 1 pound of thrust per unit. A novel direct gear driven thruster, with a Kaplan type impeller, fabricated in plexiglass, was designed for testing and prospective vehicle installation. Figure 9 shows a view of the proposed vehicle arrangements. The task of providing real-time control of the AUV I1 systems must be addressed as a parallel effort in the design spiral. A structure of the intelligent autonomous control system in the process of implementation in AUV I1 is given by Naval Engineers Journal, May 1992 197 real time on a Gespac onboard computer. Initial designs for the computer system were based on an MS-DOS operating system laptop computer. Such a machine had light weight-nly 15 Ibs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002333_s0045-7825(98)00367-3-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002333_s0045-7825(98)00367-3-Figure3-1.png",
        "caption": "Fig. 3. Root's blowers.",
        "texts": [
            " [1(0(05), 05) - E] = 0 (52) The singularity point of the envelope is determined by the equations tip = p ( O, 05) 0, 05) = 0 (53) g,(O, 05) = 0 The singularity point is indeed the point of regression if ~l=lf\u00b0Ll~\u00b0go ge, (54) where go = O/O0[gt(O, 05)], g,~ = O/005[gt(O, 05)]. The proposed approach enables to simplify the singularity equation using it in form of Eq. (44), and simplify as well the determination of go and g~b. The developed theory is illustrated with the example of Root's blowers (Fig. 3). The ratio of angular velocities of the rotors of the blower is one and the centrodes are two circles of the same radius r (Fig. 4). Movable and fixed coordinate systems S r, Sp and Sj are shown in Fig. 4. The generating curve ~7 r is a circular arc of radius p and is represented in S r as (Fig. 5) r(O) = ( - p sin O)i r + (a + p cos O)j, (55) The tangent and the normal to v r are represented as T r = r o = [ - p c o s O - p s i n 0 0] v (56) N r = T r \u00d7 k , = [ - p s i n O p c o s 0 0] T (57) Applying Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003570_37.856182-Figure13-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003570_37.856182-Figure13-1.png",
        "caption": "Figure 13. State-space diagram: x1 versus x2 for positive and small values of Kc.",
        "texts": [
            " The system behavior under these conditions is shown in Fig. 12 in a qualitative diagram of states, where states x 1 versus x 2 are depicted. On the other hand, the extreme equilibrium points are stable for positive values of the parameter Kc, but the system behavior varies depending on the magnitude of this parameter. In particular, as discussed in a previous section, no limit cycles exist if the value of Kc is small. The system behavior under these conditions is depicted in a state diagram in Fig. 13. The fact that a change in the stability of some equilibrium points has been produced, varying the parameter Kc, is a first change in the phase portrait, which occurs when the value of Kc becomes zero. In addition, another bifurcation (a saddle-node bifurcation of periodic orbits) appears when the value of the parameter Kc reaches a value Kc min. For values of Kc greater than Kc min, there are two limit cycles surrounding the band of stable equilibrium points. Under these conditions, the system evolves as shown in the state diagram in Fig",
            " 15(d)], the amplitude of the unstable limit cycle increases while the amplitude of the stable one decreases until parameter Kc reaches the value of Kc min [Fig. 15(c)]. At this value of Kc, the coalescence of the limit cycles is produced, giving rise to their extinction. For values of Kc less than Kc min but positive [Fig. 15(b)], the band of equilibrium points re- 98 IEEE Control Systems Magazine August 2000 mains stable and the amplitude of its attraction basin is infinite, since there are no limit cycles surrounding it (phase portrait of Fig. 13). Finally, when Kc reaches a negative value [Fig. 15(a)], the extreme equilibrium points of the band become unstable. This implies that if a small disturbance causes the system to evolve toward the outside of the zone| |x d1 1\u2264 , the state variables will evolve away indefinitely from their equilibrium values (recall Fig. 12). It is worth noting how the conventional saddle-node bifurcation of Fig. 1 has been transformed into a more complex one, in this case due to the dead zone. It is very interesting to note that in the saddle-node bifurcation of periodic orbits, two limit cycles are born when Kc varies from the one of part b to that of part d in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002907_3516.662865-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002907_3516.662865-Figure5-1.png",
        "caption": "Fig. 5. Pen body made with molded interconnect technology (the circles refer to the number of conductors).",
        "texts": [
            "2 This plastic has good mechanical properties and allows integration of electrical connections through a type of molded interconnect device (MID) technology, as provided by Siemens [9]. By using the Siemens\u2019 SIL process,3 it becomes possible to integrate all wiring on the pen body. The main advantage of using this technology is a further miniaturization and reduction of weight. Also, the reliability will be improved and the production will be far cheaper. In most cases, wiring is quite difficult and, thus, very expensive to assemble. Fig. 5 shows the proposed design for the pen body. The force sensor will be mounted in the hole on the left side. It contains geometric features to secure a unique and welldetermined orientation of the sensor. The tilt sensor is to be mounted in the tub-like feature behind the sensor mounting. Beyond the tilt sensor, the batteries can be inserted between two metal contacts. These contacts are to be inserted in the C-shaped holes of the pen body. At the right side of the plastic part, a connector for connecting the PCB containing all electronics can be soldered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002352_10402009508983402-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002352_10402009508983402-Figure1-1.png",
        "caption": "Fig. 1-Bearing geometry. (a) typical five-pade flexible-pad journal bearing (b) motion of the pad",
        "texts": [
            " However, the tilting-pad bearings with moving parts are mechanically complex and generally have lower damping and softer stiffness than fixed geometry bearings. Furthermore, the manufacturing tolerance stack-up existing in the tilting-pad bearing, as illustrated by Zeidan (1) and Chen et al. (2 ) , can result in a wide range of bearing clearance and preload. This variance can be pronounced for relatively small-sized bearings which have been commonly used in high-speed application. Recently, the flexible pad journal bearing, as shown in Fig. 1, has been gaining attention in bearing design for highspeed rotating machinery (3) , (4). It is a one-piece design similar to that of the conventional tilting-pad bearing without the complexity of the moving parts. Therefore, the pivot wear, manufacturing tolerance stack-up, and the unloaded pad flutter problems associated with the conventional tilting-pad bearing can be eliminated. However, due to the flexibility of the support web, the pad is not free to pitch and the destabilizing tangential oil film force always exists, even when the pad inertia is neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003685_roman.1997.646948-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003685_roman.1997.646948-Figure9-1.png",
        "caption": "Fig. 9 Simulation of golf swing motion",
        "texts": [
            "3 gives priority to the setting conditions of 0 im and thus an error may occur in the specified head velocity. Therefore, the reliability of the evaluation was examined. When E1 is 100 N m 2 and E is 2.27 kg-m2, the specified head velocity is represented as Hvs. H, is varied at intervals of 1.0 m/s in the range of 33 to 42 m/s. The expression below represents the e- value (%), which indicates the error factor between H, and Hvs. Figure 8 shows the results of this analysis. Because an error due to H, is always within+3.0%, highly reliable evaluations can be expected. The stick picture in Fig. 9 shows the swing motion when Hvs is 35 m/s. This figure shows that the torque plan satisfies the conditions of motion. If the identification of the specific characteristics of individual clubs can be automated, the golf swing motion can be correspondingly, automatically adjusted. The following points summarize the results of our examination of a golf-swing robot that can adjust its motion to the characteristics of any given golf club and to the specified head velocity. (1) In this model, releasing the wrist joint at the positive zero-cross point of the displacement of the shaft vibration maximizes the head velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003931_jsvi.1999.2484-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003931_jsvi.1999.2484-Figure2-1.png",
        "caption": "Figure 2. Geometry of the typical belt}pulley system.",
        "texts": [
            "erence between wave numbers in opposite directions, will not carry actual power #ow. Consequently, any component associated with the moving medium should be subtracted from the total power #ow in order to obtain the true power #ow. By utilizing the beam model without damping the total power can be dissolved into the true power and the component associated with the moving medium only. This concept is employed in the calculation of transverse vibrational power #ow through belt}pulley systems that include a tensioner. As shown in Figure 2, a tensioner is located between the drive and the driven pulleys. Usually, longitudinal, torsional, and transverse vibrations of the belt are coupled. Since only the transverse vibrational power #ow is addressed in this paper, it will focus on how the vertical motion of the tensioner is a!ected by the transverse vibration of the rubber belt. Although the system has three spans, l 1 , l 2 , l 3 , only the transverse vibration transmission between the \"rst and second spans, l 1 , l 2 , will be considered in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002497_jaer.1996.0022-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002497_jaer.1996.0022-Figure5-1.png",
        "caption": "Fig . 5 . Chord of intersection AB ( 5 2 L ) of soil surface with disc circular edge for a disc inclined at an angle a to the y ertical",
        "texts": [],
        "surrounding_texts": [
            "For a particular disc angle , b , there is a critical depth , d c , for which b is the appropriate critical angle ( Fig . 3 ) . This angle can be determined from Eqns (1) , (2) and (3) by obtaining an explicit expression for d c for a given value of b . The equation is a quadratic one of the form A d 2 c 1 B d c 1 C 5 0 (5) where A 5 1 2 cos 2 a sin 2 b ; B 5 2 cos a h R o cos a sin 2 b sin ( a 1 e ) 2 r j and C 5 R 2 o cos 2 a sin 2 b h 1 2 sin 2 ( a 1 e ) j The positive solution of Eqn (5) is taken which gives a value of d c which lies within the working depth of the disc . Fig . 7 shows the ef fect of disc angle ( b ) on critical depth for tilt angles ( a ) of 10 8 and 30 8 for both the 140 120 100 80 60 40 20 0 C ri tic al d ep h, d e m m 0 5 10 15 20 25 30 35 40 Disc angle, \u03b2 deg \u03b11 \u03b12 \u03b11 \u03b12 S S D D Fig . 7 . Variation of critical depth ( d c ) with disc angle ( b ) for"
        ]
    },
    {
        "image_filename": "designv11_31_0003025_978-3-0348-9179-0_4-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003025_978-3-0348-9179-0_4-Figure3-1.png",
        "caption": "Fig. 3. Cartoon showing a monolayer of protein molecules on an electrode surface, and their interaction with potentially reactive agents in the contacting electrolyte. Triangles represent electrode surface modifications that may be required for protein attachment.",
        "texts": [
            " One way to overcome this problem is to enforce conditions of total steady-state by using a rotating disc electrode or a micro electrode. Another way (at least to overcome the problem of weak and ill defined current response) is to exploit the greater sensitivity of methods such as square-wave voltammetry. 2.2.3. The immobilized configuration: A different, and arguably more satis factory, perspective is achieved by studying proteins that are immobilized on an electrode surface. The basic configuration, albeit once again the idealized case, is shown in Fig. 3. Protein molecules are induced to bind tightly to the electrode surface in the form of a stable, porous, mono/submonolayer film, oriented for facile electron transfer, and with retention of native struc tural and reactivity characteristics. The redox centres act independently and homogeneously, and remain fully accessible to ions and small reagents in the contacting electrolyte, as does all the intervening space in the interface. Ideally, the cyclic voltammetry of such systems should resemble the form shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003161_bf01258295-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003161_bf01258295-Figure1-1.png",
        "caption": "Fig. 1",
        "texts": [
            " \u2022 Off-line version, robot class: The robot is variable, i.e. a~, a~ are parameters, and the position is variable, i.e. the entries in T are parameters. The advantages of keeping values as parameters are near at hand: \u2022 One can solve the inverse kinematics for a whole class of problems (prepro- cessing), and \u2022 substitute the numerical values for the robot and/or the position into the solution formulae. ALGEBRAIC METHODS FOR C OM P UT ING INVERSE KINEMATICS 81 3. Example Consider a robot with two rotatorial joints (Figure 1). The kinematics for this robot can be described by the following Denavit-Hartenberg matrices: _ 7 r ( A 1 ) oz 1 - 7 ' c o s 01 sin 01 0 0 a 1 ----- 0 , d l = I1, 0 s i n 01 0 \\ 0 -cos01 0 ) 1 0 li ' 0 0 1 ( A 2 ) (T) OZ 2 = 0, a 2 = 12, d2 = 0 , cos 02 -s in02 0 lacos02\"~ 7 cos0 o s!02) 0 1 0 0 Position (px ,pu,pz) , orientation given by roll/pitch/yaw angles g~, *v, ~Sz. / o o s os n s n i co co si o + i s n sin 6~ cos 6~ sin 6~ sin 6 v sin 6:~ + cos 6~ cos 6:~ sin 6z sin 6 u cos ~5~ - cos 6z sin 6~ pu "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003882_00423118708969172-Figure36-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003882_00423118708969172-Figure36-1.png",
        "caption": "Fig. 36 - Front wheel suspension/steerinq system.",
        "texts": [],
        "surrounding_texts": [
            "i n i t i a l yaw a c c e l e r a t i o n f o , t h e s t e p r e s p o n s e o f t h e e x t e n d e d model would show a z e r o s l o p e a t t = O .\nF i g . 34 - The f r e q u e n c y r e s p o n s e f u n c t i o n o f t h e non-d imens iona l yaw v e l o c i t y r t o s t e e r i n ~ u t o s c i l l a t i o n s 6 ( u = 25 m/s ) . The i n f l u e n c e o f a t r a n s i e n t t y r e r e s p o n s e model w i t h 0 = 0 . 2 m h a s been i n d i c a t e d .\nF i g . 35 - The res ,nonse t o a u n i t s t e e r imnulse w i t h and w i t h o u t t h e i n f l u e n c e o f t y r e l a g ( u = 1 3 . 4 m s / s ) .\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf W\nat er\nlo o]\na t 0\n9: 10\n2 4\nO ct\nob er\n2 01\n5",
            "2 . FRONT WHEEL VIBRATIONS 2.1 Introduction various sources may be responsible for inducing front wheel vibrations. A large number of suspension and steering system parameters influence the sensitivity of the system to external or internal disturbances.\nFigure 36depicts the system restricted in the sense that the car body to which the system is attached is considered rigid and steadily moving along a straight line. The podel is kept rather general and virtually all kintls of suspension systems are covered when properly changing parameters and coordinates\nof joints, etc. A special computer programme has been developed tostudy effects of parameters on the sensitivity of the system [26].Figure37 shows the interrelation between relevant sub-systems.\nIn this contribution a great deal of attention will be paid to the tyre, a\ncomponent which transmits and generates forces which act between road and wheel. Besides, an example will be given of the application of the tyre theory to a suspension/steering system upto three degrees of freedom.\nIn figure38 a diagrammatic overview of the dynamic tyre system has been given.\nFor small deviations from the straight ahead motion a linear descript.lon of the behaviour may be given. Then, it is advantageous to recognize the fact that symmetric and anti-symmetric motions of the assumedly symmetric wheel-tyre system are uncoupled. The figure shows the separate function blocks w.Lth the input and output signals.\nThe forces and moments are considered as output quantities. They are\nassumed to act on a rigid disc with inertial properties equal to those of the tyre when considered rigid. The motions of the rigid disc and the profile of the road (w) are considered as, input quantitibs. In our problem, braking and driving torques are left out of consideration. For the freely rolling tyre the wheel angular motion about the spin axis is governed by only the internal moment M acting between tyre and rim. The five position Y coordinates of the wheel spin axis may then serve as input vector (camber angle y will not be considered here).\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf W\nat er\nlo o]\na t 0\n9: 10\n2 4\nO ct\nob er\n2 01\n5",
            "STATIONARY\nI '\nI WNAMIC 1 STEERING CDNNEtXING WHEEL-6VB '\nAXLE ASSEMBLY - rxlre W E R S I SYSTEM I \"'\"\" - I\nI I I I I U N W N C E T I R E\nHhSsEs EXCITATION I L , , , - , -- - - - - - - - - - -\nSTATIONARY\n~ i g . 37- Total system composition.\n\" YGENT IAL .Dl STORT ION AND SL1.P\n-1 RADIAL DEFLECTlON L dw/dx\nyf-*j WHEEL CHANGE OF ROLLING RAD l US\nTURN SLIP I\nLATERAL ANLI 5 ~ 1 r TORSlONAL DlSTORTlON I TYRE INERTIA\nPig. 38- Uncoupled tyre system blocks val id for small deviation6 fran the steady-state straight ahead motion\nThe remaining part of this chapter has not been reproduced here. We refer to the Proceedings of the first course on Advanced Vehicle System Dynamics, 1.C.T.S.-P.F.T. Proc. Series Vol. 1, Eds. A.D.de Pater and H.B. Pacejka, Rome, 1982, in which this chapter has been published pp. 197-236. The material is also covered by references [13,26,27,28].\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf W\nat er\nlo o]\na t 0\n9: 10\n2 4\nO ct\nob er\n2 01\n5"
        ]
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure4.48-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure4.48-1.png",
        "caption": "Fig. 4.48",
        "texts": [
            " The field winding connections with the armature must be reversed permitting the voltage across the machine to build-up using its residual magnetism. In analyzing this braking, it will be assumed that controlled switch K is perfect and that speed N does not vary during the switching cycle. In the case of the magnetic characteristic, the residual flux but not the hysteresis will be taken into account. 218 4 Operation and Characteristics of Directly Linked Choppers thus, I'= E . Ra + Rr + Rs - If K is permanently off (a = 0), from di' (Ra + Rr + Rs + Rh) i' + (La + Lr + Ls) dt = E the following can be deduced: I'= E . Ra + Rr + Rs + Rh In Fig. 4.48, the magnetic characteristic of the machine at a rotation speed N has been plotted. The intersection of this with the straight line of slope Ra + Rr + R5 and Ra + Rr + R5 + Rh gives the two boundary values of the current at this speed: I:nax for K always on (point A), I:nin for K always off (point B). The current can only build up to a noticeable value if the slope of the straight line corresponding to Ra + Rr + Rs is less than the initial slope of magnetic characteristic k0 N: ko N > Ra + Rr + Rs 4.4 Notes on Choppers in Traction Applications 219 Below a certain speed, the voltage build-up of the series motor is impossible. Moreover, the closer to this minimal speed, the lower I'max will be. (In Fig. 4.48 the curve E(i') corresponding to N/2 has been plotted. The point corresponding to the maximum current passes from A to A'.) 4.4.2.2 Controlling the Mean Current \u2022 The mean value of the current can be controlled by acting on the duty ratio a of the chopper. By linearizing the magnetic characteristic around the point corresponding to I' (point C in Fig. 4.48), the following value can be taken for E: N E = \u00a3 10 -- + k~Ni'. Nnom Hence, the equation giving current i' is N d\"' Eta--- (L. + Lr + Ls)_!_- (R. + Rr + Rs- k~N)i' = u'; Nnom dt with u' = 0, when K is on, u' = Rh i', when K is off. The solution of this equation gives: - for 0 < wt < 2nr:x, (K on): with ., ., (- wt) EtoN/Nnom [ (- wt)] 1 = 10 exp - + 1 - exp - Q R. + Rr + Rs - k~ N Q Q = (L. + Lr + L5 )w R. + Rr + Rs - k1 N with i0 denoting the value of i' for wt = 0 - for 2nr:x < wt < 2n, (K off): "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003928_0301-679x(91)90060-m-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003928_0301-679x(91)90060-m-Figure4-1.png",
        "caption": "Fig 4 Relative depth o f penetration as a Junction o f load at: I - I/r = 0.5; 2 - 1.0; 3 - 1.5; 4 - 2.0",
        "texts": [
            " is the contour area of contact) versus the pressure q = Q / A o calculated using the classical theory (curve 2) and from Eqs (9) (curve 1) for the system (N--52) of spherical punches of radius ~, located at the sites of a quadratic lattice (l is the lattice pitch) for l/+ = 0.5. Starting with A~/Ac = 0.3 the error in the calculation of the real areas of contact neglecting the mutual influence becomes noticeable. The dependence of the depth of penetration upon load Q for the system of spherical asperities under consideration is shown in Fig 4. The higher is the contact density (the smaller is the parameter l when r 31 = const), the greater is the load required to achieve the given depth of penetration. Analogous results were obtained theoretically and experimentally when studying the interaction of a system of cylindrical punches, located at the same level, with an elastic half-space (Fig 2). Based on the present results, we may conclude that calculation of characteristics of the stationary contact of rough surfaces neglecting the mutual influence of microcontacts gives overestimated values of contact rigidity (smaller depths of penetration at the same loads) and overestimated real area of contact, and the discrepancy is the greater, the greater is the number of microcontacts and the higher is their density"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003904_j.1749-6632.1986.tb23608.x-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003904_j.1749-6632.1986.tb23608.x-Figure4-1.png",
        "caption": "FIGURE 4. Graphs showing (A) the relationship between loop size and 70 recovery (mean t SEM) of DOPAC through the dialysis membrane and (B) the relationship between flow rate and % recovery (mean f SEM) using a 2 mm loop. For experimental purposes a flow rate of 0.7 pl/min or 1 pl/min and a loop size of 2 mm was adopted.",
        "texts": [
            " The C, area of the ventrolateral medulla (VLM) was electrically stimulated using modified SNE 100 (Clarke Electromedical Equipment) concentric needle electrodes (2 V, 1 msec rectangular pulses at 40 Hz for 10 sec every 30 sec for 30 min). Blood pressure was monitored at the same time following cannulation of a femoral artery. In vitro studies with the dialysis loops demonstrate a relationship between both the size of the loop and perfusion rate with percentage recovery of the amine or metabolite outside the tubing (FIGURE 4). The optimum loop size and flow rates were 2 mm and 0.7-1.0 pl/min, respectively, when the sensitivity of the assay method and the size of the brain areas of interest were taken into consideration, which is in general agreement with a previous study.20 Under these conditions the recovery for different amines and metabolites ranged between 6- 10% (TABLE 1). These recovery values have been used to estimate the extracellular concentrations of amines and their metabolites in various brain regions from the amount of the compound (pmol) measured in dialysis perfusates (TABLE 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002420_1999-01-0743-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002420_1999-01-0743-Figure10-1.png",
        "caption": "Figure 10. Wheel Forces after Throttle Off from Steady State Cornering with Rear-Wheel Drive and Electronic Controlled Clutch",
        "texts": [
            " The strong oversteer of the version with the electronically controlled coupling is caused by the coupling not closing (front axle unconnected) during overrun (throttle off). The overrun torque and the speed difference between the axles are below the activation thresholds. All of the engine braking torque is carried by the rear wheels (as in a rear-wheel drive vehicle) which causes a significant reduction in the capacity for lateral grip of the rear wheels. This causes the vehicle to oversteer (figure 10). The engine braking torque is transmitted to both axles in the transfer case and \"hang-on\" with Visco-Lok configurations. Thus the braking torque at the rear axle is reduced by the portion transferred to the front axle. This reduces the slip at the rear axle making more lateral grip available here while at the front axle the lateral grip is reduced as this axle carries some of the engine braking torque (figure 11). The distribution of the engine braking torque in the VT-P configuration can be optimized by variation of the ViscoLok characteristic (cut-in, preload) so that this variant has a good handling performance similar to the transfer case configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003668_iros.1999.812989-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003668_iros.1999.812989-Figure2-1.png",
        "caption": "Fig. 2, where Frame {O~-XoY&} and {O,-X,YtZ,} are finger base coordinate system and fingertip coordinate system respectively. The link parameters are shown in Table I . According to",
        "texts": [],
        "surrounding_texts": [
            "This paper presents a novel Cartesian impedance control for the DLR(Geman Aerospace Center) Hand based on joint torque measurements. The fingertip appears as mechanical impedance when it contacts with an unknown obstacle. The impedance parameters can be adjusted in a certain range as needed in any Cartesian coordinate system. There is no any switching mode between the motions in the free space and in the constraint environment. The paper also gives a detail analysis about the finger\u2019s kinematics and dynamics model. Experimental results have verified the effectiveness and robustness of the proposed scheme.\n1. Introduction\nThe DLR\u2019s multisensory articulated hand[ 1-21, as shown in\u2018Fig. 1, is a four fingered hand, with in total twelve degrees of freedom. It has three fingers and an opposing thumb. The actuation system is uniformly based on Artificial Muscles@[3], a tiny linear electromechanical actuator integrating DLR\u2019s planetary roller screw-drive[3] with small brushless DC motor(BLDC), which are integrated in the hand\u2019s palm or in the fingers directly. Force transmission in the fingers is realized by special tendons made of highly molecular polyethylene. To achieve high degree of modularity, all four fingers are identical, and each has three active DOFs and integrates 28 sensors. The motions of middle phalanx and distal phalanx are not individually controllable; they are connected by means of tendons in such a way as to display motions similar to those of human fingers during grasping and are actuated only by one artificial muscle. The proximal joint has 2 degrees of freedom; one is for curling motion and another is for abductiodadduction motion. There are two different position sensors for each active degree of freedom; one is a tracking converter for measuring the motor position on the basis of Hall sensors and another is the actual joint position sensor based on a\none-dimensional PSD (Position Sensing Device), which is illuminated by an infrared LED via an etched spiral-type measurement slot. The effective combination between these two kind of sensors plays a key role in the joint position control in dealing with tendon hysteresis. Also, at each joint there is a torque sensor based on strain-gauges for accurate torque control. Fine object grasping and manipulating are a challenge for the low-level control of each finger. In some typical manipulations it is very expectable that the finger appears as active mechanical impedance with variable impedance parameters in different directions, e.g., soft in the normal direction to the object surface but hard in the tangential directions. Salisbury[4] introduced fingertip Cartesian stiffness control for the Salisbury\u2019s Hand based on fingertip force sensor. The stiffness control scheme has the disadvantage of not being able to actively control the complete system dynamics, especially the system damping parameter. Hogan[S ] introduced the impedance control scheme, where impedance parameters M, B, K determine\n0-7803-5184-3/99/$10.00 0 1999 IEEE 106",
            "scheme, where impedance parameters M, B, K determine the dynamic behavior of the grasp. The dynamic property of a grasp object is dependent on the impedance properties of each grasping fingers. This paper presents a novel Cartesian impedance control scheme based on joint torque sensors and each finger could have variable dynamic properties in different axis of any Cartesian coordinate system. Based on this scheme, there is no any switching mode during the transition from or to contact motion and the finger acts as programmable mechanical impedance to any environment. The organization of the paper is as follows. Section 2 gives an overall description about the finger kinematics. Section 3 describes a dynamic equation of mechanical links based on Newton-Euler equation and actuator driving system. Section 4 introduces a new Cartesian impedance controller based on joint torques. In section 5 experimental results are analyzed in detail. Summary and future work are addressed in section 6 and 7, respectively.\n2. Kinematic Equations of the DLR Hand\nEach finger of the DLR Hand has four rotational joints, among which the last two joints are actuated only by one artificial muscle. Its kinematics configuration is shown in\nCraig[6], the coordinate transformation matrices '-;T relating frame ( i } to frame { i-1 }for the DLR hand are as follows:\n[ c2 - s2 0 0'\n1 0 0 0 1\n0 0 - 1 0 \";r =\nI C 4 - s4\n(3)\n(4)\nwhere c, = cose, , s, = sine, , this kind notation will be used throughout the paper, e.g., s,, = sin@, +e,) and\nc, = +e,) . From the equations above, the Jacobian matrix of the DLR Hand can be developed in the following according to Craig[6].\nThe above is a 3x4 Jacobian matrix. This is because there are four joints in each finger of the DLR Hand. Actually, there are only three actuators and the last two joints are mechanical coupled and are actuated only by one actuator. This matrix can not directly used as the transformation between external force and joint torques. There are two",
            "modified matrices, one is for describing the relation between the joint velocities and fingertip linear velocities, and another is for the transformation between joint torques and external force on the fingertip. These two matrices will be discussed in detail in section 4.\n3. Dynamics Modeling\nA finger dynamic system can be divided into two parts. One is called actuator dynamics including motors and mechanical transmissions, and another is called mechanical link dynamics which is structured by every links and located on outside of the motor system. The mechanical dynamic equations for one finger have been developed using the iterative Newton-Euler algorithm[6]. When the Newton-Euler equations are evaluated symbolically, they yield dynamic equations which can be written in the form:\nZ, = M, (e p + v, (e, e)+ G(e )+ F~ (e, sign@)) (7)\nwhere zL is the link driving torque, M , (e) is the 3x3\nmass matrix of the finger, V L ( e , e ) is 3x1 vector of centrifugal and Coriolis terms, G(0) is a 3x1 vector of\ngravity terms, F,@,sign@)) is a 3x1 viscous and Coulomb friction and 8 is the 3x1 vector of the joint angles. The numerical values of inertial parameters (i.e., the masses, the center-of-gravity vectors and inertia tensors) of the links and their variable names are listed in\nEach. actuator dynamics system includes a BLDC-based artificial muscle and tendon transmission system[2]. The actuator system dynamics can be described as:\nwhere, z, = 3x1 applied motor torques zL = 3x1 link joint torques Z, = 3x1 joint's torque measurements J: =3x3 transposed Jacobian matrix, explained in Sect. 4 FeXr = [F, Fy FJT external force on the fingertip Jm = 3x1 motor's inertia B, = 3x1 motor's damping constants fm = 3x1 motor's friction n = reduction ratio 323:l 0, = 3x1 motor's position SeL= 3x1 torque sensor deflections SOP 3x1 tendon's stretching KF 3x1 joint torque sensor's stiffness K,= 3x1 tendon's stiffness r = 3x1 pulley's radii\nCombining Eq. (7) and Eq. (11) to (15), we have the following relations between the input and the output 8:\nz,, = M ( e p + V ( e , e ) + G ( e ) + F(b,sign(d))+JTF, (16)\nwhere,\n1\nn M ( e ) = M,(e)+-+, v(e,e)= vL(e,e)++,e 1 ' n\nFrom the equation (13) we can see that the external force can not be measured directly by joint torque sensors. The measurement of joint torques include also inertia forces, centrifugal, Coriolis forces and gravitational forces of links. If the finger moves in a very slow speed, the"
        ]
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.69-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.69-1.png",
        "caption": "Fig. 2.69",
        "texts": [
            " Carriers trapped in the thyristor are thus enabled to escape via the gate: thyristors obtained by this means are called \"ultra-fast\" thyristors. This procedure is used in the Gate-Assisted Turn-off Thyristors (GATT); it cannot be applied to all types since there will be an increase in commutation losses if the diffused zones have not been suitably designed. 2.4.4.3 Asymmetrical Thyristor The asymmetrical thyristor or ASCR (Asymmetrical Silicon Controlled Recti fier) is made by inserting a heavily doped N'1 layer between theN 1 and P 1 layers of a conventional thyristor (Fig. 2.69a). This addition has virtually no effect on the forward blocking voltage which is dependent on the avalanche breakdown voltage of the P 2N 1 junction. On the other hand, the reverse blocking voltage is substantially reduced since it is dependent on the avalanche breakdown voltage of the P 1 N'1 junction, which is well below that of the P 1 N 1 junction of a conventional thyristor. This is due to A A P, N, K Fig. 2.68 2.4 Thyristors 85 the N'1 layer being much more heavily doped than the N 1 . The reverse blocking voltage V Ro is only about 20 V; this explains the name of asymmetrical thyristor (Fig. 2.69b). The reduction of VRo has no adverse effects in converters where a diode is connected in reverse parallel across the thyristor, the latter not having to sustain a high reverse voltage. This structure has the advantage of reducing the gate recovery time by decreasing the volume of the N 1 layer; there are fewer carriers trapped when turn-off occurs, and they take less time to recombine. We thus obtain fast thyristors intended for high-frequency applications (tens of kHz) with an anti parallel diode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.12-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.12-1.png",
        "caption": "Fig. 9.12. Elastic transmission mechanism and rigid actuating mechanism",
        "texts": [
            "46) The kinematic analysis is also simplified in cases when the motion of the elastic mechanism consists in small vibrations taking place about some equilibrium posi tion q = qo of the rigid mechanism. Such a situation occurs, e.g., in a machine when abruptly finishes a positioning process with a jump of acceleration. In this case, when the engine stops, vibrations caused by the deformations of the elastic elements occur in the system. Setting in (9.43) and (9.44) q = qo, dq / dt = 0, d 2 q / dt 2 = 0, we obtain: x = (8IIx/89)09, (9.47) In a cyclic machine with an elastic transmission mechanism and with a rigid actuating mechanism (Fig. 9.12) the output coordinate x is expressed through the input coordinate q and the vector of deformations 9 in the following way (see (9.45)): Differentiating (9.48) with respect to time and retaining the terms of first order, we obtain: (9.49) Expression (9.49) is simplified, if only small vibrations are considered in the vicinity of the equilibrium position of the rigid mechanism. Setting q = qo, dq / dt = 0, d 2q / dt 2 = 0, we have: x = (8IIx/89 )09, (9.50) x = (8IIx/89 )09. (9.51) 9.6 Dynamic Problems of Elastic Mechanisms The dynamic analysis of elastic mechanisms must be based on dynamic models that take into account their kinematic parameters: masses and moments of inertia of the links"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002824_107754639800400502-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002824_107754639800400502-Figure2-1.png",
        "caption": "Figure 2. Diagram of viscous-elastic characteristics of the oil film (a) and the model of heat exchange in the bearing (b).",
        "texts": [
            "comDownloaded from 522 at University of Newcastle on August 28, 2014jvc.sagepub.comDownloaded from 523 The Reynolds equation (1) and condition (2) define the hydrodynamic pressure distributions and time-variable functions of the hydrodynamic load capacity components WX , Wy of the bearing. Further considerations will also require data concerning variations in time of viscous-elastic properties of the lubricating film. Such properties can be determined by applying four stiffness and four damping coefficients of the oil film defined in the following way (Figure 2): where x = ax/at, y = ay/at. The coefficients Cik and d,k, similar to the pressure distribution in equation (1), vary in time in a significantly nonlinear way. They can also be written as c,k(t) and dik(t). To calculate them, we will take advantage of the perturbation calculus. The distribution of pressure p and the shape of the lubricating clearance (or oil film thickness h) as well as the derivatives of these functions can be expanded into a Taylor series in the surrounding of the current position of the journal 0 with respect to the perturbation parameters Ax, Ay, Ai, A~",
            "comDownloaded from 526 The boundary conditions for the energy equation (14) include a temperature distribution at the internal surface of the bearing bush (calculated from the conductivity equation (15)) and a given mean temperature of the journal T, assumed as the mean value of the temperature distribution at the internal surface of the bearing bush. It is assumed that the heat from the external surface of the bush is carried away by free convection. A thermal model of the bearing is given in Figure 2b. Equations (13) through (15) enable us to determine the hydrodynamic load capacity of the bearings nodes for the assumed position of the journals (\u00a30) j, (yo) j. The opposite procedure, where an attempt is made to find the positions (\u00a30) j, (yo)j for some given external loads (reaction of the system supports), requires the application of an iterative procedure in which equations (13) through (15) are also coupled with the formula for kinetostatic deformation of the rotor and supports in a general form As a consequence, it is possible to find the equilibrium positions of the journals (\u00a30) j, zoo the reaction of the supports and kinetostatic deformation of the rotor line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002780_s0927-0256(98)00103-7-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002780_s0927-0256(98)00103-7-Figure2-1.png",
        "caption": "Fig. 2. Snapshots of the microstructure of the rigid rod-like particle dispersed system of aspect ratio 10 at strain 1000.",
        "texts": [
            " The transient behavior of the microstructure and rheological properties are analyzed under two conditions, rigid and \u00afexible particles (g _c=E 0:0002, g _c=E 0:004, respectively). One hundred particles are randomly dispersed in a simulation cell with periodic boundaries. Then, the motion of particles are calculated in a simple shear \u00afow whose velocity components are written as vx \u00ff _cy; vy 0; vz 0; 9 where _c is the shear rate. As a result, in the semi-dilute to concentrated regimes, the planar orientation of particles is observed after the particles strongly align in the shear direction at the earlier stages. Fig. 2 shows two di erent views of the microstructure at a strain of 1000. The strain is de\u00aened as _ct. The system contains 5 vol% rod-like particles of aspect ratio 10. Particles are drawn as cylinders though the calculation was done by the sphere array model. The planar orientation of particles parallel to the z\u00b1x plane is observed. Since the microstructure changes in semi-dilute to concentrated systems, the relative viscosity, rxy=g _c, gradually decreases after a rapid increase as shown in Fig. 3. These results are for rigid rodlike particle dispersed systems of aspect ratio 5, in which the critical concentration between semi-dilute and concentrated regimes is about 10 vol%"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003053_s0167-8922(98)80098-9-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003053_s0167-8922(98)80098-9-Figure4-1.png",
        "caption": "Fig. 4 Relative position between rotor and stator",
        "texts": [
            " Key dynamic parameters, such as rotor angular misalignment, the relative misalignment between the rotor and the stator, and the seal clearance can be chosen to monitor. This system can also display the rotor angular response orbit and spectrums of the proximity probe signals in real-time, 3. THEORETICAL BACKGROUNG Some background of M R noncontacting mechanical seal dynamics will be introduced to form the contact criterion. Contact detection based on contact criterion, rotor angular response orbit shape, and spectrum analysis will then be discussed. Several coordinate systems are used to describe the FMR noncontacting mechanical face seals (Fig. 3 and Fig. 4). Detailed descriptions of these coordinate systems and nomenclature can be found in Green [5]. The magnitude of ~,\" is\" =,jy, +r, -2.), , .r , (2) where ~, is the stator angle, ~'r is the rotor precession. a, The rotor response, Tr, is composed of two parts: ~,~, and ~/,~, where \"t', is the rotor response to the stator misalignment, ~,,, and ~'~x is the rotor response to the rotor initial misalignment, ~,n. Since ~,,,\" is fixed in space, while y~\" rotates at speed * , co, the overall response, T~, Is a rotating vector with a time varying frequency ~r\" The magnitude of both ~rand Yr\" vary cyclically with a constant frequency, co",
            " Key dynamic parameters, such as * 8 rotor response, Tr, stator misalignment, ~,,, rotor precession, ~r, stator angle, ~,, and seal clearance are calculated in real-time from measured proximity probe signals. The relative misalignment between the rotor and the stator, y', is then calculated from the rotor response, ~,~', the stator misalignment, ~,,, the rotor precession, W~, and the stator angle, ~, according to Eq. (2) 3.2. Seal contact criterion The dimensionless local film thickness, H=h/Co, can be written as follows (see Fig. 4): H - l + r . R . cosO + 1 3 ( R - I~ ) (3) Where ~, is the dimensionless relative misa!ignment, ~\"rdCo, 13 is the dimensionless coning, 13\"ro/Co, R is the dimensionless radial position of a local point on the seal, r/ro, and 0 is the angle between the direction of the local point and the maximum fluid film thickness. Face contact will first occur at the minimum film thickness, i.e., at 0=n, either at the inside radius of the seal, Ri, or outside radius of the seal, Ro, depending on the magnitude of 13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure7-1.png",
        "caption": "Fig. 7. 2-DoF RPMs: (a) U \u03992\u2212RRRA \u2212 /SPU; (b) U \u0399\u03992\u2212RRRA \u2212 /SPU; (c) UUARRRRRA /SPU.",
        "texts": [
            " The continuous axis S2 m can be constructed by adding revolute joint Rx, perpendicular and intersecting with Rz, to the end of the limb chain RRRA Rz z and replacing R Rz x with a universal joint Uw, where w denotes the plane zx. Then, U I2\u2212RRRA \u2212 kinematic chain with two continuous axes can be obtained. Step 4. Expand the output link of the closed-loop kinematic chain to the moving platform. To actuate the continuous axis S2 m , some 6-DoF non-constraint limbs listed in Table 3 need to be inserted at proper location in parallel with the first two limbs. Without loss of generality, add a SPU limb in the symmetry plane of the first two limbs to U I2\u2212RRRA \u2212\u2322 . Then, the U I2\u2212RRRA \u2212 /SPU PM, as shown in Fig. 7a can be constructed. Similarly, if c\u03d5 s\u03d5 dc\u03d5S = ( , , 0 ; 0, 0, )2 m , the U2\u2212RRRA \u2212II/SPU PM shown in Fig. 7b can be obtained according to the same procedure. Particularly, if S2 m and S1 m are perpendicular and intersecting with each other (d = 0), i.e. c\u03d5 s\u03d5S = ( , , 0 ; 0, 0, 0)2 m , the UUARRRRRA /SPU PM which is shown in Fig. 7c can be synthesized using the above procedures. Many other 2-DOF RPMs with a virtual continuous axis can be synthesized by selecting other closed-loop kinematic chains listed in Table 3. Furthermore, if an extra revolute joint is added serially on the moving platform, the 3-DOF RPMs with a virtual continuous axis also can be constructed according to the above steps. Without loss of generality, take U2\u2212RRRA \u2212II/SPU shown in Fig. 7b as an example to analyze its DoF properties. Firstly, let the closed-loop limbs RRRAU equivalently replace with RU serial kinematic chains which are denoted by the red dashed lines in Fig. 7b. Establish right-handed coordinate system o xyz\u2212 , in which the axes of x and z are parallel with the two axes of the universal joint respectively. Let the coordinate of the hinge point of the universal joint in the 1st limb be a b( , , 0)T. Then, the kinematic pair screws of the 1st equivalent limb can be expressed in {o} as b a bS S S= (0, 0, 1 ; 0, 0, 0), = (0, 0, 1 ; , \u2212 , 0), = (1, 0, 0 ; 0, 0, \u2212 )11 m 12 m 13 m (21) And the corresponding constraint screws are a b b aS S S= (0, 0, 0 ; 0, 1, 0), = ( , , 0 ; 0, 0, 0), = (0, 0, 1 ; , \u2212 , 0)11 r 12 r 13 r (22) It can be seen from Eq",
            " The effective torque of gravity wrench of the moving platform is \u239b \u239d\u239c \u239e \u23a0\u239fG\u03c4 W=o q o o G T G (46) where, \u23a1 \u23a3\u23a2 \u23a4 \u23a6\u23a5 m g m g W r e e = ^ (\u2212 ) \u2212o G Oc o o 2 2 , Wo G is the gravity wrench of the moving platform, and r\u0302Oc is the skew-symmetric representation of vector rOc. Only the generalized force mapped by the inertial wrench and gravity wrench of the moving platform is considered, and the frictions are ignored. Then, the generalized force of the mechanism is \u03c4 \u03c4 \u03c4= +o o o A I G (47) The driving forces of the prismatic joints in the 1st and 3rd limbs are the first and second elements of \u03c4o A respectively. The redundant configuration of the mechanism shown in Fig. 7c, which have more engineering applications, is taken as a numerical example. Firstly, add two SPR driving limbs symmetrically between the base and the connecting-links in the closed-loop limb. Then, add a SPU limb to the mechanism and allocate it symmetrically with the 3rd limb. The redundant actuation mechanism is shown in Fig. 10, and its kinematic equivalent mechanism is S U U4\u2212 P / . The structure parameters of the redundant configuration are listed in Table 4. The influences of external force, gravity of the limbs, inertia force of the limbs and friction mapped to the generalized force are ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002983_026635119200700412-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002983_026635119200700412-Figure5-1.png",
        "caption": "Fig. 5. The deformation of domes.",
        "texts": [
            " Figures 4a and 4b show the load-deflection curves of the domes with the slenderness ratio of a mem- 364 International Journal of Space Structures Vol. 7 No.4 1992 the load-deflection curve and is defined as the buckling load: The dotted line shows the loaddeflection curves of the dome with n = 2 and pinroller supported. This case gives the lower bound for the buckling load. The load-deflection curves of the domes with n =4 and 6 lie between these two boundaries. There is no remarkable difference in the buckling behaviours ofthe domes with n=4 and 6.This tendency may be the same in the dome with increasing n. Figure 5 shows the deformation of the domes with n=4. The dimple buckling of the central unit dome is observed. In the same manner as the elastic analysis of a reticulated dome, the elasto-plastic buckling behaviour of a reticulated dome with central load may be understood by the analysis of a dome with the limited number of grids. The map ofthe axial forces N/Ny (Ny = the yield axial force of a cross section) at the buckling load is shown in Fig. 6. The maximum compressive axial forces are observed in the radial members of a central unit dome"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.13-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.13-1.png",
        "caption": "Fig. 2.13",
        "texts": [
            " However, the use of these diodes remains limited to medium or small currents and to low voltages (75 V). 30 2 Switching Power Semiconductor Devices \u2022 the transistor to be made saturated or conducting, \u2022 the transistor to be blocked, with low power consumption Power transistors are often obtained by triple diffusion. The N layer, which forms the collector, is the thickest, and comprises anN- region, the size of which increases with the value of the forward voltage which the transistor has to block (see Fig. 2.13). 2.2.1.1 The Transistor Effect The effect used in transistors appears when the emitter-base junction is for ward-biased (vsE > 0) and the collector-base junction reverse-biased. These biases can be obtained using the simple circuit shown in Fig. 2.13. - When voltage VsE is positive the electrons in the emitter, where they are majority carriers, are attracted towards the base, where they become minority carriers. Some electrons which have come into the base recombine with the majority holes there. The electrons which fail to recombine, easily cross the collector-base junction which is reverse-biased and reach the collector. This flow of electrons from emitter to collector, across the base which attracted them, is known as the transistor effect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003607_026635119100600305-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003607_026635119100600305-Figure5-1.png",
        "caption": "Fig. 5.",
        "texts": [],
        "surrounding_texts": [
            "the generatrix sense, admitting variation in the directrix sense. The characteristic angle 135 formed between the edges can, in consequence be constant (13 1 = 132 = 133 = etc.) or variable (13 1 *- 132 *- 133 *- etc.). Thefolding angle a6 can also be kept constant (a l = a 2 = a 3 = etc.) or variable (a l *- a2 *- a 3 *- etc.) and it angular amplitude varies from 0\u00b0 (plane position) to 90\u00b0 (maximum folding). If the folding angle is kept constant, and the con cave edges? are parallel, the result is a linear development fold. :. 13' = 26\u00b033' :. 13\" = 16\u00b006' Example: Characteristic angle 13 angle a = 60\u00b0. (Fig. 2) Analytically: tan 13' = sin a . tan 13 = 0.5 tan 13\" = cos a . tan 13 = 0.288 3. Linear Development Folds certain rules or laws must be respected, otherwise, it is likely to propose a pattern impossible to fold or to overcome the limits within which a determined plane pattern behaves properly. Leaving out the subject ofpolyhedrons here, the analysis will be focused on those forms which have their origin in the bellows type folding, since they have more interesting possibilites from the spatial point of view. Among them, those which respond to the \"cons tant repetition\" of a specific plane pattern will be analysed; this means that the basic geometric figure of such plane pattern repeats itself suc cessively without alteration in its dimensions or in its angles. Constant repetition cases to be considered pre sent two basic types of development: 1) Linear (straight) development. 2) Concentric (curved) development. This means that each parallel section in 1) or each circular sector\" in 2) is successively equal and in its repetition, a series of spatial forms are pro duced, going from the vaulted ones, helicoidal ones, spatial frames, etc., for those of a linear development, to the domed, fungiform, torus, for the concentric ones, admitting different variants with reference to curvatures, angles pattern and to type of folding. The basis plane pattern to be considered extends according two directions: a) directrix sense, b) generatrix sense (Fig. 1). 228 International Journal of Space Structures Vol. 6 No.3 1991 O.L. Tonon Graphically: with centres on C and F and radius CA and FD, draw semicircles AB and DE, project from C and F the chosen folding angle a on both semicircles, determining in the intersections, points A', B', and D', E', which indicate the posi tion of edges A'D' and B'E' in horizontal projec tion. On an auxiliary axis x x, points C, 0, F, and A', D', are projected; A' is revolved so as to obtain C\" and D' is revolved to obtain F\". Then, with cen tre at 0 and radius OC = OF, draw another semicircle and tangents to it from points C\" and F\" to obtain C' and F', which united to 0 complete the vertical projection or silhouette.\" Then complete the horizontal projection. Increasing the limits of the pattern in the direc trix sense (greater number of sectors) an approach to the envelope curve is achieved. It is proposed, for example, a silhouette suppor ted on a horizontal plane composed of4 equal sec tors (f3 = constant). (Fig. 3) If the total of the silhouette comprises 180\u00b0,each sector will be: 180\u00b0 4 = 45\u00b0 = 2W .'. W = 22\u00b030' Such silhouette is valid for any value of'Bwhenever f3>W. With a fixed value for f3, the folding angle a becomes an unknown. Analytically: if f3 = 30\u00b0 tan W sin a tan f3 = 0.7174 tan f3\" = cos a . tan f3 = 0.4022 .', f3\" 21 \u00b054' Graphically: Having the silhouette as datum, draw a horizontal axis xx coinciding with the point F\" and towards it revolve 0\" and C\", where 0 and C that limit sectors are obtained. Fixing f3 = 30\u00b0 the plane form can already be constructed. To find the folding angle a it is necessary to draw a semicircle on the plane form, with centre at F and radius FD = FE and to revolve point F' from the silhouette on it. Points D' and E' are found in its intersection. Such points united to F indicate the real magnitude of the folding angle a. For the horizontal projection it is necessary to lower the points of the silhouette, becoming a in real magnitude in the extreme sectors. The case of f3 constant only permits to obtain envelopes of circular silhouettes. For any other kind of profiles: eliptic, parabolic, etc. or to be able to regulate the raise at will, it is necessary to use variable angles f3. (f31 *- f3 2 *- f32 *- f33 *- etc.) The case, as well as the previous one can be solved from a priori determined silhouette, or else knowing the plane form. To state a silhouette of this kind correctly, the following relation should be verified: where [y - (f3; + f3;)] is generally the data (i.e. for a silhouette supported on ahorizontal plane it is equivalent to 90\u00b0). The expression relates the silhouette angles one to another and so it will have been stated correctly. Graphically, it can be constructed from the out side or from the center, through advanced points following the sequence illustrated. (Figs. 4 and 5). International Journal of Space Structures Vol. 6 No.3 1991 229 Geometry of Spatial Folded Forms 230 International Joumal of Space Structures Vol. 6 No.3 1991 oi. Tonon Not only the condition offolding a constant can produce foldings oflinear development. When the concave edges are not parallel in their plane pat- :. ~3 = lr35' tan ~1 Q _ tan ~; = 0.480 tan 1-'2 - sin a tan ~~ tan ~4 =. = 0.263sm c tan ~; tan ~3 = sin a = 0.316 Example: Fixing for silhouette ~; = 15\u00b0 and increasing successively the dimension ofeach sec tor, keeping e constant, the result will be ~; = l3\u00b030',~; = 9\u00b0 and ~~ = 7\u00b030' from the direct read ing of its angles. Then for a folding angle a = 30\u00b0, it will be: (Fig. 7) Analytically: tan ~; sin a = 0.535 For silhouettes supported on a horizontal plane - whose angular variation is 180\u00b0 - those of 6 sec tors are the most adequate, because they offer a good margin to make corrections and they can produce different types of profiles. Example: for a great raise silhouette the charac teristic central angle ~ should be greater than the others. If~; + ~; + ~; = 45\u00b0;~; = 22\u00b0,~; = 13\u00b0, and ~; = 10\u00b0 can be fixed (Fig. 6). The polygonal responds to an eliptic curvature whose successive centres are in the intersection of the perpendiculars to the concave edges drawn from each vertix -C'C\", 0'0\", F'F\", etc. On taking the silhouette to 8 sectors for the same angular variation of 180\u00b0 even if it approaches more to the envelope curve, its capacity of varia tion and the degree of rigidity will be also percep tively diminished, for, having rigidity directly proportional to the characteristic angle B, when ~ diminishes, the rigidity also diminishes. The thickness e in the silhouette measures the degree ofrigidity and its excessive diminishing can produce structurally unstable foldings. \\ \\ \\ I I I silhoJett e V.P. H. P. plane pattern Fig. 7. International Journal of Space Structures Vol. 6 No.3 1991 231 Geometry of Spatial Folded Forms - I = - 0.894 1530 26':. Y1.2 = PIane pat t ern v. P. Analytically: tan ~; = sin u2 . tan ~2 = 0.304 tan ~; = sin u3 . tan ~3 = 0.237 sin ~I . sin (~2-[,) cos u2 = cos u3 = . A \u2022 (A 1::) = 0.758sm fJ2' sm fJI-U I I I s i IhDIU et t e tern and they are folded up to reaching parallelism, foldings of linear development are obtained with variable angles c. The silhouettes are ofsimilar characteristics, but unlike the previous ones, in these ones to keep the supporting edge straight can be stated, making u 1 = 0 0 in the folding condition. In this way the silhouette does not condition the supporting plane and its is possible to graduate the rigidity from a maximum for the central sector to a minimum in the extremes. For example, a plane pattern of characteristic angles ~I = 300 , ~2 = 250 , ~3 = 200 , whose concave extreme edges deflect in an angle [, = 40 , on being folded up to condition u j = 00 , the result is: (Fig. 8) _---:;:::\"'i\"\"':::::=------;;::7\"~--_ d., =0\u00b0 H. P. Fig. 8. 232 International Journal of Space Structures Vol. 6 No.3 1991 oi. Tonon It can be seen in the graphic (Fig. 9) that in a first part up to a2 = 40\u00b041' the sector corresponding to a j has not begun folding yet (a l = 0\u00b0); from there the whole stars folding with different values for a\\ respect of a2 up to both coincide in a l = a2 = 90\u00b0. 4. Concentric Development Folds When departing from the same plane pattern of parallel concave edges, a sector folds more than another - folding condition a variable  non-parallel sections and folds of concentric development are generated, in their successive repetition. From all possible folding variants for this con ditions only one will be analysed, the one corresponding to the extreme sector without fold ing (c, = 0\u00b0) and to the central sector totally folded (ae ~ 90\u00b0), and from all possible relative positions ofthe silhouette in the space, only two in particular will be studied; those corresponding respectively to the horizontal and vertical situation ofthe concave edges in the most folded sector or central one. The horizontal one will generate dome forms and the vertical one, fugiform types. An analytic method to solve folds of these characteristics has been developed from the given horizontal projection of a circular sector and reconstructing from there the silhouette and the plane pattern. This permits to reach the profile required wih a suitable handling of the data. For domes, the horizontal projection adopts a International Journal of Space Structures Vol. 6 No.3 1991 triangular shape defined by the angle 8' and dis tances Xl; X2, X3, etc. (Fig. 10). Such distances X indicate the number of sectors conforming the plane pattern and are those that regulate the greater or smaller raise as they differ more or less between them. The angle 8' should be, besides, even multiple of 360\u00b0 to obtain an integer number of circular sectors. Stated in this way, each horizontal projection corresponds to only one silhouette and in its resolution, it is necessary to work alternatively on the two planes which pass one through 0IC and the other through 01A. (Fig. 11). This silhouette is taken as auxiliary to determine some angles or edges that find in true magnitude on it. As a is variable, each sector adopts a different folded angle, identifying itself according to the following criteria: For the sector OC: a j = folding angle in OCA and OCB a; = folding angle in OAM and OBN For the sector OF: a2 = folding angle in OFD and OFE a; = folding angle in OMD and ONE For the sector 0IF: a3 = folding angle in 0IFD and 0IFE a; = folding angle in 0IDMI and OIEM j a; = a;, and a2 = a3 but it is necessary to differen tiate them for the process of calculation. Example: A pattern of 3 sectors is proposed; the 233 Geometry of Spatial Folded Forms necessary data to fix are: 8', Xl, X2 and X3. (Fig. 12). Analytically: Folding angles of intermediate faces are calculated at first, , I I,, I I I 1 aux. 5;/ f 'I 1 ~x,-, main- ,-, -'~~---+--:-..------=~ sin 8' tan ~ =-- 3 cos a3 1) X3 a) cosa2 = Xl b) casa]' = cosa2, X2. cos8' Xl 2) tan~; = sin a3 \u2022 tan ~3 Then, step by step calculate the others unknown as indicated in Table 1. 3) , tan ~3 tan ~3' = --~-,cos u 6) cos Y2',3' 5) tan B; = sin a2 \u2022 tan ~2 tan ~2 = Xi' tan ~3 X2 . tan ~3 - Xi where Xi = Xl\u00b7 tan 8' . cos (~;+~;,) International Journal of Space Structures Vol. 6 No.3 1991 4)MAIN SILH. AUX. SILH. 1) tan ~3 2) tan ~3 3) tan ~3' 4) tan ~2 5) tan ~2 6) cos Y2' 3' 7) tan W2, 8) tan ~1 9) cos Yl.2 234 D.L Tonon 7) tan ~;, = sin u2' . tan ~2 Process of calculation for the others unknown: 2) tan ~4' 3) tan ~4 AUX SILH. I) tan ~4 MAIN SILH. Xii' tan ~2 tan ~2 . (Xl-X3)-Xii where Xii = Xl\u00b7 sin &'. COS[~3+~;'+(-Y2',3')] tan ~1 =8) 9) tan ~. tan ~2 . (I-cos u2) - 1 cos Yt2 = 1--sin? c . tan? A 2 ....2 4) tan ~3 5) tan ~3 6) tan ~3' 7) cos Y3.4 8) tan ~2 9) tan ~2 10) tan ~2' II) cos Y2'.3' 12) tan ~I 13) cos YI.2 tan ~~ = sin u4, ' tan ~4 = 0.151 .', ~~ = 8\u00b036' With the variation of the data, the silouette should be regulated, trying not to overcome certain max imum and minimum values. So, for example, the differet characteristics angles ~ will be able to osci late between a minimum of 10\u00b0 for the most folded sectors and a maximum of 50\u00b0 for the least folded, being adequate the angle &' of the circular sector between values of 6\u00b0 and 16\u00b0. For a pattern of4 sectors the method is the same, only the number of steps increases on the process of resolution. As the polygonal has a greater number of sides, it requires a reuced angle &' or on the contrary, the limits stated for angles will be exeeded. This reduces in a certain way the capacity ofvariation in the silhouette, but, in tum, it enables a greater approach to the envelope curve. Example: with &' = 6\u00b0; Xl = 7; X2 = 6.8;X3 = 6; and X4 = 4, as data for the horizontal projection, the process of resolution is as follows (Fig. 13). I) 2) 3) Xl\u00b7 tan &' tan ~4 = X4 = 0.184 , tan ~4 tan ~4' = &' = 0.185cos 4) Xi = Xl\u00b7 sin &' . cos (~~+~~,) = 0.6915 Folding angles of intermediate faces: = 0.309 .'. ~3 = lrIO'"
        ]
    },
    {
        "image_filename": "designv11_31_0003052_980220-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003052_980220-Figure8-1.png",
        "caption": "Figure 8. Submodel I. Describes basic motion of the vehicle (degrees of freedom: xO1, yO1, \u03c81)",
        "texts": [
            " The road surface irregularities are also inputs. They have a determined 3D form. They may be a result of real road measurements or the realisation of stationary gaussian random process describing real road according to ISO recommendations [28]. For some motion cases (mainly even road motion) it is possible to simplify and speed up model construction process. Division into partial models was applied [16]. The main model is divided into 3 type coupled sub-models. For example for car model they are: \u2022 submodel I (Fig. 8) which describes basic motion of the vehicle (degrees of freedom: , ), \u2022 submodel II (Fig. 9), which describes body and unsprung masses vibrations (degrees of freedom: , \u03d51, \u03d11, ), \u2022 submodels III (Fig. 10), which describes rotations of wheels (degrees of freedom: \u03d55, \u03d56, \u03d57, \u03d58). The submodel II generates current values of normal reactions of the road that are input values for the tyre model (mentioned above). Truck model is divided in analogical way. In this case submodel II has dependent front suspension",
            "8 4 6 Body CG height h [m] (d \u03c8\u03c8 /d t) [ ra d/ s] right right left left &\u03c81ss S S SS EE E E S S S S EE E E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 P 0 : 1.5 0 9 P 1: 1.5 6 6 P 2 : 1.7 3 6 P 3 : 1.8 4 6 Body CG height h [m] t [ s] right right left left &\u03c81 13 E - result of experiment, S - result of simulation The presented results as well as many others show good compatibility between simulation and experiment for biaxial car and truck model. EXAMPLE OF MORE COMPLICATED STEERING SYSTEM MODEL APPLICATION The combination of submodel I (Fig. 8), 4 submodels III (Fig. 10) and steering system submodel (Fig. 7) was applied to simulate small car motion. Normal reactions of the road were described using quasi-static formulas, assuming existence of four supporting spring elements for each wheel (suspension and tyre elasticity in series). Fig. 33\u00f736 show results obtained for low velocity (~10 km/h). Fig. 33 presents time histories of steering-wheel angle \u03b1k as well as moments on steering-wheel Mk. Fig. 34 shows CG trajectory on road plane Oxy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002900_20.141296-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002900_20.141296-Figure2-1.png",
        "caption": "Fig. 2. Infinite cylinder of electrical conductivity U and magnetic permeability p excited by a homogeneous sinusoidal magnetic field in parallel to its axis. Cylinder radius is R.",
        "texts": [
            " The total ac relative magnetic permeability averaged over the whole plate section is . mb It is seen that as a result of the eddy current effects induced in the plate, the plate material has a new effective magnetic permeability pyGmge which is smaller than the conventional intrinsic magnetic permeability p,, without eddy currents. A similar thinking can be conducted about an infinite cylinder of electrical conductivity U and magnetic permeability p , excited in parallel to its axis by a homogeneous sinusoidal magnetic field (Fig. 2). The complex values of the magnetic fields and eddy currents in the infinite cyl- inder will be where Zo(ar) and ZI(ar) are modified Bessel functions. According to an approach similar to that used for the previous semi-infinite plate, the eddy-current magnetic susceptibility of the very long cylinder is while the effective eddy current susceptibility and relative effective permeability averaged on the cylinder section will be 111. EDDY CURRENT MAGNETIZATION F SIMPLE TwoDIMENSIONAL CONFIGURATIONS The magnetization induced by a magnetostatic, field in a generalized ellipsoid in free space can be obtained from the analogous electrostatic theory of polarization [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002321_jsvi.1999.2384-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002321_jsvi.1999.2384-Figure1-1.png",
        "caption": "Figure 1. Timoshenko shaft.",
        "texts": [
            " In the \"rst example, the proposed method is compared with the FEM from reference [7]. In the second example, a two-stepped rotor-bearing system problem is considered to illustrate the advantage of the proposed method in design. In the \"nal example, the proposed method is applied to a general, multi-stepped rotor-bearing system to show the applicability of the method. The numerical study shows that the proposed method is very useful for the dynamic analysis or design of rotor-bearing systems. A Timoshenko shaft model is shown in Figure 1. The equations of motion for the Timoshenko shaft, which contains gyroscopic moment, shear deformation and rotary inertia, can be written in complex co-ordinates as f\"kAGA/! Lp LxB , m\"EI d L/ Lx , Lf Lx \"!oA L2p Lt2 , Lm Lx !f\"oI d L2/ Lt2 !jXoI p L/ Lt , (1) where p and / are the complex, transverse and angular displacements respectively, de\"ned as p\"y#jz, /\"h y #jh z . In addition, f and m are the complex shear force and moment respectively, de\"ned as f\"f y #j f z , m\"m y #jm z . o, G and E are the density, shear modulus and Young's modulus respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003993_fld.1650060704-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003993_fld.1650060704-Figure9-1.png",
        "caption": "Figure 9. Variation of power loss with bearing speed E = 0.65, inlet temperature = 40\" C",
        "texts": [],
        "surrounding_texts": [
            "One of the main objectives of this investigation (as stated earlier) is to provide a method for predicting temperature variations in a high-speed misaligned lubricant film and its consequent effect on the load-carrying capacity and power loss. To achieve this, the previously developed model has been applied to a journal bearing that had a bush of length and radius 36.8 mm with a clearance ratio ( R , - R , ) / R , of 0004. The lubricant used was Shell Tellus 27 which has a density of 860 kg/m3 and a specific heat of 2000 J/kgK, which were assumed to be constant. The temperature dependence of the lubricant viscosity is obtained by assigning values of M = - 3.878 and B = 9.85 in the Walther equation (9). For this set of numerical experiments MISALIGNED HYDRODYNAMIC JOURNAL BEARINGS 45 1 the bearing shaft was assigned a rotational speed of 40,000 rev min- ' with a centre-line eccentricity ratio of 0-65. The overall distortions of the lubricant film pressure and temperature fields are depicted pictorially in Figures 4(a), (b) and (c) for shaft inclinations of 0, 0.001 and 0.002 radians, respectively. Generally, for a shaft that is constrained to misalign in the direction of the applied load, the peak pressure does not move in a streamwise direction, although increasing misalignment reduces slightly the extent of the cavitated region (or area of subzero pressure). However, the temperature increases continuously along the streamwise length of the film with the most rapid increases associated with the largest pressure gradients in the film. 452 J. 0. MEDWELL AND D. T. GETHIN The axial variations of pressure and temperature, where the maximum values of these quantities occur, are shown in Figures 5 and 6. The circumferential positions at which peak pressures and temperatures are generated do not coincide for the cases considered here. Generally the maximum pressure is located at a position some 60 per cent of the arc length (/3) from the main supply inlet. However, the maximum temperatures, because of the continued heat dissipation in the lubricant film, occur near to the onset of cavitation. The results for the misalignment displayed in Figures 4(a), (b) and (c) are limited by the eccentricity ratio. To avoid surface contact between the shaft and bush when considering higher values of misalignment, the eccentricity ratio has to be reduced. This has the initial consequence of reducing the length of the cavitated zone in the partial arc film, permitting a fuller film to be established. However, the increased misalignment reduces further the minimum value of the lubricant film thickness while moving its position nearer to the upstream location. This enables cooler lubricant to flow into the regions downstream of the minimum clearance location. The cumulative effect of this is shown in Figure 7, where lines of constant lubricant temperature have been drawn to provide an isotherm map, thus showing that a distinctive 'hot spot' has been generated. Some global performances for a misaligned bearing are shown in Figures 8 and 9 for an eccentricity ratio of 0.65. The isothermal solution, which is based on a constant lubricant temperature equal to that of inlet (i.e. 40\" C), as expected, predicts far greater load and power losses than the full thermohydrodynamic solution. A further numerical experiment was carried out where the power loss computed using the thermohydrodynamic solution is used in a simple MISALIGNED HYDRODYNAMIC JOURNAL BEARINGS 453 454 J. 0. MEDWELL AND D. T. GETHIN THERMOHYOROOYNAMIC ISOTHERMAL (BULK TEMPERATURE) ISOTHERMAL (INLET TEMPERATURE) -0- THERMOHYOROOYNAMIC a-0 THERMOHYORODYNAMIC ISOTHERMAL (BULK TEMPERATURE) ISOTHERMAL (INLET TEMPERATURE) 0 THERMOHYOROOYNAMIC a=O MISALIGNED HYDRODYNAMIC JOURNAL BEARINGS 455 energy balance, together with the predicted lubricant flow, to estimate the bulk lubricant temperature. This is equivalent to the sump temperature that would be monitored in situations where a bearing is likely to be highly stressed. If this temperature is used in the isothermal procedure, then the load and power loss characteristics compare closely with the thermohydrodynamic solution. The results of the aligned case are also included in the Figures where it can be seen that for a fixed eccentricity ratio, misalignment has significantly increased the load-carrying capacity only of the bearing. This is a consequence of the high peak pressures generated by misalignment, which more than offset the reduction in lubricant viscosity brought about by the accompanying increased temperatures. However, it should be pointed out that the increase in load carrying capacity is based on the midplane eccentricity ratio and is not in conflict, therefore, with the conclusions of other workers'V6 since their contention of a reduction in load carrying capacity is based on minimum film thickness. In reality, the journal would position itself within the bush so as to react to the applied loading exactly. Finally the maximum and bulk lubricant temperature variations with speed for a misalignment of 0.002 radians and an eccentricity of 0-65 are shown in Figure 10. It can be seen that although the bulk temperatures exhibit modest rises over the inlet lubricant temperature, the maximum temperatures generated are dangerously high and would certainly be a limiting parameter in such a bearing operation."
        ]
    },
    {
        "image_filename": "designv11_31_0002459_941761-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002459_941761-Figure6-1.png",
        "caption": "Fig. 6 Off-line of Action Contact during Approach.",
        "texts": [
            " The off-line of action analysis plots show a smoother transition from one pair to two pairs of teeth in contact between -8.0 and -6.0 degrees roll and from two pairs to one pair of teeth in contact between 5.0 and 7.0 degrees roll. There is general agreement in the 2 trend of the transmission error predicted by the off-line of & (a) Pinion root action models of LDP and CAPP. The actual values of the Pinion tip transmission errors are, however, slightly different because of the different compliance models. Figures 6 and 7 are obtained using CAPP. They show the lines of load acting on the gear teeth. Fig. 6 shows the pinion during approach. Here contact starts from the root of the pinion. At -7.8 degrees of roll there is only one tooth pair in contact. At -7.4 degrees of roll, a second pair of teeth has 2 come have been into contact. only one Theoretically, tooth pair in contact. at this position, The second there p a . would has (b) Pinion root come into contact early due to tooth deflection. On this second Pinion tip tooth, contact occurs at a point above the start of the active profile (SAP). The contact on the second tooth is off the line of action. This can be seen in Fig. 6. An exaggerated view of the circled region is drawn for clarity. At -6.0 degrees of roll, contact has moved to the line of action. Fig. 7 shows contact during recess. At 5.2 degrees of roll, there are two pairs of teeth in contact and contact is along the 2 line of action. Theoretically, at 6.2 degrees of roll, the first pair & (c) Pinion root of teeth should have left contact. But due to tooth deflection, Pinion tip the first pair is still in contact at the tip of the pinion. This can be seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003299_jsvi.1996.0908-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003299_jsvi.1996.0908-Figure3-1.png",
        "caption": "Figure 3. Subtraction of the middle loop line.",
        "texts": [
            " -  Masing\u2019s principle is suitable for a system containing spring and constant friction elements [5]. Many real hysteresis loops of vibration isolators are near the loop of the system with non-zero stiffness without friction K and with displacement dependent friction force H= cU (where U is displacement, Ca is a coefficient) (Figure 2). This system will be transformed in accordance with Masing\u2019s principle. In order to eliminate the element K, one can subtract the loop middle line L(U) from the loop contour and obtain the co-ordinate F*=F\u2212L(U) (Figure 3). To eliminate the \u2018\u2018friction displacement\u2019\u2019 dependency, one can divide F* by the friction force H(U). Thus, in the new coordinate system, U, F**=F*/H(U), a constant friction element with friction force equal to unity (Figure 4) is obtained. After this transformaion, process A\u2013D, B\u2013G and C\u2013E are non-parallel, and one requires an additional transformation of these processes, namely a similarity transformation in the direction of the U-axis. Its initial point coincides with the projection of the initial point of the process on the U-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure8-1.png",
        "caption": "Fig. 8. (a) The perceived and projected patterns (PPi; P rPi and PPj ; P rPj) generated by a main robot and two secondary ones. (b) The actual shapes of two traffic patterns Li; Lj generated by a main robot.",
        "texts": [
            " 6), and the projected pattern is the one generated also by the main robot but it represents a view of the possible perceived pattern from the secondary robot\u2019s position. The pattern is not necessarily identical to the actual perceived pattern by the robot because of the CFN constraints [5]. The generation of the pattern is a product of the distances produced by triangles like (ABC). The synthesis of the and patterns is where denotes the composition of the two patterns expressed as the union of the corridors, which compose the perceived and projected patterns. The following illustrative example shows the traffic patterns, which includes three robots [Fig. 8(a)]. The robot is the main robot and are secondary ones. Then, the synthesis of the corridors produce a perceived pattern for the robots and where their hypothetical intersection point Similarly, the corridors generate another pattern for the robots where their Then, the projected patterns and are composed from the corridors and , respectively. Thus, the two traffic priority patterns are and as shown graphically in Fig. 8(b). Proposition: If CFNS are two traffic patterns then the following conditions are true. i) If then there are four different moving robots in the area ii) If then there are at least three moving robots in the area where with and or or Notation: The alphabet of the traffic patterns includes eight different elements shown graphically in Table I, where each element defines the priorities of its own robots as or or or TABLE I TRAFFIC PRIORITY PATTERNS Traffic Priority Alphabet In this subsection the set of the primitive traffic priority patterns for two moving robots is presented (Table I)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003521_20.278771-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003521_20.278771-Figure1-1.png",
        "caption": "Fig. 1. Coadinates for slider-disk contact. (a): Side view. (b): End view.",
        "texts": [
            " Further, we model the effects of both the contact forces and the airbearing forces throughout the time the slider is touching the disk. In what follows, we first describe the formulation of this model, then outline its analysis. We close by examining results from the model for a baseline configuration, together with a sensitivity study to examine the effects of different modifications to the baseline specifications. MODEL FORMULATION Consider a slider colliding with a disk at C as indicated schematically in Fig. 1. To describe the subsequent kinetics of the configuration, we use rectangular coordinates (x, y, z) with origin 0, as well as pitch angle 8 and roll angle $ through the center of gravity of the slider, G. The origin 0 is constrained to lie directly under G yet at the level of the mean asperity height on the disk; thus z sets the height of G above this level. The action of the air bearing throughout contact is approximated by a set of four identical springs placed on the center lines of the two slider rails and one quarter of the untapered slider length away from the untapered slider ends"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003040_s0956-5663(97)00060-2-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003040_s0956-5663(97)00060-2-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammograms at a poly(1,3DAB)/PQQ/gold electrode: (a) in a deoxygenated phosphate buffer (pH 8\u00b71, I = 0\u00b71); (b) in a deoxygenated phosphate buffer (pH 8\u00b71, I = 0\u00b71) in the presence of PQQ 0\u00b73 mmol/l in solution. Scan rate 10 mV/s.",
        "texts": [
            " Such a pH value was a good compromise between the PQQ electroactivity and the activity of the enzymes which are less active at pH values higher than 8\u00b71. The PQQ amount was varied from 0\u00b76 to 3\u00b75 mmol/l. From the cyclic voltammetry we observed that the minimum concentration which gave an appreciable analytical signal was 0\u00b76 mmol/l, then the current peak increased with the concentration of PQQ, and at a concentration higher than 3 mmol/l the current peak was constant. So we concluded that the amount of PQQ entrapped was also constant. Fig. 2(a) shows the voltammetric redox behaviour of PQQ entrapped in poly(1,3-DAB). The voltammetric picture is similar to that obtained with PQQ at the bare electrode. Similar results were obtained with poly(1,4-DAB), while poly(4aminobiphenyl) showed that a low amount of PQQ was entrapped in the polymeric structure. The electrochemical behaviour of PQQ at solid electrodes has been extensively studied and clarified (Kano et al., 1990). The voltammetric behaviour of PQQ in a deaerated solution on a Au/poly(1\u00b73-DAB) electrode in the range from + 0\u00b76 to \u2212 0\u00b74 V versus SCE shows a cathodic peak with the complementary anodic one, and the electron transfer involves two protons and two electrons according to the well-known mechanism PQQ + 2H+ + 2e,PQQH2 The current is proportional to v1/2 and to the PQQ concentration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003124_s0301-679x(00)00116-x-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003124_s0301-679x(00)00116-x-Figure2-1.png",
        "caption": "Fig. 2. The test section of the Line Contact Test Rig",
        "texts": [
            " It is once again pointed out that the non-averaging method is sufficiently general and may be used to determine the rheological parameters of the limiting shear stress if tL\u2013p relations other than Eq. (15) are used. The initial slope of the traction curve and the peak traction coefficient are the two measured variables that are used to calculate the elastic shear modulus and limiting shear stress of the fluid. The traction curves generated by any high-precision traction machines may be used. In this paper, a recently built precision line-contact EHL test rig [17] is used for the traction measurements. Fig. 2 shows the test section of the rig, in which a cylindrical ring and a two-raceway roller form a good internal line contact. The contact pressure, inlet temperature and rotating velocities of the ring and the roller can be controlled independently. To achieve a high contact pressure and reduce the surface tangential compliance of the contact components, a tungsten carbide roller and ring are used. The ring and roller are fine-ground and then handpolished to a mirror-like finish of RMS roughness less than 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002761_1.568457-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002761_1.568457-Figure2-1.png",
        "caption": "Fig. 2 Texas A&M University, Turbomachinery Laboratory high-speed hydrostatic bearing test rig",
        "texts": [
            " The specific objectives of the tests were as follows: 1 Determine the rotordynamic coefficients ~stiffness, damping and mass coefficients! of each seal geometry for specific operating conditions; 2 Measure seal leakage; 3 Use measured rotordynamic coefficients to calculate whirl- frequency ratios; 4 Evaluate the accuracy of the computer code MUDY in pre- dicting seal performance. Measurements were recorded at three pressure differentials ~1.38, 2.41, and 3.45 MPa! and three shaft rotation rates ~10,200, 17,400, and 24,600 rpm!, with the seal\u2019s rotor centered in its stator. Figure 2 presents a view of the unmodified hydrostatic-bearing test rig. The test rotor is supported at its ends by two hydrostatic bearings. The test bearing supports itself on the test rotor and is centered with respect to the support-bearing pedestals by six axial cables. The cables restrain pitching motion of the test item and cause it to move radially ~parallel to the shaft! during excitation. They are also used to statically align the test item with respect to the rotor. For the present investigation, the test-bearing assembly was replaced with the test-seal assembly illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003092_s0039-9140(98)00121-0-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003092_s0039-9140(98)00121-0-Figure1-1.png",
        "caption": "Fig. 1. Voltammogram for a 0.5 mmol dm\u22123 ferrocyanide solution in 0.1 mol dm\u22123 KCl at stationary solution (a) and the corresponding hydrodynamic voltammograms at 2.4 (b) and 3.8 ml min\u22121 (c). Working electrodes: 0.75-mm platinum disc electrode (A) and 5-mm platinum disc microelectrode (B).",
        "texts": [
            "3 mol dm\u22123 HCl was added and, after 10 min, the absorbance of the solutions was measured at 550 nm in a Micronal B382 spectrophotometer (Sa\u0303o Paulo, Brazil). 3.1. Voltammetric experiments in flowing system The voltammogram for a 0.5 mmol dm\u22123 Fe(CN)6 4\u2212 +0.1 mol dm\u22123 KCl solution was recorded at a slow scan rate (10 mV s\u22121) in a quiescent solution for all set of electrodes and this procedure was repeated at increasing flow rate conditions, so a set of hydrodynamic voltammograms was recorded as well. Fig. 1 shows the voltammetric curves obtained for both the 5-mm radius microelectrode and the conventional sized electrode, and for this latter the effect of the enhanced mass transport on the shape of the voltammogram is clearly seen since it changes from the expected peaked shape in stationary solution to the sigmoidal one when steady-state conditions are attained. Moreover, the high flux The limiting current for an electroactive species into a wall-jet detector depends on the flow rate of the running carrier, chemical properties of the system (concentration, viscosity, diffusion coefficient) and some physical parameters (the dimensions of both the nozzle and the electrode)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure6-1.png",
        "caption": "Fig. 6. (a) Representation of the free space CFNS(ti) generated by Rm using the distances d j m: (b) Generation of a perceived pattern PP (ti) by Rm using the corridors C1(ti); C2(t2); C3(t3):",
        "texts": [
            " Notation: A robot is considered as the main robot for its own free navigation space generated by it while all the other moving objects (robots) detected in the that space are considered secondary ones. Definition: A Perceived Pattern is defined as the free navigation area CFNS where represents the max number of corridors in the same free navigation space, and there are only two moving robots Moreover, in a the directions of the moving robots are defined and the intersection point is defined also if (see Fig. 6). Note that at the left side of the perceived robot, is the first corridor of and at the right side of the same perceived robot, is the last corridor of It is also important for each robot to have the ability of detecting, perceiving the shape, defining the directions and calculating the velocities of other moving objects in the same navigation space [5]. Generation of Traffic Priority Patterns The generation of traffic priority patterns requires the synthesis of the appropriate perceived patterns with main goals the isolation of two moving robots only in the same free subspace generated by a set of corridors. More specifically, a traffic priority pattern is generated by the synthesis of a perceived pattern and its corresponding projected pattern (see Fig. 7). The perceived pattern is the one generated by the main robot (as shown in Fig. 6), and the projected pattern is the one generated also by the main robot but it represents a view of the possible perceived pattern from the secondary robot\u2019s position. The pattern is not necessarily identical to the actual perceived pattern by the robot because of the CFN constraints [5]. The generation of the pattern is a product of the distances produced by triangles like (ABC). The synthesis of the and patterns is where denotes the composition of the two patterns expressed as the union of the corridors, which compose the perceived and projected patterns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002836_1.2804340-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002836_1.2804340-Figure1-1.png",
        "caption": "Fig. 1 External ironing test apparatus",
        "texts": [
            " So it may be reasonable that the difference in pressure, p-q, is very small and lubricant in a pit may flow out along the dynamically advantageous direction which may be influenced by the direction of friction stress, pressure gradient and surface textures of both the tool and work- piece. Viewed in this light, both the models proposed by Azu shima et al. and Kataoka et al. seem to be partial. In the present study, the outflow behavior of lubricant is observed while measuring the plastic strain in the surface layer which impels the lubricant in the pits to flow out. Based on the observation, a model is proposed to estimate variations in the friction stress and surface textures. 2 Experimental Conditions 2.1 Test Apparatus. Figure 1 shows the main compo nents of the apparatus which was mounted on the same deepdrawing test machine used in the previous experiment (Wang et al., 1994). A die (2) inserted into a die holder (T) is attached to the machine by a screw. A punch \u00a9 is simply mounted in a punch holder. A test cup is inserted into the head of the punch and ironed from its external side when the punch is pushed upwards. After interrupting ironing and withdrawing the punch Contributed by the Production Engineering Division for publication in the JOURNAL OF ENGINEERING FOR INDUSTRY"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002290_951039-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002290_951039-Figure2-1.png",
        "caption": "Figure 2. Geometry of Cam and Roller Follower Motion",
        "texts": [
            " This research concentrated on understanding the roller follower slippage mechanism by analyzing the friction at the interfaces of roller/roller pin and roller/cam through theoretical analysis and experimental study. Figure 1. Valve Train Schematic, Cummins L-10 Engine RELATIVE ANGULAR VELOCITY OF ROLLER FOLLOWER (\u03c9f) - To determine the roller follower slippage from the measured roller angular velocity, a computation of relative angular velocity at each cam angle is required. The difference between this theoretical angular velocity and the measured value is considered to be roller slippage. The following derivation is based on the assumption that the roller follower rolls without slipping. Figure 2 shows the geometry of cam and roller follower motion. The basic idea to derive relative angular velocity (\u03c9f) came from the fact that the roller velocity (Vr) can be computed starting from either the lever pivot center (Q) or the cam center (O). Here, the roller velocity (Vr) is the velocity of a roller center which is projected to the tangential contact line. The contact point C(x,y) at each cam angle was analytically obtained from cam manufacturing data (r) by using the envelope theory.(5) The distance (rc) from the cam center to the contact point can be expressed as rc = (x2 + y2) 1-2 (1) The contact point velocity (Vc) is Vc = rc\u03b8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003090_20.582711-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003090_20.582711-Figure3-1.png",
        "caption": "Fig. 3. Grouping field lines for inductance calculation. Fig. 4. Two pole equivalent circuit for aligned inductance computation. (only half the model is shown) .1 L",
        "texts": [
            " With such a laminaition geometry, it is recognised that two parameters significantly affect the unaligned inductance value: a) the distance from the stator pole surface to the rotor interpolar surface; this is the minimum distance that field lines must travel to enter the rotor. b) the rotor diameter which, together with the stack length, set the area of magnetic ireluctance in air. Manuscn t received March 18 1996. Dr, A. hichaelides, Dr. C. fiollock and Mr. C. M. Jolliffe are with the De artment of Engmeenng, University of Wamck, Coventry C V ~ YAL, U. K.. 0018-9464/97$10.00 0 1997 IEEE 2038 a) Group classlfication ofJield lines. In the proposed analytical method for q-axis inductance computation, the field lines are divided into numbered groups, as shown in Fig. 3 . Field lines of Group 1 leave the stator pole surface to enter the rotor interpolar surface. These are modelled as straight line sections. Field lines of Group 2 are modelled as sections of circular arcs. Field lines of Group 3 leave the stator pole side to enter the rotor pole side and are modelled as sections of ellipses with a governing equation may be computed using Simpson\u2019s rule which states that an integral leave the stator pole surface and enter the rotor pole side, and jf(4 dx (9) can be expressed as and of varying length. Field lines of groups 1 - 3 are assumed to be linked by all turns per phase. A final group (Group 4) consists of field lines that leave the stator pole side and enter the stator yoke. These are fringing field lines that do not link all turns per phase and are represented as sections of ellipses. b) Evaluation of elliptical path length. Referring to Fig. 3 , the elliptical paths from the side of the stator pole to the side of the rotor pole find their centre, 0, where the projections of the stator and rotor pole sides meet. Field lines of this group are bounded by the limiting ellipses with equations where yo . y,, are the ordinates which divide the area under Jf(x))cIx into strips of wdth d c) Inductance computation The computation of the length of the magnetic flux lines through air, and the area through which the field lines must flow, leads to the estimation of magnetic reluctance, R In the unaligned rotor position, the magneto-motive force (MMF) drop in iron may be neglected and the flux is found using Ohms law for magnetic circuits, that is, where R, is the total airgap reluctance (in the unaligned position) As this is a two pole-per-phase machine, (4) (5) Rt = 2Rg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002958_70.508438-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002958_70.508438-Figure2-1.png",
        "caption": "Fig. 2. A, B and their possible relationships.",
        "texts": [
            " This problem is in itself a difficult one. The complex nature of the problem is best illustrated through an example. Suppose that two polyhedral solids A and B are in collision and that their geometrical models and sensed locations are known. An intersection relationship between A and B can be derived [3], [SI, [21], which may not be pure contact relationship due to sensing uncertainties. The derivation may yield intrusions of one object into the other, absence of some contact points or no contact at a11 between the two objects. Fig. 2(a) shows a possible relationship between polyhedra A and B as the result of derivation from the models of A and B and their sensed configurations. Clearly such a relationship is impossible in reality, whereas, based on this derived relationship, there is more than one contact situation that may actually occur due to uncertainties, as shown in Fig. 2(b). Notice that an intrusion in the derived relationship, as it is caused by uncertainties, always means a possible contact, but absence of certain contacts in the derived relationship does not mean that those contacts cannot possibly occur in reality (e.g., see Fig. 2, where the point p of A may actually contact B as shown in Fig. 2(b)). Thus, it is quite difficult to determine the set of all possible contact situations between A and B taking into account location uncertainties. The approach proposed in [24] simplified the problem by demanding the satisfaction of some geometric constraints, and thus was not completely general. On the other hand, the technique introduced in this paper, of growing objects by location uncertainties, fundamentally facilitates the finding of such a set in a general way. With the set serving XIAO AND ZHANG: GROWING A POLYHEDRON BY ITS LOCATION UNCERTAINTY as an initial guidance, as demonstrated in 141, 1251, 1201, additional sensing means, such as force/moment or vision sensing, can be used to reduce the set through confirming the existence (or nonexistence) of each possible contact situation",
            " Given two polyhedral objects PI and P, in contact, the algorithm assumes that one of the objects, say, PI , is fixed, and that only P2 has location uncertainty. Thus the problem becomes that of growing PI by the position uncertainty of P:! and growing P2 by its own orientation uncertainty only\u2019 (see Appendix C for a proof). By checking the intersection between every pair of (approximated) grown regions of elements from the two objects respectively and with proper reasoning, the algorithm efficiently generates a set of PC\u2019s slightly larger than Spc . As an example, for the two contacting objects A and B shown in Fig. 2, the algorithm spent 0.572 seconds of CPU time on a SUN SPARC IPX to generate an output set of PC\u2019s. Detailed description, analysis, and evaluation of the algorithm can be found in [27]. It is important to emphasize that although an implementation generally involves certain approximation due to lack of better algorithms for computation, the significance of the exact de- or equal to E , . \u2019 Note that the algorithm should work equally well even if both Pi and P2 have location uncertainties since it is equally easy to approximate the grown regions by both position and orientation uncertainties with the S-tope model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure13-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure13-1.png",
        "caption": "Fig. 13. Suspension of Six-cylinder Oil Engine",
        "texts": [
            " Both vertical and horizontal primary out-of-balance couples are present on this engine and, to obtain insulation against these as well as the 13-order torque harmonic, a suspension giving a high degree of rotational flexibility about all axes must be employed. This was achieved by using a V-arrangement of sandwich mountings very close to the centre of gravity, with the front rubber sandwich mounted so that its compression axis also passed roughly through the centre of gravity. The degree of insulation obtained is excellent. Engine movement under shock, torque-reaction, and when passing through resonance on starting and stopping, is quite large but has not proved troublesome. As shown in Fig. 13, buffers were fitted to restrict movement at the output Proc Instn Mech Engrs (A.D.) flange but further trials with special dampers are continuing in order to obtain better control. For this type of engine and also some four-cylinder oil engines, a special design of damper as discussed in an earlier section would be of real benefit. A comparatively orthodox suspension of a six-cylinder oil engine is shown in Fig. 13, together with the vibration readings obtained and those calculated. The rear mounting uses large rubber shear sandwiches precompressed in pairs. The precompression permits a higher stress in the rubber without loss of fatigue life. Adjustable torque-reaction buffers are fitted so that correction can be made for slight differences in stiffness of the mountings and, when necessary, for permanent set. The fore-and-aft stiffness of this type of rear engine mounting arrangement is very high and, unless a very long and heavy gearbox is fitted, the high flexibility of the rear mountings in a transverse direction is not detrimental. To save space in fitting, the rear mountings are not arranged with the edges of the plates vertical in end NO 1 1957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub.comDownloaded from SUSPENSION OF INTERNAL-COMBUSTION ENGINES Amplitude at indicated points f in. Engine speed, revlmin I 4 5 I M C I M C ! l 2 1 3 / M C / M C ( M C IN Position of axis from test results as shown in Fig. 13a VEHICLES 340 400 480 29 Marked * Marked x Marked o a Side elevation. b End view of front mountings. c Detail of rear mounting. d Scrap end view on rear mountings. at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub.comDownloaded from Plan showing results of test and disposition of mountings. Proc Instn Mech Engrs (A.D.) NO 11957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub.comDownloaded from SUSPENSION OF INTERNAL-COMBUSTION ENGINES IN VEHICLES 31 view. The stiffness of the mounting is the same in any direction in the shear plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002860_s004070050024-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002860_s004070050024-Figure8-1.png",
        "caption": "Figure 8",
        "texts": [
            " The motion of the ring is thus MR = \u00b5R \u00d7 \u03c9r (15) Hence from (14) and (15) MC MR = 2 3 \u03c9r\u00b5C/\u00b5R\u03c9r = 2\u00b5C 3\u00b5R (16) as given by Newton Ratio 3 \u201c\u2014and this motion of the ring, uniformly continued about the axis of the cylinder, is to the uniform motion of the same about its own diameter performed in the same periodic time as is the circumference of a circle to double its diameter.\u201d The motion MR of the ring when rotating about the axis BB\u2032 with angular velocity \u03c9 is given by (15). Denote by M\u2032 R its motion when rotating with the same angular velocity about one of its diameters. Then, since the circumference of a circle of diameter d is \u03c0d, Newton states that MR M\u2032 R = \u03c0d 2d = \u03c0 2 Figure 8 shows half the ring with centre 0 and diameter CC\u2032. We imagine the whole ring to rotate with angular velocity \u03c9 about CC\u2032. Because we are defining motion as the arithmetic sum of the linear momenta we will get the motion of the whole ring by doubling motion of the half ring shown. We have taken the mass of the ring to be \u00b5R and so the mass of the small element shown of length dl = rd\u03b8 is \u00b5R \u00d7 dl circumference = \u00b5R \u00d7 rd\u03b8 2\u03c0r = \u00b5Rd\u03b8 2\u03c0 The element is moving in a circle of radius y = r sin \u03b8 and so its speed is \u03c9r sin \u03b8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002277_jphysiol.1922.sp002021-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002277_jphysiol.1922.sp002021-Figure1-1.png",
        "caption": "Fig. 1. Fig. 2.",
        "texts": [],
        "surrounding_texts": [
            "meter in order to control the strength of the stimulus. From this it passed into a transformer, which insulated the stimulating circuit from direct electrical connection with the magneto, and so helped to avoid electrical disturbances. It was then transformed again, a make and break key (K2) being placed in the primary circuit of this second transformer and the nerve being stimulated by the current from the secondary. A key (K1) was placed in the secondary circuit as a short-circuit key, the keys K1 and K2 forming part of the contact breaker, so that the interval between the opening of K1 and K2 determines the duration of the stimulus. The tendinous end of the muscle of a fresh gastrocnemius-sciatic preparation of Rana temp., was immersed in boiling Ringer's solution in order to obtain a monophasic electric response. By means of the screw adjustment the muscle fibres were stretched so that when stimulated only a minimal movement should occur. The two non-polarisable electrodes of the galvanometer circuit were hooked on, one electrode to the uninjured end and one to the injured end of the muscle. After it had been covered up the preparation was allowed to stand for half-anhour, so that it might reach a steady state, and then the injury current balanced. 26-2 399 B. A. McSWINEY AND S. L. MUCKLOW. In the experiments in which the duration of the stimulus was varied readings were taken with increasing periods, and repeated with decreasing periods of stimulation, and an attempt made to eliminate the effects of fatigue by taking the mean of the two readings of any one period. In experiments in which the frequency of the stimulus was varied, the arms of the contact breaker were set to give a stimulus of approximately one second. A connection was made with one segment of the distributor of the magneto, so that only one shock in eight was given to the nerve. The nerve was stimulated and the reading of the galvanometer taken. Readings were then taken using two, four and eight segments of the distributor. The speed of rotation of the magneto was measured by a revolution counter and stop watch. The magneto was driven at different speeds by changing the belt on the pulleys, readings at each speed being taken from the galvanometer. In every experiment, readings were taken first with increasing and then with decreasing frequencies, and the mean taken of the readings at any one frequency, to eliminate the effects of fatigue. The experiments described above were repeated at various temperatures. After a change of temperature, the muscle was allowed to remain at rest for 30 minutes so that its temperature might approximate to that of the chamber. In all experiments the results are given in arbitrary units for galvanometer deflection. The relation between the duration of the stimulus and the total electrical change. The experiments of which Fig. 3 is typical were repeated at various temperatures as shown in the upper curve of Fig. 3. In all cases the total electrical change was proportional to the duration of the stimulus. It was found that the muscle, which had necessarily to be injured at one end, died too rapidly to allow experiments to be made on one muscle at more than one temperature. Different muscles therefore were used in these experiments, so that nothing can be gained from a comparison of the slopes of the line at different temperatures. Hartree and Hill(3) investigated the relation between the total initial heat production and the duration of the stimulus under similar conditions, and a comparison of the curves they obtained with those in Fig. 3, will show that the two sets of curves bear little resemblance to one another. The heat-production is not a linear function of the duration of the stimulus though it becomes linear if the stimulus is continued; the linear portion however, if produced backwards, does not pass through 400 ELECTRICAL CHANGE IN MUSCLE. the origin. As there is every reason for assuming that the heat-production is proportional to the production of lactic acid, it would appear therefore, in contradiction to the hypothesis suggested by Mines (1), that the electrical changes which occur in a muscle on contraction do not bear any quantitative relation to the production of lactic acid. The relation between the frequency of stimulation and the total electrical change. Within the limits dealt with in these experiments, the total electrical change in a stimulus of fixed duration is proportional to the frequency of stimulation. Typical results are shown in Fig. 4. Hill(2) found, under similar conditions, that increased frequency of stimulation caused increased heatproduction up to the limit when complete tetanus resulted-beyond this point however, which occurs well within the range of the linear relation of the total electrical change to frequency, the heat-production was independent of the frequency of stimulus. Hence the heat-production 401 B. A. McSWINEY AND S. L. MUCKLOW. and the total electrical change do not bear the same relation to the frequency of stimulation, therefore the total electrical change is not quantitatively proportional to the production of lactic acid. The linearity of the relation between the total electrical change and the frequency of stimulation is not affected by temperature, and gave similar results to Fig. 3."
        ]
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure19-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure19-1.png",
        "caption": "Fig. 19. Graphical Construction for Mounting Performance",
        "texts": [
            " It would seem logical to \u2018crack\u2019 the chzssisless body and that could be done without weakening the structure. However, the main point was to reduce the transmission of vibration from the engine, and the best tool for this purpose was the vibration theory condensed into such a form that results could be derived without lengthy and cumbersome calculations, and the method should clearly show the influence of the various factors. The following method of evaluating mounting schemes as illustrated by Fig. 19 had been used by his firm for many years. The method was basically for systems with two planes of symmetry but it had given satisfactory results even if the condition had not been strictly satisfied. The circle was drawn with its centre on the principal axis and through the ends of the radius of gyration and the radius of transverse spring resistance. It intersected the axis at two cardinal points which were the locations of two equivalent point masses ml and m2 and two equivalent springs s1 and s2",
            " a single mounting as close to point m2 as was practicable, which could theoretically have a quite high vertical and fore-and-aft stiffness, but would require a comparatively small transverse stiffness to take care of the small rolling and yawing vibration amplitude. The front mountings should preferably be located in the transverse vertical plane through ml. If the front mountings were located at approximately the height of the c.g. then they could be made comparatively stiff in a transverse and fore-and-& direction. However, if the mountings could be located high, then there was no reason why they should not be made comparatively soft in all directions. With reference to Fig. 19 the conditions which the equivalent masses had to satisfy were : ml+mz = M mlAl = mzA2 mlA12+m2A22 = MRm2 from which A2 A1+& m l = M - AlA2 = R,2 The equivalent springs had to satisfy the conditions : Sl+S2 = s SIB1 = s~BZ slB12+s2B22 = s R , ~ from which B2 Bl+BZ B1 B1+B2 s1= s- s 2 = s - BIB, = Rs2 It was obvious that the intersection of the circle and the centre-line located the only two points which satisfied the above conditions. No 1 1957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub",
            " The study of off-resonance conditions in connection with engine mountings was a most interesting subject, and Mr. Nicolaisen\u2019s comments in that respect were appreciated. The diagrammatic method of obtaining the two natural frequencies of a system with two planes of symmetry as described by Mr. Nicolaisen had been studied with interest. The author had usually employed methods of calculation where the solution of a quadratic equation had to be found as the equations given in the appendix reduced to that form for the conditions assumed in Fig. 19. The use of a Mohr\u2019s circle diagram might, however, be preferred by some engineers. He would agree that boom could be caused by the vibrations which could be ignored in preliminary mounting selection and for that reason he had mentioned them but had also stressed that they were not of major importance for initial calculation. In practice it had not been found that a properly selected arrangement of interleaved mountings gave rise to the difficulties mentioned by Mr. Nicolaisen. On the contrary, it had been found that by replacing large plain sandwich Proc Instn Mech Engrs (A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002907_3516.662865-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002907_3516.662865-Figure2-1.png",
        "caption": "Fig. 2. Structure of the sensor body.",
        "texts": [
            " In order to fit everything into a pen, the geometrical restrictions of the sensor are an outer diameter of 12 mm, an inner diameter of 7.5 mm, and a total sensor length of 20 mm. Given the envisaged application of the sensor, it has to be suited to mass production. This is the only way to reduce the overall sensor cost. Also, the double use of the sensor has severe implications on the definition of the required sensitivity. The rated (writing) forces are 2 N. The maximal writing forces normally do not exceed 5 N. Accelerations primarily range from 3 to 3 m/s and normally not exceed 5 m/s . As shown in Fig. 2, the sensor body consists of a ringshaped deformable aluminum structure provided with 16 strain gauges. The piezoresistive technology (strain gauges) was chosen due to its high sensitivity, cost effectiveness, and the possibility of automating the manufacturing process. For the first prototypes, semiconductor strain gauges were used. The outer cylinder is connected to the pen body, which acts as a mechanical ground. Inside the radial beams, the pen holder assembly is to be mounted. It includes the ink cartridge, the mechanical stops, and the inertial mass for measuring accelerations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003934_20020721-6-es-1901.00884-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003934_20020721-6-es-1901.00884-Figure2-1.png",
        "caption": "Fig. 2. Scheme of the robot.",
        "texts": [],
        "surrounding_texts": [
            "Keywords: Robot calibration, optimal trajectory, parameter estimation, trajectory planning.\n1. INTRODUCTION\nThe determination of a good robot dynamic model, and consequently of the parameters that define it, is fundamental for the application of various advanced control schemes, as well as for simulation purposes. Several papers and books appeared in literature, dealing with robot dynamic calibration: see e.g. (Kozlowski, 1998), (Neuman and Khosla, 1985), (Swevers e t al., 1997) and (Gautier and Khalil, 1990) about the use of different dynamic models for calibration, and the determination of the minimum set of identifiable parameters.\nThe estimation of the identifiable parameters is usually achieved by application of a Least-Squares criterion to the motion or the energy equations of the robot. However, the quality of the provided estimate is strongly influenced by the trajectory executed by the robot during the acquisition of the experimental data used for the calibration.\nsupported by Ministero dell\u2019UniversitL; e dells Ricerca Scientajica e Tecnologica.\nStart,ing from (Armstrong, 1987), perhaps one of the earliest papers about this topic, different solutions have been proposed to find trajectories that well excite the robot dynamic model used for calibration, by finding an optimal sequence of joint position-velocity and/or acceleration points, to be subsequently interpolated as in (Armstrong, 1987), (Caccavale and Chiacchio, 1994), and (Gautier and Khalil, 1992), or by looking for an optimal trajectory within a given parameterized family, as in (Swevers e t al., 1997) and (Calafiore e t al., 2001).\nAll these methods are based on different optimization criteria, which should theoretically guarantee some characteristics of the computed estimates, e.g. the minimization of the uncertainty bounds or of the estimate bias due to unmodeled dynamics errors. In some cases, special simple trajectories can be also adopted, as in (Visioli and Legnani, 2000).\nThis paper deals with the dynamic calibration of a two-dof SCARA robot: a good calibration is fundamental in this case, since no knowledge of its\n43 1",
            "Two DC motors actuate the first two joints moving the gripper in the x-y plane. The quote of the gripper is actuated by a third DC motor by means of a speed reducer and by a pinion-rack transmission. The vertical motion (direction Z) is decoupled with respect to X and Y and it is not considered in this paper.\nThe mechanical transmissions of the first two joints include two Harmonic Drive speed reducers\nThe controller is a standard PC, using a Pentium processor and QNX4 real time operating system. The servo loop sampling time is 1 ms. The drives are configured in torque mode, and the desired torque is evaluated by a standard decentralized PID controller.\nDuring normal operation the following data are collected and stored: the desired and the measured motor rotations, the estimated motor velocities, the desired and the measured motor torques, determined from the motor current measures.\n2.2 Robot d y n a m i c model\nUsing standard methodologies, a dynamic model of the robot is constructed in the form\nwhere U is the vector of the motor torques, P is a vector of m constant parameters to be identified, W is a 2 x m matrix depending on the joint position, velocity and acceleration, and Q is the joint vector coordinate, defined as Q = [ q ~ , q2] .\nVector P includes the dynamic parameters of the robot, plus some parameters describing the energy loss in the mechanical transmissions (friction).\nThe dynamic parameters are defined in order to obtain a complete and minimum model ((Gautier and Khalil, 1990)). The so determined parameters, collected in the dynamic parameters vector P d , are\nT",
            "where li is the length of link i, I,, is the inertia moment of link i with respect to joint axis i, ma is the mass of link 2, sax and say are the coordinates of the center of mass of link 2 with respect to the frame of the second link, Jmi are the sum of the inertia of the motor i plus that of the corresponding speed reducer.\nOn the basis of some previous experimental tests, a third order model has been considered to represent friction on joint i, including motors, speed reducers, and joints friction terms\nuf,i = aoisign(4i) + a1i4i + azisign(4i)4, + a3iii.\n(3) The friction parameters vector Pf is then defined as\n(4)\nA more detailed friction model should include a term of losses, proportional to the torque transmitted by the speed reducer from the motors to the links. This term is equal to u/r or ur depending on the direction of the power flow (where r is the reducer efficiency). The inclusion of this term would make equation (1) non linear with respect to the parameters. For this reason, and after verifying that this term was small compared to that of equation (3), it has been neglected.\nFinally two parameters represent a torque offset in the joints. They could represent errors in the acquisition hardware or asymmetry of the joint friction with respect to the velocity\n2 3\nT pf = [aoi, ail, a21, a31, a 0 2 , a12, a 2 2 , a321 .\nSummarizing, P is a 15-element vector, given by\nT P = [PZ PT PT] ,\nRelation (l), which is linear with respect to P , can be used to estimate the parameters vector P , collecting the values of U , Q, Q, Q, at n time instants, from tl to t,, during the execution of a task, thus obtaining an equation of the form\ny = H P + v (6)\nwith y := [ U ( t l ) . . . U(t , ) lT , and\nwhere is assumed to be the zero mean measurement noise vector, uncorrelated from P , having autocorrelation matrix R,, and His the regression matrix, assumed to be deterministic.\nP can then be estimated by using a recursive formulation of the LS algorithm: let Hi := W(ti) and yi represent the i-th row of H and the it h torque measurement, respectively; let Pi and Sp,( be defined as the estimate of the parameter vector P , given the measurements up to i, and the relative covariance, respectively; the estimate can then be recursively updated using the following recursions\nf\u2018i+i =f\u2018i + Ki+i(yi+i - Hi+if\u2018i), f\u2018o = P , Ki+1 = SP,iH&I(RW + Hi+1Sp,iH&1)r1,\nSP,i+1 = SP, i - Ki+1Hi+1SP,i, SP,O = R P ,\nwhere P is some a priori information about P (considered as initial condition for the recursive estimation), having covariance matrix R p . If no a priori knowledge is available, as in our case, then Rp = 00, and it follows that the amplitude of the estimation error depends on II = H T R i l H .\nThe execution of a particular robot trajectory during calibration determines H , and consequently II. Different \u201cmeasures\u201d on II have been defined in literature to (try to) predict in some sense the quality of the computed estimate of P . The most frequently used (see (Ljung, 1987)) are the condition number of II, J k := cond(II) (to be minimized), and the determinant of II or some scalar measure depending on it: for instance, the so-called D-optimality criterion makes use of index Jd := logdet(II) (to be maximized).\nIn a previous paper (Calafiore e t al., 2001) by some of the coauthors, the optimal trajectory search was performed using a procedure based on genetic algorithms, and the so-determined trajectories were utilized to identify the dynamic parameters of a robot, achieving results that were considered quite satisfying. However, no comparison was made with the estimates obtained using some other kind of trajectories. It is not clear then how important is the use of such trajectories for"
        ]
    },
    {
        "image_filename": "designv11_31_0003052_980220-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003052_980220-Figure7-1.png",
        "caption": "Figure 7. Optional passenger car steering system submodel describing geometric, elastic and damping properties (including dry friction) as well as freeplay in the steering box (\u03b1pl - total freeplay value)",
        "texts": [
            " x y zO O O1 1 1 , , \u03c81 \u03b6 \u03b6 \u03b6 \u03d1 1 1 1 4 2 3 4O O O' ', , , \u03b6 \u03d1 \u03b6 \u03d1 1 4 1 9 4 9O O , , , 2 3 4 The steering system model, apart from geometric properties, describes also its elastic properties in the way similar to presented in [1]. It is assumed lack of geometrical roll-steer (resulting from geometrical constrains existing in the steering system as well in the suspension). Dry friction and freeplay in steering system perform an important function in the system dynamics [1, 22]. It is possible to use an optional car steering system submodel (e.g. Fig. 7, 4 dof submodel; co-ordinates: steering angle of the left \u03b12 and right \u03b13 wheel, steering box input shaft angle of rotation \u03b1p, steering-wheel angle \u03b1k ), which also describes damping properties (including dry friction according to algorithm presented in [5]) and freeplay in steering box (an algorithm according to the theory presented in [22]). Force and moment inputs result from aerodynamic drag, wheel rolling resistance, braking, driving. The steeringwheel angle is treated as an external input",
            " , P1 2 3 14 &q & & &\u03d5 \u03d1 \u03d11 2 1 2 4 2 0= = = 0414111 411111 =\u03d1\u22c5\u03d1=\u03d1\u22c5\u03d5=\u03d1\u22c5\u03d5= =\u03d1\u22c5\u03c8=\u03d1\u22c5\u03c8=\u03d5\u22c5\u03c8 &&&&&& &&&&&& 0' 3 ' 2 4' 3 ' 24 ' 3 ' 24 O11O11 O11O11 O11O11 O11O11O11 =\u03b6\u22c5\u03d1=\u03b6\u22c5\u03d1= =\u03b6\u22c5\u03d1=\u03b6\u22c5\u03d5= =\u03b6\u22c5\u03d5=\u03b6\u22c5\u03d5= =\u03b6\u22c5\u03c8=\u03b6\u22c5\u03c8=\u03b6\u22c5\u03c8 &&&& &&&& &&&& &&&&&& 6 7 For small values of angles (\u22640.2 rad) (Eq. 5) (Eq. 6) (Eq. 7) (Eq. 8) Consequently, it is possible to derive equations of motion separately for every submodel assuming (for given simulation step) constant value of forces and moments, the source of which is another submodel. OPTIONAL CAR STEERING SYSTEM SUBMODEL \u2013 The model (Fig. 7) consists of four rigid bodies: \u2022 steering-wheel (I\u03b1k [kgm2] - moment of inertia related to steering-wheel axis), \u2022 steering column together with steering box gear (I\u03b1p [kgm2] - moment of inertia related to steering-wheel axis), \u2022 left and right wheel together with knuckles (I\u03b12, I\u03b13 [kgm2] - moments of inertia related to king-pin axis). Other denotations mean: \u2022 kk, [Nm/rad] - stiffness of the steering column, \u2022 k2, k3 [Nm/rad] -stiffness of left and right part of steering linkage, \u2022 Mtp, [Nm] - dry friction moment in steering box, \u2022 Mt2, Mt3 [Nm] - dry friction moments in left and right king-pin bearings, \u2022 ck, cp, c2, c3 [Nms/rad] - coefficients of equivalent viscous damping in steering column, steering box, left and right king-pin bearings",
            " \u2022 Mk, [Nm] - external moment on the steering-wheel, \u2022 Mabc7, Mabc8 [Nm] - aligning moment of left and right wheel reduced to king-pin axis, \u2022 ip, [-] - steering box ratio, \u2022 iz2, iz3, [-] - ratio of left and right part of steering linkage. iz2, iz3 are functions of road wheel steering angles \u03b12, \u03b13: iz2 = iz2(\u03b12) (Eq. 9) iz3 = iz3(\u03b13) (Eq. 10) The submodel has four degrees of freedom: \u2022 steering-wheel angle \u03b1k, \u2022 steering box input shaft angle of rotation \u03b1p, \u2022 left road wheel steering angle \u03b12, \u2022 right road wheel steering angle \u03b13. Equations of motion were derived using force method. The second part of Fig. 7 shows how steering box freeplay \u03b1pl is taken into account. \u03b1p0 is \u03b1p value for equilibrium state in linkage, i.e. forces in left and right tie rods are equal in the middle of the steering rack: (Eq. 11) where \u03b1zb2, \u03b1zb3 stand for toe-in angle values for left and right wheel. The following denotations were used: \u2022 spring force moments Mkk = kk \u22c5 (\u03b1p - \u03b1k) (Eq. 12) (Eq. 13) (Eq. 14) where (Eq. 15) (Eq. 16) \u2022 viscous damping moments Mck = ck \u22c5 (Eq. 17) Mc2 = - c2 \u22c5 (Eq. 18) Mc3 = - c3 \u22c5 (Eq. 19) \u03d5 \u03d1 \u03d11 1 4, , cos cos cos\u03d5 \u03d1 \u03d11 1 4 1= = = sin\u03d5 \u03d51 1\u2245 sin\u03d1 \u03d11 1\u2245 sin\u03d1 \u03d14 4\u2245 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 p p z zb p z zb z z k i i k i i k i k i 0 2 2 2 2 3 3 3 3 2 2 2 3 3 2 = \u22c5 \u22c5 \u2212 + \u22c5 \u22c5 \u2212 + ( ) ( ) M k i ik p p z zb2 2 2 2 2= \u22c5 \u2032 \u22c5 \u2212 +( ) \u03b1 \u03b1 \u03b1 M k i ik p p z zb3 3 3 3 3= \u22c5 \u2032 \u22c5 \u2212 +( ) \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1p p pl p pl p pl pl p pl , = \u2212 < < + \u22c5 + < < \u2212       0 2 2 2 2 2 for + e for p0 p0 mp p0 p0 e mp pl pl pl pl = \u2264 \u2212 \u2212 < < + \u2212 \u2265 +         1 2 0 2 2 1 2 for for for p p0 p0 p p0 p p0 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1 ( & & )\u03b1 \u03b1p k\u2212 &\u03b1 2 &\u03b13 8 \u2022 dry friction moments (Eq",
            "8 4 6 Body CG height h [m] (d \u03c8\u03c8 /d t) [ ra d/ s] right right left left &\u03c81ss S S SS EE E E S S S S EE E E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 P 0 : 1.5 0 9 P 1: 1.5 6 6 P 2 : 1.7 3 6 P 3 : 1.8 4 6 Body CG height h [m] t [ s] right right left left &\u03c81 13 E - result of experiment, S - result of simulation The presented results as well as many others show good compatibility between simulation and experiment for biaxial car and truck model. EXAMPLE OF MORE COMPLICATED STEERING SYSTEM MODEL APPLICATION The combination of submodel I (Fig. 8), 4 submodels III (Fig. 10) and steering system submodel (Fig. 7) was applied to simulate small car motion. Normal reactions of the road were described using quasi-static formulas, assuming existence of four supporting spring elements for each wheel (suspension and tyre elasticity in series). Fig. 33\u00f736 show results obtained for low velocity (~10 km/h). Fig. 33 presents time histories of steering-wheel angle \u03b1k as well as moments on steering-wheel Mk. Fig. 34 shows CG trajectory on road plane Oxy. Fig. 35 presents steering-wheel moment Mk as a function of steering-wheel angle \u03b1k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure14-1.png",
        "caption": "Fig. 14. Engineering applications.",
        "texts": [
            " The model of the mechanism is established and simulated by simulation software (Adams) as shown in Fig. 12. Then, the strokes, velocities, accelerations and driving forces (non-redundant) curves of the prismatic joints can be measured as shown in Fig. 13. The results obtained by Matlab are consistent with that measured from Adams, which verifies the correctness of the above models of mechanism kinematic equivalent, kinematics and dynamics. The actuators can be chosen roughly according to the results. A 3-D rending model to an engineering application is shown in Fig. 14. This paper defines the virtual continuous axis, and proposes its mathematical criteria. The type synthesis approach for RPMs with a virtual continuous axis is proposed. 2-DoF RPMs with arc-rail-slider or cross slipper are constructed and analyzed by screw theory. The RPMs with a virtual continuous axis synthesized in the paper have the property of static-load-balancing and ample load space, which have good application prospects in tracking and simulating field for large-scale heavy-weight apparatus"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002538_s0007-8506(07)63252-1-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002538_s0007-8506(07)63252-1-Figure4-1.png",
        "caption": "Fig. 4 Beam integrator producing a rectangular uniform power disiribution",
        "texts": [
            " A uniform surface treatment requires a corresponding power density, which is normally not the case. Cross sections of the described beam profiles are the so-called TEM modes which may vary with the output power. Several optical systems have been developed to equalize power density. Examples are fast scanning mirrors which integrate over a given period of time, and facetted mirrors which fold segments of the beam profile on top of each other in the same spot. A uniform power distribution can also be obtained by a highly reflective tube, as applied in the Twente integrator (Fig. 4) which combines some interesting features. The incident beam is split by an axicon lens. After a few reflections on the integrator walls, a uniform power distribution is obtained on the exit of the prismatic integrator. A lens with adjustable magnification projects that distribution on the surface to be treated. beam density (Wkm j Optics In industry such sophisticated optics are rarely used up to now. Instead, ordinary optics with large focal lengths and corresponding spot sizes are still being used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003980_b002603o-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003980_b002603o-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of a CFBRDE.",
        "texts": [
            " Reagent grade potassium bromide (KBr) and amino acids were purchased from Wako (Osaka, Japan) and were used without further purification. Stock solutions of the amino acids were prepared with water, which was purified by a Milli-Q system (Millipore Co., France). Prior to LC analysis, the sample solutions were made up fresh by dilution with water. A 50 mM phosphate buffer solution (pH 7.5) containing 10 mM KBr was employed as mobile phase. The pH of the buffer solution was adjusted with 0.1 M phosphoric acid and 0.1 M NaOH. Fig. 1 shows a schematic representation of the CFBRDE. The electrodes were fabricated by photolithography and dry-etching techniques11 from a carbon film of pyrolyzed 3,4,9,10- perylenetetracarboxylic dianhydride on the plastic films (with a thickness of about 200 mm). The disk electrode (3 mm in diameter) was separated from the ring electrode (1 mm width) by a gap of 0.5 mm. For the amperometric measurements, a CFBRDE was installed in a radial thin layer flow cell (BAS Japan, Tokyo, Japan) with a 25 mm thick Teflon gasket (the dead volume was 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002333_s0045-7825(98)00367-3-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002333_s0045-7825(98)00367-3-Figure9-1.png",
        "caption": "Fig. 9. For illustration of generation of singular points of profile v",
        "texts": [
            " Our investigation has been performed for the design parameters (p-= 0.713r, a = 0.96r). It was proven that two singularity points occur in the neighborhood of point M determined by (0 o = 84.8 \u00b0, ~b o = 11.9 \u00b0) and (0 o = 99.2 \u00b0, ~b o = 27.8\u00b0). These two points are simultaneously points of regression and the piece of envelope ~o has the shape of a 'swallow tail'. Such a piece of the envelope is represented to an enlarged scale in Fig. 7(b). Note: In the case of Root 's blowers, there is such a point of the line of action (point P in Fig. 9 where equation singularity (35) or (36) is satisfied. However, a singularity point of Xo is not generated at P because v(p) ~ . (r) and - (p) r ~=V. Eqs. (35) or (36) is satisfied just because vectors v~ IUtr are collinear. At point P of line of action, a regular point of ~p but not a singular point of ~ , is generated. The appearance of singularities is a herald of the oncoming undercutting. Fig. 8 shows that the extension of the length of the circular arc of curve 2f, is accompanied by undercutting of envelope .,Yp (in the 'swallow tail' part). Undercutting of envelope 2?p may be avoided by limitation of parameter 0 that must be in the range 0 <~ 0 < Oj~ m, where 0t~mcorresponds to the point of singularity of .Sp. Fig. 8 shows the family of circular arcs X~ and the envelope 2?p. Fig. 9 show a segment of line of action that corresponds to the meshing of X~ and Xp. The drawings illustrate that singularity points of ~p are generated at points M, and M e of line of action L where the normals to L pass through point Op of rotation of the driven rotor. The discussed approach for determination of singularities can be applied for a cycloidal gearing with a pin tooth (Fig, 10) of the pinion (driving gear). Examples of such a cycloidal gearing are: (i) the meshing of the pin tooth and the chamber in Wankel engine [9] (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002937_pl00014419-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002937_pl00014419-Figure14-1.png",
        "caption": "Fig. 14. (a) An assembly with m + 1 contact points. Object 1 touches object 2, and an immovable obstacle. (b) The assembly is split, and in the new assembly, object 1 is fixtured. Due to the contact constraints on object 1, only two fixels are required for form-closure. Objects 2 through n are fixtured as a separate group (fixels for these objects are not drawn).",
        "texts": [
            " That is, in Figure 13(a) a force of the form \u03bbn is applied to object 1, and a force of\u2212\u03bbn is applied to object 2, due to contact. After splitting the contact, a force \u03bb1n might be applied to object 1, and a force \u2212\u03bb2n might be applied to object 2. Thus, we will need to show that even though we have treated each contact between objects as two separate constraints (as in Figure 13(b)), the forces that actually arise at the contact point will be the same as would occur if the contact really was split. Given the original assembly shown in Figure 14(a), we would split the contact between objects 1 and 2 as shown in Figure 14(b). We then separately fixture object 1 by itself, ignoring its contact with object 2 but making use of the constraint on object 1 induced by the splitting. As the example in Figure 14(b) shows, object 1 requires only two fixels for form-closure. Next, we separately fixture the assembly consisting of objects 2 through n, as denoted in Figure 14(b) (the fixels are not shown in this figure). Again, we ignore the contact between objects 1 and 2 and instead make use of the constraint induced by the splitting. The final fixel set produced is simply the union of the two fixel sets. THEOREM 7.1. Given an assembly of n planar objects with an acyclic contact graph, and such that a pair of objects has at most one mutual contact point,8 a minimal set of fixels yielding form-closure can be found in O(nN 6 f ) time. PROOF. The proof is by induction on the number of contact points",
            " Clearly, an assembly with n objects and no contact points can be minimally fixtured for form-closure by applying an exhaustive search algorithm separately to each object. Given a set of Nf fixels, the maximum time to fixture object i minimally is O(N 6 f ). All n objects can be minimally fixtured for form-closure in at most O(nN 6 f ) time. We assume that the theorem applies for assemblies with m contacts, and consider an assembly with m + 1 contacts. Since the contact graph of the assembly is acyclic, there must be some object that contacts only one other object. (Note that contact with immovable obstacles has no effect on the contact graph; hence in Figure 14(a) object 1 is said to contact only one other object, namely object 2.) Without loss of generality, we assume that object 1 contacts object 2, and no other objects. We label this contact as contact m + 1. We split the assembly, as shown in Figure 14(a). Separately fixturing object 1 requires at most O(N 6 f ) time. Likewise, separately fixturing the assembly consisting of objects 2 through n, ignoring contact m+1 but taking the new constraint on object 2 into account, 8 We believe that the theorem applies even if a pair of objects contact each other at multiple points. requires O((n \u2212 1)N 6 f ) time, by inductive assumption. We claim that the union of the fixels chosen for the two separate problems will in fact yield form-closure for the entire assembly",
            " The matrix V1, like U1, only describes forces involving object 1, so all but the first three rows of V1 are zero. Similarly, the first three rows of V2 are zero as well. We claim that FA \u222a FB induces form-closure on the entire assembly. The contact matrix for the original, unsplit assembly has the form U = [U1 | U2 | um+1], the contact matrix U\u2032 for the split assembly has the form U\u2032 = [U1 | U2 | uA | uB], where uA = (d1, 0, 0, . . .) and uB = (0, d2, 0, . . .). Now consider the assembly with contact m+1 split, as in Figure 14(b). Since FA achieved form-closure on a single object (namely, object 1), the composite matrix [U1 | uA | V1] must have rank 3. Similarly, FB form-closed the other n \u2212 1 objects, so the composite matrix [U2 | uB | V2] has rank 3(n \u2212 1). Since um+1 = uA + uB , this implies that rank[U1 | U2 | um+1 | V1 | V2] = rank[U | VFA\u222aFB ] = 3n. Thus, FA \u222a FB satisfies the first condition of Theorem 3.3. The fixel set FA \u222a FB also satisfies the second condition of Theorem 3.3. Since the fixel sets FA and FB form-close all the objects in the split assembly, by definition rank[U\u2032 | VFA\u222aFB ] = 3n and there exist strictly positive vectors \u03bb and \u03b1 such that U\u2032\u03bb+ VFA\u222aFB\u03b1 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003052_980220-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003052_980220-Figure10-1.png",
        "caption": "Figure 10. Submodel III. Describes rotations of wheels (degrees of freedom: \u03d5j, j=5, 6, 7, 8)",
        "texts": [
            " They may be a result of real road measurements or the realisation of stationary gaussian random process describing real road according to ISO recommendations [28]. For some motion cases (mainly even road motion) it is possible to simplify and speed up model construction process. Division into partial models was applied [16]. The main model is divided into 3 type coupled sub-models. For example for car model they are: \u2022 submodel I (Fig. 8) which describes basic motion of the vehicle (degrees of freedom: , ), \u2022 submodel II (Fig. 9), which describes body and unsprung masses vibrations (degrees of freedom: , \u03d51, \u03d11, ), \u2022 submodels III (Fig. 10), which describes rotations of wheels (degrees of freedom: \u03d55, \u03d56, \u03d57, \u03d58). The submodel II generates current values of normal reactions of the road that are input values for the tyre model (mentioned above). Truck model is divided in analogical way. In this case submodel II has dependent front suspension. x yO O1 1 , \u03c81 zO1 \u03b6 \u03b6 \u03b6 \u03d1 1 1 1 4 2 3 4O O O' ', , , 5 EQUATIONS OF MOTION THE MAIN MODELS \u2013 The equations of motion were derived from Lagrange equations of 2nd kind. In the matrix format the equations take the following form: (Eq",
            "8 4 6 Body CG height h [m] (d \u03c8\u03c8 /d t) [ ra d/ s] right right left left &\u03c81ss S S SS EE E E S S S S EE E E 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 P 0 : 1.5 0 9 P 1: 1.5 6 6 P 2 : 1.7 3 6 P 3 : 1.8 4 6 Body CG height h [m] t [ s] right right left left &\u03c81 13 E - result of experiment, S - result of simulation The presented results as well as many others show good compatibility between simulation and experiment for biaxial car and truck model. EXAMPLE OF MORE COMPLICATED STEERING SYSTEM MODEL APPLICATION The combination of submodel I (Fig. 8), 4 submodels III (Fig. 10) and steering system submodel (Fig. 7) was applied to simulate small car motion. Normal reactions of the road were described using quasi-static formulas, assuming existence of four supporting spring elements for each wheel (suspension and tyre elasticity in series). Fig. 33\u00f736 show results obtained for low velocity (~10 km/h). Fig. 33 presents time histories of steering-wheel angle \u03b1k as well as moments on steering-wheel Mk. Fig. 34 shows CG trajectory on road plane Oxy. Fig. 35 presents steering-wheel moment Mk as a function of steering-wheel angle \u03b1k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002459_941761-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002459_941761-Figure7-1.png",
        "caption": "Fig. 7 Off-line of Action Contact during Recess. Pinion tip",
        "texts": [
            "4 degrees of roll, a second pair of teeth has 2 come have been into contact. only one Theoretically, tooth pair in contact. at this position, The second there p a . would has (b) Pinion root come into contact early due to tooth deflection. On this second Pinion tip tooth, contact occurs at a point above the start of the active profile (SAP). The contact on the second tooth is off the line of action. This can be seen in Fig. 6. An exaggerated view of the circled region is drawn for clarity. At -6.0 degrees of roll, contact has moved to the line of action. Fig. 7 shows contact during recess. At 5.2 degrees of roll, there are two pairs of teeth in contact and contact is along the 2 line of action. Theoretically, at 6.2 degrees of roll, the first pair & (c) Pinion root of teeth should have left contact. But due to tooth deflection, Pinion tip the first pair is still in contact at the tip of the pinion. This can be seen in Fig. 7 and again the contact is off the line of action. Figure 8 shows the load distribution obtained from LDP using the off-line of action model. The load is projected on the pinion tooth plane of action. The horizontal direction represents the facewidth of the pinion. Figures 8-a, 8-b, and 8- c show the load distribution in the premature contact region. In 2 (a) P i o n root the theoretical case, there would be only one pair of teeth in contact at these mesh positions. But in Fig. 8-a the second pair Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003177_1.2831304-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003177_1.2831304-Figure1-1.png",
        "caption": "Fig. 1 Configuration of the modified incremental projection method for the steady-state solution of the non-proportional cyclic loading problem",
        "texts": [
            " (1993) used Zarka's projection method (Zarka, 1980) but in an incremental form to find an approximate eigenstrain field. In the present analysis, a modified incremental projection method is employed. The nonproportional loading path is di vided into several segments. The elastic deviatoric stress states are denoted as (5'fj)\u201e and {S'j)\u201e+x, respectively, at the beginning and end points for the nth increment and C\u201e and C\u201e+i represent the yield surfaces corresponding to iS\"y)\u201e and (5fj)\u201e+i, respec tively (Fig. 1). The modified back stress (Ty),, is assumed to be originally within C\u201e prior to the current increment. Using a von-Mises yield criterion, the numerical procedure for a modi fied incremental projection method (Fig. 1) is listed as follows. {Yy), = Q. (17) {Y;j)\u201e^, = iYy\\ iifiiy)^Q (18) iy>j)n.^ = (5J)\u201e.l - KylkuUI i f / ( 6 ; ) > 0 (19) where ^y = (5'y)\u201e+i - {Yij)\u201e. In general, the method provides an approximate way to determine the modified back stress path. A final modified back stress field at the steady state can be obtained after applying the projection method repeatedly through each segment of the elastic loading path. After the eigenstrain field, c~^Yy, is obtained, the numerical solution of the inelastic problem is carried out using the finite element method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure11-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure11-1.png",
        "caption": "FIGURE 11. Cross section of a hydrostatically supported bearing holder in a bearing testing machine.",
        "texts": [
            " A further application of hydrostatic lubrication, which may be of interest here, is in machines for measuring the friction force or torque of bearings or other test surfaces. In such machines, the friction force on the sta- tionary member is counterbalanced by springs or dead weights until the member is in equilibrium. It is then important that no extraneous static friction be present in the supports which might hinder virtual displacement of the member as the friction force changes. Hydrostatic lubrication is clearly indicated for these supports. FIGURE 11 demonstrates the appli- Burwell: Full Fluid Lubrication 775 cation in a journal-bearing testing machine. Hydrostatic lubrication is applied between the bearing holder and the loading shoe so that there is no static friction on the bearing holder arising from the loading shoe. It is also possible to use the same high pressure oil to apply the load to the loading shoe and to lubricate the bearing holder surface hydrostatically. This concludes the discussion of new fluid lubrication principles. The remaining section will be devoted to the thermal aspects of bearings lubricated by any fluid means"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003303_12.275681-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003303_12.275681-Figure2-1.png",
        "caption": "Figure 2: Planetary Geartrain Assembly.",
        "texts": [
            " This figure displays components of the rotor test rig facility used for aerodynamic loading of blades in hover. The torque to the rotor blades is provided by an electric motor which drives a planetary geartrain whose output is connected to the rotor shaft via a belt drive. The planetary geartrain provides a reduction of 4:1, and the belt-drive provides an additional reduction of 5:3. Therefore, the overall transmission reduction of this system is approximately 6.67:1. Closer inspection of the planetary geartrain (see Figure 2) reveals that there are three planet gears, a sun gear and a ring gear. The planet gears have 24 teeth with a standard pitch. Two piezoelectric strain sensors were placed 120 degrees apart along the circumference of the ring gear. Strain time histories from these sensors were used as input for the DHWT. 47 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/23/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx 4.1 Experimental Method 4 RESULTS ON SIMULATED FAULTS Three simulated fault cases were considered in this analysis: missing tooth, spalled gear, and cracked gear. These three cases are displayed in Figure 3. The first test run used only undamaged gears. For each subsequent run, one good planet gear from the geartrain of Figure 2 was replaced with a damaged planet gear. Time series data was collected using an Hewlett Packard model 35650 data acquisition system. In each case both stationary and non-stationary analyses were performed. 4.2 Stationary Analysis 4.2.1 Fourier transform (= f(tm))Kurtosis = N 2 f(tm)2) The most common technique in vibration signature analysis is to compute the FFT or power spectrum of the time signature from the measured time series. The FFT of the strain time history for each test run is displayed in Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003709_ias.2000.882064-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003709_ias.2000.882064-Figure3-1.png",
        "caption": "Fig. 3: Stator flux with the possible applicable voltage space vectors.",
        "texts": [
            " The outputs of these comparators, h, and h, for flux and torque, respectively, with the section where the 0-7803-6401-5/00/$10.00 0 2000 IEEE actual flux is located form together the input values of a predefined look-up table (see [2] and Fig. 1). The DTC algorithm is based on the control of the flux on the basis of the stator equation. After neglecting the ohmic voltage drop in (l), remains which will imply that the flux will tend to follow the direction of the applied stator voltage space vector, see Fig. 2. In the particular situation of Fig. 3, the stator flux has to increase, which will automatically exclude the voltage space vectors, V3, V4 and V5. Voltage vector VI will only imply a flux increase and is not used in the traditional DTC method. Vector Vz will take care for a torque increase (counterclockwise is considered positive) and vector V6 for a torque decrease. The zero voltage vectors Vo and V7 are applied when the torque is in the vicinity of its reference. These zero vectors will take care for a low switching frequency for reducing losses in the power semiconductors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure16-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure16-1.png",
        "caption": "Fig. 16. (a) The perceived shape of the space CFNS(ti) generated by the robot R5: (b) The simplified traffic patterns L4; L7; L2; L6 generated by R5:",
        "texts": [],
        "surrounding_texts": [
            "Since the major goal of the traffic language is to assist an autonomous robot to represent and understand the traffic priorities of the other moving objects in the same navigation space avoiding collisions, it is necessary that the synthesis of traffic priority patterns to be defined semantically. Notation: a) (commutative) with b) (associative) with and Definition: The length of a perceived pattern is defined as the number of corridors which compose the pattern. Corollary: Two perceived patterns (generated by the same or different robot, at the same time for two different moving objects) with the same length are not necessarily identical in shape. Definition: The synthesis # (semantically) of two traffic patterns determines the order of the robots priorities one against the other. Proposition: (commutative) Proof: Let assume that three robots are moving in the same navigation space, as shown in Fig. 10. The robot is the main one and are the secondary robots. For this particular case, and Thus, the pattern produces the relationship between the robots\u2019 priorities. The pattern provides the priority relationship Thus, the synthesis provides the relationship (1) among the robots\u2019 priorities. Now, the synthesis provides (2). These two relationships are identical, which means that Following this process easily it can be proved the general case Proposition: (associative) Proof: Similar to commutative. Notation: (identity traffic pattern) for every Corollary: In a free navigation space with secondary moving robots there is a possibility of existence of the following traffic pattern configurations. 1) There is a maximum of two patterns with . 2) There is a maximum of one pattern with or . 3) There are patterns such that where Corollary: In a free navigation space FNS if there are the traffic patterns and the there is not the pattern where the sequence of the values for the indexes are and or and or and Traffic Complexity Table II presents the traffic complexity of moving robots in a CFNS under two different assumptions. \u2022 In the first assumption, called individual, a robot views all the other moving robots, generates all the traffic patterns from its own position and calculates all the possible traffic priorities of the other robots against its own priority. \u2022 In the second assumption, called global, every robot views all the other moving robots, generates all the traffic patterns and calculates all the possible traffic priorities for all the moving robots including itself. V. ILLUSTRATIVE EXAMPLES In this section, two illustrative examples for traffic cases are provided and solved by using the KYKLOFORIA language. In the first example, the traffic case includes six moving robots in a free navigation space shown in Fig. 11. Figs. 12\u201317 provide the shape of the free navigation spaces observed TABLE III SIMULATED RESULTS FOR FIG. 18 by each moving robot and the traffic patterns generated by each of them in their own free space. In the Fig. 18, the velocities of the moving robots are considered the same, thus the traffic priority relationships generated by the traffic language are given in Table III. Each moving robot knows the traffic priority relationships in the same free space. Thus, the robot makes use of its own which is higher than and goes out of the narrow corridor. At a time min, covers a distance of 4.5 m. The robot has to wait of a period of 0.6 min, and then it proceeds into the open corridor by covering a distance of 1.4 m in 0.485 min. Initially, covers a distance of 1.3 m in 0.325 min, then it slows down and waits for 0.55 min before it proceeds into the narrow corridor following the robot and covering a distance of 0.9 m in 0.23 min. The robot using its own higher priority over covers a distance of 4.5 m. The robot waits for 0.75 min and then proceeds forward by covering a distance of 1.5 m. Finally, the robot covers a distance of 4 m in 1.125 min because it spends some time to change its direction. Note that, and TABLE IV SIMULATED RESULTS FOR FIG. 19 (a) (b) Fig. 14. (a) The perceived shape of the space CFNS(ti) generated by the robot R3: (b) The simplified traffic patterns L1; L7; L2; L6 generated by R3: change their directions (as shown in Fig. 9) avoiding a possible collision. In the case that the velocities of the robots are considered different, then Table IV shows the traffic priority relationships and the robots traffic paths and locations are given in Fig. 19. In particular, present a traffic behavior similar to the previous case with the same velocities, by using the Table IV. covers a distance of 4.9 m with m/min. covers a distance of 1.4 m with m/min. covers a distance of 1.3 m with m/min and a distance of 0.6 m with m/min. waits until passes the intersection point and then covers a distance of 1 m with m/min. covers a distance of 4.8 m with m/min. Finally, covers a distance of 2.5 m with m/min. The second example explains the use of the language for the improvement of the traffic schedule of a particular robot under the assumption that the local traffic flow in a certain region is almost the same every time that the robot enters that region. In this case, the robot enters the region from left to right at time and spends min crossing it. At that time, there are three other moving robots crossing the same region from different directions (see Fig. 20). The traffic flow extracted by the robot in that region, is represented by the following language words: The symbol & represents the synthesis operator between words for the formulation of the traffic flow extracted by a robot traveling through a region where In this particular case there is no delays during the traveling. Fig. 21 shows the same region, at a different time where the robot enters the region from the right to the left in order to cross it by following the reverse path of Fig. 20. At this time there are four other moving robots and a fifth one is coming to the same region. The traffic flow extracted by the robot is represented by the following words: where In this particular case there are delays due to conflicts between the robots directions and traffic priorities. More specifically, the robot has to wait until and pass first and then it continues its own path. This mean that the robot knows the time required to cross the region, and in the latter case it took more time, At this point the robot analyzes the traffic flow perceived by itself and modifies its traffic path for a future cross of the same region under a traffic flow similar to More specifically, it follows the next algorithmic steps: 1) Check each word , for patterns . 2) Search for possible patterns , to replace in a word . 3) Replace the first with an in . 4) Rearrange the word into a new one , which includes the affects on the other patterns due to replacement ( instead of ). 5) If the new word includes less number of patterns then use it in the new , else go to 2 to replace the next with an in . 6) If the new overall traveling time is less than the original then proceed else no changes Thus, Fig. 22 shows the new modified traffic path. The new traffic flow extracted by is represented by the following words: where Thus, the new traffic flow includes less conflicts and no significant delays for the robot"
        ]
    },
    {
        "image_filename": "designv11_31_0003000_ip-epa:19982170-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003000_ip-epa:19982170-Figure1-1.png",
        "caption": "Fig. 1 Internal fan system",
        "texts": [
            " Introduction As the end windings of high speed induction motors are usually very long, a considerable part of the copper loss is concentrated there: Zautner [l] observed that approximately 69% of the copper loss was concentrated at the end windings. The ventilation system for removing the heat generated is provided by the fan effect caused by the rotor bar extensions and wafters fixed to the rotor end ring, Fig. 1. As a large portion of the heat emitting surface area of the stator winding belongs to the end windings, the effectiveness of the end region ventilation system materially affects the temperature distribution of the whole stator winding. This ventilation system produces a complex threedimensional, turbulent, unsteady flow field. Its optimisation requires careful management of the convective heat transfer and the resultant ventilation losses. A prerequisite to achieving this is a fundamental understanding of the effects of the parameters that control the flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002245_ee.1945.6440880-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002245_ee.1945.6440880-Figure3-1.png",
        "caption": "Figure 3. Line-to-line short circuit on a syn",
        "texts": [
            "i-^Positive-sequence resistance chronous machine 68 TRANSACTIONS Kirschbaum\u2014Transient Electrical Torques ELECTRICAL ENGINEERING Rz\u2014Negative-sequence resistance Ra\u2014D-c resistance of stator Tdo\"\u2014Subtransient-open-circuit time con stant in direct axis\u2014seconds Tdo'\u2014Transient-open-circuit time con stant in direct axis\u2014seconds Machine and system quantities (per unit unless noted otherwise): e\u2014Instantaneous machine (or system) voltage i\u2014Instantaneous-phase current E\u2014Effective machine (or system) volt age Xs\u2014System reactance Re\u2014External resistance \u00ab, 0, 5\u2014Angles defined in Tables I and II /\u2014Fundamental frequency in cycles per second co\u20142vf t\u2014Time in seconds after the initiation of the circuit transient Appendix II. Line-to-Line Short Circuit During a line-to-line short circuit, Figure 3a, the alternating armature currents can be calculated by using the method of sym metrical components. With the positiveand negative-sequence networks connected as shown in Figure 3b, the sequence com ponents of armature current can be deter mined, and from these the armature current. The instantaneous voltage of phase a be fore the short circuit is ea \u2014 E cos (wt+a) This voltage is proportional to the rotor flux, which, after the short circuit, decays because of the demagnetizing effect of the armature current. The decrement factor for this flux has been derived by Doherty and Nickle and is 1 U - [Xd'+Xri-Xo] in per unit M = -[Xd*+X2\u20142XoJin per unit o The a-c symmetrical components of cur rent are tax\u2014 \u2014*o2 \u2014' EFsin (t-\\-a) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002735_0094-114x(92)90062-m-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002735_0094-114x(92)90062-m-Figure2-1.png",
        "caption": "Fig. 2",
        "texts": [
            " The crux of force analysis of multiloop spatial mechanism is to solve the constrain reactions of main pairs which connect the central link and branches. Once the reaction on main pairs are obtained, the reactions on all other pairs are easy to calculate. For the hypothetic mechanism shown in Fig. I(c), after the main pair in branch AC(r -, I) in which link 4 is the real input link is disconnected from the central link, the actions of the central link on the branch, including force \u00a2r,s and moment ~'ts, are expressed in a six-dimensional vector _E6s - ( ~ ) T , which is resolved along the local reference system 06 - X6 Y6Z6, as shown in Fig. 2. For the local reference system, the Z6 is along the kinematic pair's axis Sk, Xk along ~k-s~, and Yk is determined by right-hand law. The origin Ok is located at the center of the kth pair. The fixed reference system is Oo - Xo YoZo. As the virtual displacement 6~7~ of point 06 is related with the virtual displacement 6q~*(n = 1,2 . . . . 6) in the branch as _,_ a 8 0 6 , 6S, , . - 6\u00a2,* T v .2 + . . . + 6 \u00a2 , . (7) From the definition of kinematic influence coefficient [7, 8], expression (7) can be rewritten as 6 (8) In the same way, the virtual angular displacement 6~_p of central link is related with 6~* as well, such that: 6 Y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.6-1.png",
        "caption": "Fig. 9.6. Determination of the reduced stiffness of a mechanism",
        "texts": [
            " In an involute meshing the contact stiffness of a spur gearing is defined as the ratio of the force, acting at the contact point and directed along the common normal of the teeth profiles, to the total deformation of the teeth, arising at the contact point (Fig. 9.5). For gearings with steel wheels the stiffness can be determined according to the formula [10, 11] Cl2 = kb, where b is the width of the gear rim and k = 15 x 109 N/m 2 . 9.2 Reduction of Stiffness. Inlet and Outlet Stiffness and Flexibility of a Mechanism (9.6) Let us consider a mechanism (Fig. 9.6) with an elastic element with stiffness equal to c. We fasten the input link GA, thus fixing the value of coordinate q, and apply at point K a force P directed along the axis Kx. Then, a balancing force F directed from B to A, and a deformation () occurs at the elastic element. From the principle of virtu'll work we find that Ft5() + POx = 0, (9.7) where t5() and Ox are virtual displacements. From here we obtain F = -p(Ox/ t5())= -P(dx/ d()} (9.8) Force F causes a small increment of the elastic element, opposite in direction to this force: /1() = -F / c",
            " (9.9) As a result of the deformation of link AB a displacement of point K occurs: Ax = (dxl dO) !:J. 0 = -(dxl dO)Fc-1 = (dxl dO)2 Pc-I. (9.1 0) The ratio cK:x = PI Ax = c(dx I dO)-2 (9.11) is called the stiffness of the elastic element reduced to the x -axis at point K. Analogously the reduced flexibility is defined: (9.12) In the same way a reduced angular stiffness of an elastic element with respect to some axis is defined. In order to determine the angular stiffness of an elastic element (Fig. 9.6) with respect to axis D we apply a moment M to link BD, and let the link tum through on angle !:J.a. From the relationship M!:J.a + F!:J.O =0 wefmd From here we obtain the reduced stiffness CD: (9.13) Let us consider a mechanism with two elastic elements arranged in series (Fig. 9.7). In this case we have where 0\\ and O2 are deformations of the elastic elements. Defming the total dis placement of point K in the direction Kx, we obtain Ax = (ax I 001 )!:J.81 + (ax I 882 )!:J.82 = p(cJI (ax I 881 f + c2\"1 (ox I 882 )2 )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003570_37.856182-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003570_37.856182-Figure8-1.png",
        "caption": "Figure 8. Diagrams of the describing and transfer functions.",
        "texts": [
            " The open-loop transfer function of the system is L j G s Kc( ) ( )\u03c9 = August 2000 IEEE Control Systems Magazine 93 while the describing function of its nonlinearity has the following expression [23]: N A A d M d d f d A d A d M ( ) , ,= < \u2264 \u2212 \u2212           < \u2264 0 0 1 1 2 1 1 1 2 if if d d f d A f d A d A 2 1 2 1 2\u2212     \u2212           <          , if where ( )f x x x x( )= + \u22122 1 2 \u03c0 arcsin . This describing function does not depend on the frequency and is always real and greater than or equal to zero. The negative of its inverse, \u22121/ ( )N A , is shown in Fig. 7. It starts from \u2212\u221e for very low amplitudes until it reaches a negative maximum. After that, it tends again to \u2212\u221e for very high amplitudes. The Nyquist plots of L s( ) and \u22121/ ( )N A are drawn in a polar diagram in Fig. 8. Although the graph of \u22121/ ( )N A is on the real axis, this graph has been plotted off of it to display its shape. It can be seen that the graphs of L s( )and \u22121/ ( )N A do not intersect each other since the model is second order, and therefore the open-loop transfer function can only cut the real axis at the origin and at frequencies tending toward infinity. The fact that there is no intersection between the two graphs implies that there is no theoretical possibility of existence of limit cycles according to the describing function method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003712_cdc.1994.411123-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003712_cdc.1994.411123-Figure2-1.png",
        "caption": "Figure 2: A 5-axle trailer system with the f i s t and third axles steerable. This is the only configuration of the 5-axle system with two steering wheels which does not satisfy the conditions for converting to extended Goursat normal form.",
        "texts": [
            " Without presenting the calculations, which are similar than those above, it is noted here that the five-axle system with either the first and second axles steerable or the first and last axles steerable satisfies the conditions for conversion into extended Goursat normal form. The constraints have the same form. For the 1-2 steering system, T can he chosen as dx5 and the Goursat coordinates are found as zo = x5,z: = y5, and 2: = 4. For the 1-5 steering system, x can be chosen as dxl, and the Goursat coordinates are defined as 2' = x(, 2: = y4, and 2: = 4. Example 2. 5-axle, 1-3 steering. The final instance of the 5-axle trailer system has the first and third axles steerable, as sketched in Figure 2. The vector 9 = (25, y5,85,84,93,8~,81,~} represents the state. The constraints are that each axle roll without slipping: a' = sinO,dx, - cos9,dy, i = 1,2,4,5 a3 = sinbdx3 - cosddy3 ThePfaftiansystemis I = {a',a2,a3,a4,a5},andacomplementto the system is given by {dd, d81, dx3 1. This basis is adapted to the derived flag, I = {a', a2, a3, a4, a5} I ( ' ) = {a2, a4, a5} 1 ( 2 ) = {a5} i o } 1 ( 3 ) = however, the congruences are nof satisfied: da' E CI dB1 A dx5 da2 I c2 a' A dx5 + k2 a' A a3 da3 E c3 d$ A dx5 mod I da4 E c4 a3 A dxs mod I ( ' ) de5 E cg a4 A dx5 mod d2) In order to have { l ( 2 ) , r } integrable, x must be chosen as x = dx5 (mod {a4,a5})"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002958_70.508438-Figure17-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002958_70.508438-Figure17-1.png",
        "caption": "Fig. 17. Illustration of the grown region G, of a cube.",
        "texts": [],
        "surrounding_texts": [
            "XIAO AND ZHANG: GROWING A POLYHEDRON BY ITS LOCATION UNCERTAINTY 559\nis the grown region of the plane a by the orientation uncertainty of P , where a ( M ) denotes the corresponding plane which a occupies when P is at orientation M . A , ( k ) can be abbreviated as A,.\nTheorem 7: For a plane a which contains a face f E P and therefore rigidly attached to P, the boundary surface of the grown region A , ( M ) of a consists of two surfaces Af,, and A,,,,, such that\n1) if 0 is on a, Af,, and A,,,, are the boundary surfaces of the two nappes of the circular cone with angle being (7r/2 - E , ) whose apex is at 0 (Fig. 15(a)); 2) if 0 is not on a and d denotes the distance vector from 0 to the closest point d E a, and K denotes the circular cone with angle being ( ~ / 2 - E , ) whose apex is at position d/ cos E , , then Af,, is the boundary surface of the nappe of K further from 0 along d, and A,,,, consists of the boundary surface of the other nappe and the grown surface D, of the point d as described in Theorem 4 (Fig. 15(b)).\nProof: First, let us focus on the case where 0 is on a. Consider a unit normal vector n of a originated from 0. n is rigidly attached to a, and thus to P. By Definition 2, when P is at all orientations in No, the vector n is within the orientation uncertainty cone of angle eo with vertex at 0 (Fig. 16). When n sweeps the boundary surface of the cone,\nfar\n(a)\nFig. 15. The surface of A,.\nFig. 16. The normal vector n of a.\nthe plane a, always perpendicular to n, sweeps the boundary surface of A, accordingly, which is the surface of the circular cone as stated in the theorem (Fig. 15(a)).\nIn the case where 0 is not on a, the position vector d of d is a normal vector of a. When P is at all orientations in No, by Definition 2, d is within the orientation uncertainty cone of angle E , with vertex at 0, and by Theorem 3, the point d is on a spherical surface D, with the boundary circle Z(d). When d sweeps the boundary of the cone, i.e., when d sweeps the circle l ( d ) , the plane a, always perpendicular to d, sweeps the boundary surface of A, accordingly, which is the surface as stated in the theorem (Fig. 15(b)).\nD. Growing a face f of P\nfixed, DeJnition 7: For any face f E P if the position of P is\nT o ( & ) = U f ( M ) M \u20ac N , ( M )\nis the grown region of the face f by the orientation uncertainty of P , where f ( M ) denotes the corresponding planar surface which f occupies when P is at orientation M . F , ( k ) can be abbreviated as Fa.\nTheorem 8: For any (planar) face f E P, which is bounded by e l , e 2 , ..., em edges, where m 2 3, the grown region F, of f is a closed region obtained by the union of the grown regions &:, E:, ,,., E,\", and the part of the grown region A, of the plane a containing f which is bounded by &: , \u20ac2, . . . , E,\".\nProof: Because the planar face f is a closed set that is the part of the plane a bounded by the edges e l , e 2 , . . . , em, by Definitions 6 and 7, the grown region To of f is also a closed set that is the part of the grown region of a bounded by the grown regions of the edges of f .\nV. GROWING A P BY BOTH POSITION\nWe first define the grown regions of a point, an edge, and a face of P by location uncertainty, consisting of both position and orientation uncertainties.\nAND ORIENTATION UNCERTAINTIES",
            "560 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 12, NO. 4, AUGUST 1996\nDefinition 8: For any point q E P or rigidly attached to P, any edge e E P, and any face f E P, the regions Q(L), E ( L ) , and 3 ( L ) , defined as\nare the grown regions of the point y, the edge e, and the face f by the location uncertainty of P respectively, where q( L ) , e (L ) , and f ( L ) denote the corresponding point, edge and face which y, e, and f occupy respectively when P is at location L. Q(i), &(E), 3(i) can be abbreviated as Q, E , and 3 respectively. If q = w, a vertex point of P , then Q can also be denoted as V .\nGiven a point q, an edge e, or a face f of a polyhedron P , whose estimated location is L = (p, &f), to obtain V , E, and 3, we can first obtain the grown region &,(PI of q , Eo(p) of e, or 3,(p) o f f (Section IV), and then grow the obtained V,, &, or 3, by position uncertainty ep .\nNote that since V,, E,, and 3, are not polyhedral, Section I11 cannot be readily applied to growing them by position uncertainty. However, growing a region by position uncertainty is not difficult to achieve in the first place: by \u201crolling\u201d the position uncertainty ball along the boundary surface of the region, in our case, the boundary surface of a V,, E,, or F,, with the center of the ball on the surface, the boundary surface swept is the boundary surface of the grown region V , E , or 3.\nSpecifically, the grown region & can be obtained by translating the surface &, (described in Theorem 3) up and down a distance E , and filling the gap between two translated images of Q, by \u201crolling\u201d the position uncertainty ball along the boundary curve of &, with the center of the ball on the curve. The description of the grown region & of an edge can be obtained based on the grown region Q of a point by similar derivations as those in Section IV-B. The grown region A of a plane a containing a face f E P by both position and orientation uncertainties can be obtained by translating the surface A,,,, of A,(p) (see Section IV-C) toward the center of rotation 0 a distance E , and the surface At,, away from 0 a distance ep . Finally, the grown region 3 of the face f can be described based on A and the grown regions I \u2019 s of the bounding edges of f in the similar way as described in Theorem 8.\nVI. GROWN REGIONS, GROWN SHELL REGIONS, AND CORE REGIONS OF A POLYHEDRON\nGiven the grown regions of individual faces of a polyhedron P: Fp\u2019s, T o \u2019 s , and F\u2019s, as the results from Sections 111-V, respectively, we can describe three types of uncertainty-related regions for the polyhedron P itself: the grown regions of P, the grown shell regions of P, and the core regions of P as the following.\nDejinition 9: For a polyhedron P its grown regions 8, by position uncertainty, Go by orientation uncertainty, and s by location uncertainty are the closed regions bounded by the union of FP\u2019s, the union of Fa's, and the union of 3 \u2019 s respectively, of the faces of P ; its grown shell regions S, by position uncertainty, So by orientation uncertainty, and S by location uncertainty are the union of FP\u2019s, the union of 3 , \u2019 s , and the union of 3 \u2019 s respectively, of the faces of P ; its core regions C, by position uncertainty, CO by orientation uncertainty, and C by location uncertainty are the set differences (& - S,, 6, - S,, and B - S respectively.\nThe meanings of these regions are given in the following theorem.\nTheorem 9: G,, go, and are the uncertain regions possibly occupied by P under position, orientation, and location (i.e. both position and orientation) uncertainties respectively. S,, So, and S are the uncertain regions possibly occupied by the boundary surface of P under position, orientation, and location uncertainties respectively. C,, CO, and C are the regions definitely occupied by P regardless of position uncertainty, orientation uncertainty, and location uncertainty respectively.\nProof: The interpretations of the grown regions and the grown shell regions are quite obvious so that we only focus on those of the core regions below. By Definition 9, the core region C, is the region enclosed by the region S,. For a fixed orientation of P, let P ( p ) denote the region which P occupies at position p. Since b\u2019p E NP, the boundary surface of P ( p ) is contained in S,, thus P ( p ) 3 C,. Similarly, for a fixed position of P, let P ( M ) denote the region which P occupies at",
            "XIAO AND ZHANG: GROWING A POLYHEDRON BY ITS LOCATION UNCERTAINTY 561\norientation M , and we can show that VM E No, P ( M ) 3 Co. Furthermore, let P(L) denote the region which P occupies at location L, and we can show that V L E N, x No, P ( L ) 3 C .\nNote that when uncertainties are too large, the core regions can become empty. Specifically, when the position uncertainty E , is so large that the family of grown regions of the (boundary) faces of P becomes a cover of P at p, then G, = s, and C, = 0. That is, no region is guaranteed to be occupied by P . Similar phenomenon can occur to core regions CO and C.\nFigs. 17-19 illustrate the grown regions G,, Go, and G respectively of a cube whose object frame is established at its center.\nVII. APPLICATION To CONTACT RECOGNITION\nA. Contact Model\nA contact situation between two polyhedra can be described in terms of the topological contacts among their surface elements, i.e., faces, edges, and vertices.\nDejinition 10: Aprincipal contact (PC) is the single contact between a pair of topological surface elements from different objects which are not the boundaries of other contacting topological elements (if there is more than one pair in contact).\nFor example, the upper leftmost picture in Fig. 20 shows a PC of face-face (f-f) and not of edge-face or face-edge (fe or e-f) or other types. Theoretically, there are ten types of possible PC\u2019s as shown in Fig. 20.\nDefinition 11: A contact formation (CF) represents a contact situation as the set of principal contacts formed (e.g.,\nNote that the concept of CF is mostly aimed at describing a contact situation between two nonconvex objects. For two convex objects in contact, the CF should contain only a single PC .\n{< fllf,\u201d >,< e M >,. . .>I.\nf-f\ne-v v-e\nf-e e-f\nf-v v-f e-cross\nFig. 20. Principal contacts. e-touch v-v\nB. Approach\nBased on the contact model defined, the problem of contact recognition (as introduced in Section 1) can be formulated as: given two polyhedral objects PI and P2 in collision, their geometric models, and their estimated locations, find the contact formation between them taking into account location uncertainties.\nFirst, we can apply the technique of growing polyhedra by their location uncertainties to obtaining the set of all possible (due to uncertainties) principal contacts between PI and P2. We denote such a set as SPc.\nSince contacts only occur between the boundary surfaces of two objects, all possible contacts between PI and P2 due to uncertainties manifest to intersections between their grown shell regions only. As the result, we can analyze the intersection between the grown regions of one pair of surface elements (u1, u2) at a time, where u1 (or u2) is either a face, an edge, or a vertex of PI (or P2), and continue the process until all pairs of such intersecting regions are considered. We certainly can also consider all such pairs of grown regions in parallel with a parallel processor. In any case, the task then is simplified to that of finding a mapping from the intersection between the two grown regions of u1 and u2 to whether or not the principal contact < u1, u2 > possibly exist. The implementation of such a task is described in the following subsection.\nOnce the set S,, is obtained, other sensing means can be used to reduce the set. Specifically, vision and/or forcelmoment sensing data can be used to verify if a PC in S,, actually exists or not [25], [4]. The vision and force/moment sensing can expect to eliminate nonexisting PC\u2019s and to reduce Spc , in the most desirable case, to a valid contact formation. Such contact formation shall represent the actual contact situation between PI and P2.\nC. Implementation Although from Sections 111-V, we can describe analytically the grown regions of two surface elements, since the grown regions are nonpolyhedral and nonconvex, how to compute the kind of intersection between two such regions efficiently poses a great challenge. Nevertheless, since we aim at realtime recognition of contacts, to be computationally efficient is necessary.\nOur practical solution at present includes the following two approximations:"
        ]
    },
    {
        "image_filename": "designv11_31_0003022_978-1-4471-1501-4_1-Figure1.2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003022_978-1-4471-1501-4_1-Figure1.2-1.png",
        "caption": "Figure 1.2: Kinematic parameters with modified Denavit-Hartenberg nota tion.",
        "texts": [
            " Notice that the matrix b Re is orthogonal, and its columns bne , bse , bae are the unit vectors of the end-effector frame axes X e, Ye, Ze. Denavit-Hartenberg notation An effective procedure for computing the direct kinematics function for a general robot manipulator is based on the so-called modified Denavit Hartenberg notation. According to this notation, a coordinate frame is attached to each link of the chain and the overall transformation matrix from link 0 to link n is derived by composition of transformations between consecutive frames. With reference to Fig. 1.2, let joint i connect link i-I to link i, where the links are assumed to be rigid; frame i is attached to link i and can be defined as follows. \u2022 Choose axis Zi aligned with the axis of joint i. \u2022 Choose axis Xi along the common normal to axes Zi and Zi+l with direction from joint i to joint i + 1. \u2022 Choose axis Yi so as to complete a right-handed frame. Once the link frames have been established, the position and orienta tion of frame i with respect to frame i-I are completely specified by the following kinematic parameters: ai angle between Zi-l and Zi about Xi-l measured counter-clockwise, li distance between Zi-l and Zi along Xi-l, {)i angle between X i- l and Xi about Zi measured counter-clockwise, di distance between Xi-l and Xi along Zi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003761_1.1701875-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003761_1.1701875-Figure2-1.png",
        "caption": "Fig. 2 Element model of a 3R robot",
        "texts": [
            " into Lagrange equation d dt S ]T ]$q\u0307%e D2 ]T ]$q%e 1 ]V ]$q%e 5$ f ex%1$ f in% (8) yields @M #e$q\u0308%e1@K#e~$q%e2$qr%e2$qt%e!5$ f ex%1$ f in% (9) where $ f ex% and $ f in% are the applied external forces and nodal forces from adjacent elements, respectively. Eq. ~9! is the dynamic equation of the element Transforming the vectors and matrixes of Eq. ~9! into the system coordinates, the dynamic equation of the element expressed in system coordinates can be obtained as @M #s$q\u0308%s1@K#s~$q%s2$qr%s2$qt%s!5$ f ex%s1$ f in%s (10) where, the subscript s denotes the system. Figure 2 shows an example of element model for a flexible 3R manipulator. Each element of the manipulator has its own elemental equation as shown in Eq. ~10!. Putting all the elemental equations together, and considering the damping effect in the system, the dynamic equation of the flexible manipulator can be obtained as following form: @M #$q\u0308%1@C#$q\u0307%1@K#~$q%2$qr%2$qt%!5$Fex1%1$Fex2% (11) Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 where @M # , @C# and @K# are system mass matrix, damping matrix and stiffness matrix, respectively",
            " In this section, a numerical example of two planar flexible robot arms manipulating a rigid object passing through a desired trajectory is presented. The two manipulators are identical and each of them has three flexible links. The length of all links is 0.254 m. The height and width of cross-section are all 0.00508 m. The damping ratio is 0.03. The modulus of elasticity and shear modulus are 7.131010 N/m2 and 2.631010 N/m2, respectively. The material density of aluminum is 2700 kg/m3. As shown in Fig. 2, each link is divided into 5 six-node beam elements. The cooperation of two manipulators is illustrated in Fig. 3. The holding points are A and B, respectively. The grasping configurations are rigid. The distance between the two holding points Lob is 0.05 m. The mass center of the object is at point C. The mass m0 and inertia moment I0 of load are 0.05 kg, 3.125 31025 kg m2, respectively. c15p/3, c252p/3, u150, u25p . Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.9-1.png",
        "caption": "Fig. 2.9",
        "texts": [
            " The turn-off switching can be characterized by: o the reverse recovery timet,,; this is the time needed for the current to turn back to zero; it is timed from t 0 ; o the reverse recovery charge QR; this is the charge corresponding to the existence of a reverse current during the period (t 0 , t,, ). In order to give the precise value oft,, and QR, the following data must be indicated: o the forward current intensity I before commutation, o the time rate of change of the current decrease di/dt, o the reverse voltage applied during turn-off, o the junction temperature. The waveforms in Fig. 2.9 show the influence of time rate of change di/dt and value I of the switched current on the variations of t,, and QR. 2.1 Diodes 27 2.1.3.3 Switching Losses Losses in the diode are usually calculated using idealized waveforms as m 28 2 Switching Power Semiconductor Devices i,v or-~~~~~-----~ -~~\u00b7 ---------.---C-L -VAMt-----'--J Fig. 2.10 2.1.4 Notes on Special Diodes A diode's performances can be judged in three main ways: \u2022 if it can block a higher reverse voltage; \u2022 if its forward-voltage drop in ON state is lower; \u2022 if its switching time is shorter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003332_s0045-7949(98)00128-x-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003332_s0045-7949(98)00128-x-Figure2-1.png",
        "caption": "Fig. 2. Cable under pure tension treated as an axially symmetrical, plain strain problem.",
        "texts": [
            " In the orthotropic sheet theory, the individual layers of wires in an axially preloaded cable are treated as a series of partly self-prestressed cylindrical orthotropic sheets whose non-linear elastic properties are averaged to form an equivalent continuum, and the same kinematical relations are valid for any shape of wires in the continuum. It then follows that the kinematical relations listed in Appendix I, which were originally derived for spiral strands with round wires, are also applicable to any layer of locked-coil ropes irrespective of the detailed shape of the wires in individual layers. Using the notation of Fig. 2, consider a wire element of length dl, mean helix radius in the cable, r, subtending an angle df on a perpendicular cross-section of the cable. For a mean axial stress, s0, and e ective radial and circumferential contact stresses sR and sN based on gross elemental area (i.e. rDrDf), the radial inward equilibrium equation becomes: s0 cos a sin2a r dl cos a rdr df\u00ff sN cos a dl cos a drdf sR r dsR dr dl dr df 0; 1 or s0 tan 2a\u00ff sN sR r dsR dr 0: 2 In the above, s0, sN and sR are all expected to be positive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002824_107754639800400502-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002824_107754639800400502-Figure14-1.png",
        "caption": "Figure 14. The load diagrams of bearing bush number 6 under external forces-different versions of initial clamping: (a) case 1, (b) case 2, (c) case 3, (d) case 4.",
        "texts": [
            " The aim of this research is to define the effect of accidental assembly errors connected with bushes\u2019 clamping in the supports and also to estimate the possibilities of optimizing the bush external fixings. There is no reliable information about this subject in the literature. The computer programs (KINWIR and NLDW) elaborated at IFFM enable this kind of analysis, owing to the complex three-dimensional thermal model of the bearing nodes. The computational research was conducted for various cases of assembly and initial clamping of the bearing bushes (Figure 14). The initial clamping caused deformation of at University of Newcastle on August 28, 2014jvc.sagepub.comDownloaded from 534 the oil clearance (see Figure 15). Such a strong change in the shape of the oil clearance results in changes in the dynamic characteristics of the system under the synchronous external restraint (see Figure 16). It seems that the bearing bush assembly as in Figure 11 d (case 4) is the most profitable for the operation of the whole system, especially for bearing number 6. It is characteristic that the effect of deformation of the oil clearance is relatively small under the external restraint of frequency 2 times the rotational frequency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002322_tt.3020060106-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002322_tt.3020060106-Figure3-1.png",
        "caption": "Figure 3 Scuffed discs",
        "texts": [],
        "surrounding_texts": [
            "A GL-4 pass level oil was formulated with 2.75 wt.% additive B, as per the recommendations of the manufacturer. This oil, as expected, could accept a load of 80 kg without any scuffing. The metal transfer in terms of weight loss or gain of the discs was also small up to this load level. Beyond this, a sudden large change was noticed, both in scuffing and in disc weight loss. A repeat run at the fail level confirmed this finding. The results are given in Table 4 (see p. 75). Similarly, the same additive was used to obtain an oil at GL-5 level. Here also at failure, sudden scuffing and metal transfer occurred. This was at a load of 140-160 kg with a clear pass up to 120 kg (see Table 5, p. 75). This gives an indication that there is a distinct transition between evaluating oils at GL-4 and at GL-5 level, and that it appears possible that one can use this method for GL5 oils as well. Further work is required to establish this. Tribotest journal 6-1, September 1999. (6) 73 lSSN 1354-4063 $8.00 + $8.00 74 Bisht and Singhal To demonstrate further the discriminating ability of this test procedure, additive B was blended at an intermediate level of 4.4 wt.%, which is a treatment level midway between a GL-4 and a GL-5 level oil. The results are given in Table 6. It is seen from this that the failure load is at about 120 kg, i.e., midway between the two oils previously evaluated. This has given further confidence in the ability of the test method to discriminate between these oil quality levels. Tribotest journal 6-2, September 1999. (61 74 ISSN 2354-4063 $8.00 + $8.00"
        ]
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure5-1.png",
        "caption": "Fig. 5. Representation of the distance WCm(ti) for the corridor Cm(ti):",
        "texts": [
            " Definition: A corridor is defined as the triangular surface in 2-D space when its distances satisfy the following conditions: (1) (2) where and are well predefined thresholds and represents the rotation-angle of the particular distance with respect to magnetic north. The index represents the th navigation corridor in the same navigation space CFNS Definition: The \u201cleft boundary\u201d of a navigation lane is defined as the distance which satisfies the following condition: (3) Definition: The \u201cright boundary\u201d of a corridor is defined as the distance which satisfies the following condition: (4) Corollary: The minimum distance between two obstacles and in a corridor where is to the left of and is to the right of is given by (5) where (see Fig. 5). The distance is compared with the width of a robot to define if the corridor is considered open or closed for that robot. Note that in the Fig. 5(b) and (c) the robot will not receive back \u201claser beam\u2019s reflections\u201d for the measurement of the distances and since the reflections disappear in the open space, In this case the robot uses its \u201cexperience\u201d stored in the knowledge base, and makes the assumption that there is an \u201copen\u201d space, thus the type of an open or closed corridor is determined by the distances and associated with the knowledge of an open space in a way similar to Fig. 5(a). The basic algorithmic steps behind this navigation strategy are based on the human navigation behavior in an unknown space. In particular, an autonomous mobile robot has to perform the following actions that a human does in an unknown space. \u2022 Visual scanning of the surrounding free navigation space. \u2022 Extraction and representation of the shape from the free space. \u2022 Detection of other moving objects. \u2022 Classification of the moving objects into mobile robots, human and other. \u2022 Prediction of the objects\u2019 motions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002879_20.582741-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002879_20.582741-Figure1-1.png",
        "caption": "Fig. 1 Magnetization model.",
        "texts": [
            " The magnetizaition M with hysteresis characteristics is calculated using the curling model theory which can consider a vectorial1 magnetization rotation. The curling model is useful to trace the vectorial magnetizing process. In the curling model theory, the magnetization direction $ is determined by the following equation[4][5]: f( $ )=Ku sir112( B - 4 ) - H - Ms - sin( $ - w )=0 (2) where Ku, H and Ms are a single magnetic domain anisotropic constant, the magnetic filed strength and the saturated magnetizal.ion, respectively. 0 , $ and w are the angle of the easy axis, the magnetization and the magnetic field strength as shown in Fig. 1. In addition, a ciiitical magnetic field strength Hn, which considers the reversal of the easy axis, is given by the following equation[4.] [5]: (3) (2Kui'Ms) 1.08S-2. (1-1.08s -2) Hn= ~ ((1-1.08:S'2)2-sin2( 8 - w)(1-2.16S-2)]1n where S is a paraimeter which indicates the degree of incoherent magnetic rotation. Thevalue of Ku and theangle 0 of theeasy axis have 0018-9464/97$10.00 0 1997 IEEE 21 14 the distributions such as normal distribution, respectively. Each value of Ku and each angle of the easy axis have their own probabilities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002907_3516.662865-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002907_3516.662865-Figure10-1.png",
        "caption": "Fig. 10. Sensor integration of the SMA-actuated microvalve.",
        "texts": [
            " To detect fracture, conducting strips can be printed on the critical places. If the device breaks, the electrical connection is broken. As there are two valves, the second valve will prevent a complete release of the main reservoir. In both cases, the device has to report this to the external controller, after which the device has to be removed as soon as possible. The electrical connections for the sensors and the SMA actuator can be integrated on the plastic body of the valve using the above-mentioned SIL technology (see Fig. 10). Leak detection is achieved via pads 1 and 2, fracture detection via pads 2 and 3, and power supply to the SMA via pads 4 and 5. Because of the small dimensions, soldering is not done on metal pins, but via pads on the side of the valve. In this way, the valve has become a surface-mounted device (SMD). The SMA can be made solderable by electrolytic deposition of copper on the structured NiTi surface. In this case, the SMA wire is replaced by a structured ribbon. This component consists of multiple wires mechanically in parallel (i.e., equal strength), but electrically in series (i.e., higher resistance). Fig. 10 also shows an example of such a ribbon machined with microelectrodischarge machining. In the design of Fig. 10, the pretensioning screw is also omitted. thus reducing the number of components to two. In this case, the pretensioning function is realized by mounting a prestressed shape memory element. This final design is again a demonstration of the proposed mechatronic approach, resulting in a highly integrated product obtained through a combination of functions in a single component; the plastic body finally combines the functions of mechanical pinching, return spring, electrical carrier, and various sensing functions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.8-1.png",
        "caption": "Fig. 9.8. Determination of the stiffness of a transmission mechanism",
        "texts": [
            "15) Let us now fasten the output link, fixing coordinate rp, and let us apply moment M\" to the input link. We will call inlet stiffness of the mechanism the ratio of this moment to the angular displacement I1q of the input link caused by this moment. Analogously to (9.15) we have: cq = e;1 = [el (aq / aOI Y + e2 (aq / a(2)2 ]-1 . (9.16) Let us consider one more example which is important for the solution of many practical problems. Let us find the flexibility reduced to the output of a transmission mechanism (Fig. 9.8). To this end, we fix the input link - the motor rotor 0, and we apply a unit moment M at the output. We want to find the flexibility of the elastic elements, reduced to the mechanism output. In order to achieve this, it is necessary to multiply the flexibility of each element by the squared ratio of the variation of the output coordinate and the magnitude of deformation of the element. We obtain: (. )-2 eOlrp = eOI '12 , where i)2 is the transmission ratio of the gearing, rb) is the radius of the base circle of wheel 1 (see Fig. 9.5). Adding together the flexibilities (9.17), we find the outlet flexibility of the mechanism: (9.18) Thus, when making a reduction to the output of a transmission mechanism, the flexibility of an elastic element is divided by the squared transmission ratio, which relates the deformation of this element to the output coordinate. In an analogous way the flexibility of a transmission mechanism, reduced to its input is defined. For the mechanism shown in Fig. 9.8 we obtain: 9.3 Reduced Stiffness and Reduced Flexibility of a Mechanism with Several Degrees of Movability (9.19) (9.20) Let us consider a mechanism with several degrees of movability. An example of a mechanism with three degrees of movability ensuring the positioning of a planar platform BD is shown in Fig. 9.9. Here motors 1,2 and 3 are installed at joints 0, form, and the rotors are connected with links OA, BD and FE through coaxial, elastic transmission mechanisms. Input coordinates of these mechanisms are the rotation angles of the rotors q), Q2' Q3' and output coordinates are the rotation angles lI'l> lI'2' lI'3\u00b7 We denote by cl> c2' c3 the stiffnesses of the transmission mechanisms reduced to their outputs, by i), i2, i3 the transmission ratios and by 0), \u00b02 , 03 the deformations of the mechanisms reduced to their outputs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002924_70.744609-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002924_70.744609-Figure3-1.png",
        "caption": "Fig. 3. Closed-loop kinematic chain.",
        "texts": [
            " Since only the force along the -direction is controlled in the sawing task, a Jacobian which relates the force vector, to the joint minimum actuators is given as (14) where denotes a matrix of dimension of which is the third rows of Note that the force control in the sawing task is different from those in previous works [2], [6], [14], [21], [22], in that the contact position is continuously changing. We resolve this problem by continuously updating the kinematic mapping according to the position information of the system. The dynamics of a general closed-chain manipulator can be represented in terms of a minimum (independent) coordinate set being equal in number to the minimum number of inputs (i.e., mobility) required to completely describe the system kinematics. Consider a closed-loop kinematic chain shown in Fig. 3. Assume that the system is in a state of equilibrium. Then, the effective load referenced to the independent joints, which is described in terms of the system\u2019s effort sources and externally applied loads and effective gravity loads as follows, must be zero, that is (15) where denotes the matrix excluding the row corresponding to the additional passive joint from since the passive joint cannot be activated, and we define (16) (17) (18) (19) and (20) The inertial load and gravity loads, referenced to the independent input set, are obtained from the open-chain dynamics via a virtual work-based transfer method employing and denote the efforts of the independent and dependent joints, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002326_1.483175-Figure15-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002326_1.483175-Figure15-1.png",
        "caption": "Fig. 15 Effect of optimized parameters on dimensional instability",
        "texts": [
            "8 Validation of Optimum Parameters on Actual Components of Jet Engine. The predicted optimum parameters for the tolerance range of 10 to 20 microns were validated for practical application on compressor disc. By using these optimized v, f, d, a, and r the 400 (10.02, 0.00) mm locating diameter was machined. Immediately after machining dimensions were checked, it was found to be 400 (10.010, 0.00) mm. After 360 hours, the same dimension was 400 (10.015, 0.00), which is within the acceptable tolerance band. Figure 14 and Fig. 15 show the effect of nonoptimized and optimized parameters on dimensional changes. The results prove the validity of this optimization technique and the parameters for the practical applications. The following conclusions emerged form the present study: om: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/28/20 1 Investigations on plastic deformation characteristics of Inconel 718 concludes that shear localized chips of Inconel 718 very similar with titanium Ti-6Al-4V alloy. Deformation twinning is noticed in Inconel 718 and titanium alloy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003299_jsvi.1996.0908-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003299_jsvi.1996.0908-Figure2-1.png",
        "caption": "Figure 2. Deformation process of the system with displacement-dependent friction.",
        "texts": [
            " However, this principle is not applicable to systems with large non-linearity and non-symmetry of hysteresis loops. The non-linear transformations allow one to use Masing\u2019s principle for this systems will be found. 2. -  Masing\u2019s principle is suitable for a system containing spring and constant friction elements [5]. Many real hysteresis loops of vibration isolators are near the loop of the system with non-zero stiffness without friction K and with displacement dependent friction force H= cU (where U is displacement, Ca is a coefficient) (Figure 2). This system will be transformed in accordance with Masing\u2019s principle. In order to eliminate the element K, one can subtract the loop middle line L(U) from the loop contour and obtain the co-ordinate F*=F\u2212L(U) (Figure 3). To eliminate the \u2018\u2018friction displacement\u2019\u2019 dependency, one can divide F* by the friction force H(U). Thus, in the new coordinate system, U, F**=F*/H(U), a constant friction element with friction force equal to unity (Figure 4) is obtained. After this transformaion, process A\u2013D, B\u2013G and C\u2013E are non-parallel, and one requires an additional transformation of these processes, namely a similarity transformation in the direction of the U-axis. Its initial point coincides with the projection of the initial point of the process on the U-axis. Its coefficient is inversely proportional to the segment a(U), i.e., the change in U between the initial point of the process and the point where the process intersects the U-axis. In the new co-ordinates, U*a = =U\u2212Ua =/a(Ua) (or U*b , U*c ); F**, 0022\u2013460X/97/250903+05 $25.00/0/sv960908 7 1997 Academic Press Limited Masing\u2019s principle is fulfilled (Figure 5). One can also see in Figure 2 that triangles CMN and BPQ are similar, H(U)/a(U)= constant, and it is sufficient to know only the function H(U) for the transformation in the U-axis direction. Next L(U) and H(U) will be found for a real vibration isolator. For the system shown in Figure 2, L(U) and H(U) are the half-sum and half-difference of loading and unloading processes during sliding in the friction element. The ends of the hysteresis loop are not used for the definition of L(U) and H(U). One can approximately find the length of these sections using Masing\u2019s principle. According to this principle, the initial point of the primary loading curve lies on the line where the friction force equal zero. For the system shown in Figure 2, this is the middle line of the hysteresis loop L(U). One can double the displacement Ug from the initial point of the primary loading curve to the coincidence of this curve with the loading process (Figure 2) and subtract this section from the ends of loop. Thus, if one knows the hysteresis loop with the displacement amplitude Amax , one can obtain the functions L(U) and H(U) on the interval [\u2212Amax +2Ug ; Amax \u22122Ug ]. Therefore, Amax must be as large as possible. If the loading and unloading processes, Fl and Fu , of this large loop, are known, one can determine the non-linear functions L(U)= (Fl +Fu)/2 and H(U)= (Fl \u2212Fu)/2. To obtain the initial point of the primary loading curve on the middle line, the deformation processes with reducing amplitudes are recommended"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure11-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure11-1.png",
        "caption": "Fig. 11. Three-point Petrol Engine Mounting",
        "texts": [
            " In order to achieve this control of engine movement under vertical shock loads the spacing between the front mounting, rear mounting, and centre-of-gravity of the power unit must be in a certain relationship fixed by the inertia of the power unit about a transverse axis. A detailed explanation of this mounting system is given in published literature (Harrison 1956). It is, however, not always easy to fix mountings in the required positions, as the front mountings usually have to be just in front of the centre of gravity where other fittings preclude the location of engine mountings. Compromise solutions are therefore often used as, for example, the arrangement shown in Fig. 11 which is employed very successfully on a number of vehicles in regular production. It will be noted that no torque reaction or other buffering arrangements are provided. Even in bottom gear, torque-reaction movement is not sufficient to necessitate such fittings, some control being provided in any case by engine connections. The eccentric bush makes a very simple, cheap, and effective rear mounting in this particular installation. The NO 11957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002500_0045-7825(94)90191-0-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002500_0045-7825(94)90191-0-Figure1-1.png",
        "caption": "Fig. 1. Generalized coordinates of element (i).",
        "texts": [
            " In this formulation, it is assumed that (1) the material of the rotor is elastic, homogeneous and isotropic, (2) the plane cross-sections initially perpendicular to the neutral axis of the rotor remain plane, but no longer perpendicular to the neutral axis during bending, (3) the deflection of the rotor is produced by the displacement of points of the center line, (4) the axial motion of the rotor is small and can be neglected, (5) the shaft is flexible, while disks are treated as rigid, and (6) internal damping and aerodynamic forces are neglected. The finite element method is used to model the shaft. Referring to Fig. 1, let X~Y~Z~ be a Cartesian coordinate system with its origin fixed to the undeformed beam element. The xiy~z i is a Cartesian coordinate system after the deformation of the beam element. The xiy~z i coordinate system is rotated with respect to the X ' Y ' Z ' coordinate system through a set of angles ~0,/3 and y, as shown in Fig. 2. To describe the general orientation of any cross-section of the beam element, one first rotates it by an angle (0 + ~0) around the X~-axis, then an angle/3 around the new y-axis (denoted by Y~2), and lastly by an angle y around the final z'-axis. The instantaneous angular velocity vector o3 of the xiyiz ~ frame may be expressed as o3 = (o + + + 5,; , & = ; , (1) where L ]2 and /( are unit vectors along the axes X, yi 2 and z i. Transforming Eq. (1) to the X Y Z coordinate system, we can write M.A. Mohiuddin, Y.A. Khulief / Comput. Methods Appl. Mech. Engrg. 115 (1994) 125-144 127 o3= w,, = c o s ( O + ~ o ) - - } s i n ( O + ~ o ) . sin(O + ~o) + y cos(O + q~) 2.2. Kinetic energy of the shaft (2) Referring to Fig. 1, let qi be any point in the undeformed beam element i. Point qi is defined by the vector ?o, with respect to the XiY~Z~ coordinate system. Point q~ is then transformed to point pi in the 128 M.A. Mohiuddin. Y.A. Khulief / Comput. Methods AppI. Mech. Engrg. 115 (1994) 125-144 deformed state of the beam element. The location o f p ~ with respect to the X~Y~Z ~ coordinate system is given by the vector ?, while its global position is defined by the vector ?p. For simplicity of notation, the superscript i is dropped when writing position vectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003762_b:kica.0000009054.21403.21-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003762_b:kica.0000009054.21403.21-Figure7-1.png",
        "caption": "Fig. 7. Rate constant of reaction (I) as a function of the strength of proton sites for (1) NaxH3 \u2013 xPW12O40 (x = 1\u20133) or (2) HZSM-5 zeolites.",
        "texts": [
            " 44 No. 6 2003 TIMOFEEVA et al. Such behavior was also observed in the dealkylation reaction of 2,6-di-tert-butylphenol in the presence of H3PW12O40 and H3PW12O40/SiO2 [3]. Bulk H3PW12O40 is a strong Br\u00f8nsted acid, whose strength is greater than that of proton sites in HZSM-5 zeolite [1, 2]. Table 3 summarizes the rate constants k' and ks of reaction (I), specific surface areas, and strength of acid sites determined as proton affinity (PA) for HZSM-5 zeolites and HPA (bulk and supported on CFC). Figure 7 demonstrates the dependence of the rate of reaction (I) on the strength of the acid sites. Although the reaction was homogeneous in the presence of NaxH3 \u2212 xPW12O40 (x = 1\u20133) or heterogeneous in the presence of zeolites, a Br\u00f8nsted-type correlation was observed in both cases. The strength of acid sites in the HPA/CFC samples was evaluated from kinetic data (with the use of curve 2 in Fig. 7). It was found that the acidity of proton sites decreased upon supporting HPA onto CFC. The strongest sites were detected in the sample of 9% H3PW12O40/CFC-3, whereas the strength of proton sites significantly decreased upon supporting HPA onto N-CFC and became close to the strength of proton sites in HZSM-5 (Al) zeolites (PA = 1170 kJ/mol). It is most likely that the difference in the strength of the acid sites of HPA/CFC-3 and HPA/N-CFC is related to the character and strength of the interaction of HPA proton sites with the surface groups of carbon"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002660_0925-8388(96)02353-5-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002660_0925-8388(96)02353-5-Figure1-1.png",
        "caption": "Fig. 1. Cylindrical segment of Ip =90\" magnetised along the radial direction at an angle of 45\u00b0.",
        "texts": [
            " 0925\u00b78388/96/$15.00 \u00a9 1996 Elsevier Science S.A. All rights reserved PII S0925-8388(96 )02353-5 2. Experimental Injection moulded Nd2Fe t 4B magnetic material of density p - 4.6 g cc-) and energy product (BH)max 5 MGOe has been pressed into the form of cylindrical segments in order to investigate the possibility of preparing cylindrical magnetic multipoles which could be used as magnetic gears [4]. The cylindrical bonded magnet segments obtained have a length of about 3 cm and an angle width lp of 90\u00b0 or 45\u00b0, Fig. 1. These segments are easily magnet ised along radial direction at an angle lp/2 using a 176 D.M. Tsamakis et al. I Journal of Alloys and Compounds 241 (1996) 175-179 10 Resin Bonded _. 3500,...-----------------, 2 3 4 5 6 Density (g/cm3) Fig. 2. Dependence of the energy product (BH)max on the density p of the material. 20001500o 1000 _ 2000 a ~ 1500 3000-;- '\"i 2500 500 1000 Nl (r.p.m) (main) Fig. 3. No load operation. coupling relation between 4-4. 4-8 and 8-4 gear systems. ..... \u2022\u2022\u2022...,. fa 8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003362_ac0005363-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003362_ac0005363-Figure1-1.png",
        "caption": "Figure 1. Schematic configuration of the on-capillary tubular solgel carbon composite electrode (not drawn to scale): (A) separation capillary, (B) plastic tubing, (C) sol-gel carbon composite, (D) nail polish coating, (E) glass tubing support, and (F) copper wire.",
        "texts": [
            " Under a microscope, the plastic tubing was clamped firmly and the separation capillary was carefully pulled back to a desired length (l) so that a tubular electrode was formed surrounding the exit end of the separation capillary. Subsequently, the on-capillary carbon sol-gel composite electrode was left to polymerize for 4 days under laboratory ambient conditions. Finally, the surface of the sol-gel carbon composite was very carefully covered with a thin coating of nail polish excluding the little exit needed for capillary to emerge. Figure 1 illustrates the schematic diagram of the novel on-capillary sol-gel carbon composite electrode. Cu2O-modified tubular on-capillary electrodes were prepared following the same procedure above except that a thoroughly blended mixture consisting of 0.04 g of Cu2O powder and 0.5 g of graphite powder replaced the pure 0.5 g of graphite powder. Characterization and Optimization. The integrated oncapillary tubular detector in this CEEC system consisted of a solgel carbon composite tubular electrode affixed permanently at the end of the separation capillary. The critical parameters affecting the performance of this integrated unit shown in Figure 1 are the wall thickness (\u03b4) at the separation capillary outlet and length (l) of the tubular electrode. Etching the outside wall of the exit end of the separation capillary provides a means for reducing the capillary thickness. Thus, this effectively sets up a steep diffusion profile at the tubular electrode as the solution flows through the exit end of the capillary. The sensitivity of the detector was improved significantly when \u03b4 was thin. Figure 2 shows the effect of \u03b4 on both separation efficiency and background noise for the detection of dopamine (200 \u00b5M) in a typical CE separation buffer consisting of 20 mM phosphate buffer at pH 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003244_(sici)1097-4563(199603)13:3<163::aid-rob4>3.0.co;2-q-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003244_(sici)1097-4563(199603)13:3<163::aid-rob4>3.0.co;2-q-Figure4-1.png",
        "caption": "Figure 4. Variables describing the motion of a robot.",
        "texts": [
            " FORMULATION OF THE PATH PLANNING PROBLEM The objective of a path planning problem is to direct the robot end-effector along a desired path without collision. The end-effector path of the manipulator is composed of 1 segments, and each segment has equally spaced m path points. The orientation of the end-effector may, or may not, be specified at these points. The end-effector location can be changed by activating the robot joints. Therefore, for an ??-joint robot, where, 8 q k is the proposed change in the value of joint k variable. Figure 4 shows these quantities for a serial robot with revolute joints. The path planning problem can be described as a sequence of minimization problems. The objective of each of these problems is to ensure the proximity of the end-effector to the path points while preventing link-obstacle and link-link collisions. These - intersections are added as follows, where, 0: obstacle collision measure. nhaz: number of links in hazardous regions. nobs;: number of the obstacles in the hazardous region where link i is"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003588_2000-01-1786-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003588_2000-01-1786-Figure3-1.png",
        "caption": "Figure 3. Diagram showing the cross-sectional views of a four-lobe bore and a ring.",
        "texts": [
            " if , ; if , ; if ,1 c2, 1 c12c c2,1c 1 1c, 1c, , \u03b3\u03b3\u03b3\u03b3 \u03b3\u03b3\u03b3\u03b3\u03b3 \u03b3\u03b3 ji n ji n ji ji jif ( )                 \u2206 \u2212 +        \u2206 \u2212 \u2206\u2206\u2248\u2206\u2206 \u2212\u2212 t h t hh yx t h yx t jiji ji t jiji ji ji )1( ,, , )1( ,, , , \u03b8\u03b8 \u03b8\u03c1 \u2202 \u03b8\u2202\u03c1 ( ) ( ) ( ) ji jiyjix t h yxqxqy , ,, \u2202 \u03c1\u03b8\u2202\u2206\u2206=\u2206\u2206+\u2206\u2206 \u2206( ) ,q i jx \u2206( ) ,q i jy ( ) ( ) ( ) ( ) ( ) jiji jijiji qq qqq , p out x,, c out x, , p in x,, c in x,,x \u2212\u2212 +=\u2206 ( ) ( ) ( ) jijiji qqq , p out y,, p in y,,y \u2212=\u2206 5 BORE DISTORTION AND RING CONFORMABILITY \u2013 In this work, the effect of bore distortion at a crosssection of the cylinder was taken into account. It should be noted, however, that the influence of any axial variations in the bore shape (e.g., tapering) was not included. In other words, it was assumed that the crosssectional shape of the cylinder bore remained unchanged along the axial direction. This may not be realistic, but it is acceptable as a first approximation. Figure 3 presents diagrams of the cross-sectional views of a four-lobe distorted bore and a ring. Bore distortions at a cross-section were described by a collection of Fourier series. The ring conformability was evaluated using an empirical approach [12]. SURFACE ROUGHNESS \u2013 The effect of surface roughness on frictional forces was taken into account by employing the Stribeck type technique. This was implemented by the following procedure. At a given computational cell, a so-called \u2018lambda ratio\u2019 ( ) was evaluated; depending on its value, the lubrication mode was identified",
            "5 3 F ilm th ic kn es s ( h m in ) , \u00b5m Top ring 2nd ring Oil ring TDC TDCF TDC 0 60 120 180 240 300 360 420 480 540 600 660 720 Crank angle, deg. 0 0.5 1 1.5 2 2.5 3 F ilm th ic kn es s ( h m in ) , \u00b5m Top ring 2nd ring Oil ring TDC TDCF TDC 8 min. EFFECT OF BORE DISTORTION \u2013 In order to demonstrate the capability of the current piston-ring pack lubrication model, a symmetrical four-lobe cylinder bore was also used to conduct some calculations. The geometry of the bore has been illustrated in Figure 3a. Figure 11 illustrates variations of a \u2018minimum\u2019 film thickness (hx,min , see Figure 2b) with the bearing and crank angles obtained with a power-law model for the SAE 10W-50A oil, = 10 \u00b5m and N = 1000 rev/min. It can be seen that the film thickness varies significantly both along the circumference of the cylinder bore and over the engine cycle. It is noteworthy that in the vicinity of the dead centre firing (\u03b8 = 360o), the film thickness does not change with the bearing angle. This indicates that the ring is fully conformed to the distorted bore, hence no gas blowby will occur over the ring face in the region under discussion for the given level of bore distortion. This arises since the combustion chamber gas pressures are higher on this part of the stroke, these acting on the back of the ring cause an outboard deformation of the ring which is sufficient to cancel the bore distortion. It is also noted that immediately after the TDCF region, the film thickness distribution has a peak in the distorted region of the bore (see Figure 3a) with its value being about 10 \u00b5m. This suggests that the ring is hardly deformed. This happens because the average gas pressure acting on the ring face is slightly higher than that exerting on the ring back. This is due to the fact that the predicted inter-ring gas pressure is higher than the cylinder pressure, and the ring is predicted to be on the bottom of its groove during this part of the stroke. Thus, the resultant static pressure will counteract the elastic pressure of the ring, consequently the ring is barely deflected, leaving a large film gap between the ring and liner. As a result, the reverse gas blowby may occur over the ring face in the distorted area of the bore. Figure 12 shows the shear rate at the location of hx,min (see Figure 3b) under the top ring as a function of the bearing and crank angles obtained with a power-law model for the SAE 10W-50A oil, = 10 \u00b5m and N = 1000 rev/min. It can be seen that over most of the engine stroke the shear rate is over 106 s-1, and it varies significantly with the bearing angle due to bore distortion. F ric tio na l f or ce , N In st an ta ne ou s po w er lo ss , W \u2206 m \u2206 m 9 Figure 13 presents the fmep of the ring pack as a function of the bore distortion for the SAE 10W-50A oil and two fluid models at N = 1000 rev/min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003649_978-94-015-9064-8_48-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003649_978-94-015-9064-8_48-Figure3-1.png",
        "caption": "Figure 3. Unit vectors ji and jp,i",
        "texts": [
            " Therefore 9 can be chosen such that it is applied only for the first few iterations and chosen to be zero for the last, so (14) will hold. In the following section, an application for 9 will be shown to escape singular configurations. The proposed function 9 can be used as well for handling redundancies, like joint limit avoidance, obstacle avoidance, singularity avoidance etc ... 3. Reliability Measure for the Jacobian Transpose JT Kinematic description of the mechanism will be mainly done by two vectors: j i and j p,i (see also figure 3). Both vectors shall be normalized direction vectors. ji points along the rotation axis of a rotational joint. jp,i points along the connecting line of minimal distance between two successive joints i-I and i. If jpi has no direction, joint i-I and joint i are in the same place, it is defined to be j p,i = j i-I. Prismatic axes are not considered further on. The previously mentioned problem occurs, when two axes are put into a parallel state. (15) This can easily be detected by dot product of two vectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003232_physreve.53.6115-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003232_physreve.53.6115-Figure1-1.png",
        "caption": "FIG. 1. Schematic representation of the SANS device equipped with the cone and plate cell whose plane is parallel to the twodimensional multidetector plane. The neutron beam crosses the observation window which is placed at 4 cm from the rotation center.",
        "texts": [
            " The mixture has the following phase transition temperature ~cooling rate 25 \u00b0C/mn!: I~ isotropic! \u2192 104 \u00b0C N~nematic! \u2192 99 \u00b0C SAl~smectic! \u2192 35 \u00b0C Tg~glassy!. Five grams of the mixture of hydrogenated polymers and of polymers deuterated on the main chain have been prepared by evaporation from a chloroform solution. The mixture is heated to the isotropic phase and placed between the faces of a rotating quartz window and a fixed cone of an aluminium alloy ~transparent to neutrons! of angle a53\u00b0 ~see Fig. 1!. Small resistances ensure the heater of the set and can provide a range of temperature between room temperature and 180 \u00b0C whereas the speed of the rotating window can vary from the static state to 100 rpm providing a maximum shear rate of g\u0307.200 s21. The trajectory of the neutrons ~beam diameter 7.6 mm! intercepts the top of the quartz window of 531063-651X/96/53~6!/6115~6!/$10.00 6115 \u00a9 1996 The American Physical Society the shearing matching at around 4 cm from the rotation center so that the shearing lines can be considered in the window as a horizontal flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003664_s0167-8922(03)80157-8-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003664_s0167-8922(03)80157-8-Figure6-1.png",
        "caption": "Figure 6. Picture and i l lus t ra t ion of ven t ra l surface",
        "texts": [
            "2 N multiplied by the average area of ventral surface of the foot. Therefore, a snarl does not slip down and can easily hold itself on the wall in the rest state because a snail's weight is 0.08 N. decreases with the increase of shear rate and the shear stress has a plastic yield Value and then increases with shear rate. 4. LOCOMOTION CHARACTERITICS 4.1. Observation of pedal wave The snail's movements (horizontal, vertical and reverse on ceiling) on a transparent plate were observed from behind by a CCD camera. Fig. 6 shows a picture and schematic illustration of a ventral surface of the foot. As shown in the figures, snails can move forward by the pedal waves that go forward from the back part of the body to the front. [1,2,4]. The pedal wave on a horizontal surface has a wavelength of about 9 mm, a frequency of 1.3Hz, periodic time 0.8 1/s on average and the propagation speed of 17.4 mm/s is about 6 times of movement velocity of a snail. and shear ra te Fig. 5 shows the variation of the shear stress versus shear rate obtained by the cone-plate type viscometer",
            " As shown in the figure, the shear stress has a plastic yield value and increases almost linearly as shear rate increases. Secreted mucus of a snail is a kind of nonNewtonian fluid that has the characteristics of a visco-plasitic (Bingham) fluid because the viscosity The observation of marks put on the ventral surface of the foot was also done. One mark was put on the center of the ventral surface and another was put on the side. In about 1 mm width of the periphery of the ventral surface as shown in fig.6 (b), the pedal waves do not generate and that part moves smoothly with the snail's locomotion. It is considered that this part plays the role to hold the whole body on the surface (namely sucker effec 0. According to the enlarged observation of this part, it has many wrinkles in the radial direction that have a kind of suction action in the peripheral water or mucus. In fact, it is observed that peripheral water of the snail is sucked in when a snail is set on a wetted surface. Figs.7, 8 and 9 illustrate the relationship between time and moving distance of a snail under each surface condition obtained by the observation of the mark's motion on the ventral surface of the foot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002907_3516.662865-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002907_3516.662865-Figure6-1.png",
        "caption": "Fig. 6. Concept for a solid drug delivery device.",
        "texts": [
            " The decomposition is a very slow process, such that the drug can be made highly concentrated. By increasing the volume, the timespan for dosing could be extended. All current implementations exhibit permanent exposure to the body. However, the decomposition is not always constant in time and also differs from patient to patient [14]. The proposed delivery device for solid drugs could offer the possibility of regulating the release rate by alternately exposing and covering the drug. The proposed concept, shown in Fig. 6(a), has the form of a shell containing the solid drug. To deliver the drug, the shell opens and brings the drug in contact with the tissue. In this design, the body enclosing the drug, the electronics, and the SMA actuator is made of silicon rubber, both for its biocompatibility and its flexibility. The shell opens when the SMA wire acts on a metal skeleton embedded in the body. The shell\u2019s hinge is a flexible joint using the flexibility of the enveloping silicone rubber. The overall length of the device is about 35 mm. Fig. 6(b) shows a photograph of the real prototype manufactured by traditional electrodischarge machining. The shell-type design involves a number of engineering problems that are not yet completely solved. First, the shell\u2019s movement can irritate the surrounding tissue. Moreover, the human tissue can grow into the opening and prevent the device from closing (or opening). Last, but not least, this principle requires long opening times to dissolve the drug. Because of the low energetic efficiency of SMA actuation, the shell cannot be powered continuously"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003971_bf00035012-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003971_bf00035012-Figure1-1.png",
        "caption": "Fig. 1. Scheme representing the possible effects of a flash on an oxygen evolving complex in the SI state (see text).",
        "texts": [
            " The majority of OECs in the $1 state attain the state $4 after three flashes, and cause the observed maximum of oxygen production (Vermaas et al. 1984). The progressive damping in the oscillation of the Oz evolution sequence reflects the random re-distribution of OECs among the S-states with time. This re-distribution is caused by the probability of an OEC to stay in the same S-state, ~ (called a \"miss\"), and the probability to undergo a double-advancement through two S-states,/~, each time a flash is given (Forbush et al. 1971). The probability of a single advancement, 7, is then given by 1 - ~ - /L The scheme in Fig. 1 represents the possible effects resulting from a flash on an OEC in the Sl state, according to Kok's model. A miss results in the OEC staying in the $1 state, represented by a closed loop. A double-hit results in the advancement to the $3 state, and a single-hit results in an advancement to the $2 state. In the dark, the $2 and $3 states can deactivate to $1 (Kok et al. 1970). The progressive damping of the oscillation is mainly due to \"misses\", i.e. a failure to advance from the state S, to the state Sn+l when a flash is given (Lavorel 1978)",
            " This variation cannot be predicted from one of the models above, in which the properties of OECs are assumed to be constant. These models permit the assumption that oxygen evolution under flashing light depends only on the properties of OECs, and not on the acceptor side of PSII (Butko 1988). However, the deactivation rates of the $2 and $3 states were shown to be very dependent on the redox state of photosystem II electron acceptors (Radmer and Kok 1973, Diner 1977). Furthermore, deactivations contribute to misses, as can be demonstrated using Fig. 1. An OEC in the $1 state, undergoing a single-hit to the $2 state, can deactivate back to $1 in the dark interval between flashes. The effect of a single-hit followed by a deactivation from $2 is therefore the same as that of a \"true\" miss on the state S~. Thus, in an oxygen evolution sequence, single-hits followed by deactivations cannot be distinguished from \"true\" misses (Radmer and Kok, 1975). Even at a high flash frequency (5 Hz), $2 deactivation was shown to contribute to the number of apparent misses (Packham et al",
            " Thus, the oxidation of plastoquinone is due to a greater number of charge separations by PSI than by PS II. To quantify plastoquinone oxidation, we computed the delay between the D-level in the control and in the experiment with pre-flashes. Since for a given number of flashes, we already know the miss probability (Meunier et al. 1989), we investigated the miss probability as a function of the flash- .-e 14 -~ to r,- 6 0.. (/) 03 2 I I I I I 0 40 80 120 FLASH INDUCED D-LEVEL DELAY (ms) Fig. 4. The average miss probability (percent) computed from Fig. 1 as a function of the D-level flash-induced delay. induced D-level delay in Fig. 4. The relation between misses and the D-level delay is best represented by a straight line (on the graph), found by linear regression. Therefore, we conclude that the lowering of the miss probability with the flash number is highly correlated (determination coefficient: R 2 = 0.996) with the progressive oxidation of plastoquinone. We also observed a change in the miss probability with the flash frequency (Fig. 5). We found that the longer the dark interval, the higher the misses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002307_rob.4620120203-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002307_rob.4620120203-Figure4-1.png",
        "caption": "Figure 4. Two three-link manipulators with revolute joints grasping an object and performing a simple harmonic motion.",
        "texts": [
            " The first example uses the simple pseudoinverse solution to resolve the kinematic redundancy of each redundant manipulator. In this case, drift phenomenon occurs.25 The second example applies the Compact QP method with an objective function considering drift free. As such, the drift 128 Journal of Robotic Systems-2995 problem of this closed-chain robotic system is demonstrated to be solved. 6.1. Example 1 and 1 cycle per second in frequency. The planned motion for the c.8. of the object expressed in the inertial coordinate frame is: As shown in Figure 4, a closed-chain robotic system, which is formed by two three-link manipulators with revolute joints, is illustrated as the example mechanism to manipulate a common object. The parameters of the manipulators are listed in Table I. Also, the radius and the mass of the object are 0.5 m and 2 kg, respectively. The initial position of the object's c.g. expressed in the inertial coordinate frame is: with = 1.7033 m. The object is planned to travel in a straight line simple harmonic motion with equal accelerations and velocities in '2 and '2 directions and without rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002735_0094-114x(92)90062-m-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002735_0094-114x(92)90062-m-Figure4-1.png",
        "caption": "Fig. 4",
        "texts": [
            " According to the idea of hypothetic mechanisms we add one link and one pair in El and FG branches, respectively. The original mechanism becomes a six-d.f, hypothetic mechanism for which the six links in the basic plane O--XY are input links. The lengths of the links, a and b, are Lo and Lb. The diameter of the central link is D~. All parameters of the mechanism are listed in Table !. For its displacement, velocity and acceleration analyses refer to Refs [6, 8, 9]. The resolved pairs for branch OEI are shown in Fig. 4. The senses of six revolute pairs are: unit vector $, is along the sense of Z, $2--L,, $4 - Lb, $5-$2 \u00d7 $,, unit vector $e is along the sense from point I toward the center of central link, $5-$4 \u00d7 $4. The local reference system at point E, E-Xz YsZt, is along $5, $2 \u00d7 $3 and $2, respectively. The local reference system at point L I-X:XIZI, is along $5, $4 \u00d7 $5 and $4, respectively. The fixed reference system is O-XYZ. As the 104 Z. Hu, u ~ mai H. B. W~vo kinematic p~dr connzcted with the central link is a g)herical pair, only three unknown components of the motion on the main pair need to be ~lved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002924_70.744609-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002924_70.744609-Figure5-1.png",
        "caption": "Fig. 5. Description of the grasped object.",
        "texts": [
            " Besides the above example, more complex criteria involving groups of actuators can be possibly incorporated [11], [28]. Now, according to the compliance relation of (35), the joint angles are adjusted such that the force error can be eliminated. The interaction force and moment between the dual arms and the environment can be measured using two F/T sensors attached to the end of each robot. Then, in a state of static equilibrium the relationship between the measured force/torque vectors and the interaction force/torque vector can be derived from Fig. 5, and is given as (47) where denotes a gravity load vector and the matrix denotes the mapping between the grasped force vector of the th robot and the moment exerted by the environment on the grasped object. denotes the moments vector exerted on the grasped object by the th robot. and are measured at the F/T sensor attached to the end of each robot. V. VELOCITY CONTROL FOR SAWING TASK In general, the sawing task is performed along a straight line in a plane. For this task, we need to control the translational motions along the and directions and the rotational motion about the -axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003548_70.720342-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003548_70.720342-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a wheeled mobile robot. The minimal model for a wheeled mobile robot consists of two wheels, one steerable and one fixed, and a mechanism to vertically stabilize the robot. The axle line, centerline, and wheels are shown, along with variables used in the text. The underlying coordinate system is a standard Cartesian system, with origin at any point. The reference angle is measured from the standard zero position\u2014horizontal to the right\u2014and the zero of the steering angle is along the center line. Both increase counterclockwise; in the figure both angles are negative.",
        "texts": [
            " Consequently it can be moved between any two positions and orientations in such a way that the odometer point moves along a straight line. Thus the minimal distance is just the Euclidean straight-line distance between initial and final positions of the odometer. Accordingly, we consider a WMR with a single fixed axle carrying one or more wheels that are constrained to roll. As discussed in, for example, [6] this is the only interesting case of a WMR with unsteerable wheels that are constrained to roll. For purposes of visualization, a \u201cminimal\u201d interesting WMR is a bicycle (Fig. 1). Since there is no steering lock, we assume the control (handlebars) can rotate without constraint horizontally. A priori, the second wheel is at the odometer point; however, as mentioned above, there is no loss of generality in considering this wheel also a control wheel. That is, in our minimal model, the third wheel is both a control and the position of the odometer. It turns out that it is convenient to model motion in the reverse direction by letting the control \u201cpoint backward;\u201d that is, with the handlebars rotated more than 90 from the straight-ahead forward direction. With this convention, the controls of critical paths are smooth (differentiable). The relevant mathematical notation is also indicated in Fig. 1. The line from the front wheel perpendicular to the axle line is called the center line of the WMR, and the length of the segment of the center line from the front wheel to the axle line is denoted The angle between the free wheel and the center line is called the steering angle and is denoted Suppose the free wheel is located at some position ( ) in a plane, and the angle of the center line with respect to the -axis is Without loss of generality, suppose the free wheel moves over the plane with unit speed (equivalently the independent variable is arc length )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure22-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure22-1.png",
        "caption": "Fig. 22. Modes of Vibration of Four-cylinder Engine Floating in space",
        "texts": [
            " A performance estimate could usually be quickly made by means of the method he had outlined. To further facilitate such estimates his h made use of a series of graphs which gave all the pertinent data for V-arranged mountings in a condensed and convenient form, and some of those were illustrated in Fig. 21. Before selecting flexible mountings and arrangement for a particular engine, it was practical to consider the modes of vibrations of the engine if it was floating in space. After all, it was the object of the mountings, as regards vibration insulation, to simulate that condition. Fig. 22 showed a construction for finding the modes of vibration of a fourcylinder engine. 2nd-order force causes rotation around points m2. 2nd-order torque causes rotation around line DD. K2Z.Z /3 = a -tan {Ky x tan a} A circle with its centre on a line parallel to the crankshaft and passing through c.g., with the 2nd-order force as tangent, and through the end of the radius of gyration, would locate the points ml and m2 as centres of percussion with respect to each other. That would show that the 2nd-order force produced a vibration around the axis through m2 at right angles to the paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002211_1.1707606-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002211_1.1707606-Figure3-1.png",
        "caption": "FIG. 3. The constant temperature oven.",
        "texts": [
            "-inch copper tube, 54 inches 20 Reference 13, E. Ott, p. 1020; Reference 11. 391 [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: 130.18.123.11 On: Thu, 18 Dec 2014 05:54:13 A-Marker on wire. B--Steel scale. C-Frictionless pulley. D-Cork stopper. E-Small cork stopper with capillary tube. F-End heater of Nichrome wire. G--Tube heater of nichrome ribbon. H-Stirrup. long, being used as the inner chamber. (See Fig. 3.) The tube, covered with a thin layer of asbestos insulation, was heated and controlled' electrically by a Nichrome ribbon heater wrapped around it. Pipe lagging and end heaters were added to help maintain a reproducible tempera ture uniform to l\u00b0C along the useful length of the tube. The temperature along the chamber was measured by means of a traveling thermo couple which could be held taut in the tube at the same position as that to be occupied by the cord. The thermocouple junction was at first wrapped with single yarns of the various cords tested to eliminate the possibility of errors from . radiation effects, but the difference between the temperatures with the thermocouple wrapped and unwrapped was found to be less than the one degree tolerance. Other thermocouples soldered to the outside of the copper tube at points along its length were used to detect any changes in temperature while the cord was in position. The cord was tied at each end to a small metal stirrup as shown in the insert of Fig. 3. The entire length of the cord was kept in the uniform temperature zone. Steel wires fastened to the stirrups led to supports beyond each end of the tube. The elongation (both thermal and elastic) of the wires was taken into consideration, but it was less than one percent of the cord elongation in nearly all cases. Lengths were accurately measured from a marker on the left-hand wire by means of a Geneva cathetometer and an accurateste~l scale. The wire at the left end passed 5JVer a special \"frictionless\" ball-bearing 392 J-Thermocouples soldered to copper tube",
            " VOLUME 16, JULY, 1945 now being assembled for the purpose of obtaining better data on cyclic loading of tire cords at various temperatures, moisture contents, and load ranges. It Was pointed out earlier that some of the elasticity phenomena herein described are prob ably related, at least in part, to the moisture content of the tire cord. In order to determine the influence of this factor, some of the experi ments were repeated on cords which had been dried and were maintained in a dry condition during the test period. The drying was accomplished by the use of a second tubular oven similar to that described in connection with Fig. 3. The length of cord was placed inside a long glass tube which was then slipped into the oven heated to approximately 105\u00b0e. A slow stream of air from a drying train was passed through the glass tube for an hour. The glass tube containing the dry cord was then quickly transferred to the test oven and slipped out again, leaving the cord in the test chamber. The air passing into the test oven through the tube 0, Fig. 3, was preheated to the temperature of the experiment so that the temperature equi librium of the constant-temperature zone would not be disturbed by the introduction of the dry air. In this way, the predried cord was transferred to the test chamber without exposure to room air and was kept dry during the period of the experiment. Measurements were made on an untreated cotton cord (B3), because the effects observed for this cord in undried condition were fairly large. Final elongations with a load of 1 pound for 1 hour followed by a load of 7 pounds for 1 hour were measured over the temperature range as described in Section 2 above"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003237_0020-7403(93)90037-u-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003237_0020-7403(93)90037-u-Figure2-1.png",
        "caption": "FIG. 2. A general nonlinear rotor-bearing system.",
        "texts": [
            " If the transfer matrix of the shaft derived in a lumped sense is used in a system with nonlinear bearings, a vast memory size is required and the accuracy of the solution is poor [10]. The disk is assumed to be a rigid body involving the gyroscopic effect. By substituting Eqn (4) into the equilibrium and compatibility relations between two sides of an unbalancing disk, the transfer matrices are shown in the following: {S~}, = [ D , ] { S , } , , (14) { S,}, = [D,] { S,},, for synchronous and p-multiple whirls. TRANSFER MATRIX EQUATION OF THE GLOBAL SYSTEM A rotor system supported by two nonlinear bearings at points i andj as shown in Fig. 2 is used to demonstrate how the transfer matrix method is applied to solve for the steady-state responses. Only nonlinearity which comes from the restoring force of the bearings is considered. Since the dynamic behavior of shaft segments A, B and C is linear, the formulation of transfer matrices by multiplication can be incorporated within these sections. However, the transfer matrix of the nonlinear bearing cannot be constructed in a standard form because the restoring force is a nonlinear function of deflections, which cannot be multiplied by the transfer matrices of shaft sections and disks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.24-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.24-1.png",
        "caption": "Fig. 2.24",
        "texts": [
            " - commutation turn-on time tcon' the time between applying the turn-on control signal and the end of the switch turn-on (the current having increased and the voltage decreased to its ON-state value). 42 2 Switching Power Semiconductor Devices 2.2.4.1 Establishing the Current When a current step I 81 is applied to the base of a non-conducting transistor with a positive voltage veE\u2022 the collector current increases gradually from zero to a value I, imposed by the external circuit when conduction is established (Fig. 2.24). - The current total establishment time is the sum of \u2022 the delay time td, taken by ic to go from 0 to I/10, \u2022 the rise time tr, taken by ic to go from I/10 to 9Ij10; - In physical terms, the delay corresponds to the time needed by the majority carriers to cover the space charge of the transition zone of junction B-E. The \"transition charge\", e.g. the charge which corresponds to the disappearance of this zone, is carried by i8 . The emitter electrons have not yet reached the base, the transistor effect has not appeared and the collector current remains negligible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002761_1.568457-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002761_1.568457-Figure5-1.png",
        "caption": "Fig. 5 Dynamic loading system",
        "texts": [
            " For the present investigation, the test-bearing assembly was replaced with the test-seal assembly illustrated in Fig. 3. Highpressure water is injected radially at the center of the assembly with two diametrically opposed locations. The water splits and exits axially across twin test seals whose geometries were defined in Fig. 1. Exit orifice seals are used at each end to hold a slight back pressure. Figure 4 presents an assembly drawing of the test rom: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 05/20/2 seals and housing. The design of Fig. 4 allows interchangeable test seal elements. Figure 5 illustrates the static and dynamic loading arrangement for testing hydrostatic bearings. The hydrostatic bearings have high stiffnesses, and a static load is applied from a pneumatic cylinder to yield specified static eccentricity ratios out to 0.5. Zonic hydraulic shaker heads are used to provide dynamic excitation alternately in the direction of the static load and perpendicular to it. For the present tests, the seals are comparatively weak, and the hydraulic heads are used for both static positioning and excitation",
            " The pressure drop across an individual seal is approximated as the average of the two pressure drops measured across the left and right test seal elements. Desired operating points for pressure and temperature are set from these measurements. Relative motion between the seal-housing and the rotor are measured with high-resolution eddy-current probes. Two motion probes are provided at one end of the assembly for X and Y relative motion, and four probes are provided at the other end (1X , 2X ,1Y ,2Y ). The latter probes provide rotor-growth versus running-speed information. As illustrated in Fig. 5, accelerometers are mounted in the X and Y directions. Rotordynamic coefficients are identified by shaking the housing alternately in the X and Y directions. Measurements required for identification include relative motion between the seal\u2019s rotor and stator DX(t),DY (t); input excitation forces Fex(t), Fey(t); and housing acceleration X\u0308(t),Y\u0308 (t). Pseudo-random excitation is used with identification in the frequency domain according to the procedures discussed by Rouvas and Childs @5#. Experimental and theoretical results will be presented as a function of the following taper parameter: q5 C in2Cexit C in1Cexit (4) For constant clearance, q50, for convergent seal geometries, q "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002260_jrproc.1931.222419-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002260_jrproc.1931.222419-Figure9-1.png",
        "caption": "Fig. 9",
        "texts": [
            " The directional characteristic of the 995 996 Bashenoff and Mjasoedoff: Effective Heiqht of Closed Aerials closed aerial in a horizontal plane has in this instance the form of a figure-eight and as to its contour is more or less similar to the curve E = Eo cos X, where 0 is the angle formed by the radius vector with the plane of the aerial, and Eo a certain constant quantity. The dislocation of the loop of current will result in a deformation of the diagram and will render the aerial less directive. In order to illustrate this point let us examine the electrical field in a horizontal plane of a square closed aerial (see Fig. 9). Let the equation of the distribution of the current be: 27x j -Icos + a. Let the distance between the geometrical center of the aerial 0 and any point in space be equal d. The vertical component of the intensity of the field, created by wire A1B1 at this point is 120rIr 3/2h /2wx 2rd 2rt 7rhE = - Ad J cos +a) dx.sinQwd\u00b12 - cos +1 (we take as positive the direction of the current in the wire AB, and the image A lBl is taken into consideration). Taking here 27rd 27rt + = F X T and integrating, we get: 120I /2rh \\7rh /wh \\ El = dcos - +a sin- sin F-- cos q",
            " On the contrary El, has its maximum at 0 = 90 degrees and its minimum with 4 = 0 degrees. With a sufficiently small h/x the value EII changes when q is changed along a curve whose shape resembles a circle, thus behaving like an open antenna. At a =0 EII = 0 and E = El. If in this case h<<X, then from the expression determining EI(6g) after making the changes 7rh 7rh -rh cosX 7rh cosq sin -= and sin o we obtain 120rI 2irh2 Ei ~~cosq cosF Xd X i.e., the usual formula for the field of a closed aerial with a quasi stationary current. In Fig. 9 are given the curves EI, EII, and E for a square closed aerial at X = 2P = 8h and a = w/8 (loop of current at point A1). All these deductions thus made with respect to the effect caused by displacement of the current maximum on the resulting electrical field of a square frame for points in a horizontal plane, can also be extended to other types of closed aerials, symmetrical with respect to the vertical. It is also easy to demonstrate the fact that, unlike the field of a closed aerial with a uniformly distributed current, the field in open space due to a symmetrical closed aerial with a non quasi stationary current, even with a symmetrical distribution of current, is free from the aerial constituent (EII) of the component of the vector of intensity 998 Bashenoff and Mjasoedoff: Effective Height of Closed Aeriali of the electrical field, which is perpendicular to the plane under examination, only in respect to such a plane out of the ones perpendicular to the plane of the closed aerial, which is also perpendicular to the axis to which the aerial geometrically as well as electrically (distribution of current and potential) is symmetrical, and that in case of a non quasi stationary current, besides the component of the vector of the intensity of the electrical field, perpendicular to one or the other of the planes perpendicular to the plane of the closed aerial, there also exists a component of the vector which is parallel to the plane under examination"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002569_1.2828770-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002569_1.2828770-Figure3-1.png",
        "caption": "Fig. 3",
        "texts": [],
        "surrounding_texts": [
            "(yl - f:')n\\\nizl ~ z!;'>)\u00ab!4'\u0302 = 0\n\\Zw Zw )\"wy - ^\nl(S\u00bb').,(fi\u00bb'.>\u00bb') 0 (5)\nwhere\nMor^ ilf\"' = M.^n^'^'^\nThe separation of the contacting surfaces for grid point T is calculated by the expression\nsir, 6)\nV(4 x'^'? + (y!:' - y'^'f + (zl'\u0302 ' - z\\f)' (6)\nwhere\n\u00bb(\u00ab) M\u201e\u201er<\u00ab\nEHD Lubrication Analysis. The full thermal elastohydrodynamic analysis of lubrication of the new type and of the commonly used worm gearings has been carried out. The perti nent equations governing the pressure and temperature distribu tions and the oil film shape are the Reynolds, elasticity, energy, and Laplace's equations. The analysis has been carried out in a local cylindrical coordinate system (Fig. 2), which is more suitable due to the specific geometry of worm gearings, than a Cartesian system. Point contact EHD lubrication analysis is\napplied because of the shape of the instantaneous contact lines and due to the point contact occuring in worm gears manufac tured by oversized hobs.\nThe following general Reynolds equation for EHL point con tact is used\nJL dr dr r dr r^ 06 \\ dO\nOr \\F,\nVo d (F,\nThe functions FQ, F2, and F3 were defined in the papers (Simon, 1981a and 1981b).\nThe full energy equation is applied\n/ dT vo dT dT OCA v.. 1 1- II, \u2014 ^ \"I \u00ab- - 90 ' dz '\u2022 dr\n, / dT^ 1 dT i'd'r g2j g2j ' de^ \"\u0302 dz^\ndp vgOp dve\ndz (8)\nJournal of IVIechanical Design MARCH 1997, Vol. 1 1 9 / 1 0 3\nDownloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/31/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "EHD load carrying capacity for different types of worm gearings\n(JJOII\nV = Voe >p-0{T-T\u201e)\nPol 1 + 1 + j3ip\n(12)\n(13)\nThe load is calculated from the pressure by simple integration\nW ^n''' jft\u00ab/\u00bb, (r, e)rdrd9 (14)\nThe equation governing the heat transfer in the worm and in the gear tooth is Laplace's equation\nThe friction factor is defined by the ratio of the frictional force to the load and it can be written as\nd^T,\u201e I 1 ^ r . 1 d'T\u201e dX, dr^ r Or r ' 89^ dz^\n(9)\nwhere, m = w for the worm thread, and m = g for the gear tooth.\nThe boundary conditions for Eqs. (7), (8), and (9) have been fully described by Simon (1981a).\nThe composite normal elastic displacement of the contacting surfaces in point (r, 9), caused by the pressure distribution p(R, 0 ) is given by\nThe Reynolds, elasticity, energy, and Laplace's equations represent a highly nonlinear integrodifferential system. This system of equations is solved by using the finite difference method and numerical integration. The finite difference method is based on a three-dimensional grid mesh in the oil film and in the solids. The linear systems of equations, obtained by using finite difference approximations of the Reynolds, energy, and Laplace's equations, are solved by the successive-over-relax-\n0.0100\nd(r,0) VH, VQ, V ( r\np(R,&)RdRd@ 0,0075\nwhere\nv( cos^ - Rcos\u00aey + (rsin 6--R sin 0)^\n(10) I\u2014 o u S. 0.0050 c o o\n\u2022^ 0.0025 K,\nThe oil film thickness is defined by the, expression\nh{r,9) = h^,\u201e + d{r,9) + s{r,9) (11)\nThe viscosity variation with respect to pressure and tempera ture and the density variation with respect to pressure are in cluded:\n0 45 90 135\n% [deg.]\nFig. 4 Power losses in the oil film for different types of worm gearings\n104 / Vol. 119, MARCH 1997 Transactions of the ASME\nDownloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/31/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "-100 - 5 0 0 50 100\n?, Cmm]\nComputed Results On the basis of the presented theoretical background, the computer program developed for the EHD lubrication analysis in Archimedean, involute, convolute, Cavex (with circular axial worm profile), and thread-ground (the worm is ground by a conical grinding wheel) worm gearings (Simon, 1985a), is ex tended to handle the lubrication analysis in the new type of worm gearing. This program contains a subroutine which gener ates a three-dimensional finite difference mesh in the oil film and in the solids with changing intervals along the oil film. The intervals decrease gradually as they approach the pressure peak. But to keep the discretization error to a minimum, a uniform grid is used in the domain of high pressures. Unfortunately, no adequate test results for worm gear lubrication are available in the literature, therefore, no direct comparison of the computed results can be made. To improve the precision of the obtained results, a convergence investigation is carried out by changing the size of the intervals and the number of grid points in the finite difference mesh. The investigations have shown, that a very good convergence of the calculated results can be obtained by using a mesh in the oil film containing 2691 grid points. Meshes with the same number of grid points are appUed for the. temperature distribution calculation in the worm thread and in the gear tooth.\nBy using this computer program, the EHD lubrication charac teristics of a fully conjugated worm gear, with the following basic set of input data are calculated: w\u201e = 3 mm, z,\u201e = 2, z\u0302 = 27, dQ\u201e = 24 mm, x\u201e = 1.1, dg\u201e = 350 mm, a^ = 20 deg.. Pi = 20 mm, p2 = 35 mm, A\u0302 \u201e, = 2000 rpm. The influence of the type of worm gearing, worm and gear tooth numbers, worm pitch diameter, tooth height, profile angle, radii of profile curva tures, addendum modification factor (profile shift), minimum oil film thickness, worm speed, and lubricant viscosity on EHD load carrying capacity (an expression commonly used for the load of the oil film, calculated by Eq. (14) for a prescribed value of the minimum oil film thickness), maximum oil film and flash temperatures, and on power losses has been investigated. A small part of the obtained results is presented in Figs. 3 to 8.\nThe variation of the EHD load carrying capacity and power losses through a mesh cycle for three types of worm gearings: Archimedean, thread-ground, and for the new type is shown in Figs. 3 and 4. As it can be seen, the new type of worm gearing has a much higher EHD load carrying capacity and much lower power losses than the other two types of commonly used worm gearings. This is perhaps the result of the favorable position of\nthe instantaneous contact lines in the new type of worm gearing (Simon, 1994). Also it can be noted, that in the case of full EHD lubrication the power losses and the corresponding friction factor are desirably low.\nIn Figs. 5 through 8, the factors kj, kw, and kfr represent the ratios of the flash temperature, EHD load carrying capacity, and power losses in the oil film, calculated for the new type worm gearing with arbitrarily chosen design and operating parameters, and the same EHD characteristics obtained for the presented basic set of input data.\nThe influence of radii of the bicircular grinding wheel profile for worm grinding on the EHD lubrication characteristics is presented in Figs. 5 and 6. The convex worm profile, which corresponds to the concave grinding wheel profile, is repre sented by the negative values of radii p\\ and p2, therefore, their positive values indicate a concave worm profile. As it can be seen, the EHD load carrying capacity (represented by the ratio k\u201e) is much higher and the power losses (feyr) are lower for\nJournal of Mechanical Design MARCH 1997, Vol. 119 / 105\nDownloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/31/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.14-1.png",
        "caption": "Fig. 9.14. Determination of the stiffness of an epicyclic gear train",
        "texts": [],
        "surrounding_texts": [
            "stiffnesses Cl2 and c23' respectively, along the common normals to the teeth surfaces at the contact points. The moduli of all wheels are identical. Answer: where rH is the radius of the planet carrier, Z2 and Z2* are the teeth numbers of the planet pinion, a is the meshing angle."
        ]
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure3.3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure3.3-1.png",
        "caption": "Fig. 3.3",
        "texts": [
            "3 Remarks a) When indicating the function to be carried out by a \"switch\", it is not enough to show (in the voltage-current axes system) the branches of characteristics on which it will have to be able to operate. The switchings from ON to OFF or vice versa have to be indicated. If this is not indicated, no difference should appear between a conven tional thyristor (Fig. 3.1 b) and a thyristor with forced commutation circuit (Fig. 3.lc). The bidirectional controlled turn-on/turn-off switch (Fig. 3.2b) would be mistaken for the two thyristors connected in antiparallel as used in AC regulators (Fig. 3.3). turn-off semiconductor switch the diagram must connect a device capable of ensuring the continuous flow of current i. Such a device is frequently a diode (Fig. 3.4a); current i switching off in TC is linked to the current rise in D and conversely. In many reversible DC-DC and DC-AC converters, there are two switches made up of a controlled semiconductor device and a diode in antiparallel (Fig. 3.4b). Current transfer takes place between TC 1 and D 2 or vice versa, and between TC 2 and D 1 or vice versa"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002566_014233129701900205-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002566_014233129701900205-Figure2-1.png",
        "caption": "Fig 2 Configuration of 2-link hydraulic manipulator model",
        "texts": [
            " The TA9 is approximately 1.5m long, has a mass of 36kg and is powered by a hydraulic supply operating at 175 x 1C? Ni 1,M2 (2500 psi) giving a maximum payload of about 80 kg. The robot has limited instrumentation, potentiometers to measure joint angles, and a force/torque sensor which has been retro-fitted to the end-effector. This setup is reflected in the implemented controllers. The TA9 has seven degrees-of-freedom (7-DOF), but for the purpose of the simulation, only the shoulder slew and elbow joints are modelled (Fig 2). Restricting the manipulator model to 2-DOF enables the controllers to be implemented without the additional complexities of the full 7-DOF robot. It gives some indication of possible performance when the 7-DOF case is considered, although it is recognised that in this case gravity terms will play a more important role in changing the apparent system dynamics. Both the shoulder slew and elbow are revolute joints and are actuated by linear hydraulic rams (acting about the joint pivot) which are in turn regulated by electrohydraulic servo-valves. This 2-DOF manipulator model results in a robot which operates in a horizontal plane. The manipulator dynamic model is derived in the conventional manner, and is augmented with the nonlinear dynamics of the actuator. This includes compressibility of the oil, piston leakage, servo-valve nonlinearities and geometry of the pivot mechanism. The environment is modelled as a simple spring having stiffness, K~, and is located at &horbar;1.05m along the axis ({O} in Fig 2), with the origin of the world coordinate frame coinciding with the base frame of the manipulator ({C} in Fig 2). &dquo; The derivation of this model is more fully described in Lane et al (1996), and produces realistic results that have been experimentally verified. The model and all the at Afyon Kocatepe Universitesi on April 28, 2014tim.sagepub.comDownloaded from 109 subsequent controllers are implemented in the Matlab/ Simulink simulation environment. 3. The t/~G-I~F and virtual environment controller, This section details a robust hybrid position/force controller developed at L1RMM, which is based on sliding mode control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure13-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure13-1.png",
        "caption": "Fig. 13. (a) The perceived shape of the space CFNS(ti) generated by the robot R2: (b) The simplified traffic patterns L6; L7; L7; L7 generated by R2: *The robot R6 cannot be perceived by R2 at the time ti; since it is behind R4:",
        "texts": [],
        "surrounding_texts": [
            "Since the major goal of the traffic language is to assist an autonomous robot to represent and understand the traffic priorities of the other moving objects in the same navigation space avoiding collisions, it is necessary that the synthesis of traffic priority patterns to be defined semantically. Notation: a) (commutative) with b) (associative) with and Definition: The length of a perceived pattern is defined as the number of corridors which compose the pattern. Corollary: Two perceived patterns (generated by the same or different robot, at the same time for two different moving objects) with the same length are not necessarily identical in shape. Definition: The synthesis # (semantically) of two traffic patterns determines the order of the robots priorities one against the other. Proposition: (commutative) Proof: Let assume that three robots are moving in the same navigation space, as shown in Fig. 10. The robot is the main one and are the secondary robots. For this particular case, and Thus, the pattern produces the relationship between the robots\u2019 priorities. The pattern provides the priority relationship Thus, the synthesis provides the relationship (1) among the robots\u2019 priorities. Now, the synthesis provides (2). These two relationships are identical, which means that Following this process easily it can be proved the general case Proposition: (associative) Proof: Similar to commutative. Notation: (identity traffic pattern) for every Corollary: In a free navigation space with secondary moving robots there is a possibility of existence of the following traffic pattern configurations. 1) There is a maximum of two patterns with . 2) There is a maximum of one pattern with or . 3) There are patterns such that where Corollary: In a free navigation space FNS if there are the traffic patterns and the there is not the pattern where the sequence of the values for the indexes are and or and or and Traffic Complexity Table II presents the traffic complexity of moving robots in a CFNS under two different assumptions. \u2022 In the first assumption, called individual, a robot views all the other moving robots, generates all the traffic patterns from its own position and calculates all the possible traffic priorities of the other robots against its own priority. \u2022 In the second assumption, called global, every robot views all the other moving robots, generates all the traffic patterns and calculates all the possible traffic priorities for all the moving robots including itself. V. ILLUSTRATIVE EXAMPLES In this section, two illustrative examples for traffic cases are provided and solved by using the KYKLOFORIA language. In the first example, the traffic case includes six moving robots in a free navigation space shown in Fig. 11. Figs. 12\u201317 provide the shape of the free navigation spaces observed TABLE III SIMULATED RESULTS FOR FIG. 18 by each moving robot and the traffic patterns generated by each of them in their own free space. In the Fig. 18, the velocities of the moving robots are considered the same, thus the traffic priority relationships generated by the traffic language are given in Table III. Each moving robot knows the traffic priority relationships in the same free space. Thus, the robot makes use of its own which is higher than and goes out of the narrow corridor. At a time min, covers a distance of 4.5 m. The robot has to wait of a period of 0.6 min, and then it proceeds into the open corridor by covering a distance of 1.4 m in 0.485 min. Initially, covers a distance of 1.3 m in 0.325 min, then it slows down and waits for 0.55 min before it proceeds into the narrow corridor following the robot and covering a distance of 0.9 m in 0.23 min. The robot using its own higher priority over covers a distance of 4.5 m. The robot waits for 0.75 min and then proceeds forward by covering a distance of 1.5 m. Finally, the robot covers a distance of 4 m in 1.125 min because it spends some time to change its direction. Note that, and TABLE IV SIMULATED RESULTS FOR FIG. 19 (a) (b) Fig. 14. (a) The perceived shape of the space CFNS(ti) generated by the robot R3: (b) The simplified traffic patterns L1; L7; L2; L6 generated by R3: change their directions (as shown in Fig. 9) avoiding a possible collision. In the case that the velocities of the robots are considered different, then Table IV shows the traffic priority relationships and the robots traffic paths and locations are given in Fig. 19. In particular, present a traffic behavior similar to the previous case with the same velocities, by using the Table IV. covers a distance of 4.9 m with m/min. covers a distance of 1.4 m with m/min. covers a distance of 1.3 m with m/min and a distance of 0.6 m with m/min. waits until passes the intersection point and then covers a distance of 1 m with m/min. covers a distance of 4.8 m with m/min. Finally, covers a distance of 2.5 m with m/min. The second example explains the use of the language for the improvement of the traffic schedule of a particular robot under the assumption that the local traffic flow in a certain region is almost the same every time that the robot enters that region. In this case, the robot enters the region from left to right at time and spends min crossing it. At that time, there are three other moving robots crossing the same region from different directions (see Fig. 20). The traffic flow extracted by the robot in that region, is represented by the following language words: The symbol & represents the synthesis operator between words for the formulation of the traffic flow extracted by a robot traveling through a region where In this particular case there is no delays during the traveling. Fig. 21 shows the same region, at a different time where the robot enters the region from the right to the left in order to cross it by following the reverse path of Fig. 20. At this time there are four other moving robots and a fifth one is coming to the same region. The traffic flow extracted by the robot is represented by the following words: where In this particular case there are delays due to conflicts between the robots directions and traffic priorities. More specifically, the robot has to wait until and pass first and then it continues its own path. This mean that the robot knows the time required to cross the region, and in the latter case it took more time, At this point the robot analyzes the traffic flow perceived by itself and modifies its traffic path for a future cross of the same region under a traffic flow similar to More specifically, it follows the next algorithmic steps: 1) Check each word , for patterns . 2) Search for possible patterns , to replace in a word . 3) Replace the first with an in . 4) Rearrange the word into a new one , which includes the affects on the other patterns due to replacement ( instead of ). 5) If the new word includes less number of patterns then use it in the new , else go to 2 to replace the next with an in . 6) If the new overall traveling time is less than the original then proceed else no changes Thus, Fig. 22 shows the new modified traffic path. The new traffic flow extracted by is represented by the following words: where Thus, the new traffic flow includes less conflicts and no significant delays for the robot"
        ]
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure12-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure12-1.png",
        "caption": "Fig. 12. Suspension of Three-cylinder Oil Engine",
        "texts": [
            "comDownloaded from SUSPENSION OF INTERNAL-COMBUSTION ENGINES IN VEHICLES 27 Proc Zmtn Mech Engrs (A.D.) NO I 1957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub.comDownloaded from 28 M. HOROVITZ REAR VIEW advantages of this design have now led to further uses even in the heavy vehicle field. In a four-cylinder underfloor engine installation in a coach, three such eccentric bushes were employed as the sole mounting elements. Floating power in the fullest sense had to be employed for a three-cylinder oil engine shown in Fig. 12. Both vertical and horizontal primary out-of-balance couples are present on this engine and, to obtain insulation against these as well as the 13-order torque harmonic, a suspension giving a high degree of rotational flexibility about all axes must be employed. This was achieved by using a V-arrangement of sandwich mountings very close to the centre of gravity, with the front rubber sandwich mounted so that its compression axis also passed roughly through the centre of gravity. The degree of insulation obtained is excellent",
            " There were very few engines where that solution, which obviously entailed 100 per cent deflection testing, was really necessary, but that method was used for aircraft instruments which must be kept in very good alignment under acceleration loads. Much work was being done to improve control of stiffness but he would mention that synthetic rubbers were no different to natural rubber in creating that difficulty. He was most interested in Mr. Perrett\u2019s remarks on the mounting arrangement illustrated in Fig. 12. The changes to the front engine mounting to make it less critical to stiffness variations showed how engineering could be used to eliminate deficiences which the chemists specializing in rubber were trying hard to resolve. He could not agree with Mr. Nicolaisen that the symmetrical system had no advantages over an arbitrary mounting arrangement. From Fig. 2 and Table 1, it would be seen that for the asymmetrical system, torque harmonics would give resonances about three axes BIB,, B2B2, and B3B3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003712_cdc.1994.411123-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003712_cdc.1994.411123-Figure1-1.png",
        "caption": "Figure 1: A 5-axle trailer system with the first and fourth axles steerable.",
        "texts": [
            " The 5-axle system with two steering wheels is the first example in which interesting things begin to happen. Assuming that the first axle is steerable, there are four possible positions for the second steering wheel. Three of these four cases satisfy the conditions for converting t,o extended Goursat normal form; the fourth does not. Two of the examples will be presented in some detail to give the reader a flavor for the type of calculations which are required. Example 1. 5-axle, 1-4 steering trailer system. Consider the :,-axle system with the first and fourth axles steerable, as sketched in Figure 1. The configuration space can be parameterized by the x, y position of the third axle, the hitch angles e,, and the steering angle of the third axle 6. Let q = {x3, y3,05,91,03,92,81, d} represent the state. 4. Mobile Robot Examples The constraints are that each axle rolls without slipping: a' = sinBidx, - cosO,dy, i = 1,2,3,5 a4 = sinddxq - cosddyr The Pfaffian system is thus I = {a1 ,az ,a~ ,a4 ,a5} nd a complement to this system is: (dd,d&,dx3}. This basis of constraints is adapted to the the derived flag, I = t a l , az, a3, a 4 , 0 5 ) I ( ' ) = {aZ, a3, a\"} I ( 2 ) = { a 3 } 1(3) = (01 and satisfies the congruences: do' E q ( 9 ) d81 A dx3 mod I da2 E c 2 ( 9 ) a' A dx3 mod I ( ' ) d o 5 ~ ( 9 ) a4 A dx3 mod I ( ' ) du3 E c3(q) u2 A dx3 By a simple rescaling of the basis, the functions c , (q ) can be eliminated to get the Goursat congruences (3) exactly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure14-1.png",
        "caption": "Fig. 14. Suspension of Four-cylinder Oil Engine in Rear of Bus",
        "texts": [
            " The various points around the principal axis mark the positions of the axis as calculated from the vibration readings obtained well above and well below this axis. The calculated amplitudes are in very good agreement with those actually obtained. This suspension is one which shows that in the absence of incidental vibrations, theory will bring success in practice. The same type of main engine mounting is used at the front of the four-cylinder oil engine fitted at the rear of a bus as shown in Fig. 14. A number of trials were carried out on this engine before the solution was eventually found. The secondary out-of-balance force, combined with a rather flexible chassis, made it essential to fit mountings with a large degree of vertical and rotational flexibility. Rubber in shear mountings are, therefore, used for the rear high point mounting, so making the suspension system very flexible and to resemble more closely the original floating power than is usual nowadays. With rubber in compression in the fore-and-aft direction for both front and rear mountings in the scheme shown in Fig. 14, special provision had to be made to allow for tolerances in the fittings without stressing the front mounting against the rear mountings. For this reason it is more usual to design for rubber in shear fore-and-aft, for either the front or the rear mountings. Finally, an example of a three-cylinder opposed-piston engine (Fig. 15). Due to the rockers on this engine, a distinct primary vertical out-of-balance couple is present which is reduced to a minimum by balancing, so that for practical purposes only a horizontal out-of-balance couple remains"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003554_20.619680-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003554_20.619680-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of moving magnet linear actuator for gas compression. (0 valve assembly @ piston @ laminated core @I permanent magnet 0 coil 0 spring)",
        "texts": [
            " We analyze the dynamic characteristics of a reciprocating linear actuator for gas compression. The axisymmetric finite element method(FEM) considering the saturation effect of the magnetic material is used, and electrical circuit equation, mechanical dynamic equation and pressure dynamics are coupled. In the FE analysis, we adopt a moving line technique to save computation time and to perform the process efficiently. The pressure dynamics of the gas in the compressor is modeled using the law of thermodynamics. Fig. 1 shows the analysis model corresponding to Sunpower Inc. The material of the permanent magnet is NdFe-B, and the magnetization direction is radial[5]. Manuscript submitted January 28,1997 Sang-Baeck Yoon, +82-2-290-0342, fax +82-2-295-7111 I imotor@unitel .Co. kr 11. DYNAMIC FINITE LEMENT ANALYSIS A. Field Equation Axisymmetric FEM is applied to the analysis because the phenomena of field are constant concerning the rotation direction. The axisymmetric FE analysis of the reciprocating actuator is performed with the following assumptions: 1) the current and magnetic vector potential have only a B component without a dependence on 0, 2) the movement direction of the actuator is axial only, 3) the core is laminated ideally, and 4) the conductivity of the permanent magnet is ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003718_iros.1999.812833-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003718_iros.1999.812833-Figure3-1.png",
        "caption": "Figure 3: Configuration for the calculation of ERP (Estimated Reflection Point). T I , r2 are measured range data from robot\u2019s position PI , P2, respectively. When these range data originate from the same flat wall, ERP R I , R2 are on the intersections of the flat wall and two perpendicular lines through PI , P2.",
        "texts": [
            " If there is a matched wall found in the map, the wall is considered to be the actually measured one, and the robot\u2019s position is corrected based on the MLE (Maximum Likelihood Estimation) method using the information about that wall. If no matched wall is found in the map, or two or more matched walls are found, the position correction will not be done for safety reason. 4 Process for Position Correction 4.1 Extraction of flat wall The following method will be used to verify whether a series of ultrasonic range data is generated by one flat wall or not. As shown in Figure 3, let us consider that a couple of range data T I , r-2 are obtained by an ultrasonic sensor when the robot was located an, S(z l , K), P2 ( 2 2 , y 2 ) , respectively. If these range data originate from the same flat wall, the reflection points on the wall should be on the intersections of the flat wall and two perpendicular lines through PI, P2, because the ultrasonic wave is reflected specurlarty at the flat wall surface[7]. We call these points \u201cERP (Estimated Reflection Point)\u201d. Now, we name two ERPs, RI and R2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002521_027836499201100506-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002521_027836499201100506-Figure3-1.png",
        "caption": "Fig. 3. Telescopic leg link structure.",
        "texts": [
            " The leg position with respect to the body is determined by ( 1 ) the hip angle \u2019P between the negative direction of axis Bz and a telescopic link of the leg and (2) the leg length L (the distance of the hip point B to the foot S) (see Fig. 2). The leg mass is m.L, the distance from the foot to the center of mass is p, and the inertia moment of the leg with respect to the center of mass is JL, The leg makes contact with the support surface in a point. Interaction between the foot and the support surface is reduced to the reaction force of the support surface. A structural diagram of the telescopic leg link is shown in Figure 3. The load-carrying structure of the leg ( 1 ) with stops 2 and 3 is provided with a spring (4) and a coupling (5) that can move along the leg. The coupling length 6 can be changed by means of the actuator (6). The axis (7) of a hip hinge \u2019P is fixed to the coupling. The spring ends are fixed to the lower stop (3) and the coupling. The upper stop (2) restricts the motion of the coupling (i.e., restricts the leg length). The mass of the coupling is included in the mass of the part m\u00a1 of the body. The leg length L is the distance from the axis to the foot. The maximal length of the leg is limited by Lo corresponding to the position of the coupling 5 on the upper stop 2. The force F generated by the telescopic link of the leg is determined by the force produced by the spring and the friction of the coupling against the load-carrying structure of the leg (see Fig. 3). We assume that the friction is reduced to the dry friction; then , where k is the spring stiffness, L* is the leg length when the spring is in rest position, and Ffr is the dry friction force value. The coupling length will be called the spring compression actuator length. \u2019The value of 8 may change within the limits As a result of eq. (1), by changing the spring compression actuator length 6, we can vary the force generated by the telescopic leg link when the values of L and L are fixed. 3. Machine Motion and Control Algorithms The support surface is the horizontal plane ~G = 0, where (G(71) is the support surface equation",
            " Then, after linearizing the motion equations, we perceive that the motion control problem is decomposed into three separate parts (the control loops): . Vertical motion control (maintenance of the assigned hopping height). ~ Horizontal motion control. ~ Body attitude stabilization. The vertical motion control (maintaining the given hopping height) is carried out by means of the spring compression actuator displacement. In the flying phase, the leg is completely straightened out, L = Lo, or the coupling is located on the upper stop (2) (see Fig. 3). In the beginning of the support phase, the vertical velocity of the body is negative. The body is first decelerated to zero velocity in the coordinate ( (the deceleration phase) and then accelerates up to the velocity required to perform the next hop (the acceleration phase). Ti is the duration of the flying phase, To is the duration of the support phase, Td is the duration of the deceleration phase, and Ta is the duration of the acceleration phase; thus To = Td + Ta. In the deceleration phase, the body compresses the leg spring, accumulating energy in it, and goes into the acceleration phase to increase the potential and kinetic energies of the body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003049_bfb0032596-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003049_bfb0032596-Figure6-1.png",
        "caption": "Figure 6: Origin of a path from S to P. a) before, b) after the connections are learned.",
        "texts": [
            " Each spreading neuron has an inhibitory obstacle-point-inpm (O), by witch it is inhibited if it is part of an obstacle, and an exitatory target-point-input (T), by witch it can be activated periodically to create a wave Each neuron in the spreading layer has a corresponding neuron in the path layer to which it is connected be an exitatory connection (P). Each neuron in tile path layer is connected to each of its eight neighbors with three connections, one permanent and two learning ones. In addition each neuron has three inputs. Figure shows the inputs and the connections to tile left neighbors of a neuron in the path layer. Figure 6 is used ~o explain how the path layer works: An oriented connection is to be learned from tile starting point S to the first point P of Ule path. To learn this connection, the corresponding neuron of S (neuron S) in the path layer must be source-learning active and simultaneously neuron P must be target- learning active. Figure a shows the initial situation when no connection is learned yet. S gets a source-learning activation by a continual signal at its input start_in. The source actiwltion leads also to a spike activation, so the neuron spikes continuously, passing a source-learning inhibition over the permanent connection s inhib to P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002958_70.508438-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002958_70.508438-Figure14-1.png",
        "caption": "Fig. 14. E, w.r.t. the frame of P can be obtained by coordinate transforms.",
        "texts": [
            "12 = /31 < P 2 . Thus, the grown region &, can also be obtained by applying Theorems 4 and 5 to the two situations respectively; the combined result is the same as described in Theorem 6. Fig. 13 illustrates the surface &,,described in Theorem 6. The general description of &, with respect to the object frame of P can be obtained easily through the transform from the spherical coordinates to the Cartesian coordinates and then the rotational transfonn from o - xyz to the object frame o - xpypzp of P (Fig. 14). d e I r I min(sinp,,sinpz) PI - \u20ac0 5 8 I P 2 + \u20ac0 can also be derived following Appendix B. C. Growing a Plane a Containing a Face f of P Dejhition 6: For a plane a which contains a face f E P and therefore rigidly attached to P, if the position of P is fixed A,($) = U a ( M ) M E N , (A) XIAO AND ZHANG: GROWING A POLYHEDRON BY ITS LOCATION UNCERTAINTY 559 is the grown region of the plane a by the orientation uncertainty of P , where a ( M ) denotes the corresponding plane which a occupies when P is at orientation M "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003393_physreve.57.1886-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003393_physreve.57.1886-Figure1-1.png",
        "caption": "FIG. 1. Schematic view of the inclined line consisting of microfacets whose inclination b can vary according to their position. On the scheme only the facets hit by the ball have been drawn. xi (i 50,1,2, . . . ) denotes the position of the successive collision impacts, while b i is the inclination of the corresponding facets.",
        "texts": [
            " III we analyze the motion of the ball as a function of the inclination of the facets. We first treat the case where the facet inclination is assumed to be constant along the line. Then we investigate the case where the inclination of the facets varies along the line with a welldefined spatial periodicity. In Sec. IV we examine the effect of noise associated with facet inclination on the ball behavior. Section V contains the conclusion and prospects for future investigation. The rough line, on which the ball is dropped, is depicted in Fig. 1. The line forms an angle a with respect to the horizontal, while the microfacets make an angle b with respect to the inclined line. The facet inclination is not necessarily uniform, but can vary along the line. In the general case, the facet orientation is taken to be dependent of the facet position x along the line and given by the function B(x). The size of the facets is not taken into account here and is unimportant for our purpose. Let us describe the motion of the ball on this line. At time t50, the ball is launched from the position x5x0 on the line with an initial velocity VW 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003052_980220-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003052_980220-Figure1-1.png",
        "caption": "Figure 1. Passenger car model structure together with assumed coordinate systems",
        "texts": [
            " ADAMS, SIMPACK or DADS) use very fast and efficient workstations as Silicon Graphics or Sun. However, many practical problems may be solved by medium class simulation models. This paper presents two of them, that can be effectively run on PCs. Most of the attention was focused on showing results of experimental verification of simulation models. VEHICLE MODEL STRUCTURES The physical model of the car [7, 8, 9, 11, 12, 13] is based on the structure of a biaxial vehicle with independent front wheels and dependent rear wheels (Fig. 1). It consists of 8 mass-elements treated as rigid bodies (body, rear axle beam, two front unsuspended masses, four rotating wheels). The biaxial truck model [9, 10, 13] (Fig. 2) has a similar structure, but the front suspension is dependent. It consists of 7 rigid mass elements bodies (body, front and rear axle beams, four rotating wheels). Vehicle motion is described in fixed coordinate system Oxyz connected with the road and in many local systems connected with the model bodies (Fig. 1 and 2). Both models have 14 dof (degrees of freedom): 3 co-ordinates of vehicle body centre of gravity O1 position in fixed system Oxyz ( ), 3 angular co-ordinates of body position (yaw , pitch \u03d51 and roll \u03d11), 4 co-ordinates of unsprung masses relative motion (car: ; truck: ), 4 angular coordinates of wheels\u2019 rotation (\u03d55, \u03d56, \u03d57, \u03d58). Non-linear elastic-damping suspension characteristics (Fig. 3 and 4) were adopted, including non-linearities (limiters, dry friction, asymmetry of shock-absorbers). Three-dimensional location of the kingpin axis is described in the body-fixed system O1\u03be1\u03b71\u03b61 (Fig. 1) by the kingpin inclination and the castor angles. Apart from this the wheel plane is the camber angle from the normal line to the contact plane. These angles are functions of suspension deflection. They are determined during presimulation suspension analysis. Suspension compliances are taken into account but in very general way [8], without inclusion of bushing elements models. The pneumatic tyre model [8] describes interaction with even and uneven road surface. Account was taken of elastic-damping properties in the radial direction (Fig. 1, 5 and 6) and of elastic properties in the lateral and longitudinal direction (Fig. 1). The tyre shear forces and aligning moment model is a semi-empirical model (HSRIUMTRI [3] or Magic Formula [17]). It includes the influence of the wheel centre velocity, normal reaction of road and camber angle. In low frequency analysis, transient properties of tyre are neglected. When considering higher frequency phenomenon [14] first order differential equation for lateral force is applied based on von Schlippe-Dietrich theory [15]. Account was also taken of the influence of king-pin inclination, caster, and toe-in angles on forces and moments generated in the footprint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003840_jsvi.2002.5051-Figure25-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003840_jsvi.2002.5051-Figure25-1.png",
        "caption": "Figure 25. Motoring facility (views of different parts).",
        "texts": [
            " The motoring facility comprises a variable-speed electric motor and a driving system which enables the engine to be motored at different speeds: manufacturer: ASEA FULLER, type, KB24; power: 42/44 hp; speed, 167\u20131670 r.p.m. The drive system consists of the drive shafts and belts and an electro-mechanical clutch. A set of pulleys is used to drive and multiply the speed generated by the electric motor. The electro-mechanical clutch is coupled to the main shaft to control and smooth the power engagement between the driving system and the engine. The Internal Combustion Engine (ICE). The engine used is a four-cylinder in-line, fourstroke, overhead camshaft, compression ignition unit of 1 8 l (Figure 25): manufacturer: FORD; engine code: RTC/RTD; bore 82 5mm; stroke: 82 5mm; maximum power: 60 bhp (DIN) at 4800 r.p.m; maximum torque: 110Nm at 2500 r.p.m. 4.1.2. Acoustic chamber The motoring facility was assembled outside the acoustic chamber where the engine was set-up. This chamber is a simple acoustically isolated room with an independent floor, and has the dimensions of 3 75m width, 3 15m length and 2 36m height. The walls and roof are treated with 100mm rockwool acoustic absorption. The reverberation time of the chamber was measured in octave bands from 32 5 to 8000Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003565_20.582697-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003565_20.582697-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of the circuit connection of an SRM.",
        "texts": [
            " One immediate advantage of this approach is that the need of remeshing at different position is completely eliminated. In addition, this scheme greatly reduces the amount of disk storage required and also allows a more consistent approach to be used in both the pre and post processing stages since, in a loose sense, the same mesh is used at all time. V. EXAMPLE Here we use the 3D scheme described above to model a Switched Reluctance Motor(SRM) connected to its inverter circuit dynamically. The SRM used has 6 stator and 4 rotor poles. Fig. 4 shows a schematic diagram of the circuit connection of the SRM. Windings on diagonally opposite stator poles are connected in series to form a single phase. By controlling the switch on/off time of each of the phase, a motoring torque is developed to pull the rotor round. To reduce the size of the finite element model, we have only modelled a quarter of the motor in the simulation by using symmetry conditions and periodic constraints. Each stator phase was switched on for 30 mechanical degrees when the approaching rotor pole is 55' from the stator pole"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002290_951039-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002290_951039-Figure8-1.png",
        "caption": "Figure 8. Schematic of Roller Follower Lever",
        "texts": [
            " The roller will slip when the friction force is smaller than the tractive force. At this time, the available tangential force (the friction force) becomes insufficient to provide the tractive force that is required for the roller pin friction torque and the roller inertia torque. The friction force (Ff) was obtained in equation 21. The tractive force (Ft) is derived from the roller pin friction torque and the roller inertia torque as follows. The schematic of the roller follower lever is shown in Figure 8. From a torque balance, the tractive force can be obtained from the roller pin friction torque (Tf) and the roller inertia torque (Ti): The roller pin friction torque (Tf) was obtained by similarity analysis. The roller inertia torque (Ti) was computed by the mass moment of inertia (Ir) of a roller and the absolute angular acceleration of a roller: Ti = Ir (\u03b1f-\u03b1\u03b9) where \u03b1r is the relative angular acceleration of a roller and \u03b1\u03b9 is the angular acceleration of the lever. The calculated roller inertia torque at each speed is shown in Figure 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002497_jaer.1996.0022-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002497_jaer.1996.0022-Figure4-1.png",
        "caption": "Fig . 4 . Pressure areas and area of uncut soil of discs in a gang projected on to a y ertical plane for a 5 0 8 ( upper : ele y ation ; lower : plan ; A p 5 ACFB 5 DEFG ; A o v 5 BFG ; A g 5 BFG ; A u 5 CFE )",
        "texts": [],
        "surrounding_texts": [
            "The critical tilt angle ( a c ) occurs when the tilt of the disc is equal to the angle made by the tangent to the rear spherical surface , in a diametral plane of this surface , at a point where it intersects the circumferential plane of the disc . When this angle is reached the rear surface will contact the soil . The value of the critical angle is given by a c 5 \u03c0 / 2 2 e (4) For the shallow disc , a c 5 69 ? 9 8 and for the deep disc a c 5 57 8 , so that for the practical range of a (15 8 to 25 8 ) the critical angle is not reached and the rear spherical surface of the discs will not contact the soil surface ."
        ]
    },
    {
        "image_filename": "designv11_31_0002894_15.3.235-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002894_15.3.235-Figure2-1.png",
        "caption": "Figure 2 Bracket-wire system showing the forces (/\", and P2) and couples (A/, and A/2) acting on the two sections of the wire span (referenced L, and L2 in the Appendix) with the bracket tilted at an angle 0.",
        "texts": [
            " In sliding mechanics, bending of the archwire produces forces acting on the bracket which provide a couple to resist further tipping of the tooth. Unfortunately, these forces also give rise to friction. If this friction is excessive, binding occurs, until, under the action of the couple alone the tooth uprights itself sufficiently to free the wire in the bracket. Tooth movement thus progresses in a series of jerks with slip and uprighting movement occurring alternately. Analytical method With reference to Fig. 2, the archwire may be considered as consisting of two cantilevers. The necessary steps are then as follows. 1. For each cantilever the force P and couple M required to deflect the free end a distance y and tilt it through an angle 6 such that it would fit into the bracket slot is then determined. 2. The total couple on the bracket is then given by: M=(Pl + P2)(W/2) cos 6 + Ml + M2 where the subscripts refer to the cantilevers shown to the left and right in Fig. 2, respectively. 3. The net vertical force on the bracket is then: span 18.4 cm in length with an enlarged bracket 1.95 cm wide fitted with a mechanism capable of recording the forces and couple applied to the bracket for different angles of tilt and different positions along the span. The experimental jig consisted of a modified vernier microscope framework (Fig. 3, lower diagram) from which the microscope housing had been replaced on the lateral cross-slide C by a 0.5 inch (1.27 cm) diameter bar which carried a vertical mild steel cantilever beam of rectangular cross-section",
            " American Journal of Orthodontics and Dentofacial Orthopedics 96: 249-254 Waters N E, Stephens C D, Houston W J B 1975 Physical characteristics of orthodontic wire and archwires. Part 1. British Journal of Orthodontics 2: 15-24 Weine F S 1976 Endodontic therapy. C V Mosby St Louis, USA Appendix As noted in the analytical method section above the assumption is made that the archwire may be considered as two cantilevers with their free ends inserted into each end of the slot on the bracket of the tooth being retracted. Then, with reference to Fig. 2, and with the assumption that the wire deflections are small in comparison with the free length of wire in each case, the force P and couple M requires to deflect the free end of each cantilever a distance y and tilt it through an angle 9 may be determined by simple beam theory (Timoshenko, 1955). With the convention that the subscripts 1 and 2 refer to the posterior and anterior part of the span, respectively, this gives: = 6*G*(L2+W)*Ai/L2i M! = 3*G* ,/L12 : = 3*G*(W+4*L2/3)*AJL22 where the expressions have been written in BASIC for ease of insertion into a computer program"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002732_3.21203-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002732_3.21203-Figure1-1.png",
        "caption": "Fig. 1 State and output variables.",
        "texts": [
            " By equalizing the plant dynamics across the flight envelope, gain scheduling is avoided and a single outer-loop design can be performed. The equalized plant is described by A = -0.1689 0.0759 -0.9952 -26.859 -2.5472 0.0689 9.3603 -0.1773 -2.4792 B = , = r i.oooo I o 0 0.9971 0 0.0755 (11) The state, control, and output vectors are given by * = [/3 p r]T u = [P ji}T y = tf (12) The states, inputs, and outputs are, in order: sideslip, body axis roll rate, yaw rate, sideslip acceleration, stability axis roll acceleration, sideslip, and stability axis roll rate. Figure 1 shows the difference between body axis and stability axis roll rates, where a. is the angle of attack and V is the velocity vector. The primary measure of manual flight control performance is adherence to flying quality requirements. These requirements are given in terms of low-order transfer functions that approximate the desired dynamics between pilot input and aircraft response over the frequency range considered important.2 The lateral stick and pedal commands from the pilot translate into a sideslip angle command and a stability axis roll rate command"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003950_pime_proc_1990_204_140_02-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003950_pime_proc_1990_204_140_02-Figure1-1.png",
        "caption": "Fig. 1 Typical pivoted abutment S cam brake",
        "texts": [
            " The combined effects of mechanical and thermal distortions in the circumferential and axial directions on brake performance can be investigated by means of a three-dimensional analysis. Such an analysis is formulated here to include most of the major parameters that occur between sliding members during braking and it is shown how these influence the torque behaviour of a S cam brake during a single brake application. The simulation was based upon a S cam-operated pivoted abutment type of leading and trailing shoe brake assembly of diameter 420 mm and width 175 mm as illustrated in Fig. 1. On application of the brake the braking process was divided into a series of time steps of 1 s throughout the stop. For each time step, a pressure distribution, assumed constant over the time step, S2.00 + .05 Proc Instn Mech Engrs Vol 204 at Purdue University Libraries on June 10, 2015pid.sagepub.comDownloaded from 94 C WATSON AND T P NEWCOMB Fig. 2a Brake shoe and friction material is determined. From the pressure distribution the heat input to the nodes is calculated, and hence the temperature profile and the thermal distortions within the brake assembly can be determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003022_978-1-4471-1501-4_1-Figure1.5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003022_978-1-4471-1501-4_1-Figure1.5-1.png",
        "caption": "Figure 1.5: Definition of mutual position and orientation between two ar bitrary frames.",
        "texts": [
            " The transformation between two consecutive link frames is defined by (1.2) in terms of four parameters for each link. Nevertheless, eq. (1.7) involves two additional transformations; namely, from the base frame b to link 0 frame, and from link n frame to the end-effector frame e. Let us determine the parameters that describe such transformations. We can define the base frame b arbitrarily. In order to define frame 0 with respect to frame b, six parameters (-Yb, bb, O!b, lb' ih, db) are needed, in general, as illustrated in Fig. 1.5 for the mutual position and orientation between frames i-I and i. The transformation matrix is bTO = Rot(Z, 'Yb)'I'rans(Z, bb)Rot(X, O!b)'I'rans(X, lb)Rot(Z, t?b)'I'rans(Z, db). (1.116) The subsequent transformation from frame 0 to frame 1 is given by (1.2), i.e., \u00b0T1 = Rot(X,at}Trans(X,it}Rot(Z,'I?t}Trans(Z,dt}. (1.117) Combining (1.116) with (1.117) and observing that a1 and i1 can be always taken equal to zero gives bTl = Rot(X, ao)Trans(X, io)Rot(Z, 'l?o)Trans(Z, do) . (1.118) Rot(X, a~ )Trans(X, a~ )Rot(Z, 'I",
            "1, d~ = db +d1 \u2022 As can be recognized from (1.118), the overall transformation from frame b to frame 1 can be formally defined in terms of two sets of four parameters, similarly to the case of two consecutive link frames. Likewise, we can define the end-effector frame e arbitrarily, and then the transformation from frame n to frame e is nTe = Rot(Z, /'e)Trans(Z, be)Rot(X, ae)Trans(X, ie)Rot(Z, 'l?e)Trans(Z, de) (1.119) where the six parameters be,be,ae,ie,'I?e,de) are defined with reference to Fig. 1.5. Proceeding as above leads to expressing the overall transformation from frame n - 1 to frame e as n-1Te = Rot(X,a~)Trans(X,I~)Rot(Z,'I?~)Trans(Z,d~)\u00b7 (1.120) Rot(X, a n+1)Trans(X, i n+1)Rot(Z, 'l?n+1)Trans(Z, dn+1) where a~ = an, l~ = in, 'I?~ = 'l?n + 'Ye, d~ = dn + be and an+! = ae, in+! = ie, 'l?n+! = 'l?e, dn+! = de are the two sets of four parameters defining the transformation. As a consequence, the overall transformation from the base frame to the end-effector frame can be described by n + 2 sets of 4 parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003668_iros.1999.812989-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003668_iros.1999.812989-Figure4-1.png",
        "caption": "Fig. 4 Experimental Testbed for Impedance Control",
        "texts": [
            " Block Diagram of Cartesian Impedance Control for the DLR Hand memory; and there are several U 0 boards such as ADC, DAC, PI0 which are installed in a separate box . All software development is done on the separate box which connects to a SUN workstation via ether net. The box takes care of the user interface, while most real-time computations and data U 0 needed for the hand control are performed by several DSP boards. Using the Cartesian impedance control scheme developed in section 4, an experimental testbed has been built as shown in Fig. 4. According to a desired trajectory, the fingertip should move along X-axis in the finger base coordinate system from point 'a' to point 'b' with a constant linear speed at 50rnds. However, because there is an obstacle between these two points the fingertip can not reach point ' b physically and an impact appears when the fingertip makes contact with the obstacle. The entire experimental results are shown in Fig. 5. From Fig. 5(a) the fingertip can not continue to move along the dot-lined predefined trajectory in X-axis at about 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002580_1.2833527-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002580_1.2833527-Figure2-1.png",
        "caption": "Fig. 2 Geometry of the grooved seal face",
        "texts": [],
        "surrounding_texts": [
            "V. Person\nB. Tournerie\nJ. Frene\nUniversite de Poitiers, Laboratoire de Mecaniqje des Solides,\nURACNRS861, S.P. 2M. I, BR 179, 86960, Futuroscope,\nCedex, France\nA Numerical Study of the Stable Dynamic Behavior of Radial Face Seals With Grooved Faces This paper presents a simple numerical method for modeling the dynamic tracking modes of a grooved face seal. The stability is verified using a method derived from that developed for smooth face seals. The method, enabling the calculation of the kinematic parameters which describe the steady-state response of the grooved seal, is of interest in designing this type of seal. A parametric study is presented for the case of a rotor face with eight semicircular grooves. The principal effect of the grooves is to increase the hydrostatic component of the load. In turn, this makes the seal less sensitive to fluctuations of the hydrodynamic phenomena. Sinusoidal waviness is used to simulate the periodic distor tions induced by the grooves and affects the dynamic behavior only in the presence of cavitation. This occurs for very small values of the film thickness and, consequently, for very small leakage flow. In this case, the dynamic response of the seal is then strongly dependent upon the hydrodynamic effects.\nIntroduction Modeling of the behavior of mechanical face seals can be approached using either linear or nonlinear models. In the non linear model the hydrodynamic forces generated in the lubricant film depend nonlinearly upon the displacements of the floating element. In the general case, all the forces which act upon the floating element are time dependent, so that it is not possible to obtain an analytical expression for them. Therefore, the non linear differential equations of motion are usually solved by means of iterative numerical methods, such as Adams methods. This approach allows the modeling of the transient response to a perturbation as well as modeling of modes where tilt and axial' displacement change in the course of rotation (Etsion, 1982; Tournerie and Frene, 1984; Green and Etsion, 1986). However, this iterative procedure is not well adapted to the stable \"dy namic tracking\" mode because convergence is very slow in the neighborhood of the steady-state solution.\nIn the linear approach, it is assumed that the displacements of the floating element are small perturbations about a fixed equilibrium position, a hypothesis which is valid in practically all applications. The forces generated in the film are linearly dependent upon the displacements and velocities of the floating element. These forces are calculated by means of fluid film stiffness and damping coefficients established for the equihbrium position. The equations of motion are then obtained in terms of these dynamic coefficients and of those of the flexible support. For seals with faces which are both smooth and narrow, and in which cavitation is suppressed, the dynamic coefficients, the forces and the equations of motion can be expressed in closed form (Green and Etsion, 1983; Wileman and Green, 1991, 1995). The stability thresholds and the solutions for the kinematic parameters can be obtained analytically. Thus, it is possible to directly determine the effect of the various parame ters upon the dynamic response (Green and Etsion, 1985).\nThis paper deals with liquid seals with faces which are tapered, wavy, and grooved. Mayer (1989) observed that this face geome try reduces friction and improves seal performance. The face ge ometry does not permit analytical solution of the Reynolds equa-\nContributed by the Tribology Division of THE AMERICAN SOCIETY OP MECHANI CAL ENGINEERS and presented at die ASME/STLE Joint Tribology Conference, San Francisco, Calif., October 13-17,1996. Manuscript received by the Tribology Division February 22, 1996: revised manuscript received June 3, 1996. Paper No. 96-Trib-40. Associate Technical Editor: R. F. Salant.\ntion, and both the forces and the dynamic coefficients of the fluid film used throughout the analysis are calculated numerically. The case which has been studied is that of a flexibly mounted stator with three degrees of freedom: a rotating tilt, the precession of this tilt and an axial displacement. A Newton-Raphson procedure is employed to solve the nonlinear equations of motion for the dynamic tracking mode, which is the desired behavior for the majority of applications. In most cases, the stability limits are approximately known from experience, but the stability of the cases analyzed in this work was nonetheless verified using a small perturbation method. The model is restricted to the cases in which grooves and waves exist only on the rotor and the effect of the initial stator misalignment is not taken into account. Thus, the geometry is constant in a reference fixed in the rotor. These as sumptions allow an efficient, approximate solution for the effect of deep grooves, which provides a more rapid alternative to a complete nonlinear analysis. Although this study does not consider the static response to the initial stator misalignment, it nevertheless provides valuable results for the tilt which results from the rotor misalignment.\nModeling of the Seal Ring Dynamic Behavior A radial face seal consists of a seal seat and a seal ring. The geometric and kinematic model of the seal considered in this work is shown in Fig. 1. The seal seat rotates about the za axis with a constant angular velocity to. The seal ring is flexibly mounted so that it can move axially along the za axis and tilt about the Xoi and yoi axes of the inertial system. The three degrees of freedom of the seal ring can be described using either the angles XM XJ and the centerline clearance / or using the three parameters, X;. V/> and I (Fig. 1).\nIn this study, the seal is assumed to operate in the dynamic tracking mode for which these latter three parameters are con stant and are equal to x?, y'? and la. The positions of the points M\\ and M2 (Fig. 1) on the seal ring and seat, respectively, and their velocities relative to the inertial reference can be defined in a local cylindrical coordinate system using\nOM, = rcr + [L, + (r - r,)/?, + r ( x t sin 9 - x\\ cos 9)]ZQ\nOM2 = re, + [Li + (r - r,)/32 + rxi sin (6* - ujt)\nVcA/,) = r(x{ sin 6 - Xi cos l9)zo\n+ e(r,e-ojt)]zo (1)\nJournal of Tribology JULY 1997, Vol. 119 /507\nCopyright \u00a9 1997 by ASME\nDownloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "Z2 ^0\nrotor/seal seat\nTable 1 Rotor geometry\ninner radius, n mean radius, r\u201ei outer radius, r^ number of grooves, n depth of the grooves, hg radius of curvature of the grooves, R width of the grooves, d\n44 X 10\"' m 47 X 10\" 'm 50 X 10\"' m\n8 5 X lO\"\"* m 40 X 10\"' m 1 X 10\"' m\nwhere\nX'l = Xi cos (ut + (pi) X\\ = Xi sin {ut + ipx) (2)\nand e(r, Q - w?) describes the groove depth and the waviness of the rotating face.\nThe forces and moments, which act upon the stator, consist of contributions from the fluid film in the sealing gap, from the flexible support, and from the hydrostatic pressure acting on the back side of the ring. In grooved face seals, the pressure distribution in the sealing gap is calculated using a finite element method which has been described in previous papers (Huitric, Bonneau and TOumerie, 1993; Tournerie et al., 1994). In the case of rupture of the lubricant film, the cavitated region is determined using Murty's algorithm. The force and moments resulting from the pressure field in the case of noncontacting faces are calculated numerically using the following equations:\nNomenclature\nM,\nB = balance ratio D = damping coefficients (Ns/m) FJO = initial spring (and secondary seal) axial force (N) Fpo = hydrostatic force acting on the back side of the seal (N)\nFj = axial force about z axis (N) hg = depth of the groove (m)\nh\u201e,in = minimum film thickness (m) / - seal ring transverse moment of\ninertia (kg.m^) K = stiffness coefficients (N/m) / = centerline clearance (m)\nm - seal ring mass (kg) My = moments about x and y axes\n(N.m) A' = rotational speed (rpm)\np = p(r, 6) = pressure (Pa) r = radial coordinate (m) t = time (s)\nV(M,) = surface velocity in cylindrical coordinates (/ = 1, 2)(m/s)\nW = hydrodynamic load (N) z = axial coordinate (m) ff = relative coning angle\n/5 = ( ;02- /9 . ) ( rad) /3u 02 = coning angles of stator and ro\ntor faces (rad) 9 - angular coordinate (rad) fj, = dynamic viscosity (Pa.s) X - relative misalignment (rad)\nXi = stator misalignment (rad) Xu x i = stator misalignment about j\u0302 oi\nand yoi axes (rad)\n( )\nX2 = rotor misalignment (rad) ip, = phase angle (rad) u> = angular velocity of rotor\n(rad/s) ( ) = first and second time deriva\ntives\nSubscripts e = outer side\n/ =film g = groove i = inner side s = support sp = spring ss - secondary seal 1 = stator 2 = rotor\n508 / Vol. 119, JULY 1997 Transactions of tlie ASME\nDownloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "M, \u2022xj \u2022 -1 pr^ sin ddrdd jxo\nM \u2022y.f = ( / : / : pr cos 6drd6 1 yoi (3)\nW = fZn flit - I I prdrdB )zo\nThe flexible support, which consists of springs and a secondary seal, also applies a force and moments (Green and Etsion, 1985):\nM,\u201e, =\nM,,,\nK,^r%x\\ K,,r Ix'i D,,,,rix\\ 2 2 2\nK.,rl,x] K,.,rlx\\ D.rlx\\\nXoi\nyo. (4)\nThe hydrostatic pressure acting on the back side of the ring results in the force\nl\u0302 ;)0 \u2022n-[Pi(rl ~ r?) + p,{rl - rL)]zo (5)\nThe system of three nonlinear equations of motion of the flexi bly mounted stator for the case of dynamic tracking depends only upon the three unknowns Xi. \u00a5'\"> \u0302 o\nM,,., + M,j - in = F.ixl, (p?- lo) = 0\nM,,, + Myj - m = FiiXu <pl lo) = 0\nF,,, + W + F\u201e\u201e = FJCX?, 'PU /O) = 0 (6)\nStability Verification The method used to test the dynamic stability of the seal is based upon the analytical methocl developed by Green and Et sion (1985) for the case of narrow, smooth face seals. The equations of motion are written in linear form in the inertial system in terms of the dynamic coefficients of the film and of the support. For grooved face seals there is no analytical solu tion and fluid film coefficients must be numerically calculated. It was found that, under certain conditions, the dynamic coeffi cients which were zero for the case of smooth faces, because of symmetries in the film geometry, are also zero or negligible for the case of grooved faces. Stability conditions are verified numerically using the expressions obtained with the RouthHurwitz criterion.\nNumerical Procedure for Steady Solution\n(a) Initial values of Xi> V'u and / are chosen (i.e., xT\\ ifiT\\ '\"'\") as explained below.\n(b) The nonlinear system (Eqs. (6)) is solved using the Newton-Raphson method to obtain the three parameters x\u00b0< ipl, 1\u00b0 which define the equilibrium position of the seal ring. Convergence requires the initial values to be sufficiently close to the solution; a good approximation is x'\"\" = Xa and i '\u0302\"\" = 0, with / calculated to provide hydrostatic equilibrium in the axial direction.\n(c) The stability of the equilibrium position is verified. In general, the initial conditions described in (b) are sufficiently\nJournal of Tribology JULY 1997, Vol. 1 1 9 / 5 0 9\nDownloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv11_31_0002761_1.568457-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002761_1.568457-Figure3-1.png",
        "caption": "Fig. 3 Test-seal assembly",
        "texts": [
            " The test rotor is supported at its ends by two hydrostatic bearings. The test bearing supports itself on the test rotor and is centered with respect to the support-bearing pedestals by six axial cables. The cables restrain pitching motion of the test item and cause it to move radially ~parallel to the shaft! during excitation. They are also used to statically align the test item with respect to the rotor. For the present investigation, the test-bearing assembly was replaced with the test-seal assembly illustrated in Fig. 3. Highpressure water is injected radially at the center of the assembly with two diametrically opposed locations. The water splits and exits axially across twin test seals whose geometries were defined in Fig. 1. Exit orifice seals are used at each end to hold a slight back pressure. Figure 4 presents an assembly drawing of the test rom: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 05/20/2 seals and housing. The design of Fig. 4 allows interchangeable test seal elements. Figure 5 illustrates the static and dynamic loading arrangement for testing hydrostatic bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002395_ip-epa:19951591-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002395_ip-epa:19951591-Figure1-1.png",
        "caption": "Fig. 1 B Stator slot current density b Stator slot angular position",
        "texts": [
            " Using the symmetrical component theory, the stator induced phase voltages can be found, and then an equivalent circuit is developed. Applying Kirchhoffs mesh law to the equivalent circuit, the phase currents are calculated. Finally, the output torque is obtained for any speed from standstill up to synchronous speed. follows: 3 Stator current sheet As the slots on the stator periphery have the same shape, it is enough to derive the current sheet equation for one slot, and to add the partial effects of the individual slots. Now considering one conductor per slot, and taking the point o as a reference origin, see Fig. 1, the current density (current per slot opening width) for slot k can be represented by a Fourier series as i ( t ) idt) Jk = + - 1 cos [n(Xl - X,)] A/rad 2n 11 The stator current sheet can now be obtained by adding the current density for all slots on the stator periphery as 88 m J, = c Jl\" \"=l = n = l f rn [+cos [n(X, - X,) ] 1 Consider now each slot comprising of a number of conductors equal to N,, and, since the above equation has been derived on the basis of a positive slot current, a unit vector Z, with + 1 or - 1 may be used to correct this"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003687_isie.1999.801773-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003687_isie.1999.801773-Figure5-1.png",
        "caption": "Fig. 5. EMM for vehicle and one link part",
        "texts": [
            " In the mobile manipulator, however, much calculation effort is required to obtain Mu, so we consider Mu as arm MVta, vehicle and one link part Mv,,l indepently. EMM in Arm part For arm part, to utilize the dexterous performance of arm, we consider to keep the small EMM for all direction. Then, w,,~ is decided as performance index for arm\u2019s configuration to keep high manipulability. Then, null-space torque references are given by the following equitation. EMM in Vehicle & One Link part For vehicle and one link part (Fig.5), we investigate the relation between Mv,,l and configuration as shown in Fig.6. From the results, it is found that Mv,vl has singular\u2019 points in different motion direction. To avoid the singular point in the arbitrary motion, it is preferable that EMM is not directly utilized for the cost function of null-space. Then, we determine a selection of M,f$<, Mi${, which is suitable as the reference for Mobile Manipulator --Y Motor I I Encoder &-- Force Sensor r------------ - - - - - - - - - - - _, I _ _ _ _ _ _ _ _ _ _ _ _ "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003022_978-1-4471-1501-4_1-Figure1.3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003022_978-1-4471-1501-4_1-Figure1.3-1.png",
        "caption": "Figure 1.3: Anthropomorphic manipulator with frame assignment.",
        "texts": [
            "6) In order to derive the direct kinematics equation in the form of (1.1), two further constant transformations have to be introduced; namely, the trans formation from frame b to frame 0 (bTO) and the transformation from frame n to frame e (nTe), i.e., (1.7) Subscripts and superscripts can be omitted when the relevant frames are clear from the context. Direct kinematics of the anthropomorphic manipulator As an example of open-chain robot manipulator, consider the anthropomor phic manipulator. With reference to the frames illustrated in Fig. 1.3, the Denavit-Hartenberg parameters are specified in Tab.!.!. Computing the transformation matrices in (1.2) and composing them as in (1.6) gives (1.8) o o 10 _____ _ CHAPTER 1. MODELLING AND IDENTIFICATION where for the position, and ( C1 (C23 (C4 C5C6 - 8486) - 82385C6) - 81(84 C5C6 + C4 86)) \u00b0n6 = 81 (C23 (C4C5C6 - 8486) - 82385C6) + C1 (84C5C6 + C4 86) 823(C4C5C6 - 8486) + C23 8 5Cs ( ct{ -C23( C4C586 + 84C6) + 823 8 5 86) + 81 (84 C5 8 6 - C4 C6)) \u00b086 = 8t{-C23(C4C586 + 84C6) + 8238586) - C1(84C586 - C4 C6) -823(C4C586 + 84C6) - C23 8 58 6 (1",
            " In the case of a three-degree-of-freedom arm, for given end-effector posi tion ope and orientation \u00b0 Re, the inverse kinematics can be solved according to the following steps: \u2022 compute the wrist position \u00b0P4 from ope; \u2022 solve inverse kinematics for (ql, q2, q3); \u2022 compute \u00b0 R3(q1. Q2, Q3); \u2022 solve inverse kinematics for (q4, qs, q6). Therefore, on the basis of this kinematic decoupling, it is possible to solve the inverse kinematics for the arm separately from the inverse kine matics for the spherical wrist. Inverse kinematics of the anthropomorphic manipulator Consider the anthropomorphic manipulator in Fig. 1.3, whose direct kine matics was given in (1.8). It is desired to find the vector of joint variables q corresponding to given end-effector position ope and orientation oRe; with out loss of generality, assume that ope = \u00b0P6 and 6 Re = I. Observing that \u00b0P6 = \u00b0P4, the first three joint variables can be solved from (1.9) which can be rewritten as (1.16) From the first two components of (1.16), it is ql = Atan2{py,p.,) (1.17) where Atan2 is the arctangent function of two arguments which allows the correct determination of an angle in a range of 211\"",
            "39) yields the result that the matrix I I n can be computed as the product of three matrices (1.40) where remarkably the first two matrices are full-rank. In general, the values of h and i leading to the Jacobian i In,h of simplest expression are given by i = int(nJ2) h = int(nJ2) + 1. Hence, for a manipulator with 6 degrees of freedom, the matrix 3 J6,4 is expected to have the simplest expression; if the wrist is spherical (P46 = 0), then the second matrix in (1.40) is identity and 3 J6 ,4 = 3 J6 \u2022 As an example, the geometric Jacobian for the anthropomorphic ma nipulator in Fig. 1.3 can be computed on the basis of the matrix 0 i383 - d4 -d4 0 0 0 0 i 3C3 0 0 0 0 3J6 = -i3C2 + d4 823 0 0 0 0 0 (1.41) 823 0 0 0 84 -C48S C23 0 0 1 0 Cs 0 1 1 0 C4 848S Analytical Jacobian If the end-effector position and orientation are specified in terms of a min imum number of parameters in the task space as in (1.14), it is possible to compute the Jacobian matrix by direct differentiation of the direct kine matics equation, i.e., x = (::) = Ja(q)q, (1.42) where the matrix Ja(q) = 8kj8q is termed analytical Jacobian",
            " By incorporating the motor inertia and the two friction coefficients into the set of dynamic parameters, we can write the dynamic model as (1.67) where u is the (n x 1) vector of driving torques, 7f' is a (13n x 1) vector of dynamic parameters 7f' = (7f'l (1.68) with 7f'i = (Iixx Iixy Iizz Iiyy Iiyz Iizz (1.69) mirix miriy miriz mi Imi FBi F'lJi )T , and cp(.) is an (n x 13n) matrix which is usually termed regressor of the dynamic model. Dynamic model of the anthropomorphic manipulator As an example of dynamic model computation, consider the first three links of the anthropomorphic manipulator in Fig. 1.3. Derivation of the complete dynamic model would be tedious and error prone. For manipulators with more than 3 degrees of freedom, it is convenient to resort to symbolic soft ware packages to derive the dynamic model. Link linear and angular velocities can be computed as in (1.58), giving and \u00b0po = 0 lpl = 0 2'h = 0 3P3 = (.e3s3ti2 \u00b0wo = 0 lWl = (0 0 1 f 2W2 = (S2til 3W3 = (S23til . .)T C2Ql Q2 c23til ti2 + ti3 )T , respectively. It follows that the inertia matrix is (1.70) where Hll = 1m1 + Itzz + 8~12\"'''' + 282C212\",y + C~12YY +8~313\"'''' + 2823C2313\",y + C~313yy + 2l3c2c23m3T3\", -2l3c2823m3T3y + l~c~m3 H12 = 82 12\"'21 + C2 12yz + 823/a\"\", + C2313yz -l382m 3T3z H 13 = 82313\"\", + C23/ayz H22 = 1m2 + 12zz + 2l3c3m3T3'\" - 2l383m3T3y + l~m3 + 13zz H 23 = 13zz + l3C3m3T3'\" -l383m 3T3y H33 = 1m3 + 13zz , from which the elements of the matrix C can be computed as in (1",
            "67) for N random values of q, q, ij, i.e., _ _ ( ~ ( ql , ~l , ijd ) ~- . ~(qN,qN,ijN) (1.114) such that the number of rows is (typically much) greater than the number of columns. No matter how parameter reduction is accomplished, eq. (1.67) can be rewritten as u = Y(q,q,ij)p (1.115) where p is an (T xI) vector of base dynamic parameters and Y (.) is an (n x T) matrix which is determined accordingly. As an example of dynamic parameter reduction, consider the complete 6-degree-of-freedom anthropomorphic manipulator in Fig. 1.3. Using the general rules for j = n, . .. ,1 gives the following sets of reductions: I~xx = I6xx - I6yy I~xx = Isxx + I6yy I~zz = Iszz + I6yy I I mSTSy = mSTSy + m6T6z m; = ms +m6 for link 6, and thus the base parameters are: I~xx' I6xy , I6zz , I6yz , I6zz , m6T6x, m6T6y; I~xx = Isxx + I6yy - Isyy I~xx = I4zx + Isyy I~zz = I4zz + Isyy I I m4T4y = m4T4y - msTsz m~ = m4 +ms +m6 for link 5, and thus the base parameters are: I5xx , Isxy , Iszz , Is yz , I5zz , msTsx, mSTSy; I~xx = I4xx + Isyy - I4yy I~zz = I3xx + I4yy + 2d4m 4T4z + d~(m4 + ms + m6) I~zz = I3zz + I4yy + 2d4m 4T4z + d~(m4 + ms + m6) m~T~y = m3T3y + m4T4z + d4(m4 + ms + m6) m~ = m3 +m4 +ms +m6 for link 4, and thus the base parameters are: I4xx ' I4xy , I4xz, I4yz , I4zz , m4T4x, m4T4y; I~xx = I3xx - I3yy + I4yy + 2d4m 4T4z + d~(m4 + ms + m6) I~xx = I2xx + I3yy I~xz = I2xz - l3m 3T3z I~yy = I2yy + l~(m3 + m4 + ms + m6) + I3yy I~zz = I2zz + l~(m3 + m4 + ms + m6) m~T~x = m2T2x + l3(m3 + m4 + ms + m6) m~T~z = m2T2z + m3T3z m~ = m2 +m3 +m4 +ms +m6 for link 3, and thus the base parameters are: l~xx' hxy, 13xz , 13yz , lLz, m3r3x, m~r~y; l~xx = hxx - 12yy - e~(m3 + m4 + m5 + m6) l~zz = l1zz + 12yy + e~(m3 + m4 + m5 + m6) + 13yy for link 2, and thus the base parameters are: l~xx' 12xy , 12xz , 12yz , l~zz' m~r~x' m2r2y; the parameters l 1xx , hxy, hxz, h yy , hyz, m1rlx, m1r1y, m1 rlz, m1 have no effect on the dynamic model and the only parameter of link 1 is l~zz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003928_0301-679x(91)90060-m-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003928_0301-679x(91)90060-m-Figure8-1.png",
        "caption": "Fig 8 Stationary shapes of worn surface rotating about the axis O0 (see schema); ~ = R~/R2 - [).3; p - r/R:. 1 - A = 0.05; a~ = 0.001; 2 - A = 0.1, a~ = 0.01; 3 - A = 0.05, al = 0.01; 4 - A = 0.001, al = 0.001",
        "texts": [
            " Curve 4 represents a smooth axially symmetric punch whose contact face within the contact area of radius R is of t h e f \u00b0 r m : Z ( R ) = 4 ( 1 - v ~ ) Q R E ( R ) is the complete second-kind elliptical integral) and ensures uniform distribution of pressure over the contact area. This punch is the limiting case of the above model in which the size of each punch tends to zero and their density a/l to 1/2 provided that the contact areas are equal. Calculations show that the difference in height between the worn punches, located in different layers of the model, increases with the punch density. Because the wear rate depends on speed as well as load, the stationary form (15) of a worn surface depends critically upon the type of motion of the system of punches, see Fig 8. Calculations were carried out for a system of cylindrical punches which are uniformly located inside the circular region (R~, R2) rotating with constant angular velocity ~o about the central point. Curves 1 and 3 were constructed at the same values of the relative area of contact A = 0.05 (A = Na2/(RZ-R2)) and at at = a/R2 equal to 0.001 and 0.0l, respectively. Curves 1, 4 and 3, 2 were constructed for punches of the same size but at different A. The calculations show that at a constant value of a~ the difference of the plot of 8~(p)/8~(~) from the plot of ~/9, corresponding to the height distribution of punches without allowance for the mutual influence, is the greater, the higher is the relative area of contact A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003053_s0167-8922(98)80098-9-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003053_s0167-8922(98)80098-9-Figure3-1.png",
        "caption": "Fig. 3 Seal model and coordinate system",
        "texts": [
            " Key dynamic parameters, such as rotor angular misalignment, the relative misalignment between the rotor and the stator, and the seal clearance can be chosen to monitor. This system can also display the rotor angular response orbit and spectrums of the proximity probe signals in real-time, 3. THEORETICAL BACKGROUNG Some background of M R noncontacting mechanical seal dynamics will be introduced to form the contact criterion. Contact detection based on contact criterion, rotor angular response orbit shape, and spectrum analysis will then be discussed. Several coordinate systems are used to describe the FMR noncontacting mechanical face seals (Fig. 3 and Fig. 4). Detailed descriptions of these coordinate systems and nomenclature can be found in Green [5]. The magnitude of ~,\" is\" =,jy, +r, -2.), , .r , (2) where ~, is the stator angle, ~'r is the rotor precession. a, The rotor response, Tr, is composed of two parts: ~,~, and ~/,~, where \"t', is the rotor response to the stator misalignment, ~,,, and ~'~x is the rotor response to the rotor initial misalignment, ~,n. Since ~,,,\" is fixed in space, while y~\" rotates at speed * , co, the overall response, T~, Is a rotating vector with a time varying frequency ~r\" The magnitude of both ~rand Yr\" vary cyclically with a constant frequency, co"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003733_0378-4371(90)90278-z-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003733_0378-4371(90)90278-z-Figure2-1.png",
        "caption": "Fig. 2. The translation of a volume element traversing the surface from its initial to final state. The dashed and full lines represent the surface at the initial and final state.",
        "texts": [],
        "surrounding_texts": [
            "A U = - f d3r f ( r ) . z l (r) s0 ~T]. (13) f( o o s o = f d 3 r L \\ ~ b + ~cr a ~ b / ~ b +"
        ]
    },
    {
        "image_filename": "designv11_31_0002420_1999-01-0743-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002420_1999-01-0743-Figure2-1.png",
        "caption": "Figure 2. Schematic Diagram of Visco-Lok",
        "texts": [
            " The viscous coupling, with its degressive characteristic, is not always able to adequately fulfil these requirements. The Visco-Lok unit was developed to meet these demands. The Visco-Lok can be used as a \"hang-on\" coupling, transfer case limited-slip differential and rear axle limitedslip differential. A detailed description of the Visco-Lok coupling is given in [1]. The unit has the following characteristics: \u2022 fully enclosed, \u2022 speed (difference)-sensing, \u2022 variable, linear characteristic, \u2022 external control is not required. The Visco-Lok consists of a multiplate clutch and a hydraulic pump (figure 2). A speed difference across the device causes pressure to be developed in the fluid shearing pump. This pressure in the viscous fluid is used to actuate a piston which compresses the clutch plates. The closure of the clutch transfers torque from one side to the other. The torque transfer is dependent on the pressure developed and hence directly dependent on the speed difference. Typical characteristic curves for this device are shown, schematically, in figure 3. The shape of the curve can be varied by adjusting the cut in point and the slope"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003213_bf00633557-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003213_bf00633557-Figure1-1.png",
        "caption": "Fig. 1. Schematic drawing of the Multi Mode Electrode from Metrohm (By courtesy of the producer). A = mercury reservoir; B = glass capillary; C = needle valve; D = nitrogen inlet",
        "texts": [
            " I f this holds for sea water, stripping voltammetry should also apply to alkaline and alkaline-earth salts themselves. Examples of application for high purity materials of this kind are presented. All experiments were carried out with the electrode stand (model 647 or 663) of Metrohm, applying either the Multi Offprint requests to: R. Naumann Mode Electrode (MME) in the HMDE mode (Hanging Mercury Drop Electrode) or the Rotating Disc Electrode (RDE) with a glassy carbon tip. A schematic drawing of the MME is given in Fig. 1. From this one can see that the mercury is placed in a closed system. It is operated under nitrogen pressure of about 1 bar. The RDE was used in order to form a mercury film electrode in situ on the glassy carbon support. The electrodes were controlled either by the Metrohm VA processor model 647 or by the Autolab system from ECO Chemie. The differential pulse technique was used throughout, with a pulse amplitude of 50 mV. Therefore, the stripping techniques used were designated Differential a Mercury film electrode formed in situ on a Rotat ing Disc Electrode with glassy carbon tip b DPASV, Differential Pulse Anodic Stripping Voltammetry c DPCSV, Differential Pulse Cathodic Stripping Voltammetry d DPAV, Differential Pulse Adsorptive Stripping Voltammetry e HEPES, 2-[4-(2-Hydroxyethyl)-l-piperazinyl]-ethane sulfonic acid f DMG, Dimethylglyoxime g PIPES, Piperazine-l,4-bis-(2-ethane sulfonic acid) di-sodium salt h BES, N,N-Bis-(2-hydroxyethyl)-2-aminoethane sulfonic acid i DASA, 1,2-Dihydroxyanthraquinone-3-sulfonic acid J DTPA, Diethylene triaminepentaacetic acid k Potassium chlorate is added only in case of DPAV with catalytic current Element Addition s [ng/g] Limit of [ng/g] n = l0 determination [ng/g] (ppb) Bi 4 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure6-1.png",
        "caption": "Figure 6. Spatial flexible manipulator",
        "texts": [
            " Once all the dynamic terms are obtained and the whole number of constraints is stated, the equations of motion may be established, and an algorithm for their integration should be selected. Equations of motion may be derived through Lagrange multipliers or penalty methods and, afterwards, they can be integrated using an explicit or implicit integrator. A spatial flexible manipulator of the type of those used in the space shuttle is presented as an application of the method. It is an open-loop system consisting of four bodies connected by revolute pairs, as it can be seen in Figure 6. Its properties are: L1 = 0.3 m, Lz = 4 m, L3 = 5 m, L4 = 0.5 m, E = 6895e07 N/m2, p = 2699 Kg/m3, inner and outer radius of bodies 2 and 3, ri = 0.04 m, I , = 0.05 m. Besides, there is a lumped mass of 200 Kg just in the middle of the last body in the kinematic chain, representing a load. As it can be seen, bodies 2 and 3 are much longer than the others, and they have tubular sections. Hence, they are modeled as flexible bodies, while bodies 1 and 4 are considered as rigid. The robot has been modeled as shown in Figure 7, where point 1 and the y-component of unit vector 3 are fixed",
            " Kim and Haug,\" using also a Component Synthesis method, as well as Avello,\" using natural co-ordinates and large deformations, carried out the simulation of this manipulator under the FLEXIBLE MECHANISMS THROUGH NATURAL COORDINATES AND COMPONENT SYNTHESIS 3545 following guidance conditions for the angles at the joints (gravity effects are neglected): j & [ t - $ s e n ( F ) ] , O < t < T , e, = e4 = [s. t 2 T 3546 J. CUADRADO, J. CARDENAL AND J. GARCiA DE JAL6N Initial and final configurations of the robot are shown in Figure 6. The value of parameter T is 15 s, but the simulation is carried on during 25 s, thus obtaining the system residual oscillations once the imposed motion has finished. The same simulation is also carried out considering all the bodies as rigid. Co-ordinates x, y and z of the last body tip are calculated in both cases. As final result, the difference between co-ordinates is plotted in Figure 8. This plot can be compared with those obtained by the previously mentioned authors: the correlation among them is excellent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003846_pime_proc_1987_201_061_02-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003846_pime_proc_1987_201_061_02-Figure5-1.png",
        "caption": "Fig. 5 Boundary surfaces of partial solution domain",
        "texts": [
            " This introduced the discontinuity of the temperature gradient at the rear boundary between the final PSD and the Proc Instn Mech Engrs Vol 201 No 8 3 at UNIV CALIFORNIA SAN DIEGO on November 3, 2015pib.sagepub.comDownloaded from PSD of the previous time step. This problem was considered by adopting the backward increase of the PSD, when the forward increase of the PSD ended. The initial temperature of this newly generated PSD was determined also so as to satisfy the continuous temperature gradient. When the PSD moved in the FSD, the boundary conditions of the PSD were changed as shown in Fig. 5 and Table 1. In this paper, however, the conduction boundary was treated as the imaginary convection boundary. Since the conduction boundary has no temperature discontinuity with the environment, the equivalent environmental temperature T A was determined from the temperature difference of the conduction boundary as follows (Fig. 6): where T, is the node temperature oi the conduction boundary, the internal node temperature of the conduction boundary, AL the distance between the internal node and the conduction boundary node and Ax the distance between the conduction boundary and the imaginary environment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.15-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.15-1.png",
        "caption": "Fig. 9.15. Elastic mechanism ofa robot",
        "texts": [],
        "surrounding_texts": [
            "stiffnesses Cl2 and c23' respectively, along the common normals to the teeth surfaces at the contact points. The moduli of all wheels are identical. Answer: where rH is the radius of the planet carrier, Z2 and Z2* are the teeth numbers of the planet pinion, a is the meshing angle."
        ]
    },
    {
        "image_filename": "designv11_31_0002616_0020-7403(96)00057-4-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002616_0020-7403(96)00057-4-Figure1-1.png",
        "caption": "Fig. 1. Tooling configurations in a CWR: (a) one-roll; (b) two-roll; (c) three-roll; (d) flat wedge; (e) concave wedge.",
        "texts": [
            " Because of the complexities associated with the deformation, theoretical analyses of the CWR process tend to employ only approximate solutions which are based on many simplifying assumptions. The objective of this paper is to present a simplified method to determine the mean contact pressure between a tool segment and a forging in CWR processes. CHARACTERISTICS OF CWR PROCESSES Cross wedge rolling is a process of metal forming where a product (a forging or a preform) is worked as the result of the operation of tool wedge segments located on rolls or concave or flat penals on rolling mills (see Fig. 1). A typical toot segment for a cross wedge rolling process (Fig. 2) consists of four basic zones: a knifing zone, a guiding zone, a forming zone and a sizing zone. In the knifing zone, a tool enters a billet (to a depth Ar) reducing its diameter to the desired value d. Then over the length of the guiding zone this reduction advances to the whole perimeter of the product. This zone, especially in the cases of rolling at small Ar, is often neglected. In the forming zone, as the result of the reaction of side walls of the wedge the previously formed keyseat is widened in the direction from the centre towards the face surface of the product to the desired width 1 (or 21)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure8-1.png",
        "caption": "Fig. 8. Front Engine Mounting Arrangement Using Rubber-bushed Links",
        "texts": [
            " On the other hand some recent German papers (Stoke 1954) indicate that rubber mountings working at high stresses, or those with high stiffness in one or the other direction, are more likely to transmit highfrequency vibration and noise. If this proves to be correct on all applications, the interleaved mountings may in the future be replaced by larger plain sandwich mountings. Links in a vee instead of mountings give exactly the same characteristics, and if long links with radially stiff rubber bushes are used the correction angle becomes quite small. A typical front mounting application is shown in Fig. 8. The correction angle is extremely small. An underfloor six-cylinder oil engine mounting is shown in Fig. 9 where front and rear mountings consist of two interleaved units in a vee. In view of the angular position Proc Instn Mech Engrs (A.D.) NO 1 1957-58 at PENNSYLVANIA STATE UNIV on June 4, 2016pad.sagepub.comDownloaded from 26 M. HOROVITZ FORE-AND-AFT FRONT MOUNTING CONTROL LINK SCRAP SECTION O N REAR MOUNTING CROSS-MEMBER U F%. 9. Suspension of Under-oor Horizontal Oil Engine Torque reaction buffers not shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003967_s0022-5193(89)80069-4-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003967_s0022-5193(89)80069-4-Figure1-1.png",
        "caption": "FIG. 1. (a) The speculated structure of a flagellar motor. The L and P rings are thought to serve as a mere bushing required for passage of the rod through cell envelope. In our model, we assume the M-ring is the rotor and the protein disk embedded in the cytoplasmic membrane is the stator. The rotation of the rotor is conducted to the rod, hook, and then to the flagellum. (b) Surfaces o f the rotor (left) and the stator (right), which are facing each other in the motor. The rotor has 16 R-sites (which are fan-l ike-shapes with central angle a ) , and the stator has 15 S-sites. (c) The rotor and the stator represented on angular coordinate. R-sites and S-sites are arranged every 22-5 deg and 24 deg, respectively, according to their numbers . An R-site and an S-site are electrodes which can be charged by protons in the external medium and the cytoplasm, respectively. Protons can flow between an R-site and its opposite S-site. The surface of the stator is uneven and waving sinusoidally where a unit wave is an S-site.",
        "texts": [
            " (21) (iib) Discharging current. Next, we discuss the proton conductance between an opposed pair of R-site and S-site. Considering the size of the basal body, we assume the distance D between a pair of two sites changes periodically by the following function of the R-site position on an angular coordinate 0 set up on the stator disk around the axis, D(0) = A + B cos (150) (nm); 0 ~ 0 < 27r (radian) (22) A = 2.0 (nm) B = 1.5 (nm). That is, the distance D changes periodically between 0-5 nm and 3.5 nm. As Fig. 1(c), this distance change is due to the uneven sinusoidal surface of the stator where a unit change corresponds to an S-site. Reasonably assuming that the proton conductance between the R- and S-sites, G2, depends on the distance between the two, we put G2 as shown in Fig. 2 in which G 2 is given (on one S-site) as a function of the relative position of an R-site 0 against its opposite S-site. The largest value is G2 = 1.24x 1 0 - 1 2 (S) at the closest distance, and the smallest one is G 2 = 7.62 x 10 -~s (S) at the furthest"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure6-1.png",
        "caption": "Fig. 6. Kinematic chains with a virtual continuous axis: (a) R \u03992\u2212RRRA \u2212\u2322 ; (b) R \u0399\u03992\u2212RRRA \u2212 ; (c) RARRRRRAR.",
        "texts": [
            " 5d) and RRRR [46], noting that RRRA, ARRA and RRRR are all arranged to parallelogram. Based on the constraint screw-based synthesis method, replacing the arc-rail-slider joints in the A R R Az z z z1 2 3 4 with the equivalent kinematic chains obtained in Section 3.2, closed-loop kinematic chains with a virtual continuous axis can be constructed. Taking RRRA for example to explain the synthesis procedure in detail. Replacing the two arc-rail-slider joints in A R R Az z z z1 2 3 4 with two same RRRA chains can obtain the 2\u2212RRRAR closed-loop kinematic chain, as shown in Fig. 6. oP1 and oP2 can be taken as virtual side link (VSL), while oF1 and oF2 can be taken as virtual rack (VR) [45]. Different arrangement of the two VSLs can obtain the virtual continuous axis with different location relative to the output link. If the two VSLs intersect to a point above the output link, as shown in Fig. 6a, t \u2265 0a and \u03d5 \u03c00 \u2264 \u2264a , where, ta is the vertical distance from the point to the output link, and \u03d5a is the angle between the two VRs. Similarly, when the two VSLs intersect to a point below the output link, t \u2265 0b and \u03d5 \u03c00 \u2264 \u2264b , as shown in Fig. 6b. When \u03d5a (\u03d5b) equals to zero, i.e. F1 is coincident with F2, the side-links of the two RRRA kinematic chains can be fixed together. Simultaneously, if t = 0a (t = 0b ), the output link crosses the intersection point of the two VSLs, as shown in Fig. 6c. In the same way, many closed-loop kinematic chains with a virtual continuous axis can be synthesized as listed in Table 2. With the mathematical criteria for virtual continuous axis and the closed-loop kinematic chains with a virtual continuous axis, a procedure in synthesis of PMs with a virtual continuous axis can be developed as below. Step 1. Write out the expression of rotation axes using the screws, and identify the properties of the axes. Step 2. Construct kinematic chains with a virtual continuous axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002231_s0001924000100818-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002231_s0001924000100818-Figure4-1.png",
        "caption": "Fig. 4 one-half of the ring is shown together with the loading. The location of the origin of the fixed system of co-ordinates differs from that in Sec. 3. The effect of this change upon the equations of Sec. 3 is readily found. It is assumed arbitrarily that the directions of the principal axes of inertia of every section coincide with the principal normal, and with the binormal, respectively, of the curve.",
        "texts": [
            " Its components are p , = V 2 ( 8 / a ) [1 - (\u00ab /\u00ab )\u00bb ]* ) p y = - V 2 ( * / a ) [ i - ( S / a ) 2 M \u2022 \u2022 \u2022 (14) p , = i - 2 (s/\u00ab)2 J The length of the radius of curvature is calculated with the aid of Eq. 4. It is p = ( i . / V j ) [ i - ( i / f l ) , ] \u00bb . . . . ( iS) 42 N. J . HOFF. The binormal vector B is calculated from Eqs. 5. Its components are 6x = i - ( s / a ) 3 1 6 y = ( s / a ) 2 \\ . (16) b z = - V 2 ( s / a ) [ i - ( s / a ) 3 ] l J Due to the double symmetry of both ring and loading, stresses and distortions are identical in the four quarters of the ring. It suffices, therefore, to consider only one quarter. If a cut is made both at s = o and s = a, in Fig. 4, the following force and moment components must vanish in the cuts because of the symmetry :\u2014 At 8=0: the shear force parallel to x, the shear force parallel to z, and the torque (moment vector parallel to y); At s = a: the shear force parallel to z ; and the torque (moment vector parallel to x). Moreover, and still because of the symmetry, the tensile force at 8 = 0 (force parallel to y) is P , and the shear force parallel to y at s=a is also P . The values of some more force and moment components follow then from the requirements of static equilibrium : At 8=0: the moment vector parallel to x is \u2014 Py"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure10-1.png",
        "caption": "Fig. 10. S R U U S2\u2212 P / ARRRRRA /2\u2212 PU.",
        "texts": [
            " Then, the generalized force of the mechanism is \u03c4 \u03c4 \u03c4= +o o o A I G (47) The driving forces of the prismatic joints in the 1st and 3rd limbs are the first and second elements of \u03c4o A respectively. The redundant configuration of the mechanism shown in Fig. 7c, which have more engineering applications, is taken as a numerical example. Firstly, add two SPR driving limbs symmetrically between the base and the connecting-links in the closed-loop limb. Then, add a SPU limb to the mechanism and allocate it symmetrically with the 3rd limb. The redundant actuation mechanism is shown in Fig. 10, and its kinematic equivalent mechanism is S U U4\u2212 P / . The structure parameters of the redundant configuration are listed in Table 4. The influences of external force, gravity of the limbs, inertia force of the limbs and friction mapped to the generalized force are ignored. The mass and the moment of inertia of the moving platform together with the load are m = 39110.19 kgo , and I diag= (118118.74,118118.74, 235197.58) kg mo 2 respectively. Applying the Z X\u2212 Euler angle, the motion laws of the moving platform are given as follows: \u03b3 t \u03c0t \u03b1 t \u03c0t{ ( ) = 9 sin(2 /5) ( ) = 17 sin(2 /5)\u2218 \u2218 (48) According to the models established in Section 6, the strokes, velocities and accelerations curves of the prismatic joints can be obtained by mathematical software (Matlab) as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.4-1.png",
        "caption": "Fig. 9.4. Mechanism with a nonreleasing constraint",
        "texts": [
            " Hence, we will not consider as elastic a mechanism, whose elastic elements serve for the realization of the functions of a rigid mechanism, e.g., for the force closure of the follower in the cam mechanism shown in Fig.9.3a. In the latter case a mechanism with elastic elements is obtained if the elasticity of the follower rod is taken into account (Fig. 9.3b). c) A mechanism with elastic links is realized only if the introduced elastic elements increase the number of degrees of freedom of the mechanical system. To achieve this the releasing constraints must become elastic ones. The rigid mechanism, shown in Fig. 9.4a has an excessive constraint but does not become an elastic mechanism when we introduce the elastic element shown in Fig.9.4b, since, in this case, the number of degrees of freedom does not increase. d) Henceforth, it is assumed that within the limits of small deformations of the elastic elements, these elements have linear elastic characteristics and that they obey Hooke's law. A basic characteristic of an elastic element is its stiffness c or flexibility e = I I c. Stiffness of a linear elastic element is called the ratio of the generalized force applied to the element, and the deformation caused by this force. The linear stiffuess is c =PIA N/m, (9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003738_s0925-2312(01)00661-0-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003738_s0925-2312(01)00661-0-Figure1-1.png",
        "caption": "Fig. 1. The frames de0nition.",
        "texts": [
            " A successful programming using instruction usually depends on known task and environment and is time-consuming. Instead, the robot can be programmed by a teacher\u2019s demonstration to simplify this process. It is known as \u201cteaching by showing\u201d or \u201cprogramming by demonstration\u201d and has been widely used in industry robot with the aid of a \u201cteach pendant\u201d. In this section, we present a new \u201cteaching by showing\u201d scheme for robot trajectory programming with the help of a camera instead of a \u201cteach pendant\u201d as shown in Fig. 1. The programming process is described as follows: First, a teacher grasps a tool or simply an object, and does a demonstration. At the same time, a static camera records the trajectory of some selected features of the object on the image plane. It describes the desired trajectory of the object. Then, let the manipulator grasp the same object and do the training repetitively. With the aid of the proposed ILC, a perfect replay of the demonstrated trajectory can be achieved ultimately. Suppose that the transformation between the general coordinates and the selected features is expressed as x= #($), where we have no restriction on how to select the vector of the general coordinates $\u2208Rm and the features x\u2208Rn",
            " The coordinates of these 4 feature points on a tool frame Ft are selected to be FtP1 = [0:1 0:1 0]T; FtP2 = [0:1 0 0:1]T; FtP3 = [0 0:1 0:1]T; FtP4 = [0:1 0:1 0:1]T: The trajectory is generated by a velocity screw T =[V !]T = sin(0:6t)[0:3 0:3 0:3 0:3 0:3 0:3]T acting on the tool frame with an initial state of Fc Ft R=   0 0 1 0 1 0 \u22121 0 0   ; FcPFto =   0 0 2   ; where Fc is the base frame attached to the static camera, Ft is the tool frame attached to the robot end-eDector, Fc Ft R is the rotational matrix of Ft related to Fc, and FcPFto is the vector of Ft\u2019s origin in the frame Fc. The frame de0nitions are shown in Fig. 1. The feedback and adaptive gains of the control law are selected to be K2 = 3 in Eq: (17); F(i \u2212 j)=10 in Eq: (8); Fl(i \u2212 j)=2 in Eq: (11): In order to avoid any singularity of the proposed control law, W\u0302 l(t; i); l=1; : : : ; n; are adjusted within a known bound only. This bound has a maximum of \u00b1 50% deviation around the desired trajectory and the initial weights W\u0302 l(t; 0) are set to the lower bound. Finally, let the width of the deadzone in (3) be fi =5\u00d710\u22127, then we begin to train the neural networks within a region of = {x : \u2016e(t; i)\u20166 3\u00d710\u22124}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003224_70.704227-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003224_70.704227-Figure1-1.png",
        "caption": "Fig. 1. The planar 2R manipulator.",
        "texts": [
            " Equation (4) helps answer this: if 0 and , then as One of the first works on path reparameterization was [11], which demonstrated its feasibility in the case of a straight-line path intersecting the outer boundary singularity of a planar 2R 1 It is possible for #00 j (s) to approach infinity at a singularity even if #0 j(s) does not. robot. Because this work connects well with the results of this paper, it will be reviewed here. The inverse kinematic solution for a planar 2R robot with the base located at the origin (Fig. 1) is given by (5) Notice that has two possible solutions (positive or negative), which in turn implies two solutions for . Now assume 1, and consider the produced by a straight-line motion defined by , 0, as shown in Fig. 2. Choosing the positive solution for in (5) gives as plotted in Fig. 2(b). The singularity occurs at 2. Now, within a left neighborhood of 2, one can show that (6) Consequently, , which approaches as . From the chain rule , it is clear that any nonzero path velocity at 2 will produce an infinite value for "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003672_a:1023048802627-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003672_a:1023048802627-Figure8-1.png",
        "caption": "Figure 8. Kinematics of 6-DOF PUMA type robotic manipulator.",
        "texts": [
            " After all iterations, in block 11, the latest saved joint coordinates are considered to be the optimal with the end-effector positioning accuracy of Lini (ISO 9283, 1998). The Cartesian coordinates of the new working point can be calculated and new trajectory can be planned into the newly obtained working point with the maximum end-effector positioning accuracy. PUMA type robotic manipulator was used to perform computer simulation of end-effector pose accuracy improvement with joint error maximum compensation. The kinematics scheme of the 6-DOF PUMA type robotic manipulator is presented in Figure 8. The joint coordinates have the following limits: q1 (\u2212160\u25e6\u2013 160\u25e6), q2 (\u2212225\u25e6\u201345\u25e6), q3 (\u2212225\u25e6\u201345\u25e6), q4 (\u2212110\u25e6\u2013170\u25e6), q5 (\u2212100\u25e6\u2013100\u25e6), q6 (\u2212266\u25e6\u2013266\u25e6). The other parameters of the PUMA type robotic manipulator have the following values (see Figure 8): a2 = 0.4138 m, a3 = 0.02032 m, d2 = 0.14909 m, d4 = 0.43307 m, d6 = 0.05625 m. The end-effector positioning accuracy improvement for 6-DOF PUMA type robotic manipulator was performed using local optimization search in the working point Pinitial (base Cartesian coordinates: x = 0.0045 m, y = 0.1661 m, z = \u22120.7212 m) with joint coordinates: q1 = 0.5236 rad, q2 = 0.7853 rad, q3 = 2.7925 rad, q4 = \u22120.1745 rad, q5 = 0.8726 rad, q6 = 0.7854 rad, with joint errors: q1 = 0.0001 rad, q2 = 0.001 rad, q3 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure3-1.png",
        "caption": "FIGURE 3. Cross section of journal-bearing oil film and plot of pressure distribution in the film.",
        "texts": [
            " The general solution, including transverse flow, or side leakage, as it is often called, eluded exact solution for a number of years, although numerous approximate solutions were proposed. This brings us to the first of the recent developments which I wish to discuss in some detail. The journal bearing, even in the absence of transverse flow, presented a difficulty which does not seem to have been entirely resolved during the first decades of this century. As may be seen in the cross section of a journal bearing, shown in FIGURE 3. Side Leakage and Film Ruplure iri Joicriaal Bearings. 762 Annals New York Academy of Sciences there is always a diverging section. In such a section, the reverse of the argument given above can be easily applied, leading to a prediction of reduced and possible negative pressures in this region. Since a liquid cannot withstand any tension (except under very undisturbed laboratory conditions), it was early recognized and confirmed experimentally that the oil film broke or cavitated when the pressure dropped much below the pressure of the atmosphere and produced a mixture of air or oil vapor bubbles and oil in the remainder of the diverging section, in which the pressure never exceeded atmospheric pressure. The questions of where the film broke and how this affected the pressure distribution in the preceding section of compact film apparently were not analyzed in much detail. It was sometimes thought that the pressure became negative in this region, as indicated by the dashed line in the graph of FIGURE 3. It now appears definite that the pressure and, also, the pressure gradient simultaneously become zero a t the point where the film ruptures, as shown by the full line curve in the graph. Its location, 0 2 , is definitely related to the point 0 1 where the oil again becomes compact and capable of developing a positive pressure. The location of both these points, the leading and trailing edges of the film, are determined by both the oil supply and the eccentricityof the shaft in the bearing space",
            " Conversely, with large oil supply and small eccentricity, the two ends of the oil film approach each other on the other side of the bearing and form a complete film. When this occurs, the theoretical equation developed by Sommerfeld (in the case of an absence of side leakage) is applicable. Oil film rupture can also take place in partial bearings, for example, when Burwell : Full Fluid Lubrication 763 the partial bearing is extended to a point such as OS under the same conditions of the full bearing shown in FIGURE 3. The proper conditions a t the trailing edge of the bearing seem to have been hinted by Reynolds and have been discussed by Gumbel,' Stieber,' and Swift? Calculations based on them have been made by Cameron and Christopherson,lo and Waters,\" as discussed below. It has been diflicult to obtain an analytical solution of the problem of side leakage in journal bearings. Kingsbury\" devised a very ingenious electfical analogue, utilizing the flow of electricity through an electrolyte in a tank of varying depth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003415_el:19980376-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003415_el:19980376-Figure1-1.png",
        "caption": "Fig. 1 Switching vectors and statorhotor flux vectors",
        "texts": [
            " Acstrnley Multilevel hysteresis comparators are discussed, including a new quasi-form, which incorporates standard hysteresis with error reference levels, for use in direct torque control schemes for induction motors. Introduction; Direct torque control (DTC) is expected to replace vector control in the future for high performance induction motor drives [l]. In DTC schemes, the objective is to reduce both the stator flux anld torque errors to zero using hysteresis comparators to select the optimum voltage vector [2]. The switching vectors associated with DTC are shown in Fig. 1. These vectors are selected to regulate the angle between the stator and rotor flux vectors, also shown in Fig. 1. Table 1 contains the lookup table that is used to select the voltage vectors depending on fludtorque errors and the stationary reference frame sector which the stator flux vector occupies. The torque hysteresis comparator is of the kind proposed by Takahasi [2] and has three levels, as shown in Fig. 2, the third level being for large negative torque errors. The three possible torque states along with the two possible flux states combine to produce six selections, as is evident from the lookup table"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002520_1.2802457-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002520_1.2802457-Figure1-1.png",
        "caption": "Fig. 1 Acrobot schematic",
        "texts": [
            " The learning control law that updates the switching interval vector is derived from Eq. (8) by using the actual state trajectory in computing the terminal state error and the required Jacobeans: - k\u201e(I ~ A'*A')Vw' (12) where the superscript c represents the cycle number, x',\u201e is the measured terminal state during the cycle c and A'' is the Jaco bean matrix A evaluated along x^. The effectiveness of this approach is illustrated in the following simulation case study. The learning algorithm was applied with success to the prob lem of the acrobot, illustrated in Fig. 1. The initial state of the system is the \"straight down'' position (i.e., 1\u0302 = 0, 2\u0302 = 0) at rest, and the desired terminal state is the \"straight up\" position (i.e., 8, = IT, 62 = 0), also at rest. We will denote the masses and centroidal moments of inertia of the two links by mi, OTJ, I,, l^ (which take into account the motor inertia at the second joint), their center of mass positions by l,c, ko which are measured from the joint of each respective link, the link lengths by l,, and k, and the gravitational accelera tion by g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002881_1.2832456-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002881_1.2832456-Figure2-1.png",
        "caption": "Fig. 2 Configuration of misaligned bearing",
        "texts": [
            " The FRFs are obtained at different speeds and for different levels of misalignments for each test bearing. Measurement of Misalignment. Different levels of hori zontal misalignment has been imposed on the test bearing by controlled twisting of the test-bearing housing about its centre. Angle of twisting misalignment, 0^. has been obtained by mea suring relative lateral movement between the test bearing and the journal at either side of the bearing. These lateral displace ments have been measured using eddy probes. Degree of Misalignment. Figure 2 shows the configuration of a misaligned journal bearing. The severity of misalignment has been represented by a parameter, D\u201e, degree of niisalignment as discussed in Safar (1984). The misalignment ratio, \\ , is defined as; X. = \u00b1/3z/c\u201e; where Cm is the diametral clearance and P is the angle of misalignment. Let \\\u201e, be the maximum possible misalignment ratio, k^ be the misalignment ratio at the bearing end, \u00a3\u201e be the eccentricity ratio at the mid-plane, </> be the attitude angle under aligned condition and (/> be the angle between the plane of misalignment and the axial plane con taining the load vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002213_1.1707468-Figure14-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002213_1.1707468-Figure14-1.png",
        "caption": "FIG. 14.",
        "texts": [
            " It is to be noted that when a pure shear equilibrium is examined, the force polygon becomes a figure similar to the space polygon. (b) Projection on a Plane Parallel to the Frames In this case components of the end loads parallel to the frames are required. ~n being the projected length of a member n on the frames, L the distance between frames, F.,.', F nil the axial loads in the member n at the end frames, the projections on the planes of the frames are: in' = Fn' ~n:L; in\" = Fn\" ~n:L. (57) Knowing the loads in',j n\", force diagrams can be determined by a method similar to that of Fig. 13. Figure 14 shows the procedure. Loads at the ends of a' a\", called A', A\", are drawn end to end. Their sum is al\" al'. The equilibrium of panel (1) is determined by drawing through aI\" and aI' parallels to the sides and diagonals corresponding to a' and a\". The operations from there on are similar to those of Fig. 13, but the loads are not represented along a base line, and must be measured along each member. The directions of the loads must be chosen in such a manner that in the completed figure the sequence be, for instance, D\", C\", B\", A\", A', B', C', D', which shows that two opposite forces B', B\" are meas ured in same direction along their line of support /31\"f3/. It results that compression forces are measured in one direction, while tension forces are measured in opposite direction. Thus, in Fig. 14, starting from the top, compression forces are drawn from F' toward F\" and tension forces are drawn from F\" toward F'. Once the force VOLUME 15, JULY, 1944 polygon is completed, the value of the resultant of the shears acting along the frames is deter mined. It is the force aollo. Its location is deter mined by a classical construction of addition of forces, which is represented in Fig. 14, using an arbitrary pole R and the forces acting on the frame F'. The resultant is shown in position. A check can be made by .repeating the same operation at the other frame. By combining various unit solutions, shear centers or stress centers can be determined by intersection of two such resultants. Then, arms can be measured for the calculation of moment coefficients for torsion bending and the torsion bending constant may be determined. In case of closed profile, a cut is always made in order to start the calculation, and a unit solution is made under pure shear transmission. If in Fig. 14 the force placed on a'a\" is equal to a'a\" at a certain scale, the space polygon for shear trans mission becomes the force polygon. From that force polygon and an arbitrary pole the resulting couple can be determined. (c) Extension to Non-Parallel Frames The equilibrium of a developable membrane can be examined between two non-p~rallel 559 [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: 136",
            " Thus, it is necessary to draw two directions of sets of lines defining the loads at the two frames, respectively parallel to the two frames. The force polygon is drawn starting at the intersection of the two first lines, defining the origins of loads A' and A\", respectively, and it must end at the intersection of the two last lines, which gives a control of the equilibrium. The detail of the force polygon is the same as in Fig. 13, and forces and shears are measured in the same manner. (2) Projection on a Plane Parallel to the Intersection of the Two Frames The construction Fig. 16 is comparable to that of Fig. 14 for parallel frames. It differs by the fact that the intersections of each panel with both frames, instead of being parallel, intersect along the line of intersection of the two frames. The construction of the force polygon is identical in both cases. As in Fig. IS, space and force polygon are not similar. For open structures, resultants and points of application can be determined in a manner similar to that corre sponding to parallel frames. For closed structures an important difference must be emphasized: Distribution corresponding to shear without end axial loads does not correspond to a torque, but to a resultant which is located along the line of intersection of the frames"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003145_1.2889650-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003145_1.2889650-Figure1-1.png",
        "caption": "Fig. 1 Experimental test apparatus",
        "texts": [
            " 118, APRIL 1996 rotordynamical behavior are of current concern. The objective of the present work is to develop an understanding of possible coupUng between the dynamics of disk and shaft that may be induced by bearing clearance effects and to provide guidance to designers concerned with such systems. Experimental Model In order to investigate whether bearing clearance can lead to significant coupling between rotor and disk vibration, experi mental tests were performed with a rotor test rig. A drawing of the test rig is shown in Fig. 1. The rotor used in this study has two basic components: a flexible disk and a shaft. The steel shaft is 0.375 in. diameter and 16.0 inches long. The flexible disk is a circular aluminum plate 0.0125 inches thick and 14.0 inches in diameter. The natural frequency of its lowest one nodal diameter bending mode is about 40 Hz. It is attached with four bolts to a 2.0 inch diameter hub mounted with a press fit to the center of the shaft. The rotor shaft is supported by bushings at two ends. The left end of the shaft is placed directly in the bushing base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure1-1.png",
        "caption": "Figure 1. General flexible body",
        "texts": [
            " As variables we use the natural co-ordinates, developed at CEIT and ESII of San Sebastian for rigid multibody systems simulation (see Reference 7), and extended here for the flexible case with small deformations. In Reference 9, an extension of these same variables for the large deformations case can be found. The three resulting formulations-for rigid and flexible bodies of both type-are absolutely compatible and can be used together if a mechanism is composed by bodies of the three types mentioned. Consider the general flexible body shown in Figure 1. The first step consists of establishing the moving frame, that is, the local frame rigidly attached to the body. To attain it, one point-the origin (ro in the figureband three orthogonal unit vectors-the local base (u, v, w in the figurebare defined. Therefore, when carrying out the modeling of a flexible body, at least one point and three unit vectors will always be needed. If other points or unit vectors are defined in a body, they will be referred to as points and vectors in excess. It must be said that, in some cases, an orthogonal local frame rigidly attached to the body cannot be defined, because the three vectors of the base may lose their orthogonality when the body undergoes deformation",
            " GARCfA DE SAL6N Once kinematics have been seen, dynamic terms should be developed. Firstly, at the body level and afterwards for the whole multibody system. These terms are: the mass matrix, the vector of velocity dependent inertia forces, the vector of elastic forces and the vector of applied forces. Let us first show how to obtain these terms at body level. The mass matrix and the vector of velocity dependent inertia forces are calculated simultaneously for each body. The virtual power of inertia forces of a general body as the one shown in Figure 1 may be expressed as but, as seen in equation (l), r = ro + Ai; (9) i = i o + A t + ~ i (10) i: = f o + A t + - + A + (1 1) and, differentiating twice with respect to time, we obtain, Then, the substitution of (10) and (11) into expression (8) leads to, fi = (toT + rTkT + iTAT)(ro + Af + 2Ai + Ai)p dV (12) s. In this last expression we already find some variables, as the origin of the local frame ro and the rotation matrix A (whose columns are the unit vectors u, v and w). However, the local vector i; and its derivatives still appears, that should be written in terms of the amplitudes of the static and dynamic modes, as seen in the previous section: # S t # dyn f = f"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003110_0379-6779(93)90277-4-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003110_0379-6779(93)90277-4-Figure4-1.png",
        "caption": "Figure 4. Model of growing conducting zones that corresponds to the current-time relationship given in eqn 1.",
        "texts": [
            " In spite of these differences, the experimental potentiostatic transients for the oxidation of leucoemeraIdine at room temperature are described remarkably well by the theory developed for the two dimensional electrocrystallization of anodic films on mercury. This can be explained if it is assumed that the conducting strands initially propagate preferentially normal to the electrode surface as the result of a high electric field at the 'tip' of the strand which will accelerate electron transfer and proton migration. Once stands have propagated across the film, the transformation can proceed by the expansion of the conducting 'cylinders' as shown in figure 4. It should be noted that the analogy with electrocrystallization is based entirely on geometrical considerations. It seems unlikely that the oxidation process leads to the formation of a separate phase with a well defined chemical potential. Instead at the molecular level, the conducting 'zones' can be thought of as a network of interpenetrating polymer chains which although highly disordered, effectively forming a solution of the two redox states. We now attempt to explain why the shape of the transients changes when the temperature is decreased"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure18-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure18-1.png",
        "caption": "Fig. 18. Representation of the robots traffic flow with same velocities.",
        "texts": [
            " \u2022 In the second assumption, called global, every robot views all the other moving robots, generates all the traffic patterns and calculates all the possible traffic priorities for all the moving robots including itself. V. ILLUSTRATIVE EXAMPLES In this section, two illustrative examples for traffic cases are provided and solved by using the KYKLOFORIA language. In the first example, the traffic case includes six moving robots in a free navigation space shown in Fig. 11. Figs. 12\u201317 provide the shape of the free navigation spaces observed TABLE III SIMULATED RESULTS FOR FIG. 18 by each moving robot and the traffic patterns generated by each of them in their own free space. In the Fig. 18, the velocities of the moving robots are considered the same, thus the traffic priority relationships generated by the traffic language are given in Table III. Each moving robot knows the traffic priority relationships in the same free space. Thus, the robot makes use of its own which is higher than and goes out of the narrow corridor. At a time min, covers a distance of 4.5 m. The robot has to wait of a period of 0.6 min, and then it proceeds into the open corridor by covering a distance of 1.4 m in 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure5.27-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure5.27-1.png",
        "caption": "Fig. 5.27",
        "texts": [
            " The damping of the oscillating circuit itself must be sufficient to limit the increase in oscil lations. Otherwise, the position of the free-wheeling diode must be modified, as shown in the second diagram of Fig. 5.26. In this case, the increase in the r.m.s. value of the current in inductor L is added to drawbacks linked to the increase in the number of thyristors. 5.6 Extension of the Study to the Step-Up Chopper 5.6.1 Presentation of the Method In Chap. 3, we initially represented the step-up chopper (see Fig. 3.7) with the position of elements and the conventional signs indicated in Fig. 5.27a. How ever, it was already noted (see Sect. 5.2.2.3) that no basic difference exists between the buck and the boost choppers. These remarks will enable all the results of the analysis of commutation circuits carried out for the step-down chopper to be used in the case of the step-up chopper. Diode D can obviously be moved from the positive terminal to the negative terminal of voltage source U, and the arrows of voltage u' and current i can be reversed (these will simply have negative average values). This is the difference between Figs. 5.27a and 5.27b. If the right-hand side of this figure is then turned around, this gives the configuration in Fig. 5.27c. It can be seen that the step-up chopper is derived from the step-down chopper by simply moving the current source terminal which is directly connected to the voltage source negative terminal from this terminal to the positive terminal of the latter. If A was connected to B', this would give a buck chopper; A connected to B gives a boost chopper. Compared with the results obtained for the buck chopper, this change in connections causes 5.6 Extension of the Study to the Step-Up Chopper 273 \u2022 a shift of voltage u' by a constant value equal to - U, \u2022 a shift of current i by a constant value equal to -I'"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002900_20.141296-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002900_20.141296-Figure3-1.png",
        "caption": "Fig. 3. Two-dimensional configuration consisting of an infiite cylinder excited by an ac magnetic field perpendicular to its axis. (a) Schematic arrangement. (b) One-dimensional arrangement chosen for the evaluation of the effective eddy current permeability. (Cylinder is cut from an appropriate semi-infinite plate.)",
        "texts": [
            " The magnetostatic model in calculating the demagnetizing factor of finite bodies supposes that the body material is homogeneous. However, this is not the case for the effectively equivalent permeability associated in the present paper with eddy currents. As a result, the employment of the average eddy current permeability as a uniform magnetic permeability all over the body volume constitutes only a simplifying way to treat the real situation. One of the studied two-dimensional configurations consists of an infinite cylinder, excited by an ac magnetic field perpendicular to its axis (Fig. 3(a)). This configuration can be useful in construction of special ac motors. Results regarding the eddy current forces exerted on such a configuration by ac magnetic fields were reported in the literature [lo]. The demagnetizing factors are L, = Ly = 0.5, and L, = 0. The next step is to choose a suitable value for the eddy current relative permeability p FtvCelage in place of p, in expression (23). The chosen eddy current permeability should be evaluated for a one-dimensional configuration from which the cylinder two-dimensional configuration can be cut, and for that one-dimensional configuration the demagnetizing factor associated with the induced eddy-current magnetization is zero. It seems that a good choice in this case is the eddy current permeability of a semi-infinite plate magnetized in parallel to its surface (Fig. 3(b)). The thickness of the semi-infinite plate is chosen equal to the diameter of the cylinder. The eddy current average magnetization of the cylinder magnetized by ac fields in perpendicular to its axis will be (according to expression (23)): p, singh ab 1 + 1 -~ ab cosh ab Using the expression (24) of the eddy current average magnetization, the force exerted on a very long conductive cylinder of p, = 1 by two horizontal wires parallel to the axis of the cylinder (Fig. 4) can be evaluated. The wires current excitation is sinusoidal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003651_978-1-4615-2520-2_20-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003651_978-1-4615-2520-2_20-Figure2-1.png",
        "caption": "Figure 2. Schematic diagram of the workpiece and the weld pool",
        "texts": [
            " Numerical Parameters The simulations were performed for a stationary 150 amp, direct-current-electrode-neg ative (DCEN), 21 volt, GTA weld into a 24 x 24 x 6mm workpiece of the aluminum alloy 6061. This alloy was chosen due to its widespread use in the aerospace industry. In order for a simulation to predict accurate results, all of the relevant thermophysical properties for the given material must be known. The values for the thermophysical properties used in the present simulations are listed in Table 1. Boundary Conditions minum, as shown in Figure 2, and was assumed to be completely surrounded by air at room temperature. This figure is a schematic diagram of the system that was used in both of the 6061 aluminum simulations. The electrode was placed directly over the center. Natural con vection with the surroundings was assumed at the boundaries, with evaporation allowed from the liquid surfaces. For both of the stationary GTA weld simulations, the electrode was placed directly above the center of the surface of the specimen and held stationary throughout the simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002226_ji-3a-1.1946.0257-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002226_ji-3a-1.1946.0257-Figure3-1.png",
        "caption": "Fig. 3.\u2014Horn for beacon application.",
        "texts": [
            "1) Beacons For some purposes it is necessary to have a horn or mirror receiver with the property of giving nearly constant response to signals coming from all directions in the horizontal plane con- [ 1528 ] OWENJAND REYNOLDS: THE EFFECT OF FLANGES ON THE RADIATION PATTERNS OF SMALL HORNS 1529 tained within a sector of 180\u00b0. This can be achieved by using a horn or cheese-miiror having an aperture whose horizontal dimension is \u00a3A, the polarization being horizontal. Flanges \\\\ long containing an angle of 270\u00b0 (Fig. 3) give a pattern with the required properties. The variations in field-strength about the mean value over the forward 180\u00b0 sector are only ~\u00b1 15 %. This degree of constancy is adequate for the purpose intended. Outside the forward sector the intensity falls off steadily and if the horn or mirror were employed for transmission, 80\u00b0,, of the total radiated energy would be sent into forward directions. 1530 OWEN AND REYNOLDS: THE EFFECT OF FLANGES ON THE RADIATION PATTERNS OF SMALL HORNS (3.2) Improvement of the Match of a Horn Feeding a Cheese Mirror The narrow-aperture horn is very often applied to illumine a cheese mirror"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003761_1.1701875-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003761_1.1701875-Figure3-1.png",
        "caption": "Fig. 3 Cooperating robots",
        "texts": [
            " In this section, a numerical example of two planar flexible robot arms manipulating a rigid object passing through a desired trajectory is presented. The two manipulators are identical and each of them has three flexible links. The length of all links is 0.254 m. The height and width of cross-section are all 0.00508 m. The damping ratio is 0.03. The modulus of elasticity and shear modulus are 7.131010 N/m2 and 2.631010 N/m2, respectively. The material density of aluminum is 2700 kg/m3. As shown in Fig. 2, each link is divided into 5 six-node beam elements. The cooperation of two manipulators is illustrated in Fig. 3. The holding points are A and B, respectively. The grasping configurations are rigid. The distance between the two holding points Lob is 0.05 m. The mass center of the object is at point C. The mass m0 and inertia moment I0 of load are 0.05 kg, 3.125 31025 kg m2, respectively. c15p/3, c252p/3, u150, u25p . Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 The desired load distribution coefficients is \u00a7150.35, j150.35, z150.35, \u00a7250.65, j250.65 and z250"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002770_0043-1648(96)07226-2-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002770_0043-1648(96)07226-2-Figure9-1.png",
        "caption": "Fig. 9. Air ring with rubber seals ( I ).",
        "texts": [
            " The values of the stiffness and damping coefficients C22 and K22 of the air rings (in the plane perpendicular to the plane along which the force F: acts) are close to C** and \u00a3 ~ , and therefore their diagrams are not presented here. This remark concerns all the results presented below as well. Aiming at an increase in the value of the damping coefficient of the gas ring, we have modified the boundary conditions of the gas film by an introduction of rubber seals at both the ends of the ring, which is shown in Fig. 9. Fig. 10(a) presents the coefficient CH as a function of the frequency of vibrations of the bush for four different values of the angle % (compare Fig. 9) which defines the size of the seals. The ring parameters are as follows: L=0.11 m, R2=0.065 m, ro2 = 0.15 \u00d7 10 - 3 m, c2 = 30 \u00d7 10 - 6 m. The representation of Cn and K:: corresponding to 3,,=0 (without seals) has been transposed from Figs. 7 and 8. As can be seen, the seals whose task was to hinder the air flow along the ring axis have indeed caused an increase in the values of the coefficient C . . For instance, for v = 4 from Cn : O.29 for Sr = O to C H = O.67 for % = 2/3 \u00d7 2~r. This last result would fall inside the \"always stable\" loop (compare Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003687_isie.1999.801773-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003687_isie.1999.801773-Figure9-1.png",
        "caption": "Fig. 9. Wall pushing task in experiment 3",
        "texts": [],
        "surrounding_texts": [
            "Mobile Manipulator --Y Motor I I Encoder &--\nForce Sensor\nr------------ - - - - - - - - - - - _, I _ _ _ _ _ _ _ _ _ _ _ _ . I _ _ _ _ _ _ _ _ _ _ _ .\nMotor Driver Timer\nr-------- _-_ , r--- _ _ - - _ _ _ _ I A I D I I 1 / 0 j ,____________. I _ _ _ _ _ _ _ _ _ _ _ . - - - - - - - - - - - -, - - - - - - - - - - - _,\n---! D / A ; I Counter y--\nPersonal Computer Pentium 200MHz\n.-----_______. I _ _ _ _ _ _ _ _ _ _ _ _ .\nthe equivalent mass matrix, according to the preknown work for mobile manipulator. The configuration torque reference in null-space T T ~ is given by the configuration of the vehicle &\u2019 1 link that correspond to MC:il.\nB.2 Variable Null-space Gains by Equivalent Mass Ma-\nIn the proposed approach, the weight matrix W has large inertia W , to avoid the slip effect of vehicle. Then, the end-effector easily approaches to its singular configuration since the controller make force the correct tip trajectory motion even if the vehicle does not move active. This means that there is a trade-off to select the weight gain between the avoidance motion of slip and singular configuration. From this point of view, we introduce the variable null-space gain according to the change of configuration.\ntrix\nKx,w = WE,\"^\" - Ww,a)Kvn,w\nKX+ = IMz,wl- ~ i $ . IKPn,+\n(35)\n(36)\nHere w r a x is the maximum value of dynamical manipulability and KY:w, KF:+ are variable null-space\n,: gains.\nVI. EXPERIMENTAL RESULTS To confirm the effectiveness of proposed controller,\nseveral experiments are implemented.\nA . Experimental Conditions The mobile manipulator and the signal flow diagram of the experiment system are shown in Fig. 7. and Fig. 8. respectively.\nThe parameters on this control scheme are shown in TABLE I.\nB. Experimental Results To make clear the effect of the proposed approach, the following three case experiments are implemented.\nExperiment 1\nFig.10. shows the position step response (0.8[cm] in the direction of X-axis) under the condition that weight matrix W are I and W , respectively.\nExperiment 2\nFig.11. shows the end-effector response of a sine curve reference (amplitude l.O[m], cycle lO[sec]) under the condition of the variable null-space gain and constant one. Then, weight matrix is W,.\nExperiment 3\nFig.12. shows the result of pushing task (W = W,). Here the end-effector follow the tangental direction of the wall (position control: lamp input O.l[m/sec]) and performs force task in the vertical direction of the wall (force control: 30[N]). Then, the surface condition of wall changes and its height difference is about 3.0[cm].",
            "C. Consideration Fig.10. shows that both of the desired position and velocity is achieved by using the proposed approach with weight matrix . Fig.11. shows that using the variable gain, the dynamical manipulability keeps desirable condition and manipulability (configuration) without deteriorating the trajectory response. Fig.12. shows that decoupling force and position controller in workspace is realized.\nVII. CONCLUSIONS Considering a task oriented motion by the mobile manipulator, it is important to cooperate with the subsystems efficiently and to make its motion keep the adequate configuration for the task. When the mobile manipulator is considered as a unified system of the vehicle and the arm, it is easy to satisfy the above condition. In this paper, in order to obtain the desired hybrid control with respect to the end-effector\u2019s tasks, the performance indices, which is based on the equivalent mass matrix, are introduced to increase both of the manipulability of the arm and the stability of the vehicle motion. firthermore, the weight matrix is proposed to obtain the adequate torque\u2019s distribution. The validity of the proposal approach is confirmed by several experiments.\nREFERENCES [I] Y.Yamamoto and X.Yun, Coordinating Locomotion and\nManipulation of a Mobile Manipulator, Proc. the 31st IEEE Conf. on Decision and Control, pp.2643-2648, 1992. Y.Yamamoto and X.Yun, Modeling and Compensation of the Dynamic Interaction of a Mobile Manipulator, Proc. IEEE Int. Conf. on Robotics and Automation, pp.2187-2192, 1994. K.Shibata, T.Murakami and K.Ohnishi, Control of a Mobile Manipulator Based on Equivalent Mass Matrix, Proc. IEEE IECON 21st Int. Conf. on Industrial Electronics, Control, and Instrumentation, pp.133@1335, 1995. H.Hattori, N.Oda, T.Murakami and K.Ohnishi, A Control of a Mobile Manipulator with Considering Constraint Forces between Wheels and a Road, Proc. the 3rd FranceJapan Congress & 1st Europe-Asia Congress on Mechatronics, V01.2, pp.767-772, 1996. O.Khatib, K.Yokoi, K.Chang, D.Ruspini, R.Holmberg, A.Casd : Vehicle/Awn Coordination and Multiple Mobile Manipulator Decentmlized Cooperation, Proc. 1996 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp.54&553, 1996"
        ]
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.21-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.21-1.png",
        "caption": "Figure 2.21 recalls the setting-up of the SOA used for operation in the active region, i.e. when B-E junction is always forward-biased, and its extension to pulsed operation. The axes are normally graduated in a logarithmic scale.",
        "texts": [
            " For high values of VcEic- though these may be lower than p max- the difference in current line concentration leads to localized hot spots which accentuate this difference and may cause the destruction of the transistor by thermal runaway. (This \"direct\" second breakdown must not be confused with the \"reverse\" second breakdown. The latter arises when the avalanche - ap pearing in the OFF state if the veE value becomes too high (see Sect. 2.2.3.3) -brings about the thermal runaway of the transistor); - vertical segment DE, corresponding to maximum voltage VeEo\u00b7 \u2022 For pulsed operation (shown in broken lines on Fig. 2.21) the VeE maximum remains equal to VeEO; but: \u2022 the instantaneous value of ic may reach /eM; the acceptable instantaneous power veEie mcreases as the pulses become shorter. 2.2.3.2 Switch-Mode Operating Areas As power transistors are switching transistors, SOAs during switching are often simply referred to as \"operating areas\". The commutation process closely depends on the bias of the emitter-base junction. Two areas are to be distinguished: \u2022 the forward bias safe operating area (FBSOA), \u2022 the reverse bias safe operating area (RBSOA)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002213_1.1707468-Figure16-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002213_1.1707468-Figure16-1.png",
        "caption": "FIG. 16.",
        "texts": [
            " Thus, it is necessary to draw two directions of sets of lines defining the loads at the two frames, respectively parallel to the two frames. The force polygon is drawn starting at the intersection of the two first lines, defining the origins of loads A' and A\", respectively, and it must end at the intersection of the two last lines, which gives a control of the equilibrium. The detail of the force polygon is the same as in Fig. 13, and forces and shears are measured in the same manner. (2) Projection on a Plane Parallel to the Intersection of the Two Frames The construction Fig. 16 is comparable to that of Fig. 14 for parallel frames. It differs by the fact that the intersections of each panel with both frames, instead of being parallel, intersect along the line of intersection of the two frames. The construction of the force polygon is identical in both cases. As in Fig. IS, space and force polygon are not similar. For open structures, resultants and points of application can be determined in a manner similar to that corre sponding to parallel frames. For closed structures an important difference must be emphasized: Distribution corresponding to shear without end axial loads does not correspond to a torque, but to a resultant which is located along the line of intersection of the frames"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002616_0020-7403(96)00057-4-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002616_0020-7403(96)00057-4-Figure3-1.png",
        "caption": "Fig. 3. Distribution of the force influencing a tool segment in CWR processes.",
        "texts": [
            " The forming deformation characterising the cross wedge rolling process is defined by the reduction of a portion 6, defined as follows: 6 = do. (1) d D E T E R M I N A T I O N OF C O N T A C T P R E S S U R E It is essential to determine forces and rolling torque values for CWR processes. This makes possible not only the selection of suitable aggregates and proper devices for the process but also provides the basis to work out an automatic process control system. The rolling force Q in CWR processes can be determined when its components in the directions of the co-ordinate axes shown in Fig. 3 are known. These are the radial, Q~, axial Q~, and tangential Qx components. These particular components of the Q force can be presented as products of the metal-tool contact areas on projected onto relevant co-ordinate system planes and a mean unit pressure on the contact area. Because of the complexity of the deformation zone geometry and the deformation mechanism, the theoretical analysis of the CWR process is difficult. That is why most publications which determine rolling forces employ experimental methods to determine mean unit pressures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure12-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure12-1.png",
        "caption": "Fig. 12. Model established by Adams.",
        "texts": [
            " Applying the Z X\u2212 Euler angle, the motion laws of the moving platform are given as follows: \u03b3 t \u03c0t \u03b1 t \u03c0t{ ( ) = 9 sin(2 /5) ( ) = 17 sin(2 /5)\u2218 \u2218 (48) According to the models established in Section 6, the strokes, velocities and accelerations curves of the prismatic joints can be obtained by mathematical software (Matlab) as shown in Fig. 11a\u2013c. The driving forces curves of the prismatic joints in the 1st and 3rd limbs under non-redundant situation are shown in Fig. 11d. The model of the mechanism is established and simulated by simulation software (Adams) as shown in Fig. 12. Then, the strokes, velocities, accelerations and driving forces (non-redundant) curves of the prismatic joints can be measured as shown in Fig. 13. The results obtained by Matlab are consistent with that measured from Adams, which verifies the correctness of the above models of mechanism kinematic equivalent, kinematics and dynamics. The actuators can be chosen roughly according to the results. A 3-D rending model to an engineering application is shown in Fig. 14. This paper defines the virtual continuous axis, and proposes its mathematical criteria"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003311_2.838-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003311_2.838-Figure5-1.png",
        "caption": "Fig. 5b Landing gear vertical mode; 26.73 Hz.",
        "texts": [
            " 36 have veri ed the reliability of the aeroelastic response code for the xed hub case; becauseof lack of space, these results are not shown in this paper. The frequenciesof the rst eight elastic free vibration modes are provided in Table 2. It should be emphasized that the identi cation of these modes by the descriptive terms in the table is qualitative. In reality, these are all coupled modes, and their qualitative identication is associated with the principal contributionof the degrees of freedom mentioned in the overall motion of the fuselage. Mode shapes for two of the modes are provided in Fig. 5. To assess the effects of fuselage coupling on the helicopter hub loads, thehub shearsand moments of the fullycoupledrotor/ exible fuselage model are compared with the corresponding values of the hub xed case assuming a uniform in ow. The hub xed results are taken from Ref. 37, which uses the same rotor model as the current study. Figures 6a and 6b depict the hub loads as a function of advance ratio for both the hub xed and hub free cases. Figure 6a indicatesthat thehub shearsgeneratedwith thehub xedassumption are slightly higher than the corresponding hub free values"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003201_0921-5093(93)90344-e-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003201_0921-5093(93)90344-e-Figure2-1.png",
        "caption": "Fig. 2. Schematic illustration of the method of layer removal for measurement of the residual stresses.",
        "texts": [
            " ~ - d N _ l + v dN E \u00b09 sin2 V-' = K sin 2 lp where a , is the stress value in the measuring direction specified by the angle q0, E is the Young modulus and v is the Poisson ratio. Stress measurements were taken for two different coatings: one with injection of tungsten carbide powder into the melted material (laser surface alloying), which produced a new composite alloy at the surface; the other, undergoing laser surface melting only, giving the original composition of the steel after cooling, with a different microstructure. The stress measurements were taken after the removal of surface layers, as shown in Fig. 2; these layers were removed by successive machining followed by electrolytic polishing of 100 #m before X-ray diffraction measurements. The polishing procedure guarantees that the residual stresses due to machining are removed. Figure 3 represents a typical X-ray diffraction measurement for a coating obtained by laser surface melting. The shape and the position of the diffraction peak at the middle of the chord at 2/5 of the peak length, confirms that the precision of stress measurements is acceptable ( _+ 30 MPa)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002580_1.2833527-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002580_1.2833527-Figure1-1.png",
        "caption": "Fig. 1 Seal model and coordinate systems V(M )\u0302 = wre^",
        "texts": [
            " These as sumptions allow an efficient, approximate solution for the effect of deep grooves, which provides a more rapid alternative to a complete nonlinear analysis. Although this study does not consider the static response to the initial stator misalignment, it nevertheless provides valuable results for the tilt which results from the rotor misalignment. Modeling of the Seal Ring Dynamic Behavior A radial face seal consists of a seal seat and a seal ring. The geometric and kinematic model of the seal considered in this work is shown in Fig. 1. The seal seat rotates about the za axis with a constant angular velocity to. The seal ring is flexibly mounted so that it can move axially along the za axis and tilt about the Xoi and yoi axes of the inertial system. The three degrees of freedom of the seal ring can be described using either the angles XM XJ and the centerline clearance / or using the three parameters, X;. V/> and I (Fig. 1). In this study, the seal is assumed to operate in the dynamic tracking mode for which these latter three parameters are con stant and are equal to x?, y'? and la. The positions of the points M\\ and M2 (Fig. 1) on the seal ring and seat, respectively, and their velocities relative to the inertial reference can be defined in a local cylindrical coordinate system using OM, = rcr + [L, + (r - r,)/?, + r ( x t sin 9 - x\\ cos 9)]ZQ OM2 = re, + [Li + (r - r,)/32 + rxi sin (6* - ujt) VcA/,) = r(x{ sin 6 - Xi cos l9)zo + e(r,e-ojt)]zo (1) Journal of Tribology JULY 1997, Vol. 119 /507 Copyright \u00a9 1997 by ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003654_bf00542566-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003654_bf00542566-Figure8-1.png",
        "caption": "Fig. 8. Always stable region in space of geometrical parameters of a helical spring",
        "texts": [],
        "surrounding_texts": [
            "that domain because running through the lowest corners of the graph takes small parts of unstable regions as regions where springs never buckle. The real, complicated in shape, boundary of the stable region lies between those two curves. 3 The concept of an equivalent column The application of an equivalent column simplifies the analysis of stability of springs. Such a column is assumed to be isotropic (equally possible buckling in any direction), and than it is uniquely defined when its compression, shear and bending rigidities are given. The rigidities should be established in such a way as to ensure high accuracy of solutions. We demand that the relation between the critical strain ~cr and the ratio Ro/H o obtained using an equivalent column should form the envelope of exact solutions. Moreover, the return points, i.e. points belonging to the boundary of always stable region, should form an appropriate approximation of that domain. In the case under consideration we assume that our approximation is not lower than the so-called pessimistic boundary, Fig. 3. I t means that solutions obtained using the equivalent column have some margin of safety. Let us start from an equivalent column for a cylindrical spring, and next we will generalize the results to a spring of arbitrary shape. We start with the determination of compression rigidity of a column. For a highly compressible spring the changes of geometrical parameters are considerable and the non-linear precritical state should be connected with the actual compression rigidity of the equivalent column. We assume that the actual rigidity is described by E A = (EA)o ffc (3.1) where (EA)o is the initial rigidity in the unloaded state, and #c the modification function due to geometrical non-linearity. First of all we determine the initial compression rigidity (EA)o. Figure 4 shows the decomposition of generalized internal forces in a wire cross-section: bending moment Mb, twisting moment Mr, normal force N and shear force T are Mb = PRo sin ao, N ---- P sin s0, (3.2) Mt ~- PRo cos ~0, T --~ P cos s0."
        ]
    },
    {
        "image_filename": "designv11_31_0003100_10402009408983369-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003100_10402009408983369-Figure2-1.png",
        "caption": "Fig. 2-Schematic of test apparatus and coordinate definltion.",
        "texts": [
            " These bearings a re currently used for many applications, including the analyzing magnet of the Nuclear Structure Facility a t the SERC Daresbury Laboratory (I), the Halle optical telescope (2), the 2 10-foot-diameter tracking an- A,B = linear regression coefficients c = fluid specific heat, Jlkg K Ef = frictional energy loss, W Ep = pump energy loss, W F = force, N h = film thickness, m K = power law constant, Pa.secn M = frictional torque, N m N = rotational speed, rpm n = power law exponent p = pressure, N/m2 p, = supply pressure, N/mS A P = pressure difference, N/m2 Q = flow rate, m3/sec R = outside radius, m R, = step radius, m Re = Reynolds number, vhlv r = radial coordinate (Fig. 2) T = temperature, Celsius To = baseline temperature, Celsius TI = thermistor one temperature, Celsius T2 = thermistor two temperature, Celsius AT = temperature difference, Celsius v = fluid velocity, mlsec Y = fluid density, kg/m3 = fluid viscosity, kgls m 7 ~ ~ n - N = non-Newtonian shear stress, N/m2 o = angular velocity, radtsec Y = axial coordinate (Fig. 2) 857 D ow nl oa de d by [ Y or k U ni ve rs ity L ib ra ri es ] at 0 7: 55 1 1 N ov em be r 20 14 858 J. PETERSON, W. E. FINN, AND D. W. DAREING tenna at the NASA-Jet Propulsion Laboratory Deep Space Instrumentation Facility (3) , and Denver's Mile High Stadium ( 4 ) , among others. All applications involve moving extreme weight with minimal effort and, in some cases, high precision. In 1972, the Institution of Mechanical Engineers published proceedings on a conference solely devoted to externally pressurized bearings (2)",
            " The graphite particles had an irregular shape due to the crystalline structure of graphite. The mean effective particle diameter of the graphite powder is 17.5 microns, with 50 percent of the particles below 14.4 microns, and 90 percent under 35 microns. A detailed discussion of the testing apparatus and procedure can be found in (19). THEORETICAL FRAMEWORK and compared with experimental data. The theoretical anal- ysis predicting temperature and pressure of the hydrostatic step is based on the apparatus illustrated in Fig. 2, and assumes that (4), (20): 1. The flow is laminar (Re < 1000) and pressure induced. 2. Inertial forces resulting from bearing rotation are neg- ligible when compared to viscous shear. 3. The fluid is incompressible. 4. Temperature is constant through the film thickness. 5. The bearing surfaces conduct a negligible amount of energy out of the fluid. 6. Pressure at r = R is ambient. From energy conservation principles, the energy required to pump the fluid: Ep = Q A P and the frictional losses: are converted to thermal energy and appear in the lubricant in the form of heat"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003586_910746-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003586_910746-Figure2-1.png",
        "caption": "FIGURE 2",
        "texts": [
            " Instrumentation Savant Laboratory instruments used in gathering the data presented in this paper included the commerciallymade Tannas Scanning Brookfield Plus Eight selfcontained cooling bath shown in Figure 1. On-board temperature programming simplified both calibration and sample analyses. The eight Brookfield heads purchased with the Tannas Plus Eight bath were especially modified versions for computer use. Each head rested on a special Pennzoil-Tannas adapter commercially available to provide precise and repeatable alignment of rotor and stator. Titanium rotors and matching precision-bore glass stators were also purchased commercially. Figure 2 is a sketch of the adapter with rotor and stator. During most of the work reported in this paper, the analog voltage signals of the Brookfield Viscometer heads were transferred to multi-pen strip chart recorders and the traces analyzed by hand-picking points on the curves. These data were subsequently entered into a spread-sheet computer program for further analysis. However, in the later stages of these studies, a special computer program developed by the Tannas CQ. to meet Savant Laboratory requirements was used to directly record and calculate the desired data"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003607_026635119100600305-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003607_026635119100600305-Figure9-1.png",
        "caption": "Fig. 9.",
        "texts": [
            " In this way the silhouette does not condition the supporting plane and its is possible to graduate the rigidity from a maximum for the central sector to a minimum in the extremes. For example, a plane pattern of characteristic angles ~I = 300 , ~2 = 250 , ~3 = 200 , whose concave extreme edges deflect in an angle [, = 40 , on being folded up to condition u j = 00 , the result is: (Fig. 8) _---:;:::\"'i\"\"':::::=------;;::7\"~--_ d., =0\u00b0 H. P. Fig. 8. 232 International Journal of Space Structures Vol. 6 No.3 1991 oi. Tonon It can be seen in the graphic (Fig. 9) that in a first part up to a2 = 40\u00b041' the sector corresponding to a j has not begun folding yet (a l = 0\u00b0); from there the whole stars folding with different values for a\\ respect of a2 up to both coincide in a l = a2 = 90\u00b0. 4. Concentric Development Folds When departing from the same plane pattern of parallel concave edges, a sector folds more than another - folding condition a variable  non-parallel sections and folds of concentric development are generated, in their successive repetition. From all possible folding variants for this con ditions only one will be analysed, the one corresponding to the extreme sector without fold ing (c, = 0\u00b0) and to the central sector totally folded (ae ~ 90\u00b0), and from all possible relative positions ofthe silhouette in the space, only two in particular will be studied; those corresponding respectively to the horizontal and vertical situation ofthe concave edges in the most folded sector or central one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002319_0021-8928(95)00015-h-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002319_0021-8928(95)00015-h-Figure1-1.png",
        "caption": "Fig. 1 f",
        "texts": [
            "2), together with the momentum equations, form a closed system of equations if the tensors A, K and M are given. The slowness of the growth changes predetermines the negligible smallness of both the momentum flux due to mass inflow into an element of the medium and inertial effects; processes that are rapid compared with the growth can be taken into account by being averaged with respect to slow (\"growth\") time [1, 2]. 2. Consider the growth of an object which initially has the shape of a rectangular cylinder. We choose a fixed Cartesian system of coordinates (Fig. 1) with the origin at the base of the cylinder and the xaxis directed along the initial direction of the generators. (If necessary, we further specify: x = x 1, y = x 2, z = x3.) We will assume the material to be isotropic in its elastic properties and denote its Young's modulus, Poisson's ratio and shear modulus by E, a and ~ respectively. The growth is assumed to be transversally isotropic, the plane of isotropy being initially perpendicular to the x-axis, and after deformation being perpendicular at each point to the fibre that was initially directed parallel to the x-axis",
            " To be consistent with obse~ations of many biological objects over a wide range of loads which show the accelerating effect of tensile axial stresses (and, conversely, the slowing effect of compressive stresses) on growth, we shall always require the inequality 0 > 0 to t~e satisfied. The signs of the remaining coefficients associated with growth will neither be required nor discussed below. For small changes in the comoving coordinate lines relative to their initial directions (which does not exclude large displacements, e.g. along the x-axis) formulae (2.1) can be applied directly in the Eulerian system of coordinates shown in Fig. 1, but already as an approximation. In this Cartesian system the equilibrium equations have the form ~ k t / ~x t + F ~ = 0 (2.2) where b a = F 3 = 0, while F 1 = pg is the distribution of the volume force of gravity (with thex-axis being assumed to be directed perpendicularly). We shall assume the lateral surface of the object to be unloaded, while on the face ~ = L) we set the conditions ~y = 0, ax = - P/S(t, L), where S(t, x) is the area of the section normal to the x-axis and P = P(t) ~> 0 is the axial load applied to the face"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003025_978-3-0348-9179-0_4-FigureI-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003025_978-3-0348-9179-0_4-FigureI-1.png",
        "caption": "Fig. IS. Voltammograms showing proton-gated electron transfer at the [3 Fe-4SJ cluster in a mutant form of Azotobacter vinelandii Fd I (01 SN), and comparison with the native form which differs only very marginally in the region of the switched residue, but which shows virtually normal reversible electrochemistry. a) Initial sweep voltammograms ofOISN (solid line) and native (dashed line) forms of Fd I, adsorbed at an edge-oriented pyrolytic graphite electrode, using polymyxin as co-adsorbate, at DoC, and at scan rate 930 mY S-I. To obtain similar thermo dynamic driving forces for cluster protonation, native Fd I was measured at pH 6.S, while the DI5N mutant was measured at pH S.9. b) Simulation of the voltammetry ofOISN, pH 5.9, at scan rate 930 mY s '. Parameters used are shown in Fig. 16. (Figure ISa reproduced, with permission, from Reference 58. Copyright 1993. American Chemical Society.)",
        "texts": [
            " As will be emphasized throughout, the exploitation of voltammetric methods in order to visualize and quantify intrinsic properties of protein redox centres depends to a great extent upon taking into consideration the effects that arise from differing modes of mass transport of the redox active molecules. This can be illustrat ed very simply by reference to the representative cyclic voltammetric current responses (waveforms) shown in Fig. 1. Some relevant equations and relationships are summarized in Table 1. Application, ,)1' \\ oltammetnc methods for probing the chemistry of redox proteins 209 The familiar shaped voltammogram (Fig. I A) with oxidation and reduction currents reaching peak values at Ep = EO \u00b1 29.5/n mY (thus ~Ep = 59/n mY at 25 DC) is the limiting (ideal) result for reversible, diffusion-controlled electrochemistry at a stationary, planar electrode. The theory described in the classic paper by Nicholson and Shain also predicts that the peak current is proportional to the square root of the scan rate [11]. The same reversible, diffusion-controlled electrochemistry can also be measured under steady state conditions [12, 13]. This typically involves either rotating the electrode to achieve hydrodynamic control over mass transport, or using a micro electrode at which a radial diffusion field is achieved at sufficiently slow scan rates. The resulting voltammogram (Fig. I B) is sigmoidal and the cur rent is independent of scan rate (i. e. time). The half-wave potential E 112 is essentially equal to the formal reduction potential and is independent of the direction of sweep. By contrast, the voltammogram observed for a reversible, uncoupled electrochemical reaction of a molecule immobilized on an electrode has the form shown in Fig. I C, which is independent of electrode dimensions or rotation rate. The maximum (peak) current is proportional to scan rate and occurs at the formal reduction potential [14 -16]. As we will 210 F. A. Armstrong enlarge upon in Section 2.2, the actual electrochemical results obtained for proteins are usually less than reversible; they may involve mixtures of diffe rent mass transport characteristics 1 A, 1 B, and 1 C, and they may also in volve coupling to chemical reactions. The latter feature will form the focal point of our attention later",
            " Protein molecules are induced to bind tightly to the electrode surface in the form of a stable, porous, mono/submonolayer film, oriented for facile electron transfer, and with retention of native struc tural and reactivity characteristics. The redox centres act independently and homogeneously, and remain fully accessible to ions and small reagents in the contacting electrolyte, as does all the intervening space in the interface. Ideally, the cyclic voltammetry of such systems should resemble the form shown in Fig. I C. As described later, the voltammetric response now becomes a particularly useful signal. ELECTROLYTE metal ions, ligands , substrates Applications of voltammetric methods for probing the chemistry of redox proteins 215 Detailed studies of the electrochemical properties of cytochrome c adsorb ed at various surfaces have been carried out by Bowden and co-workers in their efforts to achieve and develop well-defined protein monolayer electro chemistry [43-50]. By analyzing both the electrochemical and protein struc tural (in situ spectroscopic) aspects, their investigations have appraised the general validity of this approach for the study of redox proteins, and provided insight into the way that a protein's properties alter between the free and the bound state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003127_(sici)1097-4563(199709)14:9<631::aid-rob1>3.0.co;2-m-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003127_(sici)1097-4563(199709)14:9<631::aid-rob1>3.0.co;2-m-Figure2-1.png",
        "caption": "Figure 2. End effector forces applied to the payload.",
        "texts": [
            " Differentiating open kinematic chain manipulators that are cooperat-equations (1) and (2) with respect to time gives the ing to manipulate the payload can be assembled torelationship between the end effector velocities and form the equations governing motion of the system:task space velocities: X\u0307E 5 JuQ\u0307 (3) HA(uA)u\u0308A 1 CA(uA , u\u0307A) 1 GA(uA) 5 tA 2 JT u,AFE,A X\u0307C 5 JCX\u0307E 5 JCJuQ\u0307 5 JuQ\u0307 (4) HB(uB)u\u0308B 1 CB(uB , u\u0307B) 1 GB(uB) 5 tB 2 JT u,BFE,B . .. where Ju is the Jacobian matrix used to map the joint Hi(u i)u\u0308i 1 Ci(u i , u\u0307i) 1 Gi(u i) 5 ti 2 JT u,iFE,i (8)space velocities to the end effector space velocities of This set of equations can be combined: J2T u H\u0303Q\u0308 1 J2T u C\u0303 1 J2T u G\u0303 5 J2T u t 2 F\u0303E (13) Each manipulator influences the payload through the forces transmitted by the end effector as shown in Figure 2, with the set of applied forces shown. The3 HA 0 HB ... 0 Hi 4 Q\u0308 1 3 CA CB . .. Ci 41 3 GA GB . .. Gi 45 3 tA tB . .. ti 4 Newton and Euler formulations are used to represent the load distribution of the payload when it is rigidly grasped by the multiple manipulators. This can be expressed by the following sets of payload dynamic equations: 2 3 JT u,A 0 JT u,B ... 0 JT u,i 4 3 FE,A FE,B . .. FE,i 4 f 5 mCr\u0308 2 mCg (14) n 5 ICg\u0307C 1 gC 3 (ICgC) (15) (9) where mC is the mass of the payload, IC is the inertia matrix of the payload, r is the position of the centerand may be compactly expressed as: of mass of the payload, gC is the angular velocity of the payload, and g is the gravity force",
            " wi I333 G (19) pact representation is and of the applied forces cancel when represented within any common frame of reference. Using the force relationship between reference coordinates in Eq. (11), Eq. (8) can be expressed in the nonredundant task wi 5 3 0 wriz 2wriy 2wriz 0 wrix wriy 2wrix 0 4 (20) space as: J2T u,AHA(uA)u\u0308A 1 J2T u,ACA(uA , u\u0307A) 1 J2T u,AGA(uA) where wri 5 hwrix , wriy , wrizjT represents the ith end 5 J2T u,AtA 2 (F M E,A 1 F I E,A)effector location with respect to the coordinates of the payload reference frame, as shown in Fig. 2. J2T u,BHB(uB)u\u0308B 1 J2T u,BCB(uB , u\u0307B) 1 J2T u,BGB(uB) Notice that not all of the forces applied to the 5 J2T u,BtB 2 (F M E,B 1 F I E,B)payload contribute to motion. Some of the forces ap- . ..plied by one manipulator may be opposed by forces generated by another manipulator in the cooperating J2T u,i Hi(u i)u\u0308 i 1 J2T u,i Ci(u i , u\u0307 i) 1 J2T u,i Gi(u i) system. For the purpose of describing the force inter- 5 J2T u,i ti 2 (F M E,i 1 F I E,i) (22)actions between the cooperating manipulators and the payload, the vector of external forces acting on each manipulator is defined as being composed of A unique set of equations can be developed that detwo parts, the part that contributes to the motion of scribes the dynamic characteristics of the system of the payload, and the part that contributes to loads cooperating manipulators in the task space reference transmitted across the payload frame by summing Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002507_s0893-9659(98)00161-x-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002507_s0893-9659(98)00161-x-Figure1-1.png",
        "caption": "Figure 1. View of t he rotary inverted pendulum. Here \u00a2 ---- lr /2 - 0.",
        "texts": [
            " E R G A M O N Applied Mathematics Letters 12 (1999) 131-134 Applied Mathematics Letters C o n t r o l o f a R o t a r y I n v e r t e d P e n d u l u m Y . Y A V I N Laboratory for Decision and Control Department of Electrical and Electronic Engineering University of Pretoria Pretoria, South Africa (Received August 1997; accepted October 1997) A b s t r a c t - - T h i s work deals with the control of a rotary inverted pendulum (see Figure 1). This device is composed of the following: an arm rotating in the horizontal plane where one of its ends is mounted on a motor shaft and where a rod is mounted on its other end. The rod's lower end is mounted on the arm's free end in such a manner that, the rod is moving as an inverted pendulum in a plane that is at all times perpendicular to the rotating arm. The problem dealt with here is to find a control law to the motor's output torque such that the inverted pendulum motion will be stabilized about a vertical axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002609_(sici)1097-0207(19961030)39:20<3535::aid-nme13>3.0.co;2-j-Figure3-1.png",
        "caption": "Figure 3. Static modes GI, a2 and a3 dues to a point",
        "texts": [
            " Consider, for example, the flexible body in Figure 2. Due to the kinematic pairs existing at its ends-they could be two revolute pairs-the modeling has been carried out with one point and one unit vector in excess. These natural co-ordinates in excess are going to be the cause of the static modes. For every point in excess, three static modes are obtained. They are the static deformation modes corresponding to unit displacements of the point along the x, y and z local axis, keeping fixed the rest of the boundaries (points and unit vectors). Figure 3 shows the static modes @(i = 1,2,3) produced by point rl of the body in Figure 2. The static mode a1 corresponds to a bending deformation in the plane (k, jj), the static mode @ corresponds to an axial deformation along y-axis and the static mode a3 corresponds again to a bending deformation, this time in the plane ( j , 2). Note the difference between modes Q1 and a3: while for al rotation at the beam\u2019s right end is free, for a3 this rotation is forbidden and the beam must remain orthogonal to the unit vector nl at that point, since boundaries shall be kept fixed, as mentioned above",
            " This means that points and unit vectors are indeed material points and directions of the body, and not merely fictitious mathematical entities. This is why, when altering their relative positions, deformation of the body appears. For every unit vector in excess, two static modes are obtained. They are the static deformation modes corresponding to a unit rotation of the vector around the two local axis \u2018more\u2019 3538 J . CUADRADO. J. CARDENAL AND J. GARCfA DE JAL6N perpendicular to it, keeping fixed the rest of the boundaries. Thus, continuing with the body in Figure 3, unit vector nl produces two modes in Figure 4. Static mode G4 corresponds to a torsional deformation around y-axis, while static mode corresponds to a bending deformation in the plane ( j , 2). We remark that the rotation of the beam at point rl around unit vector n1 is not detected by the variation of any co-ordinate. This rotation will be considered as an internal deformation of the beam, as it will be seen when studying the dynamic modes. The interest of using static modes is that their amplitudes qi(i = 1,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003931_jsvi.1999.2484-Figure9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003931_jsvi.1999.2484-Figure9-1.png",
        "caption": "Figure 9. Measurement of the input displacement of the moving belt.",
        "texts": [
            " This connection excites the belt periodically at the points where it enters and exits from the free span attached to the pulley bearing surface. When the belt rotates over the drive pulley at a rotational angular velocity u p , the point excitation at x\"0 can be expressed as w(0, t)\"w 0 exp( jqu p t), (32) where w 0 is the strength of excitation and q is the number of events at which the belt connection enters the free span per rotation. In the theoretical model of the belt vibration, equation (32) should be used as a boundary condition with other simply supported boundary conditions. Figure 9 shows the measurement layout for belt displacement by using a laser velocity sensor at the junction point between free belt span and pulley bearing surface. The length of the connection was 30 mm, the rotating speed was 1000 r.p.m. (or 16)67 Hz), and the belt connection excitation repeated every 0)251 s (or 3)94 Hz). Figure 10(a) shows the measured displacement spectrum, where the \"rst peak is at 3)94 Hz and other major peaks appear at integral multiples of this frequency. A simpli\"ed theoretical model is needed for calculating the power #ow and this can be done by the truncated spectrum modelling as w(u; 0, t)\" n + i/1 A i exp( ju i t), (33) where n is the number of truncated peaks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure12-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure12-1.png",
        "caption": "Fig. 12. (a) The perceived shape of the space CFNS(ti) generated by the robot R1: (b) The simplified traffic patterns L6; L7; L7 generated by R1:",
        "texts": [],
        "surrounding_texts": [
            "Since the major goal of the traffic language is to assist an autonomous robot to represent and understand the traffic priorities of the other moving objects in the same navigation space avoiding collisions, it is necessary that the synthesis of traffic priority patterns to be defined semantically. Notation: a) (commutative) with b) (associative) with and Definition: The length of a perceived pattern is defined as the number of corridors which compose the pattern. Corollary: Two perceived patterns (generated by the same or different robot, at the same time for two different moving objects) with the same length are not necessarily identical in shape. Definition: The synthesis # (semantically) of two traffic patterns determines the order of the robots priorities one against the other. Proposition: (commutative) Proof: Let assume that three robots are moving in the same navigation space, as shown in Fig. 10. The robot is the main one and are the secondary robots. For this particular case, and Thus, the pattern produces the relationship between the robots\u2019 priorities. The pattern provides the priority relationship Thus, the synthesis provides the relationship (1) among the robots\u2019 priorities. Now, the synthesis provides (2). These two relationships are identical, which means that Following this process easily it can be proved the general case Proposition: (associative) Proof: Similar to commutative. Notation: (identity traffic pattern) for every Corollary: In a free navigation space with secondary moving robots there is a possibility of existence of the following traffic pattern configurations. 1) There is a maximum of two patterns with . 2) There is a maximum of one pattern with or . 3) There are patterns such that where Corollary: In a free navigation space FNS if there are the traffic patterns and the there is not the pattern where the sequence of the values for the indexes are and or and or and Traffic Complexity Table II presents the traffic complexity of moving robots in a CFNS under two different assumptions. \u2022 In the first assumption, called individual, a robot views all the other moving robots, generates all the traffic patterns from its own position and calculates all the possible traffic priorities of the other robots against its own priority. \u2022 In the second assumption, called global, every robot views all the other moving robots, generates all the traffic patterns and calculates all the possible traffic priorities for all the moving robots including itself. V. ILLUSTRATIVE EXAMPLES In this section, two illustrative examples for traffic cases are provided and solved by using the KYKLOFORIA language. In the first example, the traffic case includes six moving robots in a free navigation space shown in Fig. 11. Figs. 12\u201317 provide the shape of the free navigation spaces observed TABLE III SIMULATED RESULTS FOR FIG. 18 by each moving robot and the traffic patterns generated by each of them in their own free space. In the Fig. 18, the velocities of the moving robots are considered the same, thus the traffic priority relationships generated by the traffic language are given in Table III. Each moving robot knows the traffic priority relationships in the same free space. Thus, the robot makes use of its own which is higher than and goes out of the narrow corridor. At a time min, covers a distance of 4.5 m. The robot has to wait of a period of 0.6 min, and then it proceeds into the open corridor by covering a distance of 1.4 m in 0.485 min. Initially, covers a distance of 1.3 m in 0.325 min, then it slows down and waits for 0.55 min before it proceeds into the narrow corridor following the robot and covering a distance of 0.9 m in 0.23 min. The robot using its own higher priority over covers a distance of 4.5 m. The robot waits for 0.75 min and then proceeds forward by covering a distance of 1.5 m. Finally, the robot covers a distance of 4 m in 1.125 min because it spends some time to change its direction. Note that, and TABLE IV SIMULATED RESULTS FOR FIG. 19 (a) (b) Fig. 14. (a) The perceived shape of the space CFNS(ti) generated by the robot R3: (b) The simplified traffic patterns L1; L7; L2; L6 generated by R3: change their directions (as shown in Fig. 9) avoiding a possible collision. In the case that the velocities of the robots are considered different, then Table IV shows the traffic priority relationships and the robots traffic paths and locations are given in Fig. 19. In particular, present a traffic behavior similar to the previous case with the same velocities, by using the Table IV. covers a distance of 4.9 m with m/min. covers a distance of 1.4 m with m/min. covers a distance of 1.3 m with m/min and a distance of 0.6 m with m/min. waits until passes the intersection point and then covers a distance of 1 m with m/min. covers a distance of 4.8 m with m/min. Finally, covers a distance of 2.5 m with m/min. The second example explains the use of the language for the improvement of the traffic schedule of a particular robot under the assumption that the local traffic flow in a certain region is almost the same every time that the robot enters that region. In this case, the robot enters the region from left to right at time and spends min crossing it. At that time, there are three other moving robots crossing the same region from different directions (see Fig. 20). The traffic flow extracted by the robot in that region, is represented by the following language words: The symbol & represents the synthesis operator between words for the formulation of the traffic flow extracted by a robot traveling through a region where In this particular case there is no delays during the traveling. Fig. 21 shows the same region, at a different time where the robot enters the region from the right to the left in order to cross it by following the reverse path of Fig. 20. At this time there are four other moving robots and a fifth one is coming to the same region. The traffic flow extracted by the robot is represented by the following words: where In this particular case there are delays due to conflicts between the robots directions and traffic priorities. More specifically, the robot has to wait until and pass first and then it continues its own path. This mean that the robot knows the time required to cross the region, and in the latter case it took more time, At this point the robot analyzes the traffic flow perceived by itself and modifies its traffic path for a future cross of the same region under a traffic flow similar to More specifically, it follows the next algorithmic steps: 1) Check each word , for patterns . 2) Search for possible patterns , to replace in a word . 3) Replace the first with an in . 4) Rearrange the word into a new one , which includes the affects on the other patterns due to replacement ( instead of ). 5) If the new word includes less number of patterns then use it in the new , else go to 2 to replace the next with an in . 6) If the new overall traveling time is less than the original then proceed else no changes Thus, Fig. 22 shows the new modified traffic path. The new traffic flow extracted by is represented by the following words: where Thus, the new traffic flow includes less conflicts and no significant delays for the robot"
        ]
    },
    {
        "image_filename": "designv11_31_0002421_6.1995-1442-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002421_6.1995-1442-Figure1-1.png",
        "caption": "Figure 1: Coordinate system",
        "texts": [
            " The nodal coordinate is fixed to each node and the corotational coordinate is determined from the deformed element to derive pure elastic displacement of the element. Assume we have a two-node Euler-Bernoulli beam element j whose nodes are referred to as nodes 1 and 2. Each node has translational displacement X! (i=l, 2) and Euler parameter QI' to denote the rotational translation from the initial elemental coordinate. The rotational matrix for each node is denoted as R: and the rotational matrix from the inertial to the initial coordinate is R{ (Fig.1). The x axis of the corotational coordinate is de- fined to connect node 1 and node 2 and the y axis is the projection of y axis of node 1 coordinate onto the surface normal to the x axis of the corotational coordinate. The z axis of the corotational coordinate is determined following the dextral triad rule (Fig.2). These operations result in the rotational matrix from the inertial coordinate to the corotational coordinate. In this definition of the corotational frame, all displacement of node 1 and transverse displacements are always equal to zero and the displacement vector of node 2 ( denoted as 4 ) is given as the subtraction of the given element length ~j from the d i s tance between nodes 1 and 2 after deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.10-1.png",
        "caption": "Fig. 9.10. Mechanism with five elastic elements",
        "texts": [
            " Since the deformations are small variations of some parameters (lenghts of links, angles between axes etc.) this problem is reduced to the problem of parametric analysis considered in Chaps. 3 and 4. A convenient way to solve it in the considered case is to employ the equilibrium equations, using the method explained in Sect. 4.3. It must be emphasized that when applying this method we employ the equilibrium equations for a rigid non-deformed mechanism. As an example we consider an elastic mechanism with the diagram shown in Fig. 9.10. It differs from the mechanism considered in Sect. 9.3 in that links AB and DE are assumed to be flexible in longitudinal direction; we denote their stiffnesses by C4 and c5 and their deformations with ()4 and ()5' Having fixed the inputs (the rotors of the motors), we determine the reduced flexibilities for the output link BD. They form a matrix Evp that relates vectors V = {i>x,Py,M)T and ilp = (LlxK,ilYK,ilqJ? . Next, we introduce the vector of the forces of elasticity F = (M 11'\\' M 11'2' M 11'3' F4 , F5 r, where M tpi (i = 1,2,3) are the outlet moments of the transmission mechanisms; F4 , F5 are the elastic forces in rods AB and DF",
            " These forces and moments are added to the active forces, acting on the links, in order to determine the deformations of the elastic elements caused by the combined action of active forces and inertia forces. A basic problem of the dynamics of elastic mechanisms is the investigation of vibrations in the vicinity of an equilibrium position or of a program motion. We will acquaint ourselves with methods how to formulate this problem by considering concrete examples. Let us formulate the equations of small vibrations for the mechanism shown in Fig. 9.10 in the vicinity of the equilibrium position given by the values of the input coordinates (rotation angles of the motors) qlO, q20, Q30' In this position the motors are braked and the mechanism can accomplish only small vibrations due to deformations \u00b01, \u00b02 , 03 of the transmission mechanisms and deformations of the rods AB (\u00b04 ) and DE (Os), Let us suppose that platform BD, the mass centre of which is at point K, and links OA and EF possess substantial masses. The inertia forces of the platform performing a plane motion are reduced to the resultant vector cI> with projections CPx = -mwKx and CPy = -mwKy I onto the coordinate axes, where m is the mass of the platform, and to the resultant moment M k = -J K 6 , where J K is the moment of inertia of the platform with respect to axis Kz, and 6 is its angular acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002295_pime_proc_1995_209_154_02-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002295_pime_proc_1995_209_154_02-Figure4-1.png",
        "caption": "Fig. 4 Three-dimensional effective stress distribution within the root and",
        "texts": [
            "1 per cent has been achieved in four or five iterations. 3.4 Calculation cases The calculation cases have been chosen to give an answer to the question of the influence of the contact problem class and/or the clearance between the contact surfaces on the stress state of the attachment. Three classes of contact problem have been analysed. The Q IMechE 1995 4 RESULTS OF THE STRESS CALCULATIONS The results of the three-dimensional stress analysis are limited to effective and normal contact stresses. Figure 4 presents effective stress isolines obtained from calculation of case 1 (frictionless contact of known geometry). The isolines from 1 to 7 correspond to the stress values changing proportionally from 0.25 x 10' to 1.75 x 10' N/m2. The stress distribution pattern is typical. This means that for case 3 corresponding with the frictionless contact of unknown geometry the picture of the isolines is quantitatively and qualitatively almost the same. For the calculation case 5 (frictional contact of unknown geometry) the picture of the isolines is quantitatively the same; however, the qualitative differences appear in the loading contributions of the attachment hooks, which produce further changes in the stress distribution within each hook",
            " In order to visualize the quantitative differences six tables are presented, containing the maximal effective stresses appearing at the hook notches of the blade root and disc sector in six from eleven of the element layers. The location of the maximal effective stresses corresponds with the element centroids A (Fig. 5). With the results from Tables 1 to 6 the tendency of changes of the effective stresses for the consecutive hooks and along the hooks (in the direction tangent to the curvature of the attachment) can be shown, while the tendency of changes of the effective stresses across the hooks can be seen from Fig. 4. The results of the normal contact stresses at the maximally loaded points (nodes B in Fig. 5) of the contact surfaces of the hooks are presented in Tables 7 and 8. Both left and right sides of the attachment corresponding with the convex and concave surfaces of the blade are included. The element and node layer numbers increase in the direction from the trailing to leading edge of the blade. The first and the last layers are adjacent to the disc outer planes, while the rest of the layers are placed equally between the first and last ones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003539_s0263574700010195-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003539_s0263574700010195-Figure1-1.png",
        "caption": "Fig. 1. Robot Manutec-R3 with six revolute joints.",
        "texts": [
            " The position control part may also include feedback loops with respect to integrals of position errors. There is a number of problems related to application of this control scheme. Two of them seem to be the most essential, as identified by An and Hollerbach:78 the problem of control of contact between the end-effector and the constraint surface and the problem of interaction between the force control and position control. In discussing these problems we shall use simulation results. We have simulated a particular robotic system9 Manutec-R3. The robot is presented in Figure 1. Data on this robot are given in reference 9. A Cartesian position control is assumed and local servo gains are computed to ensure stability of the robot in free space. The sampling period for position and force control is 0.001 [s], while the sampling rate for updating of Jacobian matrix and its inverse is 0.015 [s]. 3.1 Contact problem Let us consider a simple task: the robot end-effector is moving normally to constraint surface. When it hits the surface it has to produce a certain force F\u00b0(t) against the surface and to move along the surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002557_s0893-6080(97)00043-9-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002557_s0893-6080(97)00043-9-Figure2-1.png",
        "caption": "FIGURE 2. Idealized three-joint robotic manipulator. The dynamics of this three-joint robotic manipulator is highly nonlinear. A typical perturbation is when the manipulator grasps (or releases) an object. This is modelled by changing the mass (M2) at the end effector. Compensation of this perturbation is hard, especially when the mass of the object is large compared to the mass of the manipulator.",
        "texts": [
            " Results are presented elsewhere (SzepesvAri & Lrrincz, 1996b, 1996d). An interesting question is whether for classical mechanical models the perturbation of the \"geometry\" and other physical properties of the plant result in uniformly positive definite perturbation or not. The answer is positive at least for the following special case. Consider the robot arm working in the three-dimensional 7 See the appendix for the discussion of various ultimate boundedness concepts. space with 3 degrees of freedom (see Figure 2). We assume a simplified model of the arm's dynamics that seems to be a \"reasonable compromise between system complexity (and thus realism) and ease of implementation\" (Anderson & Miller III, 1992). The model is complete in that all joint coupling terms (centripetal and Coriolis torques, variable effective moments of inertia, etc.) are included. It is still an idealized model, however, in that all masses are assumed to be placed at discrete points and effects such as drive train friction are not modelled"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003942_s0957-4158(01)00045-9-Figure7-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003942_s0957-4158(01)00045-9-Figure7-1.png",
        "caption": "Fig. 7. Zirconia fuel cell.",
        "texts": [
            " It consists of a white ceramic tube with a thin wall which acts as an oxygen ion conductor [22]. On the inside is a fuel electrode, usually a mixture of zirconia particles and nickel particles, with a nickel wire to collect the electrons. Outside the cell is the oxygen electrode, a black conducting oxide material, with a wire wrapped around it supplying electrons. Fuel is flowed through the tube while air circulates on the outside. This provides a potential of around 1.1 V with a typical power output of 0:2 W=cm 2 at 800 C (see Fig. 7). The principle of operation of this device is electrochemical. Oxygen is reduced to O2 ions at the cathode and the ions are transported through the membrane to release electrons at the anode, where fuel is oxidised. The electrons then do work as they circulate around an external circuit. The benefits are high efficiency and total conversion to water and carbon dioxide. A 1 kWe device could operate at 50% efficiency with low maintenance cost. Heat is the other product, which is used to maintain the temperature of the device and also to process the raw fuel into more suitable hydrocarbons"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.9-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.9-1.png",
        "caption": "Fig. 9.9. Mechanism with three elastic drives",
        "texts": [
            "18) Thus, when making a reduction to the output of a transmission mechanism, the flexibility of an elastic element is divided by the squared transmission ratio, which relates the deformation of this element to the output coordinate. In an analogous way the flexibility of a transmission mechanism, reduced to its input is defined. For the mechanism shown in Fig. 9.8 we obtain: 9.3 Reduced Stiffness and Reduced Flexibility of a Mechanism with Several Degrees of Movability (9.19) (9.20) Let us consider a mechanism with several degrees of movability. An example of a mechanism with three degrees of movability ensuring the positioning of a planar platform BD is shown in Fig. 9.9. Here motors 1,2 and 3 are installed at joints 0, form, and the rotors are connected with links OA, BD and FE through coaxial, elastic transmission mechanisms. Input coordinates of these mechanisms are the rotation angles of the rotors q), Q2' Q3' and output coordinates are the rotation angles lI'l> lI'2' lI'3\u00b7 We denote by cl> c2' c3 the stiffnesses of the transmission mechanisms reduced to their outputs, by i), i2, i3 the transmission ratios and by 0), \u00b02 , 03 the deformations of the mechanisms reduced to their outputs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.49-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.49-1.png",
        "caption": "Fig. 2.49",
        "texts": [
            " Three types are to be distinguished: - the gate-to-source capacitance Cas\u00b7 Its dielectric is the oxide layer isolating the gate from the source. This capacitance is hardly affected by variations in voltage Vos\u00b7 - the gate-to-drain capacitance Cao\u00b7 This accounts for the space charge region which appears in the P area beneath the gate. It varies considerably with voltage v0 s, going from a value similar to Cas when the transistor is conduct ing (low v0 s) to a negligible value when it is nonconducting (high v0 s). This is shown in Fig. 2.49b. - the drain-to-source capacitance Cos\u00b7 As its effects are hidden by those of Ca0 , it is less important. The sum Cao + Cas is called input capacitance C;. 2.3 Field Effect Transistors 65 \u2022 Figure 2.50 shows the increase in voltage vGs as a function of charge QG carried to the gate by current iG during turn-on. The OFF state is the starting point: vGs equal to zero, v05 having value E imposed by the supply of the transistor. There are three distinct sections on this curve: - Section OA corresponds to the charging of the input capacitance under full voltage v05 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000052_j.mechmachtheory.2016.09.023-Figure1-1.png",
        "caption": "Fig. 1. Rotation of a rigid body constrained by a wrench.",
        "texts": [
            " If a rigid body can purely rotate around an axis, the axis can be denoted by a screw as S s r s= ( ; \u00d7 )m m m m , where sm is a unit vector indicating the direction of the axis, and rm is a vector from the reference origin to the axis. If sm and r s\u00d7m m both stay invariant during the motion, screw motion \u03b4\u03b8Sm of the rigid body is a rotation around a constant axis called continuous axis; Otherwise, that is a rotation around a variable axis called instantaneous axis. Herein, \u03b4\u03b8Sm is a twist of infinitesimal amplitude \u03b4\u03b8 around the screw Sm. Assuming a rigid body connects with other bodies or kinematic chains by n revolute joints, as shown in Fig. 1, the revolute joints can be indicated by line vector as S s r s= ( ; \u00d7 )i i i i J J J J , where si J is the unit vector denoting the direction of the axis of the revolute pair, and ri J is the position vector of si J , and i n= 1, 2, \u22ef . When the Sm is coincident with a Si J , i.e. S S= i m J , there is an actual shaft at the location of the rotation axis, and then \u03b4\u03b8Sm is called rotation around a physical axis. When the Sm is not coincident with any Si J , i.e. S S\u2260 i m J , there are not actual shafts at the location of the rotation axis, and then \u03b4\u03b8Sm is called rotation around a virtual axis, and at this point, the Sm is a virtual axis",
            " Conversely, if W \u2261 0, it indicates that every infinitesimal version of a rotation \u03b4\u03b8Sm is all permitted by the wrench f Sr, i.e. \u03b4\u03b8Sm is a continuous rotation. So the physical sufficient and necessary conditions of the continuous rotation of a rigid body constrained by f Sr, rotating around Sm, are that the virtual work is always equal to zero (W \u2261 0). Take the common perpendicular line between Sm and Sr as the axis of y, Sm as the axis of z, the intersection of y and z as the origin o, and establish right-handed coordinate system o xyz\u2212 shown in Fig. 1. Then f Sr and \u03b4\u03b8Sm can be expressed as follows: f f s\u03b1 c\u03b1 h s\u03b1 dc\u03b1 h c\u03b1 ds\u03b1S = ( , 0, ; + , 0, \u2212 )r r r (1) \u03b4\u03b8 \u03b4\u03b8S = (0, 0, 1; 0, 0, 0)m (2) where \u03b1 and d are the angle and the shortest distance between Sm and Sr respectively, and s\u03b1 \u03b1= sin , c\u03b1 \u03b1= cos , similarly hereinafter. The virtual work W that f Sr acts upon \u03b4\u03b8Sm is the reciprocal product [42] between them, i.e. W f \u03b4\u03b8 f\u03b4\u03b8 h c\u03b1 ds\u03b1 f\u03b4\u03b8\u03d6S S= \u2218 = ( \u2212 ) = 2r m r (3) where, \u03d6 h c\u03b1 ds\u03b1= ( \u2212 )/2r is the virtual coefficient [43]. So when f \u2260 0 and \u03b4\u03b8 \u2260 0, the geometrical sufficient and necessary conditions of the continuous rotation of a rigid body constrained by f Sr, rotating around Sm, are that the virtual coefficient is always equal to zero (\u03d6 \u2261 0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002860_s004070050024-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002860_s004070050024-Figure3-1.png",
        "caption": "Figure 3",
        "texts": [
            " We must now consider how Newton used these results, on the motion of the moon\u2019s nodes, in his quantitative treatment of the precession of the equinoxes. The precession of the equinoxes is the westward movement, of about 50 seconds of arc per year, of the point where the celestial equator crosses the plane of the ecliptic. This movement was identified by Hipparchus in the second century B.C. and was explained by Copernicus (though he expressed it in a somewhat different way3) as due to a slow rotation of the earth\u2019s rotation axis about a line perpendicular to the plane of the ecliptic. Figure 3 shows a cross-section of the earth through its centre C and containing the rotation axis NS. This axis is tilted at an angle \u03b1, equal to about 23 1 2 degrees, to the normal AC to the plane of the ecliptic. The precession consists of a slow rotation (period about 25 800 years) of the axis NS about AC so that it sweeps out the surface of a cone. As a result of the precession, the plane of the equator rotates about the normal AC, in a manner somewhat similar to the rotation of the plane of the moon\u2019s orbit",
            " He attributes both effects to the same cause \u2013 the difference forces, described above, and denoted by f1 and f2 in Figure 1. In this case, 3 de Revolutionibus, Book I, Chapter 11. the forces are acting, not on the moon moving freely in space, but on \u201cparticles\u201d in the body of the earth. (Newton here speaks of \u201cparticles\u201d in an unspecified sense. He does not, in this context, discuss their nature, or the forces they might exert on one another. He does, however, speculate on such matters in Query 31 at the end of the Optics.) I have indicated two of these forces in Figure 3 \u2013 here f1 acts on particle P1 and f2 on particle P2. We must imagine such a force acting on every particle in the material of the earth and, in each case, the force is proportional to the distance of the particle from the plane that, above, we called 5-the plane containing the normal AC to the ecliptic plane and perpendicular to the earth-sun line CS\u2032. Thus, f1 is proportional to P1A1, f2 to P2A2 and, in each case, the force is directed away from 5. Recall that these forces are relative or difference forces",
            " For this reason, they are also called tidal forces. If the earth were perfectly spherical in shape, and uniform in density, then, for every particle on one side of the plane 5, there would be a similar particle on the opposite side and their forces would cancel. Thus the tidal forces would produce no net movement of the earth as a whole. However, because of its rotation about the axis NS, the earth is flattened at the poles and bulges at the equator and has the elliptical cross-section shown in Figure 3. I shall call the central spherical region, whose cross-section is the circular unshaded region in Figure 3, the core and refer to the surrounding part, whose cross-section is the shaded lunules, as the external region. Newton takes the earth to be uniformly dense and so the amount of matter in any region is proportional to its volume. For the reason given above, the tidal forces in the spherical core cancel in pairs and so produce no net effect. However, because of the tilt of the axis NS to AC, there are particles in the external region to the left of 5 and above the plane of the ecliptic, such as P1 in Figure 4, that have no corresponding particle on the right"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003783_1.342274-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003783_1.342274-Figure2-1.png",
        "caption": "FIG. 2. Definitions of HI' lJ\"m' Ili\u2022em , (vB ...",
        "texts": [
            "113 On: Sun, 21 Dec 2014 06:03:41 B. Parameter s When the flux density B is sinusoidary with time t, then the associated field HI becomes a nonsinusoidal periodic wave. By means of a Fourier series, this field H, can be classi fied into the odd liodd and even Revet] components,! 1 that is, (8) Since the flux density B in (1) goes to zero when the time derivative of flux density dB / dt in (1) and the even component Hevell in (8) arrive at their maximum values, (7) is reduced to (9) where Hem ,Hi, em are shown in Fig. 2. By means of (9). the parameter s (caned hysteresis coefficient) may be represent ed by S = r ( ~~) - ftr( d::ct ) ]/Hem = (uR m =fs( dB) , Hem \\ dt ( 10) where ()) = 21r1 (j = frequcncy),.fs C) denotes a single val ued function of* , and ())Bff! is shown in Fig. 2. Co Iron loss By means of (7), iron loss per unit volume is given by W= Cp ({J)Bm)2 IfH dB (11) -\"\"----- + I,e' S where Hi, .. is an even function of the frequency-independent field Hi of (6), Obviously, the first and second terms on the right of (11), respectively, correspond to the eddy current and hysteresis losses. Particularly, the eddy current loss We is related with parameter s as Wes = q)({J)Bm )2a::.f2B~. (12) Let us consider the barHke domain walls shown in Fig. 3, i.e., Sakaki6 modified Pry and Bean's formula for eddy current loss We as foHows: 5685 We = 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002521_027836499201100506-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002521_027836499201100506-Figure2-1.png",
        "caption": "Fig. 2. Machine structure.",
        "texts": [
            " The body center of mass is on the axis By or zc = (Mi ZI + rra2z2)/m = 0, YC = (mj yj + m2y2)/m, where yc and zc are the coordinates of the body center of mass in the relative coordinate system; y, and zi are the coordinates of the center of mass of ?7~; and y2 and z2 are the coordinates of the center of mass of m2. The inertia moments of the body parts with respect to their centers of mass are denoted by J, and J2. at University of Central Florida Libraries on October 23, 2014ijr.sagepub.comDownloaded from 492 The body position in the absolute coordinate system Or~~ (the axis O( is vertical) is determined by the coordinates of the body point B, the body attitude # (Fig. 2), and the coordinate y2 of the mz center of mass in the relative coordinate system. The machine leg is telescopic and the point of leg suspension to the body coincides with the point B. The leg position with respect to the body is determined by ( 1 ) the hip angle \u2019P between the negative direction of axis Bz and a telescopic link of the leg and (2) the leg length L (the distance of the hip point B to the foot S) (see Fig. 2). The leg mass is m.L, the distance from the foot to the center of mass is p, and the inertia moment of the leg with respect to the center of mass is JL, The leg makes contact with the support surface in a point. Interaction between the foot and the support surface is reduced to the reaction force of the support surface. A structural diagram of the telescopic leg link is shown in Figure 3. The load-carrying structure of the leg ( 1 ) with stops 2 and 3 is provided with a spring (4) and a coupling (5) that can move along the leg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003973_(sici)1097-4563(200004)17:4<171::aid-rob1>3.0.co;2-6-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003973_(sici)1097-4563(200004)17:4<171::aid-rob1>3.0.co;2-6-Figure1-1.png",
        "caption": "Figure 1. Illustration of spring and body displacements \u017d . \u017d . \u017d .used in a parallel type of pre-loading, b serial through type of pre-loading.",
        "texts": [
            " In order to differentiate between the two types of pre-loading configurations, a typical Hooke\u2019s law is considered as w x w x \u017d . fs k  x y x 5a2 1 where  x is the vector of small displacement mag-2 nitudes at the outer end of the springs and  x is at1 the inner end toward the grasped object in a grasp system. The same relationship has been represented by Griffis and Duffy13 in a different way as w x \u017d . \u017d . fs k ly l 5bo where l is vector of spring lengths after the application of force and l is the vector of original springo \u017d .lengths before application of the force see Fig. 1 . In a parallel type of pre-loading application, the effect of the inner end of spring displacements  x1 is considered on the grasped object. Use of the compatibility condition relates this local displacement with the displacements at other contacts as Tw x \u017d . x s J D  D 5c1 At contacts other than preloaded,  x is zero and2 the reaction forces at all the contacts can be found as w x \u017d . f sy k  x 5dp 1 \u017d . \u017d . \u017d . \u017d .Substituting Eq. 5c in 5d , and Eq. 3 in 2 and comparing the results after rearrangement, gives y1Tw x w x w x w x \u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002658_1.2805419-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002658_1.2805419-Figure6-1.png",
        "caption": "Fig. 6 A two-link rigid manipulator",
        "texts": [
            " The superscripts (\u2022'\u0302 ) and (*'') denote the values of parameters in forward, and back ward integration paths respectively. The separation between the forward and backward paths in each time instant is defined by the vector e (Fig. 5), the compo nents of which are: Cjit, 0 = \\Xj{,Xo, uf, t) + i-\\yXj{Xf, \u00ab!\"', 01 (16) where for odd j the states representing positions must be sub tracted and for even j the states representing velocities must be added, since velocities in the backward integrations are negative of the ones in the forward integration. For example, for a Two-Link Manipulator (TLM) shown in Fig. 6 the states Xi = ip\\ and X2 = (p\\ are the rotation and the velocity of the shoulder link respectively, and the states x^ = Journal of Dynamic Systems, Measurement, and Control SEPTEMBER 1998, Vol. 120 / 415 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use (\u0302 2 and Xi = Cp2 are the rotation and the velocity of the elbow link, respectively. The norm of continuity is defined as I 1/2 (17) 1 e(r, 0 = - S (w",
            " It should be emphasized that for the FBM iterations the initial and the final conditions for the states are always met; however, some discontinuity in the states may be present at one point of the trajectory. For the SM iterations, which starts with the initial conditions of the states and the initial conditions of the costates (B = p(fo)*\u2122'^') generated by the FBM, all the states are contin uous but the final conditions may not be met. Here, to show usefulness of the FBM, we discuss an example of a two-hnk manipulator system with four states and two con trols. The physical parameters (see Fig. 6), as well as the initial and the final conditions, are taken from (Van Willigenburg and Loop, 1991), and Geering et al. (1986): /, = 2t i = 0.40 m mi = 29.58 kg m\u201e = 0 kg h = 2/c2 = 0.25 m mj = 15.00 kg mj = 6 kg A = 0.416739 kg.m\" f/f = T25 Nm h = 0.205625 kg.m' U^ = +9 Nm is the jth switch time, and (f}' *) is the final time Journal of Dynamic Systems, Measurement, and Control SEPTEMBER 1998, Vol. 120 / 417 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003846_pime_proc_1987_201_061_02-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003846_pime_proc_1987_201_061_02-Figure4-1.png",
        "caption": "Fig. 4 Movement of partial solution domain",
        "texts": [
            " As the welding makes progress, the temperature in front of the electrode rises and the temperature in the 0 IMechE 1987 rear of the electrode falls. Thus the solution domain must be newly generated in order that the boundary conditions can satisfy conditions 1 and 2. The total workpiece to be welded was defined as full solution domain (FSD) and the domain considered for the calculation of the temperature distribution was defined as partial solution domain (PSD). The relationship between FSD and PSD is shown in Fig. 4 for the various stages of the welding progress. In order to obtain the temperature distribution in the newly generated solution domain, the new initial conditions and boundary conditions were determined in the appropriate finite element equations. In this study, the initial temperature of the newly generated solution domain could be adopted from the calculated results of the previous time step, because the greater part of the new solution domain overlapped on the former solution domain. But the initial temperature on the front boundary of the new solution domain, that is on the nodal points that were newly included in the PSD, was determined from considering the heat transfer in the welding direction. It was assumed that the temperature gradient of the newly generated solution domain was the same as the boundary temperature gradient of the previous time step. If the PSD was included in the FSD, some heat would be transferred from the PSD into the FSD. This effect was compensated by considering the circumference to be a conduction boundary. As shown in Fig. 4c, the PSD did not move any more when the front boundary of the PSD met the end of the FSD. Then the temperature of the final PSD rose continuously, while the welding heat source did not pass through the PSD. This introduced the discontinuity of the temperature gradient at the rear boundary between the final PSD and the Proc Instn Mech Engrs Vol 201 No 8 3 at UNIV CALIFORNIA SAN DIEGO on November 3, 2015pib.sagepub.comDownloaded from PSD of the previous time step. This problem was considered by adopting the backward increase of the PSD, when the forward increase of the PSD ended"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000076_pime_auto_1957_000_009_02-Figure15-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000076_pime_auto_1957_000_009_02-Figure15-1.png",
        "caption": "Fig. 15. Suspmion of Three-cylkder Opposed-piston Oil Engine",
        "texts": [
            " Rubber in shear mountings are, therefore, used for the rear high point mounting, so making the suspension system very flexible and to resemble more closely the original floating power than is usual nowadays. With rubber in compression in the fore-and-aft direction for both front and rear mountings in the scheme shown in Fig. 14, special provision had to be made to allow for tolerances in the fittings without stressing the front mounting against the rear mountings. For this reason it is more usual to design for rubber in shear fore-and-aft, for either the front or the rear mountings. Finally, an example of a three-cylinder opposed-piston engine (Fig. 15). Due to the rockers on this engine, a distinct primary vertical out-of-balance couple is present which is reduced to a minimum by balancing, so that for practical purposes only a horizontal out-of-balance couple remains. Owing to consideration of other forces on the power units and points of attachment, complete symmetry of the SUSpension was not possible. The rear mountings were fitted so as to be flexible for rotational movement about the OY axis in order to keep the natural frequencies for such vibrations as low as possible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003687_isie.1999.801773-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003687_isie.1999.801773-Figure2-1.png",
        "caption": "Fig. 2. A task and the end-effector coordinate frame",
        "texts": [
            " By using this vector and new Jacobian matrix J,,, the velocity relation between \u201d work-space\u201d and \u201dnew joint-space\u201d can be described as equation (9), and the acceleration relation as equation (IO). T = J,.,e, (9) (10) T = J,$, + JrvbV where J,, = [J,,J,, J,,]. 111. A TASK FOR A MOBILE MANIPULATOR In this section, we simply show the task for a mobile manipulator in this study. First, an aim of task is that the end-effector exactly follows a continuous trajectory planned by time function. Here the end-effector coordinate frame EX -E Y - E 2 is given as shown in Fig.2. A tangential direction of the trajectory is defined as x-axis of the endeffector frame, the vertical direction on a trajectory plane as y-axis and an alternative vertical direction from the trajectory plane as z-axis. Next we consider the force influenced on the endeffector. In the task of a mobile manipulator, it is necessary to obtain the desired force response as well as the exact trajectory tracking with respect to end-effector\u2019s motion. In the following section, we propose controller that both of force and position responses are simultaneously achieved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002884_jsl.3000090202-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002884_jsl.3000090202-Figure1-1.png",
        "caption": "Figure 1 Schematic diagram of test rig",
        "texts": [
            " The general structures of the fluids studied are shown below and details of all the fluids that were tested are given in Table 2. Trimethylolpropane ester (TMP) CH2OOCR RCOOCH ,CCH, CH2 OOCR Pentaerythritoltetravalerate ester (PE) CH2OOCR CH2 OOCR RCOOCH 2CCH2OOCR Dibasic sebacic acid ester (DAE) ROOC (CH2) @ O R The infrared temperature profile method for determining the shear stress of lubricants in EHD contacts has been described previo~sly.~ The test rig is shown JSL 9-2 97 0265-6582 $7.00 + $250 98 Chang, Spikes, and Bunemann JSL 9-2 in Figure 1. A 25.4 mm diameter, 52100 stecl ball is loaded against a stationary sapphire flat and rotated at a predetermincd specd to form an EHD contact. The ball is half-immersed in lubricant and the whole test chamber, containing the ball and lubricant, is heated and maintained at a fixed tcmpcrature. The test rig is located on a traversing stage driven by stepper motors, so that the rig can be moved horizontally undcr computer control. A stationary, custom -built, infrared emission microscope is positioned above the test rig and, initially, this is focused through the sapphire window on to the centre of the elastohydrodynamic contact using the contact's optical interference pattern as a guide"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003973_(sici)1097-4563(200004)17:4<171::aid-rob1>3.0.co;2-6-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003973_(sici)1097-4563(200004)17:4<171::aid-rob1>3.0.co;2-6-Figure2-1.png",
        "caption": "Figure 2. Wedge shaped planar object grasped by two frictional contacts.",
        "texts": [
            " 4 to generate a desirable motion with respect to an external load. The preloads can offset the motion induced by an external load and change the motion to a desirable direction. This can be achieved by one preload at one contact. However, preloads can also be applied through two or more contact points to generate a fine motion. The motions generated by each preload are superposed since they are linear operations. These can be optimally obtained by using constraint III. CONFIGURATION IN A WEDGE SHAPED OBJECT A wedge-like object shown in Figure 2 has been grasped by two fingers exhibiting frictional point contacts. The stiffness of each contact finger is modelled by means of an elastic element along the inward normal and another in the tangent direction of each contact. The four contact unit screws are described by the columns of matrix J as follows: w xJs S , S , S , S1n 1t 2n 2t cos w ysin w ycos w ysin w ysin w ycos w ysin w cos w s 2 2 0 h sin w 0 h sin w 3 3 \u017d .15 where w is the half angle of the wedge and h is the vertical height of the wedge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003718_iros.1999.812833-Figure5-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003718_iros.1999.812833-Figure5-1.png",
        "caption": "Figure 5: Configuration for the matching process in",
        "texts": [
            " In this method for flat wall detection, the shape of the robot\u2019s trajectory doesn\u2019t have to be a line: It could be an arbitrary curve. 4.2 Selection of Landmark The environmental map consists of vectors expressing wall surfaces which will be used as landmarks. We call each vector WVEM (Wall Vector in Environment Map). The DWV should be matched to the WVEM to know which flat wall is detected. The matching process will be done as follows. For the preparation for the matching process, the detected vector T,T, is projected onto one of vectors ai of WVEM and the projected vector is denoted by V,V, (see Figure 5 ) . The distances d l and d2 between two end points of the vector T,T, and two end points of the projected vec+ + + the landmark selection. The detected vector T,T, is projected onto a vector a, in the environmental map. _j __$ tor V,V, are calculated. The detected vector matches a vector in the environmental map when the following conditions are satisfied: 0 The orientation of the vectors are almost the same. + The vector V,V, is included in the vector a,. 0 The distances d l and d2 are short enough"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003244_(sici)1097-4563(199603)13:3<163::aid-rob4>3.0.co;2-q-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003244_(sici)1097-4563(199603)13:3<163::aid-rob4>3.0.co;2-q-Figure1-1.png",
        "caption": "Figure 1. Robot shrinkage and obstacle expansion. (- - -) Obstacle boundaries for link i. (.. - - -) Obstacle boundaries for links i + 1 and i + 2.",
        "texts": [
            " If an obstacle is Li and Trabia: Adaptive Path Planning and Obstacle Avoidance 165 Collision detection can be a very time-consuming process. TWO types Of ColIisions may occur when the robot is following a path: not a polygon, it can be always approximated by one with reasonable accuracy. Each obstacle is expanded in every direction by a distance equal to half the width of the rectangle enclosing each robot link. l7 Separate databases containing the boundaries of the expanded obstacles for each link are created. As shown in Figure 1, when considering intersection between a link (i) with half width di and an obstacle, the obstacle is expanded in every direction by the distance of di. On the other hand, links (i + 1) and (i + 2) have the same half width d,+*. Therefore, a database containing the corresponding expanded coordinates of the obstacles is used for these two links. Expansion of obstacles is carried out before the beginning of path planning. Using this technique, the problem of collision detection between a link and an obstacle is reduced to checking an intersection between the line representing the link and those representing the edges of the expanded obstacle (Appendix A)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002512_0954407971526362-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002512_0954407971526362-Figure1-1.png",
        "caption": "Fig. 1 Belt and pulley meshing overview",
        "texts": [
            " A belt's tooth is joined to its adjacent lands by frictionless hinges and the tooth contact load with a pulley groove is described by a simple foundation model in which contact pressure at a point depends only on the tooth displacement there (8). Tooth force and moment equations are solved to predict tooth loadings and articulations. Loadings are compared with low-speed experimental measurements. These considerations of entry and exit lead to a better understanding of the life observations (7) but a full explanation requires a better model still. Figure 1 introduces the belt\u00b1pulley contact problem to be modelled. A geometrical angle of wrap \u00e8a is defined. It is the angle between the normals to the lines of action of the tight and slack side belt tension forces Tt and Ts. Within Proc Instn Mech Engrs Vol 211 Part D D04395 # IMechE 1997 the angle of wrap there are Nf belt teeth=pulley grooves fully meshed. Outside the angle of wrap there are additional teeth=groove contacts in partial mesh. A fully meshed tooth, for example tooth i in Fig. 1, subtends an angle \u00e8p at the centre of the pulley, related to the number of teeth Nt on the pulley by \u00e8p 2\u00f0 Nt (1) A part \u00e8l of \u00e8p is taken up by land contact and a part \u00e8g by tooth\u00b1groove contact. In this paper it is assumed, as in Fig. 1, that a pulley groove becomes a fully meshed contact once its centre line is within the angle of wrap by more than \u00e8g=2. It is also assumed that at each of the tight and slack sides there is only one partially meshed contact. The angular position of the partially meshing pulley groove at the tight side is described by the angular position \u00e8t of its centre line; and likewise, \u00e8s describes the angular position of the slack side partially meshing tooth. \u00e8t and \u00e8s vary as the pulley rotates but they are related by the geometrical requirements \u00e8t \u00e8a \u00e8s (Nf 1)\u00e8p, \u00ff\u00e8g=2 < \u00e8t, \u00e8s < \u00e8l \u00e8g 2 (2) Equation (2) serves to determine Nf and \u00e8s for any angular position of the pulley, defined by \u00e8t. It also constrains meshing and unmeshing to occur within one pitch of pulley rotation. This restriction, the better the higher the belt tension and the smaller the pulley diameter, is discussed in Section 5. The fully meshed modelling has been published before (5) but is summarized here for convenience of later use. By convention, as in Fig. 1, the fully meshed belt pitches are labelled 1 to Nf , from the tight to the slack side; and the land associated with a particular tooth is anti-clockwise from the tooth. Figure 2a is a detail of the forces on the general pitch i. It shows the belt cord tension changing from Ti at the boundary with pitch (i\u00ff 1) to Ti 1, with an intermediate value T9i at the junction between the tooth and land. It also shows the circumferential component Qi of the tooth\u00b1groove contact load and the land friction force Fi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003698_978-3-540-46516-4_9-Figure9.3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003698_978-3-540-46516-4_9-Figure9.3-1.png",
        "caption": "Fig. 9.3. Models of a rigid and an elastic cam mechanism",
        "texts": [
            "1 c the flexibility of the joint is reflected by the introduction of two one dimensional elements. b) It will be assumed that the considered mechanism, in principle, has to be rigid in order to realize a program motion, and that small deformations of the elastic elements lead to deviations of its motion from the program motion, i.e. to dynamic errors. Hence, we will not consider as elastic a mechanism, whose elastic elements serve for the realization of the functions of a rigid mechanism, e.g., for the force closure of the follower in the cam mechanism shown in Fig.9.3a. In the latter case a mechanism with elastic elements is obtained if the elasticity of the follower rod is taken into account (Fig. 9.3b). c) A mechanism with elastic links is realized only if the introduced elastic elements increase the number of degrees of freedom of the mechanical system. To achieve this the releasing constraints must become elastic ones. The rigid mechanism, shown in Fig. 9.4a has an excessive constraint but does not become an elastic mechanism when we introduce the elastic element shown in Fig.9.4b, since, in this case, the number of degrees of freedom does not increase. d) Henceforth, it is assumed that within the limits of small deformations of the elastic elements, these elements have linear elastic characteristics and that they obey Hooke's law"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002912_3477.604097-Figure15-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002912_3477.604097-Figure15-1.png",
        "caption": "Fig. 15. (a) The perceived shape of the space CFNS(ti) generated by the robot R4: (b) The simplified traffic patterns L6; L6; L7; L7; L8 generated by R4:",
        "texts": [],
        "surrounding_texts": [
            "Since the major goal of the traffic language is to assist an autonomous robot to represent and understand the traffic priorities of the other moving objects in the same navigation space avoiding collisions, it is necessary that the synthesis of traffic priority patterns to be defined semantically. Notation: a) (commutative) with b) (associative) with and Definition: The length of a perceived pattern is defined as the number of corridors which compose the pattern. Corollary: Two perceived patterns (generated by the same or different robot, at the same time for two different moving objects) with the same length are not necessarily identical in shape. Definition: The synthesis # (semantically) of two traffic patterns determines the order of the robots priorities one against the other. Proposition: (commutative) Proof: Let assume that three robots are moving in the same navigation space, as shown in Fig. 10. The robot is the main one and are the secondary robots. For this particular case, and Thus, the pattern produces the relationship between the robots\u2019 priorities. The pattern provides the priority relationship Thus, the synthesis provides the relationship (1) among the robots\u2019 priorities. Now, the synthesis provides (2). These two relationships are identical, which means that Following this process easily it can be proved the general case Proposition: (associative) Proof: Similar to commutative. Notation: (identity traffic pattern) for every Corollary: In a free navigation space with secondary moving robots there is a possibility of existence of the following traffic pattern configurations. 1) There is a maximum of two patterns with . 2) There is a maximum of one pattern with or . 3) There are patterns such that where Corollary: In a free navigation space FNS if there are the traffic patterns and the there is not the pattern where the sequence of the values for the indexes are and or and or and Traffic Complexity Table II presents the traffic complexity of moving robots in a CFNS under two different assumptions. \u2022 In the first assumption, called individual, a robot views all the other moving robots, generates all the traffic patterns from its own position and calculates all the possible traffic priorities of the other robots against its own priority. \u2022 In the second assumption, called global, every robot views all the other moving robots, generates all the traffic patterns and calculates all the possible traffic priorities for all the moving robots including itself. V. ILLUSTRATIVE EXAMPLES In this section, two illustrative examples for traffic cases are provided and solved by using the KYKLOFORIA language. In the first example, the traffic case includes six moving robots in a free navigation space shown in Fig. 11. Figs. 12\u201317 provide the shape of the free navigation spaces observed TABLE III SIMULATED RESULTS FOR FIG. 18 by each moving robot and the traffic patterns generated by each of them in their own free space. In the Fig. 18, the velocities of the moving robots are considered the same, thus the traffic priority relationships generated by the traffic language are given in Table III. Each moving robot knows the traffic priority relationships in the same free space. Thus, the robot makes use of its own which is higher than and goes out of the narrow corridor. At a time min, covers a distance of 4.5 m. The robot has to wait of a period of 0.6 min, and then it proceeds into the open corridor by covering a distance of 1.4 m in 0.485 min. Initially, covers a distance of 1.3 m in 0.325 min, then it slows down and waits for 0.55 min before it proceeds into the narrow corridor following the robot and covering a distance of 0.9 m in 0.23 min. The robot using its own higher priority over covers a distance of 4.5 m. The robot waits for 0.75 min and then proceeds forward by covering a distance of 1.5 m. Finally, the robot covers a distance of 4 m in 1.125 min because it spends some time to change its direction. Note that, and TABLE IV SIMULATED RESULTS FOR FIG. 19 (a) (b) Fig. 14. (a) The perceived shape of the space CFNS(ti) generated by the robot R3: (b) The simplified traffic patterns L1; L7; L2; L6 generated by R3: change their directions (as shown in Fig. 9) avoiding a possible collision. In the case that the velocities of the robots are considered different, then Table IV shows the traffic priority relationships and the robots traffic paths and locations are given in Fig. 19. In particular, present a traffic behavior similar to the previous case with the same velocities, by using the Table IV. covers a distance of 4.9 m with m/min. covers a distance of 1.4 m with m/min. covers a distance of 1.3 m with m/min and a distance of 0.6 m with m/min. waits until passes the intersection point and then covers a distance of 1 m with m/min. covers a distance of 4.8 m with m/min. Finally, covers a distance of 2.5 m with m/min. The second example explains the use of the language for the improvement of the traffic schedule of a particular robot under the assumption that the local traffic flow in a certain region is almost the same every time that the robot enters that region. In this case, the robot enters the region from left to right at time and spends min crossing it. At that time, there are three other moving robots crossing the same region from different directions (see Fig. 20). The traffic flow extracted by the robot in that region, is represented by the following language words: The symbol & represents the synthesis operator between words for the formulation of the traffic flow extracted by a robot traveling through a region where In this particular case there is no delays during the traveling. Fig. 21 shows the same region, at a different time where the robot enters the region from the right to the left in order to cross it by following the reverse path of Fig. 20. At this time there are four other moving robots and a fifth one is coming to the same region. The traffic flow extracted by the robot is represented by the following words: where In this particular case there are delays due to conflicts between the robots directions and traffic priorities. More specifically, the robot has to wait until and pass first and then it continues its own path. This mean that the robot knows the time required to cross the region, and in the latter case it took more time, At this point the robot analyzes the traffic flow perceived by itself and modifies its traffic path for a future cross of the same region under a traffic flow similar to More specifically, it follows the next algorithmic steps: 1) Check each word , for patterns . 2) Search for possible patterns , to replace in a word . 3) Replace the first with an in . 4) Rearrange the word into a new one , which includes the affects on the other patterns due to replacement ( instead of ). 5) If the new word includes less number of patterns then use it in the new , else go to 2 to replace the next with an in . 6) If the new overall traveling time is less than the original then proceed else no changes Thus, Fig. 22 shows the new modified traffic path. The new traffic flow extracted by is represented by the following words: where Thus, the new traffic flow includes less conflicts and no significant delays for the robot"
        ]
    },
    {
        "image_filename": "designv11_31_0003419_s0389-4304(96)00049-5-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003419_s0389-4304(96)00049-5-Figure2-1.png",
        "caption": "Fig. 2. Measurement method of tooth load.",
        "texts": [
            " The tight side tension was measured by strain gauges placed on the idler support and the effective tension was measured by gauges placed on the crank pulley. The average tension in operation is defined 038%4304/97/$17.00 Copyright \u00a9 1997 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved Pll S0389-4304(96)00049-5 JSAE9730065 as the set tension T~ and is obtained from the following equation using these tensions: T,,, = T, - T~/2 (1) (T t = tight side tension, T~ = effective tension). The method of measuring tooth loads is shown in Fig. 2. The tangential loads applied to the hatched area were measured by strain gauges placed in slits which were cut on both sides of the pulley teeth. Table 1 shows the characteristics of the three types of belts having the STPD tooth profile for the measurement. 3. Experimental results and discussions 3.1. Occurrence of transverse vibration The spectrum analysis maps of the belt noise and vibration are shown in Fig. 3. The noise consisted mainly of the low-frequency component occurring at the meshing order and the high-frequency component above 5 kHz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003489_jsvi.1997.1496-Figure15-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003489_jsvi.1997.1496-Figure15-1.png",
        "caption": "Figure 15. Schematic representation of the models used in the numerical simulations: (a) simple block driven with prescribed motion V as obtained from experiment; (b) spring\u2013mass system for simulating the dynamics of the whole system.",
        "texts": [
            " With these tests as background, the model parameters used in the simulations that follow were: C1 = m, r=1, m=0\u00b725, h=0\u00b73\u20131\u00b72 s/m, and Dc =15\u201325 mm (the latter values being chosen according to the asperity sizes taken from Figure 3). The remaining parameter, C2, was taken as the inverse of a characteristic velocity, chosen as the maximum relative velocity achieved in the experiment of interest. Two different numerical models were considered in the results that follow, as depicted schematically in Figure 15. The case in Figure 15(a) represents a model whereby a measured slip trajectory is given as input, and the predicted frictional traction history is compared to that observed in the experiment, facilitating assessment of the friction law independent of the dynamics of the system in which the interface is embedded. Such model predictions were obtained by numerical integration of equation (4) using a return map strategy analogous to thos incorporated in computational plasticity. In the second model type (Figure 15(b)), the dynamics of the entire system are taken into account, taking the variables f, A, m, tN , k, as input data and subsequently comparing the prediction to experiment. Assuming cosine mode shapes for the deflected beam and using Hamilton\u2019s principle [20] one easily obtains the mass of an equivalent one-dimensional oscillator, m*x\u0308+ cx\u0307+ kx= tT , (8) with m*=g L 0 m(y)8(y)2 dy+m8(L)B , (9) where m(y) is the distributed mass of the elastic beam per unit length, 8(y) is the assumed mode shape and m the mass of the rigid head. The stiffness k and the damping c (very small) were measured directly, and in general varied from experiment to experiment. Response of this model was found by applying a variant of Newmark time integration to system (8). 4.3.1. One-dimensional block driven with prescribed velocity First, the numerical model of the first type is considered (Figure 15(a)), using it to verify that representative frictional responses from our experiments could be reproduced. Figure 16 depicts the experimental and numerical results obtained for a particular combination of system parameters. This particular case corresponds to a combination of beam stiffness (k=8446 N/m), forcing amplitude (A=2 mm) and normal force (tN =5\u00b76 N) that produces slip behaviour throughout each cycle for all forcing frequencies studied. Acceptable agreement with experimental results is to be noted for all frequencies, with the response being characterized by a delicate interaction between softening state variable effects and strengthening viscous effects",
            " However, the counter-clockwise evolutions observed in experiment cannot be predicted by the state variable model. This is the case because the model assumes that frictional force is an increasing function of recent slip, so that the apparent coefficient of friction must fall when the velocity (in absolute value) is decreasing (implying clockwise loops). Examining now some experimental cases where stick may occur, the results of Figure 18 are presented, where the system parameters k=8446 N/m, f=5 Hz and tN =8\u00b72 N are held fixed while the forcing amplitude is varied. Wherever possible, the model of Figure 15(a) is still utilized, but for parameter combinations where stick appears in typical cycles the model of Figure 15(b) must be used (since for perfect stick the frictional traction is indeterminate for zero relative sliding velocity). Again, for the cases shown, good agreement with experimental results is to be noticed. Permanent stick occurs in Figure 18(a) and (b), with larger amplitude forcing producing some slip and an accompanying drop in maximum friction force. In summarizing these predictions, it is emphasized that a simple Coulomb model will predict only step like evolutions of tT /tN in response to changes in sign of sliding velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002213_1.1707468-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002213_1.1707468-Figure1-1.png",
        "caption": "FIG. 1.",
        "texts": [
            " As the generators of a developable surface are lines of curvature, the lines AI, orthogonal to the generators, constitute the second set of lines of curvature. We call p the radius of curvature of the edge of regression The metric elements of the surface, i.e., the ratios: in which Sl, S2 are the arcs along the curves coordinates, and also the direction cosines Lip L 2, L3 of the normal to the surface are equal to: A2-A1 E1= (N'2+N'2+N'2)!(A2-A1) =--; E2= 1; P L 2=-p(f3\"h'-fl\"fa'); (5) La = - p(ft\"H - H'f/). Also: a2x __ m = (A2- Al)fm'\" - fm\"; aA12 The geodesic curvatures of the curves AI, A2 are. as it appears from Fig. 1, 1 1 -=--; rl A2-AI 1 -=0. r2 (6) 547 [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: 136.165.238.131 On: Sat, 20 Dec 2014 06:42:07 The principal curvatures of the surface are: JI'\" J2111 Ja''' JI\" h\" Ja\" p3 1 \"'Lh'\" (j2\" Ja' - fa\" J2') h' JI' Ja' R' (A2-~q)(\"'LH'2)~ (A2- Al) 1 (7) -=0. R\" simply related to the torsion T of the edge of regression 1 T Tp R' fl rl (8) The general equations of equilibrium are written between the applied surface loads and the stress flows",
            " If C and D are zero, in the case p = 0, the stress flows are zero along the edge of regression, and in the case p = -1, the stress flows are finite along the edge. The last hypothesis will not be examined; assuming that the surface loads are finite in every point, it appears that the stress flows along the edge of regression are determined VOLUME 15, JULY, 1944 C(Al) nl=O; n12=\u00b7 ; (A2- Al)2 pC' (AI) pC(Al) D(Al) n2= + +--. (A2-Al)2 (A2-Al)3 A2- Al (12) The generators being tangent to the edge of regression, it results that the ~tress flows n2 do not appear as forces perpendicular to the edge of regression, but as shear flow, the value of which is, from Fig. 1, in which the triangle ABC is considered as infinitely small: If D is different from zero, and C is equal to zero, there is a finite shear flow along the edge of regression, and more generally, the shear flow has the value: ii12=n12-limit [~n2(A2-Al)]' (14) >'2=1.1 P From the results established above, the condi tions of statically determined equilibrium of the membrane can be deduced. Case I. The membrane does not include its edge of regression. 549 [This article is copyrighted as indicated in the article",
            " 551 [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: 136.165.238.131 On: Sat, 20 Dec 2014 06:42:07 TORS (NO DISTRIBUTED LOAD) Equations (10) become in that case: CO\\!) nl=O, n12=----, (A2 - >\\1)2 pC' (AI) pC(AI) D(AI) n2= + +--. (A2-AI)2 (A2-AI)3 A2- AI (19) >'1 is the arc along the edge of regression, while A2 - >'1 is the radius of geodesic curvature rl of the curves >'1 (see Fig. 1). Thus it can be written: C(AI) C' (AI) pC(AI) D(AI) \u2022 n12 =--; n2 =--+--+--. (20) rl2 ' r12 r13 rl I t appears that n12 is given by the relation of shear in tapered panels, the apex of the panel being at the edge of regression. In order to examine n2, consider, instead of the flow, the total force acting between two generators sepa rated by an angle da. rlda is the distance between the two generators at any point. Thus, the force is (noting that pda=dAI) (see Fig. 8) C' (AI)dAI C(AI)dAI dF2=n2rlda =D(AI)da+ + "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002770_0043-1648(96)07226-2-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002770_0043-1648(96)07226-2-Figure6-1.png",
        "caption": "Fig. 6. Air ring with direct feeding system.",
        "texts": [
            " (23) bypo gives finally the equation: /~d.qd-- VkAk'/r d = (\"R\" d - \"/rdO ) ~ f f F g 3 ( 2 5 ) with unknown \"/T d (note, that vd is a function of \u00a2rd). The subscript 0 denotes the initial value of the pressure ratio. Eq. (25) produces, together with Eq. (15), a system of two non-linear equations with unknowns % and Uk. The solution of this system is not an easy task. It is done by the method of successive approximations. In our investigations we also used gas rings with a direct feeding system, as those shown in Fig. 6. The mathematical model of such a ring is of course based on the Reynolds Eq. (2) and on the equations describing the relation between the mass flow through a feedhole of the radius ro2, the gas film pressure distribution surrounding the feedhole, and the pressure drop for a feedhole of the cross-section A k = 2./fvo2h 2. These equations have been written above as Eqs. (4)-(15) with Pl =t7o, i.e. ~'d = 1. The mathematical models of both the rings provide data on the components of the loading force in the direction of the axis x and y: L/R22~r o 0 LIR22~r F",
            " ~ m 0,5 0,25 ~(a) I I I 0 5 10 15 20 C. 0,'~ 0,5 ~ 0,25 (b) 0 0 . . . . . . . . R a =0.065 rn . . . . . R2 =0.070 m m - - = . I f r 5 10 15 P 20 01t I , ~ [ ........ O~ :25\"104m . . . . . cz =30~lO'em e=:35~104m 0,751 o , 5 1 o,251 (c) 5 10 15 P 20 6 3 6 Fig. 7. Damping coefficient of air ring withdirect feedingsystem: (a) R2=0.065 m, cz=30X 10- m; (b) ro2=0.15 x 10- m, cz=30X 10- '- (c) R2=0.065 m, roz=0.15x 10 -3 m. tern o f the b e a r i n g s ) . T h e length o f the r ing L = 0.11 m w a s equal to the length of the beating (Fig. 6). Figs. 7 and 8 show the values of the damping coefficient C,~ and the stiffness coefficient gaa of the ring (in the plane along which the force Fz acts) for different values of the radius re2 of the feedholes, the ring radius Re and the clearance c2 between the bush and the casing. As one can see, the changes of these basic parameters do not exert any significant influence on the value of the stiffness coefficient,orespecially on that of the damping coefficient. As opposed to the arbitrarily selected constant values of the stiffness and damping coefficients Kp and Cp of the springs and dampers which support the bush shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002829_(sici)1521-4109(199902)11:2<139::aid-elan139>3.0.co;2-o-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002829_(sici)1521-4109(199902)11:2<139::aid-elan139>3.0.co;2-o-Figure3-1.png",
        "caption": "Fig. 3. Cyclic voltammograms obtained at a histidine modi\u00aeed electrode for a) 2.5 mM and b) 5.6 mM cytochrome c. Conditions same as Figure 1.",
        "texts": [
            " Therefore, the modi\u00aeed electrode reported in this article has many possible uses, especially when a puri\u00aecation of the macromolecules cannot be carried out. Electrodes modi\u00aeed with biological molecules might be more useful if the CMEs are employed to the bioelectrochemical \u00aeeld. In situ spectroelectrochemical measurements were carried out using an optically transparent thin layer cell with a histidine modi\u00aeed silver net electrode as a working electrode in order to make sure that the enhanced current response, shown in Figure 3, could be ascribed to the redox reactions of cytochrome c. Figure 4 displays the UV-vis spectra for 0.5 mM cytochrome c at a series of controlled potentials. It was observed that the peak near 409 nm increased, and also two peaks near 520 nm and 550 nm arose and increased, with the decrease of the applied potential and vice versa. We conclude that the protein does participate in redox reactions at the modi\u00aeed electrode [22]. The in situ spectroelectrochemical study for myoglobin is shown in Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003237_0020-7403(93)90037-u-Figure3-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003237_0020-7403(93)90037-u-Figure3-1.png",
        "caption": "FIG. 3. T h e c o n f i g u r a t i o n o f the n u m e r i c a l examples .",
        "texts": [
            " [15] deal with the transient vibrations of a rotating shaft with nonlinear spring passing through a major critical speed with a very small and constant acceleration. In their experiments, the amplitude traced the upper resonance curve when the shaft was accelerating and then jumped to the lower curve of smaller amplitude at a specific speed. Here we attempt to simulate these nonlinear phenomena by the transfer matrix method. A simple rotor model with one disk supported by two ball bearings as shown in Fig. 3 is considered. The bearing is assumed to have cubic nonlinear spring and linear damping characteristics, i.e. the bearing force is: Fy = Kx Y+ K3 y3 + C~', (23) where KI and K3 are the linear and nonlinear stiffness coefficients and C is the linear damping coefficient of the spring. The physical parameters of the rotor system are listed in Table 1. Because of the cubic nonlinearity, nonsynchronous 3 x whirl or rev/3 whirl are combined with synchronous whir in the steady-state responses. The superharmonic resonance will occur at rotating speed o9 = 1/3f~ ( = synchronous critical speed of linear system) and the subharmonic resonance will occur at co = 3 x f~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002497_jaer.1996.0022-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002497_jaer.1996.0022-Figure2-1.png",
        "caption": "Fig . 2 . Bearing and pressure areas of a disc at an angle b to the direction of motion projected on to a horizontal plane ( A b h 5 AFB ; A 9 p h 5 AFBC ; A c 5 AECD )",
        "texts": [],
        "surrounding_texts": [
            "The cultivating disc is a segment of a thin spherical shell and its critical dimensions are shown in Figs 1 to 5 . The principal parameters are the radius of the rear spherical surface , R 0 ( Fig . 1 ) the thickness of the disc material , t , and the radius of the circle of the sharpened edge in the circumferential plane of the disc , r ( Figs 1 and 5 ) . Other disc parameters can be deduced in terms of these dimensions . The tilt angle of the disc , a ( Figs 1 and 5 ) is defined as the angle which the circumferential plane makes with the vertical plane . The disc angle , b ( Fig . 2 ) is the angle which the circumferential plane makes with the horizontal direction of motion of the plough . The depth of disc soil working , d ( Fig . 1 ) is the vertical distance from Ro e a r c Soil level Soil l evel Rs L \u03b2c d Fig . 1 . Geometrical parameters of a disc tilted at an angle a to the y ertical plane ( upper : ele y ation ; lower : plan ) the soil surface to the lowest point of the circle which forms the circumferential edge of the disc ( Fig . 1 ) . For any disc , the angles a and b and the working depth , d , are the factors which determine the areas of the front and rear surfaces of the disc which engage the soil and are of importance in relation to the magnitudes of the consequent forces acting on the disc . When a disc is working in soil the rear spherical surface will be in contact with soil if the disc angle is less than a critical angle , b c ( Fig . 1 ) . This angle is reached when the direction of motion is tangential to the circle of intersection of the soil surface with the rear surface of the disc , at the point where it intersects the chord of intersection . If the disc angle , b , is equal to or greater than this angle , there is no soil contact with the rear surface and the vertical and horizontal bearing areas are zero . Expressions for the calculation of b c are given in Section 3 . 1 . For a particular disc angle , b , there is a critical depth , d c , for which the angle b is equal to the critical angle , up to which there is no soil contact with the rear surface of the disc . An equation for determining values of d c is given in Section 3 . 2 . The bearing area is defined as the area of the rear convex surface of the disc engaged with soil and will exist when b , b c . Expressions for this area when projected on to a horizontal plane ( A b h ) (area AFB in Fig . 2 ) are given in Section 4 . 2 . 2 and on to a vertical plane , normal to the direction of motion ( A b ) (area ABE in Fig . 3 ) , in Section 4 . 2 . 1 . The pressure area is defined as the area of the concave front surface of the disc engaged with the soil , which represents the area of soil cut by the disc . Expressions for this area projected on to a horizontal plane ( A p h ) (area AFBCD in Fig . 2 ) are given in Section 4 . 2 . 1 and on to a vertical plane , normal to the direction of motion ( A p ) (area BCDE in Fig . 3 ) , in Section 4 . 1 . 1 . When working in gangs there is generally some overlap of the areas of soil cut by adjacent discs . For a particular disc spacing there is a critical angle , b 0 , above which there will be overlap of the cut areas . There will also be a critical spacing , g c , for a particular disc angle , at less than which there will be partial overlap of the worked areas . Expressions for these critical values are given in Section 5 . 1 . The area of overlap between discs ( A o v ) (area BFG in Fig . 4 ) is derived in Section 5 . 1 and the uncut area ( A u ) (area CEF in Fig . 4 ) in Section 5 . 3 . The gang area ( A g ) (area BDEF in Fig . 4 ) , or the area cut by a single disc , is considered in Section 5 . 2 . The disc may be sharpened externally or internally . The formulae derived in Sections 3 to 5 apply to an internally sharpened disc . The ef fect of external sharpening is discussed in Section 6 in relation to the width of the bevelled surface and to critical disc angle . Modifications required to the formulae for an externally sharpened disc are also discussed . In practice , disc sizes are given in terms of the diameter of the circumferential or edge circle (2 r ) and their concavity ( c ) , which is the depth from the plane of the edge circle to the inner spherical surface . Disc sizes range from 500 to 900 mm edge circle diameter with concavities over a range from 75 to 165 mm . 10 , 11 The thickness of discs is usually between 5 and 9 mm , depending on disc size . In terms of the basic parameters of the disc , the concavity , c , is given by c 5 R o 2 ( R 2 o 2 r 2 ) 1/2 2 t for inside sharpening and by c 5 R o 2 h R o 2 t ) 2 2 r 2 j 1/2 2 2 t for outside sharpening . In the calculations presented in this paper , a shallow and a deep disc are considered , sharpened internally and of dimensions representative of a typical disc size , which is usually in a range 600 to 700 mm edge circle diameter . 1 2 For the shallow disc , R o 5 915 mm and r 5 315 mm ; for the deep disc R o 5 560 mm and r 5 305 mm . The disc thickness ( t ) was equal to 5 mm in both cases . The discs were , therefore , of approximately equal size but of dif fering concavities . For the shallow disc c 5 51 mm and for the deep disc c 5 85 mm , for inside sharpening . In practice , for disc ploughs 1 2 the disc angle ( b ) ranges between 35 8 and 55 8 and is commonly in the range 40 8 to 45 8 . The tilt angle of the disc 1 2 ( a ) is normally in the range 15 8 to 25 8 . The spacing between discs ( g ) when working in a gang 1 2 is usually in the range 180 to 300 mm . In the calculations presented in this paper , the working depth of the discs 1 3 ( d ) was considered over a range from 60 to 180 mm ."
        ]
    },
    {
        "image_filename": "designv11_31_0003025_978-3-0348-9179-0_4-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003025_978-3-0348-9179-0_4-Figure8-1.png",
        "caption": "Fig. 8. Idealized cyclic voltammograms expected for catalytic electron transport by an adsorb ed enzyme having two redox centres A and B. The four different traces 1-4 are explained in the text.",
        "texts": [
            " To an initial approximation, the enzyme's properties might be described by an electrochemical version of the Michaelis-Menten equation, as given in Table 1. The Michaelis constant KM and turnover number kcat are the generalized parameters determining icat , which becomes the dominant term if iE and itransport are optimized to the degree that their reciprocals effectively vanish. The catalytic current is a direct measurement of tum over rate. Moreover the voltammogram is a plot of rate versus electron-motive driving force. To illustrate just the basic principles, we refer next to Fig. 8, which shows model (faradaic-only) cyclic voltammograms plausible for an immo bilized enzyme having two redox centres A and B. Trace 1 is a \"reversible\" (non-turnover) voltammogram obtained at a stationary or rotating electrode (in this situation, both give the same result). The two pairs of peak-like signals A and B correspond to reversible redox transitions of the two centres. Trace 2 is obtained upon introducing a low concentration of reducible sub- Applications of voltammctric methods for probing the chemistry ofredox proteins 225 strate and rotating the electrode to maintain a steady state under hydro dynamic control",
            " Here the tunnel-diode effect arises by intro duction of rigid requirements for the sequential ordering of electron transfer and of substrate binding or product release. This situation is analogous to substrate inhibition, the substrate in question being the electron. If SOH can bind reactants or release products only when a certain centre (for example the FAD) is oxidized, then the enzyme will cease to function when the rate of reduction of this centre exceeds the rate of substrate interchange. In the context of Fig. 8, the FAD would be both catalytic and regulatory site. In terms of function, this property would have the ability to regulate the direction of electron transport. Reverse electron flow (which would act to reverse the direction of the TCA cycle) would be allowed under normal con ditions but would be suppressed if the quinone pool potential becomes too negative. It is interesting to speculate that SOH may have evolved from FRD, in effect involving the imposition of a \"ratchet-like\" restriction on the reverse reaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003761_1.1701875-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003761_1.1701875-Figure1-1.png",
        "caption": "Fig. 1 Element",
        "texts": [
            " Contributed by the Design Automation Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 2001; revised September 2003. Associate Editor: H. M. Laukarani. 442 \u00d5 Vol. 126, MAY 2004 Copyright \u00a9 20 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 included in the generalized coordinates which was used by Yang and Sadler @9,10#, and Simo and Vu-Quo @11,12#. The dynamic equation of the system is derived as follows. 2.1 Finite Element Model. As shown in Fig. 1, the Timoshenko beam element with multiple nodes and Lagrange shape function are used here. The node number can be selected according to requirement on precision. All quantities are referred to the inertial frame. A shows the initial position of element. Through a rigidbody translation, it goes to position B. After a rigid-body rotation, it moves to position C. From an elastic deformation, the beam arrives at position D. The final displacement vector U and rotation b of the element can be written as U5Ut1Ur1U f b5br1b f (1) where, Ut , Ur , U f are the displacement due to rigid-body translation, rigid-body rotation, elastic deformation, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002857_0890-6955(95)00052-6-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002857_0890-6955(95)00052-6-Figure2-1.png",
        "caption": "Fig. 2. Power flow diagram of an induction motor [4].",
        "texts": [
            " The rotation speed of the magnetic field which is also called the synchronous speed ns (rpm) can be expressed as: 120f ns = - - (1) P where f is the frequency of stator in hertz and p is the number of poles per phase. In reality, the rotor rotation speed, i.e. the rotation speed of an induction motor, is always slightly less than the synchronous speed ns. The slip s expressed as a percent of the synchronous speed is defined as the difference between the synchronous speed ns and rotor speed n, that is: ns - n - - - ( 2 ) S n s Figure 2 illustrates how electrical energy is converted into mechanical energy in an induction motor. First, electrical power Pin flOWS from the line into the three-phase stator. Owing to the stator copper losses, a portion of electrical power P~\u00a2~ is dissipated as heat in the windings. The other portion of electrical power Pil is dissipated as heat in the stator core due to the iron losses. Therefore, the remaining electrical power Pag is carried across the air gap and transferred to the rotor by electromagnetic induction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002292_s0141-9331(99)00045-9-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002292_s0141-9331(99)00045-9-Figure1-1.png",
        "caption": "Fig. 1. Scheme of the robot.",
        "texts": [
            " This methodology, in fact, allows rules expressed in a language close to the natural one to be converted into a numerical algorithm [5,6]. In the following sections the mathematical model of the system is initially shown, then a fuzzy control law is proposed, showing the results obtained in simulation. Then the practical realisation of a prototype of the robot is illustrated, with particular attention to the hardware implementation of the fuzzy regulator, performed by using the ST52E301 microcontroller. Finally, the results of application of the fuzzy controller to a real system are presented and discussed. Fig. 1 shows a scheme of the kinematics of the robot. Following the Denavit\u2013Hartenberg convention, the two joint angles u 1 and u 2 are chosen, and the dynamic equations 0141-9331/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0141-9331(99)00045-9 * Tel.: 1 39-95-7382321, fax: 1 39-95-330793. E-mail address: gmuscato@dees.unict.it (G. Muscato) of the model of the manipulator can easily be derived [7]: t1 t2 \" # l2 2m2 1 2l1l2m2C2 1 l2 1 m1 1 m2 \u00ff l22m2 1 l1l2m2C2 l2 2m2 1 l1l2m2C2 l22m2 24 35 u 1 u 2 \" # 1 2m2l1l2S2 _u 2 2 2 2m2l1l2S2 _u 1 _u 2 m2l1l2S2 _u 2 1 \" # 1 f1 _u 1 f2 _u 2 \" # where t 1 is the torque applied to joint 1, t 2 the torque applied to joint 2 (in the case considered it is zero), li the length of each link, m1 the mass of link 1; m2: the mass of link 2; Ci: cos ui; Si: sin ui; fi the friction factor of each joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002907_3516.662865-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002907_3516.662865-Figure1-1.png",
        "caption": "Fig. 1. Main components of the SmartPen.",
        "texts": [
            " In the proposed design, the following three mechatronic features can be distinguished: \u2022 overall system design, including multiple sensing elements, mechanical stops, and data processing circuitry; \u2022 force sensor design, consisting of a miniaturized hybrid integration of electrical and mechanical elements; \u2022 design of the pen\u2019s housing, which forms the mechanical ground and the electrical interconnection of all elements. The SmartPen is to be considered as a normal pen, enabling simultaneous acquisition of the written characters (or drawings) by a computer. The current prototype of the device is the size of a marker. By a further miniaturization of the different components, it should finally be the size of a standard pen. Fig. 1 shows the main components. The pen uses a standard ink cartridge mounted in a hollow shaft. This shaft is connected to a three-component force/acceleration sensor. The shaft has a particular design, so that it also acts as a mechanical stop for the force/acceleration sensor. Behind this subassembly, a tilt sensor is mounted. This sensor is a commercial tilt sensor and is used to measure the tilting angles of the pen. Behind the tilt sensor, a rechargeable battery pack is inserted to power the device"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003168_s0261-3069(99)00070-9-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003168_s0261-3069(99)00070-9-Figure2-1.png",
        "caption": "Fig. 2. The use of tooling inserts to avoid tooling islands.",
        "texts": [
            " Generally, for shallow components, a horizontal build is preferred on the grounds of minimum build time; where deep cavities are required, a vertical build could be quicker. Both strategies are demonstrated in Fig. 1. The advantage of building horizontally is that the \u017dwaste from the cavity can be used to make the core if .a laser or similar is used for processing . Problem areas occur when islands or up stands are required. There are several potential solutions to this. \u017d .1. The use of tooling inserts as islands see Fig. 2 . 2. Locate from dowels; dowel holes can be cut into \u017d .the required laminates see Fig. 3 but require enough space to be used. 3. Secure the islands to the edge of the tool by using \u017d .tabs see Fig. 4 . The tabs are added to the CAD model and automatically cut during the laser process to add support to the island. This method automatically supports islands in the tool because any up stands are automatically supported within the vertical laminate, as demonstrated in Fig. 5. \u017d .From the candidate joining methods Table 2 several could be ruled out fairly quickly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure8-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000119_j.1749-6632.1951.tb54237.x-Figure8-1.png",
        "caption": "FIGURE 8. Cross section of the oil film 01 i( journal bcariiig uiider d rutdting load showing the niutions of the shaft and bearing surfares relative to the line-of-centers.",
        "texts": [
            " If the load in FIGURE 6 does not change in magnitude but simply rotates in the same direction as the shaft rotation, the shaft center or the line-of-centers will move in the same direction in an attempt to maintain the same angle 4 with the load direction. Thismotion has an unexpected effect. If we fix ourselves in a position relative to the line-of-centers and move with it, the shaft will probably still be moving in the clockwise direction relative to us, but the bearing surface will be moving past us in the opposite direction. These relative motions are indicated in FIGURE 8. I t may be seen from this figure that, relative to the line-of-centers (and the oil film geometry remains constant only in relation to this line), the shaft is drawing oil into the converging wedge on the right, thereby increasing pressure in this region in the manner described by Reynolds. At the same time, however, the bearing surface is dragging the oil out of this region, thereby lowering the pressure. The reverse situation occurs in the film on the other side of the line-of-centers. The total effect is that this motion of the line-of-centers will result in a decrease in the pressure developed in the converging wedge (which pressure has been called the \u201cwedge film\u2019\u2019 component) from what the pressure would be under a constant load. On the other hand, if the line-of-centers were forced to move in the opposite direction from the shaft rotation in PIGUKE 6, the direction of the bearing motion in FIGURE 8 would be reversed and the bearing, as well as the shaft, would be dragging oil into the wedge on the right. The result would be a greatly increased pressure materially assisting in the load support furnished by the shaft rotation. The effect of load rotation, therefore, is uncertain. It may decrease the load capacity or it may increase it. It turns out that this depends Burwell: Full Fluid Lubrication 769 on the relation between the angular velocity (we) of the line-of-centers and the angular velocity (q) of the shaft about its own center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003524_37.569718-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003524_37.569718-Figure4-1.png",
        "caption": "Fig. 4. Principle of finger-shaped tactile sensor",
        "texts": [
            " As aresult, the number of elements and wires increases enormously when a large sensing area or high resolution is required. To overcome these problems, a finger-shaped tactile sensor using an optical waveguide capable of detecting the contact location of the object and the surface normal of the contacted object was developed. The developed tactile sensor uses an optical phenomenon that enables the tactile information to be converted to an optical image [12]. The principle of the sensor is shown in Fig. 4. The optical waveguide is a hemispherical shell of glass and is covered with elastic rubber. An appropriate air gap exists between the waveguide and the cover. The inside of the waveguide is illuminated by the light source and the injected light maintains total internal reflection at the boundary of the glass and the air. Thus, the light is enclosed by the waveguide. When an object contacts the elastic cover, the cover is depressed as part of it contacts the waveguide. Then the light enclosed in the waveguide is scattered at the contact location because the total intemal reflection conditions are no longer satisfied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003000_ip-epa:19982170-Figure12-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003000_ip-epa:19982170-Figure12-1.png",
        "caption": "Fig. 12 porosity = 0% Flow field in a radial plane through the wafters (computed) for",
        "texts": [
            "15 porosity = Flow Jield 100% in a radial plane through the wafters (computed) for The velocities generated by the \u2018fan\u2019 are predominantly tangential at around 85% of rotor tip speed, with a very small radial component, averaging only 5% of tip speed. Since the circulating flow rates are low, the tangential velocity is dominant throughout the entire flow field: there is a large volume of strongly swirling flow (average velocity around 60% of tip speed) surrounding the \u2018fan\u2019, and a region of much slower swirling flow (average velocity around 15% of wafter tip speed) behind the end winding, Fig. 12. 4.2 30%open Opening the windings 30% creates an additional circulation route through the end winding itself, Fig. 9. The flow velocities generated along the length of the \u2018fan\u2019 are increased, including those induced by the bar end fan that was previously stalled. The velocity generated is still predominantly tangential (around 85% of tip speed), but the radial component has doubled with a maximum of around 100% of wafter tip speed. The majority of the flow still circulates without passing through the winding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002721_12.281111-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002721_12.281111-Figure1-1.png",
        "caption": "Figure 1. Coaxial powder feed nozzle for laser cladding.",
        "texts": [
            " The influence of the shielding gas on the jet flow and the catchment efficiency was analysed by both theory and experiments. Flow visualisation with image analysis is used to check this simulation and some initial studies are reported on the effects of flow parameters on the catchment efficiency and degree of powder focus. The powder used in the tests was stainless steel 304L powder. Clad trials were performed on a mild steel substrate with a 1.0 kW CW CO laser with a constant table speed of 10 mm/s. Coaxial cladding nozzle The design of the coaxial nozzle structure is ifiustrated in Figure 1. The design specification included compact size, efficient energy interaction between the laser beam and the powder outside the nozzle assembly, and shrouded gas flow which would tend to focus the powder stream. The nozzle is composed of three separate parts. The central hole through which the laser beam and shield gases pass; the surrounding annular zone into which the powder flows and is blown out by its carrier gas as a cone into the laser beam outside the nozzle; and an outer annular gas jet",
            " 2,2i=1-e d (6) The numerical relationship of equation (6) between the catchment efficiency and the diameter ratio (dID) ofthe clad to the powder stream is shown in Figure 10 . It can be found that the catchment efficiency will be increased with d/D and approaches 80% at d/D= 1.5. In our optics setting and nozzle size the diD' is about 0.26 and it could be . substituted in equation (3) to calculate the value of dID through the beam axis. An important relationship between the catchment efficiency and geometric paramders of stand-off distance and spraying angle was established in Figure 1 1 . The catchment efficiency is compared to the experimental data with varying spraying angle. It is seen that the spraying angle and the initial diameters of the powder and laser beam will significantly affect the catchment efficiency. In our case, the reduction of the spraying angle which is controlled by the velocity of the compound jets will increase the catchment efficiency up to 40% at the spraying angle of about 10\u00b0 for both inner and outer gas velocities of 2 rn/s. Conclusions This study demonstrates a nozzle design to improve jet spraying on clad surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure3.2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure3.2-1.png",
        "caption": "Fig. 3.2",
        "texts": [
            " Transistors can only withstand a very low reverse voltage; a diode must be connected in series with them in order to obtain the characteristic of Fig. 3.1c. However, as will be seen, it is often the case that controlled turn-on/turn-off switches do not have to block negative voltages. TC will once more denote those switches whose characteristic shows only two branches (Fig. 3.ld), if they allow for the change from OA to OB and vice versa. 3.1.2 Bidirectional \"Switches\" \u2022 In many DC-DC and DC-AC converters, a diode D must be connected in antiparallel with the controlled turn-on/turn-off device (Fig. 3.2a). If TC and D are both used during the same operational mode, the function ofTC is to turn on or off the positive current i at suitable moments. Diode D must allow current i to flow when that current reverses its polarity, during the time interval when this \"switch\" must be on. 3.1 \"Switches\" Classification 113 In other cases, the diode current settles or disappears suddenly as the result of the turn-off/turn-on of a different controlled \"switch\" from the one across which it is connected. In such cases, the diode ensures that the current continues to flow",
            " The schematic characteristic in the diagram has a negative-current branch OD, but negative-voltage branch OC has disappeared since it is incompatible with the presence of a diode. If using an asymmetrical GTO thyristor or a transistor, there is no need to add a diode in series with TC to produce this component. \u2022 Some DC-DC converters (or frequency changers, see Vol. 2, Appendix) require bidirectional \"switches\" capable of controlling the turn-on and the turn-off of the current in both directions. Such \"switches\" can be composed of two controlled turn-on/turn-off devices TC 1 and TC 2 connected in antiparallel (Fig. 3.2b). Each of these must be able to block a positive or negative voltage across it. If two transistors are used, a diode must be connected in series with each of them. Therefore, the use of a single transistor in a four-diode bridge is generally preferred (Fig. 3.2b') 3.1.3 Remarks a) When indicating the function to be carried out by a \"switch\", it is not enough to show (in the voltage-current axes system) the branches of characteristics on which it will have to be able to operate. The switchings from ON to OFF or vice versa have to be indicated. If this is not indicated, no difference should appear between a conven tional thyristor (Fig. 3.1 b) and a thyristor with forced commutation circuit (Fig. 3.lc). The bidirectional controlled turn-on/turn-off switch (Fig. 3.2b) would be mistaken for the two thyristors connected in antiparallel as used in AC regulators (Fig. 3.3). turn-off semiconductor switch the diagram must connect a device capable of ensuring the continuous flow of current i. Such a device is frequently a diode (Fig. 3.4a); current i switching off in TC is linked to the current rise in D and conversely. In many reversible DC-DC and DC-AC converters, there are two switches made up of a controlled semiconductor device and a diode in antiparallel (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003168_s0261-3069(99)00070-9-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003168_s0261-3069(99)00070-9-Figure6-1.png",
        "caption": "Fig. 6. Simple \u2018top hat\u2019 test tool.",
        "texts": [
            " It was important to test whether these bonding mediums could stand up to the rigours imposed by each of the tooling applications. To this end the experiments included: \u017d .v single lap shear ASTM: D 1002-94 ; \u017d .v flexural strength ASTM: D 1184-93 ; v lap shear at elevated temperatures; and v lap shear after exposure to common coolants. The success of the joining tests prompted the use of live testing of simple primitive tools. One of the tool designs tested was a simple top hat arrangement which \u017d .was designed for ease of manufacture. The tool Fig. 6 was joined according to the temperature requirements of the process with either an adhesive, braze or high\u017d .temperature braze Table 3 and then skimmed to remove stair steps on a lathe. The tools were sent to the industrial partners for production environment testing. The test procedure followed a basic pre-measurement on a CMM machine, followed by the tests and a recheck of measurements after testing. The production environment tests included the following: v vacuum integrity; v thermal cycling to the desired process tempera- tures; v component run-off; and v surface finish measurement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002459_941761-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002459_941761-Figure4-1.png",
        "caption": "Fig. 4 CAPP Model of the potential Contact Zone.",
        "texts": [
            " No assumptions are made about the regions which will come in contact and the entire face of the mating tooth pairs is considered as having potential points of contact. The face of the driving gear is divided into a user defined number of slices. In the mid plane of each slice, a point is found which is closest to the mating tooth. The actual separation between the point and the mating surface is computed. If this separation is less than a user defined separation tolerance (should be greater than the tooth deflection), a rectangular grid is laid about that point and that point is considered to be a potential contact point. Figure 4 shows the contact grid on a helical gear. The grid runs diagonally across the tooth and when it reaches the tip of the tooth, it goes along the tip. This is because the tip is the point at that section which is closest to the mating tooth. Therefore if any point at this section is going to come in contact, it is the tip. This method has been implemented in the Contact Analysis Program Package (CAPP). Singh [lo] has used this method to analyze spur and helica gears. Narayan [l l] has used this to study worm gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002824_107754639800400502-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002824_107754639800400502-Figure6-1.png",
        "caption": "Figure 6. The construction sketch of the large-size rig for the investigation of dynamics of the rotor line. 1 = supports; 2 = foundation frame; 3 = foundation; 4 = clutches ; 5 = electric engine; 6 = transmission; 7 = slide bearings; 8 = discs; 9 = external fixings of the bushes.",
        "texts": [
            " EXAMPLES OF EXPERIMENTAL VERIFICATION OF THE MODEL The models of individual subsystems such as slide bearings or the rotor line were verified during many years of experimental research conducted at the Institute of Fluid-Flow Ma- at University of Newcastle on August 28, 2014jvc.sagepub.comDownloaded from 529 chinery of the Polish Academy of Sciences (IFFM) (Kicinski, 1986; Kicifiski and Matemy, 1993). To verify the complex model of the whole rotor-bearings-supports/foundation system, a large-size experimental rig was built. A diagram of this rig is presented in Figure 6. There is a five-support rotor with a total length of more than 6 m; the diameter of the shaft and the bearing journals is 0.1 m, and the diameter of the discs is 0.4 m. The distance between the supports is 1.4 m. Hydrodynamic transverse slide bearings of length /width ratio L/ D = 0.5 and relative circular-cylindrical radial clearance 0 R/ R = 0.0015 - 0.0018 were applied for the experiment. The discs\u2019 imbalance corresponding to the displacement of their centers of mass 8 = 25 x 10-6 m was the exciting force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003433_elan.1140090914-Figure6-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003433_elan.1140090914-Figure6-1.png",
        "caption": "Fig. 6. a) Cyclic voltammogram of 1 mM BQ in phosphate buffer (pH7.3) at BPG electrode; b) as in a) with 0.0121 g of Celin tablet in lOmL phosphate buffer (pH7.3); scan rate 30mV/s.",
        "texts": [
            " From the slope, kfl[AH2], a second-order homogeneous rate constant, kZ, for the reaction between BQ and AH2 was obtained as 1.8 x 1O\"M-I s-' (at pH 7.3). This may be compared with the value 1.3 x 105?0.2 M-' s-' for Prussian Blue modified electrode [ 151 and 1.5 x lo7 M-' s-' reported for polyvinylferrocene-modified electrode [ 141. It was considered useful to analyze the AH, content in a Vitamin C tablet by the proposed method. Celin (Glaxo, Bombay, India) tablet was finely powdered. The CV of a solution of Celin dissolved in phosphate buffer in presence of 1 mM BQ is shown in Figure 6b. From the measured current and using the calibration plot, the amount of AH2 in the Celin tablet was estimated to be 339.4mg which is in fair agreement with the value reported on the package (333mg). The analysis was made three times and the standard deviation obtained was 0.90. The statistical analysis of the data has shown that there is a 95 % chance that the true mean (p) lies within the range 338-342. 4. Conclusion It may be concluded that BQ facilitates the electrochemical catalytic oxidation of AH2 as indicated by the fairly large value of the rate constant between BQ and AH2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003489_jsvi.1997.1496-Figure1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003489_jsvi.1997.1496-Figure1-1.png",
        "caption": "Figure 1. Schematic of test apparatus.",
        "texts": [
            " It will be shown that the state variable model can predict multi-periodicity and chaos as observed in experiment where a simpler Coulomb description cannot. The outline of the paper is as follows. In section 2, the experimental set-up is briefly presented. Results obtained from this experimental apparatus are presented in section 3, while section 4 gives a brief review of the friction model used in the numerical study as well as a summary of the numerical results obtained using it. Finally, some concluding remarks are given in section 5. A schematic of the apparatus used in the experiment is shown in Figure 1. Two identical horizontal spring steel beams, referred to as the main beams, are cantilevered between the rigid blocks and support the masses, accelerometers, and the beams 1 and 2 as shown in the figure. A steel sphere mounted at the end of the vertical beam 2 is sliding with dry friction over the friction plate, which is itself attached to the linear slide. This slide is excited harmonically by an electromagnetic shaker, so that friction between the steel plate and the sphere induces lateral motion of the cantilevered mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003584_b978-0-7506-0119-1.50006-0-Figure1.1-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003584_b978-0-7506-0119-1.50006-0-Figure1.1-1.png",
        "caption": "Figure 1.1(a) Dividing cutting action; (b) shaving cutting action",
        "texts": [
            "1 Material cutting techniques The first cutting tool used by mankind is likely to have been a piece of broken bone or splintered flint. The deficiencies of these materials as cutting tools started a search to find better tool materials and more efficient cutting methods. This search is still going on: a new technique to cut materials is developed when the existing methods are not efficient or not quick enough. The first and simplest cutting action would have been the splitting or dividing of materials using a chopping action with a thin wedge- or knife-shaped tool, as shown in Figure 1.1a. With this type of action and tool it is difficult to produce components to precise sizes or accurate shapes. The need arose for a cutting action where control could be maintained over the amount of material being removed. The shaving action shown in Figure 1.1b was developed, which makes possible the removal of thin sections of the material from selective areas requiring change of shape or size. With the shaving action the depth of cut can be accurately controlled. The accuracy of the work produced by the cutting technique is entirely dependent on the relative movements of the work and the tool. It required the development of machines where the positional relationship and movements of the work and the tool could be controlled accurately for components to be produced to the Computer numer i ca l control of m a c h i n e tools desired size and shape"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002512_0954407971526362-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002512_0954407971526362-Figure4-1.png",
        "caption": "Fig. 4 A schematic view of the low-speed belt test rig",
        "texts": [
            " It will be shown in Section 4 that tooth root cracking belt failures correlate better with a simple addition of the two strains \u00d8 \u00eb td 6M Kt t2 w (17) than with either strain measure separately. The sensitivity of \u00d8 to belt operating conditions and changes of belt pitch geometry and material properties around the actual values in Table 1 will be reported. A low-speed belt torque transmission rig has been built to enable the build up and decay of contact forces to be measured as a belt tooth enters and leaves mesh with a pulley groove (Fig. 4). Torque is transmitted between pulleys mounted on two parallel shafts, one driven and one braked by a 0.37 kW motor. The system is designed for both shafts to rotate at the same rate (equal sized pulleys) and variable speed gearing allows rotation speeds from 1 to 20 r=min. Torque is measured by calibrated strain gauges mounted directly on the parallel shafts (torque loss can be calculated from the difference in torque on the driving and Table 1 Input conditions for a 19.75 mm wide HTD1 belt running on a HTD pulley Operating conditions Belt pitch conditions Belt material properties Nt 19 Pb 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003017_978-3-642-52454-7-Figure2.66-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003017_978-3-642-52454-7-Figure2.66-1.png",
        "caption": "Fig. 2.66",
        "texts": [
            " But the ensuing modification of the circuit topology can lead to this destruction (e.g. see Vol. 1, Chap. 7, \u00a7 4). 2.4 Thyristors 83 2.4.3.5 Overvoltage Protection Current variation in the circuit inductances (di/dt limitation or stray inductan ces) bring about voltage surges which must not go beyond the maximum acceptable values. Moreover, when the thyristor turn-off is achieved, the return of voltage vr to value E should take place at a rate smaller than the critical value of dvjdt. The thyristor is therefore protected by an RC circuit (Fig. 2.66a), which reduces the voltage surge amplitude and decreases the rate of rise of vr. When the free-wheeling diode starts to conduct, voltage E is applied across series connected elements /, R and C. Resulting waveforms of current i, and voltages v and vr are shown in Fig. 2.66b. Resistance R must be rated so that the current peak due to the capacitor discharge at turn-on thyristor does not exceed the maximum acceptable value for ir. Figure 2.67 shows different topologies which enable the charge and discharge time constants of the capacitance to be varied. (In Figs. 2.66 and 2.67, the auxiliary circuit, which turns off the thyristor, is not shown.) 84 2 Switching Power Semiconductor Devices 2.4.4 Special Thyristors Special thyristors operate on the same principles as conventional thyristors but are slightly modified so as to improve one or other characteristic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003457_elan.1140050209-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003457_elan.1140050209-Figure2-1.png",
        "caption": "FIGURE 2. Flow injection peaks for (A) hydrogen peroxide and (B) glucose for solutions of increasing concentrations (mM): (A) 1 (a), 2 (b), 4 (c), and 7 (d); (B) 1 (a), 2 (b), 4.5 (c), and 5.5 (d). The resulting calibration plots are also shown. Operating potentials: (A) +0.40 and (B) +0.50 V.",
        "texts": [
            " Figure 1 shows hydrodynamic voltammograms (HDVs) obtained under flow injection conditions for glucose, cysteine, and hydrogen peroxide in the range of potential from 0 t o 600 mi,'. As expected, large anodic currents with respect to unmodified electrode were observed for the three conipounds in the 0.35 to 0.5 V potential region, using sodium hydroxide (0.1 M ) as mobile phase. Typical amperometric responses for glucose and hydrogen peroxide, together with the regression lines, are reported in Figure 2 . Maximum response of the Co(I1, 111) CME for glucose was observed at potential around +O.S V, and the height was proportional to its coticentraticm. This can be explained by a mechanism involving catall Co( 111) species of the modifier, similar to what was found by Santos and Haldwiri [6] using a cobalt phtalocyanine modified electrode (CoPC CME). I Iowever, with respect to CoPC CME, the response of the Co(I1, 111) CME remains stable after repetitive injections o f the analy-te, and no pulsing o f the potential was required to maintain the electrocatalJ-tic aci"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0000112_tce.1952.6371894-Figure4-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0000112_tce.1952.6371894-Figure4-1.png",
        "caption": "Figure 4 (right). Operating segments of the magnetization constraint for the four modes of amplifier operation",
        "texts": [
            " Neverthe less, at either type of discontinuity the numerical values in the load and control circuit voltage equations 1 and 2 are dif ferent in the interval immediately before and the interval immediately after the discontinuity. As will be seen later, it is more convenient to let (Jequal the value of wt' at which either type of discontinuity occurs, and to rewrite the load circuit and control circuit voltage equations as d d .u N. ~+N ~+L ~+R . a dt a dt a dt at-a =Ea sin (wt+8) (3) I I \u2022I, I_c- _ Figure 3 (right). Symmetrical and asymmetrical magnetization loops for a rec tangular loop core materia I Figure 1 (left). Series-connected magnetic amplifier circuit These are illustrated in Figure 4. Solu tions for the currents and fluxes as func tions of time will be obtained for each of these modes of operation. In obtaining the transient response of the amplifier due to step changes in the control voltage, two types of discontinui ties occur. One type is a discontinuity due to externally changing the control voltage. The other type is a discontinuity encountered when operation proceeds Mode I: core I unsaturated and core II unsaturated. Mode II: core I saturated and core II un saturated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002645_1.2889688-Figure2-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002645_1.2889688-Figure2-1.png",
        "caption": "Fig. 2 Nodal coordinates of the shaft element",
        "texts": [
            " (1) may be compUcated functions of the spatial variables for a system configuration, so an exact parameter identification may not be feasible. This implies that the direct use of Eq. (1) for identification purpose is not practical. Since in practice the diameter of a shaft often changes stepwise along the axial direc tion, we propose an identification approach based on the finite element method. Let ^f be the nodal displacement vector of the ith element with eight degrees of freedom, four degrees of freedom of dis placement in the x and y directions and four of rotation about the X and y coordinates (see Fig. 2). Let <px and c\u0302 j, be the interpolation functions of the x and y coordinates, which are the lowest degree admissible polynomials, i.e., the cubic spline. In particular, we have <]1 = [Xi, yi, 19yi, I9xi, Xj+i, y,+i, Wj,(,+i), W^(,+i)] (2) <A;c = [< l\u0302x, 0, (f>2x, 0, (\u0302 3;,, 0, <\u0302 4\u0302 , 0, ] ' (3) (f)y = [ 0 , <^i^, 0 , -(l>2y, 0 , (f>3y^ 0 , -<^4y] ' 4>y (4) (5) By using Galerkin's formulation of the weighted residual method (Meirovitch, 1980), we obtain the element mass, damp ing, and stiffness matrices for the shaft: Af- = Ip'A'i I (0;((^i + (j)y4)y)d^ (translation mass matrix) Jo M\\ = If/P I (cf>'x<))x + (I)y4>'y)d\u00a3, (rotatory mass matrix) Jo G' = VlJUP I (</)y0i - <f>x<}>'y)d$, (gyroscopic matrix) Jo K'i = \u00a3,\u2022/"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0003694_robot.1988.12285-Figure10-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0003694_robot.1988.12285-Figure10-1.png",
        "caption": "Figure 10: Reaponse of the Manipulator in Maneuver I I",
        "texts": [
            " Although seemingly slight, errors of this magnitude could mean the difference between success and failure in a given task. Moreover, even a modest change in the input torques can lead to significantly larger discrepancies. As another verification of the simulation code, the total energy of the system and the work done by the control inputs were monitored. For the rigid model, the two remained balanced to within 0.8%, while for the elastic model they remained balanced to within 0.2%. Work done is plotted in Figure 9 for both models. Maneuver I1 The second maneuver traces a three-dimensional trajectory as shown in Figure 10 which displays the I - y and I - z projections. The trajectory (for the rigid model) is prescribed by p, i = 1 , 3 y, i = 1 , 2 , 3 7 t 7 r r e y = a,(t - -sin(n-)), where a1 = 0.075s-', a2 = u3 = 0.05s-' and r = 10s. Plots for three of the joint angles and the corresponding rates are given 1542 Maneuver I ) time ( S I time (si Figure 7: Discrepancy in Posit ion Figure 8: Discrepancy in Orientation -Rigid 0 5 time ( S I Figure 9: Work Done I543 in Figures 11 and 12. The tip-position discrepancy (Figure 13) a t the end of the maneuver is about 18 cm, certainly not a negligible difference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_31_0002735_0094-114x(92)90062-m-FigureI-1.png",
        "original_path": "designv11-31/openalex_figure/designv11_31_0002735_0094-114x(92)90062-m-FigureI-1.png",
        "caption": "Fig. I",
        "texts": [
            " According to this characteristic, we can obtain supplementary equations of force analysis, so that force analysis of any complex muitiloop spatial mechanism can be independently completed inside each branch. The crux of force analysis of multiloop spatial mechanism is to solve the constrain reactions of main pairs which connect the central link and branches. Once the reaction on main pairs are obtained, the reactions on all other pairs are easy to calculate. For the hypothetic mechanism shown in Fig. I(c), after the main pair in branch AC(r -, I) in which link 4 is the real input link is disconnected from the central link, the actions of the central link on the branch, including force \u00a2r,s and moment ~'ts, are expressed in a six-dimensional vector _E6s - ( ~ ) T , which is resolved along the local reference system 06 - X6 Y6Z6, as shown in Fig. 2. For the local reference system, the Z6 is along the kinematic pair's axis Sk, Xk along ~k-s~, and Yk is determined by right-hand law. The origin Ok is located at the center of the kth pair"
        ],
        "surrounding_texts": []
    }
]