[ { "image_filename": "designv10_13_0001516_60.986436-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001516_60.986436-Figure1-1.png", "caption": "Fig. 1. SMIG operating on a single-phase grid.", "texts": [ " The objective of this paper is to investigate the performance of a three-phase induction generator with the Smith connection (SMIG) when operating on a single-phase power grid. A systematic analysis of the SMIG will be presented, and the conditions for perfect phase balance will be deduced. It will be shown that, for medium and heavy loads, perfect phase balance in the induction machine is possible by using only capacitive phase converters. With dual-mode control, satisfactory operation over the normal speed range can be obtained. Experimental results will be presented to validate the theoretical analysis. Fig. 1 shows the Smith connection for a three-phase induction generator operating on a single-phase power system. The rotor is assumed to be rotating in such a direction that it traverses the stator winding in the sequence A\u2013B\u2013C. For generator operation, the rotor speed must be slightly higher than the positive-sequence rotating field. The \u201cstarts\u201d of the stator phases A, B and C are denoted by 1, 2, 3 while the \u201cfinishes\u201d are denoted by 4, 5, 6. Terminals 4 and 6 are common and form the \u201cpseudoneutral\u201d point N. Terminals 1 and 2 are both connected to one line of the single-phase grid while terminal 3 is connected to the second line. Terminal 5 (the \u201cfree\u201d terminal) is connected to the neutral point N via capacitance , and to terminal 3 via capacitance . It should be noted that the generator performance is sensitive to the phase connection for a given direction of rotor rotation. A comparison of Fig. 1 with the Smith connection for the motoring mode [11] reveals that phases B and C have been interchanged, a condition necessary for proper phase balancing as will be explained in Section III. In this paper, the motor convention has been adopted for the direction of currents. The Smith connection is essentially an asymmetrical winding connection. But, with an appropriate choice of the terminal capacitances, it is possible for the induction generator to operate with balanced phase currents and phase voltages. As shown in Fig. 1, the B-phase current is the sum of the capacitor currents and . Consider the phasor diagram in Fig. 2(a), drawn for the special case for perfect phase balance. The current leads (or ) by rad and hence lags by rad. The voltage (which is equal to ), is equal to . The capacitor current leads by rad and hence it lags by rad. For generator impedance angles between rad and rad, the phase current can be synthesized with the required magnitude and phase angle to give phase balance, by using suitable values of and ", " The generator operates as if it were supplying a balanced three-phase load, hence the efficiency is the same as that obtaining when the generator operates on a balanced three-phase grid. Balanced conditions are valid for a given set of capacitance values and speed only. When the rotor speed changes, the circuit conditions are disturbed and a new set of capacitance values is required to balance the generator again. Performance analysis of the SMIG for the general off-balance operation can be carried out using the method of symmetrical components, the circuit being considered as a special case of winding asymmetry. Referring to Fig. 1 and adopting the motor convention for the induction machine, the following inspection equations [14] may be established: (1) (2) (3) (4) (5) (6) (7) (8) where , , and . The following symmetrical component equations for a starconnected system [15] may also be written: (9) (10) where is the complex operator . From (5), (6) and (8), the following equation may be deduced: (11) Equation (11) is valid whether the generator is balanced or not. From (2), (3) and (11) (12) From (10) and (12), it is apparent that zero-sequence current and voltage are absent in the generator system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002723_physreve.76.061901-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002723_physreve.76.061901-Figure2-1.png", "caption": "FIG. 2. Pairs of semiflexible filaments characterized by their stiffness and length L that are separated a distance d, when they sediment under the action of a uniform external force field Fe for three different geometries; in the three cases we show the relevant parameters. I Geometry I: Parallel filament sedimenting due to a uniform force transverse to the plane defined by them. II Geometry II: Sedimenting coplanar filaments. III Geometry III: Sedimenting collinear filaments.", "texts": [ " SEDIMENTATION OF A PAIR OF FLAMENTS We will now consider pairs of symmetric filaments of length L and rigidity , at a distance d and subject to an external uniform force field Fe. We assume that Fe is parallel to ez and that the polymers lie initially perpendicular to the applied field, along the ex direction. The details of the cooperativity induced by the hydrodynamic coupling are sensitive to the initial configuration. To distinguish between different effects induced by hydrodynamics, we will consider three different geometries, as depicted in Fig. 2, which correspond to parallel geometries I and II and collinear geometry III filaments. Geometries I Fig. 2 a and II Fig. 2 b preserve the mirror symmetry with respect to the filament\u2019s center while geometry III Fig. 2 c will allow us to explore the effects of translation-rotation coupling. We will see that geometry I conserves the symmetries of the one-filament case, and geometry II breaks the up-down symmetry. The presence of a second chain modifies the friction exerted on the first filament. As a result, the filament shape and velocity will change as a function of the distance between chains. Depending on their initial conditions, the presence of 061901-3 a second thread can induce rotation of the sedimenting polymer, breaking the mirror symmetry. We will characterize this translation-rotation coupling through the deformation asymmetry parameter D = 1 \u2212 N 1 + N , 5 where k= xk\u2212xmin is the distance along the x direction between the kth bead and the lowest bead, as shown in Fig. 2 a . The parameter D ranges between \u22121,1 , and reflects the transverse asymmetry of the filament ends. For a single filament, there is no shape asymmetry and D=0. The first geometry under consideration involves two filaments that are parallel and transverse to the external force Fig. 2 a . Due to the initial configuration, they will sediment at the same speed with D=0 and keeping their initial separation d. After a short time interval, in which HI propagate and the filaments\u2019 inertia decays, they reach their steady state sedimentation velocity and deform into shapes analogous to the ones described for single polymer sedimentation. Since in our model HI propagate instantaneously, the sedimentation velocity of the initially straight filaments after one time step will deviate from its free draining value v0 Fe /N 0; in Appendix A we compute this initial velocity", " As a result of such coupling, two sedimenting filaments affect each other at large distances, and the coupling becomes quantitatively relevant at distances of the order of the filament\u2019s size. For a given separation d, the velocity change due to hydrodynamic cooperativity decreases with B. More rigid filaments have a larger filament section exposed to the flow induced by the neighbor filament, leading to a larger relative velocity increase. B. Geometry II: Sedimenting coplanar filaments We consider next a pair of straight parallel chains separated a distance d under the action of a uniform external field coplanar and transverse to the two filaments, as depicted in Fig. 2 b ; the symmetry of the geometry ensures again D =0. The upper chain bends less than the lower one, A1 A2, and sediments faster because it is subject to a smaller drag due to the solvent counterflow. Similar phenomena have been reported for the sedimentation of other flexible objects, such as drops 23,24 . In Fig. 4 we display the relative sedimentation velocity vr v2z \u2212 v1z as a function of a pre- 061901-4 scribed interfilament distance d. The sedimentation velocity increases with B until the filament deformation reaches the plateau depicted in Fig", " We have verified that the filaments sedimentation velocity decays as d\u22121, while their relative velocity vr decays as d\u22122 Fig. 4 because the leading contribution of O d\u22121 cancels out exactly. Such a behavior is general and valid for all values of B and in Appendix B we discuss such a dependence on the basis of a simplified limiting model. Finally, we analyze the sedimentation of two collinear filaments under the action of a uniform transverse field. To this end, we consider a pair of filaments which are initially straight and with a minimal bead-to-bead distance d, as shown in Fig. 2 c . The hydrodynamic coupling induces a sedimentation velocity which differs from free draining motion v0. Due to the instantaneous propagation of HI in our model, deviations from v0 are observed after one time step. In Appendix A we compute this initial velocity when bending is negligible. The presence of the second filament induces in general a relative displacement of the filaments and also a rotation because the mirror symmetry is lost. The time scales at which filaments rotate and displace depend on filament flexibility", " thanks Distinci\u00f3 de la Generalitat de Catalunya for financial support. APPENDIX A: INITIAL SEDIMENTATION VELOCITIES In the initial stages of their sedimentation, straight filaments have not deformed significantly. In this regime it is possible to obtain analytical expressions for their sedimentation velocities at the Oseen level. In particular, we are interested in the velocity that a straight filament oriented along the x direction induces in a second collinear filament a distance d away, as depicted in Fig. 2 c . The external field is applied perpendicular to both filaments, along the z direction, and hence the distance between beads reduces to their separation along the x direction. As a result, the velocity on bead i due to bead j in the direction of the external force, can be expressed as vi1 H = 3a 4 Fe 0 j 1 xj \u2212 xi , A1 where we have assumed that bead i belongs to the filament on the left while j is a filament belonging to the filament on the right-hand side of the pair, and hence the sum runs over the beads of this second filament" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.18-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.18-1.png", "caption": "Fig. 6.18 A wooden shield wagon (\u6728\u5e54). a Original illustration (Mao 2001). b Structural sketch of roller device. c Structural sketch of shield device", "texts": [ " The pulley is connected to the frame with a revolute joint JRx. The rope is connected to the pulley and the spiked link with a wrapping joint JW and a thread joint JT, respectively. Figure 6.17b shows the structural sketch. Before the Jin Dynasty (AD 265\u2013316), Mu Man (\u6728\u5e54, a wooden shield wagon) had been used in wars (Zhang et al. 2004). Its earliest function was to cover soldiers when they climb city walls. Later it became a defense device for protecting them from enemies\u2019 rock balls as shown in Fig. 6.18a (Mao 2001). The wooden shield wagon can be divided into two parts: the roller device and the shield device. The roller device is a mechanism with two members and one 126 6 Roller Devices joint, including the frame (member 1, KF) and wheels on the frame as the roller members (member 2, KO). The wheel is connected to the frame with a revolute joint JRz. Figure 6.18b shows the structural sketch of the roller device. The shield device is a mechanism with four members and three joints, including the frame (member 1, KF), a connecting link (member 3, KL), a rope (member 4, KT), and a shield (member 5, KB). The rope is connected to the connecting link and the shield with thread joints JT. The connecting link is connected to the frame with a joint that translates along the x-axis and rotates about the y and z axes, denoted as JPxRyz. Figure 6.18c shows the structural sketch of the shield device. The design of the joint between the frame and the connecting link facilitates the soldiers operating the shield easily and minimizing the harm from the enemies\u2019 rock balls. There are four devices that cannot be classified under the five types mentioned above, including Huo Zi Ban Yun Lun (\u6d3b\u5b57\u677f\u97fb\u8f2a, a type keeping wheel), Mu Mian Jiao Che (\u6728\u68c9\u652a\u8eca, a cottonseed removing device), Bo Che (\u7d34\u8eca, a linen spinning device), and Tao Che (\u9676\u8eca, a pottery making device)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.2-1.png", "caption": "Fig. 9.2 A donkey-driven mill (\u9a62\u7931) a Original illustration (Wang 1991), b Structural sketch", "texts": [ " Thus, it can be considered as a mechanismwith three members and two joints, including the frame (member 1,KF), a rope (member 2, KT), and a sieve (member 3, KL). The rope is connected to the frame and the sieve with thread joints JT. Figure 9.1b shows the structural sketch. 9.1.2 Lv Long (\u9a62\u7931, A Donkey-Driven Mill) Lv Long (\u9a62\u7931, a donkey-driven mill) uses animals to rotate a wooden wheel, through a rope or a belt, to drive the mill disc installed on the base. The device is a typical application of rope transmission in ancient China as shown in Fig. 9.2a (Wang 1991). Since the wooden wheel rotated by animals has a larger diameter than the mill disc, the device would be a rope transmitting mechanism that can increase the mill velocity and enhance the device\u2019s efficiency. Furthermore, since a rope or a belt is wrapped across the wooden wheel and the mill disc, it can increase the contact areas and friction forces, making the grinding work more stable. 192 9 Flexible Connecting Mechanisms It is a mechanism with four members and four joints, including the frame (member 1, KF), a wooden wheel (member 2, KU1), a mill disc (member 3, KU2), and a rope (member 4, KT). The wooden wheel is connected to the frame with a revolute joint JRy. The rope is connected to the wooden wheel and the mill disc with wrapping joints JW. The mill disc is connected to the frame with a revolute joint JRy. Figure 9.2b shows the structural sketch. There are five water lifting devices, including Lu Lu (\u8f46\u8f64, a pulley block), Shou Dong Fan Che (\u624b\u52d5\u7ffb\u8eca, a hand-operated paddle blade machine), Jiao Ta Fan Che (\u8173\u8e0f\u7ffb\u8eca, a foot-operated paddle blade machine), Gao Zhuan Tong Che (\u9ad8 \u8f49\u7b52\u8eca, a chain conveyor cylinder wheel), and Shui Zhuan Gao Che (\u6c34\u8f49\u9ad8\u8eca, a water-driven chain conveyor water lifting device). Each of these devices is a Type I mechanism with a clear structure and is described below: Lu Lu (\u8f46\u8f64, a pulley block) is used for lifting well water as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002298_s1526-6125(05)70080-3-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002298_s1526-6125(05)70080-3-Figure1-1.png", "caption": "Figure 1 Schematic of LENS\u2122 Process", "texts": [ " A simple relation between these build parameters and deposition is developed, using experimental results to determine empirical constants. Experimental results suggest that deposition can be related to the product of mass flow rate and energy per unit area through a power relationship, and could prove useful in estimating an appropriate layer thickness. Keywords: Laser Engineered Net Shaping, Rapid Prototyping, Freeform Fabrication, Titanium, Design of Experiments Laser Engineered Net Shaping (LENS\u2122) is a rapid prototyping process that builds metal prototypes from CAD data by layered deposition. Figure 1 shows the schematic of the LENS\u2122 equipment, illustrating how parts are built. Griffith et al. (2000), Arcella and Froes (2000), and Froes (2000) provide excellent overviews of the process, discussing a variety of materials that have been used, and Steen (2003) has written a useful review article on processing materials with lasers. Three-dimensional objects are represented using the stereolithography\u2014STL\u2014file format, which has become the de facto standard for rapid prototyping (Huang, Zhang, and Han 2003)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002145_iros.2000.895302-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002145_iros.2000.895302-Figure9-1.png", "caption": "Fig. 9 Prototype of the Float differntial toruqe sensor", "texts": [ " The wire drawn out from its winding pulley is hooked around the other pulley that is rotation free. This pulley is pulled by the spring for applying the tension on the wire. And the compressive force of coil spring, which is accumulated by turning the worm gear, has been applied on pulley by the link in this tensioner unit. 3 3 Float differential torque sensor It is useful to obtain torque information, which works in each axis in order to realize the advanced and three-dimensional motion control. As a torque sensor, \"Float differential torque sensor\" shown in Fig.9 is introduced. It is easy to maintain this sensor and the additional equipment. The motor is supported rotation freely from the base by ball bearings, and it is connected by the hard spring between the motor and base. By measuring the strain gauge mounted on this spring, the reaction torque of the motor is detected. Generally the strain gauge is applied to the output itself in order to measure the torque of the actuator. However this sensor has high reliability and generality, because it removes the wiring of collector ring or strain gauge from the output, which infinity rotates[4]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure10-1.png", "caption": "Fig. 10. Tooth surface with a superimposed marking compound surface (black solid line).", "texts": [ " The marking compound surface is denoted by C\u03022\u00f0u2;v2; c2\u00de and the position vector s\u03022\u00f0u2;v2; c2\u00de of a generic point on it is defined as follows: s\u03022\u00f0u2;v2; c2\u00de \u00bc s2\u00f0u2;v2\u00de \u00fe h\u00f0u2;v2; c2\u00den2\u00f0u2; v2\u00de; \u00f027\u00de where h\u00f0u2;v2; c2\u00de is a scalar function defined on the u2v2-plane and n2\u00f0u2;v2\u00de is the unit normal vector to s2\u00f0u2; v2\u00de. The function h\u00f0u2; v2; c2\u00de defines the shape of the marking compound surface and its parameters are contained in the vector c2. An example of marking compound shape is presented in (31). A graphical representation of a sample marking compound surface over the gear tooth is depicted in Fig. 10. The surface C\u03022, expressed in the fixed space E3 f , is denoted by C\u0302f 2 and its position vector is denoted by s\u0302f 2\u00f0u2;v2;u2\u00de, as in (15). For a given meshing condition we estimate the instantaneous contact area as the intersection curve between eC1 and C\u03022. We fix the mating members to be rotated by u1 and u2\u00f0 u1\u00de (see Eq. (26)) and we approximate the instantaneous contact area through solving the following non-linear system: sf 1\u00f0u1;v1; u1\u00de \u00bc s\u0302f 2\u00f0u2; v2; u2\u00f0 u1\u00de\u00de: \u00f028\u00de Closed form solution of (28) is not known and hence it must be calculated point-wise" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001662_s0094-114x(01)00082-9-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001662_s0094-114x(01)00082-9-Figure11-1.png", "caption": "Fig. 11. Bearing contact of a straight beveloid gear pair with parallel axes.", "texts": [ " It is reasonable to find the ratio a=b approaches to a limited value when the cone angles tend to zero, which represents that a crossed axes helical gear pair is in point contact. Fig. 7(c) illustrates a straight beveloid gear pair mounted with the parallel axes. The pinion and gear are identical to those in Example 1 (cf. Section 5.1). However, the gear is now turned over to allow the heel of the gear to engage with the toe of the pinion. Thus, the axes of pinion and gear are now parallel. Cases 7\u20139 simulate the meshing of the gear pair under the following assembly conditions: Fig. 11 illustrates the bearing contacts of the gear pair on the pinion surface under three assembly conditions. Meanwhile, the TCA results and TEs are listed in Table 4. Under the ideal assembly condition (case 7) or with a mounting position deviation without an axial misalignment (case 8), similar to a spur or helical gear pair mounted with parallel axes, the bearing contact is a line contact and the TEs equal zero. However, when an axial misalignment occurs (case 9), the bearing contact becomes an edge contact and the TEs are induced as shown in Table 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001897_ip-epa:20030365-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001897_ip-epa:20030365-Figure3-1.png", "caption": "Fig. 3 Axial rotor geometry of test machine centres of bearing magnets J centres of position sensors - magnetic forces acting on rotor ) reaction of magnetic bearings", "texts": [ " The test motor was equipped with radial magnetic bearings to measure the forces and to generate the eccentric motions of the rotor. Only the radial bearings were installed, because the electrical machine itself acts as an axial bearing. The radial bearings were ordinary eight-pole heteropolar bearings with bias-current linearisation. Magnetic-bearing operation and the parameters of this particular bearing type are listed by Lantto [15]. The calibration of the active magnetic bearings and the measurements were done following the procedure presented in [6]. The axial rotor geometry of the test motor is shown in Fig. 3. To get the pure conical motion in the measurement, one extra calibration was done. The trajectory of the rotor was determined in such a way that the total force acting on the rotor was zero (i.e. F1\u00bc F2). Then, the centre point of the rotor is concentric and the conical motion causes only the moment acting on the centre point of the rotor. The measured total force F acting on the rotor during the eccentric motion and the moment M acting at its centre are measured through the forces F1 and F2 acting on the magnetic bearings, using the basic laws of mechanical 564 IEE Proc" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002796_ichr.2007.4813872-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002796_ichr.2007.4813872-Figure2-1.png", "caption": "Fig. 2. Model of a bipedal robot.", "texts": [ " The equation of motion of the bipedal robot is written as follows: zG(t)\u2212 zZ z\u0308G(t) + g x\u0308G(t)\u2212 xG(t) = \u2212xZ(t), (1) zG(t)\u2212 zZ z\u0308G(t) + g y\u0308G(t)\u2212 yG(t) = \u2212yZ(t), (2) z\u0308G(t) = fz(t) M \u2212 g. (3) where t is time, pZ = [xZ(t) yZ(t) zZ ]T is ZMP [8], g is the acceleration of the gravity, pG = [xG(t) yG(t) zG(t)]T is COG, and fz(t) is the ground reaction force. This equation is an approximation which is valid when the influence of the change in angular momentum is small compared with the influence of the motion of COG. The model is shown as Fig. 2. Because the ground is not usually pulling the robot, fz(t) \u2265 0. (4) Because the ZMP xZ(t), yZ(t) corresponds with the center of the ground reaction force, it should be in the support region. This requirements gives the next force condition pZ \u2208 S(t). (5) Where S(t) is a convex region on the ground z = zZ . It is determined from the points of contact of the robot\u2019s feet (or other limbs) with the ground. To derive the solution of Eq.(1),(2), previous studies assumed the height of COG was constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002411_ac00250a047-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002411_ac00250a047-Figure5-1.png", "caption": "Figure 5. Robotic work statiion (top view): (Bl-B6) beaker positions, (BU1 and BU2) buffer positions, (EB) electronic balance, (Hl-H4) end-effector assemblies holding pH electrode and liquid handling tips, (I) interface containing optically Isolated relays,, (M) microcomputer, (MS) mixing station, (P/B) pipet/buret, (PM) pH meter, (R) robot, (V) dispenser valve.", "texts": [ " pH determinations are made with a digital ionalyzer (Mode 601A, Orion Research Inc., Cambridge, MA) with a glass pH electrode (Model 91-04, Orion). The pH meter outputs data in a binary-coded decimal format. This information is ANALYTICAL CHEMISTRY, VOL. 54, NO. 13, NOVEMBER 1982 2349 I r-- p H 3 w H 4 transferred to the microcomputer via 14 parallel 1/0 lines in. terfaced by using the same interface card that reads the electronic balance (Model AIO, SSM Microcomputer Products). Work Station. Figure 5 shows how the devices described above are arranged about the robot within its work envelope. Since the robot cannot see or otherwise perceive its environment, objects within the work envelope must be located at predefined positions. The pH electrode, pipet/biuret tip, and dispenser tip are located by specially fabricated end-effector assemblies shown in Figure 6. These assemblies are composed of a locator block which encase$! the electrode or tip and a U-shaped holder. The block is made of stainless steel and has sufficient mass to resist tilting caused by tubes or wires attached to the device mounted in the block", " Positions BU1 and BU2 are also marked for two 50-mL beakers containing buffers used to calibrate the pH meter. Software. The softwaire routines which drive the RSPS are written entirely in Applesoft BASIC. These routines enable the robot to calibrate the pH meter and perform an entire pH titration. Table I shows the steps performed by the RSPS in calibrating the pH meter. The RSPS assumes that approximately 20 mL of each buffer and a magnetic stirring bar have been placed in 50-mL beakers at positions BU1 and BU2, shown in Figure 5, and that the robot has been initially parked in its calibration position. Table I1 details the steps required to perform an entire pH titration. The sequence of events begins with a dialogue in which the user inputs the name of the standard, its formula weight, and a target molarity for a stock solution. The computer then requests the volume and molarity of standard that in to be achieved by a The microcomputer is involved in each step. It is not essential to turn the calibrate or temperature knobs to force the meter reading to agree with the known buffer pH. The pH calibration could be performed mathematically once the standard buffers have been measured. The ability to turn the knobs, however, demonstrates the dexterity of the robot. dilution of the stock solution. The microcomputer also requests the name and molarity of the stock titrant and the volume and molarity of titrant desired from a dilution of the stock. The RSPS assumes that the user has set up the work station as shown in Figure 5 where position B1 is occupied by a 30-mL beaker approximately half full of dried standard, positions B3, B5, and B6 are occupied by 50-mL beakers containing only a magnetic stirring bar, position B4 contains a 50-mL beaker approximately half full of stock titrant, holder H1 contains the pH electrode, holder H3 contains the pipet/buret tip, holder H4 contains the solvent dispenser tip, a 200-mL beaker containing rinse water is positioned below the pipet/buret tip at H3, and the robot is initially parked in its calibration position", "9999, indicating excellent linearity. The entire contents of the pipet were discharged when the pipet was used as a transfer pipet. Repetitive volume transfers in the range of 0.5-5 mL indicate a delivery precision of fS(O2)g \u00bc fR(O1,uz4 )g. Hence, the mobility of this 6R overconstrained chain is continuous with one d.o.f. The motion between link 3 and link 7 is the rotation about axis (O1,uz4 ) and is directly realized by adding the D revolute pair as shown in Fig. 3. In this hybrid 7R form, if any one among the 7R pairs is locked, the resulting mechanism has one d.o.f. and always has two distinct regular generators of spherical motions without superfluous passive motion. For instance, a generalized double-Hooke0s 6R chain endowed with one d.o.f. for any locked pose of the removed revolute D pair occurs. As a consequence, there is a total of two global or finite d.o.f. in this kind of 7R chain. In Fig. 4, a hybrid spherical\u2013spherical 7R DM mechanism has the same geometrical arrangement of joint axes as that of Fig. 3. The mechanical bond fL(7,4)g between link 7 and link 4 is the intersection set of two displacement subsets fG1g and fG2g {G1} \u00bc {R(O1,uZ1 )}{R(O2,uZ2 )}{R(O1,uZ3 )} {R(O2,uZ4 )} and {G2} \u00bc {R(O2,uZ7 )}{R(O2,uZ6 )}{R(O1,uZ5 )} Hence, from the group theory and set equation (1), the motion of link 4 relative to link 7 is depicted by {L(7,4)} \u00bc {G1}> {G2} \u00bc {R(O1,uZ1 )}{R(O2,uZ2 )}{R(O1,uZ3 )} {R(O2,uZ4 )}> {R(O2,uZ7 )} {R(O2,uZ6 )}{R(O1,uZ5 )} This is the union set of two displacement onedimensional manifolds, which can readily be explained as follows", " On the basis of set theory notations, it can be written as {L(7,4)} $ {1=S(O1)}< {1=S(O2)} No sub-chain is a generator of another subgroup of displacements except the possible generation of the improper subgroup fDg by a sequence of six R pairs. Actually in the singular pose, fR(O1,uZ1 )gfR(O2,uZ2 )g fR(O1,uZ3 )gfR(O2,uZ4 )gfR(O1,uZ5 )gfR(O2,uZ6 )g = fDg. As a matter of fact a product of six one-dimensional subgroups cannot be six-dimensional if the linear span of the twists that represent allowed infinitesimal displacements is not six-dimensional. From the analysis of Fig. 3 mechanism, it is known that the vector space of twists is five-dimensional. Hence, locally in the singular pose, fL(7,4)g \u00bc 1/S(O1)g < f1/S(O2)g. The bond fL(7,4)g has a bifurcation towards two spherical working modes starting from the singular pose. However, any mechanism working in each of its two possible modes destroys the local linear dependency of the six R twists. After any working themechanism becomes a truly spatial 7R linkage, i.e. includes a generator of fDg and therefore the bond fL(7,4)g can become a one-dimensional manifold in fDg" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.5-1.png", "caption": "Fig. 7.5 A water lifting device (\u9db4\u98f2). a Original illustration (Ortai et al. 1965), b Structural sketch", "texts": [ " This device includes a scale link (member 1, KL), a hanging rope (member 2, KT1), and a scale rope with a hook (member 3, KT2). The scale link is connected to the hanging rope and the scale rope with thread joints JT. It is a Type I mechanism with a clear structure. Figure 7.4b shows the structural sketch. 142 7 Linkage Mechanisms 7.1.5 He Yin (\u9db4\u98f2, A Water Lifting Device) He Yin (\u9db4\u98f2, a water lifting device) is a device to draw water from a lower position to a higher level for irrigation as shown in Fig. 7.5a (Ortai et al. 1965). The device contains a long slot as a lever and a wooden stand as a fulcrum. The slot is made from bamboo or wood. At the end of the slot is Hu Dou (\u623d\u6597, a scoop). When the device is working, the scoop falls into the river to scoop water. Then the scoop is raised, the water in it flows through the slot into the farmland near the shore. It is a mechanism with two members and one joint, including a wooden stand as the frame (member 1, KF) and a long slot as the moving link (member 2, KL). The long slot is connected to the frame with a revolute joint JRz. It is a Type I mechanism with a clear structure. Figure 7.5b shows the structural sketch. 7.1.6 Jie Gao (\u6854\u69d4, A Shadoof, A Counterweight Lever) Jie Gao (\u6854\u69d4, a shadoof, a counterweight lever) is used to lift water from a well or river, also known as Diao Gan (\u540a\u6746), Ba Gan (\u62d4\u6746), Jia Dou (\u67b6\u6597), or Qiao (\u6a4b) as shown in Fig. 7.6a (Pan 1998). It is the earliest irrigating machine in ancient China and also a typical application of the principle of lever. Its structure includes a vertical stand and a lever arm. One end of the lever arm is attached to a connecting link, and the other end is tied with a heavy stone" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001403_0021-9673(96)84622-x-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001403_0021-9673(96)84622-x-Figure5-1.png", "caption": "Fig. 5. Drawing of (top) static and (bottom) rotating internal filtration modules: 1, fermentation medium; 2, membrane; 3, motor; 4, filtrate recovery. From Ref. [20].", "texts": [ " The major conclusion of these studies was that blocking of the membrane occurs to a lesser degree if the pore size is increased, i.e., if microfiltration instead of ultrafiltration membranes are utilized. However, microfiltration membranes with pore sizes of 0 .2/~m generally were not sufficient to provide a proper protection of the analytical system. In order to decrease this obviously problematic membrane fouling of internal filtration modules, a membrane device was constructed that can rotate at a speed of 0-6000 rpm (Fig. 5) [20]. The centrifugal force thus created removes fouling substances from the membrane surface and yields a constant filtrate flow. In the present application a filtrate flow of 1 ml/min was obtained at a rotation speed of 5000 rpm. A static variant, which is also depicted in Fig. 5, was sufficient for the monitoring of an alcoholic fermentation, whereas the (apparently more complex) lactic acid and polysaccharide fermentations studied required the rotating module for reliable sampling. At least one internal filtration unit is commercially available, it is the ABC module marketed by Advanced Biotechnology (MiJnchen, Germany). It consists of a unit supporting the tubular membrane, which can be made of a variety of polymeric and ceramic materials and can have a wide range of pore sizes" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003568_s00502-013-0133-5-Figure13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003568_s00502-013-0133-5-Figure13-1.png", "caption": "Fig. 13. Elmo motion controller mounted on PCB and connected to brushless motor inside the joint\u2014IHRT", "texts": [ " SimMechanics has a number of blocks of physical components, such as body, joint, constraint, coordinate system, actuator, sensor etc. The PID controller designed in this paper, is a generic control loop feedback mechanism which attempt to correct the error between a measured process variable and a desired set point by calculating and then outputting a corrective action that can adjust the process accordingly, based on three parameters (Fig. 12). Motion controllers used at Archie, includes digital servo drives and network motion controllers Fig. 13. The joints are synchronized in order to provide coordination movement for all robots\u2019 joints. Since each joint is basically connected to motion controller program via the proposed communication interface for an individual motion, the interface should provide appropriate setting ability for position and velocity profile of each joint in Archie. The problem with the Simmechanics toolbox was the lack of object collision, which is crucial for the simulation, as the normal and friction forces between the floor and the robot are keys for gait" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003019_3.44521-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003019_3.44521-Figure1-1.png", "caption": "Fig. 1 Helicopter carrying a hanging load.", "texts": [ " The control variables are the longitudinal and lateral inclinations of the rotor NFP relative to the fuselage, the collective pitch, and the tail rotor pitch. However, near hover, the yaw motion and the vertical motion are very nearly uncoupled from the longitudinal and the lateral motions. This results in a secondorder model for yaw motion with tail rotor pitch as control, a second-order model for vertical motion with main rotor collective pitch as control, and a twelfth order model for longitudinal and lateral motions with longitudinal and lateral cyclic pitch as controls. Figure 1 shows the coordinate system used to describe the motions of a helicopter carrying a hanging load. It is assumed that the load is carried by several cables attached to the helocopter at a point below its center of mass. The hanging load acts like a pendulum. Let: x,y,h - longitudinal, lateral, and vertical position deviations from the desired hover point Uy v, w = three components of linear velocity fS(O)g \u00bc fR(O,u)g. Hence, the mobility of this 6R chain is generally continuous with one d.o.f. of finite motion. This type of overconstrained mobility, which can be explained by the intersection of two displacement subgroups is said to be exceptional; see reference [13]. Furthermore, when the pair at D in Fig. 2 is also removed, the resulting kinematic chain with 6R has the same arrangement of joint axes as that of the aforementioned 6R exceptional chain. The infinitesimal, local, or instantaneous mobility still has one d.o.f. but generally finite relative motion cannot happen. The true d.o.f. is zero except for the special case of symmetrical arrangement of paradoxical chain of Bricard form. To sum up, the kinematic chain of Fig. 1 has two global d.o.f., which can readily be explained as follows. When any one pair among the seven revolute pairs is locked, the resulting mechanism has one d", " \u2018Regular\u2019 means without superfluous passive mobility in the generation of planar motion and spherical motion. If any one more revolute pair is locked, the chain becomes a stiff structure. Hence this chain has two finite d.o.f. in total. Modifying the pair linking without modifying the pair positions does not change the d.o.f. of infinitesimal motion. On the other hand, the finite mobility is quite different if the pair axes are maintained and if the links between the pair axes are modified. Referring to Fig. 2, the DM hybrid planar\u2013spherical 7R mechanism is an imbrication of two trivial kinematic chains. One chain is a planar chain made up of four parallel revolute pairs A, B, C, and D. The other one is a spherical chain with four revolute pairs G, F, E, and D, all axes of which intersect at point O. The planar kinematic chain A-B-C-D is associated to the displacement subgroup fG(u)g of planar gliding perpendicular to u. The spherical kinematic chain G-F-E-D is associated to the subgroup fS(O)g of spherical rotations about point O", " In addition, fG(u)g > fS(O)g \u00bc fR(O,u)g (or \u00bcfR(D,u)g). This rotation about the axis (O,u) is directly realized in the Z7 revolute pair. In this mechanism, either a planar 4R motion with one d.o.f., or a spherical 4R motion with one d.o.f. is obtained. Any planar working prohibits the spherical working and vice versa. Moreover, a truly spatial mode with one d.o.f. becomes allowed after any working in the planar mode or any working in the spherical mode. The following is a more detailed group-based explanation. In the chain loop of Fig. 2, two displacement subsets fG1g and fG2g are produced by the parallel setting of two serial chains between link 7 and link 5 {G1} \u00bc {R(A,u)}{R(G,uZ2 )}{R(B,u)}{R(F,uZ4 )} {R(C,u)} and {G2} \u00bc {R(D,u)}{R(E,uZ6 )} Then, based on group algebraic structure and the set closure equation (1), the mechanical bond fL(7, 5)g of relative motions of link 5 relative to link 7 will be the intersection set as {L(7,5)} \u00bc {G1}> {G2} \u00bc {R(A,u)}{R(G,uZ2 )}{R(B,u)}{R(F,uZ4 )} {R(C,u)}> {R(D,u)}{R(E,uZ6 )} Now three R pairs that have converging axes are locked and then these pairs will produce only the identical displacement; that is, fR(G,uZ2 )g \u00bc fEg, Proc" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure2-1.png", "caption": "Fig. 2. Coordinate transformation from Sc to Sm.", "texts": [ " The normals to the rack cutter generating surfaces are represented in coordinate system Sc as N\u00f0i\u00de c \u00f0u; l\u00de = Lca;bLag;bh\u00f0l\u00deN\u00f0i\u00de g;h\u00f0u\u00de; \u00f0i = 1;2\u00de \u00f07\u00de where Lca;b = cos\u03b1d sin\u03b1d 0 \u2213sin\u03b1d cos\u03b1d 0 0 0 1 2 4 3 5 \u00f08\u00de Lag;bh\u00f0l\u00de = cos\u03b4 0 sin\u03b4 0 1 0 \u2213sin\u03b4 0 cos\u03b4 2 4 3 5 \u00f09\u00de N\u00f0i\u00de g;h u\u00f0 \u00de = cos\u03bb \u2212sin\u03bb 0 2 4 3 5; \u00f0i = 1;2\u00de: \u00f010\u00de Here, angle \u03bb is determined as \u03bb=tan\u22121(2apf (i)(u\u2212u0)) and angle \u03b4 is determined as \u03b4=tan\u22121(2ald (i)(l\u2212 l0)). Eqs. (7)\u2013(10) yield N\u00f0i\u00de c \u00f0u; l\u00de = cos\u03b4 cos\u03bb cos\u03b1d\u2213 sin\u03bb sin\u03b1d\u00f0 \u00de \u2212cos\u03bb sin\u03b1d\u2212 sin\u03bb cos\u03b1d sin\u03b4 sin\u03bb sin\u03b1d\u2212 cos\u03bb cos\u03b1d\u00f0 \u00de 2 4 3 5; i = 1;2\u00f0 \u00de: \u00f011\u00de where the upper and lower signs correspond to the left (\u03a31) and right (\u03a32) profiles of the rack cutter. 2.2. Applied coordinate systems In order to consider generation of a helical gear, coordinate transformation from Sc to Sm, according to Fig. 2, is applied. Angle \u03b2 represents the helix angle of the helical gear. The rack cutter generating surfaces and the normals are represented in coordinate system Sm as rm u; l\u00f0 \u00de = Mmcrc u; l\u00f0 \u00de; \u00f012\u00de Nm\u00f0u; l\u00de = LmcNc\u00f0u; l\u00de \u00f013\u00de where Mmc = cos\u03b2 0 sin\u03b2 0 0 1 0 0 \u2212sin\u03b2 0 cos\u03b2 0 0 0 0 1 2 664 3 775; \u00f014\u00de Lmc = cos\u03b2 0 sin\u03b2 0 1 0 \u2212sin\u03b2 0 cos\u03b2 2 4 3 5: \u00f015\u00de Fig. 3 shows the initial and current positions of the generating rack cutter and the to-be-generated helical gear. By using the geometry of the rack cutter previously represented, the to-be-generated helical gear will incorporate the desired corrections to the gear tooth surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002816_bit.260220514-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002816_bit.260220514-Figure7-1.png", "caption": "Fig. 7. Calibration curve for choline chloride.", "texts": [ "0), and glycine buffer (pH 10.0). The results are shown in Figure 6. The rate of DO consumption was found to be significantly af- AMPEROMETRIC DETERMINATION OF CHOLINE 1079 fected by the buffer concentration and the type of buffer. Tris-HC1 buffer lOmM, (pH 8.0) was used in subsequent studies. The assay procedure was carried out by the method described in the Materials and Methods section. A calibration curve was prepared using 20 p1 choline chloride as a standard solution (1- 10mM). The results are shown in Figure 7. A linear relationship was observed at choline concentrations below 0.lmM. Therefore, a sample solution containing choline above 0 . lmM must be diluted with buffer. The reproducibility of the response was examined using the same samples (0.2mM). The response was reproducible within +2.3% of the relative error when a medium containing 0.2mM choline chloride solution was used. The standard deviation was 4.6pM in 100 experiments. The long-time stability of the immobilized enzyme and the choline electrode was examined" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.1-1.png", "caption": "Fig. 7.1 Pestle devices. a A tap pestle (\u8e0f\u7893) (Pan 1998), b A trough pestle (\u69fd\u7893) (Wang 1991), c Structural sketch, d Atlas of feasible designs, e Imitation of original illustration (Yan and Hsiao 2010)", "texts": [ "1 Ta Dui (\u8e0f\u7893, A Foot-Operated Pestle), Cao Dui (\u69fd\u7893, A Water-Driven Pestle) Pestle devices such as Ta Dui (\u8e0f\u7893) and Cao Dui (\u69fd\u7893), that pound grains by a hammer and remove the husks from rice or wheat, have been widely applied since the Han Dynasty (206 BC\u2013AD 220) (Zhang et al. 2004). The operating method of the devices is similar to a hand-operated mortar with a pestle. The effect of the device depends on the mass of its hammer head and also on the speed at which the hammer head hits the grains. Through the function of levers, pestle devices not only save effort but can also be easily operated at work. Ta Dui (\u8e0f\u7893, a foot-operated pestle\u2019a tap pestle) consists of a wooden frame, a stone hammer head, and a wooden handle as shown in Fig. 7.1a (Pan 1998). The stone hammer head is connected to the wooden handle as an assembly namely the tilted hammer. The tilted hammer along with the wooden frame as the fulcrum constitutes a lever. During operation, the operator taps the end of the tilted hammer\u2019s handle by his foot. The function of lever helps the hammer\u2019s head reach the required speed and momentum (the product of the mass and the speed of the hammer head) when falling down. Cao Dui (\u69fd\u7893, a water-driven pestle\u2019a trough pestle), as shown in Fig. 7.1b (Wang 1991), has a similar structure as Ta Dui except that it includes a waterscooping container at the end of its tilted hammer. The device is usually installed near water. When it draws water from upstream into the container, the water\u2019s weight presses down one end of the tilted hammer and causes the other end of the hammer head to rise. Then the container rotates, the water inside goes out, and the hammer head falls down to pestle the grains since the weight of the hammer head is over the empty container again. Although Ta Dui and Cao Dui have different power sources, they have the same structural characteristics. Both of them are a linkage mechanism with two members and one joint. They both have a wooden frame (member 1, KF) and a tilted hammer as the moving link (member 2, KL). The tilted hammer is connected to the frame with an uncertain joint J\u03b1. They are Type II mechanisms with uncertain types of joints. Figure 7.1c shows its structural sketch. Considering the types and the directions of motion of the tilted hammer, J\u03b1 has three possible types: the tilted hammer rotates about the x-axis, denoted as JRx, as shown in Fig. 7.1d1; the tilted hammer not only rotates about the x-axis but also translates along the x-axis, denoted as JPxRx , as shown in Fig. 7.1d2; and the tilted hammer not only rotates about the x and y axes, but also translates along the x and z axes, denoted as JPxzRxy, as shown in Fig. 7.1d3. The translation along the x-axis or z-axis is to enable them to more easily pestle grain from the corresponding direction. Figure 7.1e shows an imitation of the original illustration of a foot-operated pestle in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b. 138 7 Linkage Mechanisms 7.1 Levers 139 7.1.2 Si (\u9401, A Grass Cutting Device), Sang Jia (\u6851\u593e, A Mulberry Cutting Device) Si (\u9401, a grass cutting device) and Sang Jia (\u6851\u593e, a mulberry cutting device) are both cutting devices for processing forage as shown in Fig. 7.2a, b (Wang 1991). Si is used to cut grass to feed cows, and Sang Jia cuts mulberry to raise silk worms. Their components are similar and include a knife made from wrought iron and a wooden base" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003602_telfor.2013.6716373-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003602_telfor.2013.6716373-Figure2-1.png", "caption": "Fig. 2. Servomotors used for the robots.", "texts": [ " Aurel Gontean is with Applied Electronics Department, Faculty of Electronics and Telecommunications, \u201cPolitehnica\u201d University of Timisoara, Rom\u00e2nia, V. P\u00e2rvan Av., no. 2, 300223, Timisoara, Rom\u00e2nia (e-mail: aurel.gontean@etc.upt.ro). We can see that it has 4 DOF (degrees of freedom) and is the version with 5 + 1 motors. The last motor is for rotating the gripper. Each motor can be named to show the function for what is meant. The first motor is the base, the second is the shoulder, the third is the elbow, the fourth it he wrist, the fifth is the gripper and we can have a wrist rotate additional motor too. On Fig. 2. we can see the servomotors. The first picture is the HS-422 servomotor and the second picture is an inside look of the servomotor. As we can see we have a gear set and an electronic board. The servomotor can\u2019t rotate 360\u00ba, because it\u2019s mechanically stopped at 180\u00ba. The servomotors have 3 wires, one red (5V), one black (GND) and one yellow (PWM signal). Actually the position of the motor is set by the ATmega168 microcontroller from the SSC-32 servo control board which sends a PWM signal through the yellow cable to the motor" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003131_s12206-009-0623-x-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003131_s12206-009-0623-x-Figure3-1.png", "caption": "Fig. 3. Contact area parameters.", "texts": [ " Considering the roughness of the tooth flank surfaces (hmin), the hydrodynamic force is assumed to be saturated when the distance between the flanks is positive but less than hmin [13]. The total hydrodynamic force must be calculated by summation when two pairs of teeth come into contact. A negative value of x& indicates a recession of the meshing gear teeth with each other, which does not contribute to the hydrodynamic force. The tooth surface radii of curvature p\u03c1 and g\u03c1 are expressed as ( tan ) ( tan ) p p p g g p r s s r s s \u03c1 \u03c6 \u03c1 \u03c6 = \u2212 + = + \u2212 (13) where \u03c6 is the pressure angle. In Fig. 3, the LOA is from A to B. L, P, and H are the lowest point of singletooth contact (LPSTC), the pitch point, and highest point of single-tooth contact (HPSTC), respectively, and s is the distance from the starting point (A) to the contact point (C) along the LOA. To synchronize the time-varying stiffness with the tooth meshing phase, the distance of the contact point (s) is expressed as a function of time (Fig. 4). As the magnitude of s varies periodically with the tooth mesh frequency mf , it can be Fourier-transformed and expressed as shown in Eq", " The direct contact Coulomb friction force Fef is expressed as ef enF F\u00b5= . (17) The friction coefficient between the teeth in direct contact is assumed to be constant [4,5]. The hydrodynamic sliding friction force, Fhf, obtained by the half-Sommerfeld condition, is expressed as [11] 2 o s hf b u RF h \u03c0 \u03b7 = (18) where us is the sliding velocity of the mating gears expressed as s p gu u u= \u2212 . (19) The moment arms of the friction forces Fef and Fhf acting along the OLOA direction continue to change as meshing progresses (Fig. 3). The moments of the friction forces acting on the pinion and gear are 1 2 1 1 2 22 22 2 1 2 ( sin ) ( sin ) ( sin ) ( sin ) , , ( ) 2 , ( ) 2 ( ) , ( ) efp ef fp cp hfp hf fp cp efg ef fg cg hfg hf fg cg p fp fcp fcp g fg fcg fcg cp p cg g T F r T F r T F r T F r where r arctg B C r arctg B C r B C r r B C r \u03b8 \u03b8 \u03b8 \u03b8 \u03c0\u03b8 \u03b8 \u03b8 \u03c0\u03b8 \u03b8 \u03b8 = = = = = \u2212 = = \u2212 = = + = + (20) where rcp and rcg are the distance from the center to the contact point of the pinion and gear, respectively. As the friction forces change direction at the pitch point (s = sp), the sign of the torque (Tefp and Tefg) caused by the direct contact friction force (Fef) should change when the contact point passes the pitch point during meshing" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002968_s0263574708004645-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002968_s0263574708004645-Figure6-1.png", "caption": "Fig. 6. The simplest walking model walking down a slope \u03b3 of 0.004 rad. The model is disturbed by random floor irregularities.", "texts": [ " Foot scuffing at mid stance is ignored so that the swing leg can swing from the rear to the front. The model has no control or actuation and it gains energy by walking down a slope of 0.004 rad. The model has two DoF, the stance leg can rotate with respect to the floor around its point foot and the swing leg can rotate around the hip. The two DoF of this second-order system results in a four-dimensional state space. We define the four state dimensions as the angle and angle rate for both the stance leg and the swing leg, [\u03c6st , \u03c6\u0307st , \u03c6sw, \u03c6\u0307sw] (Fig. 6). It has been shown that the simplest walking model can walk in a stable cycle on a flat surface and can overcome small disturbances.5 The largest single step-down it can overcome has a height difference of 0.13% of its leg length. A higher step-down will result in a state at which the deviation of the nominal trajectory becomes larger every step and finally results in a fall. In this study we use floor irregularities as disturbance source. Floor irregularities are the most common disturbances for walking robots" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003718_s12008-012-0163-y-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003718_s12008-012-0163-y-Figure5-1.png", "caption": "Fig. 5 Simulation of the generating gear meshing with the workpiece", "texts": [ " The machine tool kinematic motions shown in Fig. 4 are not really used to generate face-milled spiral bevel gears. The swivel angle, the tilt angle and the tool rotation angle are set to zero. Nevertheless, all of them are implemented in the tooth flank generation algorithm. The present work is illustrated with an example of spiral bevel gear manufactured with the face-milling method. The machine tool architecture enables recreating the meshing motion between the workpiece and an imaginary generating gear as shown in Fig. 5. The tool materializes a gear tooth and thus follows the same trajectory. It turns around the cradle axis which is that of the gear. So, the cradle motion depends on the workpiece rotation. The generation of face-milled spiral bevel gears requires a relation linking the cradle to the workpiece rotation angle. A roll ratio is applied between the cradle and workpiece angles. Its function is changed and extended with the modified roll method. The tooth flank topographies are thus changed. The Eq. (3) gives the representation of the cradle angle in terms of the workpiece angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003176_17452759.2011.613597-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003176_17452759.2011.613597-Figure5-1.png", "caption": "Figure 5. Pin shackle assay a) sketch b) in universal testing machine.", "texts": [ " The tensile test consists of loading the snap hook with an axial force (Figure 4a) and evaluating the behaviour of the pieces made with each process. Axial force is the natural strain of the snap hook part. In this assay the sealing of the snap hooks is deleted because it does not have any effect on tensile strength because the objective of sealing is to ensure closure. The snap hook assay involved a clamp fixture spindle with two stainless steel U-bolts (Figure 4b) which were changed after each experiment. A pin shackle compression test (Figure 5a) was used to analyse the behaviour of pin shackles manufactured with a forming (forging) process compared to the behaviour of the same part manufactured using an SLM process. In the pin shackle the axle that assures the closure of the element was deleted and then replaced by two pins that compressed the pin shackle (Figure 5b). The two pins were used in both experiments together with a clamp spindle. Compression to which the pin shackles are exposed may cause a bending stress in the part meaning that the compression, tension and neutral zones appear in the same section of the part (Figure 6). In this assay, non natural strain was applied to the pin shackle to study the behaviour of the part. However, both behaviours were compared because the same configuration was used. A compression assay was used to analyse the difference between compression resistance behaviour of wheel supports produced through a forming (stamping and bending) process and an SLM process" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001348_s0167-6105(97)00299-7-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001348_s0167-6105(97)00299-7-Figure1-1.png", "caption": "Fig. 1. Cricket ball situated in a free stream.", "texts": [ " The current paper describes experiments carried out to determine by direct measurement the aerodynamic forces of both stationary and spinning cricket balls for different orientations of the seam to the free stream for a wide range of seam angles. Some tests were also performed on an artificially roughened ball. The results are presented as lift, drag and side forces on the ball which may be non-dimensionalised by dividing by mg or 0.5op\u00ba2d2/4 and are analysed in terms of boundary layer theory and Magnus effect. Fig. 1 shows a cricket ball moving through air with a relative velocity \u00ba perpendicular to the yz plane. The resultant force acting on it can be resolved into three mutually perpendicular forces, namely the drag force D, the lift force \u00b8 and the side force S, acting in the directions x, y, z, respectively. Whether or not all three component forces are present at any particular time depends upon the seam angle and any spin which may be imparted to the ball. For a given air velocity, the angle of the seam plane from the vertical xy plane is defined in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002335_1.2406088-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002335_1.2406088-Figure3-1.png", "caption": "Fig. 3 Geometrical paramete", "texts": [ "org/about-asme/terms-of-use f fl n w s q fi a p c u t w s t a e d g M t fi i u fi 1 Downloaded Fr reedom vector associated with the shaft jth cross section The displacement at any potential point of contact Mij on the anks of the pinion teeth in the direction of n1, unit outward ormal to the flanks, is deduced as 1 Mij = u1j O1j + 1j O1jMij . n1 = V1 Mij Tq1j 3 here V1 Mij T= cos b sin t , cos b cos t , sin b ,\u2212sin b Rb1 in t\u2212x1j cos t , \u2212sin b Rb1 cos t+x1j sin t , Rb1 cos b ; 1j T = v1j ,w1j ,u1j , 1j , 1j , 1j R1 ; and R1 S 1 ,T 1 ,Z is the frame xed to the pinion-gear center line Fig. 3 ; b is the base helix ngle; t the apparent pressure angle; Rb1 the base radius of the inion; and x1j represents the coordinate of a potential point of ontact Mij as described in Fig. 3. All the auxiliary degrees of freedom in q1j are condensed by sing the shape functions of the two-node shaft element and 1 Mij is finally expressed in terms of the three translations and hree rotations at the two nodes of the shaft element vector X1 as 1 Mij = V1 Mij T P1 O1j X1 4 ith P1 O1j , the shape function matrix expressed in O1j Displacements 1 Mij are then imposed at the free ends of the pring elements on the pinion side in Fig. 1 which materialize ooth structural stiffness and contribute to the mesh strain energy s developed in Eq", " 5 \u2013 7 , the displacement at any potential point of contact on the flanks of the gear teeth in the direction n2, unit outward normal, can be written in terms of the FE modal unknowns q and a structure vector V2 Mij depending on the position vectors MpijMij as 2 Mij = V2 Mij T Q Mij N N1 . . . N N8 q 8 where V2 Mij T= \u2212cos b cos ,\u2212cos b sin ,\u2212sin b , sin b T1T2\u2212x2j cos \u2212Rb2 sin +yMpij ,\u2212sin b T1T2\u2212x2j sin +Rb2 cos +xMpij , cos b Rb2\u2212yMpij sin +xMpij cos ; xMpij , yMpij are the coordinates of the point Mpij in the frame R2 S 2 ,T 2 ,Z fixed to the gear; = t+ and is the time-varying angle between R1 and R2 such that \u0307 is the gear angular velocity Fig. 3 ; Q Mij is the shape function matrix expressed in Mij Dhatt et al. 18 ; and N N contains the lines of the matrix N corresponding to the three degrees of freedom at node N , i.e., the eight nodes surrounding Mpij. The other geometrical parameters are defined in Fig. 3. 2.4 Equations of Motion. Considering N t tooth pairs in \u201efor clarity, damping is not shown and only ion contact with the ith tooth or the ith foundation discretized into Transactions of the ASME x?url=/data/journals/jmdedb/27842/ on 05/03/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use n = m w b t t d t s m p o e g t F 5 p J Downloaded Fr i t slices and denoting dk Mij , the displacement of solid k k 1 corresponds to the pinion, k=2 to the gear , the instantaneous esh strain energy reads Um = 1 2 k=1 2 i=1 N t j=1 ni t Kk Mij dk Mij \u2212 k Mij 2 + Gk Mij dk Mij 2 + Dk Mij 2dk Mij 2 2 + 1 2 i=1 N t j=1 ni t kc Mij d1 Mij \u2212 d2 Mij \u2212 e Mij 2 9 here Kk Mij , Gk Mij , and Dk Mij are the direct, shearing, and ending stiffness coefficients per unit of length at the jth cell of he ith foundation of solid k" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003142_s11740-009-0168-y-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003142_s11740-009-0168-y-Figure4-1.png", "caption": "Fig. 4 Measuring principle of the no-load torque of ball screws", "texts": [ " For the preloaded ball screw nut, the no-load torque is directly dependent on the preloading. The no-load torque can be determined with the formula [5]: Tp0 \u00bc K Fa0 l 2p 0:014 Fao ffiffiffiffiffiffiffiffiffiffi dm l p Ncm\u00f0 \u00de \u00f02\u00de Tp0 no-load torque l Lead (cm) b Lead angle (deg.) dm Ball pitch circle diameter (cm) Fa0 Preload (N) K Torque coefficient of ball screw K \u00bc 0:05ffiffiffiffiffiffiffiffiffiffi tan b p The preloading of the ball screw nut is according to formula 2 directly proportional to the no-load torque of the ball screw nut. Figure 4 shows the test set-up for the measurement of the no-load torque of the ball screw nut on the test stand. A beam with an adapted wheel and strain gauges is mounted on the ball screw nut. The strain gauges identify the torque which is necessary to break the friction caused by the preloading during rotation of the spindle. The spindle is rotated with a rotational speed of 100 rpm. The no-load torque was measured during a feed of 600 mm. Figure 5 shows the measured no-load torques of the ball screw nuts in new state and after a mileage of 2,000 km using the additived and nonadditived oils" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002166_bf02460303-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002166_bf02460303-Figure4-1.png", "caption": "Figure 4. The angle ~ between the translational velocity V and the rotational velocity co affects the handedness of the helix and the direction of the axis of the helix K. (a) tp<~/2: ~o is parallel to K, and the helix is right-handed. (b) ~>1r/2: co is antiparallel to K, and the helix is left-handed. (c) ~ = =/2: the trajectory is a circle. (d)", "texts": [ " There is an exception to this rule. Define 0 as the angle between V b and co b . If V b changes direction such that 0 changes from an angle less than to one greater than To/2, or vice versa, then K changes from parallel (or antiparallel) to co to antiparallel (or parallel) to co with a concomitant change in the handedness of the helix (Crenshaw, 1993a). Consider an organism that moves such that < re/2. This organism moves along a right-hand helix for which co is parallel to handedness, and K reverses direction (Fig. 4b). Note that if ~ = ~z/2 then the = 0: the trajectory is a straight line with co parallel to the direction of motion. (If = re, the trajectory is a straight line with co antiparallel to the direction of motion.) trajectory is a circle (Fig. 4c), and if 0 = 0 or rc then the trajectory is a line (Fig. 4d). Motion in which V b changes direction can also be simulated with the program presented in Appendix B. Now, {J'Jb is constant. Figure 5a presents a trajectory for which the direction ofV b changes at three discrete points (marked by dots). The changes in the direction o f V b a r e visible as kinks in the trajectory, demonstrating how the assumption of smoothness in the previous section has been violated. Nevertheless, as expected, the axes of the helical trajectories between the kinks are all straight and parallel" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002887_1.5057008-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002887_1.5057008-Figure9-1.png", "caption": "Figure 9: HPT stage 1 Liner with mesh structure manufactured by LMD [9]", "texts": [ " [2] Geometric features on the surface of a BR715 HPT case of Nickel base Nimonic PE16, with a Nickel base In 625 powder additive for bosses, brackets, and flanges, are repaired locally with just one layer deposited (fig. 6). Because of the minimal heat input from the LMD process, distortion of the component is nearly completely avoided. The contamination (oxidation) free LMD result is guaranteed by local gas shielding using the newly developed powder nozzles. [2] Page 209 of 1009PICALO 2008 Conference Proceedings On aero engine HPT parts such as NGVs (fig. 7) made of Nickel base Mar-M 002 and Liner 1 parts made of single crystal Nickel base CMSX-4 (fig. 9) mesh structures made of In 625 are applied by LMD. These mesh structures are increasing the bond and shear strength of the Mg Spinell Thermal Barrier Coating (TBC) which is applied by Atmospheric Plasma Spraying (APS) afterwards (fig. 8). Hence, a bond coat between substrate and TBC is no longer required. [9] Using new cw Ytterbium fiber Laser radiation with a wavelength of \u03bb = 1080 nm, a Laser beam diameter of dL = 280 \u00b5m and a max. Laser power of 200 W enables to achieve the specified track width of approx" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001375_1.2834123-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001375_1.2834123-Figure8-1.png", "caption": "Fig. 8 Modes of carriage for main peaks", "texts": [ " We presumed that the main peaks may be caused by the natural vibrations of the can'iages of the LGT recirculating linear ball bearings. To examine the relationship between the main peak and the mode of the carriage, an experi mental modal analysis was performed by using the mode mea suring system as shown in Fig. 7. In the modal analysis, the modes of the carriages of the test linear bearings were examined by using two accelerometers and a digital spectrum analyzer as the test linear bearing was driven at a certain linear velocity. Figure 8 (a and b) shows the modes of main peaks. In this figure, for convenience, the upper face and the side face of the carriage are indicated separately. The shaded faces show the reference faces and the blank faces show the measured mode shape. Clearly, the modes of the main peaks correspond to the modes of the rigid-body natural vibration of the carriage. In addition, the measured modes can be divided into the rolling mode, the pitching mode, and vertical mode. 4.3 Relationship Between Main Peali and Natural Vi bration of Carriage 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002667_s1560354707020037-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002667_s1560354707020037-Figure1-1.png", "caption": "Fig. 1.", "texts": [ " Eliminating N , we come to a system that is separated from the equations for v\u0307: I\u03c9\u0307 + mr \u00d7 (\u03c9\u0307 \u00d7 r) = ( I\u03c9 + mr \u00d7 (\u03c9 \u00d7 r) ) \u00d7 \u03c9 \u2212 mr \u00d7 (\u03c9 \u00d7 r\u0307) + \u03bbn + MQ. (6) Here MQ = MF + F \u00d7 r is the torque of the external forces with respect to the contact point, and r = \u2212bn. In order to obtain a closed system, we construct the kinematic equation describing the evolution of n. First note that the velocities of the points representing the contact point on the movable and the stationary surfaces are equal. This condition can be written as follows: r\u0307 = y\u0307 + \u03c9 \u00d7 y. (7) Here y is the vector drawn from the center of the stationary sphere to the contact point (Fig. 1). We have y = an, where a is the radius of the stationary sphere. From (7) one easily obtains n\u0307 = kn \u00d7 \u03c9, k = a a + b . (8) REGULAR AND CHAOTIC DYNAMICS Vol. 12 No. 2 2007 If a, b < 0, we have the outer rolling as shown in Fig. 1. If a < 0, b > 0, |a| > b and k = |a| |a|\u2212b > 0, we have the inner rolling of the ball over the sphere (Fig. 2), and if a > 0, b < 0, a < |b|, k = \u2212 a |b|\u2212a < 0, we have the outer rolling of the sphere over the ball (Fig. 3). Put a = \u221e, k = 1 for the case of the ball rolling over the plane and b = \u221e, k = 0 for a planar rolling over the sphere. Differentiate the constraint (3), by virtue of (8) we obtain (\u03c9\u0307,n) = 0. Hence, using the constraint itself we get the relations I\u03c9 + mr \u00d7 (\u03c9 \u00d7 r) = I\u03c9 + mb2\u03c9, I\u03c9\u0307 + mr \u00d7 (\u03c9\u0307 \u00d7 r) = I\u03c9\u0307 + mb2\u03c9\u0307" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003477_1350650111431790-Figure13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003477_1350650111431790-Figure13-1.png", "caption": "Figure 13. Build-up of shear in the fluid film in the direction of rolling.4", "texts": [ " It should be noted that, in contrast to the fluid contribution, the slip produced by the elastic deformation of the rolling elements is completely independent of rolling speed and therefore only needs to be determined once for a given normal load and contact geometry. The curves representing fluid behaviour are then further transformed by calculating average shear values and shear rates by relating the tangential displacement of the walls given by slip to the central film thicknesses at UNIVERSITY OF WATERLOO on March 25, 2015pij.sagepub.comDownloaded from at UNIVERSITY OF WATERLOO on March 25, 2015pij.sagepub.comDownloaded from \u00bc s hc \u00bc b v 1 hc \u00bc SL b hc \u00f012\u00de _ \u00bc v hc \u00bc SL v hc \u00f013\u00de with v \u00bc v1 v2, v \u00bc v1 \u00fe v2 2 \u00f014\u00de SL \u00bc v1 v2 1 2 v1 \u00fe v2\u00f0 \u00de \u00bc v v \u00f015\u00de Figure 13 explains the meaning of these expressions. The central film thicknesses were calculated as shown before according to Hamrock17 using the pressure viscosity coefficients determined for 200MPa pressure. Additionally, the friction coefficients were transformed into mean shear stresses as explained earlier in this article. Subsequently, the average shear stresses were plotted against average shear strain (Figure 14) as well as against average shear rate (Figure 15). The purpose was to judge if the fluid is predominantly behaving elastic or viscous", " With increasing shear, respectively, shear stresses the slopes of the measured curves become less steep and the limiting values l are reached at larger shear values than with the formula. However, the formula is supposed to give the real relationship for the fluid which can be locally applied, whereas the measurements represent an averaged shear stress as a function of average shear in the contact. When defining as the shear in the middle of the contact, the minimum shear at the inlet will be 0 and the maximum shear at the outlet 2 , if one assumes constant film thickness and relative tangential velocity throughout the contact (Figure 13). Therefore, the limiting shear stresses will not be reached at all points of the contact area at the same time. If the assumption of a sensible contribution of elastic shear strain would hold true for the entire contact, infinitely high slip values would be required to reach the limiting stress at the inlet to the contact, as shear strain always starts from zero and increases during the passage of the contact. As a first approximation, one may integrate over the interval from 0 to 2 in order to obtain the corresponding , in rolling contact (Figure 18) \u00f0 \u00de \u00bc 1 2 Z2 0 \u00f0 \u00ded \u00f016\u00de In this way, one obtains modified Bair\u2013Winer curves for the rolling contact which match the measured values quite well, especially for 5 and 12m/s, (Figures 16, 17, 19 and 20), where shear stresses are plotted versus shear strain" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002736_j.jmatprotec.2008.03.065-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002736_j.jmatprotec.2008.03.065-Figure3-1.png", "caption": "Fig. 3 \u2013 The function of transmission error, 2, is a second order polynomial function in a cycle of meshing.", "texts": [ " To solve the above-mentioned problems, Livtin (1994) suggested applying a second order polynomial function of transmission error to absorb the linear one. His idea arose from the fact that the summation of a second order polynomial and a first order one is still a second order polynomial. By assigning the gear drive a pre-designed parabolic function of transmission error, the gear drive can become robust against inevitable random errors. The piecewise continuous motion curve is transformed into a globally continuous one; thus, the level of gear vibration and running noise can be reduced significantly. As shown in Fig. 3, the second order polynomial function is represented as follows: 2 = 4\u01312\u03b5 T2 \u2212 8\u0131\u03b5 T2 1 + 4\u03b5 T2 2 1 (4) Although the motion curve has become continuous, the curve of the slope of the motion curve is still discontinuous. The variation in the slope of the motion curve is still a source of gear vibration and noise. In order to reduce the level of running noise of a gear box, it is necessary to reduce the difference in slope of the motion curve at the tooth replacing point. The second order polynomial function also falls short in that it requires the further elimination of material near the tooth top and tooth bottom, which leads to a reduction in the bending strength" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure10-1.png", "caption": "Fig. 10 Graphical construction of the moving centrodes as Jer\u030ca\u0301bek\u2019s curves for W 5 0 with U 1 and U \u00a3 1", "texts": [ " The algebraic curves representing the moving centrodes of a centered slider-crank/rocker mechanism are also recognized and proven to be Jer\u030ca\u0301bek\u2019s curves for the first time. In fact, these curves have been studied and analyzed by Va\u0301clav Jer\u030ca\u0301bek (1845\u20131931) of the Czech Republic, as reported in Ref. [21]. The original graphical construction of a Jer\u030ca\u0301bek\u2019s curve is shown in Fig. 9 for the case of a closed curve, but we have also demonstrated that the same graphical construction is also true for the whole family of moving centrodes of centered slider-crank/rocker mechanisms. Thus, referring to Fig. 10 and taking into account the graphical construction of Fig. 9, the Jer\u030ca\u0301bek\u2019s curves for the centered mechanisms (W\u00bc 0) of types C (U< 1) and A (U> 1), along with the particular case of the Scott-Russell mechanism (U\u00bc 1) are obtained. This graphical construction is developed with respect to the moving frame f \u00f0X; x; y\u00de, which is attached to the coupler link BC, and considering the particular mechanism configuration, where the piston is at the upper dead point. Thus, circle a of center X\u00bc (0, 0) and a given radius, which coincides with the size of the segment O1 m1 of Fig", "org/about-asme/terms-of-use \u2022 Point W is joined with the particular point C; \u2022 A line orthogonal to the line joining C and W is traced up to intersect in the particular point S the line across points B and W; \u2022 Repeating the same graphical construction for other rays across the origin X\u00bcB, the whole Jer\u030ca\u0301bek\u2019s curve can be traced. The moving centrode or Jer\u030ca\u0301bek\u2019s curve is a closed or open curve, when the point C falls inside or outside the circle a, respectively, while a circle is obtained for the Scott-Russell mechanism, when C falls on the circle a, as shown in Fig. 10. The method of instantaneous invariants in instantaneous kinematics was invented by Oene Bottema (1901\u20131992) and further developments were made by his favorite pupil, Geert Remmert Veldkamp, as reported in Refs. [23,24]. Referring to Fig. 11, the position of the moving frame f \u00f0X; x; y\u00de with respect to the fixed frame F\u00f0O;X;Y\u00de can be given by the Cartesian-coordinates of the origin X and by the oriented angle u. Similarly, the position of the canonical moving frame ~f \u00f0I; ~x; ~y\u00de with respect to the canonical fixed frames ~F\u00f0I0; ~X; ~Y\u00de can be given by the Cartesian-coordinates of the origin I and by the oriented angle #" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001384_978-94-017-2925-3-Figure5.9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001384_978-94-017-2925-3-Figure5.9-1.png", "caption": "Fig. 5.9. Lupke pendulum.", "texts": [], "surrounding_texts": [ "In free-vibration tests, the rubber specimen forms the spring in a mechanical system with inertia chosen so that a damped oscillation of the desired frequency results from release of a deformation. Deformation in compression, shear, tor sion, tension, or torsion plus extension have been used. Perhaps the most com-" ] }, { "image_filename": "designv10_13_0003802_icra.2013.6631390-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003802_icra.2013.6631390-Figure2-1.png", "caption": "Fig. 2. (a) Scheme that illustrates the phases of the SLIP model trajectory, and (b) stance phase", "texts": [ " Finally, Section VII contains conclusions and future work, and the Appendix provides our calculations for the approximation of the leg 978-1-4673-5643-5/13/$31.00 \u00a92013 IEEE 5656 angle dynamics during stance for the active SLIP. In this section we review the structure of the passive SLIP model and its dynamics, and we introduce its actuated version, the so-called active SLIP model. The passive SLIP is modelled as a point mass, M , attached to a massless spring leg, with length \u2113 and spring stiffness constant k. Running dynamics for the SLIP model consist of two phases (see Fig. 2(a)): the flight phase, where the body is in the air and follows a ballistic trajectory; and the stance phase, where the terminal part of the leg is in contact with the ground, and the compression/decompression of the spring completely defines the mass dynamics. As shown in Fig. 1(a), we define \u2113(t) as the leg-length as a function of time, and \u03b8(t) as the leg-angle measured counterclockwise with respect to the positive horizontal axis. while \u2113k is the spring length, and \u2113k,0 is the spring length at equilibrium", " We then chose to follow the same initial steps of the procedure to approximate \u03b8(t) proposed in [12], modifying and extending the results to adapt them to our actuated case, as shown in the Appendix. Note: in general, vnl(t) is not a constant value. Since vc is set to be a constant, the total actuator velocity required vact(t) is a time-varying function. We now propose a strategy for the choice of the actuator constant value \u2113c. Let us divide the stance phase in two parts, separated by the point of maximal leg compression: a first part, where \u2113\u0307(t) \u2264 0, and a second part, where \u2113\u0307(t) \u2265 0, as in Fig. 2(b). Our main control action consists in choosing two constant values for \u2113c: one for the first part, \u2113c1, and one for the second part \u2113c2, of the stance phase. The decision of choosing only two constant values for the actuator displacement as opposed to a time dependent function (as, for example, in [16], [17], and [20]) has been dictated by the purpose of keeping the system as simple as possible, without much loss on performance. Fig. 3(a) and 3(b) provide an example of how, by setting only two actuator values, it is possible to reach in one step a wide range of apex states, influencing both apex height, apex velocity and apex forward position, in all directions" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure16-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure16-1.png", "caption": "Figure 16. The Cache System for 19 bits.", "texts": [ " The Bit Carousel is rotated to the next available bit station, and the drill linear stage is then used to reach into the Bit Carousel and mate with a bit. After mating and locking onto the bit, the drill linear stage retracts, leaving a fresh bit attached to the drill. The drill is un-docked from the Bit Carousel, and the Dust Cover is closed. Cache Ground Station and the Cache The Sample Cache with the installed Bit Sleeves is constrained by a Ground Station which includes a number of rollers, as well as a Pin Puller (Figure 16). The rollers constrain the Sample Cache radially, while the Pin Puller constrains it axially and rotationally. Once all of the Bit Sleeves are filled with Bits, the Pin Puller is actuated, and the rollers guide the Sample Cache as it is removed from the Ground Station to be placed on the ground (Figure 17). Upon core acqusition, bits with rock samples inside, are inserted into protective sleeves within the Cache. A hermetic seal is made between the bit neck and the top of the sleeve (Figure 18)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002145_iros.2000.895302-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002145_iros.2000.895302-Figure4-1.png", "caption": "Fig. 4 Composition of the joint unit", "texts": [], "surrounding_texts": [ "To begin with, the prototype of the joint unit is made in order to develop the ACM mechanical model that realizes three-dimensional and various functions The joint unit has 2 degrees of freedom and can do pitch and yaw motion. Its dimension is 20Ox190x180mm, and i t is over 2.5kg including all parts. There are two motors in the joint unit, and pitch and yaw motions are performed by the coupring the outputs. The workspace is maximized by offsetting pitch and yaw axis. And, this uni t has new mechanisms called \"M-Drive\" and \"Float differential torque sensor\". The former is to prevent the mechanical destruction by excessive load, and the latter is the detection mechanism of torque at each drive axis. And the making of the self-containd system is possible in the future, so that there is room for such as control computer, motor driver, and battery. -2243- This unit has 2 passive wheels on the both side for obtaining the frictional property for the glide propulsion. Thus, it is easy to slip in the direction along the trunk, and it is difficult to slip in the direction which is orthogonalized with it. Though the interference of wheels and the effect of the slip angle are considered because of the curvature discreteness, placing the axle in the midpoint of each joint has reduced these effects. Table 1 Specifications of the prototype unit Actuator Dimension Weight Torque Angular velocity Workspace . - . 20W DC Motor x2 (Coupled) 200x 260 / 260 deg 90x180 mm 2.5 kg 5 kgfm 8 rpm (yaw / pitch) 3.1 Wire type differential mechanism It is necessary that the actuator unit is high output mass ratio, because large moment affects the root when the neck is lifted. As the solution, the differential mechanism using the harmonic gear is introduced. This mechanism is lightweight because it is composed of not bevel gears but wire and pulley. The harmonic gear is a differential system which has one input and two output parts. One output is attached to pitch shaft and the other is attached the pulley. 2 sets of these are placed on a pitch shaft. The wire and pulley configuration is shown in Fig.6, and the endpoint of the wire is fixed in the yaw pulley. The rotation in the pitch axis is carried out in the case that two pulley outputs are same directions in viewing from the pitch shaft, and the yaw axial motion is carried out when the pulley outputs are is reverse-directions, This actuator unit is adopted the coupled drive which is the method of maximizing output performance by cooperatively utilizing as possible all actuators that are installed. 3.2 Torque limiting mechanism M-Drive\" The ACM is hyper-redundant serial link system. The principal problem of existing systems is the inability to withstand unexpected external forces due to excessive moments at its root joints, so the torque limiter is necessary. Though usual torque limiter is bulky, it can be realized by adding simple parts in the wire drive system. The basic principle of M-Drive can be explained from the expression of the fiction transmission between the string and the pulley. In Fig. 7 (a), let T , and T, ( TI c T,) are the string's tension, ,U is the friction coefficient between the string and the pulley, and 8 is the winding angle of strings. The condition in which the slip occurs is the following. T, >TI exp( PO 1 So the maximum value of T,can be decided by TI which is set beforehand and by far smaller tension than T,. T, is the driving force of the pulley, and the torque that generates the tension over the maximum value of T, is not transmitted by slipping[3]. - 2244 - It is constructed as shown in Fig.7 @) and Fig.8. The wire drawn out from its winding pulley is hooked around the other pulley that is rotation free. This pulley is pulled by the spring for applying the tension on the wire. And the compressive force of coil spring, which is accumulated by turning the worm gear, has been applied on pulley by the link in this tensioner unit. 3 3 Float differential torque sensor It is useful to obtain torque information, which works in each axis in order to realize the advanced and three-dimensional motion control. As a torque sensor, \"Float differential torque sensor\" shown in Fig.9 is introduced. It is easy to maintain this sensor and the additional equipment. The motor is supported rotation freely from the base by ball bearings, and it is connected by the hard spring between the motor and base. By measuring the strain gauge mounted on this spring, the reaction torque of the motor is detected. Generally the strain gauge is applied to the output itself in order to measure the torque of the actuator. However this sensor has high reliability and generality, because it removes the wiring of collector ring or strain gauge from the output, which infinity rotates[4]. Harmonic gear is used in the actuator unit, so this torque sensor is adopted as the flexspline is supported rotation freely from the pitch shaft as Fig.10 shows. 3.4 Basic experiments The operation test of this prototype unit is carried out. This unit is position controlled by returning the value of sum or difference of two potentiometers which are set in the pitch and yaw axis to each motor driver. It has been confirmed that there are no problems such as the interference for this unit and that it normally operates. For the float differential torque sensor, it is confirmed that it has the sufficient linearity and its deviation is little in Fig.11. The external force is applied to the unit that is position controlled as performance test of M-Drive. A pair of outputs of torque sensors is in Fig.12. The left part shows an aspect under the permission torque, and then this joint unit acts as usual servo system. On the other hand, there is the leveling off in the right part, and it is a cause that the supeffluous torque does not arise by slipping. External force[kgfl Fig.11 Experiment of the float differential torque sensor -5 O; I J 0 2 4 6 8 Time[sec] -sensor A -sensor B Fig.12 Experiment of M-Drive -2245- 3.6 Improve the joint unit Dimembn Weight Torque Angle velocity 3.6.1 Consideration to the three-dimensional motion There is the case that only one in the pair of wheel contacts the ground by the body shape, because each joint does not have degree of freedom of roll motion. The suspension mechanism is added in each wheel in order to prevent this problem. And the frame rigidity is improved by establishing the top board at the uni t in order to stand the three-dimensional motion like 2 0 0 ~ 1 9 0 ~ 1 8 0 ~ 170~150~14511~~1(-46%) 2.5 kg 2 kg (-20%) 5 kglin 4.1 kglin 8 rpm 9.6 rpm 3.6.2 Improved tensoner The wire tensioner is independent composition in the primary model. The joint unit becomes smaller and lighter so that it is conbined with the motor uni t in the improved model. It is composed of the link with a free pulley and a ring around the motor. These are tied together with a torsion spring. And there are the different number of holes in the ring and the motor base. The wire tension is adjusted by the combination of the hole where the pin As a result of these improvements, it becomes about -20% in the weight and about -46% in the volume in comparing primary model. Table 2 Improvement of specification Primary Model Improved Model 4. Development of the three-dimensional Active Cord Mechanism: ACM-R2 4.1 System constitution ACM-R2 consists of 14 joint units which are straight-chained. It has ability for the propulsion at 1 m/s and the compensation for the weight of 5 units levelly. It has totally 28 degrees of freedom. Angle and torque of each joint are measured. It is possible to make self-contained system in the future, because there is space for mounting batteries, wireless LAN, etc. on the body. It has 2 motor drivers (TITECH Robot driver 2)[5], 2 amplifiers for the strain gauge and a microcomputer (HITACHI H8/3048F 16MHz). No. of unit 14 (28 degrees of freedom) Demension 2430x150~145 mm Weight 30 kg Promotion speed - 2246 - Each actuator controls its position by the motor driver, however each joint controls their torque at a local loop by returning the value of the torque sensor to the motor driver as a feedback value of the position. The processing by the microcomputer is DA converted for motor drivers (2ch), AD converted from angle or torque sensors (4ch) and serial communication to the host computer, which is in the last joint unit. The processingof the motion plan of serpentine motion, etc. is carried out in the host PC. 4.2 Fundamental operation 4.2.1 Torque control Torque control at the local loop has been implemented and is confirmed that i t can be controlled without causing abnormal vibration. And when the external force is applied to joints in a stationary state, it is also confirmed that the joint bends in the direction in order to avoid it 4.2.2 Position control Position control has been implemented by commanding the torque order in proportion to the difference in real joint angle and target one to each actuator. There are small vibrations in some joints in this control mode. The following causes are considered: That control period of the position loop is late, that the resolution of the AD conversion of the joint angle is low and noise. The vibrations are disposed of in raising the communication speed between the host PC and microcomputers on each joint, and redoing the wiring to endure the noise for these problems. There is no problem for the operation by these improvements, as long as the accuracy of the position is not so required in the present state. The experiment of ACMR-2 lifting its head as a sickle neck is carried out by manual control. And, the propulsion using control method, which makes each joint angle to change in sine wave like, is carried out as well as the conventional mechanical model. 5. Conclusions The ACM with three-dimensional motor capacity is discussed in this paper. It has various functionalities, and it is made good use by ACM possessing the ability of three-dimensional motion. Then, ACM-R2 that is the mechanical model with the three-dimensional capacity is actual made. It is a high performance model so that i t has M-Drive (torque limiter) and Float differential torque sensor. It is confirmed effectively operating of these mechanisms, and the experiment of fundamental operation is carried out. As a future work, It will be realized that manipulation and locomotion for adapting the body shape to the surroundings in order to keep the stability without overtuming. And the proposed new propulsions are to be verified by the real machine. It will be concretely examined control methods which utilize the torque information in order to achieve these. Acknowledgment This research is supported by The Grant-in Aid for COE Research Project of Super Mechano-Systems by the Minstry of Educaton, Scince,Sport and Culture. References [I] Shigeo Hirose : \u201cBiologically Inspired Robots (Snake-like Lo- comotor and Manipulator)\u201d, Oxford University Press, 1993 [2] Gen ENDO, Keiji TOGAWA ,Shigeo HIROSE : \u201cStudy on self-contained and Terrain Adaptive Active Cord Mechanism\u201d,in Proc. of IEEE/RSJ International Conference on Inteligent Robots and Systems, pp1399-1405,1999 [3] S.Hirose, Richard Chu : \u201cDevelopment of a Lightweight Torque Limiting M-Drive Acuator for Hyper-Redundant Manipulator Float Arm\u201d, in Proc. IEEE International Conference on Robotics and Automation, pp2831-2836,1999 [4] S.Hirose, K.Kato : \u201cDevelopment of the Float Differntial Torque Sensor\u201d, in Proc. of JSME Conference on Robotics and Mechatronics, IC1 2-6, 1998 (in Japanese) [5] E.F.Fukushima, T.Tsumaki,S.Hirose : \u201cDevelopment of a PWM DC Motor Servo Driver Circuit\u201d,in Proc. of RSJ95,pp1153-1154,1995 (in Japanese) - 2247 -" ] }, { "image_filename": "designv10_13_0003544_tcst.2012.2221091-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003544_tcst.2012.2221091-Figure4-1.png", "caption": "Fig. 4. Forces and moments acting on the aircraft body.", "texts": [ " One may construct the aerodynamic forces Xa and Za in terms of both lift and drag as follows: [ Xa Za ] = \u2212 [ cos\u03b1 \u2212 sin \u03b1 sin \u03b1 cos\u03b1 ] [ D L ] where L denotes the wing lift, D denotes the wing drag, and \u03b1 = atan2(w, u) is the angle of attack. The lift and drag components are described by L = 1 2 \u03c1(u2 +w2)AwCL(\u03b1) (3a) D = 1 2 \u03c1(u2 +w2)AwCD(\u03b1) (3b) respectively, where \u03c1 \u2208 R is the atmospheric pressure, Aw \u2208 R is the wing\u2019s planform area, CL(\u03b1) \u2208 R is the coefficient of lift, and CD(\u03b1) \u2208 R is the coefficient of drag (see [21] for more details). A graphical representation of these forces and moments is provided in Fig. 4. In these computations, we have assumed that the lift and drag contributions due to the propeller slipstream are negligible due to its alignment with the wing\u2019s zero lift line. The same does not hold, however, for the aerodynamic actuators. In order to model the aerodynamic interaction between the free-stream flow and the propeller slipstream on the aerodynamic actuators, we compute both contributions separately and combine them together in the end using superposition (this strategy was successfully used in the practical setup described in [13])" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002901_0278364909348762-Figure27-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002901_0278364909348762-Figure27-1.png", "caption": "Fig. 27. The prototype of the hybrid robot, PEOPLER-II.", "texts": [ " This cycle has such features that the successive switching with power saving from L-type to Wtype and again to L-type via CRC proceeds straightforwardly without necessitating the adaptation phase in any environment of ascending and descending. Results of the simulation have been described so far, and we have learned many important conditions, equations, motion series that are helpful in developing programs for making the switch effectively. These are summarized in Table 1. In order to verify the simulation results, we used the robot PEOPLER-II shown in Figure 27. The controller is located at the back side of the robot. The battery occupies the downside of a driver\u2019s seat at this moment. Table 2 lists specifications and performances of the hybrid robot, PEOPLER-II. Control programs are coded in J and downloaded into the robot controller. Figure 28 shows a diagram explaining the details of our control law strategy. Basically, a driver gives the type of motion by selecting one of the W-type roll, turn, spin, and L-type walk, turn, spin. Of course, the driver assigns the leg posture control law (LPCL) in the L-type with the value of max depending on the amount of turn and spin in advance" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001490_s0094-114x(99)00060-9-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001490_s0094-114x(99)00060-9-Figure5-1.png", "caption": "Fig. 5. R\u00b1S\u00b1S\u00b1R spatial chain.", "texts": [ " The elements in this matrix represent the numerical value of the joint between two elements that are directly connected; e.g. a revolute or slider pair is represented by 1, a cylindrical pair by 2 and a spherical pair by 3. Taking each row of elements of the adjacency matrix represents a vector, the extent to which a vector becomes a subset of the other can be computed on the earlier lines using Eqs. (6) and(7). A subset matrix may be formulated and the sum of all the elements of this matrix is indicative of parallelism, i.e. higher the value greater is the parallelism. For example, let us consider a R.S.S.R. Fig. 5. A.C. Rao /Mechanism and Machine Theory 35 (2000) 1103\u00b111161114 C 2664 0 1 0 1 1 0 3 0 0 3 0 3 1 0 3 0 3775: 18 The corresponding subset matrix is S 2664 1 0 0:5 0 0 1 0 1 0:33 0 1 0 0 1 0 1 3775: 19 Sum of all the elements which may be called S-value of the chain is 6.83. Similarly, the adjancy and subset matrices can be formulated for every chain and compare their S-values. Higher values indicate more parallelism. 1. Each link of a kinematic chain is assigned a fuzzy membership (\u00aet). A fuzzy vector is developed in terms of \u00aets for each link, depending upon its adjacency, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.18-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.18-1.png", "caption": "Fig. 9.18 A cotton drawing device (\u6728\u68c9\u8ee0\u5e8a) a Original illustration (Wang 1991), b Structural sketch", "texts": [ " This is a mechanism with four members and four joints, including a wooden stand as the frame (member 1, KF), a warping roll with a handle (member 2, KU1), Si Yue (member 3, KU2), and the silk thread (member 4, KT). The warping roll is connected to the frame with a revolute joint JRx. The silk thread is connected to the warping roll and Si Yue with wrapping joints JW. Si Yue is connected to the frame with a revolute joint JRy. Figure 9.17c shows the structural sketch. 9.4.7 Mu Mian Kuang Chuang (\u6728\u68c9\u8ee0\u5e8a, A Cotton Drawing Device) In the book Nong Shu\u300a\u8fb2\u66f8\u300b, Mu Mian Kuang Chuang (\u6728\u68c9\u8ee0\u5e8a, a cotton drawing device) has the similar function and structure as Jing Jia (\u7d93\u67b6, a silk drawing device) as shown in Fig. 9.18a (Wang 1991). The difference is that Jing Jia is used to organize silk threads while Mu Mian Kuang Chuang deals with cotton yarns. Figure 9.18b shows the structural sketch. (a) (b) 9.4 Textile Devices 213 T ab le 9. 2 F le x ib le co n n ec ti n g m ec h an is m s (1 9 it em s) M ec h an is m n am es B o o k s N o n g S h u \u300a \u8fb2 \u66f8 \u300b W u B ei Z h i \u300a \u6b66 \u5099 \u5fd7 \u300b T ia n G o n g K ai W u \u300a \u5929 \u5de5 \u958b \u7269 \u300b N o n g Z h en g Q u an S h u \u300a \u8fb2 \u653f \u5168 \u66f8 \u300b Q in D in g S h o u S h i T o n g K ao \u300a \u6b3d \u5b9a \u6388 \u6642 \u901a \u8003 \u300b S h ai G u (\u7be9 \u6bbc )F ig . 9 .1 T y p e I S u i Ji n g \u300a \u788e \u7cbe \u300b L v L o n g (\u9a62 \u7931 )F ig . 9 .2 T y p e I C h u Ji u \u300a \u6775 \u81fc \u300b S u i Ji n g \u300a \u788e \u7cbe \u300b N o n g Q i \u300a \u8fb2 \u5668 \u300b L u L u (\u8f46 \u8f64 )F ig " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003887_s10999-011-9167-1-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003887_s10999-011-9167-1-Figure1-1.png", "caption": "Fig. 1 Hemispherical model of a finger tip", "texts": [ " The strain energy potential is given by, W \u00bc EIm 6 ln 1 I1 3 Im \u00fe 1 d J2 el 1 2 \u00fe ln\u00f0Jel\u00de \u00f013\u00de If the natural logarithm is expanded, the resulting form will be similar to the Yeoh-Model. The coefficients, however, are predefined functions of Im. Also there are many similarities between Gent and Arruda\u2013 Boyce model. 1.8 Yeoh model The Yeoh model (1993) is similar to the reduced polynomial form based on the first strain invariant and is given W \u00bc XN i\u00bc1 ci0 I1 3 i\u00fe XN i\u00bc1 1 di Jel 1\u00f0 \u00de2i \u00f014\u00de A cross section of the hemispherical soft fingertip model composed of incompressible, homogeneous non-linear elastic and isotropic material is illustrated in Fig. 1. The loading of the fingertip is normal to the rigid plane in contact with the tip, and the tip is fully constrained on the upper surface as shown. ANSYS Version 11.0 standard FEM software having capability to solve hyper-elasticity is used for solving the nonlinear elastic contact problem with hemispherical fingertip geometry. To verify various hyper-elastic models an experimental case study is taken from Xydas and Kao (1999) as depicted below. The fingertip model is having a radius of 7.65 mm" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003067_amc.2008.4516082-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003067_amc.2008.4516082-Figure6-1.png", "caption": "Fig. 6. Yaw moment", "texts": [ "4 Vx [m/sec] 0 double support single support double single Fig. 4. COG\u2019s velocity in sagittal plane before improvement 1 2 3 4 0.1 0.2 0.3 0.4 0 0 [sec]t Vx [m/sec] double support single support double single Fig. 5. COG\u2019s velocity in sagittal plane after improvement One of the restriction factors for fast biped walking is the influence of the yaw moment around the support leg. In this section, we discuss the yaw moment compensation. The yaw moment is one around support leg caused by acceleration and deceleration of the swing leg(Fig.6). If this moment becomes larger as the walking speed increases and exceed the maximum friction force between the support foot sole and the floor, the support foot rotates and slips, so that, the biped walking becomes unstable. We decided to compensate the yaw moment by rotating the waist joint of MARI-3. First, we analyze the dynamic relationship between the yaw moment and rotation of the waist joint referring to Fig.7. In this figure, we assume that the robot is regarded as 3 mass point model, torso and both legs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003410_ajpa.21329-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003410_ajpa.21329-Figure1-1.png", "caption": "Fig. 1. The apparatus setup during data collection. Open diamonds represent digitized points, arcs show joint angles used in the analysis.", "texts": [ " As such, it aims to identify mechanisms and adaptations in gibbons that contrast with leaping animals with a more typical body plan, reflecting this specialization. MATERIALS AND METHODS Data were collected during 24 spontaneous leaps from an adult female white-cheeked gibbon (Nomascus leucogenys, age: 6 years, mass: 8.7 kg) in the Wild Animal Park Planckendael (Belgium). A wooden pole was rigidly fixed to a strain gauge forceplate (AMTI, OR6-7, Watertown, MA) and positioned at the entrance to the indoor partition of the gibbon enclosure (see Fig. 1). Force and moment data in vertical (FZ, Mz, respectively), craniocaudal (FX, MX) and mediolateral (FY, MY) directions were collected at 500 Hz using a National Instruments (NI, Austin, TX) USB data acquisition module and custom-written software in National Instruments LabVIEW (version 8.2). The leaps were simultaneously recorded using two orthogonally positioned (lateral and craniocaudal views) high-speed video cameras (AOS, X-Pri, Baden Da\u0308ttwil, Switzerland) at 120 Hz. The lateral view was used for kinematic analysis while the cranio-caudal view was used to ensure that the leaps were executed orthogonally to the lateral view camera", " Although not quanAbbreviations aX craniocaudal acceleration aZ vertical acceleration FX craniocaudal force FZ vertical force KE kinetic energy ME mechanical energy MX craniocaudal moment MZ vertical moment m mass PE potential energy PM mass specific power SX craniocaudal displacement SZ vertical displacement vX craniocaudal velocity vZ vertical velocity vR resultant velocity v0 initial velocity WM mass specific work. American Journal of Physical Anthropology titatively analyzed, these leaps were qualitatively similar to the female gibbon (see results and discussion). Approximations of 15 anatomical landmarks (i.e. left and right toe, ankle, knee, elbow, wrist and fingertip and hip, shoulder and ear at one side) were digitized in 2D from the lateral view videos using custom written software (NI, LabVIEW, 8.2, see Fig. 1, open diamonds for landmarks). Joint angles were defined as follows; Ankle joint angle, between the dorsum of the foot and the anterior of the shank; knee joint angle, between the posterior of the thigh and the posterior of the calf; hip joint angle, between the anterior of the trunk and the anterior of the thigh; wrist joint angle, between the palmar surface of the hand and the posterior of the forearm; elbow joint angle, between the forearm and the anterior of the upper arm; shoulder joint angle, between the anterior of the trunk and the posterior of the upper arm (Fig. 1, arcs). The shoulder joint is the only joint that is capable of circumduction, and an angle of 08 at the shoulder joint was defined as when the arm is directly in line with the trunk and inferior to the shoulder. Positive angles (0\u2013 1808) at the shoulder joint occur when the arm is anterior to the trunk (i.e. shoulder joint flexion), negative joint angles (2180 to 08) occur when the arm is posterior the trunk (i.e. shoulder joint extension), at 1808 and 21808 the arm is held vertically, directly in line with the trunk, with the shoulder inferior to the arm (see Fig. 1). Joint angles during take-off were smoothed using a cubic spline and resampled to the duration of the stance phase of the take-off foot. For the analysis, the limbs were categorized into (1) the take-off hind limb, the last hind limb to have contact with the pole; (2) the lead hind limb, the opposing hind limb to the take-off hind limb; (3) the take-off forelimb, the ipsilateral forelimb to the take-off hind limb; and (4) the lead forelimb, the ipsilateral forelimb to the lead hind limb. Stance phase was defined as the period from when the take-off foot touched down until the take-off foot left the pole, when take-off occurred", " The angular excursion of the take-off forelimb wrist joint was larger during orthograde two-footed (132 6 858) leaps than orthograde squat (34 6 58) leaps, with orthograde single-footed (56 6 68) and pronograde single-footed (93 6 58) leaps demonstrating wrist joint angle values in between (Table 1). The contralateral forelimb angles were highly variable American Journal of Physical Anthropology between and within leap types. In all leaps types, the lead forelimb upper arm was in line with the body and inferior to the shoulder (i.e. hanging down; shoulder joint angles close to zero degrees, Fig. 1) during early stance, then the shoulder joint flexed gradually (going through positive joint angles, pronograde single-footed, Fig. 7) or extended gradually (passing through negative joint angles, orthograde single-footed, orthograde twofooted and orthograde squat, Fig. 7). The angular excursion of the lead forelimb shoulder joint during orthograde squat leaps (180 6 408) was higher than for orthograde two-footed leaps (72 6 118), with orthograde singlefooted (95 6 218) and pronograde single-footed leaps (60 6 98) spanning both groups" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002581_ichr.2006.321302-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002581_ichr.2006.321302-Figure3-1.png", "caption": "Fig. 3 Interpretation of the joint 1 angle as a elevation aim angle.", "texts": [ " The closed-form inverse kinematic solution for the wrist position can be completed by the closed-form inverse kinematic solution for the hand orientation given in annex. To check the relevance of the proposed method we will first develop a comparison between the redundancy control based on joint 1 angle and the one based on arm angle . A. Comparison of redundancy control approaches based on shoulder abduction and \"arm angle\" Although it is a joint variable, the abduction-adduction angle 0O of our kinematic model has a clear meaning in the task space, as illustrated in Fig 3: it represents the angle between the projection of the arm segment in the vertical plane (S, Xbase , Zbase) and the vertical reference axis Zbase around the fixed shoulder abduction-adduction axis. 0 -imposed E wristppsition -0.2 aL -0.3 .4j = >elboW traJoctory -0.4 0.5 0.2 -0.5-0.2 o\\ (a) Parameter 0O controls the arm elevation in a different manner from Seraji's arm angle. To compare the effect of the two parameters, we propose the following simulation: using the inverse kinematic model parametrized in 0O we impose a fixed wrist location and at the same time an 0O angle change is imposed between two given values" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002661_978-1-4615-9882-4_4-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002661_978-1-4615-9882-4_4-Figure2-1.png", "caption": "Figure 2 Kinematic configuration and notation", "texts": [ " Optimal control theory was applied to a manipulator system, for which the inputs are joint torques (which are a function of time) and the desired output is an end point displacement motion. In optimal-control theory terms, the system model is the manipulator, with initial conditions. The control objective is to drive the system to the end conditions such that the performance index is minimized. This performance index is time of travel. The equations of motion indicate that for a planar two degree of freedom manipulator (Figure 2) this is a fourth-order non-linear two-point boundary value problem. A numerical solution is indicated. From optimal control and dynamics theory certain initial assumptions may be made: (1) admissible control is bang bang; (2) each joint control has a maximum of two switch points; (3) total + torque time equals the total- torque time for the first joint if the end conditions represent stationary states. The first assumption is an extension of linear optimal-control theory and, although not a law, it appears to be a reasonable simplifying assumption with high prob ability of correctness for this problem" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002930_j.mechmachtheory.2009.02.003-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002930_j.mechmachtheory.2009.02.003-Figure4-1.png", "caption": "Fig. 4. Schematic cutting mechanism of an hourglass worm wheel.", "texts": [ " It is noted that k is the lead angle of the worm in the middle plane (the section of the minimal diameter) of the worm, and it is changing along the worm axis. Based on the developed mathematical model of the ZN-type hourglass worm, a three-dimensional tooth profile of the ZN-type hourglass worm is plotted as shown in Fig. 3. Coordinates of the hourglass worm surface points can also be calculated by applying the developed mathematical model. An hourglass worm-type hob cutter, which is identical to the ZN-type hourglass worm, is used for the generation of hourglass worm wheel. The schematic cutting mechanism of an hourglass worm wheel is shown in Fig. 4. Coordinate system esign parameters of the ZN-type hourglass worm and blade cutter. Parameters gle of the blade cutter (Fig. 2a) k 5.0 pressure angle of the blade cutter a 20.0 module of the blade cutter mn 2.0 mm/tooth rcle radius of the blade cutter rp 47.04 mm rcle radius of the blade cutter rb 21.92 mm r of thread of the worm T1 1 gle of the worm k 5.0 rcle radius of the worm r1 22.0 mm ngle of the worm gear set c 90.0 Sh(Xh,Yh,Zh) is associated with the hourglass worm-type hob cutter, S2(X2,Y2,Z2) is attached to the hourglass worm wheel, So(Xo,Yo,Zo) and Sp(Xp,Yp,Zp) are the reference coordinate systems for the hourglass worm-type hob cutter and worm wheel, respectively, and Sf(Xf,Yf,Zf) is the fixed coordinate system. Axes Zh and Z2 are rotation axes of the ZN-type hourglass wormtype hob cutter and worm wheel, respectively. Parameter c measured from Zf -axis to Zp-axis, is the cross angle of the hourglass hob cutter and worm wheel. Parameter H is the shortest center distance of these two rotation axes, and it can be expressed by H \u00bc rh \u00fe r2; \u00f019\u00de where rh and r2 are the pitch radii of the hourglass worm-type hob cutter and worm wheel, respectively. In Fig. 4, /h and /2 are the rotation angles of the hourglass worm-type hob cutter and worm wheel, respectively, during the cutting process. Therefore, angular velocity of the worm wheel can be expressed in reference coordinate system Sp(Xp,Yp,Zp) by x \u00f0p\u00de 2 \u00bc d/2 dt k\u00f0p\u00de \u00bc x2k\u00f0p\u00de; \u00f020\u00de where symbol k(p) denotes the unit vector of Zp-axis. This angular velocity can also be represented in coordinate system Sh(Xh,Yh,Zh) as follows: x \u00f0h\u00de 2 \u00bc Lhpx \u00f0p\u00de 2 \u00bc cos /h sin /h cos c sin /h sin c sin /h cos /h cos c cos /h sin c 0 sin c cos c 2 64 3 75 0 0 x2 2 64 3 75 \u00bc xh m2h sin /h sin c m2h cos /h sin c m2h cos c 2 64 3 75; \u00f021\u00de where m2h \u00bc x2 xh ", " (26) yields: f \u00f0u1;/1;/h\u00de \u00bc \u00f0D\u00f0k\u00de1 sin /1 D\u00f0k\u00de2 cos /1\u00de\u00bd\u00f0 A\u00f0k\u00de1 cos k sin /b \u00fe A\u00f0k\u00de2 cos /b\u00demb1 n \u00f0 E\u00f0k\u00de1 \u00de\u00f0 A\u00f0k\u00de1 C1 \u00fe A\u00f0k\u00de2 C2 G cos /1\u00de o Rhzm2h sin c cos /h Rhy\u00f0 1 m2h cos c\u00de \u00fe Hm2h sin /h cos c \u00fe \u00f0 E\u00f0k\u00de1 \u00de\u00f0 A\u00f0k\u00de1 B1 A\u00f0k\u00de2 B2 \u00fe G sin /1\u00de \u00f0D \u00f0k\u00de 1 cos /1 D\u00f0k\u00de2 sin /1\u00de n \u00fe \u00f0 A\u00f0k\u00de1 cos k sin /b \u00fe A\u00f0k\u00de2 cos /b\u00demb1 h io Rhx\u00f0 1 m2h cos c\u00de Rhzm2h sin c sin /h Hm2h cos /h cos c\u00bd \u00fe \u00f0D\u00f0k\u00de1 cos /1 D\u00f0k\u00de2 sin /1\u00de\u00f0 A\u00f0k\u00de1 C1 \u00fe A\u00f0k\u00de2 C2 G cos /1\u00de n \u00f0D\u00f0k\u00de1 sin /1 D\u00f0k\u00de2 cos /1\u00de\u00f0 A\u00f0k\u00de1 B1 A\u00f0k\u00de2 B2 \u00fe G sin /1\u00de o Rhym2h sin c sin /h \u00fe Rhxm2h sin c cos /h \u00fe Hm2h cos2 /h sin c\u00fe Hm2h sin2 /h sin c \u00bc 0: \u00f027\u00de Equation (27) is the so-call equation of meshing that relates the surface parameters of hourglass worm-type hob cutter to the cutting motion parameters of the generated hourglass worm wheel. According to the coordinate systems shown in Fig. 4, the locus of the hourglass worm-type hob cutter can be represented in coordinate system S2 by R2\u00f0u1;/1;/h\u00de \u00bcM2pMpf MfoMohRh\u00f0u1;/1\u00de \u00bc M2hRh\u00f0u1;/1\u00de; \u00f028\u00de where M2h \u00bc a11 a12 sin /2 sin c H cos /2 b21 b22 cos /2 sin c H sin /2 sin c sin /h sin c cos /h cos c 0 0 0 0 1 2 6664 3 7775; \u00f029\u00de a11 \u00bc cos /2 cos /h \u00fe sin /2 cos c sin /h; a12 \u00bc cos /2 sin /h sin /2 cos c cos /h; b21 \u00bc sin /2 cos /h cos /2 cos c sin /h; and b22 \u00bc sin /2 sin /h \u00fe cos /2 cos c cos /h: Parameter c represents the cross angle of the ZN-type hourglass worm gear set" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002548_j.mechmachtheory.2006.04.007-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002548_j.mechmachtheory.2006.04.007-Figure3-1.png", "caption": "Fig. 3. arm in", "texts": [ " The limitation of such an algorithm is that pt 6 f 6 2pt L1 \u00bc vt cosecab 8 0 6 vt < pt L2 \u00bc \u00f0pt \u00fe vt\u00decosecab 8 0 6 vt < \u00f0f pt\u00de \u00bc f cosecab 8 \u00f0f pt\u00de 6 vt < \u00f0f pt \u00fe f1\u00de \u00bc \u00f0f \u00fe b tan ab \u00f0pt \u00fe vt\u00de\u00decosecab 8 \u00f0f pt \u00fe f1\u00dept 6 vt < pt L3 \u00bc \u00f0f \u00fe b tan ab \u00f02pt \u00fe vt\u00de\u00decosecab 8 0 6 vt < \u00f0pt f2\u00de \u00bc 0 8 \u00f0pt f2\u00de 6 vt < pt L \u00bc L1 \u00fe L2 \u00fe L3 \u00f03\u00de Friction force is considered to be positive when the contact line segment is above the pitch line and negative otherwise. The direction of the friction force is perpendicular to the line of action in the transverse plane parallel to the cross section of the gears and pinion, and perpendicular to the contact lines in the sectional plane showing the contact zone (because the contact lines moves diagonally) as illustrated in Fig. 3. Since this paper aims at determining the friction force only for torsional vibration characteristics of the gear system i.e. the rotation of gears (h), only the direction perpendicular to the line of action (in the transverse plane) will be discussed. The normal force acting on the helical gear can be obtained by the expression: F \u00bc P xpr \u00f04\u00de where P is the power fed to the pinion, xp is the speed of the pinion and r is the pitch circle radius of the pinion. This normal force is assumed to act on a number of segments of the contact lines as assumed by other authors [3\u20135]", " The normal force on each segment can be found by the following equation: F ij \u00bc F L Lij \u00f05\u00de where Lij is the instantaneous length of ith contact line and jth segment. The algorithm developed for finding the friction force is as follows: where L12 \u00bc \u00f0f f3\u00decosecab L11 \u00bc L1 L12 L22 \u00bc \u00f0f f3\u00decosecab 8 0 6 vt < \u00f0f \u00fe f1 pt\u00de L21 \u00bc L2 L22 L21 \u00bc f3 cosecab 8 \u00f0f \u00fe f1 pt\u00de 6 vt < pt L22 \u00bc L2 L21 L31 \u00bc f3 cosecab 8 0 6 vt < \u00f0f \u00f0f3 \u00fe f4\u00de\u00de L32 \u00bc L3 L31 L31 \u00bc L3 8 \u00f0f \u00f0f3 \u00fe f4\u00de\u00de 6 vt < pt \u00f07\u00de The terms f3 (equal to distance PC shown in Fig. 3) and f4 are shown in Fig. 2(d), which can be found from the following equation: f3 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 a \u00f0r cos /t\u00de 2 q r sin /t f4 \u00bc 2pt b tan ab \u00f08\u00de where ra is the addendum circle radius of pinion. The sign convention of the frictional torque is considered as positive when it facilitates the rotation and negative otherwise. For the pinion, the moment arm of the friction force is calculated from the point A i.e. the tangent point of the line of action to the base circle of the pinion as shown in Fig. 3. The following algorithm has been formulated for determining frictional torque: T f1 \u00bc l F L L1 AC f vt 2 8 0 6 vt < \u00f0f f3\u00de \u00bc l F L L12 AC f \u00fe f3 2 l F L L11 AC f \u00fe f3 vt 2 8 \u00f0f \u00fe f3\u00de 6 vt < pt T f2 \u00bc l F L L22 AC f \u00fe f3 2 l F L L21 AC f \u00fe f3 pt vt 2 8 0 6 vt < \u00f0f pt\u00de \u00bc l F L L22 AC f \u00fe f3 2 l F L L21 AC f3 2 8 \u00f0f pt\u00de 6 vt < \u00f0f \u00fe f1 pt\u00de \u00bc l F L L22 AC f3 \u00fe L22 sin ab 2 l F L L21 AC f3 2 8 \u00f0f \u00fe f1 pt\u00de 6 vt < pt T f3 \u00bc l F L L32 AC f3 \u00fe L32 sin ab 2 l F L L31 AC f3 2 8 0 6 vt < \u00f0f \u00f0f3 \u00fe f4\u00de\u00de \u00bc l F L L3 AC L3 sin ab 2 8 \u00f0f \u00f0f3 \u00fe f4\u00de\u00de 6 vt < pt T f \u00bc T f1 \u00fe T f2 \u00fe T f3 \u00f09\u00de The values of the lengths of the segments of contact lines will be as per Eq. (7). The value of AC (shown in Fig. 3) can be expressed as AC \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 a \u00f0r cos /t\u00de 2 q \u00f010\u00de The algorithm is applied to a helical gear system whose specifications are provided by the manufacturer and described in Table 1. The base helix angle (ab) and transverse pressure angle (/t) can be obtained from the following equations [21] Table Specifi Sl. no. 1 2 3 4 5 6 7 8 9 10 sin ab \u00bc sin a cos / \u00f011\u00de tan /t \u00bc tan / sec a \u00f012\u00de The algorithm developed in the above section is used to find the time-variation of contact lengths, friction force and frictional torques for the defect-free helical gear system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002796_ichr.2007.4813872-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002796_ichr.2007.4813872-Figure1-1.png", "caption": "Fig. 1. Bipedal locomotion with vertical COG oscillation.", "texts": [ " Of course, vertical motion is necessary in running. Morisawa et al.[6] proposed a pattern generation method of bipedal walking constrained on a parametric surface. Sugihara et al.[7] proposed a compensation method of vertical motion using numerical integration. These methods used numerical calculation to obtain the vertical COG oscillation. In this paper, we proposed a analytic solution to treat vertical COG oscillation for bipedal walking. The bipedal locomotion with vertical oscillation is shown in Fig.1. The key idea of our method is dynamical 3D-symmetrization. This method symmetrizes dynamic characteristics of vertical motion and horizontal motion by constraining vertical COG motion using a differential equation. The method using the analytic solution is fast and reliable, and can be used for online walking movement generation. The rest of this paper is organized as follows. Section II describes the dynamics of bipedal robot, the calculation of the analytic solution and the determination of coefficients" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001486_s0921-8890(01)00171-3-Figure19-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001486_s0921-8890(01)00171-3-Figure19-1.png", "caption": "Fig. 19. The evolution of a system of two clusters initially on different sides of the minimum, with the smaller cluster at higher g.", "texts": [ " 18 illustrates the system evolution when the clusters are initialized on different sides of the minimum with the larger cluster at a higher g value than the smaller cluster. In this case, the larger cluster will lose pucks to the smaller cluster. Since the slopes are equal, the loss of pucks is directly proportional to the relative loss of g. Thus, the larger cluster cannot \u201ccatch up\u201d in g to the smaller. The result is that the process will continue until the initially smaller cluster passes the minimum of g and begins rising in g to meet the initially larger cluster. We end up with a system of two identically-sized clusters. In Fig. 19, we illustrate the evolution of a system of two clusters initially on different sides of the minimum. Initially, if the smaller cluster is at a higher g than the larger cluster, it will lose pucks to the larger cluster. This results in the gradual decrease in size of the smaller cluster until it is absorbed completely by the larger cluster. Thus, if both regions have the same slope, there are two possible outcomes: the clusters merge to form one cluster, or the clusters equipartition the pucks. In this subsection, we assume that the magnitude of the slope of region 1 is smaller than that of region 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003345_j.jfranklin.2011.08.002-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003345_j.jfranklin.2011.08.002-Figure2-1.png", "caption": "Fig. 2. Geometric scheme of the platform P.", "texts": [ " Let us consider the inverted Stewart platform which consists of a base platform and a mobile one, both with the shape of an equilateral triangle, of sides a and b, a4b, respectively. The vertexes of the base are joined to the corresponding vertexes of the mobile platform by actuators of lengths, li \u00f0i\u00bc 1; 2,3\u00de, variable and bounded. These actuators are fastened to the base platform at the points Ai \u00f0i\u00bc 1; 2,3\u00de by cylindrical joints with axes of rotation perpendicular to the segment AiA0 \u00f0i\u00bc 1; 2,3\u00de, forming the respective angles gi, and they are connected to the mobile platform in the corresponding points Bi \u00f0i\u00bc 1; 2,3\u00de by spherical joints (see Fig. 2). The type of joints used to connect the platforms, both base and mobile, through the actuators allow us to reduce the six original degrees of freedom to three: two rotations (a and b) and one translation (h). a and b are the rotations of the center of mass of the mobile platform (B0) respect the axis y0 and x0, respectively and h is the vertical position of B0 respect to A0, as is shown in Fig. 2. We also possess a GPS device placed in the center of mass of the base platform (A0, see Fig. 2) to measure its position with respect to the ground and angle sensors positioned in the mobile platform to measure the aforementioned angles. The position of the center of mass of the mobile platform (B0) can be recovered using the position of A0 and the geometry of platform P. We shall assume that the measurement errors of the GPS device are negligible for our application. The position to be stabilized is a\u00bc b\u00bc 0 and h\u00bc h0. To obtain the equations that describe the movement of the platform P we use Lagrange\u2019s equations considering the independent variables a, b and h as the generalized coordinates", " Consequently the functional can be expressed the following way: max Jx\u00f00\u00deJrm Z 1 0 Xn j \u00bc 1 x2 j \u00f0t\u00de ! dt\u00bc m2nmax: Thus way we can reduce the min\u2013max problem (22) to the following extremal problem of finite dimension: m2nmax-min K2Q : \u00f030\u00de Besides, from Theorem 1, the estimated state x\u0302 is used to realize the control u0, i.e., the control u0 should be designed as u0\u00f0t\u00de \u00bcKnx\u0302\u00f0t\u00de \u00f031\u00de with x\u0302\u00f0t\u00de being designed as in Eq. (15). Let us consider the following structural dimensions for our platform P : a\u00bc 0:5 m; b\u00bc 0:3 m; g\u00bc 9:81 m=s2; h0 \u00bc 0:2 m; g0 \u00bc 601 and m\u00bc 3 kg (see Fig. 2). Then, the system (1) becomes _x1 \u00bc x2, _x2 \u00bc \u00f0 1:875x1\u00de 3:464\u00f0u01 \u00fe u11\u00de \u00fe \u00f05:196wxx1\u00de, _x3 \u00bc x4, _x4 \u00bc \u00f0 0:3433x3\u00de 0:2105\u00f0u02 \u00fe u12\u00de \u00fe \u00f00:5762wyx5 0:8421wy\u00de, _x5 \u00bc x6, _x6 \u00bc \u00f0 0:25x5\u00de 0:3333\u00f0u03 \u00fe u13\u00de \u00fe \u00f0 wyx3\u00de, y\u00bc \u00f0x1,x3,x5\u00de >, \u00f032\u00de where wx\u00f0t\u00de \u00bcwy\u00f0t\u00de \u00bc 0:1\u00fe 0:5 sin t, u0 \u00bc \u00f0u01,u02,u03\u00de > is the nominal control and u1 \u00bc \u00f0u11,u12,u13\u00de > compensate the external perturbation. The vector state x consists of six state variables: x1 \u00bc a a0, x3 \u00bc b b0, x5 \u00bc \u00f0h h0\u00de=h0, x2, x4 and x6 represents the velocity of x1, x3 and x5, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003663_tmag.2012.2221134-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003663_tmag.2012.2221134-Figure2-1.png", "caption": "Fig. 2. Top and side view of the corner segment of the rectangular coil. Definition of the local coordinate system.", "texts": [ " 1, the forces and torques produced by the straight segment , , , and in the global coordinate system can be derived analytically as follows: (5) (6) where (7) (8) and where is the volume of the Segment of the coil and so on, and is the effective torque arm [5], [7]. To the corner segments, the force and torque produced by them can be calculated numerically with the composite numerical integral rule [9] and Newton-Leibniz formula. Since all the corner segments have the same calculation method, Segment is selected as an example. Fig. 2 shows the model of Segment and a new local coordinate system. The local coordinate system is denoted with the superscript , and the expressions of the orientation transformation matrix [5], [7] between the two coordinate systems are shown as follows. (The rotation angles are: To Segment , , , and . To Segment , , , and . To Segment , , , and . To Segment , , , and . Where , , and are the rotations about the -, -, and -axes, respectively.) (9) (10) As shown in Fig. 3, the Segment is divided into parts by using the composite numerical integral rule, the force and torque exerted on each part can be calculated analytically by using the Newton-Leibniz formula" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003453_j.ymssp.2012.12.001-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003453_j.ymssp.2012.12.001-Figure3-1.png", "caption": "Fig. 3. Schematic representation of the measured gearbox consisting of one planetary and two helical stages.", "texts": [ " The right side represents the \u2018grid & generator\u2019 and is composed of an electrical machine (motor 2) and an optional speed reducer. Analogous to the operation of a wind turbine, the \u2018wind\u2019 side of the test rig is speed controlled, whereas the \u2018generator\u2019 side is torque controlled. In between, the test gearbox (gearbox 2) is driven at a certain time varying speed by the \u2018wind\u2019 and loaded with a certain time varying torque by the \u2018generator\u2019 and thus experiences test conditions very similar to wind turbine behavior. A gearbox consisting of one planetary and two helical gear stages schematically represented in Fig. 3 was chosen for the measurements. The planetary system traditionally consists of a planet carrier (PC), planets and a ring wheel [11,12]. In this gearbox a cage planet carrier with three identical equally spaced planets is used. The planet ring is fixed. All gear contacts between the planets, ring and sun are helically shaped. The helical part of the gearbox consists of two stages. On the low speed shaft (LSS), indicated by number 1 in Fig. 3, the slow wheel is pressed. This is in contact with the teeth on the intermediate shaft (ISS), marked by number 2. On the intermediate shaft a high speed wheel is mounted, which establishes contact with the teeth on the high speed shaft (HSS), indicated by number 3. The applied simulation model is a generic full flexible multibody model of the full test-rig setup including the two back to back gearboxes, electrical machines and dynamic controller. A schematic representation of the model used, is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002656_ic00134a077-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002656_ic00134a077-Figure4-1.png", "caption": "Figure 4. Thin-layer cyclic voltammograms of M 12- molybdophosphoric acid in 10% dioxane mixed solution containing 0.2 M H2S04: scan rate 2 mV s-l; initial potential +0.60 V vs. SCE; initial scan direction cathodic. Points of reversing scan: (a) after the first cathodic peak; (b) after the second cathodic peak; (c) after the third cathodic peak.", "texts": [ " So that such an influence of the ratio of dioxane on the thin-layer cyclic voltammograms could be explained, the reaction mechanisms given in Scheme I were proposed. Both the first and the second reduction processes of 12-MPA are reversible two-electron transfer regardless of the ratio of dioxane. This was ascertained by reversing scan direction at the potentials right after the first cathodic peak and right after the second one. The voltammograms obtained in 10% dioxane (10) Strickland, J. D. H. J . Am. Chem. SOC. 1952, 75, 862, 868, 872. ( 1 1 ) DeAngelis, T. P.; Heineman, W. R. J . Chem. Educ. 1976, 53, 594. mixed solutions, for example, were shown in Figure 4. The six-electron reduction product of 12-MPA formed at the third reduction step seems to become less stable with decreasing ratio of dioxane. The six-electron reduction product may undergo some homogeneous reaction in a thin-layer solution to change rapidly to some heteropoly compound [P-Mol at a low ratio of dioxane. It is not clear what this heteropoly compound is, although it is oxidized to the two-electron reduction product of 12-MPA at the peak potential a2. In aqueous solutions, the six-electron reduction product of 12-MPA changes to [P-Mol almost quantitatively", " The value of c0/cR at each potential is calculated from the spectra by eq l where AR is the (1) c O / c R = ( A R - A ) / ( A - AO) absorbance of the completely reduced form, A. is that of the oxidized form, and A is that of the mixture of the oxidized and the reduced form. A linear Nernst plot (I in Figure 6 ) corresponding to the first reduction process of 12-MPA in 50% water-dioxane solution gave a value for Eo\u2019 of +0.310 V vs. SCE from the potential-axis intercept and an n value of 1.87 from the slope, when the values of A. and AR were obtained from curves a and e in Figure 4, respectively. A linear Nernst plot (I1 in Figure 6 ) , corresponding to the second reduction process, gave a value for Eo\u2019 of +0.178 V vs. SCE and an n value of 1.87 when the values of A. and AR were obtained from curves e and q in Figure 5, respectively. These results strongly suggest that both the first and the second reduction processes of 12- MPA in 50% water-dioxane solutions containing 0.2 M H2S04 are of a reversible two-electron transfer. The spectral changes accompanying the third reduction of 12-MPA are shown by curves r-u in Figure 5B" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003957_iros.2011.6094783-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003957_iros.2011.6094783-Figure9-1.png", "caption": "Fig. 9 Phases of stairs-descending assist.", "texts": [ " The robot might be able to assist the user by moving automatically according to the prepared trajectory in order to realize natural human motion when the user descends stairs. However, it is difficult to recover the user\u2019s balance when the user loses own balance for some reason because the COG of the user might move outside the supporting leg. In the stairs-descending assist which is proposed in this paper, the COG of the user is moved to the next step after the user puts the swing leg on the next step to avoid these situations. The phases of the stairs-descending assist are shown in Fig. 9. In the first phase as shown in Fig. 9(a), the user moves own swing leg to the next step. Then the robot generates the additional torque for the perception-assist as necessary to prevent the COG and ZMP of the user from moving outside the supporting leg. When the robot wants to modify ZMP, the robot generates the additional torque at the ankle joint motor of the supporting leg. If ZMP moves near the boundary of the support polygon, the additional torque of the ankle joint motor is generated to move ZMP to the center of the support polygon. On the other hand, when the robot wants to modify COG, the robot generates the additional torques at the hip, knee and ankle joint motors of the supporting leg and tries to change the posture of the upper body region because the movement of the mass of the upper body is the most effective way to change COG. In the second phase as shown in Fig. 9(b), the robot tries to put the user\u2019s swing leg on the next step while the COG and ZMP of the user remain in the supporting leg. To realize this motion, the robot rotates the user\u2019s hip, knee and ankle joint of the supporting leg automatically until the swing leg is put on the next step. The robot tries to move the COG of the user down to the z-axis direction with having kept the COG of the x-axis direction in the support leg. In this proposed method, since the COG and ZMP of the user remain in the supporting leg during the motion, it is comparatively easy to keep the user\u2019s balance, and the robot can try to modify the user\u2019s balance by adding the additional torque to the supporting leg. The robot judges the end of first phase by the position of the swing leg based on the encoders. After that, the robot starts the perception-assist of the second phase when the user moves the swing leg down to the next step. The robot shifts to the final phase after the user\u2019s swing leg is put on the next step. In the final phase as shown in Fig. 9(c), the user tries to move the COG and ZMP to the next step, and move another leg to the next step. The supporting leg changes during this motion. The robot helps the user\u2019s motion based on ZMP in order to prevent the user from losing the balance. In the proposed stairs-descending assist, although the user\u2019s motion is not always a natural motion, the robot can assist the user\u2019s motion always because the COG and ZMP of the user remain in the support polygon, and the user can descend stairs safety while being supported by the robot", " 10 and 11, the subject\u2019s right leg entered the virtual wall at about 3 seconds. Then, the robot judged that the subject might stumble on the stairs, and generated the additional motion modification force along the virtual wall. The subject could ascend the stairs without stumbling on the stairs by the perception-assist of the robot. The experimental result when the subject descended the stairs is shown in Figs. 12 and 13. Each line expresses the same as Figs. 10 and 11. In Figs. 12 and 13, (a), (b), and (c) show each phase as shown in Fig. 9. In the first phase as shown in range (a), the subject moved own right leg to the next step in the direction of x axis. In the second phase as shown in the range (b), the robot rotated the hip, knee, and ankle joint of the subject\u2019s left leg (supporting leg) while keeping the posture of right leg (swing leg) in order to put the right leg on the next step. From Fig. 12, ZMP is the almost constant value and remains in the supporting leg in the range (b). After the second phase, the robot encouraged the subject to shift ZMP and the weight of the subject from the left leg to the right leg in final phase as shown in the range (c)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003818_s11771-011-0753-z-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003818_s11771-011-0753-z-Figure4-1.png", "caption": "Figure 4 shows a specific unit of the inner-rotor running angle of \u03b83=22.5\u00b0 (\u03b82=20\u00b0) with the following geometric parameters: R=32.0 mm, Rr=4.0 mm, N=8 and eccentricity E=3.5 mm.", "texts": [ " Thus, when a couple is applied to the inner-rotor, it will rotate a small amount \u0394\u03b8 about its axis, until the tooth deformations \u03b4i (=li\u0394\u03b8) are sufficiently large to provide forces whose combined moments about O3 are equal to Tin (see Fig.5). At any instant, about half of the teeth will have contact forces which contribute to the moment Tin; while at the remaining teeth, a small separation opens up, and there is in fact no contact. Black arrows shown in Fig.5 Derivation of contact force at i-th inner-rotor J. Cent. South Univ. Technol. (2011) 18: 718\u2212725 721 Fig.4 represent the magnitude range of the contact force for the reference position, while the white arrows represent no force. If the input torque Tin about O3 is given (Fig.5), the contact force to the inner-rotor Fi at any tooth Ni can be found from the condition of moment equilibrium with the aid of the Palmgren relation [14] ,( e n ii kF \u03b4= where n=10/9) as \u2211 = + = N j n j n i i l lTF 1 1 in (8) where the value of li can be calculated in the form: \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b = *3 sin i i ii m Rr l \u03b1\u03b7 (9) and \u03b7i is the active zone discerning parameter", " If the normal forces at contact points are known, it is possible to evaluate the Hertzian contact stress, pH, at the contact point of the i-th inner-rotor as * * H \u03c02 HR EFp i= (10) where H is the rotor thickness, E* is the reduced modulus of elasticity, and R*=(1/\u03c1i+1/Rr)\u22121, is the composite radius of curvature. In this relation, the value of the radius of curvature \u03c1i is determined using the Euler-Savary equation [15] in the form: contact stresses for the case when the input torque Tin=5.0 N\u22c5m with the same geometric parameters of Fig.4. Material properties are E=210 GPa and =\u03bd 0.29 for all the rotors, and the rotor thickness is H=9.25 mm. The simulation work is now taken under study for the same geometric and input parameters with Section 3.1. The specific volume (or the theoretical displacement) is evaluated to be 12.62 cm3/rev and determined using the following formula: HNAV \u22c5\u22c5\u0394=th (13) where \u0394A is equal to the difference of the maximum chamber area and the minimum chamber area. The Fig.6 Hertzian contact stresses at contact points manufacturing, clearance and thermal effects are not taken into account in this preliminary approach" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003123_icems.2009.5382652-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003123_icems.2009.5382652-Figure1-1.png", "caption": "Fig. 1. Configurations of 4/2 SRM", "texts": [ " The motor is 4/2SRM that has 4 poles on the stator and 2 poles on the rotor to obtain the high speed drive. With the least number of poles, it can adjust the high speed drives because it is easy to increase the current. In this paper, the motor and its basic characteristics are illustrated at first. Then, the simulation model based on the characteristics is composed. Finally, the torque and efficiency \u2013 speed characteristics from experiment and simulation are discussed to determine the excitation angle. II. 4/2 SRM MODEL The configurations and specifications of 4/2 SRM are shown in Fig. 1 and Table. I, respectively. This is 2-phase motor and has the least number of poles because it can be high efficiency in a high speed area. In case of 4/2 SRM, it has enough intervals of time between each phase to build the current up even though it drives at high speed. Therefore, the current can contribute to a torque. There are two possible objections will be raised to the few poles: one is that it has a dead zone near the unaligned position not to produce a torque[5]; the other is about torque vibrations. To solve the former problem, a stepped airgap on a tip of the rotor poles works. On the other hand, the latter can be no problem since it drives in high speed area that the vibration can be ignored. The windings at each phase are series connections, and the stator is laminated to 0.02mm to reduce iron losses. Furthermore, in this paper, unaligned position is defined as -90deg and 90deg, and aligned position is as 0deg. For example, in case of Fig.1 based on A-phase, this is 0deg. A photo interrupter with a timing cam in Fig. 1, is used as a position sensor. The sensor produces two pulses per a revolution, and the build-up and build-down are used to determine excitation timings. Fig. 2 describes the drive circuit. The FET and diode are P2HM1102H made by Nihon Inter Electronics Corporation not to flow a reverse recovery current, even the high frequency. The two FET, AH and BL, are simultaneously switched on. The other FET, CH and DL, do as the same. The control of the motor adopts singlepulse operation and hard switching" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003491_20120905-3-hr-2030.00031-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003491_20120905-3-hr-2030.00031-Figure2-1.png", "caption": "Fig. 2. Scheme of the actuated joint placed on the quadrotor\u2019s arms.", "texts": [ "00031 In order to obtain an UAV able to fly decoupling linear and rotational movements, thus allowing operations that are not usually possible with standard flying vehicles, the proposed quadrotor has some structural differences with respect to standard devices. The most important difference is shown in Fig. 1, where a scheme of the proposed quadrotor is reported. As it can be seen, an actuated rotational (pivot) joint ri is installed on each arm of the vehicle, thus allowing to rotate the corresponding propeller by the angle \u03b1i. In this manner, the force Pi generated by the propeller may be directed along any direction in a plane orthogonal to the corresponding arm (the plane \u03c0i in Fig. 2). Another difference with respect to a standard quadrotor is the rotating direction of the thrusters. In fact, as shown in Fig. 3(a), in a standard quadrotor the couple of propellers {1, 3} rotates clockwise, while propellers {2, 4} rotate counter-clockwise. This configuration ensures that, in hovering maneuvers, it is always possible to rotate the quadrotor about its z-axis by slowing down opposite propellers, but preserving the balance of the counteracting torques. In our case, as depicted in Fig", " if s = [s1, s2, s3] T , then s\u00d7 is the skew-symmetric matrix s\u00d7 = [ 0 \u2212s3 s2 s3 0 \u2212s1 \u2212s2 s1 0 ] (2) Since it is of interest to show the potentiality of the new quadrotor and not to analyze in detail the physical properties of the model, second order effects related to aerodynamics effects, such as the propellers flapping or the gyroscopic precession torques due to the angular speed of the propellers (Hoffmann et al., 2007), (Prouty, 2001), or due to the actuators dynamics, have been neglected. By defining as \u03b3i (> 0) the rotation velocity of the i-th propeller, and with \u03b1i the orientation of the i-th pivot joint (see Fig. 2), the terms f b and \u03c4 b in Eq. (1) can be defined by considering that the corresponding propeller affects the dynamics of the quadrotor in two ways: by generating a propulsion force Pi orthogonal to the propeller itself, and by generating a counteracting torque \u0393i (see Fig. 4). In particular, as described in (Pounds et al., 2010), it is possible to consider these two contributions as: Pi = kf,i\u03b3 2 i (3) \u0393i = k\u03c4,i\u03b3 2 i + Ir,i\u03b3\u0307i (4) where Ir,i is the motor inertia and kf,i, k\u03c4,i are two parameters that depend on the air density and on geometrical properties of the i-th propeller (see (Pounds et al" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003026_1.3212679-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003026_1.3212679-Figure9-1.png", "caption": "Fig. 9 A serially connected C R mechanism", "texts": [ " The necessary and ufficient condition for a general circular surface to be one of the onstraint circular surfaces generated by the mechanisms is to be roved in the following using the set of Euclidean invariants. 6.1 The Necessary and Sufficient Condition for a Circular urface to Be a C R Surface. C R circular surfaces are a class of urfaces that can be generated by a point P attached to a base hrough a serially connected C R mechanism. They can be decribed in an arbitrary fixed reference frame i , j ,k , as in Fig. 9, y assuming that 1 0. Otherwise C R circular surfaces will deenerate to a particular type of circular surfaces whose circle lanes are always parallel to a fixed plane, which are of little nterest. Suppose that the fixed line LA passes through a fixed point A0, 1 is designated as the constant inclination angle of LA with repect to the line LB, a1 denotes the normal distance between the wo lines, the points A and B are the intersecting points of their ommon perpendicular, and d2 is the distance between the spine urve M and the point B" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001714_rnc.604-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001714_rnc.604-Figure3-1.png", "caption": "Figure 3. Current: de\"nition of incidence angles.", "texts": [ "f K , the sliding condition (4) will be satis\"ed. So, the control will be totally de\"ned if the maximum uncertainty about the function f is known. It must be emphasized that this function is related to the environmental and mooring sway forces and yaw moments. 3.1. Design of the controller robust to current variations When the ship is only under current action the controller must guarantee the stability and performance requirements due to uncertainty about the direction and velocity of the current and about its model. Taking (see Figure 3), the angle between current direction and theX-axis, and its maximum variation, it can be written as follows: ; (;(; ! ( ( # In the present formulation, it is considered that the whole state vector (x, y, , xR , yR , ) is measured. The best estimate of the function f is obtained using nominal environmental conditions (;K \"(; #; )/2 and ) \" ) in (13b), and will be referred to as f K (x, x ). The application of (14) requires the maximum error on f . In the present case, this error is caused by uncertainties in current direction and intensity and in the model of current and mooring lines forces" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001384_978-94-017-2925-3-Figure5.13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001384_978-94-017-2925-3-Figure5.13-1.png", "caption": "Fig. 5.13. A torsion pendulum device.", "texts": [ " A number of other properties can be obtained from the trace. For example, the average ratio of heights of successive oscillations gives an arbitrary measure PHYSICAL TESTING OF VULCANIZATES 161 of resilience of the rubber which, expressed as a percentage, is termed the Yerz ley resilience. In a trace such as that of Fig. 5.12, the Yerzley resilience equals Another type of free-vibration instrument is the torsion pendulum, 13 \u2022 33 a clas sic for studying dynamic properties of rubber. Many designs of apparatus have been used; that in Fig. 5.13 will illustrate the principles. The bottom of the ribbon-shaped specimen is rigidly attached while the top is fastened, either sol idly or through a torsion wire, to a structure having an adjustable mnment of inertia. The weight of this device is counterbalanced through a cord having negligible torsional stiffness. When the test is performed, the inertial system is displaced through a small angle (about 1.5\u00b0) and released. The shear modulus may be calculated from the period; 13 the shorter the period the greater the modulus" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.12-1.png", "caption": "Fig. 4.12 A cow-driven paddle blade machine, a Original illustration (Wang 1968), b Structural sketch, c Chain", "texts": [ "11b shows a horizontal animal-driven mill that was driven by animals to produce an output rotation in the same direction through a simple gear train (Lu and Hua 2000). The book Nong Shu\u300a\u8fb2\u66f8\u300b (Wang 1968) has a detailed introduction of a waterdriven and a cow-driven paddle blade machines that use gears to transmit power. Furthermore, the cow-driven paddle blade machine can also be seen in paintings of the Tang Dynasty (AD 618\u2013907). The books Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b (Pan 1998) and Nong Zheng Quan Shu\u300a\u8fb2\u653f\u5168\u66f8\u300b (Xu 1968) also have discussions about this device. Figure 4.12a shows a type of cow-driven paddle blade machine from the book Nong Shu\u300a\u8fb2\u66f8\u300b (Wang 1968). The machine is driven by a horizontal large gear (member 2, KG1) to drive the vertical small gear (member 3, KG2) to produce the rotating motion of the horizontal shaft. Then the 4.4 Gear Mechanisms 75 rotating motion is passed to the sprockets and chain (member 4, KC) to draw water. The upper sprocket is connected to the horizontal shaft and the small gear as an assembly. The lower sprocket (member 5, KK) is connected to the frame and the chain" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002980_978-3-642-01153-5-Figure3.1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002980_978-3-642-01153-5-Figure3.1-1.png", "caption": "Figure 3.1.1 , , 0 pattern of synchronous machines", "texts": [ "i i However, the rotor resistance neglected, the equations above can be much reduced and used easily. Studying d, q, 0 axes, we have mentioned that the currents di and qi represent the stator d-axis and q-axis mmfs which are observed from the reference axes that rotate with the rotor. Discussing , , 0 axes now, from equations (3.1.3) and (3.1.4) we can know that the currents andi i represent the stator -axis and -axis mmfs respectively, in which -axis coincides with the stator a-axis and -axis leads ahead of -axis by an angle of referring to Fig. 3.1.1, so those axes are static ones relative to the stator. In addition, , , ,d q d qi i and ,d qu u in d, q, 0 axes represent the currents, flux-linkages and voltages in the fictitious circuits of the stator d-axis and q-axis respectively. Similarly, , , ,i i and ,u u in , ,0 axes represent the currents, flux-linkages and voltages in the fictitious circuits of the stator -axis and -axis referring to Fig. 3.1.1. Thus, we AC Machine Systems 172 have another physical model of synchronous machines which is an equivalent 2-phase synchronous machine. From equation (3.1.9) we can see that there is on speed emf in , , 0 axes. That is not difficult to understand, because , , 0 axes are static ones and , don\u2019t rotate relatively to the stator. (2) 1, 2, 0 axes The transformation matrix in the reference axes is 2 11 12 13 2 21 22 23 31 32 33 1 1 1 3 3 3 1 1 1 3 3 3 1 1 1 3 3 3 a a a aC (3.1.12) in which j120 1 3e j 2 2 a is the complex operator" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.12-1.png", "caption": "Fig. 9.12 A linen spinning device (\u87e0\u8eca) a Original illustration (Wang 1991), b Structural sketch", "texts": [ " There are eight textile devices with flexible connecting mechanisms including Pan Che (\u87e0\u8eca, a linen spinning device), Xu Che (\u7d6e\u8eca, a cocoon boiling device), Gan Mian Che (\u8d95\u68c9\u8eca, a cottonseed removing device), Tan Mian (\u5f48\u68c9, a cotton loosening device), Shou Yao Fang Che (\u624b\u6416\u7d21\u8eca, a hand-operated spinning device), Wei Che (\u7def\u8eca, a hand-operated spinning device), Jing Jia (\u7d93\u67b6, a silk 9.3 Handiwork Devices 205 drawing device), and Mu Mian Kuang Chuang (\u6728\u68c9\u8ee0\u5e8a, a cotton drawing device). Each of these devices is a Type I mechanism with a clear structure and is described below: 9.4.1 Pan Che (\u87e0\u8eca, A Linen Spinning Device) Pan Che (\u87e0\u8eca, a linen spinning device), also known as Bo Che (\u64a5\u8eca) is shown in Fig. 9.12a (Wang 1991). It is a tool to transform hemp fibers into yarns and belongs to the Chan Lu (\u7e8f\u7e91) process in the fiber processing steps. The operator holds Xian Lu (\u7dda\u7e91, a hand bar) on one hand and the other hand pulls the yarn around the hand bar, causing Xian Ren (\u7dda\u7d4d, a spinning wheel) to spin. 206 9 Flexible Connecting Mechanisms It is a mechanism with three members and two joints, including a wooden frame as the frame (member 1, KF), a spinning wheel (member 2, KL), and the yarn (member 3, KT). The spinning wheel is connected to the frame with a revolute joint JRz. The yarn is connected to the spinning wheel with a wrapping joint JW. Figure 9.12b shows the structural sketch. 9.4.2 Xu Che (\u7d6e\u8eca, A Cocoon Boiling Device) Xu Che (\u7d6e\u8eca, a cocoon boiling device) is used to boil cocoons in the preparatory process before silk extracting as shown in Fig. 9.13a (Wang 1991). In the device, a pulley is placed on the wooden stand and hooked by a rope. The other end of the 9.4 Textile Devices 207 rope is tied to a cloth bag in which silk cocoons are located. An urn with hot water is placed on the ground and the cloth bag is soaked in the urn. When the device is working, the operator can pull the rope to control the soaking and heating degree of the silk cocoons" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001951_tmag.2004.832173-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001951_tmag.2004.832173-Figure3-1.png", "caption": "Fig. 3. Static torque profiles for all the four phases of the motor having relative eccentricity of 50%.", "texts": [ " It is observed from this figure that the fundamental torque is not changing much with relative eccentricity up to 50% and then increases; because of the considerable reduction in airgap on one side of the rotor. Fig. 2 shows the variation of the 8 , 10 , 14 , and 15 harmonic torques with relative eccentricity. It is observed that there is increase in the 8 , 10 , and 15 harmonic torques with increase in relative 0018-9464/04$20.00 \u00a9 2004 IEEE For the motor having relative eccentricity of 50% static torque profiles for all the four phases are shown in Fig. 3. It can be observed that the torque profiles for all the four phases are not the same. This happens because of the fact that the relative eccentricity causes the airgap under aligned condition to be different for different poles. Table II shows the peak magnitudes of these four static torque profiles. Average flux density at the excitation of 10 A in various parts of the motor at different relative eccentricity error is given in Table III. Fig. 4(a)\u2013(c) shows the flux density variations in different parts of the motor at various relative eccentricity errors for the excitation of 10 A" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001948_robot.2001.932980-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001948_robot.2001.932980-Figure6-1.png", "caption": "Fig. 6: Dimensions of 5-DOF IZPUR robot (in mm)", "texts": [ "2 The NRJ approach STEP 1: Solvability Denote the number of revolute joints as m. If m 5 3: then k = 1, and continue with the construction of the virtual wrist; (Step 2). Otherwise, exit and use the numerical inverse kinematics. STEP 2: Virtual wrist construction Revolute twists allocation - Let C r j = ( w r J , v r J ) E se(3) denote the revolute twists, where r j E N , j = 1:. . . , m. Then (1 = (0 ,0 , 1 , 0 , 0 , 0 ) E3 = (-1,0,0,0,140, -425) <5 = ( 0 , 1,0, 0,600,315) the robot is shown in Fig.6. The DOF of the robot: n = 5 . The POE equation of the robot is h h gsl (0) = eElel . . . e\u20ac5'5gst (0) = gd (21) The joint twists of the manipulator are given as: ( 2 = (O,O, 0, 0, 0,1) E4 = (O,O, 1,140,70,0) The initial and desired poses of the end-effector, g,t(O) and gd are given as: 0.94028 -0.18221 0.28753 65.41 -0.29140 0.005734 0.95658 388.14 -0.17595 -0.98324 -0.047706 289.39 0 0 0 1 h h A A h e4i0i . . . eFT1OF1 . . . e&2Qp2 . . . ,E7.,QF,, . . . ,&on =T= R p (I8) Virtual wrist decomposition - Let ti, = ( W r J , 0) denote the relocated revolute joint twist parallel to & The orientation Because there are two intersecting axes in the middle, Step 1: Solvability - The location of the wrist: i s = 3, i , = 4" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002145_iros.2000.895302-Figure13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002145_iros.2000.895302-Figure13-1.png", "caption": "Fig. 13 Suspension built-in Passive Wheel", "texts": [], "surrounding_texts": [ "To begin with, the prototype of the joint unit is made in order to develop the ACM mechanical model that realizes three-dimensional and various functions The joint unit has 2 degrees of freedom and can do pitch and yaw motion. Its dimension is 20Ox190x180mm, and i t is over 2.5kg including all parts. There are two motors in the joint unit, and pitch and yaw motions are performed by the coupring the outputs. The workspace is maximized by offsetting pitch and yaw axis. And, this uni t has new mechanisms called \"M-Drive\" and \"Float differential torque sensor\". The former is to prevent the mechanical destruction by excessive load, and the latter is the detection mechanism of torque at each drive axis. And the making of the self-containd system is possible in the future, so that there is room for such as control computer, motor driver, and battery. -2243- This unit has 2 passive wheels on the both side for obtaining the frictional property for the glide propulsion. Thus, it is easy to slip in the direction along the trunk, and it is difficult to slip in the direction which is orthogonalized with it. Though the interference of wheels and the effect of the slip angle are considered because of the curvature discreteness, placing the axle in the midpoint of each joint has reduced these effects. Table 1 Specifications of the prototype unit Actuator Dimension Weight Torque Angular velocity Workspace . - . 20W DC Motor x2 (Coupled) 200x 260 / 260 deg 90x180 mm 2.5 kg 5 kgfm 8 rpm (yaw / pitch) 3.1 Wire type differential mechanism It is necessary that the actuator unit is high output mass ratio, because large moment affects the root when the neck is lifted. As the solution, the differential mechanism using the harmonic gear is introduced. This mechanism is lightweight because it is composed of not bevel gears but wire and pulley. The harmonic gear is a differential system which has one input and two output parts. One output is attached to pitch shaft and the other is attached the pulley. 2 sets of these are placed on a pitch shaft. The wire and pulley configuration is shown in Fig.6, and the endpoint of the wire is fixed in the yaw pulley. The rotation in the pitch axis is carried out in the case that two pulley outputs are same directions in viewing from the pitch shaft, and the yaw axial motion is carried out when the pulley outputs are is reverse-directions, This actuator unit is adopted the coupled drive which is the method of maximizing output performance by cooperatively utilizing as possible all actuators that are installed. 3.2 Torque limiting mechanism M-Drive\" The ACM is hyper-redundant serial link system. The principal problem of existing systems is the inability to withstand unexpected external forces due to excessive moments at its root joints, so the torque limiter is necessary. Though usual torque limiter is bulky, it can be realized by adding simple parts in the wire drive system. The basic principle of M-Drive can be explained from the expression of the fiction transmission between the string and the pulley. In Fig. 7 (a), let T , and T, ( TI c T,) are the string's tension, ,U is the friction coefficient between the string and the pulley, and 8 is the winding angle of strings. The condition in which the slip occurs is the following. T, >TI exp( PO 1 So the maximum value of T,can be decided by TI which is set beforehand and by far smaller tension than T,. T, is the driving force of the pulley, and the torque that generates the tension over the maximum value of T, is not transmitted by slipping[3]. - 2244 - It is constructed as shown in Fig.7 @) and Fig.8. The wire drawn out from its winding pulley is hooked around the other pulley that is rotation free. This pulley is pulled by the spring for applying the tension on the wire. And the compressive force of coil spring, which is accumulated by turning the worm gear, has been applied on pulley by the link in this tensioner unit. 3 3 Float differential torque sensor It is useful to obtain torque information, which works in each axis in order to realize the advanced and three-dimensional motion control. As a torque sensor, \"Float differential torque sensor\" shown in Fig.9 is introduced. It is easy to maintain this sensor and the additional equipment. The motor is supported rotation freely from the base by ball bearings, and it is connected by the hard spring between the motor and base. By measuring the strain gauge mounted on this spring, the reaction torque of the motor is detected. Generally the strain gauge is applied to the output itself in order to measure the torque of the actuator. However this sensor has high reliability and generality, because it removes the wiring of collector ring or strain gauge from the output, which infinity rotates[4]. Harmonic gear is used in the actuator unit, so this torque sensor is adopted as the flexspline is supported rotation freely from the pitch shaft as Fig.10 shows. 3.4 Basic experiments The operation test of this prototype unit is carried out. This unit is position controlled by returning the value of sum or difference of two potentiometers which are set in the pitch and yaw axis to each motor driver. It has been confirmed that there are no problems such as the interference for this unit and that it normally operates. For the float differential torque sensor, it is confirmed that it has the sufficient linearity and its deviation is little in Fig.11. The external force is applied to the unit that is position controlled as performance test of M-Drive. A pair of outputs of torque sensors is in Fig.12. The left part shows an aspect under the permission torque, and then this joint unit acts as usual servo system. On the other hand, there is the leveling off in the right part, and it is a cause that the supeffluous torque does not arise by slipping. External force[kgfl Fig.11 Experiment of the float differential torque sensor -5 O; I J 0 2 4 6 8 Time[sec] -sensor A -sensor B Fig.12 Experiment of M-Drive -2245- 3.6 Improve the joint unit Dimembn Weight Torque Angle velocity 3.6.1 Consideration to the three-dimensional motion There is the case that only one in the pair of wheel contacts the ground by the body shape, because each joint does not have degree of freedom of roll motion. The suspension mechanism is added in each wheel in order to prevent this problem. And the frame rigidity is improved by establishing the top board at the uni t in order to stand the three-dimensional motion like 2 0 0 ~ 1 9 0 ~ 1 8 0 ~ 170~150~14511~~1(-46%) 2.5 kg 2 kg (-20%) 5 kglin 4.1 kglin 8 rpm 9.6 rpm 3.6.2 Improved tensoner The wire tensioner is independent composition in the primary model. The joint unit becomes smaller and lighter so that it is conbined with the motor uni t in the improved model. It is composed of the link with a free pulley and a ring around the motor. These are tied together with a torsion spring. And there are the different number of holes in the ring and the motor base. The wire tension is adjusted by the combination of the hole where the pin As a result of these improvements, it becomes about -20% in the weight and about -46% in the volume in comparing primary model. Table 2 Improvement of specification Primary Model Improved Model 4. Development of the three-dimensional Active Cord Mechanism: ACM-R2 4.1 System constitution ACM-R2 consists of 14 joint units which are straight-chained. It has ability for the propulsion at 1 m/s and the compensation for the weight of 5 units levelly. It has totally 28 degrees of freedom. Angle and torque of each joint are measured. It is possible to make self-contained system in the future, because there is space for mounting batteries, wireless LAN, etc. on the body. It has 2 motor drivers (TITECH Robot driver 2)[5], 2 amplifiers for the strain gauge and a microcomputer (HITACHI H8/3048F 16MHz). No. of unit 14 (28 degrees of freedom) Demension 2430x150~145 mm Weight 30 kg Promotion speed - 2246 - Each actuator controls its position by the motor driver, however each joint controls their torque at a local loop by returning the value of the torque sensor to the motor driver as a feedback value of the position. The processing by the microcomputer is DA converted for motor drivers (2ch), AD converted from angle or torque sensors (4ch) and serial communication to the host computer, which is in the last joint unit. The processingof the motion plan of serpentine motion, etc. is carried out in the host PC. 4.2 Fundamental operation 4.2.1 Torque control Torque control at the local loop has been implemented and is confirmed that i t can be controlled without causing abnormal vibration. And when the external force is applied to joints in a stationary state, it is also confirmed that the joint bends in the direction in order to avoid it 4.2.2 Position control Position control has been implemented by commanding the torque order in proportion to the difference in real joint angle and target one to each actuator. There are small vibrations in some joints in this control mode. The following causes are considered: That control period of the position loop is late, that the resolution of the AD conversion of the joint angle is low and noise. The vibrations are disposed of in raising the communication speed between the host PC and microcomputers on each joint, and redoing the wiring to endure the noise for these problems. There is no problem for the operation by these improvements, as long as the accuracy of the position is not so required in the present state. The experiment of ACMR-2 lifting its head as a sickle neck is carried out by manual control. And, the propulsion using control method, which makes each joint angle to change in sine wave like, is carried out as well as the conventional mechanical model. 5. Conclusions The ACM with three-dimensional motor capacity is discussed in this paper. It has various functionalities, and it is made good use by ACM possessing the ability of three-dimensional motion. Then, ACM-R2 that is the mechanical model with the three-dimensional capacity is actual made. It is a high performance model so that i t has M-Drive (torque limiter) and Float differential torque sensor. It is confirmed effectively operating of these mechanisms, and the experiment of fundamental operation is carried out. As a future work, It will be realized that manipulation and locomotion for adapting the body shape to the surroundings in order to keep the stability without overtuming. And the proposed new propulsions are to be verified by the real machine. It will be concretely examined control methods which utilize the torque information in order to achieve these. Acknowledgment This research is supported by The Grant-in Aid for COE Research Project of Super Mechano-Systems by the Minstry of Educaton, Scince,Sport and Culture. References [I] Shigeo Hirose : \u201cBiologically Inspired Robots (Snake-like Lo- comotor and Manipulator)\u201d, Oxford University Press, 1993 [2] Gen ENDO, Keiji TOGAWA ,Shigeo HIROSE : \u201cStudy on self-contained and Terrain Adaptive Active Cord Mechanism\u201d,in Proc. of IEEE/RSJ International Conference on Inteligent Robots and Systems, pp1399-1405,1999 [3] S.Hirose, Richard Chu : \u201cDevelopment of a Lightweight Torque Limiting M-Drive Acuator for Hyper-Redundant Manipulator Float Arm\u201d, in Proc. IEEE International Conference on Robotics and Automation, pp2831-2836,1999 [4] S.Hirose, K.Kato : \u201cDevelopment of the Float Differntial Torque Sensor\u201d, in Proc. of JSME Conference on Robotics and Mechatronics, IC1 2-6, 1998 (in Japanese) [5] E.F.Fukushima, T.Tsumaki,S.Hirose : \u201cDevelopment of a PWM DC Motor Servo Driver Circuit\u201d,in Proc. of RSJ95,pp1153-1154,1995 (in Japanese) - 2247 -" ] }, { "image_filename": "designv10_13_0002561_0021-9290(82)90253-6-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002561_0021-9290(82)90253-6-Figure1-1.png", "caption": "Fig. 1. Free body diagram for segment 9 (right shank).", "texts": [ " It is also possible that an external torque may be applied to these distal segments. A convenient modelling technique is to reduce such a force system by equipollence to a single force and torque at a point fixed within the distal segment. For this reason it is assumed that a force and torque act at knuckle III on each hand (5, 9) and at the distal phalanx of each great toe (13, 17). These points may therefore be regarded as 'pseudo joints'. A free body diagram of a typical segment (the right shank) is shown in Fig. 1. The inertial reference frame R : O X Y Z is orientated such that the Y axis is directed vertically upward. It may be noted that the force and torque at the ankle joint ( - F I 2 and -T12) a r e given negative signs. The joint force and torque acting on the distal end of each segment (except for the pseudo joints 5, 9, 13 and 17) are given negative signs in order to satisfy Newton's law of action and reaction. The location vectors d and p are directed distally and proximally respectively, while the numerical subscript is used to indicate the segment numbers. Newton's principles of linear and angular momentum may be applied to segment 9 in Fig. 1 to yield (Andrews, 1974): F i t -- FI2 = mq(a 9 + g) (1) T i t - T12 + (P9 x Fl1 ) - d 9 x F12 ) = I~19 (2) where a 9 is the linear acceleration of the center of mass of segment 9 and H9 is the time rate of change of angular momentum of segment 9 about its own center of mass. Vector equations (1) and (2) hold for both two- and three-dimensional motion. The rest of this paper is restricted to the case of twodimensional motion in the vertical XY plane of the inertial reference frame R : O X Y Z . (This planar assumption serves to reduce the mathematical com- plexity of the problem but it does not affect the generality of the solution procedure)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure8.8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure8.8-1.png", "caption": "Fig. 8.8 A vertical-shaft wind-driven paddle blade machine, a Real object (Lin et al. 2009), b Simulation illustration (Lin et al. 2009) c Structural sketch", "texts": [ " When downwind, the sail automatically turns perpendicular to the direction of the 178 8 Gear and Cam Mechanisms wind to gain maximum energy; while upwind, the sail turns parallel to the direction of wind to receive the minimum resistance. This principle makes the device unaffected by the variation of the wind, nor does the device change the rotating direction. However, due to its large size, after the 1980s, the device has been replaced by electric water pumps or by internal combustion engines. In recent years, experts and scholars redesigned and reconstructed a real object of the vertical-shaft Feng Zhuan Fan Che in the original size as shown in Fig. 8.8a (Lin et al. 2009; Sun et al. 2009; Lin and Lin 2012). Since the swing of the sail does not affect the output of the mechanism, the wind sails, the vertical shaft, and the large horizontal gear can be considered as an assembly (member 2, KG1). The other members and joints are identical to the ones in Niu Zhuan Fan Che (\u725b\u8f49\u7ffb \u8eca, a cow-driven paddle blade machine). Figures 8.8b and c show the simulation illustration and the structural sketch, respectively. A horizontal-shaft Feng Zhuan Fan Che has three\u2013six wind sails" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002554_j.biosystems.2006.09.015-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002554_j.biosystems.2006.09.015-Figure10-1.png", "caption": "Fig. 10. Phase portraits of van der Pol equations for bistable (A) and autoosc coordinates (C). For detailed explanations see text.", "texts": [ " Grabovs dynamic variable along dy/dt = 0 isocline will be slow enough. In any case, the conditions for reproducing the overshoots within the framework of Eq. (1) are enough robust. Let us discuss in more details the regime of autooscillations which correspond to growth pulsations (GP). The above mentioned deformations of the perisarc and hence the rudiments themselves during GP should be roughly proportional to the pressure-time products. Therefore, the slower be the rate of the variable movement along rs branch, directed towards pressure increase (Fig. 10B), the greater be the deformation. As already mentioned, the rate can be retarded by shifting to below dx/dt = 0 isocline, that is, by diminishing B values. As a result, the shape of a GP record in stress-time coordinates will be asymmetric with its branch pqr more steep than rsp (Fig. 10C), what fits the observations. Therefore the Eq. (1) are rich enough for reproducing the main regimes used in our models. Systems 87 (2007) 204\u2013214 Now let us correlate the equations parameters with those used in our models. First, one can see that the \u201cglobal threshold\u201d (GT) parameter used in CE-feedback model is proportional to (xm \u2212 xp) distance. In the terms of Eq. (1) the latter can be affected in several ways. For example, it can be diminished by reducing the absolute value(s) of at least one of the following parameters: k, B, D (in these cases increased is xp value) and/or A/C ratio (this increases xm = 4/3A(A/3C)1/2)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002624_j.talanta.2007.12.015-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002624_j.talanta.2007.12.015-Figure2-1.png", "caption": "Fig. 2. Sensor set-up: plastic housing with different membranes and electrodes for the detection of the gaseous analyte formaldehyde.", "texts": [ " zavarzinii strain ZV 580 and subequent electrochemical detection of released electrons with the id of 1,2-naphtoquinone-4-sulfonic acid (NQS) as mediator Fig. 1). The flux of electrons was recorded in an amperoetric measurement at +200 mV vs. Ag/AgCl reference (3 M Cl, 210 mV vs. NHE) using a potentiostat (PGSTAT 12, Eco hemie, The Netherlands). The sensor device consists of a 3-electrode configuration with isks of woven graphite gauze (Alfa Aesar, \u00d8 = 15 mm) as workng and counter electrode included in a plastic housing (Fig. 2). oth electrodes were contacted with Pt-wire (\u00d8 = 0.2 mm). he gas diffuses into the liquid phase via a 15 mm diameer Teflon membrane (FALP02500, Millipore, France). Loss of nzyme is restricted by a dialyses membrane with a MWCO f 12,000\u201314,000 Da (Medicell International, London, Great ritain). Gaseous formaldehyde samples were collected from the head pace above aqueous solutions of known concentration. The H2O concentration in the gas phase above the solution was calulated according to the equation given by Dong and Dasgupta 15] as shown in Table 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002435_s1474-6670(17)53666-6-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002435_s1474-6670(17)53666-6-Figure1-1.png", "caption": "Figure 1: Aircraft coordi nate systems", "texts": [ " the equations of 1l1otion can be written as mi'= R fa+mq (1) (2) (3) where fa and Ta arc the force and moment acting on the aircraft expressed relati\\'e to the aircraft. Here. the a subscript means that a quantity is expressed with respect to the aircraft reference frcullC' . A. Force and Moment Generation For the sake of presentation. we will focus our at tention on a particular aircraft. the Y .. \\.\\'-8B Harrier produced by :-'lcDonnell Aircraft COmp311Y (19S2. 1983) . The Harrier is a si ngle. seat transonic light attack \\' !STOL (\\,errical!shorr takeoff and land ing) aircraft powered by a single turbo-fan engine. Figure 1 sho\\\\' s the aircraft with the coordinate frame . A. attached at the (nominaI) cent er of mess. The .r-a..xis is directed forward toward the nose of the airc raft and is also known as the roll a..xis since positi\"e rotation abOll! the .r-;Lxis coincides wi th rolling the air craft to the right (from the pilot's point of ,\u00b7iew). The y-axi s is 386 .J. Hallser. S. Sastn' alld (;. ~1c\\lT directed toward the right wing and is called the pitch a..xis (pos itive rotation is a pitch up). The z. 0, E > 0 and a E IR\" denotes the set of all continuous differentiable increasing functions sat(z) = [sat(xl) sat(a2) ... sat(c,,)lT such that ~ 4 1 , [51. 0 1x1 2 Isat(z)l 2 m 1x1 0 E 2 Isat(z)l 2 m~ V x E IR : 1x1 < E V 5 E IR: 121 2 E where I . I stands for the absolute value. 0 Figure 1 depicts the region allowed for functions belonging to set 3 ( m , ~ , a ) . For instance, the nonlinear vector function sat(+) = [sat(tl) sat(t2) . . sat(&,)lT, considered in Arimot0 [3], whose entries are given by sin(x) if 1x1 < n/2 { -1 i f z I - - a / 2 sat(x) = Sin(x) = 1 if x 2 n/2 (2) belongs to set F(sin(l), 1, z). Other examples are: the tangent hyperbolic function tanh(1:) = -, which belongs to F( tanh( 1) , 1 , z ) , and the nonlinear function *, which belongs to F(1/2,1, z). 3.1 A class of nonlinear PID controllers Let us propose the following control law r = I i p i j - - K U q + I S j sat(q(a)) du+V#,(ij) (3) where K p = Ki/a, ISu and ICi are diagonal positive definite n x n matrices, sat(q) E F(m, E , G ) , Ua($ is a kind of C1 artificial potential energy induced by a part of the proportional term of the controller whose properties will be established later, and (Y is a constant satisfying I' with /" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002389_pime_proc_1987_201_092_02-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002389_pime_proc_1987_201_092_02-Figure1-1.png", "caption": "Fig. 1 Spacecraft configuration", "texts": [ " Although this study was successful, in the sense that an acceptable controller was found, the final design was the result of a compromise between the transient behaviour and the steady state accuracy. In this paper a simple extenGon to the SOC is proposed which obviates the need for this compromise. 2 SUMMARY OF PREVIOUS STUDY For ease of reference the results of the authors\u2019 previous study (14) are summarized below. 2.1 Process model The process used in the design study was a hypothetical flexible communications satellite similar in configuration to that of the French multi-mission platform SPOT (Fig. 1). For the conditions of small angle manoeuvres and small angular rates, the spacecraft dynamics may be represented by the following differential equations describing roll, pitch and yaw attitudes, and the solar array bending motion (15): T = E(+ - &,&) - 64 4 + QZ\u2019I = 8T(& - Go&) (1) (2) The M S was received on 16 April 1986 and was accepted for publication on 29 July 1986. where T is the error torque acting on the vehicle (difference between external torques and the control torques), E is the 3 x 3 inertia matrix, is the vector of modal deformation coordinates of dimension m, 6 is a 3 x m matrix whose columns are the moment of the mode shape oi, i = 1, ", " Figure 10 shows the satellite response to the SOC when the modal frequencies [equation (2)] are reduced by a factor of 2. The controller copes well with this mismatch condition and a significant deterioration in performance does not occur until the modal frequencies are reduced to 25 per cent of the nominal values (Fig. 11). Similarly, increasing the modal frequencies does not degrade the system performance significantly until they are five times the nominal values (Fig. 12). The solar array (see Fig. 1) is mounted on a boom that is orientated parallel to the negative pitch axis. The array can rotate about this axis to maximize its exposure to solar energy. However, it has been assumed above that the array is fixed parallel to the roll axis. Therefore another possible mismatch condition occurs when the orientation of the solar array is changed. The satellite response to the SOC for a 90\" change in orientation, which is the worst possible case, is shown in Fig. 13. The roll attitude response on the initial run is poor but is improved during subsequent runs, with an acceptable performance occurring on the fifth run" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001653_s101890170034-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001653_s101890170034-Figure1-1.png", "caption": "Fig. 1. (a) Scattering geometries for bend mode and (b) splay mode detection.", "texts": [ " i\u03bd and f\u03bd are the components of the polarization of incident and scattered light, respectively, thereby referring to a particularly chosen, q-dependent Cartesian coordinate system {e1, e2, e0} with e0 parallel to the optical axis, e2 = (e0 \u00d7 q) / |e0 \u00d7 q|, and e1 = (e2 \u00d7 e0) / |e2 \u00d7 e0|. The relaxation rates \u03c4\u22121 \u03bd (q) of the two scattering components are ruled by effective rotational viscosities \u03b7\u03bd (q): \u03c4\u22121 \u03bd (q) = K3q 2 \u2016 +K\u03bdq 2 \u22a5 \u03b7\u03bd (q) \u00b7 (2) The viscosities \u03b7\u03bd (q) are scattering geometry dependent combinations of the Leslie coefficients. In our experiments we used two different geometries: (i) In case of the \u201cbend geometry\u201d (Fig. 1a) the director is aligned in the scattering plane and is approximately parallel to the scattering vector. Then mode 1 in equation (1) vanishes because of i0 = i1 = 0, and mode 2 reduces to nearly pure bend: R = ( \u03c0\u2206\u03b5 \u03bb0 )2 kBT f2 0 K3q2 \u00b7 (3) The relaxation rate \u03c4\u22121 bend for this mode is determined by the ratio of K3 and the effective bend viscosity \u03b7bend: \u03c4\u22121 bend = K3 \u03b7bend q2 \u00b7 (4) The effective viscosity \u03b7bend is the rotational viscosity \u03b31 reduced by a term depending on the Leslie coefficient \u03b12 and the Miesowicz shear viscosity \u03b7c: \u03b7bend = \u03b31 \u2212 \u03b12 2 \u03b7c \u00b7 (5) (ii) In case of the \u201csplay geometry\u201d (Fig. 1b) the director is aligned perpendicular to the scattering plane. Then the bend contribution in equation (1) vanishes because of q\u2016 = 0, and in general a superposition of splay and twist deformations is detected, the respective weights being determined by the scattering angle dependent factors f2 \u03bd . In the q range of our experiments, the splay contribution is predominant because of f2 1 f2 2 , resulting in R = ( \u03c0\u2206\u03b5 \u03bb0 )2 kBT f2 1 K1q2 \u00b7 (6) The corresponding relaxation rate \u03c4\u22121 splay is determined by the ratio of K1 and the effective viscosity \u03b7splay with \u03c4\u22121 splay = K1 \u03b7splay q2 (7) and \u03b7splay = \u03b31 \u2212 \u03b12 3 \u03b7b \u00b7 (8) When dealing with non-crosslinked nematic polymers rather than low molar mass nematics, the equations (3\u20138) can still be applied" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002273_1077546304042047-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002273_1077546304042047-Figure7-1.png", "caption": "Figure 7. Center bolt clamping assembly (Society of Automotive engineers, 1985).", "texts": [ " This design is widely used in military vehicles and trucks where the service is severe. Plain end mounted eye is commonly used for variable rate springs. The construction can be built as a flat leaf on a curved pad, or as a curved leaf on a flat or curved pad. The Berlin eye is used to direct longitudinal loads centrally to the main leaf, thereby reducing the tendency of the eye to unwrap. The rigid body motion between the leaves is eliminated by the center bolt and alignment clips. The center bolt, shown in Figure 7, is required to hold the spring leaves together. The center clamp provides a permanent tie between the leaves and the spring seats. The functions at GEORGIAN COURT UNIV on December 11, 2014jvc.sagepub.comDownloaded from at GEORGIAN COURT UNIV on December 11, 2014jvc.sagepub.comDownloaded from of the clamp, which must remain tight during service, are to attach the spring firmly to its seat to prevent breakage through its center, and to prevent breakage of the center bolt due to horizontal forces" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001565_s0925-4005(98)00285-8-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001565_s0925-4005(98)00285-8-Figure2-1.png", "caption": "Fig. 2. Calibration curve of INO measured amperometrically with the NP enzyme electrode(in phosphate buffer: pH 7.8, Temp. 24\u00b0C): 1st day ( ); and 7th day ( ).", "texts": [], "surrounding_texts": [ "3.1. Estimation of hypoxanthine, inosine and inosine monophosphate To estimate the three metabolites in fish, the calibration curves for IMP, INO and HX were obtained using the fabricated NT, NP and XO enzyme electrodes. For estimation of hypoxanthine the XO enzyme loaded electrode was taken as anode in the electrochemical cell with Pt cathode and SCE reference electrode in phosphate buffer. A polarising voltage of 0.7 V (versus SCE) was applied to initiate the electrode reaction. The background current was stabilised at a few mA within 30 min. HX solution in phosphate buffer was then added to the electrolyte solution, the enhancement of current was noted. Such measurements were made on addition of varied amount of HX solution and a calibration curve was drawn. Same technique was adopted to obtain calibration curves for IMP and INO using NT and NP loaded PPy electrodes respectively. In Figs. 1\u20133, we show the calibration plots for HX, INO and IMP. The two curves present the data obtained with a freshly prepared electrodes and with a 7-day-old electrode stored in phosphate buffer. XO electrode show linear behaviour upto 2 mM of HX after which saturation is obtained. NT electrode shows such linear behaviour upto 1 mM of IMP whereas NP electrode shows linear behaviour upto 1.5 mM of INO. In Fig. 4, we show the efficiency of the XO enzyme electrode with varied amount of enzyme loading. It is observed that loading above 0.3 IU of XO does not increase the sensitivity of the enzyme electrode. The Fig. 1. Calibration curve of HX measured amperometrically with the XO enzyme electrode (in phosphate buffer: pH 7.8, Temp. 24\u00b0C): 1st day ( ); and 7th day ( ). two plots represent the behaviour of a freshly prepared and a seven-day old XO enzyme electrode. 3.2. Estimation of HX, INO and IMP in fish extract and determination of H 6alue The estimation of HX, INO and IMP in the fish extract was made with XO, NP and NT enzyme electrodes following the same procedure as used for estimation of these metabolites in solution discussed in the earlier section. The plots of current enhancement versus the volume (ml) of fish extract added are shown in Fig. 5. Only the linear portion of the plots (upto 0.8 ml) was used for H value estimation. We estimated the amount of IMP, INO and HX in a particular volume of fish extract (using linear part of the plot) from the calibration plots of Figs. 1\u20133 and determined the H values by using equation (3) over 15 days of storage. In Fig. 6, we show the plot of H values of Catla-Catla against number of storage time extending upto 11 days and stored at \u221212\u00b0C. The Fig. 3. Calibration curve of IMP measured amperometrically with the NT enzyme electrode (in phosphate buffer: pH 7.8, Temp. 24\u00b0C): 1st day ( ); and 7th day ( ). Fig. 5. Estimation of ATP metabolites in fish (Catla\u2013Catla) extract (phosphate buffer: pH 7.8, Temp. 24\u00b0C): (i) HX, 1st day ( ), 7th day ( ); (ii) INO, 1st day ( ), 7th day ( ); and (iii) IMP, 1st day ( ), 7th day ( ). correctness of our procedure is demonstrated in the inset which shows that in the linear range of these plots (in the range of 0\u20130.8 ml of fish extract) the same value of H is obtained at all fish extract volumes and that the H value changes with storage time of the fish meat. It is generally accepted that H=0 for the fresh fish and increases as fish degrades on storage. In Fig. 6, it is seen that in our sample (Catla-Catla, stored at \u221212\u00b0C) the H value increases slowly upto 7 days of storage(H 36) and beyond 8th day it increases very rapidly and attains a high value of 60 on 11th day. It is therefore, believed that the fish is unsuitable for human consumption after 7 days of storage at \u221212\u00b0C. Our microbial count data of Catla-Catla specimen stored similarly, as shown in Fig. 7, are in conformity with these results. In our experiment it is also noted that sensitivity of the enzyme electrodes decreases gradually and after 7th day deterioration is significant. This may be due to leaching out of enzymes from the electrodes or denaturation of the enzymes." ] }, { "image_filename": "designv10_13_0001607_s0167-8922(01)80156-5-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001607_s0167-8922(01)80156-5-Figure2-1.png", "caption": "Figure 2: FZG twin disc machine", "texts": [ " For the investigation two standard test methods were used. For all lubricants the coefficient of friction was measured in the FZG twin-disc test rig. Some of the lubricants were additionally investigated in the FZG back-to-back gear test rig. 2. LUBRICANTS For the investigation 19 different synthetic lubricants and, as a reference, two mineral oils were investigated. The basic types of lubricants are given in Table 1. All lubricants are of the vicosity grade ISO VG 150. The coefficient of friction was measured in the FZG twin disc machine (Fig. 2). The test discs are separately driven by two AC motors. For continuous variation of speed, traction drives are mounted between the motors and driving shafts. The upper disc is mounted in a skid, which is connected over two flat springs to the frame. The flame can be rotated over the pivot and thus the upper disc can be pressed against the lower disc. The load is applied by a spring which itself is loaded by the load actuator. If the two discs have different speed, a frictional force is generated which moves the upper skid" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002492_s0022-5193(89)80155-9-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002492_s0022-5193(89)80155-9-Figure2-1.png", "caption": "FIG. 2. Force versus length for linear and non-linear elastic elements. (a) Force rises linearly with length of elastic elements used in the \"unit-worm'\" (Hooke's Law). The lines represent length-force relationships o f the relaxed F(L, O) and activated F(L, 1 ) elastic element. The corresponding constants are 1 and 16, as used for the Chapman-mat r ix (Figs 13 and 14). The intermediate line shows F(L, 1 ) - F(L, 0) and correlates with the active length-tension curve in (b). Force equals zero at minimal length ( = 1 U). (b) Length-tension curves of leech longitudinal muscles for comparison. Curves fitted to data of Miller (1975) obtained from Haemopis sanguisuga L. F(L, 0) denotes passive and F(L, 1) - F(L, O) active length-tension curve. F(L, 1), curve of isometric maxima. Such curves can also be incorporated into the model.", "texts": [ " In this way, we account to a certain extent for the combined stiffness of the epidermis and muscle layers. Our model has a total of 8 N + 4 edges. We assume these to be springs each with a specific length tension relationship, which may depend on the position of the edge within the body. More precisely, following our replacement of the muscles by separate springs, we use the term force instead of tension. For a typical muscle, we express the force F in terms of the length L and the activation parameter a, which we normalize from 0 to 1. Figure 2(a) shows a linear relationship between F and L as in Hooke 's law, whereas Fig. 2(b) shows a typical non-linear relationship, derived from actual data (Miller, 1975). Passing from the linear to the non-linear case in our simulations can clarify the role of the non-linear length-tension relationship in a hydrostatic skeleton. In each case, F(L, 0) gives the passive tension curve and F(L, 1) the curve of the isometric maxima. The quantities, which are usually obtained experimentally, are F(L, 1)-F(L, 0) [Fig. 2(b)]. The potential energy stored in a muscle of length L and activation a is obtained by integrating the force P(L, a)= F(l, a) dl. (2.2) Lmin Here we have normalized the potential to be zero at the minimal length Lm~,, below which the muscle cannot contract. The total energy of our hydromechanical system is 8 N + 3 Eto,a, = ~ P)(L), aj), (2.3) j = o where Lj is the length, a i the activation and P~ the potential function o f t h e j t h spring. C O M P U T E R M O D E L O F T H E H Y D R O S K E L E T O N 383 The equilibrium positions of our system are defined by the minima of the total potential energy under the constraint of constant volume", " (3.8) This fixes Qo in the origin, Q2 on the y-axis and Q~ in the yz-plane. The complete problem [eqns (3.7) and (3.8)] now has a total of 12N + 6 unknowns (258 if N = 21). Any local minimum of eqns (3.7) and (3.8) corresponds to a stable steady state of the whole system, and it is easily seen that such a minimum exists under mild assumptions on E. However, whether these minima are unique depends on the shape of the force functions in respect to the length. If this relationship is linear [as in Fig. 2(a)], several solutions with different degree of stability exist, if the volume is above a critical value. The bifurcation behavior of the problem is under investigation. At a local minimum of eqn (3.7) there exists a Lagrange multiplier p (e.g. Norrie & de Vries, 1978, section 7) such that a__EE aV 6qdk ( Q o , . . . , Q,N+3)= P ~---~k ( Q o , . . . , Q4N+3), j = 0 , . . . , 4 N + 3 ; k = 1,2,3. (3.9) Comparing this with the total differentials in eqn (2.4), we see that p is exactly the internal pressure", " One can show that the pressure max imum in eqn (A2) also occurs without the assumpt ion (A6), but we have no explicit formula for this case. Finally we note that the occurrence o f a pressure max imum certainly depends on the length-tension relationship. We take, for example, E (x, y, z) = f(x) + f(y) + f(z) in eqn (A4), where f is a potential funct ion satisfying f(1) = 0, f(x) > 0 for x > 1. Then eqn (A7) generalizes to p(o) = O - 2 / 3 f ' ( v 1/3) Using the force funct ion f ' (x ) = tan (x - 1) (which is closer to experimental findings than Hooke ' s law, see Fig. 2) an easy calculat ion shows that p (v ) is now strictly increasing. Hence, in this case there is no pressure maximum." ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001949_iros.2003.1248797-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001949_iros.2003.1248797-Figure3-1.png", "caption": "Figure 3: The AMPM. The ZMP is allowed to move over the ground, and its position must be linearly dependent to that of the COG. The horizontal component of the ground force vector is allowed to change, by an amount which must be linearly dependent on the COG.", "texts": [ " The ZMP of the humanoid robot is considered as the origin of this coordinate system. 2 Enhanced Inverted Pendulum Model A new model of the COG is proposed here, which enhances the IPM in two ways: (1) the ZMP is allowed to move over the ground, (2) the ground force vector does not have to be parallel to the vector between the ZMP and the COG, as far as its horizontal element is linearly dependent on the COG position. As a result, rotational moment is allowed to be generated by the ground force. Their relationship is depicted in Figure 3. The position of the COG is ( x , H ) , the position of the ZMP is ( a x + b, 0 ) , and the normal vector of the ground force is parallel to vector (cx+ d , H ) . The relationship between the acceleration of the COG and its position becomes: F, : F,, = 3 : ( E + g ) = ( c z + d ) : H. As the height of the COG is z = H , we can write (1) 9 H 3 = - ( c x + d ) . The solution for this differential equation can be written as where T, = a, and CI, CZ are constant values. As initial parameter values are set at x = xo and i = vo at t = 0, the constant values CI, Cz are , cz = xo + $ - uo T, 2 xo + $ + 210 T, 2 Cl = Then, the ground force vector can he written as m ( -& + c 2 e & ) F, = mx= - Cle F, = m g T, where m is the mass of the system", " Parameters in equations are set manually and angular momentum during motion can be controlled by setting these appropriately. The first demo of normal gait is shown in Figure 8. The step length is set to 0.6m, the initial velocity in the single support phase to l.Om/s. The acceleration of the COG during this gait along the anterior axis and lateral axis are shown Figure 9. As can be seen, the acceleration values are continuous even when switching from single support phase to double support phase. The angular acceleration of the flexion/extension of (a) the hip joint, and (b) the knee joint is shown in Figure 3. As can he seen, the acceleration of these joints is also continuous. Next, the angular momentum around the frontal axis during the motion is increased hy setting the value of c, in Equation 5 from 0.1 to 0.7. The model swings its upper body in the frontal plane according to the magnitude of the applied moment. The final demo is a motion in which the angular momentum around the y-axis is enlarged (Figure 3). When a large moment is applied around the y-axis, the upper body swings largely in the sagittal plane and the model easily loses its balance. In order to prevent this, parameters are set to make each step large in this demo. 4 Summary and Future Work In this paper, we proposed a new approach to generate gait motion. The algorithm, the Enhanced Inverse Pendulum Model, is based on the Inverse Pendulum Model. It allows to include moment around the COG and guarantees C2 continuity during the whole motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002894_ias.2007.202-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002894_ias.2007.202-Figure12-1.png", "caption": "Fig. 12. Temperature control setup", "texts": [ " With the observer, the flux variation according to not only temperature variation but also manufacturing tolerance can be compensated by the proposed scheme. V. EXPERIMENTAL RESULTS In the experiment, a dynamo system in Fig. 11 is installed with the IPMSM and the Induction Machine (IM). The machine parameters of the tested IPMSM are shown in Table 1. An iron hood covered by glass fiber is installed upon the IPMSM to insulate the motor thermally. And, a heating resistor which is operated by the auto-temperature controller is installed inside the hood, in Fig. 12 . To stabilize the system in the thermal sense, the IPMSM was heated and the temperature of IPMSM has been maintained at the preset temperature for a while. A highly accurate torque sensor is installed between IPMSM and IM, and the IPMSM is operated in torque control mode while the IM is operated in speed control mode. Let us first examine problems in conventional torque control method caused by changes in temperature. Comparing the result of applying the current reference at 30[ ] to IPMSM at 30[ ] and IPMSM at 110[ ], it can be seen that as the temperature changes the accuracy of the torque control decreases" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002736_j.jmatprotec.2008.03.065-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002736_j.jmatprotec.2008.03.065-Figure2-1.png", "caption": "Fig. 2 \u2013 The function of transmission error, 2, is a first order polynomial function in a cycle of meshing.", "texts": [ " However, in reality, the output angle cannot precisely 2 bey Eq. (1) owing to the disturbances of inevitable random oise factors such as elastic deformation, manufacturing and ssembly errors. The real rotation angle of the output gear inus the theoretical rotation angle is termed as the function of transmission error, which is defined as 2 = 2( 1) \u2212 ( N1 N2 ) 1 (2) This function is a periodic function with period T = 2 /N1 and independent variable 1. Within a period T, 2 has three shapes, as described below. The worst shape of 2 is depicted in Fig. 2, where 2 is a straight line and can be represented as the following first order polynomial function: 2 = c0 + c1 1 (3) This kind of 2 occurs when a traditional non-modified gear 6 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 3\u201313 vibration and noise. At the same time, edge contact often happens; this induces a significant concentration of stress at the tooth edge and reduces the lifetime of a gear drive. To solve the above-mentioned problems, Livtin (1994) suggested applying a second order polynomial function of transmission error to absorb the linear one" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003475_1.4005467-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003475_1.4005467-Figure4-1.png", "caption": "Fig. 4 Representation of DH frames for YZ EAJs", "texts": [ " Moreover, in the definitions of DH parameters the rotation due to the twist angle precedes the one due to the joint angle, as evident from Fig. 9 in the Appendix. Therefore, the DH parameters for the YZ EAJs can be extracted from the expression of the equivalent rotation matrix QYZ as follows: \u2022 The first two terms Q XQh1 correspond to the twist angle a1\u00bc 90 and joint angle h1. \u2022 The final two terms Q\u00feXQh2 represent the twist angle a1\u00bc 90 and the joint angle h2. The DH parameters for the YZ EAJs are listed in Table 4, whereas the DH frames corresponding to the intersecting revolute joints are shown in Fig. 4. The frames are assigned as follows: \u2022 For a1\u00bc 90 , axis Z1 is perpendicular to ZR, and it represents the joint axis of revolute Joint 1 connecting the imaginary link #1 to the reference link #R. \u2022 For a2\u00bc 90 , axis ZM is the obvious choice for the joint axis of the second revolute joint, as ZM is perpendicular to Z1. Joint 2 connects the moving link #M to the imaginary link #1. The rotation matrix QYZ for the YZ EAJs can be derived from the DH parameters of Table 4. It is shown in the fourth row of Table 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002111_s11044-005-4196-x-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002111_s11044-005-4196-x-Figure1-1.png", "caption": "Figure 1. Architecture of the proposed hybrid manipulator.", "texts": [ " The most studied type of parallel manipulator is the so-called general GoughStewart platform, a fully parallel mechanism. The forward position analysis of a general Gough-Stewart platform is a challenging intensive task which yields forty possible solutions [12]. On the other hand, as it is shown in [13], the acceleration analysis of an in-parallel manipulator does not represent any difficulty when the theory of screws is employed. This work deals with the kinematics of the hybrid manipulator showed in Figure 1, which is a sequence of two parallel manipulators. The lower parallel manipulator, a variant of the translational in-parallel mechanism introduced in [14], is composed of a moving platform, namely a translational platform, connected to a fixed platform by means of three independent or actuator limbs, and two passive kinematic chains. Each independent limb is composed of a Universal-Prismatic-Spherical, or for brevity UPS-type, serial manipulator. On the other hand, the upper parallel manipulator is composed of a moving platform, namely the end-platform, connected to the translational platform of the lower parallel manipulator, by means of three independent limbs, also UPS-type", " The forward position analysis consists in computing the coordinates of the universal joints attached to the lower face of the translational platform, expressed in the reference frame XY Z , given the length of the independent limbs of the lower parallel manipulator. In order to simplify the forward position analysis, the reference frame XY Z is attached to the fixed platform in such a way that the line a1, which denotes the separation between the universal joints U1 and U2, is parallel to the Y axis. With reference to Figure 1, the corresponding geometric scheme of the lower parallel manipulator is showed in Figure 2. Thus immediately emerges that a\u2032 1 = q2 1 \u2212 q2 2 + a2 1 2a1 , (8) and q12 = \u221a q2 1 \u2212 a\u2032 2 1 . (9) Furthermore, a closed loop expression can be written as follows q3 + S3 = q12 + a4. (10) Taking into account the following compatibility expressions (q1 \u2212 q2) \u00b7 (q1 \u2212 q2) = a2 1, (q1 \u2212 S3 \u2212 q3) \u00b7 (q1 \u2212 S3 \u2212 q3) = a2 2, (q2 \u2212 S3 \u2212 q3) \u00b7 (q2 \u2212 S3 \u2212 q3) = a2 3. (11) Then, after a few computations, the coordinates of the universal joints, attached to the translational platform, expressed in the reference frame XY Z , result in U1 = (UX , a\u2032 1, UZ ), U2 = (UX , a\u2032 1 \u2212 a1, UZ ), U3 = (UX + a4 cos(\u03c0/2 \u2212 \u03b2), a4 sin(\u03c0/2 \u2212 \u03b2), UZ )", " On the other hand, the solution of the kinematics of the upper parallel maninpulator is similar to the methodology of analysis applied to the lower parallel manipulator, excepting the forward position analysis. Thus only the forward position analysis and the most relevant results of the velocity and acceleration analyses of the upper parallel manipulator will be presented in this section. The forward position analysis is stated as follows. Given the length of the three upper independent limbs, compute the coordinates of the upper spherical joints attached to the end-platform expressed in the reference frame xyz. According with Figure 1, the geometric scheme of the upper parallel manipulator is showed in Figure 4. Thus immediately emerges that a\u2032 5 = q2 4 \u2212 q2 5 + a2 5 2a5 , (25) and q45 = \u221a q2 4 \u2212 a\u20322 5 . (26) Furthermore, a closed loop can be written as follows U4 + a5 + q45 \u2212 a6 \u2212 h = 0. (27) Then, after a few computations the coordinates of the spherical joint S45 = (S45x , S45y, S45z) are given by S45x = U4x + a\u2032 5, S45z = h + (\u2212B \u00b1 \u221a B2 \u2212 4AC/(2A), S45y = \u221a a2 6 \u2212 S2 45x \u2212 S2 45z, (28) where A = 4 ( U 2 4 + h2 ) , B = 4h(C1 \u2212 C2), C = 4U 2 4y C2 \u2212 2C1 C2 + C2 2 + C2 1 , C1 = U 2 4y + h2 \u2212 q2 45, C2 = U 2 4x + 2U4x a5 + a\u20322 5 \u2212 a2 6" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003430_978-0-85729-898-0-Figure7.1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003430_978-0-85729-898-0-Figure7.1-1.png", "caption": "Fig. 7.1 Two 3-joint cooperative manipulators handling a common load. In this example the second joint of the manipulator on the left is passive", "texts": [ " G. Siqueira et al., Robust Control of Robots, DOI: 10.1007/978-0-85729-898-0_7, Springer-Verlag London Limited 2011 153 Section 7.5 presents the results of the application of these methods to the UARM. In this section, we develop the complete kinematic and dynamic model of cooperative manipulators, giving a special attention to the interaction forces between the load and the manipulators\u2019 end-effectors. Consider a robotic system with m manipulators rigidly connected to an undeformable load (see Fig. 7.1, where the case m \u00bc 2 is illustrated for clarity of presentation). Let qi be the vector of generalized coordinates of manipulator i and xo \u00bc \u00bdpT o /T o T be the k-dimensional vector of load position and orientation. In the three-dimensional space, po \u00bc \u00bdxo yo zo T is the position of the origin of the frame attached to the center of mass of the load (frame CM) with respect to an appropriately selected origin (e.g., the base of one of the manipulators), and /o \u00bc \u00bduo to wo T is a minimal representation of the load orientation using, say, Euler angles or RPY (roll-pitch-yaw) angles", " The control law applied to the actuated joints is given by sa \u00bc smg \u00fe ss; \u00f07:8\u00de where sa is the vector of torques at the active joints, smg is the motion control law with compensation for the gravitational torques, and ss is the squeeze force control law. In the following, a method to compute the Jacobian matrix Q\u00f0q\u00de for cooperative robotic systems with m [ 1 is shown. From Eq. 7.2, m _xo \u00bc D1\u00f0q1\u00de _q1 \u00fe D2\u00f0q2\u00de _q2 \u00fe \u00fe Dm\u00f0qm\u00de _qm: \u00f07:9\u00de Assume that, among all n joints in all manipulators, na joints are actuated and np joints are passive. The positions of the passive joints are grouped in the vector qp and the positions of the actuated joints are grouped in the vector qa (see Fig. 7.1, where qij represents the jth joint of the manipulator i). Partitioning Eq. 7.9 in quantities related to the passive and actuated joints, we obtain: m _xo \u00bc Xm i\u00bc1 Dai\u00f0qi\u00de _qa \u00fe Xm i\u00bc1 Dpi\u00f0qi\u00de _qp \u00bc Da\u00f0q\u00de _qa \u00fe Dp\u00f0q\u00de _qp; \u00f07:10\u00de where a refers to the actuated joints and p to the passive joints. Considering again Eq. 7.2, we can find two more expressions relating the velocities of the passive and active joints. When m is even, Xm i\u00bc1 \u00f0 1\u00dei\u00fe1Di\u00f0qi\u00de _qi \u00bc 0; \u00f07:11\u00de which can be partitioned as Xm i\u00bc1 \u00f0 1\u00dei\u00fe1Dai\u00f0qi\u00de _qa \u00fe Xm i\u00bc1 \u00f0 1\u00dei\u00fe1Dpi\u00f0qi\u00de _qp \u00bc Ra\u00f0q\u00de _qa \u00fe Rp\u00f0q\u00de _qp \u00bc 0: \u00f07:12\u00de It is interesting to note that such relationship cannot always be found in individual manipulators with passive joints [7]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002145_iros.2000.895302-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002145_iros.2000.895302-Figure6-1.png", "caption": "Fig. 6 Motion of the wire differential mechanism", "texts": [ "1 Wire type differential mechanism It is necessary that the actuator unit is high output mass ratio, because large moment affects the root when the neck is lifted. As the solution, the differential mechanism using the harmonic gear is introduced. This mechanism is lightweight because it is composed of not bevel gears but wire and pulley. The harmonic gear is a differential system which has one input and two output parts. One output is attached to pitch shaft and the other is attached the pulley. 2 sets of these are placed on a pitch shaft. The wire and pulley configuration is shown in Fig.6, and the endpoint of the wire is fixed in the yaw pulley. The rotation in the pitch axis is carried out in the case that two pulley outputs are same directions in viewing from the pitch shaft, and the yaw axial motion is carried out when the pulley outputs are is reverse-directions, This actuator unit is adopted the coupled drive which is the method of maximizing output performance by cooperatively utilizing as possible all actuators that are installed. 3.2 Torque limiting mechanism M-Drive\" The ACM is hyper-redundant serial link system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure3-1.png", "caption": "Fig. 3. (a) Initial position of centrodes c of rack cutter and 1 of th", "texts": [ " (7)\u2013(10) yield N\u00f0i\u00de c \u00f0u; l\u00de = cos\u03b4 cos\u03bb cos\u03b1d\u2213 sin\u03bb sin\u03b1d\u00f0 \u00de \u2212cos\u03bb sin\u03b1d\u2212 sin\u03bb cos\u03b1d sin\u03b4 sin\u03bb sin\u03b1d\u2212 cos\u03bb cos\u03b1d\u00f0 \u00de 2 4 3 5; i = 1;2\u00f0 \u00de: \u00f011\u00de where the upper and lower signs correspond to the left (\u03a31) and right (\u03a32) profiles of the rack cutter. 2.2. Applied coordinate systems In order to consider generation of a helical gear, coordinate transformation from Sc to Sm, according to Fig. 2, is applied. Angle \u03b2 represents the helix angle of the helical gear. The rack cutter generating surfaces and the normals are represented in coordinate system Sm as rm u; l\u00f0 \u00de = Mmcrc u; l\u00f0 \u00de; \u00f012\u00de Nm\u00f0u; l\u00de = LmcNc\u00f0u; l\u00de \u00f013\u00de where Mmc = cos\u03b2 0 sin\u03b2 0 0 1 0 0 \u2212sin\u03b2 0 cos\u03b2 0 0 0 0 1 2 664 3 775; \u00f014\u00de Lmc = cos\u03b2 0 sin\u03b2 0 1 0 \u2212sin\u03b2 0 cos\u03b2 2 4 3 5: \u00f015\u00de Fig. 3 shows the initial and current positions of the generating rack cutter and the to-be-generated helical gear. By using the geometry of the rack cutter previously represented, the to-be-generated helical gear will incorporate the desired corrections to the gear tooth surfaces. Those corrections will then be generated by plunge shaving of the gear. Movable coordinate systems Sm and S1 are rigidly connected to the rack cutter and the helical gear, respectively. Coordinate systems Sn and Sf are fixed ones" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002230_112515.112566-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002230_112515.112566-Figure3-1.png", "caption": "Figure 3: Brick solution using Newton- Raphson.", "texts": [ " Example 1: the brick In this problem, the brick of Figure 2 must be configured to satisfy the three coincident constraints graphically depicted as the grey lines between the brick\u2019s markers bl, b2, b3 and the desired locations, denoted by markers gl, g2, g3 fixed in the global coordinate frame. Equations can be developed to relate the configuration variables of the brick\u2019s coordinate frame to those of the global coordinate frame. The numerical solution of these equations, using Newton-Raphson, is illustrated graphically in Figure 3. Each of the grey outlines represents an intermediate configuration of the brick during the solution. The figure depicts only every third iteration of Newton-Raphson, and step sizes were clipped to improve the behavior of the algorithm. 21t should be noted that the plan of IUeaSurements and actions that satisfy the constraint network do not necessarily correspond to a physically-reahzable plan for assembling a collection of real objects. Since the objects in a GCSP are purely geometric, they have no volume or other physical properties", " This satisfies coincident (b3, g3) without violating coincident (bl, gl). This action also removes two of the remaining rotational degrees of freedom; in order to preserve the two already-satisfied constraints, all future actions must be rotations about v2. To satisfy the final constraint, TLA drops perpendiculars from b2\u00b0 to v2, and from g2 to v2, and rotates the brick about V2 by the angle between the perpendiculars. This brings the brick to its final configuration. The solution is very deliberate, as opposed to the meandering of the numerical approach of Figure 3. The sequence of actions performed above constitute a plan for moving the brick from an arbitrary position to one satisfying the constraints. For this part of the problem solution, TLA reasons only about geometry, actions and degrees of freedom. No equations are developed, and no model requiring configuration variables or other abstract state is needed. Constraints are satisfied by measuring the brick\u2019s geometric properties (often using additional geometric constructions) and then moving it. The brick-moving plan derived using this method is next used to solve for the brick\u2019s configuration variables as represented in a computer; this may be done regardless of how the local coordinate frame of the brick is described" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure8.12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure8.12-1.png", "caption": "Fig. 8.12 A simplified reconstruction concept of vertical-wheel water-driven wind box, a (5, 6) simulation illustration b (5, 6) structural sketch", "texts": [], "surrounding_texts": [ "Based on the view of modern mechanism, this chapter analyzes the devices with gear and cam members in the ancient books described in Chap. 2, as listed in Table 8.1. There are six agricultural devices with gears, four water lifting devices with gears, and two cam mechanisms. Among them, there are 10 mechanisms (Zha Zhe Ji, Lian Mo, Shui Mo, Lian Er Shui Mo, Shui Zhuan Lian Mo, Shui Long, Lv Zhuan Tong Che, Niu Zhuan Fan Che, Shui Zhuan Fan Che, Shui Du) with certain structures (Type I), and two devices with only text descriptions without illustrations, such as the wind-driven paddle blade machine and vertical-wheel waterdriven wind box. However, the wind-driven paddle blade machine has survived the real objects and has two different types sorted by the position of the main shaft. According to the real objects, the wind-driven paddle blade machine still can be considered as Type I. Since the vertical-wheel water-driven wind box contains only text without illustration and real object, it may have various feasible designs and can be considered as a mechanism with uncertain numbers and types of members and joints (Type III). There are a total of 11 original illustrations, 12 structural sketches, five simulation illustrations, five imitation illustrations, one prototype, and four real objects described in this chapter. Furthermore, their power sources include human, animals, wind, and water. 186 8 Gear and Cam Mechanisms T ab le 8. 1 G ea r an d ca m m ec h an is m s (1 2 it em s) M ec h an is m n am es B o o k s N o n g S h u \u300a \u8fb2 \u66f8 \u300b W u B ei Z h i \u300a \u6b66 \u5099 \u5fd7 \u300b T ia n G o n g K ai W u \u300a \u5929 \u5de5 \u958b \u7269 \u300b N o n g Z h en g Q u an S h u \u300a \u8fb2 \u653f \u5168 \u66f8 \u300b Q in D in g S h o u S h i T o n g K ao \u300a \u6b3d \u5b9a \u6388 \u6642 \u901a \u8003 \u300b Z h a Z h e Ji (\u69a8 \u8517 \u6a5f ) F ig . 8 .1 T y p e I G an S h i \u300a \u7518 \u55dc \u300b L ia n M o (\u9023 \u78e8 ) F ig . 8 .2 T y p e I C h u Ji u \u300a \u6775 \u81fc \u300b S h u i M o (\u6c34 \u78e8 ) F ig . 8 .3 T y p e I S u i Ji n g \u300a \u788e \u7cbe \u300b L ia n E r S h u i M o (\u9023 \u4e8c \u6c34 \u78e8 ) F ig . 8 .3 T y p e I S h u i L i \u300a \u6c34 \u5229 \u300b G o n g Z h i \u300a \u653b \u6cbb \u300b S h u i Z h u an L ia n M o (\u6c34 \u8f49 \u9023 \u78e8 ) F ig . 8 .4 T y p e I L i Y o n g \u300a \u5229 \u7528 \u300b S h u i L i \u300a \u6c34 \u5229 \u300b G o n g Z h i \u300a \u653b \u6cbb \u300b S h u i L o n g L o n g (\u6c34 \u7931 ) F ig . 8 .4 T y p e I L i Y o n g \u300a \u5229 \u7528 \u300b S h u i L i \u300a \u6c34 \u5229 \u300b L v Z h u an T o n g C h e (\u9a62 \u8f49 \u7b52 \u8eca ) F ig . 8 .5 T y p e I G u ai G ai \u300a \u704c \u6e89 \u300b S h u i L i \u300a \u6c34 \u5229 \u300b G u ai G ai \u300a \u704c \u6e89 \u300b N iu Z h u an F an C h e (\u725b \u8f49 \u7ffb \u8eca ) F ig . 8 .6 T y p e I G u ai G ai \u300a \u704c \u6e89 \u300b N ai L i \u300a \u4e43 \u7c92 \u300b S h u i L i \u300a \u6c34 \u5229 \u300b G u ai G ai \u300a \u704c \u6e89 \u300b S h u i Z h u an F an C h e (\u6c34 \u8f49 \u7ffb \u8eca ) S h u i C h e (\u6c34 \u8eca ) F ig . 8 .7 T y p e I G u ai G ai \u300a \u704c \u6e89 \u300b N ai L i \u300a \u4e43 \u7c92 \u300b S h u i L i \u300a \u6c34 \u5229 \u300b G u ai G ai \u300a \u704c \u6e89 \u300b (c o n ti n u ed ) 8.4 Summary 187 T ab le 8. 1 (c o n ti n u ed ) M ec h an is m n am es B o o k s N o n g S h u \u300a \u8fb2 \u66f8 \u300b W u B ei Z h i \u300a \u6b66 \u5099 \u5fd7 \u300b T ia n G o n g K ai W u \u300a \u5929 \u5de5 \u958b \u7269 \u300b N o n g Z h en g Q u an S h u \u300a \u8fb2 \u653f \u5168 \u66f8 \u300b Q in D in g S h o u S h i T o n g K ao \u300a \u6b3d \u5b9a \u6388 \u6642 \u901a \u8003 \u300b F en g Z h u an F an C h e (\u98a8 \u8f49 \u7ffb \u8eca ) (o n ly te x t w it h o u t il lu st ra ti o n ) F ig s. 8 .8 an d 8 .9 T y p e I N ai L i \u300a \u4e43 \u7c92 \u300b S h u i D u i (\u6c34 \u7893 ) Ji D u i (\u6a5f \u7893 ) L ia n Ji D u i (\u9023 \u6a5f \u7893 ) F ig . 8 .1 0 T y p e I L i Y o n g \u300a \u5229 \u7528 \u300b S u i Ji n g \u300a \u788e \u7cbe \u300b S h u i L i \u300a \u6c34 \u5229 \u300b G o n g Z h i \u300a \u653b \u6cbb \u300b L i L u n S h i S h u i P ai (\u7acb \u8f2a \u5f0f \u6c34 \u6392 ) (o n ly te x t w it h o u t il lu st ra ti o n ) F ig s. 8 .1 1 an d 8 .1 2 T y p e II I L i Y o n g \u300a \u5229 \u7528 \u300b 188 8 Gear and Cam Mechanisms" ] }, { "image_filename": "designv10_13_0001863_1131322-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001863_1131322-Figure2-1.png", "caption": "FIG. 2.--Frontal and lateral views of experimental set-up and subject position. Numbers denote the following: (1) circular black-metal plate (3.7 cm radius) connected by a stem (2 cm length) to a wooden-dowel handle (9 cm length, 1.8 cm diameter; 28 grams mass for plate plus handle) which subjects grasped, (2) light beams (photoelectric cells plus infrared LEDs) attached to the Plexiglas sheet with black arrows indicating the targets' positions, (3) T-shaped barrier that subjects circumnavigated (stem of the T-shaped barrier was 3.5 x 21.5 cm, and the perpendicular cross-piece was 0.3 x 32 cm), (4) suspended, clear Plexiglas sheet (6.4 mm thick) with center slit (7 x 80 cm), (5) straightbacked chair, (6) seat belts, and (7) markers (1 cm diameter) attached at the glenohumeral, elbow, wrist, and third metacarpophalangeal joints, and the center of the circular metal plate. Subjects started and ended the movement with the circular plate held steady in the lower light beam. The upper light beam only had to be interrupted by the metal plate as subjects reversed their upward motion to begin the downward phase of the task.", "texts": [ " Although it is an attractive concept that humans may use a practice strategy that uses slow movements to learn basic torque profiles and simply scale these profiles to increase speed (Hollerbach, 1982), a repatterning of torque profiles in a complex task would be inconsistent with a simple, linear scaling of torques. Experimental Methods Only a brief overview of procedures and methods is provided here, because the full details are available in Schneider et al. (1989) and Schneider and Zernicke (1989, 1990). In these experiments, subjects were asked to perform maximal-speed arm movements. Each subject was seated in front of a clear Plexiglas sheet on which arrows marked the location of upper and lower target light beams (Fig. 2). Subjects sat on a straight-backed chair while the pelvis and torso were secured to the chair by lap and shoulder seat belts to minimize trunk motion. Subjects were asked to start at the lower light beam, to go as fast as possible, circumnavigate a barrier that was placed midway between the two targets, break the upper light beam, again round the barrier, and stop in the lower light beam. Subjects were not given any instructions about accuracy, other than informing them that they had to interrupt the upper light beam and stop in the lower light beam" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003817_biorob.2012.6290924-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003817_biorob.2012.6290924-Figure2-1.png", "caption": "Fig. 2. Diagram defining study variables including tissue thickness (t), needle diameter (d), measured axial force (Fm), and measured rotational torque (Tm).", "texts": [ " The punch was not indented far enough to cause tissue fracture. During needle insertion experiments, the axial insertion force was recorded while a 0.98mm-diameter stainless steel stylet with a Framseen (triangular pyramid) tip from an 18-gauge prostate brachytherapy seeding needle (product number PSS1820AT from Worldwide Medical Technologies, LLC) was inserted into tissue. Each insertion experiment began with the needle initially outside the tissue, which was held in place by two plastic plates with small holes through which the needle could pass (Figure 2). The needle was inserted through the holes and tissue at 1mm/s, which is within the range of speeds used in epidural needle insertion [21], until the needle tip extended 5cm beyond the tissue (Figure 3). The needle was held stationary for 60 seconds so the tissue could relax. Then, the needle was cyclically retracted and inserted with a 4cm peak-to-peak amplitude. Experiments were conducted using sinusoidal motion with 10s and 45s periods and constant-velocity motion at 1.5, 2.5, 7.5, or 12.5mm/s", " At least five needle experiments were conducted for each tissue material and for each variation of needle motion, resulting in at least 35 needle experiments for each tissue. The tissue was moved between each insertion experiment to ensure that the needle did not reenter a prior needle tract. In these experiments, needle inertia and torsion were negligible because the needle was relatively light and stiff. To account for different tissue thicknesses, force and torque measurements were normalized by dividing them by the thickness of the tissue through which the needle passed, t (Figure 2). In order to compare linear needle motion to rotational needle motion, rotational positions and velocities were multiplied by the needle radius to convert them to their linear equivalents. The relationship between the equivalent linear normalized force, Feq, and the torque measurement, Tm, was Feq = 2Tm d\u00d7 t . (1) The position measurements were differentiated to determine the needle velocity, which was smoothed with a lowpass filter with a 10Hz cutoff frequency. To eliminate effects of linear slide mechanics, such as friction and vibration, noise was reduced by smoothing the force measurements with a low-pass filter with a 0", " The rightmost column compares needle rotation to translational insertion. The force profiles had some common features, such as higher needle speeds generally corresponding to increased forces and the presence of hysteresis loops. Significant differences between the tissues included the magnitude of the interaction forces and the degree of hysteresis. The reasons for these commonalities and differences are discussed in the following section. The force measured at the base of the needle is the summation of the interaction forces that occur along the needle shaft (Figure 2), which are influenced by the friction resisting relative motion between the needle and the tissue, and tissue deformation caused by frictional forces. This section discusses these two sources of interaction force behavior and how they resulted in the behaviors seen in Figures 5 and 6. We define the deformation ratio of each experiment as the ratio of the maximum normalized force during cyclic motion to the linear stiffness of each material. This is a qualitative non-dimensional indicator of the amount of tissue deformation during each experiment" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003193_j.jfranklin.2011.04.002-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003193_j.jfranklin.2011.04.002-Figure2-1.png", "caption": "Fig. 2. Geometric scheme of the platform P.", "texts": [ " Let us consider the inverted Stewart platform which consists of a base platform and a mobile one, both with the shape of an equilateral triangle, of sides a and b, a4b, respectively. The vertexes of the base are joined to the corresponding vertexes of the mobile platform by actuators of lengths, li (i=1,2,3), variable and bounded. These actuators are fastened to the base platform at the points Ai (i=1,2,3) by cylindrical joints with axes of rotation perpendicular to the segment AiA0 (i=1,2,3), forming the respective angles gi, and they are connected to the mobile platform in the corresponding points Bi (i=1,2,3) by spherical joints (see Fig. 2). The type of joints used to connect the platforms, both base and mobile, through the actuators allow us to reduce the six original degrees of freedom to three: two rotations (a and b) and one translation (h). a and b are the rotations of the center of mass of the mobile platform (B0) with respect to the axes y0 and x0, respectively, and h is the vertical position of B0 with respect to A0, as is shown in Fig. 2. We also possess two sensors to measure angular velocity, corresponding to both rotations a and b of the mobile platform with respect to the horizontal plane and a GPS device to measure the position that will allow us to recover the aforementioned angles. We shall assume that the measurement errors of the GPS device are negligible for our application. The position to be stabilized is a \u00bc b \u00bc 0 and h=h0. To obtain the equations that describe the movement of the platform P we use Lagrange\u2019s equations considering the independent variables a, b and h as the generalized coordinates", " (35), the estimated state x\u0302 is used to realize the control u0, i.e., the control u0 should be designed as u0\u00f0t\u00de \u00bc ~K Cx\u0302\u00f0t\u00de, \u00f049\u00de with x\u0302\u00f0t\u00de being designed as in Eq. (34). That is, since we have compensated the matched uncertainties and we can ensure the estimation error being arbitrarily small after an arbitrarily small time, we can design the control u0 for the nominal system but being applied to system (1). Let us consider the following structural dimensions for our platform P : a \u00bc 0:5 m; b=0.3 m; g=9.81 m/s2; h0=0.2 m; g0 \u00bc 60 y m=3 kg (see Fig. 2). Then, the matrices A and B for the motions equations (1) are A \u00bc 0 1 0 0 0 0 1:875 0 0 0 0 0 0 0 0 1 0 0 0 0 0:3433 0 0 0 0 0 0 0 0 1 0 0 0 0 0:25 0 0 BBBBBBBB@ 1 CCCCCCCCA and B \u00bc 0 0 0 1:732 1:732 3:464 0 0 0 0:2105 0:2105 0 0 0 0 1 3 1 3 1 3 0 BBBBBBBBBB@ 1 CCCCCCCCCCA : The matrix C is the same as in Eq. (4) and the vector g\u00f0w,x,t\u00de is g\u00f0w,x,t\u00de \u00bc w\u00f0t\u00dex3 \u00fe 1:3686w\u00f0t\u00dex5 w\u00f0t\u00dex3 1:3686w\u00f0t\u00dex5 w\u00f0t\u00dex3 0 B@ 1 CA, \u00f050\u00de where w(t) will be given by the expression w\u00f0t\u00de \u00bc 0:1\u00fe 0:5sint. The vector state x consists of six state variables: x1 \u00bc a a0, x3 \u00bc b b0, x5 \u00bc \u00f0h h0\u00de=h0, x2, x4 and x6 represents the velocity of x1, x3 and x5, respectively. Notice that in Eq. (50) the perturbation only affects the deviation of parameters b and h. This occurs because we assume that the wind only acts on the direction of axis y (see Fig. 2). The wished point that we want to stabilize is \u00f00,0,0,0,h0,0\u00de. Nevertheless, for our application, the changes in the height of the center of mass of the mobile platform with regard to the plane of the platform base are not of vital importance, since the platform P is set at a height of approximately 400 m from the ground and we wish to maintain the horizontal position of the mobile platform in order to keep a certain area under surveillance. That is why we are going to focus on the behavior of the states x1, x2, x3 and x4, corresponding to the deviation of a and b and their velocities" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001441_2.5490-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001441_2.5490-Figure7-1.png", "caption": "Fig. 7 Normalized probability of failure based on Probable Cause analysis of rim-loaded compresor disks. Speed: 11,200 rpm.", "texts": [ " The results of these analyses are shown in Fig. 6. From these analyses and the data of Fig. 3, a Weibull slope of 2 was chosen for the current life analysis to represent the failure distribution of both disks. By using fatigue data from the Aerospace Structural Materials Handbook,24 we calculated a stress-life exponent of 9.2 for the titanium (Ti-6Al-4V) alloy and assumed it to represent that of the disk. The results of these analyses showing the probability of failure and the failure location on each disk are shown in Fig. 7. This gure suggests that for both disks and at all load conditions the bolt holes have the highest probability of failure. All of the failure locations reported by Mahorter et al.22 for both sets of disks were bolt hole cracks.According to Mahorteret al.,22 turbine-engineLCF experiencehas shown that the bolt holes are the primary locationof engine disk failure. Results and Discussion Comparison of Lives By using the method of Zaretsky16;17;19 and the computer code Probable Cause,21 a life analysis was undertaken of two different groups of aircraft gas-turbine-engine compressor disks for which there existed fatigue data" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001711_rob.10081-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001711_rob.10081-Figure3-1.png", "caption": "Figure 3. Measurement setup for medical parallel manipulator calibration. Round-shaped objects are IRED markers.", "texts": [ " The measurement system has an accuracy to 0.1 mm and resolution to 0.01 mm. By simultaneously tracking more than 256 markers, the system can detect displacements in 6 DOFs in complex applications. So far, such a system has been used for pose measurement18 and serial manipulator\u2019s calibration.19 In measuring the tool pose in our parallel manipulator system, the first thing to do is to set up a local frame for each object to be measured. We used two group of IRED markers attached to the base and drill holder separately, as shown in Figure 3, to determine the world frame and tool frame. For each group of three IRED markers, their centroid and a vector normal to the plane passing through them are calculated. The origin of a local frame (tool or world) is located at the centroid, while Z axis is parallel to the normal vector and points upwards. Of the three markers of tool frame, two are intentionally aligned to the desired direction, which is the moving direction of the drilling tool in our work, to determine the X axis. The readings from OPTOTRAK are the 3D position information of all IRED markers in the measuring frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001432_jsvi.1997.0940-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001432_jsvi.1997.0940-Figure2-1.png", "caption": "Figure 2. The different shapes of helical springs. (a) Cylindrical; (b) barrel; (c) conical; (d) hyperboloidal.", "texts": [ " The geometrical properties of a cylindrical helix are (see Figure 1) h=R tan a, c=(R2 + h2)1/2, t= h/c2 = (1/R) sin a cos a, x=R/c2 = (1/R) cos2 a, ds= c du, (8a\u2013e) where h is the step for unit angle of the helix, R is the centreline radius of the helix, a is the pitch angle and du is the infinitesimal angular element. The horizontal radius of any point that lies on the axis of the bar is determined for barrel and hyperboloidal types of helices from R=R1 + (R2 \u2212R1)01\u2212 u pnc1 2 , (9) and for conical springs (see Figure 2) from R=R1 + (R2 \u2212R1)u 2pnc , (10) where nc is the number of active turns. Although the pitch angle of helices is considered constant, the values c, h and R will be varied along the axis for the non-cylindrical helix. Thus, the fixed reference value, R0, which can be selected arbitrarily, has been used for obtaining the differential equations in non-dimensional form c2 0 =R2 0 + h2 0 , h0 =R0 tan a. (11) The dimensionless groups for the elements of the state vector at any section of the bar are determined as follows: T 0 i = c2 0 EIn T0 i , M 0 i = c0 EIn M0 i , U 0 i = 1 c0 U0 i , V 0 i =V0 i , (i= t, n, b)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001885_1.1518502-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001885_1.1518502-Figure1-1.png", "caption": "Fig. 1 Motions for gear generation", "texts": [ " As geometry modifications are achieved on the basis of closely related machining parameters, the geometric changes of tooth surface are not easy to predict. Moreover, the meshing of the two tooth surfaces of pinion and gear can be modified and interactions of gear and pinion parameters must be also considered. A continuous cutting procedure is achieved in Klingelnberg\u2019s Cyclo-Palloid System in which tooth surfaces are basically conjugated @14#. The finishing points of the cutter edge trace the longitudinal shape of the tooth surface. The extended epicycloid is obtained by a rolling over motion ~Fig. 1!. In the figure, constant bevel pinion tooth height can be observed and the extended epicycloid path gives the curved shape of the teeth. Note that a reference point P is defined as an intersection of the mean cone distance and the extended epicycloids. Obviously, the shape and the orientation of cutter edges govern the final tooth surfaces. In practice, the tooth surfaces are mismatched for various reasons, in order to avoid either contact of extreme parts of the surface ~top, heel or toe contact", " Associate Editor: R. F. Handschuh. rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 are considered in two directions on the gear tooth surface either along the length of the pinion tooth, or along its height. Varying the radius of the head cutter carries out tooth length corrections ~Fig. 2!. Thus the curvature of the longitudinal shape of the convex side of the generating crown gear is modified. The curvature increases while the radius is reduced. This also changes machining distance ~Fig. 1!. A curved cutter edge is then introduced, as opposed to the originally straight-line cutter edge, in order to modify the height of the tooth surface ~Fig. 3~a!!. Due to the remaining conjugated points, the contact between a base tooth surface ~gear tooth surface! and a corrected tooth surface ~pinion tooth surface! in length direction or in height direction supports zero kinematics error. Regarding tooth length correction, the contact areas are located across the surface. On the contrary, for tooth height corrections, longitudinal contact areas appear" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003824_tmag.2012.2237390-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003824_tmag.2012.2237390-Figure2-1.png", "caption": "Fig. 2. Components of the stator.", "texts": [ " We also compute its static torque characteristics and dynamic characteristics by employing 3-D finite element method and finally verify it from experimental results of a prototype. The proposed outer rotor spherical actuator consists of a stator and a rotor. In the rotor, as shown in Fig. 1, four rows of identically polarized, small spherical shell-shaped permanent magnets are placed around the Z-axis. The rows are arranged so that along the Z-axis, the N and S poles alternatively appear every 22.5 degrees. Components of the stator are shown in Fig. 2. The stator has 24 electromagnetic poles (EM poles) with 310 turn concentrated windings, which are arrayed around the Z-axis at even intervals. Fig. 3 shows the assembled structure. Generally, outer rotor motors can produce a higher torque than that of inner rotor motors of the same size. By employing this structure, high output torque can be achieved in spite of the small size. In previous research [9]\u2013[11], a simple model that uses air core coils was theoretically derived. However, as the core of Manuscript received November 04, 2012; revised December 27, 2012; accepted December 28, 2012", " As for , there was a sharp dip at 500 ms and 1000 ms. This is due to the transformation of the raw data into and when the rotor comes back to the initial posture . In this posture, as shown Fig. 5, the parameter has more than one value. This problem should be solvedwhen the actuator is controlled using a closed loop controller. For in Case 2, the rotor rotates with the desired trajectory. As for , the analysis result shows an oscillation of 6 Hz. This is thought to be due to the shape of the stator. As shown in Fig. 2, the stator poles are arrayed as a hexagon. When the rotor moves in a circular motion, the transmission torque when the permanent magnets are in line with the vertex of the hexagon is not the same as when they are not in line with the vertex. Therefore periodical disturbance appeared in the dynamic characteristic. In this section, the dynamic characteristics of a prototype are compared with the analysis results. Fig. 11 shows the prototype of the actuator. The rotor is supported by a gimbal structure which has two degrees of freedom" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002777_s10846-008-9284-8-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002777_s10846-008-9284-8-Figure3-1.png", "caption": "Fig. 3 Euler angles and rotation axes", "texts": [ " A small electric helicopter is mounted on the stand as shown in Figs. 2, 3 and 4. The stand is all aluminum construction with ball bearings to allow smooth and easy movements to the helicopter. Friction at the joints is considered negligible. As a result, the helicopter can move naturally without any constraint around a 2.1 m diameter circle, flying forwards, backwards or sideways. A gas strut is used to counterbalance the weight of the stand so the helicopter does not lift any extra weight. In Fig. 3, rotations as well as the Euler angles of the helicopter are presented. In this section, we present the forward kinematic equations of the stand using the Denavit\u2013Hartenberg convention. Using this equations, position and orientation of the helicopter (end-effector) can be calculated. The flying stand (Figs. 3 and 4) has five revolute joints. Each joint rotates around an axis and the synthesis of all rotations provides the final position of the endeffector, which in our case is the place where the helicopter is mounted on the stand", " Such a system cannot be utilized for indoor experimentation, so a reference system must be developed. In robotics research, several localization systems for indoor experimentation have been developed. Usually these systems involve the use of high cost cameras, where localization is calculated through vision [18]. To avoid these high cost indoor systems, we utilize the rotary movement of the central shaft of the stand. The stand and consequently the helicopter move around a circle (planar rotation at Fig. 3) with a rotation angle which may easily be monitored. For this reason, a rotation encoder has been installed on the central shaft of the stand (Fig. 6). The encoder initializes its position to zero and then gives signed numbers that denote the current position relative to the initial position. Positive numbers denote rotation to the left while negative numbers denote rotation to the right side. The rotation encoder gives the planar position of the helicopter at each time instant. To facilitate experimentation, we have observed that the accuracy of the rotation encoder should be higher than 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.19-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.19-1.png", "caption": "Fig. 6.19 A type keeping wheel (\u6d3b\u5b57\u677f\u97fb\u8f2a). a Original illustration (Wang 1991). b Structural sketch. c Prototype", "texts": [ " Each device is a Type I mechanism with a clear structure and is described below: 6.6.1 Huo Zi Ban Yun Lun (\u6d3b\u5b57\u677f\u97fb\u8f2a, A Type Keeping Wheel) On the basis of the clay types of typography invented by Bi Sheng (\u7562\u6607) in the Northern Song Dynasty (AD 970\u20131051), Wang Zhen (\u738b\u798e) in the Yuan Dynasty (AD 1271\u20131368) replaced the clay typesets with wooden types, eliminating the 6.5 War Weapons 127 weakness of clay types that \u201c\u2026hard to attach ink, easy to be broken, and thus can not last long\u201d \u300c\u96e3\u4ee5\u4f7f\u58a8\u3001\u7387\u591a\u5370\u58de, \u6240\u4ee5\u4e0d\u80fd\u4e45\u884c\u300d. He also invented Huo Zi Ban Yun Lun (\u6d3b\u5b57\u677f\u97fb\u8f2a, a type keeping wheel) as shown in Fig. 6.19a (Wang 1991). In this device, the types are sorted by their rhymes. The pick-word worker only needs to rotate the wheel to get needed types. This device greatly enhanced working efficiency. 128 6 Roller Devices frame (member 1, KF), a wheel as the moving link (member 2, KL). The wheel is connected to the frame with a revolute joint JRy. Figures 6.19b\u2013c show the structural sketch and a prototype, respectively. 6.6.2 MuMian Jiao Che (\u6728\u68c9\u652a\u8eca, A Cottonseed Removing Device) Mu Mian Jiao Che (\u6728\u68c9\u652a\u8eca, a cottonseed removing device) is a device used in the fiber processing of cotton before weaving as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.2-1.png", "caption": "Fig. 6.2 Harvest and transportation devices. a A swamp-used cart (\u4e0b\u6fa4\u8eca). b A large cart (\u5927 \u8eca) (Wang 1991). c A hand reaper (\u63a8\u942e) (Wang 1991). d A wheat storage cart (\u9ea5\u7c60) (Wang 1991). e A four-wheel cart (\u5408\u639b\u5927\u8eca) (Pan 1998). f A single-wheel cart (\u5357\u65b9\u7368\u63a8\u8eca) (Pan 1998). g A dual-driven wheel barrow (\u96d9\u9063\u7368\u8f2a\u8eca) (Pan 1998). h Structural sketch", "texts": [ " The first three devices have two wheels, the forth and fifth have four, and the last two have a singular wheel. For the device with a symmetrical structure, only one part of the symmetrical structure is needed for analysis. Thus, all of the seven devices can be identified as a mechanism with two members and one joint, including the wagon frame as the frame (member 1, KF), and wheels set on the frame as the roller member (member 2, KO). The wheel is connected to the frame with a revolute joint JRz. Figure 6.2h shows the structural sketch. There are five grain processing devices with roller members, including Feng Che Shan (\u98a8\u8eca\u6247, a winnowing device), Mo (\u7933, an animal-driven grinder), Shui Mo (\u6c34\u78e8, a water-driven grinder), Xiao Nian (\u5c0f\u78be, a small stone roller), and Gun Shi (\u6efe\u77f3, a rolling stone). Each device is a Type I mechanism with a clear structure and described as follows: 6.3.1 Feng Che Shan (\u98a8\u8eca\u6247, A Winnowing Device) Feng Che Shan (\u98a8\u8eca\u6247), also known as Yang Shan (\u63da\u6247) or Yang Shan (\u98b6\u6247), is a hand-operated winnowing device for removing husks and dirt from the grains as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002100_pime_proc_1989_203_096_02-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002100_pime_proc_1989_203_096_02-Figure1-1.png", "caption": "Fig. 1 Schematic representation of a circular elastohydrodynamic contact", "texts": [ " Significant development of the methods employed in this work has taken place and the purpose of the present paper is to present theoretical results which cover a wide range of conditions that are representative of engineering practice. Direct comparisons have also been made between experimental measurements of central film thickness and theoretical analyses carried out under the same physical operating conditions. This paper is restricted to circular e.h.1. contacts, for which the equivalent geometry is that between an elastic sphere and an elastic plane as shown in Fig. 1. The two surfaces are separated by a lubricant film. It is assumed that the area over which elastic deformation of the surfaces occurs is small compared with the dimensions of the contacting bodies, and both surfaces are therefore treated as semi-infinite solids. The total normal elastic deformation of the surfaces is A I where A, is the area over which the pressure is nonzero. The film thickness is given by where the constant s represents the increase in the separation (measured along the common normal at the contact) between points in the two bodies which are both distant from the contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003930_cjme.2012.01.071-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003930_cjme.2012.01.071-Figure3-1.png", "caption": "Fig. 3. Forces and moments acting on a ball", "texts": [ " Accordingly, the traction vector at that point will be given by Eq. (28). Take the concatenating computation process described above consecutively starting from the leading edge c c( )x a y= till to the trailing edge c c( )x a y= - of the contact ellipse, and the slip c c ( , )x ys s and traction c c ( , )x yp p distributions within the whole contact patch can be obtained. For convenience of numerical calculation, the physical quantities in the mathematical model can be rendered dimensionless following the method proposed in Ref. [22]. Fig. 3 illustrates the tractions and moments acting on body 1, exerted by body 2. Based on the distribution of traction vector c c ( , )x yp p inside the contact patch, the tangential forces and torque can be obtained by Eqs. (29)\u2013(31): c c c c c c c ( , )d d ,x xT p x y x y= \u00f2\u00f2 (29) c c c c c c c ( , )d d ,y yT p x y x y= \u00f2\u00f2 (30) c c c c c c c c c c c c c c c c c c ( , ) d d , ( , ) d d , z y y z x x M p x y x x y M p x y y x y \u00ec\u00ef =\u00ef\u00ef\u00ef\u00ed\u00ef\u00ef = -\u00ef\u00ef\u00ee \u00f2\u00f2 \u00f2\u00f2 (31) c c c c c .z z y z xM M M= + (32) cxT and cyT are the traction components acting tangentially on the ball, while czM is the torque due to the distributed traction about inner normal of the ball at the center of the contact patch", "x zM M M= + (37) Based on the theory of rolling contact, the motion of balls and inner/outer rings can be uniquely determined simply under the interactions between the balls and raceways and the inertia force and moment. Although the equilibrium conditions for the ball and inner/outer rings are largely the same as those proposed by JONES[1], the contacting forces and moments are to be obtained by the method proposed in the former part of this paper. The forces and moments acting on the ball are illustrated in Fig. 3. The tractions components o ix xT T/ and o iy yT T/ are longitudinal and lateral tangential tractions respectively imposed by the outer and inner rings. The tractions components o ix xT T/ and o iy yT T/ simultaneously yield the moment components o ix xM M/ and o iy yM M/ about the center of the ball. The torque o iz zM M/ is induced by the distributed tangential traction about the geometric center of the outer/inner contact ellipses. Force equilibrium equations for the ball in x-axis and z-axis are given by Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002033_physreve.66.056204-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002033_physreve.66.056204-Figure2-1.png", "caption": "FIG. 2. The experimental apparatus with the bubbling rising in line and antibubbles captured in the liquid circulation.", "texts": [ " By recording with a VHS camera, we followed the formation of some antibubbles as well as their trajectories driven by the liquid circulation. Using the air flow rate as a control parameter, we characterized the dynamics by measuring the time between bubbles. We observed period doubling, intermittent behavior, abrupt enlargement of the attractor size due to the coalescence between bubbles @3#, and antibubble formation. The experimental apparatus consists of a cylindrical tube with a diameter of 11 cm and 70 cm length with a column of an aqueous solution of glycerol, as shown in Fig. 2. This kind of solution was used due to its viscosity and transparency. The air is supplied at a constant flow through a solenoid valve controlled by a proportional, integral, and derivative ~PID! controller connected to a large capacitive air reservoir. The bubbles are formed in a nozzle that is a tube with 0.78 mm inner diameter and 38 mm long placed at the bottom of the tube. The dynamics of bubble formation was studied with a noninvasive technique in the same way as was *Corresponding author", " Diagram bifurcations were constructed by letting the air flow rate decrease naturally to reduce bubbling ~turning off the PID controller!; the attractors were reconstructed with first return maps TN11 vs TN obtained keeping the air flow fixed; and the bubbling rate was calculated as f b 51/^T&. All the measurements were done at room temperature. We also recorded the bubble formation with a VHS camera to illustrate their profiles corresponding to different dynamical behaviors and to observe the antibubble population. The bubbling is represented in Fig. 2 with two antibubbles captured in the liquid circulation. The physical properties of the liquid phase were varied in the investigation by using the following solutions @% glycerol/% water ~viscosity!# @5#: 0/100 ~0.9 cP!, 20/80 ~1.6 cP!, 34/66 ~2.6 cP!, 50/50 ~5.1 cP!, 60/40 ~ 9.0 cP!, 66/34 ~14.5 cP!, and 80/20 ~47.0 cP!. As the antibubbling regime is a particular state obtained from the bubbling system, we will first describe the route to reach this regime. In Fig. 3 are shown, for six different solution concentrations, the respective bifurcation diagrams, on letting the air \u00a92002 The American Physical Society04-1 flow decrease naturally along with the bubbling" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002025_s002211209400306x-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002025_s002211209400306x-Figure4-1.png", "caption": "FIGURE 4. ( a ) Idealized effective stroke of one flagellum. Numbers follow the sequence of flagellar positions. A typical element is shown on the flagellum with normal and tangential vectors n,t . ( b ) Idealized recovery stroke. The point P propagates along the line of the cell axis with speed w.", "texts": [ " Various ways of adjusting the data can be thought of, such as scaling the measured positions of points on a flagellum by instantaneous recorded length, but they are all essentially arbitrary and would give a spurious biological verisimilitude to the results of our model. Instead, we have devised and used a highly idealized model of the flagellar beat in computing our results, as described below. We assume that the flagella beat symmetrically in a plane containing the longitudinal body axis. We do not allow for any rotation about the body axis nor model the helical swimming path. We also assume that the effective and recovery strokes are distinct. The model beat starts with the flagella fully extended parallel to the body axis (figure 4a: flagella position 1). For the effective stroke, the flagella rotate rigidly about their base (0, in figure 4a) until perpendicular to the body axis. The angular velocity of each flagellum about 0 is taken to be constant throughout the motion. The angle between the flagellum and the body axis p at any stage is denoted by 2. The other flagellum beats symmetrically. During the recovery stroke, the bending waves propagate up the flagellum from the base to the tip: with reference to figure 4(b), the propagation point P is taken to travel in the direction of the body axis, restoring the flagellum to the initial position. The flagellum bends sharply as the wave moves up the axis at a constant speed w. BiJagellate gyrotaxis in a shear j o w 145 We model the changing angle x between the flagellum and the body axis during the recovery stroke in one of two ways: (a) the angle decreases at a constant angular velocity; (b) the angle is calculated in such a way that the moment about the bending point of the viscous forces acting on the dependent part of the flagellum is zero", " For future reference, it is convenient to specify both these vectors and n and t (equation (2.4)) in terms of unit vectors p, q fixed in the cell (see figures 4 and 5). The unit vectors normal and tangential to an element on the right-hand flagellum are given by n=sinXp-cosxq and (5.5) t =cosXp+sinXq. (5.6) The position of an element on the right flagellum relative to the centre of the cell during the effective stroke is given by Y = u p + s t = (a + s c o s ~ ) p + ssinxq, (5-7) where x is the angle between the flagellum and the body axis p (see figure 4a). During the effective stroke the element moves through a right angle in time T,. The angular velocity of the flagellum is then given by Bijkgellate gyrotaxis in a shear flow 147 The velocity of the flagellar element is then given by i-=-sksinxp+skcosxq. (5.9) To obtain corresponding vectors for an element on the left flagellum, change the angle x to -x. During the recovery stroke, a bending wave propagates up the length of the flagellum, 1, at a constant velocity, w say. Thus, the recovery stroke takes w / l seconds to occur. We consider the recovery stroke in two parts: the section parallel to the body axis p and the section changing angle and retreating towards the body axis (figure 4b). The position of an element on the right flagellum in the section parallel to the body axis is given by r = ( a + s ) p (5.10) with t = p and n = -4. The straight section is of length wt where wt < 1. This element is stationary with respect to the centre of the organism 0. The position of an element in the angled segment on the right flagellum is given by (5.1 1) where i7~ < x < 7~ and t = 0 is taken at the start of the recovery stroke. The velocity of the flagellum is then given by (5.12) The angular velocity of the flagellum is calculated in one of two ways" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003794_1.4006651-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003794_1.4006651-Figure7-1.png", "caption": "Fig. 7 Angular shift of planet gear number 3 in a system with Np 5 3", "texts": [ " In addition, because the suppressed sidebands become important for the present study, they will be referred to as nondominant sidebands. Regardless of this naming convention, sidebands will also be identified by their m and n numbers. 3.2 Planet Gear Shift Effects. Up to this point, it was assumed that planet gears were evenly distributed over the planetary carrier, with geometric angles given by hp\u00bc 2p(p 1)/Np. Consider now the case when one planet gear has shifted with respect to its corresponding hp angle by a specific amount, namely, dp. The situation is illustrated in Fig. 7. The mechanical configuration of a planetary gear system generally introduces a kinematic constraint that prevents a single planet gear from moving away from its original angular position. This constraint is introduced not only by the presence of the carrier plate, but also by the meshing of the teeth at the sun versus planet and annulus versus planet gear contact points. However, although this constraint limits the relative displacement of the sun, planet, and ring gears, only an ideal planetary gear system is perfectly stiff, and a real system is not rigidly constrained" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002723_physreve.76.061901-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002723_physreve.76.061901-Figure11-1.png", "caption": "FIG. 11. Configuration of a pair of trimers under the action of an external force. The difference on bending amplitude is given by the parameter .", "texts": [ " In Appendix A, we have computed the initial sedimentation velocity for a pair of filaments where one of them moves on the wake of the neighboring one Eq. A5 . Here we provide an estimate of the rate at which they approach each other when filament deformation is small either because we focus at short times, or because B is small . We consider the simplest possible case, where the filaments are represented by trimers. We will calculate the hydrodynamic velocity due to the beads of the neighbor filament on the central beads depicted in black in Fig. 11 , defined as c1 and c2 in Fig. 11. The difference between the two velocities is a measure of their relative velocity. We characterize d as the distance between the corner beads and the bending amplitude as the separation between the central and corner beads of each filament along the direction of the applied field. The top and bottom chains will bend an amount A1 and A2, respectively, where A2 A1+ . Hence, measures the relative bending amplitude due to the different hydrodynamic coupling. The distance between consecutive beads of a given trimer is b L /2, and the force field has a magnitude Fe" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002231_robot.2003.1242095-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002231_robot.2003.1242095-Figure2-1.png", "caption": "Fig. 2: Base frame, plafform frame and leg frames.", "texts": [ " The experimental identification of the dynamic parameters is based on the use of a dynamic model linear in the parameters. This model permits to use the least squares solution to solve the estimation problem [4]. 2 Kinematic modeling of the Orthoglide The Orthoglide has three PWaR identical legs (where P, R and Pa stand for Prismatic, Revolute and Parallelogram joint, respectively). Each leg is composed of six passive revolute joints and 1 active prismatic joint, (fig. I). We define frame Fo fned with the base and frame FP fixed with the mobile platform (fig. 2). Their origins are A, and P respectively. Their axes (xo, yo, a) and (xp, yp,, zp) are parallel. The base frames of the legs are defined by the frames FA,, Fm and FA, (fig. 2 ) , whose origins are A,, Q and A3 respectively. The zAi axes are This work has been supported by the project MAX of the p r o p ROBEA of the department S n C ofthe French CNRS. along the prismatic joint axes. The Khalil and Kleinfinger notations [ 5 ] , are used to describe the geometry of the system (fig. 3). The following notations are used: L (3x1) vector of the motorized joint variables: L = h , qn 4131T; \"V, (3x1) vector of the linear velocity of the origin of the The derivative of L and 'Vo with respect to the time are denoted L and 'Vu respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003398_s11244-012-9895-y-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003398_s11244-012-9895-y-Figure4-1.png", "caption": "Fig. 4 a SEM images of multiscale carbon materials at different growth times. b Polarization of glucose oxidase electrodes supported on the multiscale carbon materials, varied by nanotube growth time. Measurements were performed in nitrogen-saturated, pH 7.1 phosphate buffer solution at 37.5 C, 50 mM glucose, rotating disk electrode at 1 mV s-1 sweep rate, 4,000 rpm. (Reprinted with permission from [90]. Copyright 2007, The Electrochemical Society)", "texts": [ "2 Aligned or Oriented CNTs Several groups have reported on the use of aligned or oriented CNTs, and some of them have succeeded in achieving current density above 10 mA cm-2 or power density around 1 mW cm-2. Research on the use of aligned or oriented CNTs is summarized in this section. Barton et al. have reported a multiscale carbon material composed of a carbon paper upon which MWCNTs were grown by chemical vapor deposition (CVD). SEM images of the material at different growth times are shown in Fig. 4a. The Brunauer\u2013Emmett\u2013Teller (BET) surface area increased by two orders of magnitude, and the electrochemical capacitance increased by about 90 % of the rate as measured by BET. A redox hydrogel composed of GOx, PVP-[Os(bipyridyl)2Cl]2?/3? and cross-linker was then coated on the material. The glucose-oxidation current density increased tenfold over the bare carbon paper: a value of 22 mA cm-2 was reached (Fig. 4b) [90]. Several other groups reported CNTs grown by CVD on various substrates, such as an Au electrode [91] and a Pt electrode, using iron nanoparticles derived from ferritin molecules [92], and carbon paper [93], which were then used as matrices for enzyme electrodes. Hydrogenase immobilized in MWCNTs grown on an Au electrode produced a hydrogen-oxidation current density of about 2 mA cm-2 [91]. DET of FDH in MWCNTs grown on a Pt electrode has been reported [92]. Another method used to prepare a vertically aligned CNT film electrode involved attaching the vertically alignedT a b le 2 co n ti n u ed 3 D el ec tr o d e m at ri ce s A n o d e C at h o d e M ax im u m cu rr en t d en si ty (h al f ce ll ) (m A cm - 2 ) M ax im u m cu rr en t d en si ty (f u ll ce ll ) (m A cm - 2 ) M ax im u m p o w er d en si ty (m W cm - 2 ) V o lt ag e at m ax im u m p o w er d en si ty (V ) F u el an d it s co n ce n tr at io n R o ta ti n g sp ee d (f o r h al f ce ll : ro ta ti n g d is c el ec tr o d e) (r p m ) R ef er en ce S W C N T C el lu b io se d eh y d ro g en as e, P V P - [O s( N ,N 0 - m et h y la te d - 2 ,2 0 - b ii m id az o le ) 3 ]2 " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003957_iros.2011.6094783-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003957_iros.2011.6094783-Figure6-1.png", "caption": "Fig. 6 User posture.", "texts": [ " From the measurement results, in the case of ascending-stairs, the averages of the height and the width of the step are 186mm and 292mm, respectively. On the other hand, in the case of descending-stairs, the averages of the height and the width of the step are 169mm and 288mm, respectively. After all, the robot recognizes one step of stairs by using the laser range finder. B. Calculation of ZMP In this paper, the robot judges whether the user falls down by calculating ZMP. The ZMP is calculated based on human model as shown in Fig. 6. The supporting leg is found by tactile switches located in both soles. Then, the posture of the user\u2019s body region is calculated by these angles based on the supporting leg as follows. aspksphspb ,,, TTTT (9) where Tb is the angle of upper body region, Tsp,h, Tsp,k and Tsp,a are the angles of hip, knee and ankle joint of the support leg, respectively. Tsw,h, Tsw,k and Tsw,a are the angles of hip, knee and ankle joint of the swing leg. The positions and accelerations of the center of gravity (COG) of upper body, thigh and shin are calculated based on each joint angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003782_1.4863809-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003782_1.4863809-Figure1-1.png", "caption": "FIG. 1. Specifications of the initial prototype magnetic gear.", "texts": [ " This paper presents a comprehensive investigation of the influence of geometry and position of the pole-pieces on torque characteristic by using finite element analysis (FEA) and experiment. First, torque and efficiency characteristics of an initial prototype magnetic gear are indicated. Next, several parameters of the pole-pieces, including lengths in the radial and axial directions and position in the radial direction, are surveyed by FEA. Finally, an improved magnetic gear is prototyped based on the FEA results, and compared to the initial magnetic gear and a conventional mechanical gear in terms of torque and efficiency. Figure 1 illustrates specifications of the initial prototype magnetic gear. The gear ratio is 10.333 given by the ratio of the inner and outer pole-pairs. The number of pole-pieces is decided by the sum of the numbers of the inner and outer pole-pairs. Figure 2 shows a general view of the experimental setup. The prototype magnetic gear is operated as a reduction gear. The rotational speed of the inner rotor is regulated to an arbitrary speed by the servomotor, while the load torque is applied to the outer rotor by the hysteresis brake" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002968_s0263574708004645-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002968_s0263574708004645-Figure2-1.png", "caption": "Fig. 2. (A) A set of 50 nonlinear trajectories in a three-dimensional state space. The dotted lines indicate that the trajectories make a jump in state space. (B) Planes slice the trajectories perpendicular. The points in these planes can be analyzed without the nonlinearities of the trajectories. (C) With the points in the planes the average trajectory and the boundary is estimated. The boundary in a plane is an ellipse. The ellipses of all the planes combined results in a tube. Note that the shown tube is created with more planes than are shown.", "texts": [ " With the local modeling method, a model can be constructed that consists of the nominal trajectory and the nominal variation around the nominal trajectory. This model is constructed with a set of \u201cgood\u201d cycles. This set consists of I trajectories in J -dimensional space. 2.2.1. Slicing the trajectories. We like to analyze the trajectories with the principal component analysis (PCA) method. PCA is a data analyzing method that removes the linear correlation between the variables by rotating the coordinate system. It is impossible to analyze the trajectories directly with the linear PCA method because the trajectories can be very nonlinear (Fig. 2A). To remove the nonlinearities we look only at the position in state space with respect to the nominal trajectory. This is done by slicing the trajectories perpendicular to the nominal trajectory with K planes (Fig. 2B). These planes are (J \u2212 1)-dimensional, one dimension lower than the space of the trajectories. The planes can be seen as cross sections of the trajectories. Each of these http://journals.cambridge.org Downloaded: 17 Dec 2014 IP address: 138.251.14.35 cross sections separately can be analyzed with PCA because the nonlinearity of the trajectory is removed. A problem with this slicing perpendicular to the nominal trajectory is that the nominal trajectory is not known (yet). The nominal trajectory can be estimated with the average of the \u201cgood\u201d trajectories in time", " The standard deviation \u03c3 for each of the uncorrelated dimensions is \u03c3 k j = 1 I \u2212 1 I\u2211 i=1 Tk ij for j = 1, . . . , (J \u2212 1). (3) The normal distribution for each of the dimensions results in a multivariate normal distribution. For this multivariate normal distribution the 95% interval is an ellipsoid. This (J \u2212 1)-dimensional ellipsoid has its axes on the rotated axes after PCA and can be rotated back into the original coordinate frame (Fig. 4). The ellipsoids found for the K slices can be combined in a tube around the nominal trajectory. Figure 2C shows an example of such a tube for a three-dimensional system. The http://journals.cambridge.org Downloaded: 17 Dec 2014 IP address: 138.251.14.35 tube is the boundary of the \u201cgood\u201d cycles and shows the nominal variation around the nominal trajectory. In the next section we will discuss how this tube can be used for the monitoring of the system. In the last section, we estimated the nominal trajectory and the nominal variation around this trajectory with the trajectories of a set of \u201cgood\u201d cycles" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002426_1350650042794716-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002426_1350650042794716-Figure1-1.png", "caption": "Fig. 1 Geometry of ball bearing and contacting elastic solids", "texts": [ " In this paper, the theoretical formulation of the stiffness and damping coefficients of a fully lubricated ball bearing is presented considering the surface roughness. Static and dynamic hydrodynamic pressure equations are derived using a linearized first-order perturbation technique. Overall equivalent bearing stiffness and damping directional matrices are obtained from static load distribution and individual ball contact stiffness and damping, which can be used directly in the finite element method (FEM) analysis of the rotor\u2013 bearing system. The two ellipsoids shown in Fig. 1 make a contact at a single point under the unloaded condition and this is called the \u2018point\u2019 contact. Geometrical parameters are summarized as follows. Curvatures in the x and y directions are defined as 1 Rx \u00bc 1 rax \u00fe 1 rbx , 1 Ry \u00bc 1 ray \u00fe 1 rby For the ball inner race contact, Rx \u00bc d\u00f0de d cos b\u00de 2de , Ry \u00bc rid 2ri d and, for the ball outer race contact, Rx \u00bc d\u00f0de \u00fe d cos b\u00de 2de , Ry \u00bc rod 2ro d The point contact spreads to form an elliptical contact due to deformation of the mating surfaces under a normal load" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003420_02640411003792711-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003420_02640411003792711-Figure1-1.png", "caption": "Figure 1. (a) Inertial frame of reference. (b) Face angle measurement convention. (c) Stroke path measurement convention.", "texts": [ " Therefore, the main aim of this study was to evaluate the validity and reliability of the TOMI1 system for measuring the 3D kinematics of the putting stroke. A secondary objective was to determine the importance of key kinematic errors, at impact, on the outcome of a putt. To operationally define the four deterministic variables, an inertial frame of reference is useful. The positive X-axis extends from the centre of the putter face along the intended initial direction of the putt and is coincident with the target line. The positive Y-axis extends vertically up from the ground and the positive Z-axis is formed according to the right-handrule (Figure 1a). Face angle is defined as the angle 892 S. J. MacKenzie & D. B. Evans formed between the target line and a line perpendicular to the putter face (Figure 1b). Stroke path is defined as the angle between the velocity vector of the putter head and the target line (Figure 1c). Putter speed is defined as the velocity of the centre of the putter face along the X-axis (target line). Impact spot is defined as the distance from the centre of the putter face to the ball contact point, along the heel\u2013 toe axis of the putter. All four variables are measured at impact. The origin of the reference frame is a theoretical position located at the centre of the putter face when the centre of the putter face is flush with the ball and both face angle and impact spot are zero. TOMI1", " This means that the raw displacement data can be expressed in the frequency domain and subsequently digitally resampled at a sufficient rate in the time domain (Hamill, Caldwell, & Derrick, 1997). This permitted the raw coordinate data from each LED to be resampled at 1000 Hz, which allowed for the precise measurement of each variable at impact. Knowing the lie angle of the putter and 3D position of the LED clip relative to the centre of the putter face allowed the global inertial reference frame to be created based on the calibrated position of the putter (Figure 1a). The coordinates of the centre of the putter face in the calibrated position were (0, 0, 0). The precise moment of impact was determined by finding the instant in the putter head\u2019s trajectory (now sampled at 1000 Hz), which was closest to the calibrated position (0, 0, 0). Validity: face angle and stroke path. The face angle and stroke path of the putter, at impact, were predetermined using the putting robot and two associated lasers, which were projected onto a wall that was inscribed with a grid", " The first putt in each set was hit off the heel, the second between the heel and the centre, the third at the centre, the fourth between the centre and the toe, and the fifth off the toe. Each putt was captured using the high-speed camera, which was positioned 1.5 m above the putting surface such that the axis of the camera lens was perpendicular to the surface and directed through the \u2018\u2018sweet spot\u2019\u2019 indicator on the top of the putter head. The field of view was 40 cm along the X-axis6 30 cm along the Z-axis (Figure 1a) and the resolution was 4406 330 pixels. Each stroke was captured at 250 Hz with a shutter speed of 1/10,000 and the field of view was illuminated with two 500-W halogen bulbs. The \u2018\u2018sweet spot\u2019\u2019 indicator on the top of the putter head was manually digitized using Maxtraq1 (Innovision Systems, Inc., Columbiaville, MI) software. The point\u2019s coordinates at address (in the calibrated position) as well as through the impact area were collected for each stroke. Impact spot was calculated as the displacement of the centre of the putter head from address to impact along the Z-axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003270_iembs.2009.5334163-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003270_iembs.2009.5334163-Figure1-1.png", "caption": "Fig. 1. Drawing views of a 7 Fr. catheter illustrating the proposed concept of the three axes fibre-optic force sensor.", "texts": [], "surrounding_texts": [ "A. Minimally Invasive Surgery (MIS) MIS allows surgeons to access the internal anatomy of a patient through small openings. The benefits of that approach are many and they have an affect both to the patient and the hospital [1]. Even though MIS has numerous advantages to present, still there are some drawbacks which make its implementation in theatres difficult [3]. One of the most important is the lack of force feedback To overcome the drawbacks, robots in surgery have been introduced and their development is playing an imperative C 978-1-4244-3296-7/09/$25.00 \u00a92009 IEEE role in the advancement of MIS [4]. Today\u2019s most renowned robot for surgical applications is the da Vinci\u2122 surgical system (Intuitive Surgical, Sunnyvale, California) [5]. Regardless of any improvement in the accuracy and safety offered by robots in surgery, the loss of haptic feedback still remains an important unsolved issue. B. Catheterisation Catheterisation is a minimally invasive approach which targets to offer treatment or examination to tissues and organs using existing routes inside a human body. Routes such as the blood vessels are used to allow thin, long and flexible instruments to reach targeted settings within the body. These instruments are called catheters and their diameter does not exceeding 3-4 mm [7]. The insertion and progression of a catheter into the body is achieved from a small incision on the groin (upper thigh), the arm, or the neck of the patient. In a catheterisation the restrictions for the size of instruments to be used originates in the size of the blood vessel. Therefore, as cameras are almost impossible to be inserted, other visualisation methods are used. Fluoroscopy and Computed Tomography (CT) are the two most common methods used today by cardiologists. These techniques employ ionising technology, such as X-rays, to represent the inner human structure. However, their use is hazardous for the human body. In addition, the quality of the tissues and organs in the returned images is poor. In order to enhance them the catheter has to inject a contrast medium inside the area of interest. Lately, scientists are interested in substituting these methods with others which have distinct advantages; one of these methods is the MRI. MRI is making use of magnetic fields to produce the images. As a result, these images are giving three dimensional representation of the internal body structure with superior quality and without emitting hazardous ionising radiations. Despite the advantages of an MRI scanner, the use of tools and instruments inside its area of operation which contain materials that could affect the homogeneity of the magnetic field must be avoided. Furthermore, the insertion of conductive wires can potentially work as an MR-antenna, which can result in potential heating effects at the tip of the wire during MR-scanning. Hence, metal materials are ineffective, as either distort the images, producing artefacts, or heating up effects putting in health risks the patients [8]-[10]. C. Force Feedback Interventional cardiologists are often able to sense the interaction of the catheter tip with the internal structures (e.g. blood vessels, atrium of the heart) while performing a catheterisation. That haptic feedback is often used to realise the position and the manoeuvres of the catheter requiring usually extensive training to achieve this expertise. Although a contact of the catheter with internal structures can be felt by the interventional cardiologist, the distinction of the involved forces is a difficult task. These forces are a combination of two secondary forces. The one originates from the friction of the catheter with the blood vessel walls and the other from the contact of the catheter-tip with the blood vessels [2]. Several systems have been developed to enhance catherisations, like Sensei\u2122 robotic catheter system (Hansen Medical, Inc., Mountain View, California) [6] and the recently developed TactiCath (Endosense SA, Geneva, Switzerland) [11]. Nevertheless, most of the solutions given today by scientist do not take into account the ease in manufacturing, the costs for production and the MRI-compatibility. In every surgical robotic system which deals with catheterisation realisation that the information carried from the interaction forces between the catheter and the blood vessels is imperative. Therefore, in this paper a new approach for detecting the contact forces from the tissue-catheter interaction is discussed. In extent, a fibre-optic sensory system is presented in a feasibility study, as a low-cost and MRI compatible solution." ] }, { "image_filename": "designv10_13_0003840_j.jfranklin.2013.05.033-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003840_j.jfranklin.2013.05.033-Figure1-1.png", "caption": "Fig. 1. Sketch figure of K;K1;\u0398;\u03a9.", "texts": [ "2) will reduce to the unsaturated controller u\u00bc \u2212\u03b2n\u00f0xa=rnn \u00fe \u03b2a=rnn\u22121 \u00f0xa=rn\u22121n\u22121 \u00fe\u22ef\u00fe \u03b2a=r32 \u00f0xa=r22 \u00fe \u03b2a=r21 xa=r11 \u00de\u22ef\u00de\u00dern\u00fe1=a; which is the same form as Eq. (3.2). Define a level set \u03a9\u225cf\u00f0x1; x2;\u2026; xn\u00dejVn\u00f0Xn\u00de\u2264\u03f1; \u03f1\u00bcminXn\u2208Rn=\u00f0K\u2229K1\u00deVn\u00f0Xn\u00deg where K is defined in Theorem 3.1 and K1\u225cf\u00f0x1;\u2026; xn\u00dejk\u00f0Xn\u00de\u2264 1 2g. Since the coefficients \u03b2i 's have been fixed, the sets K;K1, and \u03a9 are fixed as well. In addition, from Eq. (4.35), we can adjust \u03f5 small enough to ensure \u0398D\u03a9. The relation of the sets K;K1;\u0398, \u03a9 is shown in Fig. 1. As a consequence, \u2200t\u2265tn, the states will stay in the level set \u03a9DK in which by Eq. (3.26) we have _V n\u00f0Xn\u00dej\u00f01:1\u00de\u2264\u2212 1 2 \u00f0\u03be2\u03c1=a1 \u00fe \u03be2\u03c1=a2 \u00fe\u22ef\u00fe \u03be2\u03c1=an \u00de; Xn\u2208\u03a9: \u00f04:36\u00de Based on Eq. (4.36), it can be concluded that the states of the closed-loop system (1.1)\u2013 (4.2) will converge to the origin. \u25a1 Remark 4.1. In Theorem 4.1, for the convenience of the proof, we choose a saturation function (4.1) which is not continuously differentiable at the switching point. In order to construct smooth stabilizers, we can use a modified smooth saturation function instead of the traditional saturation function" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002196_j.cma.2004.07.031-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002196_j.cma.2004.07.031-Figure5-1.png", "caption": "Fig. 5. system", "texts": [ " We recall that there are two stages of determination of the initial point of tangency M of surfaces R1 and R2: (i) determination of points M \u00f00\u00de 1 and M \u00f00\u00de 2 close to the real contact point, and (ii) exact solution wherein distance d = 0 and deviation of the normals g = 0. The solution wherein d 5 0 and g 5 0 requires a very small rotation of one of members of the gear drive, let us say of the gear, to get a common point of intersection of both surfaces at point M(0). This means that surfaces R1 and R2 will be intersected. The determination of the line of intersection of R1 and R2 may be represented as determination of common points of R1 and R2. The procedure of determination of line of intersection of R1 and R2 is based on the following considerations: (i) Fig. 5(a) shows surfaces R1 and R2 and the expected line of their intersection. Point M is the exact point of tangency of R1 and R2. Point M(0) is the common point of surfaces R1 and R2 at which the position vectors of R1 and R2 coincide, but the normals to R1 and R2 deviate from each other. We consider that at point M(0) are determined: (a) the surface unit normal to R1, and (b) the coordinate lines to R1 that pass through M(0). (ii) We choose on surface R1 a point Oa close to M(0), but it is inside of the expected line L of intersection of R1 and R2. Point Oa is the origin of an auxiliary coordinate system Sa (Fig. 5(b)). Axis za is directed collinearly to surface R1 normal; one of the coordinate axis of Sa, say xa, is directed collinearly to the tangent to one of the coordinate line on R1 at point M(0). (iii) We may now consider a plane P that intersects surface R1 and R2 and is formed by line OaA and axis za (Fig. 5(b)). The orientation of this plane in coordinate system Sa is determined by angle la that is varied in the range [0,2p]. (iv) Representing surfaces R1 and R2 and common coordinate system Sf, we may obtain the line of inter- section of surfaces R1 and R2 by the branch of planes P. The branch of planes P is formed by variation of la. (v) A point of plane P is represented in Sa by the position vector qa \u00bc \u00bdda cos la; da sin la; la; 1 T : \u00f024\u00de Using coordinate transformation from Sa to Sf, we obtain equations of the branch of planes P in Sf as follows qf\u00f0da; la; la\u00de \u00bc Mfaqa\u00f0da; la; la\u00de: \u00f025\u00de (vi) Each plane P of the branch of planes intersects surface Ri (i = 1,2) by a spatial curve that may be derived by system For derivation of line of intersection of R1 and R2: (a) R1 and R2 and line of intersection of R1 and R2; (b) auxiliary coordinate Sa", " Curve ri is determined as r \u00f0i\u00de f \u00f0ui\u00f0da\u00de; hi\u00f0da\u00de;wi\u00f0da\u00de\u00de \u00f0l0 \u00bc const\u00de; f i\u00f0ui\u00f0da\u00de; hi\u00f0da\u00de;wi\u00f0da\u00de\u00de \u00bc 0: \u00f027\u00de The common point of curves r1 and r2 is determined as r \u00f01\u00de f \u00f0u1\u00f0da\u00de; h1\u00f0da\u00de;w1\u00f0da\u00de\u00de \u00bc r \u00f02\u00de f \u00f0u2\u00f0da\u00de; h2\u00f0da\u00de;w2\u00f0da\u00de\u00de \u00f0l0 \u00bc const\u00de; \u00f028\u00de f1\u00f0u1\u00f0da\u00de; h1\u00f0da\u00de;w1\u00f0da\u00de\u00de \u00bc 0; \u00f029\u00de fi\u00f0u2\u00f0da\u00de; h2\u00f0da\u00de;w2\u00f0da\u00de\u00de \u00bc 0: \u00f030\u00de The whole line of intersection of R1 and R2 is represented on surface Ri as Rf \u00bc Rf\u00f0la\u00de; \u00f00 6 la 6 2p\u00de: \u00f031\u00de (vii) We remind that the surface normals are collinear at a point of tangency of surfaces R1 and R2 and therefore equations (9) and (10) are observed. It is obvious that at least one of Eq. (9) or (10) turns into an inequality at a point of line of intersection of R1 and R2. Line L of intersection of surfaces R1 and R2 is obtained at the stage wherein the surfaces have common position vectors at a point designated as M(0) (Fig. 5(a)). However, the surface normals deviate each other at point M(0). The starting point of contact of tooth surfaces for the performance of TCA is noted as M (Fig. 5(a)). At point M coincide not only the position vectors of tooth surfaces, but the surface normals as well. Line L of intersection passes through point M(0). A contact ellipse of tooth surfaces may be determined at M knowing the principal curvatures and directions at M and the elastic deformation of tooth surfaces at M. Choosing a proper value of elastic deformation of R1 and R2, the contact ellipse of R1 and R2 may be determined. Our goal is to illustrate simultaneously line L and the contact ellipse. The contact ellipse may be represented in a plane that is perpendicular to common surface normal n (Fig. 4(b)). Line L is represented on surfaces R1 and R2 by Eq. (31), but it may be represented as well in coordinate system Sa (Fig. 5). Fig. 4(b) shows line L and the axes of contact ellipse in plane P that is perpendicular to surface normal n. Since line of intersection is a spatial curve, it deviates from plane P as shown in Fig. 4(b). The area of location of L and contact ellipse on the tooth surface, is shown in Fig. 4(a). The tooth surfaces R1 and R2 are in point tangency and the instantaneous tangency of surfaces is represented in coordinate system Sf by vector equations (Fig. 1). r \u00f01\u00de f r \u00f02\u00de f \u00bc 0; \u00f032\u00de n \u00f01\u00de f n \u00f02\u00de f \u00bc 0: \u00f033\u00de We recall that instead of equal surface unit normals, we require observation of Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003404_iros.2011.6095001-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003404_iros.2011.6095001-Figure1-1.png", "caption": "Fig. 1. Starting with the passive SLIP model, we add hip and leg motors for active control, and body moment of inertia.", "texts": [ " Existing passive walkers, such as the Cornell Walker, are capable of energy economy similar to animals, but will fall in the presence of small disturbances [1]. Robots that rely primarily on active control, such as Boston Dynamics\u2019 \u201cBigDog,\u201d can demonstrate impressive robustness to disturbances at the expense of energy economy [2]. Our goal is to create robots that combine the robustness to disturbances of actively controlled machines with the energy economy of a passive dynamic walker. In this paper, we present an actuated spring-mass model that is suitable for implementation as a real system, shown in Fig. 1(b), and an associated control strategy for planar running. The control strategy works in conjunction with our model to utilize the passive dynamics where possible for energy economy, and to add or remove energy only when necessary via actuation. We show in simulation that the combined model and controller is energetically conservative like the completely passive spring-mass model during steady-state running, but is self-stable in the presence of disturbances in the ground height or impedance. In other words, our model and controller combine the benefits of passive dynamics and active control, producing an efficient and robust running gait", ", and active force control in the This work was supported by the school of Mechanical, Industrial and Manufacturing Engineering at Oregon State University. The authors can be contacted by email at: koepld@onid.orst.edu leg length direction during the stance phase, described in our earlier publication for vertical hopping [3], [4]. Our leg angle controller is based on maintaining a symmetrical stance phase, where the velocity vector of the center of mass at liftoff will be a perfect mirror of the velocity vector at touchdown; the horizontal component will be identical, and the vertical component will be equal and opposite, as shown in Fig. 1(a). A symmetrical stance phase leads to an equilibrium gait, because each stance phase is identical to the last if there are no outside disturbances. For a given springmass model, with a particular center-of-mass velocity vector at touchdown, there is a particular leg angle at touchdown that will result in a symmetrical stance phase. We calculate this leg angle for each instant of time during the flight phase, as the velocity vector changes, such that the spring-mass model will have a symmetrical stance phase no matter when its foot makes contact with the ground", " This novel concept of combining force control and a spring-mass model is convenient, easy to implement on a real system with dynamic and sensing limitations, and effective. Because our goal is to build robots that can match the performance, economy, and robustness of animal running, our models incorporate passive dynamics similar to those observed in animals. Spring-mass models provide a good approximation for animal running, we therefore begin with a simple model consisting of a mass bouncing on a spring, as shown in Fig. 1(a) [5]. Humans and animals make excellent use of passive dynamics, but also use active control to compensate for disturbances. For example, guinea fowl are able to accommodate a drop in ground height by rapidly extending their leg into an unexpected disturbance, as shown in Fig. 2, resulting in only slight deviation from their undisturbed gait [6]. Furthermore, biomechanics studies suggest that humans and animals adjust their leg stiffness during hopping, walking, and running to accommodate changes in ground stiffness and speed [7]", " However, force control using the deflection of series springs has been successfully implemented on legged robots such as Boston Dynamics\u2019s walking and running quadruped, \u201cBigDog\u201d, and the MIT Leg Lab\u2019s walking biped, \u201cSpring Flamingo\u201d [16], [17]. These robots use springs in much the same way as the SEA, as a force sensor and mechanical filter, but not for energy storage. When correctly applied, this approach can result in impressive performance, but at the cost of high energy consumption. Starting with the simple spring-mass model, shown in Fig. 1(a), we add hip and leg actuation as well as body moment of inertia to arrive at a realistic model for robot running, as shown in Fig. 1(b). The actuators include a motor with a torque limit and rotor inertia. We chose to omit leg mass from our model, to keep the system as simple as possible. For ATRIAS, shown in Figures 8(a) and 8(b), our eventual target robot for this control method, toe mass composes less than one percent of total robot mass. The leg actuator makes use of the existing leg spring, while we add a second rotational spring to the model for the hip actuator. The hip actuator sets the leg angle during flight and maintains zero moment about the hip during stance, such that the force-controlled model behaves like the passive model during undisturbed hopping" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003341_icma.2010.5589079-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003341_icma.2010.5589079-Figure2-1.png", "caption": "Fig. 2. Stair-climbing of the wheelchair robot. (a) Transforming on the lower floor. (b)-(c) Climbing the first several stairs. (d) Moving on the nose line with a fixed configuration. (e)-(f) Transforming to concave geometry. (g)-(h) Loading on the upper floor.", "texts": [ " Based on the information acquired from the sensors, the back and front flippers can be controlled to rotate cooperatively to make the robot transform between the initial and terminal configurations. B. Stair-Climbing Procedure To simplify the analysis, it is assumed that the robot will not yaw during stair-climbing, then the stair-climbing procedure can be divided into four phases. In phase 1, the robot moves to confront the stairs with the back, then the back and front flippers rotate anticlockwise to definite angles to make the chair retroverted, as shown in Fig 2(a). In phase 2, the robot starts to climb the first several stairs. When the pitch angle of the chair reaches a definite value, as the robot moves on, the back and front flippers rotate anticlockwise sequentially to keep the obliquity of the chair, as shown in Fig 2(b)-(c). In phase 3, the robot has climbed onto the stairs completely and goes on moving on the nose line of the stairs with a fixed configuration, as shown in Fig 2(d). The fourth phase can be divided into two steps. When the back flippers pass over the nose of the last stair completely, the first step of phase 4 starts. In this step, the robot stops moving and the back flippers rotate clockwise to make the tracked mechanisms transform to concave geometry with the assistant of the front flippers until the back planetary wheels support on the upper floor, as shown in Fig 2(e)-(f). Then the second step of phase 4 starts, the robot keeps on climbing and the back and front flippers rotate anticlockwise until the robot loads on the upper floor completely, as shown in Fig 2(g)-(h). A. Coordinate System of the Wheelchair Robot For configuration analysis of stair-climbing, the coordinate system is established in the lateral symmetry plane of the robot mechanism as shown in Fig. 3. In Fig. 3, the world frame oW-xWyWzW is established at the base point of the first stair, frame oR-xRyRzR whose coordinate axes are parallel correspondingly to those of frame oW-xWyWzW is established at the front road wheels to represent the movement of the front road wheels, frame oA-xAyAzA is fixed with the supporting frame to represent the obliquity of the chair, frame oB-xByBzB and oC-xCyCzC are fixed with the back and front flippers separately to represent the rotation of the flippers and the planetary wheels", " Configuration Analysis for Stair-Climbing As the requirement of tip-over stability analysis, the configuration analysis mostly aims at phase 2, 3 and 4 of the stair-climbing procedure when the robot has greater possibility of tip-over instability to derive the equations of chair obliquity and track length which can represent the transformation rule of robot configuration. 1) Phase 2: Configuration analysis for phase 2 is against the condition that only the back planetary wheels support on the stairs as shown in Fig 2(b). On this condition, the equation of chair obliquity can be derived as 2 2 2 2 2 3( , , , ) ( ) ( ) 0W R W R A E A Ef x h x x z r h r (2) where ( , )R R E Ex z is the coordinate of points El(r) in plane xR-oR-zR, h is the height of the stairs riser, r3 is the radius of the back planetary wheels. The final form of (3) only contains the variables , , W Ax and h . In the early and late stages of phase 2, equation (2) can represent the variation of the chair obliquity and the rotation of the back flippers as the robot moves separately" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002145_iros.2000.895302-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002145_iros.2000.895302-Figure7-1.png", "caption": "Fig. 7 Principle of M-Drive", "texts": [ "2 Torque limiting mechanism M-Drive\" The ACM is hyper-redundant serial link system. The principal problem of existing systems is the inability to withstand unexpected external forces due to excessive moments at its root joints, so the torque limiter is necessary. Though usual torque limiter is bulky, it can be realized by adding simple parts in the wire drive system. The basic principle of M-Drive can be explained from the expression of the fiction transmission between the string and the pulley. In Fig. 7 (a), let T , and T, ( TI c T,) are the string's tension, ,U is the friction coefficient between the string and the pulley, and 8 is the winding angle of strings. The condition in which the slip occurs is the following. T, >TI exp( PO 1 So the maximum value of T,can be decided by TI which is set beforehand and by far smaller tension than T,. T, is the driving force of the pulley, and the torque that generates the tension over the maximum value of T, is not transmitted by slipping[3]. - 2244 - It is constructed as shown in Fig.7 @) and Fig.8. The wire drawn out from its winding pulley is hooked around the other pulley that is rotation free. This pulley is pulled by the spring for applying the tension on the wire. And the compressive force of coil spring, which is accumulated by turning the worm gear, has been applied on pulley by the link in this tensioner unit. 3 3 Float differential torque sensor It is useful to obtain torque information, which works in each axis in order to realize the advanced and three-dimensional motion control" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001459_jsvi.1998.1988-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001459_jsvi.1998.1988-Figure5-1.png", "caption": "Figure 5. Auxiliary mechanical systems for quasi-static contact analyses. (a) Dual mesh systems; (b) idler gear.", "texts": [ " In a second step, the T 2 Shaft, bearing data Left side length Right side length External diameter (mm) (mm) (mm) Input shaft 233\u00b755 98\u00b743 80\u00b700 Output shaft 211\u00b781 76\u00b769 90\u00b700 Bearing For all bearings, radial stiffness kp =4\u00d7108 N/m excitation functions generated by each individual mesh are determined by several quasi-static contact analyses (with all shape deviations and mounting errors) conducted mesh by mesh with the proper boundary conditions on forces and moments in order to account for the influence of the neighbouring pinion-gear pairs [27]. Each stage, i.e., a pinion-gear pair and its supports, is isolated and the contributions from its mechanical environment are replaced by the equivalent set of forces and moments determined by the classical formulae in rigid-body mechanics and the finite element shape functions for double stage drives. The principle is illustrated in Figure 5 for two possible configurations of double stage gear sets. In these examples, each isolated sub-system is described by the 36-degree-of-freedom model presented in reference [22] but, depending on the complexity of the gear set, more sophisticated auxiliary models can be used if needed. The following approximations are introduced: Ncs (t)= s Ns(t) i H(Ds (Mi ))3 s Ns(t) i H(Dso (Mi )), (18) s Ncs(t) i ksi = s Ns(t) i ksiH(Ds (Mi ))3 s Ns(t) i ksiH(Dso (Mi )), (19) s Ncs(t) i ksides (Mi )= s Ns(t) i ksides (Mi )H(Ds (Mi ))3 s Ns(t) i ksides (Mi )H(Dso (Mi ))" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003776_wccit.2013.6618768-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003776_wccit.2013.6618768-Figure1-1.png", "caption": "Fig. 1: Quadrotor with each rotor tilting about two axes", "texts": [ " More advantages regarding robustness, fault tolerance and distinguished capabilities for critical missions are discussed later in this paper. This paper is organized as follows: section II presents the dynamic model of quadrotor with two DOF\u2019s tilting propellers. Section III discusses the advantages of this over conventional design and proves some of these advantages with simulation. Finally, the paper is concluded in section IV. In the following discussion we assume that the rotors are located at O1, O2, O3, and O4, and are tilted with respect to fixed rotor frames at these points Fig.1. The rotor frames are taken to be parallel to the body fixed reference frame at the center of gravity C.G. When the rotors are aligned along the body z-axis, rotor 1 and rotor 2 are assumed to rotate counterclock-wise CCW, while rotor 3 and rotor 4 rotate clock-wise CW. The forward direction is taken arbitrary to be along the body x-axis. Assume that the rotational speed of the rotor i is given by wi. Then we can say that the lifting thrust is given b\u03c92 i and the drag moment is given by d\u03c92 i . The orientation of the rotor is controlled by two rotations about the rotor fixed frame; \u03b1i, a rotation about the rotor y-axis, and \u03b2i , about the rotor z-axis, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003498_0022-2569(71)90044-9-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003498_0022-2569(71)90044-9-Figure3-1.png", "caption": "Figure 3. Four-bar linkage with a large output swing angle and favorable trans. mission angles according to Fig. 2.", "texts": [ " Since, as already mentioned, the intermediate angle ~ . also influences the size of the cam disk and therefore should lie in a particular range, a rounded-off value ~ . = 210 \u00b0 for the driven angle, and at the same time a Transmission angle /~min = 40*, was chosen. Figure 2 shows the appropriate graph, which, for angles of ~ . = 210 \u00b0 and/Zmm = 40 \u00b0, yields \u00a2 . = 90 \u00b0. By following the rules given in [2] and with some auxiliary variables, which will not be discussed in this paper) the four-bar linkage may be laid out as shown in Fig. 3. From this, one may determine not only the lengths b', e, f a n d d', but also the initial 423 position, designated by the angle between b' and the fixed base-line d'. When the output link f swings through the angle ~o. = 210\" between its extreme positions CoCt and CoCto. the driving link b' pivots through the angle coil = 91.8 ~. The particularly distinguishing mark of such a four-bar linkage with the most favorable transmission quality is that the minimum value/Zm~. = 40 \u00b0 appears several times, once as/Zmt", " 5, one first draws the locus q for the range of the positive transmission ratio and the locus q' for the range of the negative transmission ratio. A fixed link length dl = 50 has been assumed. Initially, this will be discussed for the point Q,. of q for x = 0.2. For x = 0-2 one obtains from equation (4) 1 .~ = 5_(I - -cos 36 \u00b0) = 0-096 (18) and consequently according to equation ( I O) e u = M*H. g = 3\"663 . 0-096 = 0\"351 (19) \u00a2t~=20.05o. (20) If the lever f i s rotated from its initial position as shown in Fig. 3 through 20-05 \u00b0 in the direction of the required motion, namely clockwise, one obtains from the dimensions of the four-bar linkage a rotation angle of Ctto. = 8.4 \u00b0 for the lever. For the transmission ratio of the composite mechanism one finds, according to equation (5), f o rx = 0-2: 17\" t3 = ~- x sin 36 \u00b0 = 0.923 (21 ) / and from equation (12): io.., = M~. v = 1\" 166 X 0-923 = 1\"076. (22) In the second component mechanism, namely in the four-bar linkage, one must first J.M. Vol. 6 No. 4 - F determine the transmission ratio i , ", " At the extremal positions of the follower, the transmission ratios in this leadingcomponent mechanism are of course i , = i~to = 0. This reduces equation (15) to A o = A t . i , (41) At = Ao/i,. (42) The specific acceleration At in the leading mechanism therefore only depends on the specific total acceleration Ao and on the transmission ratio itt in the second, or following component, mechanism. Using equations (13) and (14) they are calculated to be: Mot = +1\"831 and Aoto =--1\"831. Positions 1 and 10 of the second mechanism are illustrated in Fig. 3 and from this, the transmission ratios may be read off: i m = +2.77; i,,o = 0.886; therefore Art = + 1.831[2.77 = +0.661 (43) A/t0 = - 1 \"831/0\"886 = --2\"065. (44) In the dead-center positions of the leading mechanism the pole distances are qb~ = qb~0 = d~ = 50; therefore the lengths of the slide-turn vector m representing the slide\u00b0 turn ratio can be found from equation (17) to be: tact = Ati \u2022 dt = +33-05 (45) recto = Art0. dt = -103 .25 . (46) The output lever f (Fig. 6) starts from position CoCl turning clockwise with a zero velocity; it therefore has a positive acceleration Ao; and therefore according to equations (43) and (45) both acceleration A tl and me, must be positive" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002048_rob.4620080505-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002048_rob.4620080505-Figure3-1.png", "caption": "Figure 3.", "texts": [ " ,78) and the common normal link lengths are labeled aij. The twist angles between Crane, Carnahan, and Duffy: Kinematic Analysis of SSRMS 639 successive pairs of joint axes are labeled aii (6) with p the number of pole pairs, N the number of series turns per phase, 1, the effective core length and the average value of A over a phase. The stator inductance is easily derived from the second simulation since there is no current induced in rotor bars" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003535_detc2012-70621-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003535_detc2012-70621-Figure1-1.png", "caption": "Fig. 1 Representation of motion patterns.", "texts": [ " PMs which have inactive joints in some operation modes and have no inactive joint in other operation modes [22]. From the DOF (degrees-of-freedom) of different operation modes, PMs with multiple operation modes can be classified into the following two classes: 1) Invariable-DOF PMs. PMs which have the same DOF in all the operation modes [18\u201322]. 2) Variable-DOF PMs. PMs which do not have the same DOF in all the operation modes [17]. However, except for the PMs with both planar and cylindrical operation modes [17], no variable-DOF PM has been proposed. Considering that both the planar motion (Fig. 1(a)) and 3T1R motion (Fig. 1(b)) are motion patterns in common use, this paper deals with the type synthesis of PMs with both planar and 3T1R operation modes, which is the first part of our research on disassembly-free and energy-efficient reconfigurable PMs. It is noted that PMs with both planar and 3T1R operation modes are deferent from partially decoupled 3T1R PMs [24, 25]. In a PM with both planar and 3T1R operation modes, the axes of rotation of the moving platform in the planar operation mode are not parallel to the axes of rotation of the moving platform in the 3T1R operation mode" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002015_s0263574705001670-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002015_s0263574705001670-Figure2-1.png", "caption": "Fig. 2. Kinematical scheme of the manipulator.", "texts": [ " The fourth constraining chain has a different architecture. It consists of a prismatic joint attached to the base and a moving link of length l1 and mass m1, having a purely vertical displacement \u03bbD 10, velocity vD 10 = \u03bb\u0307D 10 and acceleration \u03b3 D 10 = \u03bb\u0308D 10. A Hook joint is attached to the moving platform. The moving platform is an equilateral triangle with edge l, mass m4 and tensor of inertia J\u03024. Rotations of the moving platform are defined by the angles \u03d5D 21 and \u03d5D 32 in the local coordinates (Fig. 2). The orientation of the joints A, B, C on the fixed platform (Fig. 1) is given by \u03b1A = 0, \u03b1B = 2\u03c0 3 \u03b1C = \u22122\u03c0 3 . (1) For convenience, the independent coordinates of the platform have been chosen as zG 0 , \u03b11, \u03b12, where zG 0 is the height of the platform and \u03b11, \u03b12 are the angles of the Hook joint. Assuming the passive leg D on the OD1D2D3 path, the passing matrices are derived: d10 = e\u0302, d21 = d \u03d5 21a1, d32 = d \u03d5 32a2. (2) Now, considering the OA1A2A3A4 track of the limb A, the transfer matrices are given by a10 = a \u03d5 10a1a A \u03b1 , a21 = a \u03d5 21a\u03b2a2, a32 = a1, (3) Where:25 a1 = 0 0 \u22121 0 1 0 1 0 0 , a2 = 0 0 \u22121 \u22121 0 0 0 1 0 , aA \u03b1 = cos \u03b1A sin \u03b1A 0 \u2212 sin \u03b1A cos \u03b1A 0 0 0 1 a\u03b2 = cos \u03b2 sin \u03b2 0 \u2212 sin \u03b2 cos \u03b2 0 0 0 1 , a \u03d5 k,k\u22121 = cos \u03d5A k,k\u22121 sin \u03d5A k,k\u22121 0 \u2212 sin \u03d5A k,k\u22121 cos \u03d5A k,k\u22121 0 0 0 1 (4) ak0 = k\u220f j=1 ak\u2212j+1, k\u2212j , (k = 1, 2, 3). The same equations can be written for the other two loops O-B and O-C of the mechanism (Fig. 2). Suppose the absolute motion of the platform is given by zG 0 = l1 + l6 + zG\u2217 0 ( 1 \u2212 cos 2\u03c0 3 t ) , \u03b1i = \u03b1\u2217 i ( 1 \u2212 cos 2\u03c0 3 t ) (i = 1, 2). (5) To solve the inverse kinematic problem, the passive leg can be taken as a serial 3-DOF mechanism with the coordinates determined by the conditions d\u25e6T 30 d30 = a, uT 3 { rD 10 + \u03bb D 10 u3 + dT 10 rD 21 } = zG 0 , (6) where a = a2a1 is a rotation matrix from the frame Ox0y0z0 to GxGyGzG, and rD 10 = l6 u3, rD 21 = l1 u3 d\u25e6T 30 = \u22121 0 0 0 0 1 0 1 0 , u3 = 0 0 1 , u\u03033 = 0 \u22121 0 1 0 0 0 0 0 (7) a1 = 1 0 0 0 cos \u03b11 sin \u03b11 0 \u2212 sin \u03b11 cos \u03b11 , a2 = cos \u03b12 0 \u2212 sin \u03b12 0 1 0 sin \u03b12 0 cos \u03b12 It results \u03bb D 10 = zG 0 \u2212 l1 \u2212 l6, \u03d5D 21 = \u03b11, \u03d5D 32 = \u03b12" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002468_j.jmatprotec.2005.02.202-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002468_j.jmatprotec.2005.02.202-Figure4-1.png", "caption": "Fig. 4. Robot model with distinguished and numbered inertial elements.", "texts": [ " There are constraints in the robot joints, which, in an accepted model, are represented by damping-elastic elements (11\u201316), characterised by stiffness and linear and angular suppression. In the robot model, two kinematic excitations (7,8) were considered. They come from ground tremblings, where the robot is situated and from the work of different 1. Phenomenological model of a mechanical system has been accepted in the following form: system (Figs. 5 and 6) is considered as two-dimensional with: \u2022 six inertial elements (Fig. 4), such as: - robot basis, - column of the robot, - arm, - counterbalance, - connecting rod, - mount of the gripper; \u2022 seven elastic-damping elements (Figs. 5 and 6); \u2022 two kinematic and one dynamic excitations (Figs. 5 and 6). 2. Masses and inertial elements moments of inertia of the accepted model of the system (Table 1), the linear and angular elasticity of the elastic elements and the linear and angular suppressions of the damping elements (Table 2). 3. The local co-ordinate systems of inertial elements, elasticdamping elements and kinematic and dynamic excitations (Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001536_s0167-6911(00)00105-5-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001536_s0167-6911(00)00105-5-Figure2-1.png", "caption": "Fig. 2. Imparting a linear velocity with zero spin to the puck.", "texts": [ " Then to satisfy the constraint equation de1ned by (13), we choose = tan\u22121 (\u2212V1 V2 ) : (17) It is now easily veri1ed that the choice Pb = 0; (18) Pn = m \u221a V 2 1 + V 2 2 (19) (20) satis1es Eq. (16), since sin( ) = \u2212V1\u221a V 2 1 + V 2 2 ; cos( ) = V2\u221a V 2 1 + V 2 2 : (21) This case occurs when it is desired to change only the linear velocity with the desired spin equal to zero. Thus the angle is such that the normal impulse component lies along the direction of V and the tangential impulse is zero; see Fig. 2. Case 3. If V3 is di>erent from zero and not both V1 and V2 are zero, choose such that cos( ) = V1\u221a V 2 1 + V 2 2 ; sin( ) = V2\u221a V 2 1 + V 2 2 : (22) Dividing the equation in (13) through \u221a V 2 1 + V 2 2 and using a trig identity, allows us to write this constraint equation in (13) as cos( \u2212 ) = r=2V3\u221a V 2 1 + V 2 2 : (23) We may equivalently express this as tan( \u2212 ) = \u221a V 2 1 + V 2 2 \u2212 (r2=4)V 2 3 (r=2)V3 (24) which is well de1ned since V \u2208 V. Thus, the angle satisfying (13) is given by = tan\u22121 ( V2 V1 ) \u2212 tan\u22121 \u221a V 2 1 + V 2 2 \u2212 (r2=4)V 2 3 (r=2)V3 : (25) Now, choose Pb = mr 2 V3; (26) Pn = m(V2 cos \u2212 V1 sin ): (27) Then a direct calculation shows that substituting (26) and (27) into (14) yields (16)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001486_s0921-8890(01)00171-3-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001486_s0921-8890(01)00171-3-Figure9-1.png", "caption": "Fig. 9. The robot\u2019s interaction with the cluster. The robot will determine the density characterization for clusters whose pucks fall within the angle of interaction. All other interactions will be viewed as obstacle avoidance.", "texts": [ " If we suppose that the robot is acting within an arena whose size allows accurate discrimination of two different clusters along the same line of sight, we may assume that the camera system can be used to accurately determine the depth of a given cluster. If then, upon contact, the cluster fills a sufficient region of the visual field, the cluster may be classified as large. If, however, the cluster does not fill a sufficient region of the visual field, it may be classified as small. The situation is illustrated in Fig. 9. We assume that the visual field of the robot subtends an angle denoted by 2\u03b8m. In this model, a robot will only deposit a puck if the direction of the robot is such that the cone falls completely within the cluster and it is currently carrying a puck. If the cone only falls partly within the cluster then the robot, if it is able, will remove a puck. It follows, therefore, that the range of approach angles for removal and deposit sum to the total angle of interaction of the robots cone 2\u03b8m +2\u03b8d = \u0398 , where \u03b8m is the interaction angle and \u03b8d = arcsin(R/(R + r)) \u2212 \u03b8m is the deposit angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002240_j.precisioneng.2002.12.001-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002240_j.precisioneng.2002.12.001-Figure4-1.png", "caption": "Fig. 4. Planar constraints in kinematic (left) and quasi-kinematic (right) couplings.", "texts": [ " Ideal kinematic couplings establish six localized contacts that provide well-defined constraint in desired directions and permit the freedom of motion in other directions. QKCs use ball and groove geometries which are symmetric and thus easier to manufacture, but depart from the constraint characteristics of ideal kinematic couplings by using arc contacts rather then small-area contacts. With careful design, QKCs can be made to emulate the performance of kinematic couplings. With this goal in mind, we must understand how QKC constraints differ from ideal kinematic coupling constraints (Fig. 4). In this figure, we see the projections of ball\u2013groove contact forces on the plane of coupling. The length of an arrow signifies the magnitude of a given constraint force. Fig. 4 (left) shows an ideal kinematic coupling which provides constraint between the balls and grooves in directions normal to the bisectors of the coupling triangle. Freedom of motion is permitted parallel to the bisectors. This is sufficient to achieve stable, exact constraint coupling [2]. Fig. 4 (right) indicates that the arc contacts of the QKC provide desired constraint perpendicular to the bisector and some constraint along the bisectors. Without freedom of motion parallel to the bisector, the coupling will have some degree of over constraint. The key to designing good QKCs is to minimize over constraint by minimizing the contact angle, \u03b8contact. The contact angle is defined by illustration in Fig. 5. The half angle, \u03b8jr will be used in the theoretical derivation in Appendix A. The joint in Fig. 5 represents joint 1 in Fig. 4. Arrows representing the constraint per unit length of contact arc are shown on the left sides of Fig. 5A and B. By inspection, we can see that constraint contributions that are parallel to the angle bisectors (in the y direction) can be reduced by making the contact angle smaller. This in turn reduces the degree of over constraint the joint may impose on the coupling. Unfortunately, this reduces coupling stiffness. This stiffness-constraint trade-off requires a quantitative metric to optimize coupling design", " It is interesting to note that the trade-off between stiffness and constraint is a favorable transaction at large contact angles. The theory developed in Appendix A was implemented in the MathCAD program provided in Appendix B. The model was checked by running the following tests: \u2022 Imposed translation errors in the z direction produced only net z forces. \u2022 Imposed rotation errors about the z axis of the coupling centroid produced only z moments. \u2022 Imposed displacements along one bisector of a 120\u25e6 coupling (i.e. in the y direction for the coupling in Fig. 4) did not produce net y or z moments. \u2022 The x and y reaction forces are 0 when \u03b8c is 90\u25e6 (groove becomes a flat). \u2022 When given inputs that would make the ball loose contact with the groove, the model detects this as a violation of a \u201cconstant contact\u201d constraint (see Appendix B, \u201cVerify Constant Contact Condition\u201d). A form of QKC has been used in precision automotive assemblies to provide 2/3 m repeatability in journal bearing assemblies [11\u201313]. To meet unusual stiffness requirements, the joints were not placed in the orientations that best emulate exact constraint couplings" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001643_1.1452197-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001643_1.1452197-Figure3-1.png", "caption": "FIG. 3. Outline of an experimental device.", "texts": [ " In this configuration, a cell equivalent to a segment of the earthworm is composed of a natural rubber tube ~thickness: 0.5 mm! in which a water-based magnetic fluid ~W-35! is sealed up, and the cells are connected with rod-like elastic bodies of natural rubber. The total number of cells in this robot of our trial production was eight. Moreover, a shifting magnetic field is assumed to be an electromagnet, but a permanent magnet is used in this experiment. Figure 2 shows the configuration of the microrobot. Figure 3 shows a diagrammed outline of an experimental device. First, the microrobot from our trial production was inserted into an acrylic tube ~inner diameter: 12 mm; outer diameter: 14 mm!. A pair of permanent magnets ~Nd\u2013Fe, h25315 mm! provided on the right and left sides toward the advancing direction was made to travel at 40 mm/s. The clearance between the magnets was set at 16 mm. The displacement of the microrobot was photographed with a video camera and the image was analyzed. Furthermore, the magnetic force exerted on a cell was analyzed by the finite element model ~FEM" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003438_s11071-011-0048-9-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003438_s11071-011-0048-9-Figure1-1.png", "caption": "Fig. 1 (a) Two degrees of freedom torsional vibration model of a hypoid gear pair. (b) Pinion and gear coordinate systems", "texts": [ " The results of the proposed enhanced multi-term HBM is validated by comparison to the more computationally intensive, direct numerical integration calculations. Finally, the effects of key parameters including the variation and asymmetry in the mesh stiffness and directional rotation radius on the gear dynamic responses is studied systematically through a series of parametric studies. The two degree-of-freedom torsional vibration model and the coordinate systems of a right-angle gear pair are shown in Fig. 1. The shaft and bearing are considered as rigid, and pinion and gear are modeled as rigid bodies. The mesh coupling between the pinion and gear is represented using a set of mesh stiffness and damping elements acting along a line of action dictated by the directional rotation radius. These mesh parameters are all considered as time-varying and asym- metric. The equation of motion can be derived as Ip\u03b8\u0308p + \u03bbp(\u03b4)c(\u03b4) ( \u03b4\u0307 \u2212 e\u0307 ) + \u03bbp(\u03b4)k(\u03b4)f (\u03b4 \u2212 e) = Tp, (1a) Ig\u03b8\u0308g \u2212 \u03bbg(\u03b4)c(\u03b4) ( \u03b4\u0307 \u2212 e\u0307 ) \u2212 \u03bbg(\u03b4)k(\u03b4)f (\u03b4 \u2212 e) = \u2212Tg, (1b) where Ip and Ig are the mass moments of inertial of pinion and gear, Tp and Tg are the torque applied on pinion and gear, and c(\u03b4) and k(\u03b4) are the asymmetric time-varying mesh damping and stiffness coefficients given by c(\u03b4) = { cd, \u03b4 \u2265 0, cc, \u03b4 < 0, (2) k(\u03b4) = { kd, \u03b4 \u2265 0, kc, \u03b4 < 0, (3) kd = kd1 + A\u2211 a=1 ( kd(2a) cos(a\u03c9t) + kd(2a+1) sin(a\u03c9t) ) , (4) kc = kc1 + B\u2211 b=1 ( kc(2b) cos(b\u03c9t) + kc(2b+1) sin(b\u03c9t) ) , (5) cd = cd1 + H\u2211 h=1 ( cd(2h) cos(h\u03c9t) + cd(2h+1) sin(h\u03c9t) ) , (6) cc = cc1 + J\u2211 j=1 ( cc(2j) cos(j\u03c9t) + cc(2j+1) sin(j\u03c9t) ) , (7) where cm and km (m = d, c for drive and coast side, respectively) are the mesh damping and stiffness for different tooth sides in contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.7-1.png", "caption": "Fig. 6.7 A cylinder wheel (\u7b52\u8eca). a Original illustration (Pan 1998). b Structural sketch. c Imitation of original illustration. d Real object (photoed by Guan, X.W., in Lanzhou, Gansu)", "texts": [ " Rotating the crank, the water wheel would draw water up to the shore. It is a mechanism with two members and one joint, including the frame (member 1, KF) and a water wheel as the moving link (member 2, KL). The water wheel with a crank is connected to the frame with a revolute joint JRz. Figure 6.6b shows the structural sketch. 6.4 Water Lifting Devices 115 6.4.2 Tong Che (\u7b52\u8eca, a Cylinder Wheel) Tong Che (\u7b52\u8eca, a cylinder wheel), also known as Sui Lun (\u6c34\u8f2a) or Zhu Che (\u7af9 \u8eca), is a device for scooping up water to the shore as shown in Fig. 6.7a (Pan 1998). The device consists of the frame and a water wheel. The diameter of the wheel depends on the height of the shore. After the device is installed, its wheel needs to be higher than the shore. Among each wheel\u2019s spoke is the waterreceiving board and bamboo cylinder. The device can only be used in a strong current, so the fast-moving water would push the water-receiving boards to spin the water wheel. It is a mechanism with two members and one joint, including the frame (member 1, KF) and a water wheel as the moving link (member 2, KL). The water wheel is connected to the frame with a revolute joint JRx. Figure 6.7b shows the structural sketch. Figures 6.7c and d show an imitation of the original illustration in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300band a real object, respectively. 6.4.3 Long Wei (\u9f8d\u5c3e, an Archimedean Screw) Long Wei (\u9f8d\u5c3e, an Archimedean screw) is an irrigating device imported from the West, after Xu Guang-qi (\u5f90\u5149\u555f) (AD 1562\u20131633) and Missionary Sabatino de Ursis (\u718a\u4e09\u62d4) (AD 1575\u20131620) translated the book Taixi Shufa \u300a\u6cf0\u897f\u6c34\u6cd5\u300b (Hydraulic machinery of the West) into Chinese. Its components are a tilted hollow external cylinder and a center shaft with screw threads" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003498_0022-2569(71)90044-9-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003498_0022-2569(71)90044-9-Figure5-1.png", "caption": "Figure 5. Pole curve q--q' for cam mechanisms with favorable transmission angle characteristics.", "texts": [ " Contrary to the case when the output roller has a linear path, it is not possible to increase the transmission angle (and thereby the quality of transmission of motion) arbitrarily by increasing the size of the cam disk. The transmission angle/z lies, in the case that the cam disk is driving, between the normal n to the cam profile and the center line of the cam-roll lever (Fig. 1). Since the normal, however, also determines the transmission ratio of the cam drive, the construc- tion of the first derivative of the law of motion, which contains the transmission angle as a parameter, must be used as a starting point. As shown in Fig. 5, one first draws the locus q for the range of the positive transmission ratio and the locus q' for the range of the negative transmission ratio. A fixed link length dl = 50 has been assumed. Initially, this will be discussed for the point Q,. of q for x = 0.2. For x = 0-2 one obtains from equation (4) 1 .~ = 5_(I - -cos 36 \u00b0) = 0-096 (18) and consequently according to equation ( I O) e u = M*H. g = 3\"663 . 0-096 = 0\"351 (19) \u00a2t~=20.05o. (20) If the lever f i s rotated from its initial position as shown in Fig", "~a qb\" (23) As is well known, the transmission ratio of the distance of the pole QBo = q~ from the driving-link pivot and the distance QCo = qb of the pole from the output-link pivot. The transmission ratio is positive if the pole referred to lies outside the pivot points B0 and Co; it is negative ifQ lies between these pivot points. For the mechanism position given by x = 0.2 one gets 612=+2\"23 (24) and from this /02 i/~ = .---- = 0\"483. (25) 1112 Generally, d qb= l - - i (26) Therefore in mechanism I for position x --- 0.2: 50 qbt2 = 1 - 0-483 = 96-6. (27) Turning now to consider Fig. 5, one rotates the frame line (BOA0 in Fig. 5) around B0 through the angle -Olr,, i.e. in the opposite direction from that in which the cam disk really turns from its chosen initial position. Along the ray obtained in this manner, one measures off BoQ2 = qbr., according to equation (27) and so locates a point Q2 on the part q of the cam. In Fig. 5, the construction of point QT' of the part q' of the cam is shown for position x = 0.7 in the region of negative transmission ratio. The appropriate numerical values will be given later in an example concerning curvature. In this manner, one may plot the pole locus q - q ' point by point. On one side of this the frame line BoAo is tangent at point Ao and on the other side line BOA\u00b0' is tangent at point Ao': this line BoAo' is drawn by swinging line BoA\u00b0 around Bo through an angle tko, = -91.8 \u00b0, that is, in the reversed direction", " Rays B X and B X ' are the tangents t and t' to the cam disk in the mechanism's positions in which the extreme transmission angles occur. Regarding the accuracy of the auxiliary diagram, it is to be noted that the quality of the transmission of motion cannot be defined precisely with the aid of the transmission angle (and in fact does not need be defined precisely). Angular deviations of about 0-5* occurring in the graphical representation should not noticeably influence the quality of the transmission. In Fig. 5 the unique value of the length of the cam follower is established, as well as its initial position relative to frame BoAo, for/Zm~. =/Zmt .. From the figure, the limiting values of the radius AoB = rmi, and A'B = rmax may be measured immediately. In the literature, the smallest radius rmi, is often indicated as the characteristic value; for the purposes of comparison of the cam disk size, however, the largest radius rmax is thought tO be most suitable. It can be shown, that, as tZmt. increases, the length c of the cam-roll lever decreases, although the radii rmt, and rmax increase", " It intersects B~TQ~r at the center of curvature AtT, and yields the radius of curvature pr. Design of the cam disk in the dead-center positions In both of the dead-center positions of Fig. 7 the cam points B~ and Bt~o are determined and lie on the straight line through points Ao, Bt and Bt0, because 180\" rotations of the cam disk have been assumed for the forward and reverse motion of the follower arm. The center positions Bt and Bto of the cam roll subtend the output angle ~mo at Bo. The extremal radii rml, and rmax must agree with the values of Fig. 5. The tangents t t and t~0 are perpendicular to the line B~Bto. At the extremal positions of the follower, the transmission ratios in this leadingcomponent mechanism are of course i , = i~to = 0. This reduces equation (15) to A o = A t . i , (41) At = Ao/i,. (42) The specific acceleration At in the leading mechanism therefore only depends on the specific total acceleration Ao and on the transmission ratio itt in the second, or following component, mechanism. Using equations (13) and (14) they are calculated to be: Mot = +1\"831 and Aoto =--1\"831" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002482_tmech.2006.882994-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002482_tmech.2006.882994-Figure1-1.png", "caption": "Fig. 1. Kiteplane.", "texts": [ " Lyshvski [23], [24] studied special control surfaces for MAVs that are essential for small UAVs. Although many control techniques have been proposed and compact UAVs have been developed, a practical autonomous small and light UAV that can carry a sufficient payload has not yet been widely accepted. This paper develops an autopilot system of a UAV that is small, light, and can also transport a large payload. This UAV is called Kiteplane [25], [26] as its main wing, which is its largest component, is of the shape of a kite-like delta (Fig. 1). The main wing is light and flexible as it is made up of cloth, and thus, it can be large without making the airplane heavy. Although the Kiteplane is light, it is capable of carrying a large payload. The wing\u2019s flexibility provides safety and robustness if it crashes into the ground. The center of the mass is located under the main wing and the ailerons are attached at dihedral angles. This configuration results in a stable attitude while the aircraft is in a trim state and provides easily controlled motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003413_978-1-4471-2277-7_13-Figure13.4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003413_978-1-4471-2277-7_13-Figure13.4-1.png", "caption": "Fig. 13.4 Sketch of the front view of the extended Lokomat hardware", "texts": [ " This lack of lateral movement leads to a reduced weight shifting and, thus, to a lower load transfer between treadmill and supporting leg. It is assumed that this has a negative effect on the balance training and the excitation of the cutaneous, muscular, and joint receptors. Therefore, the Lokomat version installed at the Balgrist University Hospital has been extended by three additional actuated degrees of freedom. Two degrees of freedom perform hip ad/abduction, and 1\u00b0 of freedom enables the Lokomat to accomplish a lateral pelvis displacement movement (Fig. 13.4 ). Three linear actuators have been added to drive the ad/abduction (No. 1 and 2 in Fig. 13.4 ) and the lateral pelvis displacement (No. 3). The linear drives are equipped with redundant position sensors as well as force sensors. Several control strategies have been implemented and tested with the new hip\u2013pelvis actuation. First, the new degrees of freedom have been position-controlled. For this purpose, gait trajectories of healthy subjects have been recorded, which then served as the desired trajectories for the PD position controllers. Later, a controller was developed that is able to emulate the viscoelastic properties of passive spring\u2013damper elements" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003878_j.robot.2013.08.005-Figure20-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003878_j.robot.2013.08.005-Figure20-1.png", "caption": "Fig. 20. Schematic of electrical connections for the rack component. Left: top view of part. Right: \u2018\u2018X-ray\u2019\u2019 view through the top side.", "texts": [], "surrounding_texts": [ "The design of the end-effector (or \u2018\u2018grasper\u2019\u2019) is similar to that reported in [29]. A single end-effector is used for grasping components and to tighten and un-tighten the threaded fasteners (see Fig. 19). The grasper is integral to the design of the entire system, since it effects theway parts are picked up, how they are connected to each other, and how parts must be brought into place during assembly. Furthermore, the grasper should be easy to fabricate, and if possible well-suited for miniaturization (such as the MEMS and micro-devices in [51\u201353] or the chemically actuated gripper in [54]). The end-effector consists of a spring loaded tool-piece with a slot and internal thread. For grasping a part, the internal thread of the toolmateswith the threaded tension pin on a component. After a component is placed, the tool is unscrewed from the tension pin and placed on the component\u2019s captured-nut fastener. The slot on the tool-piece self aligns with the fastener and tightens or loosens it in the manner of socket and nut. The grasper is composed of an off-the-shelf gear motor, a metal spring, and 21 plastic cast parts. Additional details on the construction and operation of the grasper can be found in [29]. A typical grasping sequence is as follows. First, the grasper threads onto a male connector on a component to be assembled. Second, the component is lifted and moved to a target location, and placed on the target using the conical pins to self-align. Third, the grasper releases from the male connector on the component. Fourth, the grasper lifts and moves over a nut on the part to be connected. Fifth, the nuts are tightened, the component is nowconnected to the target, and the grasper lifts away from the assembly. Videos of this sequence of operations can be seen in Supplemental Videos 1 and 2 (http://dx.doi.org/10.1016/j.robot.2013.08.005). The assembly sequence is reversible; the steps can be performed in reverse to disconnect a component from an assembly." ] }, { "image_filename": "designv10_13_0001843_1.2826131-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001843_1.2826131-Figure3-1.png", "caption": "Fig. 3 Surfaces of imaginary racl(-cutters", "texts": [ " 3 Localization of Bearing Contact The principle of localization of the bearing contact is explained with the imaginary process for generation of heli cal gears by two rigidly connected rack-cutters. This principle will be applied separately for N.-W. gears and modified involute helical gears. Generation of N.-W. Gears by Two Rack-Cutters. The imaginary process of generation of conjugate tooth surfaces is based on the application of two rack-cutters that are provided by two mismatched cylindrical surfaces 2, and 2\u0302 . as shown in Fig. 3(a). The rack-cutter surfaces 2, and 2^ are rigidly connected to each other in the process of imaginary generation, and they are in tangency along two parallel straight lines, a ~ a and b - b. These lines and the parallel axes of the gears form angle /3(), that is equal to the helix angle on the pinion (gear) pitch cylinder. The normal sec tions of the rack-cutters have been standardized in China [9], Fig. 4(a), and in the former USSR, Fig. 4(b) [8]. Rack-cutter surface 2^ generates the pinion tooth surface 2^, and rackcutter surface 2, generates the gear tooth surface 2\u201e. It is obvious that due to the mismatch of the surfaces of the two rack-cutters that generate the pinion and the gear, the tooth surfaces of the pinion and the gear will be in point contact at every instant. Each rack-cutter has two generating surfaces, above and below plane II, Fig. 3. Therefore, the 256/Vol. 117, JUNE 1995 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmdedb/27627/ on 05/17/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use (b) USSR standard Generation of Modified Involute Helical Gears by Two Rack-Cutters. Two imaginary rack-cutters, t and c, for the generation of pinion and gear tooth surfaces, respectively, are applied in this case as well. The rack-cutter / that generates the gear tooth surface is provided by plane 2,, and the rack-cutter c designed for the generation of the pinion is provided by cylindrical surface 2c that differs slightly from plane 2,, Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003270_iembs.2009.5334163-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003270_iembs.2009.5334163-Figure3-1.png", "caption": "Fig. 3. Left: A horizontal section view of the 7 Fr. catheter showing the shape of the two lumens and the position of the optical-fibres. Right: A vertical partial section view of the fibre-optic catheter sensor showing one of the three optical-fibres emitting and receiving light at a distance D from the mirror.", "texts": [ " Sensor Structure The sensor consists of three plastic fibre-optic cables of 250 \u03bcm in diameter, a reflective circular mirror of 2.3 mm in diameter and 0.4 mm thick with a hole in the middle, a deformable connecting material (natural latex) and a 7 Fr. plas- tic Pebax-6333SA catheter with two lumens (Arkema Inc., France). The sensor integrated with the catheter is shown in fig.2 (top). The plastic optical-fibres are aligned inside the two lumens in such way to create a circular pattern with 120 degrees spacing between them. The optical-fibres illuminating inside the catheter can be seen in fig. 2 (bottom), whereas in fig. 3(left) the alignment within the lumens of the catheter is shown. In addition, a short in length part of the plastic catheter is cut prior to the optical-fibres alignment, in order to be used as the tip of the catheter-sensor. The circular mirror is positioned concentrically at one of the two cylindrical flat surfaces of the short catheter part, leaving the way free to the lumens. The deformable material is obtained in a form of a thin film and is wrapped and glued concentrically around the main part of the catheter and the short catheter part, which accommodates the mirror. After the wrapping the catheter\u2019s tip diameter increased and reached 2.6 mm. With this technique the two parts are connected leaving 1 mm of space between the aligned optical-fibres and the reflector. The distance denoted with the letter \u2018D\u2019 in fig.3 (right) shows the free space previously described. A. Principle of operation The principle of operation for this fibre-optic scheme is based on light intensity modulation caused by the change in distance of the reflector when a force is applied at the tip of the catheter. Each one of the optical-fibres is interrogated by a super bright red LED which operates at 650 nm wavelengths. Fibre-optic couplers are employed to emit and receive the reflected light through the same single integrated optical-fibre within the catheter" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003026_1.3212679-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003026_1.3212679-Figure5-1.png", "caption": "Fig. 5 A canonical surface with a helical spine curve", "texts": [ " 5 , it follows that the tangent vector of the spine curve M is 0, that is, M =0. Thus the spine curve M is a fixed point. The circular surfaces are spheres with radius r. Case 2 exists when = =0. From Eq. 5 , it follows that M = e1. The tangent vector M are always parallel to e1, which is the normal to the circle plane. In other words, the tangent vectors of the spine curve M are always perpendicular to the circle planes. The circular surfaces become canonical circular surfaces, which have been extensively studied. Figure 5 shows a canonical circular surface, whose spine curve is a helix. For a canonical circular surface to have singular points, it is necessary that r cos \u2212 =0. If r, there will be no singular points. If = r, the singular point occurs at = /2 or =3 /2. If r, there are two singular points on the generating circle, occurring at = acos /r . Case 3 exists when = =0. From Eq. 5 , it follows that M = e2 23 Hence, the tangent vector of the spine curve M lies on the circle plane at each point of M. When is a constant, integrating Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.17-1.png", "caption": "Fig. 6.17 Throwers (\u72fc\u7259\u62cd). a Original illustration (Mao 2001). b Structural sketch", "texts": [ " Lei (\u6a91, a thrower) also known as Lei (\u96f7), is a heavy object for throwing to attack soldiers under and outside the city walls. It has many different types as shown in Fig. 6.16a (Mao 2001). It is a mechanism with three members and two joints, including a wooden link (member 1, KL), a roller (member 2, KO), and a rope (member 3, KT). The link is connected to the roller and the rope with a revolute joint JRx and a thread joint JT, respectively. Figure 6.16b shows the structural sketch. Lang Ya Pai (\u72fc\u7259\u62cd, a thrower) has the same function as Lei (\u6a91) as shown in Fig. 6.17a (Mao 2001). It increases the area of the spiked surface and is installed on a pulley to easily manipulate. It is a mechanism with four members and three joints, including the frame (member 1, KF), a pulley (member 2, KU), a rope (member 3, KT), and a spiky link (member 4, KB). The pulley is connected to the frame with a revolute joint JRx. The rope is connected to the pulley and the spiked link with a wrapping joint JW and a thread joint JT, respectively. Figure 6.17b shows the structural sketch. Before the Jin Dynasty (AD 265\u2013316), Mu Man (\u6728\u5e54, a wooden shield wagon) had been used in wars (Zhang et al. 2004). Its earliest function was to cover soldiers when they climb city walls. Later it became a defense device for protecting them from enemies\u2019 rock balls as shown in Fig. 6.18a (Mao 2001). The wooden shield wagon can be divided into two parts: the roller device and the shield device. The roller device is a mechanism with two members and one 126 6 Roller Devices joint, including the frame (member 1, KF) and wheels on the frame as the roller members (member 2, KO)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002131_j.finel.2004.04.007-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002131_j.finel.2004.04.007-Figure5-1.png", "caption": "Fig. 5. Model of anti-backlash conical involute gear transmission.", "texts": [ " (46) This expression gives the exact total interference if tj = tk . Since lubricant is present between the meshing gear flanks, the frictional forces are neglected since they are low compared with the normal forces. As a result, the contact force Fri nj acts only along the normal to the contacting surface, i.e. Fri nj = F ri xnj F ri ynj F ri znj = \u2212F ri nj n\u0302 ri nj = F ri nj [ \u2212 cos ij sin wtj \u2212j cos ij cos wtj j sin ij ] , (47) where F ri nj = |Fri nj |. (48) According to Fig. 3 and expression (23), F r1 nj = F r2 lj . (49) Fig. 5 shows a model of an anti-backlash conical involute gear transmission. When the gear transmission is in its initial position, the axial distance e is equal to e0, the gap g is equal to g0 and the spring, which has stiffness ksp, has been preloaded with the force Fsp0. Gear 1 is free to move in its axial direction, but is blocked when gap g is equal to zero. As a result, e e0 \u2212 g0. The preloaded spring eliminates backlash at rotation reversals, where low torques are transmitted, and, by allowing for axial compensation movements, avoids high peaks in friction torques due to deviations from ideal gear geometries, mounting errors and unfavourable deformations" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0000584_jrproc.1927.221149-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0000584_jrproc.1927.221149-Figure3-1.png", "caption": "Figure 3", "texts": [ " F a - a(c-a) 4a2b2 1 Fb b(c-b)L=a -log +lo I\u00b1bI-log - c b(c+b) r2(c+a)2_ Lc a(c+a) (12) + log +a c log - 2 r2(C + b)2_ r2(a2+C2) (b2+C2) (Bashenoff)6 (b) Equal-leg right triangle. This formula is easily derived (see below) F21 1 L=21 log7-3.331 (13) r in which 1 is the perimeter of the triangle. 6 For the derivation of formula (12) see Jahrb. draht. Tel. 1926, vol. 27, no. 4 and \"Transactions of the State Electrical Research Institute\" (Moscow) publ. 14. Bashenoff: Calculating the Inductance of Round Wire 8. Quadrilateral (trapezium) Of definite shape (Fig. 3). HAVING No REENTRANT ANGLES, INCLUDING OBLIQUE-ANGLED TRIANGLES 1st Method The approximate method of computing the inductance of such polygonal figures is based on the author's assumption,6 that the inductance of an oblique-angled triangle or another plane figure must, practically, be very nearly equal to the inductance of a right triangle, having perimeter and area equal to those of the given plane figure. Indeed, in selecting an equivalent simple figure whose inductance shall approximate that of the actual (more complicated) figure, the most important condition to be satisfied is that of equal perimeter", " We may certainly with still more right neglect the second and higher powers of the ratio r/a. The special formulas of Section A, omitting the terms of the order of r/a, can be written as follows: 1. Circle (21 l L=21 log--2.451\u00b1+yb (32) rJ 2. Square 21 L=21 log--2.853+yb (33) r 3. Equilateral triangle X 21 L= 2,11log--3 .197+,ub (34) rJ 4. Regular hexagon ( 21 L=21 log--2.636+/AS (35) rJ 5. Regular octagon ( 21 L=21 log--2.5610+\u00b1ub (36) 1026 Bashenoff: Calculating the Inductance of Round Wire 6. Polygon of the type shown in Fig. 3 (21 L=21 log--3.227+ya } (14) 7. Equal-leg right triangle (21 L=21 log--3. 332+.t%} (37) 8. Regular pentagon (a new formula derived by Dr. Grover) with l/V\\s=3.812 L=21 (log--2.712+y (37a) 9. Quadrilateral of the type shown in Fig. Sa (a= (/2/4), 1 = 0.353551; b= (2- /2) /4, 1= 0. 146451) (derived by Dr. Grover) /21\\ L= 21 o1g--3.091+/.4) (37b) Using formulas (32-37), we can draw the curve ak=f( \\, ) in which ak = 1- y, by plotting the points for the above nine figures, for which the value of the ratio - is well-known", " Thus, the general formula for the calculation of the inductance of singleturn closed aerials and, in general, plane figures having no reentrant angles, the value of r/l being small, will be taken as L=21(log 21-ak+8) (31) in which I is the perimeter of the figure r, radius of the wire; A, magnetic permeability of the wire material; 8, a correction factor for frequency, determined in turn by formula (5) and the curve in Fig. 1; ak, a constant, being a function of 11i/Vs and taken 1029 Bashenoff: Calculating the Inductance of Round Wire TABLE III Type of figure Circle Regular octagon Regular hexagon Square Equilateral triangle Equal-leg right triangle Quadrilateral Fig. 3. Regular pentagon Quadrilateral of Fig. 3a Irregular pentagon I Vs 3.545 3.641 3.722 4.000 4.559 4.828 4.38 3.812 4.395 4.546 ak 2.451 2.561 2.636 2.853 3.197 3.331 3.227 2.712 3.091 3.116 Source Formulas (4) and (32) Formulas (lOa) and (36) Formulas (9a) and (35) Formulas (6) and (33) Formulas (8a) and (34) Formulas (13) and (37) Formula (14) Formula (37a) Formula (37b) Exact solution for L taken with (31) to solve for ak The above pairs of values of ak and 1/Vs were used. The points are indicated in Fig. 6 by the same numbers as those here given" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002482_tmech.2006.882994-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002482_tmech.2006.882994-Figure5-1.png", "caption": "Fig. 5. Target point update. (a) Case I. (b) Case II.", "texts": [ " Let ey , ea, and ez represent the horizontal displacement from the nearest point on the reference path to the horizontal position of the airplane, the difference from the desired direction defined in Section IV-B to the heading of the airplane, and the difference in altitude from the level longitudinal reference path to the altitude of the airplane, respectively. Each waypoint is surrounded by two concentric regions denoted as Ai and Bi in Fig. 4. The airplane is said to have passed the target point when it enters the small region Ai . Under wind disturbance, however, the airplane may not be able to enter region Ai . A weak target updating criterion is introduced for these unexpected situations. In this case, the target should be updated when the airplane leaves region Bi after it has entered Bi . These two cases are summarized in Fig. 5(a). It is considered a failure if the airplane approaches the target point after flying a distance Ci along the reference path without entering region Bi [Fig. 5(b)]. In this case, the airplane is required to turn back toward the target. To achieve this task, the previous target point is mirrored across a symmetry plane defined at the current target point and a new reference path is defined as the line from the mirrored target point to the current target point. The structure of the proposed autopilot system is shown in Fig. 6. There are three fuzzy logic controllers (FLCs) incorporated into the system. One controller is employed by the lateral system and two are employed for the longitudinal system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002930_j.mechmachtheory.2009.02.003-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002930_j.mechmachtheory.2009.02.003-Figure3-1.png", "caption": "Fig. 3. Computer graph of the ZN-type hourglass worm.", "texts": [ " (18), the upper sign of \u2018\u2018\u00b1\u201d sign represents the left-side worm surface while the lower sign indicates the right-side worm surface. Table 1 lists some major design parameters of the ZN-type hourglass worm and blade cutter. It is noted that k is the lead angle of the worm in the middle plane (the section of the minimal diameter) of the worm, and it is changing along the worm axis. Based on the developed mathematical model of the ZN-type hourglass worm, a three-dimensional tooth profile of the ZN-type hourglass worm is plotted as shown in Fig. 3. Coordinates of the hourglass worm surface points can also be calculated by applying the developed mathematical model. An hourglass worm-type hob cutter, which is identical to the ZN-type hourglass worm, is used for the generation of hourglass worm wheel. The schematic cutting mechanism of an hourglass worm wheel is shown in Fig. 4. Coordinate system esign parameters of the ZN-type hourglass worm and blade cutter. Parameters gle of the blade cutter (Fig. 2a) k 5.0 pressure angle of the blade cutter a 20" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure1-1.png", "caption": "Figure 1. The \u201cOne Bit per Core\u201d approach - each core is acquired and then stored in individual bits.", "texts": [ "v=aT8q9g_0E04 We believe that the single most important factor that should be taken into consideration for sample acquisition and caching is mission risk. Our approach was to reduce the risk by implementing a \u201cOne Bit per Core\u201d approach to returning rock core samples. This approach is at the heart of the proposed MSR architecture. However, to make this architecture feasible, we also developed a number of critical technologies related to core breakoff, bit designs, and caching. The \u201cOne Bit per Core\u201d approach is illustrated in Figure 1. Each drill bit is used to acquire a single rock core. The core is then sheared off at the base using Honeybee Robotics\u2019 patented Core Breakoff technology which simultaneously breaks the core and captures it within the Bit [6]. Once the core acquisition process is complete, the Bit is encapsulated within a sleeve using a threaded connection. This particular connection also allows for hermetic sealing. All of the encapsulating sleeves are housed within the Sample Cache. As rock cores are collected, the Sample Cache is gradually populated with Bits" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001384_978-94-017-2925-3-Figure5.14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001384_978-94-017-2925-3-Figure5.14-1.png", "caption": "Fig. 5.14. Types of tear specimens.", "texts": [ " As described in the scope of ASTM D624, PHYSICAL TESTING OF VULCANIZATES 171 \"The method is useful, therefore, only for laboratory comparisons and is not applicable for service evaluations, except when supplemented by additional tests, nor for use in purchase specifications.'' Nevertheless, many such tests are run, perhaps because they seem to be logical extensions of the hand-tear evaluation so useful to the old-time compounder. Three types of tear specimens are classified by Buist: indirect tearing as in the trousers specimen of Fig. 5.14, tearing perpendicular to the direction of stretching as in the ASTM methods, and tearing in the direction of stretching as in the Russian test piece. 44 Except in the ASTM Die C specimen, nicks of prescribed lengths are cut into the region of desired stress concentration. Rate of stretching in the ASTM method is 20 inches per minute. An increase in rate normally decreases the tearing energy for SBR rubbers, but gives a more complicated effect in natural rubber. On the theory that at least a portion of tire wear is a result of high speed tearing, such a test has been considered for eval uation of abrasion resistance" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003475_1.4005467-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003475_1.4005467-Figure5-1.png", "caption": "Fig. 5 A spherical joint represented by three intersecting revolute joints", "texts": [ " \u2022 For a2\u00bc 90 , axis ZM is the obvious choice for the joint axis of the second revolute joint, as ZM is perpendicular to Z1. Joint 2 connects the moving link #M to the imaginary link #1. The rotation matrix QYZ for the YZ EAJs can be derived from the DH parameters of Table 4. It is shown in the fourth row of Table 5. Similarly, other EAJs were obtained for the two-DOF rotations. They are listed in Table 5. 3.2 EAJs for Spatial Rotations. The Euler angles represent rotation in three-dimensional Cartesian space. Hence, they are commonly used to represent a spatial rotation provided by a spherical joint. Figure 5 shows a spherical joint that connects a moving link #M to a reference link #R. The rotation between the frames FM and FR can be represented by any Euler angles set. For example, if the ZYZ set is used, one obtains the orientation matrix QZYZ given by Eq. (A2) in the Appendix. For the spherical joint represented with three intersecting joints as shown in Fig. 5, the same rotation matrix can be obtained if the equivalent rotation matrix obtained in Eq. (4) is used to define the DH parameters. The systematic development of the ZYZ and XYZ EAJs will be presented next. 3.2.1 ZYZ-EAJs. The DH parameters for the ZYZ EAJs can be extracted from Eq. (4), i.e., QZYZ \u00bc Qh1 Q XQh2 Q\u00feXQh3 , as follows: \u2022 First, the rotation matrix Qh1 \u00f0 1Qh1 , 1 being an identity matrix) corresponds to the twist angle a1\u00bc 0 and the joint angle of h1. \u2022 The next set of rotation matrices Q X and Qh2 correspond to the twist angle a2\u00bc 90 and the joint angle of h2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001607_s0167-8922(01)80156-5-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001607_s0167-8922(01)80156-5-Figure9-1.png", "caption": "Figure 9: FZG back-to-back test rig", "texts": [ " Together with the local radius of curvature p the distribution of the Hertzian stress PH along the path of contact can be derived. With the local speed and the local pressure each point on the path of contact can be simulated in the twin disc machine. With equation (5) and the parameters or, 13, and Y gained from the twin disc experiments, the coefficient of friction along the path of contact of a gear can be calculated. The results of the calculation for gear type C at standard conditions of load ( P c - 1100 N/mm ~) and pitch line velocity (vt. c = 8 m/s) are shown in Fig. 9. In the double tooth contact area the coefficient of friction is lower than in the single tooth contact area. In the region of low slip (s - 0 at point C) ~t drops to zero. 4.2. Test rig The frictional losses of cylindrical gears are measured in a modified back-to-back gear test rig [7] (Fig. 9). The test pinion and the test gear are mounted on two parallel shafts which connect them to the drive gear stage. In the drive gear stage identical gears to the test gears are mounted, so that two equal stages are closing the inner circle. The pinion shaft consists of two separate parts, which are connected by the load clutch. By twisting the load clutch using defined weights (load stages) on the load lever a defined static torque is applied, which is indicated at the torque measuring clutch. The motor has only to compensate the frictional losses in the load circle" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001740_(sici)1097-4563(199811)15:11<599::aid-rob1>3.0.co;2-o-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001740_(sici)1097-4563(199811)15:11<599::aid-rob1>3.0.co;2-o-Figure1-1.png", "caption": "Figure 1. A multiple mobile manipulation system.", "texts": [], "surrounding_texts": [ "Until recently, robotic manipulators were mechanisms rigidly attached to the ground. The need to perform difficult orrand dangerous operations in space generated the study and the consequent con- * To whom all correspondence should be addressed. struction of mobile manipulators, i.e., robotic manipulators whose bases could move.1,2 Now, mobile manipulators are not meant to operate solely in space. Mobile manipulation operating in aquatic environments is a recent and active area of research.3,4 Of course, mobile manipulators can also operate on ground, given they are attached \u017d .to a vehicle normally wheeled , and some signifi- ( ) ( )Journal of Robotic Systems 15 11 , 599]623 1998 Q 1998 by John Wiley & Sons, Inc. CCC 0741-2223/ 98/ 110599-25 cant research has already been conducted in the field.5 ] 11 Mobile manipulators extend the manipulator workspace and its ability to work efficiently. Due to the mobile base, the manipulator is capable of configuring itself to practically any operational point. In addition, it can grasp and manipulate an object in \u017d .many different ways positions and orientations . This actually means that it is a redundant mechanism, with all the inherent capabilities and problems of such systems. However, as is always the case, there is a price to pay for advantages: more difficulty in control. This difficulty is due mainly to a class of motion constraints called nonholonomic.12 ] 16 These constraints are equations involving the generalized coordinates and their derivatives in a way that makes them nonintegrable. Thus, the dimension of the configuration space cannot be reduced. Under the effect of such constraints the system maintains its controllability,17 but is generally harder to steer. Many of the models proposed for mobile manipulator systems do not include nonholonomic constraints.3,7 These models focus on the interaction of the system with its environment. Tarn et al.3 model an underwater vehicle with multiple robotic manipulators. Dynamic modeling is achieved by the use of Kane\u2019s dynamic equations.18 The motion of \u017d .the autonomous underwater vehicle AUV and momentum preservation laws impose nonholonomic constraints which are not included in the model. Khatib et al.7 model cooperating mobile manipulators, the mobile platforms of which can move on a planar surface. The dynamic equations of motion are obtained using the classic Euler]Lagrange formulation in operational space,19 assuming that the mobile platforms can move in a holonomic way. Other models include nonholonomic constraints using classic Euler]Lagrange5 and Newton]Euler formulations.9 These models are more accurate and consistent, even though they still do not consider all constraints imposed in mobile manipulator systems. In ref. 9, the no-slipping nonholonomic condition is not taken into account nor is the angular momentum preservation condition associated with tipping over, which is also missing in the otherwise complete analysis in ref. 5. Chen and Zalzala9 include in their model the nonholonomic constraint associated with the no-slipping condition. Inclusion of the constraint in the model is achieved by algebraic manipulation. Yamamoto et al.5,6 go further, including the nonholonomic constraint resulting from the no-skid- ding condition. Merging the constraints with the system\u2019s equations of motion is done using the well known Lagrange multipliers methodology. Dubowsky and Vance8 discuss the possibility of the mobile platform tipping over due to dynamic interaction with the attached manipulator. Recently, Thanjavur and Rajagopala20 modeled \u017d .an autonomously guided vehicle AGV using Kane\u2019s equations. They pointed out the merits of using Kane\u2019s approach to model vehicles and utilized some of the tools to incorporate nonholonomy. They focused on the dynamics of the vehicle indi\u017dvidual components drive and castor wheels, drive .wheel assemblies, etc. and included only the classical no-slipping and no-skidding constraints, and did not provide any necessary conditions for these constraints to be satisfied. In this article, a model within the framework of Kane\u2019s approach is proposed. As opposed to Euler] Lagrange and Newton]Euler formulations, Kane\u2019s methodology involves less arithmetic operations and is thus simpler, faster in simulation, and requires less effort in construction.3,21 Kane\u2019s equations can be easily brought to a closed form,3 which is best suited for control purposes. The multiple mobile manipulators involved in\u017dteract through the common deformable object Fig. .1 . The object is arbitrarily shaped and deformable. In such cases, the methods developed for object handling and manipulation by multiple manipulators cannot be applied, since the object has infinite degrees of freedom that do not restrict one rigid grasp relative to another. Moreover, the dynamics of the body cannot be described in a straightforward manner, since its mass center and every other point can move relative to the fixed grasp points. The deformable object is modeled by its elastodynamic equations. Then the notion of operational space is expanded to include more dimensions than a common task space, yielding a generalized operational space. Within this new framework, the simplest approximating grid structure for the deformable object becomes evident. This simplification, along with the generalized operational point concept, enables the application of Khatib\u2019s22 augmented object approach to merge the models developed for each mobile manipulator with the object model and produce a compact set of dynamic equations for the system. The combined system of the mobile manipulators linked by the manipulated object does not operate in space. The mobile platforms on which the manipulators are based move on the ground and thus interact with each other in the same way as the legs of a walking robot do, forming a closed chain. This closed chain can be visualized if one models the platforms as an unactuated joint virtual manipulator connecting each wheel to the ground.23 A systematic approach to the analysis of closed-chain systems has been presented by Tarn et al.24 They constructed a model for two cooperating manipulators calculating the Lagrange equations analytically. The process for obtaining the Lagrange function is driven by the peculiarity of the mechanism25 and the complexity of the involved calculations. Another difficulty is finding recursive computational schemes. Moreover, the computing time is relatively long for real-time controllers.26 Lin27 also reported difficulties arising from obscure dynamic phenomena. A different, popular approach to the analysis of closed-link mechanisms, originally introduced by Smith,28 is to cut the closed-chain mechanism at several joints, transforming it to an open chain. This approach was extended by other researchers.29 A milestone in the study of closedchain mechanism is the work of Luh and Zheng,26 who replaced the problem of computing the dynamics of closed-chain spatial systems to that of openlink tree-structure mechanisms subjected to unknown joint torques at the cut points. In their work, they made use of d\u2019Alembert\u2019s principle and employed Lagrange multipliers to compute the unknown torques. However, computation of Lagrange multipliers is known to be a cumbersome and computationally inefficient task. Nakamura and Ghodoussi25 pro- posed a general computational scheme of the inverse dynamics of the closed-link mechanisms which is also based on d\u2019Alembert\u2019s principle but without computing the Lagrange multipliers. The scheme is computationally efficient compared to conventional methods, however the choice for the cut joints of the closed kinematic loops depends on the redundancy of the actuators.30 Our approach to the closed chain formed follows the same philosophy. The closed chain is cut at the points of contact between the wheels of each vehicle and the ground. However, we do not proceed to calculate the forces exerted there, since it is well known that they cannot be resolved.8 Instead, we define the space of admissible values for them through a set of constraint equations. Among the duties of the control scheme that could be applied is ensuring that these forces stay within specified limits. This is accomplished by controlling the kinematic quantities of each mechanism in a way indicated by the constraint equations. The most significant constraints imposed on the system are formally stated in equation form. It is pointed out that conventional velocity constraint equations associated with no slipping and no skidding are only necessary conditions for nonholonomic motion. By themselves, they cannot guarantee nonholonomic motion; they only describe the result. The cause of nonholonomic motion is the ground reaction forces at the wheels. We state additional dynamic constraints involving the ground reaction forces which eventually provide a sufficient set of conditions for nonholonomy. The requirement for avoiding tipping over is also taken into account. Conditions for avoiding tipping over and maintaining static friction are also stated in ref. 8, where the objective is to maintain the vehicle stationary and constraints emerge from the contact conditions of the vehicle\u2019s outriggers with the ground. This could not be applied in our case, however, because now tipping over can also be caused by the combined effect of the vehicle motion. We need to formulate a condition for which the static conditions of ref. 8 will be a special case. Modeling mobile manipulation systems has not received much attention yet, with few exceptions.7,31 We hope to contribute in this direction with the main results of this article, which can be summarized as follows: v The model is constructed with the use of Kane\u2019s dynamical equation, which possesses a number of merits compared to Euler]Lagrange and Newton]Euler formulatinos in terms of both simplicity and computational effort. v Object manipulation is not restricted to rigid materials. v Deformable object modeling does not neglect any of the object dynamics, using threedimensional elastodynamic equations. v Introducing the concept of generalized operational space, it is possible to apply proposed task space methodologies in the case of infinite degrees of freedom deformable objects. v The whole system is regarded as a closedchain mechanism. v Nonholonomic constraints imposed on the mobile bases are taken into account. v Conventional nonholonomic constraint equations, which are only necessary conditions for nonholonomy, are accompanied by constraint equations at the dynamic level which complete the set and make it sufficient. v Additional sufficient conditions regarding the system\u2019s mechanical stability are included. Analytical expressions for the equations of motion are not given, since there is no specification on the number of manipulator links, thereby to account for both nonredundant and redundant manipulators. For the vehicle and the first manipulator link, calculations are carried out analytically to present our approach to nonholonomic issues with clarity and to reveal the nature of the interaction between the manipulator and the vehicle. The remainder of the procedure for the manipulator is described and specific references are given. The rest of the article is organized as follows. In section 2, Kane\u2019s methodology is applied to the problem of modeling a single mobile manipulator. Section 3 is devoted to modeling the deformable object. The combined model for the system of multiple mobile manipulators handling a common deformable object is constructed in section 4. In section 5, the dynamic constraints imposed on the system are presented and analyzed. Section 6 summarizes conclusions drawn from the present work." ] }, { "image_filename": "designv10_13_0003900_1.4023556-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003900_1.4023556-Figure1-1.png", "caption": "Fig. 1 (a) Serial link planar manipulator without drive error and (b) shift in end effector position due to drive error Fig. 2 Workspace of 2R manipulator", "texts": [ " Manuscript received January 26, 2012; final manuscript received January 7, 2013; published online March 26, 2013. Assoc. Editor: Kazem Kazerounian. Journal of Mechanisms and Robotics MAY 2013, Vol. 5 / 021003-1Copyright VC 2013 by ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use error under the influence of drive backlash and clearances is estimated as dimensionless number. A serial chain 2R manipulator consisting of two links with revolute joint is considered as shown in Fig. 1(a). Joint j1 and j2 represents ideal positions of joints for input drive. If joint clearance is taken into consideration; the nominal links are added with a virtual mass less link at each joint. The DoF of the mechanism is increased to four, whereas the mechanism with ideal joints has two-DoF. When backlash and clearance is considered as an error source, random variation in the position of the nominal links l2 and l3 is noted; and can be represented as shown in Fig. 1(b). Position of end point of each link is governed by clearance d and angle dh for respective links. The simple serial chain planar manipulator is used for analysis of an input drive error with ideal joint parameters is shown in Fig. 1(a). Link 1 is a fixed link, links 2 and 3 forming arms of manipulator, having equal length to provide maximum reachable workspace. Drives are considered to give input h1, h2 at joint j1 and j2, respectively. For maximum reach of the end effector (i.e., length j1P), length for links 2 and 3 is formulated under ideal conditions, neglecting effect of clearances such that l2 \u00fe l3 maximum reach (1) A quarter-circular workspace is allotted to end effector so that finite points are generated in workspace and end effector can be mapped as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003715_115022-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003715_115022-Figure1-1.png", "caption": "Figure 1. Sketch of the process steps for capillary self-alignment of a foil die: (a) patterning of the carrier substrate, (b) deposition of a droplet of assembly liquid, (c) coarse alignment of a functional die, (d) the liquid wets foil die forming a meniscus, (e) self-alignment of a foil die on the corresponding binding site.", "texts": [ " The aimed assembly precision for mesoscopic foil components should be suitable for foil-to-foil integration via standardized flex flat cable interconnections with pitches typically varying from a half to a few millimeters [18]. As a consequence, alignment accuracies in the order of 50 \u03bcm or less are necessary. This is in contrast to state-of-the-art microchip assembly that requires assembly precision in the order of a few microns [6]. The general process for the investigated capillary selfalignment can be described as follows (figure 1): (a) A substrate is patterned to create hydrophilic binding sites having the same size of the functional foil die. (b) A droplet of liquid is dispensed on the hydrophilic binding sites. (c) A foil die is coarsely aligned with a binding site and brought in contact with the liquid droplet by means of a micro positioner. (d) As a consequence, the liquid wets the foil die forming a meniscus. (e) Upon release of the foil die, meniscus energy minimization combined with geometrical shape matching self-aligns the foil die to the corresponding binding site with high accuracy" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002025_s002211209400306x-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002025_s002211209400306x-Figure2-1.png", "caption": "FIGURE 2. Position of an element tds of a flagellum.", "texts": [ " This says that dFflag, the viscous force exerted upon an element tds of a flagellum, where t is the unit vector tangential to the flagellum, is linearly related to the velocity of the fluid relative to the element, urel: (2.4) Lgrav = hp x mgk. df'flag = F { f(N(Bre1- n) n ds + KT(UA* t ) t ds), where n is a unit vector normal to t , in the same plane as u , ~ and t t , K N and t Thus ( ~ ~ ~ 1 * n)n = urel- (ure~ .t ) t . Bijagellate gyrotaxis in a shear flow 141 K T are dimensionless resistance coefficients in the normal and tangential directions respectively and ,u is the viscosity of water (figure 2). In order to calculate the viscous force upon the element of the flagellum, it can be seen that we require the velocity of the fluid relative to the element, ur+ The velocity of the fluid, u, is measured at the position of the element ds assuming that the presence of the flagellum has no effect upon the fluid flow. For a spherical body in a general flow field, this is made up of three parts: the flow due to the translation of the body, the flow due to the vorticity of the ambient flow and the rotation of the body, and the flow due to any ambient straining motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001570_tt.3020050303-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001570_tt.3020050303-Figure7-1.png", "caption": "Figure 7 Points on gear wheel teeth flanks at different pivot angles", "texts": [ " The teeth profiles are therefore considered to be constant for 10,000 revolutions and are then updated. Running the simulation Tribotest journal 5-3, March 1999. (5) 240 lSSN 2354-4063 $8.00 + $8.00 Wear simulation of spur genrs 241 with a different number of revolutions per interval confirms the relevance of that simplification. The interaction between the teeth is assumed to be quasi-static. The points on the teeth surfaces are aligned in such a way that the first point is at the base diameter, the last point at the tip diameter, and the points in between are on an involute curve, see Figure 7. Tribotesf journal 5-3, March 1999. (5) 241 lSSN 1354-4063 $8.00 + $8.00 242 Flodin and Andersson For a more specific description of the computer model, see Flodin and Andersson.\u2019 RESULTS AND DISCUSSION The simulated wear of the pinion and the gear are presented in Figures 8 to 10. The linear model based on the generalised Archard\u2019s wear equation correlates well with the wear model that incorporates adsorption, each showing a similar wear profile Tribotest journal 5-3, March 1999. (5) 242 ISSN 1354-4063 $8" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003399_j.snb.2012.10.021-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003399_j.snb.2012.10.021-Figure1-1.png", "caption": "Fig. 1. Constitution o", "texts": [ " Preparation of the biosensors Before use, the transducers were cleaned with ultrapure water and ethanol and the pads were covered manually with BlocJelt acrylic varnish (ITW Spraytec, Asni\u00e8res sur Seine, France) for their insulation. After that, 0.3 L of a 20 mM phosphate buffer pH 7 containing 5% (m/v) BSA, 10% (m/v) glycerol and 5% (m/v) HRP was deposited on the working pair of electrodes, while on the reference electrodes 0.3 L of a mixture containing 10% (m/v) BSA and 10% (m/v) glycerol was applied. The sensor chip was allowed to dry for 20 min at room temperature. Then, a second layer was deposited on each electrode, following the same protocol except that HRP was replaced by LODP in the enzymatic solution (Fig. 1). BSA, a lysine-rich protein with no enzymatic activity, was used as cross-linking co-reagent to help forming LODP and HRP immobilization matrices and protect both enzymes from excessive reaction with GA, which might compromise their activity [24]. Glycerol helped achieving a satisfying homogeneity of enzyme/BSA solutions and allowed limiting enzyme loss of activity during storage of the solutions at \u221220 \u25e6C between two biosensor preparations. After enzymes deposition, the sensor chip was placed for 30 min in a saturated GA vapor atmosphere" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure7-1.png", "caption": "Fig. 7 Fixed and moving centrodes for an offset slider-rocker mechanism with U 5 0.91 and W 5 0.45: r 5 330 mm, l 5 300 mm and e 5150 mm", "texts": [], "surrounding_texts": [ "The algebraic curves representing the moving centrodes of a centered slider-crank/rocker mechanism are also recognized and proven to be Jer\u030ca\u0301bek\u2019s curves for the first time. In fact, these curves have been studied and analyzed by Va\u0301clav Jer\u030ca\u0301bek (1845\u20131931) of the Czech Republic, as reported in Ref. [21]. The original graphical construction of a Jer\u030ca\u0301bek\u2019s curve is shown in Fig. 9 for the case of a closed curve, but we have also demonstrated that the same graphical construction is also true for the whole family of moving centrodes of centered slider-crank/rocker mechanisms. Thus, referring to Fig. 10 and taking into account the graphical construction of Fig. 9, the Jer\u030ca\u0301bek\u2019s curves for the centered mechanisms (W\u00bc 0) of types C (U< 1) and A (U> 1), along with the particular case of the Scott-Russell mechanism (U\u00bc 1) are obtained. This graphical construction is developed with respect to the moving frame f \u00f0X; x; y\u00de, which is attached to the coupler link BC, and considering the particular mechanism configuration, where the piston is at the upper dead point. Thus, circle a of center X\u00bc (0, 0) and a given radius, which coincides with the size of the segment O1 m1 of Fig. 9 and with the length r of the crank/rocker link, is traced. Then, a segment with the same length l of the coupler link BC is traced along the x-axis from the origin X\u00bcB. Consequently, the point C can fall inside, outside or on the circle a, by giving the points C1 (slider-rocker mechanism of type C), C3 (slider-crank mechanism of type A) and C2 (Scott-Russell mechanism), respectively. Therefore, the graphical construction is the following: \u2022 A ray is traced across the origin X\u00bcB in order to join a generic point W of the circle a; Journal of Mechanisms and Robotics FEBRUARY 2012, Vol. 4 / 011003-5 Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use \u2022 Point W is joined with the particular point C; \u2022 A line orthogonal to the line joining C and W is traced up to intersect in the particular point S the line across points B and W; \u2022 Repeating the same graphical construction for other rays across the origin X\u00bcB, the whole Jer\u030ca\u0301bek\u2019s curve can be traced. The moving centrode or Jer\u030ca\u0301bek\u2019s curve is a closed or open curve, when the point C falls inside or outside the circle a, respectively, while a circle is obtained for the Scott-Russell mechanism, when C falls on the circle a, as shown in Fig. 10." ] }, { "image_filename": "designv10_13_0001491_0278364903022012004-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001491_0278364903022012004-Figure10-1.png", "caption": "Fig. 10. The unconstrained mobile manipulator motion.", "texts": [], "surrounding_texts": [ "In this paper, a method of derivation of a fully specified system of algebraic and differential equations has been presented to solve the inverse kinematics problem for mobile manipulators. Using the Lyapunov stability theory, a full differential form generating the mobile manipulator trajectory, whose terminal attractor fulfills the above system of equations, has been derived. The generation scheme proposed provides the user with the capability to vary the level of information needed by generator (50) depending on the form of functions cj . That is, the approach presented is equally applicable to analytical descriptions of obstacles in the task space or distances (provided by the robot sensors) between the mobile manipulator and obstacles. Moreover, the control algorithms proposed in this paper generate continuous velocities (even for collision avoidance tasks) which is a desirable property in an on-line control. Numerical simulations carried out on an exemplary mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs have confirmed the theoretical results obtained in Sections 3 and 4. The approach proposed may be directly applicable to multiple mobile manipulators operating in task spaces including also (moving) obstacles. at FLORIDA INTERNATIONAL UNIV on May 24, 2015ijr.sagepub.comDownloaded from at FLORIDA INTERNATIONAL UNIV on May 24, 2015ijr.sagepub.comDownloaded from at FLORIDA INTERNATIONAL UNIV on May 24, 2015ijr.sagepub.comDownloaded from at FLORIDA INTERNATIONAL UNIV on May 24, 2015ijr.sagepub.comDownloaded from Appendix The time interval 0t \u2032, in which the increment of S is less or equal to S \u2032 \u2212 3 4 \u03b5 may formally be determined based on the following sequence of (conservative) relations max t\u2208[t \u2032,t \u2032+0t \u2032] |S\u0307|0t \u2032 \u2264 max t\u2208[t \u2032,t \u2032+0t \u2032] \u2225\u2225\u2225\u2225 ( S\u0307 w\u0307 )\u2225\u2225\u2225\u22250t \u2032 (59) and max t\u2208[t \u2032,t \u2032+0t \u2032] \u2225\u2225\u2225\u2225 ( S\u0307 w\u0307 )\u2225\u2225\u2225\u22250t \u2032 \u2264 max S(q(t))\u2265S\u2032\u2212(S\u2032\u2212 3 4 \u03b5) \u2225\u2225\u2225\u2225\u2225\u2225\u2225\u2225 \u2329 \u2202S \u2202q ,f \u232a \u2329 \u2202w \u2202q ,f \u232a + [ Q1 Q2 ]( v2 v3 )\u2225\u2225\u2225\u22250t \u2032 (60) and max S(q(t))\u2265 3 4 \u03b5 \u2225\u2225\u2225\u2225\u2225\u2225\u2225\u2225 \u2329 \u2202S \u2202q ,f \u232a \u2329 \u2202w \u2202q ,f \u232a + [ Q1 Q2 ]( v2 v3 )\u2225\u2225\u2225\u22250t \u2032 \u2264 S \u2032 \u2212 3 4 \u03b5. (61) Combining eqs. (59)\u2013(61) and denoting by W1(q) = max{det(G1), det(Gd 1)} \u221a d2 1 + d2 2 + (\u2016*1\u2016)t=t \u2032 , the upper estimation on 0t \u2032 takes the final form 0t \u2032 \u2264 S \u2032 \u2212 3 4 \u03b5 maxS(q(t))\u2265 3 4 \u03b5 W1(q) . (62) at FLORIDA INTERNATIONAL UNIV on May 24, 2015ijr.sagepub.comDownloaded from at FLORIDA INTERNATIONAL UNIV on May 24, 2015ijr.sagepub.comDownloaded from" ] }, { "image_filename": "designv10_13_0002469_bf00046687-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002469_bf00046687-Figure11-1.png", "caption": "Fig. 11.", "texts": [ " The process changes X into a Seifert surface X' for A' in the obvious way. Let ai, ot t be the oriented knots on X parallel to A~, Aj, similarly ct' for A'. If we write d for the degree of a map from an oriented knot to NEMATICS IN 3-SPACE 73 p 1 _= S 1, we have d(F ' I a') = v' d(F] a,) - vi + al o A, mod 4, d ( F 1 09) -- v s + otj o Aj but a, o Ai = a s o Ai = A, o Aj, which all together implies Theorem 1 for the case (a). (b): Observing parallel knots ai, a i for A,, Aj and the corresponding objects a s, a j, A i, Aj after the crossing process (Figure 11) we find v ' i = v i + l v ' i = v i - 1 v~= v i + 1 or v~ = v i - 1 h', o h~ = A, \u00b0 hj + 1 h'~ \u00b0 A) = hi \u00b0 hj - 1 depending on orientations, and Theorem 1 follows for the case (b). (c): We can either represent (c) by three processes (a), (b), (a- l ) , or observe a parallel ai to Ai under the process and find a; o A; = a~ o hi :t:2 and d(F' lc t ' i )= d ( F I oti):t: 2, hence v~ = v;, which proves Theorem 1. [ ] Proof of Theorem 2. By Theorem 1, we only have to consider the case r = 1 with A1 unknotted" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002999_j.phpro.2010.08.159-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002999_j.phpro.2010.08.159-Figure4-1.png", "caption": "Fig. 4. Predicted responses from Design Expert for laser power of 1400W, beam spot size of 1.5 mm and track offset of 40%", "texts": [ " For the range of process parameters considered and results produced from the trials, it was predicted that cracking is less likely to occur at 40% track offset and a high powder flowrate of 5 g/min, when a laser power of 1400W was used. Cracking is not significantly influenced by beam spot size and machine feedrate. At 40% track offset, lack of fusion defects are minimised when using a wide beam spot size of 1.5 mm. Lack of fusion defect is not significantly influenced by machine feedrate and track offset. Fig 4 shows the predicted responses from Design Expert for laser power of 1400W, beam spot size of 1.5 mm and track offset of 40%. The main objective of this work was to minimise heat input. Energy density was calculated using the following formula: Energy density (units J/mm3 ) vA P LA Pt V E \u00d7 = \u00d7 == Where, E = energy delivered, J or Ws V = volume of deposit, mm3 P = laser power, W t = time, s A = cross-section area of deposit, mm2 L = length of deposit, mm v = deposition rate, mm/s When the heat input is too low, lack of fusion occurs, as found in deposits produced using fast machine feedrate of 1600 mm/min and low laser power of 800W", " Conversely, high heat-inputs will result in cracking in the deposited material and produce excessive thermal distortion to the substrate. The root penetration of the deposited material was also examined to give an indication of the amount of heat input during deposition. It was found that the minimum root penetration was at the high powder flowrate of 5 g/min. At 5 g/min powder flowrate, the depth of root penetration was found to be independent to the machine feedrate and track offset for the range considered (see Fig 4). By combining the predicted responses from the Design Expert \u00ae software and the penetration level, favourable process parameters, for a low heat inputs high deposition rate, were developed as follows: \u2022 Laser power: 1400W \u2022 Beam spot size: 1.5 mm \u2022 Machine feedrate: 800 mm/min \u2022 Track offset: 40% \u2022 Powder flow rate: 4.9 g/min The predicted root penetration using the favourable process parameter set is approximately 0.21 mm. It is estimated that the percentage of powder leaving the nozzle that then formed the deposit was 75%, with a deposition rate of 240 g/hr" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003026_1.3212679-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003026_1.3212679-Figure2-1.png", "caption": "Fig. 2 A cross section of a circular surface", "texts": [ "org/ on 01/28/201 e3=e1 e2, and since u is a natural parameter of , it follows that e2 =1 and the coordinate frame e1 ,e2 ,e3 form a moving dextral orthonormal frame attached to each point of the spine curve C. Furthermore, e2 and e3 form a basis of the corresponding circle plane at each point of the spine curve C. Suppose that P is an arbitrary point of the circle, the vector MP equals to r e2 cos +e3 sin in the frame e1 ,e2 ,e3 . The vector of point P can thus be expressed in a fixed frame i , j ,k in Fig. 2 as P = M + MP = M + r e2 cos + e3 sin 1 Thus a circular surface can be defined as follows. DEFINITION 1. A circular surface P is the image of the map defined by P u, = M u + r e2 u cos + e3 u sin 2 where e2 u =e1 u , e3 u =e1 u e2 u , and M u is the spine curve. Parametrizing a circular surface in this way excludes circular surfaces with stationary vector e1, whose geometric properties are less interesting and to a certain extent easier to explore. 3 A System of Euclidean Invariants Let : a ,b \u2192Q be an arc-length parametrized curve on a sur- face Q, and take a frame U ,T ,V=U T along the curve where U is the unit normal of the surface and T is the unit tangent of the curve , the natural equation for this frame is d ds U T V = 0 kn g \u2212 kn 0 kg \u2212 g \u2212 kg 0 U T V 3 where s is the arc-length parameter, kn is the normal curvature, kg the geodesic curvature, and g the geodesic torsion of the curve 36 " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002545_s00221-007-0988-y-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002545_s00221-007-0988-y-Figure8-1.png", "caption": "Fig. 8 Simple velocity servo that is considered an elementary simplification of the pursuit system. The input is the 2D target velocity _p; the temporal derivative of the target trajectory p: The output acceleration \u20acx is proportional to the velocity error _p _x", "texts": [ " More experiments are necessary to determine whether there are also short-term mechanisms that adapt the cue-induced predictive pursuit to the relation of target velocity and target acceleration presented within a single experimental session. When the pursuit system is visually guided by a moving target, it obeys the two-thirds power law (de\u2019Sperati and Viviani 1997), but the scaling property (Eq. 3) predicted by the two-thirds power law was not explicitly tested with visually driven pursuit. Nevertheless, it is very instructive to analyze the implication of this scaling property on models of visually driven pursuit. For simplicity we deal only with the simple velocity servo (Fig. 8) as the most elementary functional model of the pursuit system (Churchland and Lisberger 2001). As shown in Appendix 3, a velocity servo that generates an output with the scaling property (Eq. 3) must change its feed-forward gain in proportion to the velocity scaling factor. Evidence for the existence of such an online gain control for visually driven pursuit was provided by experiments showing that the peak-to-peak modulation of visually driven pursuit velocity, induced by a modulation of the target velocity, is larger when the modulation is added to a fast carrier velocity of the target compared to the modulation response of a stationary target or a target moving with slower carrier velocities (Keating and Pierre 1996; Schwartz and Lisberger 1994; Churchland and Lisberger 2002; Carey and Lisberger 2004)", " Invariance of the position error to changes of the tangential target velocity implies that the position output x\u00f0t; v\u00de of a pursuit system is scaled in the same way as p\u00f0t; v\u00de: Thus, for an invariant position error, we obtain the following relationship for the position output: x\u00f0t; v\u00de \u00bc x\u00f0a t; v0\u00de: \u00f05a\u00de By differentiating this equation two times with respect to time, we obtain _x\u00f0t; v\u00de \u00bc a _x a t; v0\u00f0 \u00de and \u20acx\u00f0t; v\u00de \u00bc a2 \u20acx a t; v0\u00f0 \u00de: \u00f05b\u00de Thus, invariance of the position error to changes of the tangential target velocity implies that the output velocity _x is scaled linearly, and the output acceleration \u20acx is scaled quadratically with the tangential target velocity v0. This holds for any system generating a response x following the input p, not only for the velocity servo shown in Fig. 8, and corresponds exactly to the velocity dependence of the cueinduced, predictive pursuit change (see Fig. 7). Appendix 2: Time-dependent tangential velocity If the tangential target velocity is not a constant, but changes along the target path as in our experiment, it is obvious that the derivation shown above will not hold for any change of the time course of the tangential velocity, because any arbitrary change cannot uniquely be described by a single scaling factor a. However, this section shows that the conclusion of (a) still holds for arbitrary time courses of the tangential velocity and arbitrary target paths, when they are subject to a certain type of velocity scaling", " Because this scaling type is a characteristic of the twothirds power law describing natural movements, we call this type \u2018\u2018natural\u2019\u2019 velocity scaling. In analogy to the last paragraph, it follows from Eq. 4a that a position error that is invariant to natural velocity scaling according to Eq. 6 implies a quadratic relation between target speed and the output acceleration of the system. 3. An implication of scaling invariance in simple velocity servos and other linear systems Let _x\u00f0t; v0\u00de be the velocity output of a simple velocity servo (Fig. 8) in response to the velocity input _p\u00f0t; v0\u00de: This velocity output satisfies the following differential equation: \u20acx\u00f0t; v0\u00de \u00bc g\u00f0v0\u00de _p\u00f0t; v0\u00de _x\u00f0t; v0\u00de \u00f07\u00de We assume that the gain depends on the tangential velocity v0 with an unknown function g(v0). The goal of the following derivation is to identify this gain controller under the constraint that the position error of the servo is invariant to the natural velocity scaling described in (a) and (b). Thus, we assume that the servo output satisfies Eqs", " 11 reveals the required scaling property of the transfer function F: F\u00f0s; v\u00de \u00bc F s a ; v0 : \u00f012\u00de Thus, the invariance of the accuracy of the system to natural velocity scaling requires frequency scaling of the Laplace transfer function. Since such frequency-scaling involves a dynamic change of the coefficients of the linear differential equations defining the transfer function, invariance to natural velocity scaling cannot be achieved by any time-invariant linear system. Applying Eq. 12 to the Laplace transfer function of the velocity servo shown in Fig. 8 reveals that this example is a special case of the more general formulation of Eq. 12. If the integrator gain is assumed to be unity at target velocity v0, the transfer function of the servo becomes F\u00f0s; v0\u00de \u00bc 1 s 1 s \u00fe 1 : To achieve invariance of the accuracy of the servo to natural velocity scaling of the input, the complex frequency s must be divided by the scaling factor a (Eq. 12) F\u00f0s; v\u00de \u00bc F s a ; v0 \u00bc a s a s \u00fe 1 : Since the transfer function of the integrator equals 1 s ; dividing s by a is identical with multiplication of the integrator gain with a" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001510_robot.1994.350969-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001510_robot.1994.350969-Figure4-1.png", "caption": "Figure 4: A planar parallel manipulator and its notation", "texts": [ " 3 Computing the solution Innocenti has shown that the direct kinematic problem of any RRR-3S mechanism can be reduced to the analysis of a sixteen order polynomial [5]. As the equivalent mechanism of a Stewart Platform is an RRR-3S mechanism its analysis can be applied here. This approach has been implemented and an intensive numerical investigation has enabled us to find Stewart Platforms with a maximum of 8 solutions (therefore not the expected maximum number). In fact using the planar correspondence developed in the previous section it is possible to determine a 12th order polynomial. Let us consider a planar parallel manipulator (figure 4). The coordinates of the fixed articulation points A, C, F are: A : (0,O) C : (CZ, 0) E' : ( ~ 3 , d 3 ) The inverse kinematic equations are: p: = 2 + y ' (6) p; = (x + 12 cos CP - c2)' + (y + 12 sin 0)' (7) (y + 13 sin(@ + e) - d3)2 (8) p; = x 2 +y' (9) p i - p ; = R z + S y + & (10) p ; - p ; = u z + v y + w (11) = (. + 13 cos(@ + e) - + These equations can be written as: Equations (10-11) are linear in z,y. By solving this linear system and using the value of z ,y in equation (9) we get an equation in the unknown cos 0, sin 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001750_027836402321261913-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001750_027836402321261913-Figure1-1.png", "caption": "Fig. 1. n-link planar underactuated manipulator.", "texts": [ " Next, we prove the controllability of n link planar manipulators where the first joint is actuated and only one of the other joints is unactuated. Third, we show that the n link manipulators with the first joint unactuated are not completely controllable. Thus the above three results allow us to determine the complete controlllability of all kinds of n link manipulators with an unactuated joint. We also show some simulation results to discuss more general cases. We show the equation of motion of the n-link planar underactuated manipulator whose joints are all rotational (Figure 1). Let mi , li , lgi , and Ii be the mass, the length, the distance between the joints and the center of gravity, and the moment of inertia of the ith link, respectively. It is assumed that li > 0 and lgi > 0. Let also \u03b8i be the angle of the ith joint on the frame fixed on the (i\u22121)th link, and \u03c6i be the angle of the ith joint on the frame fixed on the base. For simplicity of notation, let lij and Mjk be defined by lij = lj (j < i) lgi (j = i) 0 (j > i) (1) and Mjk = { Ij +\u2211n i=1 milij lij (j = k)\u2211n i=1 milij lik (j = k)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002435_s1474-6670(17)53666-6-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002435_s1474-6670(17)53666-6-Figure2-1.png", "caption": "Figure 2: Reaction control system geometry", "texts": [ " Thus, since we can compute the required natural controls, we may consider II = (fan fa \" TI)T (the desired x-z plane force and moment) to be the control input. Then, since moments are generated by appl,' forces rather than couples, the y-a..xis force is given by (-I) Here, /3'0/1 and /Iya ,,' are sca]a.r functions of small magnitude expressing the coupling between the rolling and yawing moments and the lateral force. To illustra te 3'0/1. consider the geometry of the reaction control system shown in figure 2. :\\ote that the forces used to generate the rolling moment are not perpendicular to the y-a.xis of the aircraft. Thus. when a positive rolling moment (Tar) is commanded, a negative y-a..xis force (foy) is generated (i.e .. the airplane will initially accelerate to the left when it is commanded to roll right). In this case. /3,011 will be a negati\\'e fun ction of the aircraft sta te. \\Ve can now rewrite equations (1) and (2 ) as my -...JJa X J.....,\u00b7o (5) where B is the (state dependent. 6- by-5) matrix pro\\'iding the full vector of aircraft forces and moments ginn the con/" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001824_aero.2004.1367684-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001824_aero.2004.1367684-Figure1-1.png", "caption": "Figure 1 -Rigid wheel sinking into deformable terrain with left (0,) and right (I&) terrain interface angles shown", "texts": [ " Such techniques could enhance rover safety and mobility, through integration with control and motion planning methods. 2. VISUAL WHEEL SINKAGE STIMATION The goal of the algorithm is to measure wheel sinkage in deformable terrain from a visual image. A more detailed treatment of this method is presented in [7]. Here we assume the presence of a camera mounted on the robot body, with a field of view containing the wheel. Sinkage is defmed as a pair of angles from the vertical termed left and right terrain interface angles (see Figure 1). This represents a general description of wheel sinkage in uneven terrain. To determine these angles, only an annular region along the wheel rim (between r,, and rwheel) needs to be examined. This reduces computational requirements by eliminating much of the scene. It is assumed that the location of the wheel relative to the camera is known. This is a reasonable assumption, since many robots have rigid suspensions. Robots with articulated suspensions (such as the Sojourner rover) are generally instrumented with suspension configuration sensors", " The algorithm instead relies on a relatively simple analysis of grayscale intensity along the wheel rim. Algorithm Description The algorithm consists of three steps: 1) wheel rim identification, 2) pixel intensity computation, and 3) terrain interface identification. The following sections describe these steps. Wbeel Rim Identification and Classification411 points of interest on the wheel rim are first identified. Points of interest lie in a region between the inner wheel rim diameter r,, and the outer wheel rim diameter rwhrel (see Figure 1). For rimless wheels or tires, rwhe,, corresponds to the outer tire diameter and r, is chosen to he slightly less than rwheel. Points of interest in the annular region are divided into two regions corresponding to the left and right half of the wheel (see Figure 2). This is done since terrain entry generally occurs in one half of the wheel, and terrain exit occurs in the other. Thus the algorithm searches for one terrain interface in each region. LeA and right wheel halves are determined with respect to the vector vdown" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002414_tia.1987.4504992-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002414_tia.1987.4504992-Figure11-1.png", "caption": "Fig. 11. Current waveforms. (a) RL circuit. (b) PM machine.", "texts": [ " If the core has a nonlinear magnetizing curve, the stator phase current will change significantly, as shown in Fig. 9. The no-load phase current contains a high level of the thirdharmonic component circulating only in stator windings. The line current has no component of the order 3n, where n is a positive integer (Fig. 10). It is interesting to compare the current waveform shown in Fig. 9 with the current in a resistance-inductance (RL) circuit with saturable inductance. Both of these currents are shown in Fig. 11. The current waveform in the RL circuit is a result of copying the almost sinusoidal flux on the nonlinear magnetizing curve, obtaining the typical current peak in that way. The fundamental and the third harmonics of this current are represented by the dashed lines of Fig. 11(a). Fig. 11(b) represents the current waveform containing the third harmonic shifted 1800 to that shown in Fig. 11(a). This current corresponds to the phase current in Fig. 9. Although both solid drawn currents in Fig. 11 contain the same level of third harmonic, there is a significant difference between them. The passive RL circuit is just a consumer of the third harmonic, while the A-connected machine is a 840 OSTOVIC: COMPUTATION BY MEANS OF MAGNETIC CIRCUITS for all current harmonics except the fundamental. The energy that covers the losses of those generated harmonics comes from the supply. It is converted first to mechanical form and then to electrical, with the frequencies of currents different from the supply frequency" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003430_978-0-85729-898-0-Figure9.3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003430_978-0-85729-898-0-Figure9.3-1.png", "caption": "Fig. 9.3 Workspace and coordinate system of the cooperative manipulator UARM and desired trajectory for the model-based controllers", "texts": [ " \u2022 gamma: Defines the value for the attenuation level c: \u2022 Ki: Defines the squeeze force control parameter. The following MATLAB code implements the quasi-LPV and game theory controllers for the free-swinging joint fault configuration. 9.7 Examples 213 To validate the nonlinear H1 control methods presented in the previous sections we apply them to the underactuated cooperative manipulator shown in Chap. 7, composed of two identical planar underactuated manipulators UARM. The workspace and the coordinate system for the cooperative manipulator are shown in Fig. 9.3; the load parameters are presented in Table 9.1. The kinematic and dynamic parameters of the manipulators can be found in Chap. 1. 214 9 Robust Control of Cooperative Manipulators The goal is to move the center of mass of the load along a straight line in the X\u2013 Y plane from xo\u00f00\u00de \u00bc \u00bd0:20m 0:35m 0 T to xd o\u00f0T\u00de \u00bc \u00bd0:25m 0:40m 0 T ; where T \u00bc 5:0 s is the duration of the motion. The reference trajectory xd o\u00f0t\u00de is generated using a fifth-degree polynomial. The following external disturbances are introduced to verify the robustness of the proposed controllers: 9", "45 Time (s) Po si tio n (m ) Coordinate X Coordinate Y Desired 0 1 2 3 4 5 \u22124 \u22123 \u22122 \u22121 0 1 2 3 4 Time (s) O rie nt at io n (d eg re es ) Orientation Desired Fig. 9.4 Control of a rigid load by a system of two cooperative fully-actuated manipulators, quasi-LPV formulation 9.7 Examples 217 Table 9.3 Performance indexes, underactuated configuration Nonlinear H1 L2\u00bdex E\u00bds (N m s) E\u00bdhos (N s) Quasi-LPV 0.0154 0.9976 0.4477 Game theory 0.0103 1.0609 0.3973 218 9 Robust Control of Cooperative Manipulators In this section, we assume that joint 1 of manipulator A in Fig. 9.3 is passive. In this case, (ne \u00bc n\u00f0m 1\u00de np \u00bc 2) and therefore only two components of the squeeze force can be controlled independently. We choose to control the X and Y components of the squeeze force but not the component relative to the momentum applied to the load. The desired values for the squeeze force are Cd sc \u00bc \u00bd0 0 T : The parameters q\u00f0ex\u00de; the variation rate bounds, and the basis functions needed to compute X\u00f0q\u00de are the same ones used in the fully-actuated case. The quasi-LPV system matrices are also the same except that bM\u00f0xo\u00de \u00bc eM\u00f0xo\u00de and bC\u00f0xo; _xo\u00de \u00bc eC\u00f0xo; _xo\u00de: The parameter space was divided considering three points in the set P" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001827_robot.1996.506578-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001827_robot.1996.506578-Figure2-1.png", "caption": "Figure 2: A single binary truss module shown in state 110. The bits within the truss are numbered from left to right.", "texts": [ " Macroseopically-serial manipulator A macroscopically-serial manipulator is a manipulator that is serial on a large scale, i.e. it can be represented by a serial collection of modules (where each module is mounted on top of the previous one). Binary manipulator A binary manipulator is a macroscopically-serial manipulator that is composed of a set of modules with two-state actuators, stacked one atop the other. The modules are numbered from 1 , . . . , B , starting from the base of the manipulator. Path M N o m - Llm Each module has a frame attached to its top (Figure 2). The frames are numbered such that frame i is on top of module i, and frame 0 is the frame a.t the ma.nipulator base. Jj denotes the number of independent binary actuators in module i. Therefore, there are ZJ' different combinations of binary actuator states (and corresponding configurations) for the ith module. Manipulator state The state of a binary manipulator is a binary number, S, whose bits represent the states of each actuator in the manipulator. The state of an individual module in the manipulator is denoted by s i , which is a Ji bit binary number" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002482_tmech.2006.882994-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002482_tmech.2006.882994-Figure4-1.png", "caption": "Fig. 4. Reference path. (a) Lateral reference. (b) Longitudinal reference.", "texts": [ " This section first defines the objective of autonomous flight and then proposes the autopilot system to achieve this objective. As wind disturbances can greatly affect the motion of airplanes that have large wings and fly at low Mach numbers, such as the Kiteplane, trim flight with drift is considered to attenuate the effects of the wind disturbance. For simplicity, the reference path for the airplane is defined as lines connecting specified waypoints. The reference path is graphically depicted in Fig. 4. As the controller is divided into two subsystems, the reference path is divided into a lateral plane containing latitude and longitude [Fig. 4(a)] and a longitudinal plane containing altitude [Fig. 4(b)]. Only one waypoint, called the target point, is considered at a time and the reference path is defined as the line extending from the previous to the current target points. The target point is updated when the airplane passes the previous target point, as discussed later. Let ey , ea, and ez represent the horizontal displacement from the nearest point on the reference path to the horizontal position of the airplane, the difference from the desired direction defined in Section IV-B to the heading of the airplane, and the difference in altitude from the level longitudinal reference path to the altitude of the airplane, respectively. Each waypoint is surrounded by two concentric regions denoted as Ai and Bi in Fig. 4. The airplane is said to have passed the target point when it enters the small region Ai . Under wind disturbance, however, the airplane may not be able to enter region Ai . A weak target updating criterion is introduced for these unexpected situations. In this case, the target should be updated when the airplane leaves region Bi after it has entered Bi . These two cases are summarized in Fig. 5(a). It is considered a failure if the airplane approaches the target point after flying a distance Ci along the reference path without entering region Bi [Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001348_s0167-6105(97)00299-7-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001348_s0167-6105(97)00299-7-Figure2-1.png", "caption": "Fig. 2. Seam turned about the y axis.", "texts": [ " 1 shows a cricket ball moving through air with a relative velocity \u00ba perpendicular to the yz plane. The resultant force acting on it can be resolved into three mutually perpendicular forces, namely the drag force D, the lift force \u00b8 and the side force S, acting in the directions x, y, z, respectively. Whether or not all three component forces are present at any particular time depends upon the seam angle and any spin which may be imparted to the ball. For a given air velocity, the angle of the seam plane from the vertical xy plane is defined in Fig. 2. Here, the seam plane is turned about the y axis through angle c y measured in the horizontal xz plane. In Fig. 3, the seam plane is turned about the x axis from the vertical xy plane through angle c x measured in the vertical yz plane. Turning the seam about the z axis does not change the orientation of the seam as far as the oncoming air flow is concerned. The side force generated in the z direction is responsible for the \u201cswing\u201d of the ball. For c y positive as shown in Fig. 2, the bowler would bowl an \u201cinswinger\u201d which moves in towards the batsman, while for c y negative, he would bowl an \u201coutswinger\u201d which moves away from the batsman. A drag force will also be present in Fig. 2 but no lift force would normally be expected since, because of flow symmetry, the flow patterns and therefore the pressure distributions around the ball above and below the xz plane are theoretically the same. For all c x only a constant drag force would be expected to exist since the flow patterns are also symmetrical about the xz and xy planes. In the above cases, no spin is applied to the ball and therefore the aerodynamic forces on the ball are caused by the state of the boundary layer around its stationary surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.17-1.png", "caption": "Fig. 9.17 A silk drawing device (\u7d93\u67b6, \u7d72\u7c70) a Original illustration (Jing Jia) (Wang 1991), b Original illustration (Si Yue) (Wang 1991), c Structural sketch", "texts": [ " The large pulley is connected to the frame with a revolute joint JRz. The rope is connected to the large pulley and the spindle with wrapping joints JW. The spindle is connected 9.4 Textile Devices 211 to the frame with a revolute joint JRz. Figure 9.16c shows the structural sketch. Figures 9.16d and e show the real objects of Shou Yao Fang Che and Wei Che, respectively. 9.4.6 Jing Jia (\u7d93\u67b6, A Silk Drawing Device) Jing Jia (\u7d93\u67b6, a silk drawing device) is used to draw and coil silk in the process of silk yarn spinning as shown in Fig. 9.17a (Wang 1991). Before using Jing Jia, the silk thread needs to be coiled around Si Yue (\u7d72\u7c70, a wooden pulley wound up by silk) as shown in Fig. 9.17b (Wang 1991), and several Si Yue would be combined 212 9 Flexible Connecting Mechanisms to process warping. When the device is working, the operator rotates the handle to pull out the silk from Si Yue. The silk thread goes over a wooden stand and then it is coiled around the warping roll side by side for the purpose of collecting and combining numerous silk threads. This is a mechanism with four members and four joints, including a wooden stand as the frame (member 1, KF), a warping roll with a handle (member 2, KU1), Si Yue (member 3, KU2), and the silk thread (member 4, KT). The warping roll is connected to the frame with a revolute joint JRx. The silk thread is connected to the warping roll and Si Yue with wrapping joints JW. Si Yue is connected to the frame with a revolute joint JRy. Figure 9.17c shows the structural sketch. 9.4.7 Mu Mian Kuang Chuang (\u6728\u68c9\u8ee0\u5e8a, A Cotton Drawing Device) In the book Nong Shu\u300a\u8fb2\u66f8\u300b, Mu Mian Kuang Chuang (\u6728\u68c9\u8ee0\u5e8a, a cotton drawing device) has the similar function and structure as Jing Jia (\u7d93\u67b6, a silk drawing device) as shown in Fig. 9.18a (Wang 1991). The difference is that Jing Jia is used to organize silk threads while Mu Mian Kuang Chuang deals with cotton yarns. Figure 9.18b shows the structural sketch. (a) (b) 9.4 Textile Devices 213 T ab le 9. 2 F le x ib le co n n ec ti n g m ec h an is m s (1 9 it em s) M ec h an is m n am es B o o k s N o n g S h u \u300a \u8fb2 \u66f8 \u300b W u B ei Z h i \u300a \u6b66 \u5099 \u5fd7 \u300b T ia n G o n g K ai W u \u300a \u5929 \u5de5 \u958b \u7269 \u300b N o n g Z h en g Q u an S h u \u300a \u8fb2 \u653f \u5168 \u66f8 \u300b Q in D in g S h o u S h i T o n g K ao \u300a \u6b3d \u5b9a \u6388 \u6642 \u901a \u8003 \u300b S h ai G u (\u7be9 \u6bbc )F ig " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003601_s10846-012-9731-4-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003601_s10846-012-9731-4-Figure6-1.png", "caption": "Fig. 6 Experimental platform", "texts": [ " In the case of the altitude control, results coming from numerical simulation are shown in Fig. 5. As a result of the perturbation introduced, the helicopter tends to loose height, however the altitude control is capable to recover the desired position during a short period of time. In the scientific literature [14, 15] and on internet hobbyist\u2019s forums/markets (www.kopterworx.com), several configurations of helicopters having eight-rotors can be found. In particular, the rotorcraft proposed has all the rotors lying on the same plane. Figure 6 shows the prototype. The rotorcraft was developed at CINVESTAV UMI LAFMIA Lab, Mexico. The vehicle frame was designed following [16] to be as light as possible, while maintaining sufficient stiffness to ensure accurate state measurement and control actuation. Constructed with carbon fiber foam core laminates, an aluminium center plate and plastic fasteners, the entire weight is on the order of 1750 g, including two Li-Po batteries. The distance (center to center) between two rotors in the same axis is 62 cm" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.13-1.png", "caption": "Fig. 6.13 Tower ladder wagons. a A tower ladder wagon (\u96f2\u68af) (Mao 2001). b A tower ladder wagon (\u642d\u8eca) (Mao 2001). c A tower ladder wagon (\u642d\u5929\u8eca) (Mao 2001). d Structural sketch of roller device e Structural sketch of ladder device", "texts": [ "13a\u2013c (Mao 2001). There are some records about the tower ladder wagon in the Spring\u2013Autumn Period (770\u2013476 BC). The device should be combined with the singular wooden ladder and the moving wagon. Its structure can be divided into two parts: the roller device and the ladder device. The roller device is a mechanism with two members and one joint, including the frame (member 1, KF) and the wheels on the frame as the roller members (member 2, KO). Each wheel is connected to the frame with a revolute joint JRz. Figure 6.13d shows the structural sketch of the roller device. The ladder device is also a mechanism with two members and one joint, including the frame (member 1, KF) and a ladder (member 3, KL). The ladder is connected to the frame with a revolute joint JR. Figure 6.13e shows the structural sketch of the ladder device. (a) (b) (c) Fig. 6.11 Winnowing devices. a A winnowing device (\u63da\u98a8\u8eca) (Mao 2001). b A winnowing device (\u98a8\u6247 \u8eca) (Mao 2001). c Structural sketch 122 6 Roller Devices Pao Che (\u7832\u8eca, a ballista wagon), also known as Xing Pao Che (\u884c\u7832\u8eca) or Pao Lou (\u7832\u6a13), is a trebuchet on a moving wagon. It is used to sling rock balls to attack long-distance targets as shown in Figs. 6.14a\u2013b (Mao 2001). The Chinese character, Pao, means a ballista or trebuchet. The ballista had a long history of uses in ancient China" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001662_s0094-114x(01)00082-9-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001662_s0094-114x(01)00082-9-Figure6-1.png", "caption": "Fig. 6. Orientation and dimensions of contact ellipse.", "texts": [ " Similarly, the principal curvatures and directions of any point on the gear tooth surface R2 generated by cutter RG can be derived as well and expressed in coordinate system S2 by the same procedure. According to the TCA results, the principal directions i \u00f01\u00de I and i \u00f02\u00de I represented in coordinate systems S1 and S2, respectively, can be described in coordinate system Sf by applying the coordinate transformation matrix equation. Obviously, at any instantaneous contact point, i \u00f01\u00de I and i \u00f02\u00de I are located on the common tangent plane of the mating surfaces R1 and R2, as shown in Fig. 6. The orientation of the contact ellipse is determined by the angle c which can be represented with the following equations [5,6]: tan 2c \u00bc g2 sin 2r g1 g2 cos 2r ; \u00f034\u00de where g1 \u00bc j\u00f01\u00de I j\u00f01\u00de II ; \u00f035\u00de and g2 \u00bc j\u00f02\u00de I j\u00f02\u00de II : \u00f036\u00de Meanwhile, angle r is formed by the first principal directions of the gear and pinion tooth surfaces i \u00f02\u00de I and i \u00f01\u00de I , and it can be evaluated by r \u00bc cos 1 i \u00f01\u00de I i\u00f02\u00deI : \u00f037\u00de The half length of the major and minor axes of the contact ellipse, a and b, can be expressed in terms of the elastic approach D by [5,6] a \u00bc D A 1 2 ; \u00f038\u00de and b \u00bc D B 1 2 ; \u00f039\u00de where A \u00bc 1 4 j\u00f01\u00de R h j\u00f02\u00de R \u00f0g2 1 2g1g2 cos 2r \u00fe g2 2\u00de 1=2 i ; \u00f040\u00de B \u00bc 1 4 j\u00f01\u00de R h j\u00f02\u00de R \u00fe \u00f0g2 1 2g1g2 cos 2r \u00fe g2 2\u00de 1=2 i ; \u00f041\u00de j\u00f01\u00de R \u00bc j\u00f01\u00de I \u00fe j\u00f01\u00de II ; \u00f042\u00de and j\u00f02\u00de R \u00bc j\u00f02\u00de I \u00fe j\u00f02\u00de II : \u00f043\u00de Thus, the orientation and dimension of the contact ellipse can be determined by utilizing Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002391_elan.200302858-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002391_elan.200302858-Figure6-1.png", "caption": "Fig. 6. Cyclic voltammograms of 1 mM 2-thiouracil in buffered solutions with pH a) 3.0, b) 4.0, c) 5.0, d) 6.0, e) 7.0, f) 8.0, g) 9.0 and h) 10.0. Sweep rate 100 mV s 1.", "texts": [ "001 M solutions of both thiol with pH 7.0. The slope of Tafel plots was in the range of 121 \u00b1 138 mV.decade 1 for the applied range of sweep rate. This could indicate that oneelectron oxidation of thiol is the rate-determining step. For 2-thiobarbituric acid, no cathodic peaks were observed on the reverse scan within the investigated potential and pH range (Figure 5). But, in the case of 2-thiouracil, a cathodic peak was obtained in potentials more negative than 0.0 mV in acidic conditions (peaks a and b in Figure 6). It seems that this cathodic peak may correspond to reduction of the disulfide formed by the oxidation of thiol. As can be seen in Figure 6, by increasing the pH of the buffered solutions, the potential of this cathodic peak shifts to more negative values. At pHs greater than 5, only the oxidation wave of thiol is observed. Figure 7 shows the variation of cathodic peak current with v1/2 for the reduction of disulphide that produced from the anodic oxidation of 2- thiouracil at pH 3.0. The linearity with the square root of potential scan rate and zero intercept indicates that it corresponds to the diffusion controlled cathodic current in the reverse scan" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.33-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.33-1.png", "caption": "Fig . 5.33. Detail s of th e Layerglaze \u2122 interactio n zone .", "texts": [ " Experimental processing of layer glazed materials Apparatus. In order to facilitate the smooth addition of feedstock material, and to ensure adequate bonding with the substrate, power densities in the range of 0 .15-lXlO 5 W/cm 2 are commonly utilized. An environmental chamber allows the maintenance of a helium atmosphere around the interaction region. The process has been automated using an x-y-\u00e6-\u00d9 numerically controlled vertical milling machine which is capable of linear speeds of up to 7.62 cm/s. The experimental setup is shown in fig. 5.33. The laser beam is focused by a spherical mirror (not shown) and enters the work chamber through a small aperture at the top. Interaction with the workpiece and feedstock takes place approximately 5 cm below the aperture. A positive pressure of helium gas within the box flows steadily outward through the aperture. The wire or powder feed nozzles are attached to the chamber, and direct the feed material to the interaction zone between the beam and the arbor. The most significant effort in layerglaze processing has been the development of capability to fabricate a scale-model gas turbine disk", " Kear ments utilizing wire feed, a drop transfer phenomenon was encountered, whereby the liquid melted at the end of the feed wire did not flow smoothly and continuously onto the workpiece, but rather was transferred in discrete drops causing a bumpy, irregular deposit. The irregularities become self-perpetuating, due to the fact that the bumps, once established, tended to rake further amounts of liquid from the end of the wire. Under certain experimental conditions, it was noted that drop transfer was nearly nonexistent, and that material transfer was quite smooth. The final, most optimum relationship between the arbor and the wire feed is depicted in fig. 5.33. With the arbor rotating at a speed of w, a teardrop-shaped molten zone is obtained at steady state when the impingement spot of the optical beam is circular. The length of the molten zone is typically twice the beam spot diameter. The location of the feedstock, at this stage, turned out to be the most critical parameter. With the impingement angle of the wire feed at 30\u00b0, it was determined that most satisfactory transfer occurred when the wire contacted the arbor at the exact edge of the molten pool" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002817_bio.1006-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002817_bio.1006-Figure1-1.png", "caption": "Figure 1. Schematic diagram of the ECL detection cell: (A) side view; (B) front view. 1, vent; 2, capillary; 3, Ag/AgCl reference electrode; 4, Pt working electrode; 5, CE electrode, earthed; 6, Pt wire counter-electrode; 7, O-ring; 8, plastic optical window.", "texts": [ "05 \u03bcm alumina to obtain a mirror surface and was then rinsed with acetonitrile (ACN) and distilled water, followed by 5 min sonication. Before each experiment, the working electrode was subjected to repeated cycling in the potential range 0 to +1.8 V (Ag/AgCl) in 0.1 mol/L phosphate buffers, pH 7.5, to activate the electrode until reproducible voltammograms were obtained. Fabrication of the ECL detection cell was referred to that reported by Chiang et al. (30, 31). A schematic diagram of the ECL cell is shown in Fig. 1. The cell body (800 \u03bcL volume) was made of polytetrafluoroethylene (PTFE) and a commercial platinum disc electrode was used, for easy replacement, instead of an indium/tin oxide (ITO)-coated glass electrode, although the ITO enables a wider poten- tial control in the anodic region (31) compared to the Pt electrode. The distance from the Pt electrode surface to the capillary outlet was adjusted to 100 \u03bcm, using a microcontroller under a magnifying lens. A piece of polystylene plate (0.5 mm thickness) was cut in a round shape (8 mm diameter) to provide an optical window through which the photons were captured by an Oriel (Stratford, CT, USA) 70680 photomultiplier tube (PMT)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003543_1350650112460950-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003543_1350650112460950-Figure1-1.png", "caption": "Figure 1. Distribution of pressures needed to overcome resistance of grease flow in central lubrication system: 1 \u2013 lubrication pump, 2 \u2013 main conduit, 3 \u2013 feeder distributor, 4 \u2013 supply conduit, 5 \u2013 receiving points (friction joints).13", "texts": [ " The rheological properties of a grease composition are determined by the soap thickener (mainly its concentration, the shape of the soap floccules and their dispersivity) and the oil base.5\u20138 Also the additives and modifiers may have a significant influence.9\u201311 Effect of thickener microstructure on lithium grease flow resistance in lubrication systems While supplying grease to specific friction pairs the lubricating pump must generate such pressure in the lubrication system which will overcome several flow resistances, chiefly in (Figure 1): . the mains conduits \u2013 p1 . the feeder distributors \u2013 p2 . the supply conduits \u2013 p3 . the receiving points (friction joints) \u2013 p4 In most lubrication system components the pressure increments caused by grease flow resistances have a local character (p2, p4), whereas in the lubrication main conduits and in the supply conduits pressure increases continuously (p1, p3). Since the amount of lubricant is the largest in the conduits, grease flow resistances in them pose the greatest risk to the proper functioning of lubrication systems" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002867_icma.2009.5246352-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002867_icma.2009.5246352-Figure8-1.png", "caption": "Fig. 8. Assist force amplified gravity compensation mechanisms", "texts": [ " However, to generate the large assist moments by this mechanisms, the moment arm of the pulleys h or the spring constant K should be taken large from (1). Due to the limit of the space in the wearable device, hand K cannot be taken large, so that the sufficient large moments to support the human body weight can not be generated by this structure. To develop a useful wearable gravity compensation de vice, some mechanisms to amplify the assist moments are necessary . Thus, in this section, another type of the gravity compensation mechanism is proposed. The structure of the proposed mechanism is shown in Fig.8 . In this system, if the joint shaft rotates by B, the gear 2 rotates ~ in the counter direction. By this the internal link 1 rotates by ~ . Since the end of the internal link 2 is fixed to the linear slider I, which is located on the line across the center of the gear 2, the internal link 2 rotate by B. Thus the linear slider 1 is pushed by the length : XI = 2h sin ~ . (8) Since the linear slider 1 is connected to the linear slider 2 via the gear with the gear ratio is rl : r2, the linear slider 2 moves by 2r2h " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003555_jfm.2012.483-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003555_jfm.2012.483-Figure1-1.png", "caption": "FIGURE 1. (a) Definition sketch in two-dimensional polar view and (b) sample deformation in three-dimensional perspective view. Disturbances \u03b71 and \u03b72 are constrained by the belt support extending over \u03b61 \u2261 cos \u03b81 6 cos \u03b8 6 \u03b62 \u2261 cos \u03b82. Lengths \u03b6 are scaled by R while lengths \u03b7 are left unscaled.", "texts": [ " Of interest for coating processes and microfluidic applications is the control of droplet motion induced by means of a harmonically driven substrate (Daniel et al. 2004; Noblin, Buguin & Brochard-Wyart 2004, 2005; Noblin, Kofman & Celestini 2009; Brunet, Eggers & Deegan 2009). In these studies, a deformable drop is constrained by the substrate on which the droplet rests. In this paper, we study the linear stability of two coupled spherical-cap surfaces made by constraining a spherical drop with a solid support (see figure 1 below). The solid support conforms to the spherical surface and extends between two latitudes, \u03b82 6 \u03b8 6 \u03b81, forming a \u2018spherical belt\u2019. The resulting free surface consists of two spherical caps (disconnected) which are coupled through the liquid beneath (connected). The interfaces are pinned at the edges of the belt and their motion is governed by integro-differential equations. The perspective is set by the question: To what extent can the resultant motions be understood as those of coupled harmonic oscillators", " Next, the problem is reformulated as two coupled oscillators using the exchange volume as an embedding parameter. This reduction is particularly effective in identifying eigenvalue near-multiplicities in the plane of constraints, which are found to correlate with the exchange volume. We conclude with some remarks on the computational results. Consider an unperturbed spherical droplet of radius R, constrained by a spherical belt given through the polar angle \u03b82 6 \u03b8 6 \u03b81 in spherical coordinates (r, \u03b8), as shown in the definition sketch (figure 1). The drop interface is disturbed by time-dependent free-surface perturbations, \u03b71(\u03b8, t) and \u03b72(\u03b8, t), which are assumed to be axisymmetric and small. No domain perturbation is needed for linear problems, thus the domain is the combination of the regions internal to and external to the static droplet: Di \u2261 {(r, \u03b8) | 0< r 6 R, 0 6 \u03b8 6 \u03c0}, (2.1a) De \u2261 {(r, \u03b8) |,R< r <\u221e, 0 6 \u03b8 6 \u03c0}. (2.1b) The interface separating the interior and exterior fluids (internal boundary) is given by the union of two free surfaces and one surface of support: \u2202Df 1 \u2261 {(r, \u03b8) | r = R, \u03b81 6 \u03b8 6 \u03c0}, (2", " Coupled-oscillator approximation In the development above, the boundary conditions on the free surface y(x) are applied in the final step of the procedure by incorporation into the function space (4.7). That is, the operator equation (3.7) is independent of pinning and volume-exchange constraints. In the previous section, we have seen how identifying the exchange volume aids in physical interpretation. In this section, we recast the problem to handle the volume exchange explicitly and show that this reformulation allows a reduction to coupled oscillators. Consider the domain \u22121 6 x 6 1 split into the two free surfaces \u2202Df 1 and \u2202Df 2 as in the definition sketch \u2202D \u2261 \u2202Df 1 \u222a \u2202Df 2 \u222a \u2202Ds (figure 1). Next, subject the two free surfaces to the following volume-exchange constraints:\u222b \u2202Df 1 y1 = C, \u222b \u2202Df 2 y2 =\u2212C. (5.2) The displaced volume C is exchanged between the interfaces, preserving the total volume. By introducing Lagrange multipliers \u00b51, \u00b52, these constraints can now be shifted to the operator equation (3.7) through the introduction of the disturbance energy (augmented energy functional), as defined in the Introduction of Part 2 (Bostwick & Steen 2013), F[y1, y2;\u00b51, \u00b52] = \u222b \u2202Df 1 (\u03bb1M[y1] + K[y1] + \u00b51)y1 + \u222b \u2202Df 2 (\u03bb2M[y2] + K[y2] + \u00b52)y2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003071_tmag.2008.2001660-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003071_tmag.2008.2001660-Figure2-1.png", "caption": "Fig. 2. Single phase SRM driving circuit.", "texts": [ " This molded rotor also shows good performance at high speeds but its manufacturing process is more complex and expensive than a conventional SRM rotor because at least one or two more processes have to be appended onto the original manufacturing process. This paper presents a novel switched reluctance motor rotor shape which has ribs between the rotor salient poles on the rotor outer surface. Fig. 1 shows the proposed rotor shape, which is an aerodynamically cylindrical rotor that is magnetically identical to a conventional rotor because the ribs are magnetically saturated while the stator teeth are facing them. Using this rotor, the windage loss can be reduced dramatically at high speed. Fig. 2 shows the single phase SRM driving circuit. Because the proposed rotor has ribs between the rotor salient poles, these ribs must be saturated while the stator poles overlap the ribs in order for the rotor to get reluctance torques. Thus, the proposed rotor cannot produce sufficient torque until the ribs are saturated and the resultant torque of the proposed rotor is slightly less than that of the conventional rotor. Although Digital Object Identifier 10.1109/TMAG.2008.2001660 the torque of the proposed rotor is less than that of a conventional rotor, the windage loss of the conventional rotor is much greater than that of the proposed rotor" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002464_iet-cta:20050518-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002464_iet-cta:20050518-Figure4-1.png", "caption": "Fig. 4 Diagram showing the thrust and CG offset scheme in the yaw plane", "texts": [ " From this, it was observed that along with the control moment 2TClC, one extra moment was generated along the ZX plane because of the small auxiliary control arm length (x1\u00fe y1) along X-axis. Thus, the disturbance moment due to thrust offset (x1) and CG offset (y1) along the pitch (ZX ) plane can be expressed as M1 \u00bc TC\u00f0x1 \u00fe y1\u00de \u00fe TC\u00f0x1 \u00fe y1\u00de \u00bc 2TC\u00f0x1 \u00fe y1\u00de Therefore w1 \u00bc M1 IYY \u00f08a\u00de Similarly, to calculate the disturbance due to thrust offset and CG offset along the yaw plane, consider the case where thrust offset is x2 and CG offset is y2, as shown in Fig. 4. From the figure, it is observed that the control arm length for the right nozzle reduces by an amount (x2\u00fe y2), where the left nozzle control arm length increases by an amount (x2\u00fe y2) causing an extra moment about the yaw axis. Thus, the disturbance moment due to thrust offset (x2) and CG offset (y2) along the yaw plane (YZ ) can be expressed as M2 \u00bc TC\u00f0ld \u00fe x2 \u00fe y2\u00de TC\u00f0ld x2 y2\u00de \u00bc 2TC\u00f0x2 \u00fe y2\u00de Therefore w2 \u00bc M2 IXX \u00f08b\u00de where IXX \u00bc moment of inertia about yaw axis and IXX \u00bc IYY. Putting all the values together, the state-space model of the launch vehicle considering rigid body, actuator and 306 slosh dynamics along the pitch axis, is given as _xp1 _xp2 _xp3 _xp4 _xp5 _xp6 2 666666664 3 777777775 \u00bc 0 1 0 0 0 0 0 0 0:1264 0 2:94 0 0 0 0 1 0 0 0 0 10:77 0:0031 19:47 0 0 0 0 0 0 1 0 0 0 0 985:96 43:96 2 666666664 3 777777775 xp1 xp2 xp3 xp4 xp5 xp6 2 666666664 3 777777775 \u00fe 0 0 0 0 0 985:96 2 666666664 3 777777775 dC1 \u00fe 0 1 0 2:3897 0 0 2 666666664 3 777777775 w1 \u00f09\u00de yp \u00bc 1 0 0 0 0 0 0 1 0 0 0 0 xp1 xp2 xp3 xp4 xp5 xp6 2 666666664 3 777777775 \u00f010\u00de where xp1 is the pitch angle and xp2 the pitch rate, xp3 is the pendulum angle along pitch plane, xp4 the rate of pendulum angle along pitch plane, xp5 the actuator deflection along pitch plane and xp6 is the actuator deflection rate along the pitch plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure3.7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure3.7-1.png", "caption": "Fig. 3.7 Structural sketch of an animal-driven mill", "texts": [ " A fixed member (frame) is always coded by number 1, and there are parallel slashes under it, as shown in Fig. 3.4j. 3. Figure 3.4k shows members i and j are the same member, and member k is connected to it. 4. If two unconnected members cross each other on a sketch, a half circle is used for connecting the two sides of the member on the cross point, as shown in Fig. 3.4l. 5. An uncertain joint is symbolized as a small solid black circle. Figure 3.1 shows the mechanism of an animal-driven mill. Its structural sketch is shown in Fig. 3.7. Figure 3.2 shows the mechanism of a wooden shield wagon. The structural sketches of the roller device and the shield device are shown in Figs. 3.8a\u2212b, respectively. 48 3 Mechanisms and Machines When several links are connected together by joints, they are said to form a link chain or just a chain in short. An (NL, NJ) chain refers to a chain with NL links and NJ joints. A walk of a chain is an alternating sequence of links and joints beginning and ending with links, in which each joint is connected to the two links immediately preceding and following it" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003749_17452759.2014.949406-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003749_17452759.2014.949406-Figure2-1.png", "caption": "Figure 2. (a) Multi-layer adjustable preheating device, and (b) temperature distribution in a 1000\u00d71000 mm2 platform.", "texts": [ " Nowadays, the single-layer preheating system is widely used in SLS machines, the structure of which is shown in Figure 1(a). However, when the platform of SLS machines is enlarged to the size of more than 1000 mm, the current single-layer preheating system is not able to realise a uniform temperature field in the whole platform as shown in Figure 1(b), thus leading to part deformation. To address this problem, we develop a multi-layer adjustable preheating system based on a self-adaptive fuzzy control technique as shown in Figure 2(a) and overcome the non-uniform distribution problem of the part bed temperature field of extended large powder beds. The simulation result in Figure 2(b) reveals the relatively more uniform temperature distribution in the whole platform. D ow nl oa de d by [ T ul an e U ni ve rs ity ] at 0 8: 51 2 7 Ja nu ar y 20 15 Meanwhile, we also developed a self-adaptive preheating technique to prevent deformation of the parts with overhanging structures. In this technique, overhang layers can be identified automatically, and the preheating temperature for these overhang layers will be elevated in order to limit the occurrence of deformation or reduce the degree of deformation" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003388_s10008-010-1184-8-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003388_s10008-010-1184-8-Figure1-1.png", "caption": "Fig. 1 Structure of quinine", "texts": [ " Bcaventou) in year 1820, was first used to treat malaria in Rome in 1631, its anti-malarial reaction mechanism is that steady deoxyribonucleic acid (DNA)-quinine compound is formed from the interaction of quinine and DNA in plasmodium, and then prevents plasmodium DNA replication and ribonucleic acid transcription; accordingly, it makes curative effects. In recent years, QN is widely used in industry, pharmacology, biochemistry, and so on. Firstly, due to the four chiral centers (carbon atoms in the third, fourth, eighth, and ninth position as shown in Fig. 1) in the molecule, QN can act as a chiral ligand and catalyst in anisomerous synthesis [23]. Secondly, quinine hydrochloride or sulfate has been utilized extensively in the cosmetics industry (shampoo) and the soft drinks especially as a flavoring agent [24]. Moreover, QN also has analgesic, antiseptic, and the muscle-relaxant properties, which was found effective as additional therapy for acquired immune deficiency syndrome [25], neurodermatitis, perennial rhinitis, and other viral diseases [26, 27]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure3-1.png", "caption": "Fig. 3. Tooth surface", "texts": [ " The envelope surface Cg is then obtained as the solution of sg \u00bc pg\u00f0f\u00de; fm\u00f0f\u00de \u00bc 0: \u00f05\u00de In Section 5, we will employ a surface intersection procedure and, since we seek for a closed shape intersection curve, we need to define the complete tooth surface including the lateral surfaces. These surfaces are portions of the blank cones and are bounded by the intersection between the tooth active flanks and the blank surface. Fig. 2 shows the complete tooth surface2 C which is subdivided into five patches. The patches Ct; Cf and Cb are the topland, the front cone and the back cone surface respectively. The two flank surfaces are identified by Cv and Cx for the concave and convex side. We define a unique tooth parametrization and we map C onto a plane as shown in Fig. 3. We have divided Cf and Cb into three parts each for convenience, in order to obtain a 3 3 patch grid. We remark that the complete tooth surface has C0 continuity over the intersection curves between the active flanks and the lateral surfaces. In the previous section, we have defined the complete tooth surface C subdividing it into nine patches. Later in this paper, we will employ a surface intersection procedure and hence we need a closed form tooth surface. For this reason we perform an interpolation of the nine patches of C thus assessing the nine patches into a unique framework", " ;mf 1: \u00f08\u00de For each cj we find the intersection of the transversal cone with the face cone determining the corresponding values nj; hj and /j by solving the following non-linear system: fh\u00f0f\u00de \u00bc 0; ft\u00f0f; cj\u00de \u00bc 0; fm\u00f0f\u00de \u00bc 0: 8><>: \u00f09\u00de The full sampling grid over the tooth flank surface is found by imposing nv equally spaced points along the tool profile for each transversal cone nij \u00bc i nj nv 1 \u00f010\u00de and solving for h and / the following non-linear system: ft\u00f0nij; h;/; cj\u00de \u00bc 0; fm\u00f0nij; h;/\u00de \u00bc 0: ( \u00f011\u00de The solution of (11) for each i; j, is denoted by fij \u00bc \u00f0nij; hij;/ij\u00de. Once the flank surfaces are sampled, the remaining seven patches are sampled accordingly in order to obtain a regular sampling grid in the nh-plane in Fig. 3. The selected sampling grids are shown in Fig. 4. For compatibility reasons the adjacent points between two adjacent grids are the same. The complete tooth surface sampling is then performed using an n m grid with n \u00bc nv \u00fe nt \u00fe nx 3; m \u00bc mf \u00fe 2ml 3: \u00f012\u00de We denote by Qij 2 E3 the generic sampled point with zero-based indexing i \u00bc 0;1; . . . ; n 1; j \u00bc 0;1; . . . ;m 1. Now we find an approximate closed form of C employing a Bspline interpolation of the nine patches. The resulting surface is parametrization" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001411_i1996-00485-9-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001411_i1996-00485-9-Figure1-1.png", "caption": "Figure 1. The effect of preheat treatment on the internal friction: Curve A as-received; curves B, C and D annealed at 656 K for 5, 60 and 120 min, respectively.", "texts": [ " Hence, the values of Q;' and M, should be calculated using equation (1) for low-frequency internal friction measurements with an inverted torsion pendulum, which is similar to the consideration made by Sinning for the Collette torsion pendulum [5]. The dimensions of the specimens studied were about 0.05 X 1.5 X 25 mm3 and the frequency ,was about 0.5 Hz at room temperature. The internal friction measurements were taken either during continuous heating at a rate of 5 K min\" or isothermal annealing at different temperatures. Other measuring techniques used were all similar to those reported earlier [6]. The effect of a preheat treatment on internal friction is shown in figure 1. Curve A was obtained from an as-received specimen for which three internal friction peaks, P1, P2 and P3, are observed at about 640K ( TPJ, 678 K ( TP2) and 807 K ( TP3) with a heating rate of 5 K min\" in the temperature range studied. Curves B, C and D were obtained from different specimens which had been preheat treated at 656 K for 5 , 60 and 120 min, respectively, and then cooled down to 300 K. Curve B shows that the height of P1 decreases but its position seems to be unaffected. Both the height and the temperature of P2 are lower than those of the as-received specimens, which behave quite differently from the peak P I " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003841_061407-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003841_061407-Figure3-1.png", "caption": "Figure 3. Schematic depicting the snapshot of how a single dipole changes orientation in local shear flow. (a) T-dipole adjusts its orientation according to the difference in the flow velocity along the direction transverse to the dipole. (b) A-dipole orients itself according to the difference in the flow velocity along the dipole.", "texts": [ " We view the problem of deriving the alignment equation as a self-contained problem starting from the complex potential in (9), where the location of the initial vortex pair is not given explicitly, only the position of the dipole center and its orientation. We could postulate, similarly to the finite dipole case above, that the dipole adjusts its orientation according to the difference in flow velocity between two points that lie along the line perpendicular (transverse) to the dipole orientation, as shown in figure 3(a). Alternatively, we could postulate that the change in orientation is due to the difference in flow velocity between two points that lie along the dipole orientation, see figure 3(b). Note that the location of these points does not correspond to the location of the vortex pair that we initially used to derive the complex potential (9) and, consequently, the equations governing the dipole position (12). The notation T-dipole and A-dipole is introduced to distinguish the orientation\u02bcs response to the (T) transverse versus (A) aligned difference in flow velocity, respectively. The orientation equations for the T- and A-dipoles are obtained as follows. First, take the velocity difference \u03c9 \u03c9\u02dc \u2212 \u02dcz z( ) ( )n n,r ,l where \u03f5= + \u03b1z z i en n,l i n and \u03f5= \u2212 \u03b1z z i en n,r i n for the T-dipole and \u03f5= \u2212 \u03b1z z en n,l i n and \u03f5= + \u03b1z z en n,r i n for the A-dipole. Project the difference in velocity onto the direction of the T-dipole and the direction perpendicular to the A-dipole, respectively. Then expand in \u03f5 and discard higher-order terms. To this end, one gets the following the orientation equations \u23a1 \u23a3 \u23a2\u23a2 \u23a4 \u23a6 \u23a5\u23a5\u2211\u03b1 \u03bc \u03c0 \u02d9 = \u00b1 \u2212 \u03b1 \u03b1 \u2260 i z z Re e e ( ) . (13)n j n N i i n j 2 3 n j Here, \u00b7[ ]Re ( ) denotes the real part of the expression in parentheses. The +( ) and \u2212( ) signs correspond to the T- and A-dipoles in figure 3(a) and (b), respectively. We emphasize that the equations of motion for the T-dipole are the small \u03f5 analog of (6) and (7). The smaller \u03f5 is, the more the two models are in agreement. Interestingly, the equations for the A-dipole are equivalent to those used in Desreumaux et al (2012) and Brotto et al (2013) to model the farfield interactions of micro-swimmers in a Hele-Shaw cell. We conclude this section by noting that it is convenient to normalize time and length using the time scale \u03c0\u03f5 \u03bc=T 2 3 and length scale \u03f5=L " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003517_s00170-012-4481-9-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003517_s00170-012-4481-9-Figure6-1.png", "caption": "Fig. 6 a, b Material-specific CAD models", "texts": [ " Attempts to fabricate the structures using these models with scarf and butt joints were unsuccessful as cracks developed visibly after the eighth layer of material deposition. Residual stresses resulting from uneven thermal expansion of the two materials at the transition joint may have caused the crack initiation and propagation. A defective sample with crack at the transition joint is shown in Fig. 5. The problem with cracks necessitated a change in the design of the material models to allow for interlock joints at all the material intersections as shown in Fig. 6. Figure 6a is a fork-shaped CAD model with arms extending through the triangular-shaped structure made of material A. The fork arms in Fig. 6a were made of 0.5-mm thickness. The arms were intended to separate Ti6Al4V/10 wt.% TiC composite material tension members (with material model shown in Fig. 6b) into three discrete partitions with 0.5-mm-thick Ti6Al4V inter-layers within the structures. This deposition method significantly reduced the occurrence of cracks. Fabricated structures were tested with an ASTM D 2344 shortbeam test fixture as illustrated in Fig. 7. The load at failure was obtained for analysis. Also, the mode of failure, especially the fracture location, was studied. 3 Results and discussion 3.1 Microstructures Some of the micrographs of deposited specimens are shown in Fig. 8" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.21-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.21-1.png", "caption": "Fig. 7.21 A prototype of a horizontal-wheel water-driven wind box", "texts": [], "surrounding_texts": [ "There are four devices with linkage mechanisms that can not be classified under the above mentioned three types, including Feng Xiang (\u98a8\u7bb1, a wind box), Shui Pai (\u6c34\u6392, a water-driven), Shui Ji Mian Luo (\u6c34\u64ca\u9eab\u7f85, a water-driven flour bolter), and Tie Nian Cao (\u9435\u78be\u69fd, an iron roller). Each of them is described below: 7.4.1 Feng Xiang (\u98a8\u7bb1, A Wind Box) Feng Xiang (\u98a8\u7bb1, a wind box) is a common device for blast metallurgy in ancient China as shown in Fig. 7.15a (Pan 1998). The operator pushes the piston of the device to increase air pressure, thereby opening and closing the valve. It can provide successively higher wind pressure and wind volume to enhance the intensity of the metal and increase production. Feng Xiang is a planar mechanism with two members and one joint, including a box as the frame (member 1, KF) and a pushing rod outside the box with the piston inside. The pushing rod is connected to the piston as an assembly (member 2, KP). 7.3 Grain Processing Devices 155 The piston is connected to the frame with a prismatic joint JPx. It is a Type I mechanism with a clear structure. Figure 7.15b shows the structural sketch. 7.4.2 Shui Pai (\u6c34\u6392, A Water-Driven Wind Box) Nong Shu\u300a\u8fb2\u66f8\u300b(Wang 1991) shows another device for blast metallurgy in ancient China namely Wo Lun Shi Shui Pai (\u81e5\u8f2a\u5f0f\u6c34\u6392, a horizontal-wheel water-driven wind box) as shown in Fig. 7.16. The function of the device is to transmit water power through its linkage mechanism for wind blasting. The structure and the transmission process are explained as follows: A vertical shaft contains the upper and lower horizontal wheels. One half of the lower wheel is installed under the water, and both wheels are fixed to the shaft. The upper wheel is encircled by a rope. The rope also passes around the wooden cylinder with a crank. The connected link is attached to the crank and the left bar. The horizontal shaft is connected to the left and right bars as an assembly. The long rod is connected to the right bar and the wooden fan of the blast furnace. When flowing water spins the lower wheel, through the drive of the vertical shaft, the upper wheel spins as well. The motion is transmitted via the thick rope to the wooden cylinder with a crank. The crank drives the connecting link and the left bar of the horizontal shaft. The right bar pushes the long rod to generate the oscillating motion of the wooden fan for blasting wind into the box (Liu 1962). There are many illogical or unclear parts in the illustration of the device, such as the rope (member 3) on the wooden cylinder (member 4) is too thick, the crank (member 4) is located in the wrong position, the connecting link (member 5) has unclear joints on both ends, and the long rod (member 7) passes over the left bar (member 6). Figure 7.17 shows the result of the reconstruction design by Liu Xianzhou (\u5289\u4ed9\u6d32, AD 1890\u20131975) (Liu 1962). Although some of the unclear structure 156 7 Linkage Mechanisms have been solved, such as, making the diameter of the rope thinner, adjusting the position of the crank, solving the problem of the long rod passing over the left bar, and assigning the two revolute joints on both ends of the connecting link. However, for the connecting link, how the two assigned revolute joints can transform the rotating motion of the crank into the oscillating motion of the left bar is still unclear. According to the classifying method described in Chap. 5, the device is a Type II mechanism with uncertain types of joints. The rectangular coordinate system is defined as shown in Fig. 7.17. The x-axis is defined as the direction of the axle of the horizontal shaft, the y-axis is defined as the direction of the diameter of the horizontal shaft, and the z-axis is based on the right-hand rule. The device can be divided into three parts: a rope and pulley mechanism, a spatial crank and rocker mechanism, and a planar double rocker mechanism (Hsiao et al. 2010). Each of them is explained below: 1. The rope and pulley mechanism includes the frame (member 1, KF), a vertical shaft with the upper and lower wheels (member 2, KU1), a rope (member 3, KT), and a wooden cylinder with a crank (member 4, KU2). The vertical shaft is connected to the frame (KF) and the rope (KT) with a revolute joint JRy and a wrapping joint JW, respectively. The wooden cylinder (KU2) is connected to the rope (KT) and the frame (KF) with a wrapping joint JW and a revolute joint JRy, respectively. Figure 7.18a shows the structural sketch. 2. The spatial crank and rocker mechanism includes the frame (member 1, KF), a wooden cylinder with a crank (member 4, KU2), a connecting link (member 5, KL1), and a horizontal shaft with the left and right bars (member 6, KL2). The wooden cylinder (KU2) is connected to the frame (KF) with a revolute joint JRy. The connecting link (KL1) is connected to the wooden cylinder (KU2) and the horizontal shaft (KL2) with uncertain joints J\u03b1 and J\u03b2, respectively. The 7.4 Other Devices 157 horizontal shaft (KL2) is connected to the frame (KF) with a revolute joint JRx. Figure 7.18b shows the structural sketch. 3. The planar double rock mechanism includes the frame (member 1, KF), a horizontal shaft with the left and right bars (member 6, KL2), a long rod (member 7, KL3), and a wooden fan as the output link (member 8, KL4). The horizontal shaft (KL2) is connected to the frame (KF) and the long rod (KL3) with revolute joints JRx. The wooden fan (KL4) is connected to the long rod (KL3) and the frame (KF) with revolute joints JRx. Figure 7.18c shows the structural sketch. The function of the spatial crank and rocker mechanism is to transform the rotating motion of the crank (member 4, KU2), through the drive of the connecting link (member 5, KL1), to the oscillating motion of the horizontal shaft (member 6, KL2). The two joints on both ends of the connecting link have multiple possible types that could achieve the function mentioned above. Considering the types and the directions of motion of the connecting link and the crank, uncertain joint J\u03b1 has three possible types: the first one is that the connecting link is connected to the crank with a revolute joint JRxy; the second one is that the connecting link is connected to the crank with a spherical joint JRxyz; and the last one is that the connecting link is connected to the crank with a joint JPzRxy. Considering the types and the directions of motion of the connecting link and the left bar, uncertain joint J\u03b2 has three possible types: the first is that the connecting link is connected to the left bar with a revolute joint JRxy; the second is that the connecting link is 158 7 Linkage Mechanisms connected to the left bar with a spherical joint JRxyz; and the third is that the connecting link is connected to the left bar with a joint JPzRxy. By assigning the possible joints J\u03b1(JRxy\u3001JRxyz\u3001 JPzRxy) and J\u03b2(JRxy\u3001JRxyz\u3001 JPzRxy) into the structural sketch shown in Fig. 7.18b, nine results are obtained. However, when joints J\u03b1 and J\u03b2 are of the same type JRxy simultaneously, the device would fail to move. By removing such a case, eight feasible designs of the horizontal-wheel water-driven wind box are obtained as shown in Figs. 7.19a\u2013h. Figures 7.20 and 7.21 show the simulation illustration and the prototype of the horizontal-wheel water-driven wind box according to the design shown in Fig. 7.19g. 7.4.3 Shui Ji Mian Luo (\u6c34\u64ca\u9eab\u7f85, A Water-Driven Flour Bolter) Shui Ji Mian Luo (\u6c34\u64ca\u9eab\u7f85, a water-driven flour bolter), as shown in Fig. 7.22a (Wang 1991), has the same function as Mian Luo (\u9eab\u7f85) described in Sect. 7.3. 7.4 Other Devices 159 160 7 Linkage Mechanisms The structure of Shui Ji Mian Luo is similar to the horizontal-wheel water-driven wind box, but it replaces the long rod, wooden fan, and blast furnace on the horizontal-wheel water-driven wind box into the connecting link with a floursieving screen, rope, and box, respectively. It is a Type II mechanism with uncertain types of joints. This device can be divided into three parts: a rope and pulley mechanism, a spatial crank and rocker mechanism, and a connecting link and rope mechanism. Shui Ji Mian Luo sieves grains through the reciprocating motion of the connecting link with a flour-sieving screen (member 7). Figures 7.22b1\u2013b8 show the feasible designs of the water-driven flour bolter. 7.4 Other Devices 161 7.4.4 Tie Nian Cao (\u9435\u78be\u69fd, An Iron Roller) Tie Nian Cao (\u9435\u78be\u69fd, an iron roller), as shown in Fig. 7.23a, is mainly used to grind cinnabar ore. People use the device to grind ore into powder for the red color dye (Pan 1998). The reconstruction design of Tie Nian Cao is described in Sect. 5.3. It is a (3, 3) planar mechanism and is a Type II mechanism with uncertain types of joints. Figures 7.23b1\u2013b3 show the feasible designs of the iron roller." ] }, { "image_filename": "designv10_13_0001767_gt2004-53965-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001767_gt2004-53965-Figure9-1.png", "caption": "Figure 9 Schematic of Rolling Contact Fatigue Tester", "texts": [ " Under normal conditions it is not uncommon for a bearing life value to extend past 100 million cycles, prohibiting normal run-to-failure testing. Accelerated life testing is one method used to rapidly generate many bearing failures. By subjecting a bearing to high speed, load, and/or temperature, rapid failure can be induced. There are many test apparatus used for accelerated life testing including ball and rod type test rigs. One such test rig is operated by UES, Inc at the Air Force Research Laboratory (AFRL) at Wright Patterson Air Force Base in Dayton, OH. A simple schematic of the device is shown in Figure 9 with dimensions given in millimeters. This rig consists of three 12.7 mm diameter balls contacting a 9.5 mm rotating central rod see Table 6 for dimensions. The three radially loaded balls are pressed against the central rotating rod by two tapered bearing races that are thrust loaded by three compressive springs. A photo of the test rig is shown in Figure 10. Notice the accelerometers mounted on the top of the unit. The larger accelerometer is used to automatically shutdown the test when a threshold vibration level is reached, the other measures vibration data for analysis" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003794_1.4006651-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003794_1.4006651-Figure12-1.png", "caption": "Fig. 12 Planetary gear carrier plate of a UH-60A Blackhawk helicopter: (a) top view of a healthy plate, and (b) view of a crack on one of the posts; the crack path is indicated by the arrows. (Original photographs published by Sahrmann [27]; reproduced with permission.)", "texts": [ " Relating sideband changes to the amount of relative shift between the planet gears can form the basis for detecting and localizing faults in planetary gear systems. As mentioned earlier, one such case inspired the research of this paper, namely, the development of cracks in the planet-gear mounting post of the planetary carrier plate of the main rotor transmission of a UH-60A Blackhawk helicopter. This problem has also been studied by Blunt and Keller [26], Keller and Grabill [1], Sahrmann [27], Wu et al. [28], Hines et al. [29], and others. An illustration of the component in question, designed for a system with five planet gears, is shown in Fig. 12. A crack near one of the planet-gear mounting posts of the carrier plate would be expected to reduce the post\u2019s stiffness, allowing for a relative shift of the corresponding planet gear. Depending on the crack length, the angular shift will vary, because greater crack lengths will further compromise the kinematic rigidity of the planetary gear system, which is in line with the earlier discussion about relative gear displacements in a planetary gear system. In the examples discussed in the following text, relative angular shifts of the planet gear near the crack with respect to the deflected planet gears away from the crack, are on the order of a few hundredths of a degree for a 2 in", " Different kinds of tests have been performed in these experimental sessions, but throughout the remainder of this paper, we will be referring to two sets of experiments for which vibration data was acquired from the main-rotor transmission of Sikorsky-brand helicopters, including the Blackhawk and Seahawk helicopter models. The transmission in question uses a planetary gearbox with Np\u00bc 5 planet gears and Nt\u00bc 228 teeth in the annulus gear. The first set of experiments involved the acquisition of vibration signals from planetary transmissions, either with a 3.25 in. crack in the carrier plate (as shown in Fig. 12) or with a \u201chealthy\u201d plate (i.e., without any crack). Furthermore, the cracked plate was used in a test cell for some experiments and also in an actual aircraft for some others. Similarly, vibrations from transmissions using healthy plates were acquired both from the same test cell and from operational helicopters. The test cell is a set up that uses actual aircraft engines to power the transmission components in an effort to better replicate the on-board behavior of the mechanical components tested" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001510_robot.1994.350969-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001510_robot.1994.350969-Figure1-1.png", "caption": "Figure 1: The Stewart Platform", "texts": [ " A first geometrical demonstration is provided which uses the concept of circularity and in a second proof we show that this problem is equivalent to find a system of two planar parallel manipulators with each 6 solutions to the forward kinematic problem. A geometrical construction is provided to construct such a system and a Stewart Platform with 12 configurations is exhibited. 1 Introduction In 1965 Stewart [16] describes a mechanism intended to be used as a flight simulator. This mechanism (figure 1) consists in a triangular mobile plate connected to the ground through three identical mechanisms. This mechanism is composed of a fixed !rti- cal beam Fi on which two articulated beams are connected. These beams are in turn linked to each other and one of the beam is connected to the mobile plate by a ball-and-socket joint at the point 8,. In each of these beams a linear actuator enables to change *Work partially supported by EEC projects POSSO and PROMOTION 10504729194 $03.00 0 1994 IEEE 2160 the beam length" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure8.4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure8.4-1.png", "caption": "Fig. 8.4 A water-driven multiple grinder and a water-driven, a A water-driven mill multiple grinder (\u6c34\u8f49\u9023\u78e8) (Shi 1981), b A water-driven mill (\u6c34\u7931) (Wang 1991) c Structural sketch", "texts": [ " Each of them is a mechanism with four members and five joints, including the frame (member 1, KF), a vertical gear with a long shaft and a vertical water wheel (member 2, KG1), a grinding gear in the middle (member 3, KG2), and a grinding gear located at the end (member 4, KG3). The vertical gear is connected to the frame with a revolute joint, denoted as JRx. The grinding gears are connected to the frame with revolute joints, denoted as JRy. The meshing activities among the gears can be considered as gear joints JG. Figure 8.4c shows the structural sketch. 174 8 Gear and Cam Mechanisms There are four water lifting devices with gears including Lv Zhuan Tong Che (\u9a62\u8f49 \u7b52\u8eca, a donkey-driven cylinder wheel), Niu Zhuan Fan Che (\u725b\u8f49\u7ffb\u8eca, a cowdriven paddle blade machine), Shui Zhuan Fan Che (\u6c34\u8f49\u7ffb\u8eca, a water-driven paddle blade machine), and Feng Zhuan Fan Che (\u98a8\u8f49\u7ffb\u8eca, a wind-driven paddle blade machine). Each of these devices is a Type I mechanism with a clear structure and is described below: 8.2.1 Lv Zhuan Tong Che (\u9a62\u8f49\u7b52\u8eca, A Donkey-Driven Cylinder Wheel) Lv Zhuan Tong Che (\u9a62\u8f49\u7b52\u8eca, a donkey-driven cylinder wheel) in the book Nong Shu\u300a\u8fb2\u66f8\u300b, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003753_3.2815-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003753_3.2815-Figure2-1.png", "caption": "Fig. 2 Skin-friction balance elevation mechanism.", "texts": [ "chematic plotting of this u0 \u2014 to curve is shown in Fig. 2. Thus, for a body with a smooth surface, the sonic point is located where to reaches maximum, or dto/ds equals zero. This is in accord with the sonic condition that the acceleration does not become infinite, which is explicitly applied when 8, \u00a3, and UQ are used as dependent variables. For a certain class of bodies having sonic shoulders (an example of such a shoulder is shown in Fig. 2), the sonic point is fixed where Uox = (7 - l)1/2(7 + 1)1/2. After the sonic line the flow undergoes an expansion; UQ changes from w0* to some higher value within an infinitesimally small distance. Thus, UQ in the UQ \u2014 to diagram jumps abruptly from w0* to UQ > UQ*. To demonstrate the preceding method let us choose a simple example, i.e., a circular cylinder in a supersonic stream with Moo = 4 and 7 = 1.4 and using a one-strip approximation. The numerical integration is carried out from the stagnation point through the sonic point into the supersonic region", " The disk-shaped floating element was mounted on a pair of leaf springs which allowed the element to be displaced by the skin-friction forces. The displacement was indicated by a linear variable differential transformer whose output was converted to drag force by means of dead weight calibrations made after each run. The disk diameter was 1 in., and the opening in the tunnel floor was 0.01 in. larger, resulting in an annular gap of 0.005 in. in which the element \"floated.\" The balance was mounted on a fixed-end support beam (Fig. 2) that restricted the balance motion to translation in a direction perpendicular to the wind-tunnel floor. This beam also served as a restoring spring to return the balance to the recessed position when the displacing force was removed. A drive mechanism was constructed which permitted suitably small increments of balance translation. This mechanism consisted of a differentially threaded lead screw and a cantilever beam. Displacement changes were made by means of a hand wheel attached to the lead screw. As seen in Fig. 2, the lead screw and beam permitted a relatively large rotation of the wheel for small balance translations, thus providing the necessary precision in setting balance misalignments. A correlation between hand-wheel rotation and balance trans- Received July 27, 1964; revision received September 21, 1964. This work was performed under sponsorship of U. S. Navy Bureau of Weapons, Contract No. NOrd-16498. * Research Engineer, Defense Research Laboratory; now with Norair Division, Northrop Corporation" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002172_978-1-4613-9030-5_43-Figure43.4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002172_978-1-4613-9030-5_43-Figure43.4-1.png", "caption": "Figure 43.4: The 8 DOF model used in the example of Section 43.4. (Reprinted with permission from Yamaguchi & Zajac, IEEE Trans. Biomed. Eng. 37. \u00a9 1990 - IEEE.)", "texts": [ " As applied to the control of musculoskeletal move ments, the reader is referred to Yamaguchi (1989). 43.4.2 Results The dynamic programming controls were dis cretized in levels of 10% activation, which is commensurate with the coarse nature of muscle fiber recruitment in typical FNS applications. Subject to the computational hardware limitations of a 1 MIP VAX I1n80 computer, only 8 DOF and 10 muscles were allowable even with suitable simplifications. Degrees of freedom were as signed according the hierarchy listed in Section 42.2.3, resulting in the 8 DOF, single-step model shown in Figure 43.4. 43. Yamaguchi; Performing Dynamic Gait Simulations 673 Highly damped, stiff linear springs were as sumed to exert forces preventing the heel of the right leg, and the heel and forefoot of the left leg, from falling through the assumed ground-plane. The use of such \"soft constraints\" (Hemami et al., 1975) enabled the model to be used for the single leg support and double-leg support phases of the step, as well as the transition in between. Assuming symmetry between left and right steps allowed the time interval of the analysis to be cut in half" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001735_robot.1995.525421-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001735_robot.1995.525421-Figure1-1.png", "caption": "Figure 1: A Serial- to-Parallel Manipulator", "texts": [ " This formulation addresses two cases: 1) open-chain serial-to-parallel systems, in which each end-effector is independent; and 2) open/closed-chain serial-to-parallel systems, in which some end-effectors grasp common objects. 3.1 Open-Chain Systems The Operational Space Formulation extends immediately to the case of a robot with multiple, independently moving arms. The operational space in this case is the superset of the domains of the operational space of each manipulator. - 1057 - For the system in Figure 1, for example, the operational space coordinates are L x4 1 and the corresponding Jacobian will be a vertical concatenation of the Jacobians for each end-effector: xj is the position and orientation of the ith endeffector, and Ji(q) is the basic Jacobian which yields the velocity of the ith end-effector, given q. q is the vector of generalized joint coordinates for the entire branching manipulator system. The kinetic energy matrix, A(q) , is still given by the form (J(q>A-l(q)JT(q))-l. For an open-chain system with N end-effectors, A(q) takes the intuitively revealing form: The inertial properties of each end-effector are not only dependent upon the end-effector's own configuration, but also upon the configuration of all other end-effectors in the system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002812_s0129065708001610-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002812_s0129065708001610-Figure3-1.png", "caption": "Fig. 3. The cart-pole balancing problem.", "texts": [ " Adaptive Fuzzy Control with Output Feedback for H\u221e Tracking of SISO Nonlinear Systems 313 be a suboptimal one. The Hamiltonian matrix H = [ A \u2212(2 r \u2212 1 \u03c12 )BBT \u2212Q \u2212AT ] (36) provides a criterion for the existence of a solution of the Riccati equation Eq. (23). A necessary condition for the solution of the algebraic Riccati equation to be a positive semi-definite symmetric matrix is that H has no imaginary eigenvalues.19 4. Simulation Tests 4.1. The cart-pole balancing problem The performance of the proposed adaptive fuzzy H\u221e controller was tested in the benchmark problem of cart-pole balancing (Fig. 3). The derivation of the state equations of the cart-pole system stems from the solution of an Euler-Lagrange equation. The model presented here follows,2,3 and considers only the dynamics of the pole (inverted pendulum). Denoting by \u03b8 the angle of the pole, m the mass of the pole, M the mass of the cart and l the length of the pole, one gets \u03b8\u0308 = mlsin(\u03b8)cos (\u03b8)\u03b8\u03072 \u2212 (m + M)gsin (\u03b8) mlcos2(\u03b8) \u2212 2(m + M)l + cos (\u03b8) mlcos2(\u03b8) \u2212 2(m + M)l u (37) Setting x1 = \u03b8 and x2 = \u03b8\u0307 the state equation of the cart-pole system is obtained:[ x\u03071 x\u03072 ] = [ 0 1 0 0 ] [ x1 x2 ] + [ 0 1 ] (f(x, t) + g(x, t)u + d\u0303) (38) y = [ 1 0 ] [ x1 x2 ] (39) where the nonlinear functions f(x, t) and g(x, t) are given by f(x, t) = mlx2 2 sin(x1) cos(x1)x2 1 \u2212 (M + m)gsin(x1) mlcos2(x1) \u2212 2(M + m)l (40) g(x, t) = cos (x1) mlcos2(x1) \u2212 2(m + M)l (41) The following parameter values were chosen: m = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003952_978-1-4471-6275-9-Figure11.7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003952_978-1-4471-6275-9-Figure11.7-1.png", "caption": "Fig. 11.7 a Robotic probe for in vivo mechanical testing, b boundary ring attached to volunteer\u2019s central cheek area. From Ref. [25]. Copyright 2013 by Elsevier. Adapted with permission", "texts": [ " The facial skin of the central cheek area of five subjects was characterized. Five additional locations on the face were also characterized for one of the subjects. To the best of our knowledge, these are the first reported values of in vivo facial pre-stresses in the literature. For the experiment, a region of interest on the subject\u2019s face was isolated with a boundary ring with inside diameter of 37.5mm. A micro-robot applied a rich set of deformation cycles at 0.1Hz to the skin surface via a 4mm cylindrical probe (Fig. 11.7). The probewas attached using liquid cyanoacrylate adhesive to the surface of the skin. A series of in-plane deformations was applied followed by a series of out-of-plane deformations. The probe position and reaction force were measured and recorded along with a time-stamp for each data point. For the numerical simulation, an FE simulation of the experiment was used in an optimization framework to find material parameters and pre-stresses that best-fit the model data to the experimental data from each subject and each facial region" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001877_s0022-0728(00)00177-7-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001877_s0022-0728(00)00177-7-Figure10-1.png", "caption": "Fig. 10. Cyclic voltammograms of a poly 3 electrode (G3=7.0 nmol cm\u22122) in deaerated 0.1 M phosphate buffer (pH 7) (a) in the absence of cyanide and (b) in the presence of 5 mM cyanide (repeated potential scans); scan rate=100 mV s\u22121.", "texts": [ " The possibility to use poly 3 film for the specific molecular recognition of cyanide ions in water was also investigated. Effectively, the affinity of cyanide for the iron deuteroporphyrin in conjunction with the sensitivity and selectivity of the electrochemical methods may provide a selective sensor for the determination of cyanide in complex aqueous media. For this purpose, a poly 3 electrode (G3=2.2 nmol cm\u22122) was transferred in deaerated phosphate buffer (pH 7) and cycled between 0 and \u22121.2 V versus Ag AgCl (Fig. 10). In the absence of cyanide, the cyclic voltammogram reveals no peak system in the negative potential range. In contrast, the addition of cyanide (5 mM) induces the appearance and the growth of the reversible peak system at E1/2= \u22120.54 V. This reduction wave may be most likely due to the FeIII/II couple redox with cyanide as the axial ligand, thus illustrating the potential recognition properties of such modified electrodes towards cyanide. In this report, we have described the successful electrogeneration of conducting polypyrrole films functionalized by Cu(II), Mn(III) and Fe(III) deuteroporphyrins" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003863_iscid.2014.56-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003863_iscid.2014.56-Figure1-1.png", "caption": "Figure 1. Standard form of Denavit-Hartenberg notation.", "texts": [ "56 26 transform matrix, spatial geometric relationship between links and the reference frame is described by recursion-iteration, and the kinematics equation of the robot is built. In classic D-H method, there are four parameters for each link. Two describe the link itself, and two describe the link\u2019s connection to a neighboring link. To facilitate describing the location of each link we affix a coordinate frame to it\u2014frame i is attached to link i. The convention for affixing frame to link is as follows (Fig. 1): The Z-axis of frame {i-1}, called 1iZ , is coincident with the joint axis i. The iX axis is directed along the normal from 1iZ to iZ and for intersecting axes is parallel to 1i iZ Z [8]. The link and joint parameters may be summarized as: link length ia , the offset distance between the 1iZ and iZ axes along the iX axis; link twist i , the angle from the 1iZ axis to the iZ axis about the iX axis; link offset id , the distance from the origin of frame {i 1} to the iX axis along the 1iZ axis; joint angle i , the angle between the 1iX and iX axes about the 1iZ axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002090_0022-1759(88)90351-1-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002090_0022-1759(88)90351-1-Figure2-1.png", "caption": "Fig. 2. The electrochemical cell. A two-compartment electrochemical cell was used, constructed from pyrex glass. The chamber on the left contained the working electrode of platinum or NMP\u00f7/TCNQ - together with a platinum counter electrode; it was filled with a solution of enzyme amplifier at working strength (containing ferricyanide as appropriate) to which solutions containing NAD + were added. The chamber on the right contained the silver/silver chloride reference and was filled with a solution of enzyme amplifier at working strength. The chambers are connected by a luggin capillary.", "texts": [ " lc) employs ferricyanide as a mediator between the N A D + / N A D H cycle and a platinum electrode. Preliminary measurements were conducted with the enzyme amplifier alone in order to optimise the system for amperometric measurements before its application to a typical immunoassay. An electrochemical cell with a volume of 2 ml was used; the cell contained the working electrode, a counter electrode of platinum wire, a silver/silver chloride reference connected by a luggin capillary and a magnetic stirring bar (Fig. 2). Initially the cell was filled with a mixture of diethanolamine and phosphate buffers containing ethanol and the enzymes alcohol dehydrogenase and diaphorase. Aliquots of NAD \u00f7 were then added, followed by a brief mix with the magnetic stirring bar to ensure an even distribution throughout the cell. For the experiments carried out with the N M P \u00f7 / T C N Q - 157 electrode the stirring bar was then stopped and measurements were made in a quiescent solution. In contrast, in the cell containing the platinum working electrode and ferricyanide mediator the stirring was continued throughout the experiment" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001384_978-94-017-2925-3-Figure4.2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001384_978-94-017-2925-3-Figure4.2-1.png", "caption": "Fig. 4.2. Mooney chamber and rotor.", "texts": [ " As this is an apparent contradiction in terms, the results should always be referred to as the plasticity number. This method is described in detail in ASTM Standard D 926-83.4 Rotary Shear Instruments. A number of Plastometers of this type were developed during the rapid growth of the rubber industry in the 1920-1940 period. However, the shearing disk viscometer developed by the late Melvin Mooney5 has become the \"standard\" of the rubber industry. In this instrument a flat, serrated disc rotates in a mass of rubber contained in a grooved cavity under pressure, as shown in Fig. 4.2. The torque required to rotate the disc at 2 rpm at a fixed temperature (usually 100\u00b0C) is defined as the Mooney viscos ity.* The Mooney viscometer, which is widely used as a laboratory control instru ment, operates at an average shear rate of about 2 s -I. This is an order of magnitude higher than compression plastometers but still within the range of compression molding operation. (The modem instrument and its operation is described in detail in ASTM Standard D 1646-81.)6 This procedure involves placing a square of sample on either side of the rotor and filling the cavity by pneumatically lowering the top platen" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001345_1.1349420-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001345_1.1349420-Figure1-1.png", "caption": "Fig. 1 Gear model \u201edegrees of freedom are represented on gear only\u2026", "texts": [ " 123, SEPTEMBER 2001 Copyright rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/20 qualitative results of the first section and analyze the detection sensitivity, it is concluded by the analysis of some experimental and numerical signals. Following Velex and Maatar @8#, a pinion and a gear of a pair can be assimilated to two rigid cylinders with all six degrees of freedom ~3 translations and 3 rotations! linked by a set of elemental independent stiffnesses distributed along all instantaneous contact lines on the base plane ~Fig. 1!. Assembly with classical finite elements and lumped parameter elements leads to the following equations of motion: @M #$ x\u0308%1@C#$ x\u0307%1@Ka#$x%1@K~ t ,$x%!#$x% 5$F0%1$F~ e\u0308*~ t !!%1$G~ t ,$x%!% (1) where $F( e\u0308*(t))% includes all inertial effects produced by unsteady rigid-body rotations ~stems from kinetic energy! and $G(t ,$x%)% accounts for the influence of normal tooth flank deviations on strain energy. Denoting k(h ,t), the mesh stiffness per unit contact length associated with a potential point of contact of co-ordinates (h ,t), the analytical expressions of the two quantities which largely control the geared system dynamic response to tooth defects are: @K~ t ,$x%", "org/about-asme/terms-of-use Downloaded From: http://mechanicaldesi where L(t) is the nominal contact length at t and $V(h ,t)% is the so-called structure vector which relates the degree-of-freedom vector $x% to contact deflections D(h ,t) and tooth shape deviations e(h ,t) by: D~h ,t !5$V~h ,t !%\u2022$x%2de~h ,t ! (4a) with de(h ,t)5e(h ,t)2e*(t), e*(t) is the maximum of e(h ,t) at t. $V(h ,t)% is nil except for the components corresponding to the pinion-gear degrees of freedom. If these degrees of freedom are ranked as u ,v ,w ,f ,c ,u for pinion and gear successively ~see Fig. 1 for the definition!, the restriction of $V(h ,t)% to non-zero components reads: $V*~h ,t !%5~sinbb ,cosbb\u2022sinap ,cosbb\u2022cosap ,2Rb1\u2022sinbb \u2022sinap2~zM\u2022cosbb2xMsinbb!\u2022cosap ,2Rb1 \u2022sinbb\u2022cosap1~zM\u2022cosbb2xM\u2022sinbb!\u2022sinap ,Rb1 \u2022cosbb ,2sinbb ,2cosbb\u2022sinap ,2cosbb\u2022cosap , 2Rb2\u2022sinbb\u2022sinap1~zM\u2022cosbb1~T1T22xM ! \u2022sinbb!\u2022cosap ,2Rb2\u2022sinbb\u2022cosap2~zM\u2022cosbb l Design gn.asmedigitalcollection.asme.org/ on 01/27/20 1~T1T22xM !\u2022sinbb!\u2022sinap ,Rb2\u2022cosbb! (4b) with Rb1 ,Rb2, base radii of pinion and gear, xM ,zM , coordinates of M (h ,t) on the base plane ~Fig. 1!, T1 and T2, limits of the base plane ~Fig. 1!. The mesh stiffness per unit contact length k(h ,t) accounts for contact, tooth bending, base compliance and the normal contact condition at any potential point of contact is introduced by the unit Heaviside function H(D(h ,t)) which is zero when contact is lost and equal to one otherwise. Upon assuming that no-load transmission error is not altered by defects of small dimensions ~compared to the tooth face!, the contributions of k localized tooth defects can be extracted from global deviations and the equivalent normal deviations defined in ~4", " of experimental accelerations recorded on the CETIM test-rig in Fig. Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F 4 @13# together with the corresponding numerical simulations to assess the analytical indications which, to a certain extent, are supporting the M.C.I. method principles. Experimental timesignals were sensed by an accelerometer mounted on the test-rig housing close to one of the pinion bearings and compared with simulated accelerations at node 1 ~Fig. 1!. Figure 7~a! shows the experimental acceleration signal and corresponding M.C.I. function at the beginning of the test ~day 2! which can be considered as the reference for no-defect ~or negligible defect! conditions. It can be observed in Fig. 7~b! that 2 M.C.I. minima clearly emerge for longer tests ~day 11 for the present example! while detection from the original acceleration measurements looks more uncertain. This observation has been validated by visual inspection of the pinion and gear which revealed a large spalling on pinion tooth #16 and a less pronounced defect on pinion tooth #2 ~Fig", " $F0% 5 nominal load vector $F( e\u0308*(t))% 5 inertial force vector due to no-load transmission error e*(t) $G(t ,$x%)% 5 non-linear second member generated by mounting errors and tooth shape deviations from ideal involutes @Ka# 5 shaft, coupling, bearing, . . . constant stiffness matrix 430 \u00d5 Vol. 123, SEPTEMBER 2001 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/20 @K(t ,$x%)# 5 time-varying possibly nonlinear gear stiffness matrix L 5 normalized defect extent in the profile direction ~Fig. 2! @M # ,@C# 5 mass, damping matrices Pk(h) 5 defect depth s(t),S(y), s\u0303 5 respectively time signal, Fourier transform and cepstrum xM ,zM 5 coordinates of a potential point of contact on the base plane ~Fig. 1! bb 5 base helix angle D(h ,t) 5 deflection at a point of contact de(h ,t)5e(h ,t)2maxt$e(h ,t)% 5 equivalent normal deviation @1# Alattass, M., 1994, \u2018\u2018Maintenance des machines tournantes. Signature des de\u0301- fauts d\u2019engrenages droits et he\u0301lico\u0131\u0308daux,\u2019\u2019 Ph.D. dissertation, INSA de Lyon, p. 198. @2# McFadden, P. D., 1986, \u2018\u2018Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation of the Meshing Vibration,\u2019\u2019 ASME J. Vibr. Acoust. 108, pp. 165\u2013170. @3# Choy, F. K., Polyshchuk, V., Zakrajsek, J" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003718_s12008-012-0163-y-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003718_s12008-012-0163-y-Figure12-1.png", "caption": "Fig. 12 Relative displacements", "texts": [ " The simulated topographies are compared to the ones obtained with certified methods used in machine tool manufacturer software. The result is illustrated in Fig. 11. The distances between the two generated surfaces are lower than one micrometer. The minor gap can be due to slight numerical errors or rounding approximations in tabulating the modified roll coefficients. 3 Tooth contact analysis 3.1 Meshing simulation The relative displacement of the two parts is taken into account in the meshing simulation algorithm. As shown in Fig. 12, it is made of four independent components: the axial displacement of the master part, the axial displacement of the slave part, the offset displacement also called hypoid displacement and the shaft angle. They can be set in the design process. However, they are generally due to mounting inaccuracies, under load distortions or bearing displacements. They are zero if the pitch apexes of the two parts are coincident. The sign of their value and the displacement direction are linked according to the Gleason rule. The axial displacement value is negative if the part moves toward the pitch apex. It is positive in the opposite direction. With the configuration represented in Fig. 12, the hypoid displacement value is negative if the gear moves down or else it is positive. The signs are opposite if the hand of spiral is changed. The shaft angle displacement value is negative if the two parts get closer or else it is positive. The geometric and kinematic behavior of the contact pattern depends on the tooth flank topographies and their relative displacement. The tooth flank generation process previously explained is the core of the meshing simulation algorithm shown in Fig. 13" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003159_tcpmt.2010.2100970-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003159_tcpmt.2010.2100970-Figure4-1.png", "caption": "Fig. 4. Chemical and topological definition of binding sites. a) Superficial site, b) recessed site, c) mesa site, d) trenched site. All type of sites can in principle be used in combination with both liquid and gaseous hosting fluids. However, wetting contrast between spacer and sites is necessary only when using liquids as hosting fluids, though it is still beneficial for the latter scenario. Relative dimensions are out of scale.", "texts": [ " The fluid couple and the chemical properties of sites and spacer must allow high selectivity during the fluid coating step. Since the position of the lubricant lenses on the substrate signals to the approaching parts the presence of an available binding site, the lubricant must wet the substrate only in correspondence with the binding sites. Standard binding sites are defined by patterning thin films deposited on the surface of the substrates, and then eventually functionalizing them to tune their wetting properties [Fig. 4(a)]. While easy to fabricate, the performance of this type of sites\u2014which we will call superficial in the following\u2014may not be optimal. 1) Selectivity: When using superficial binding sites, if the wetting contrast between binding sites and spacer is not sufficiently high, coating selectivity is compromised. The comparison of water CAs measured on site and spacer surfaces provides a rough estimate of their wetting contrast. In our experience, a difference of more than 60 between the respective advancing CAs is sufficient to allow selective fluid coating", ", satellite lenses [28]). The issue of false positive assemblies is the more important the smaller the dimensions of the parts to be assembled. High surface wetting contrast is fundamental when using liquids as hosting fluids. Conversely, in dry SA the topology of the sites can additionally help selectively confining the lubricant lenses. Particularly, mesa sites (i.e., sites placed above the level of the spacer; adopted e.g., by Koyanagi et al. [40]) are surrounded by a ring of air, which repels water [Fig. 4(c)] [76]. The same result may be achieved by realizing trenches around the sites [Fig. 4(d)]. Anyway, unless chemical conditioning is also employed, dip-coating is not effective on surfaces having only topologically-defined binding sites. Moreover, superficial, mesa and trenched sites alone do not provide coating conformality (discussed below). 2) Conformality: It is important that the lubricant coat the binding sites conformally, i.e., it has to reproduce its geometrical features with high fidelity. This is necessary to fully exploit the alignment features of the geometrical patterns of the sites", " Given the uniform chemical character of the sites, the coating performance depends on the fluid coating process (see next paragraph) and on the geometrical features of the sites themselves. Particularly, sharp corners are not wet by the lubricant\u2014except in the case in which there is complete wetting (i.e., CA close to 0 ) between the lubricant and the surface. The extent of lubricant wetting into geometric features depends, more generally, on the overall geometry of the site. We demonstrated that by engraving the binding sites into even very shallow cavities [i.e., by surrounding the perimeter of the superficial sites with a thin wetting sidewall, as shown in Fig. 4(b)], the perfectly-conformal coating of arbitrary planar site geometries can be easily and systematically achieved (Fig. 5) [18]. We remark that the thickness of the sidewall of such recessed sites (e.g., of the order of few micrometers) may well be comparable with the thickness of standard substrate passivation layers, so that its integration into production lines\u2019 process flows may be simple\u2014it could require only a single additional etch step. Moreover, this simple topological enhancement makes the dip-coating process more robust against non-ideal conditioning of the binding sites" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002305_an9911600997-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002305_an9911600997-Figure3-1.png", "caption": "Fig. 3 Dependence of the current on A, the enzyme loading and B, the solution pH. Response to 5 x rnol dm-3 theophylline. Other conditions as in Fig. 1", "texts": [ " The maximum therapeutic level of theophylline, encountered in cases of toxicity, 3.3 x 10-4 rnol dm-3 (reference 6), therefore falls within the linear portion. Coated electrodes, containing no enzyme (only the cofactor within the Nafion film), yielded no response to theophylline (not shown). The senshhity 07 the theophyhe electrode is affected by various preparation and operational conditions. As expected, the response increases rapidly with an increase in the enzyme surface loading [between 25 and 60 mU (Fig. 3, curve A)]; a levelling-off is observed for higher loadings. The solution pH also has a profound effect on the sensitivity (Fig. 3, curve B). The current increases with the pH over the range 5.4-6.9, with a gradual decrease at higher values. Fig. 4, curve A, shows the dependence of the theophylline response on the concentration of the redox-mediating hexacyanoferrate(Ir1) ion. The response increases rapidly with the hexacyanoferrate(iI1) concentration up to 1 X 10-3 rnol dm-3, after which it starts to level off. The small response observed in the absence of hexacyanoferrate(ir1) is attributed to the direct oxidation of the 1,3-dimethyluric acid product [see eqn" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001450_cdc.1994.411345-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001450_cdc.1994.411345-Figure1-1.png", "caption": "Figure 1: The car is traveling along a circle of radius r . For axle-to-axle hitching, the trailer is shown t o exponentially converge, with respect to the arc length traveled by the lead car. to a circle with the same center.", "texts": [ " In addition, we compute an upper bound on the amount the trailer and kingpin hitch deviate from the car\u2019s path is calculated for the two special cases: 1. the transition from a straight line to an arc of a circle of radius T 2. the transition from an arc of a circle of radius r to a straight line. We will see that the bound for the first case is computed from the off-tracking of the kingpin hitch and the bound for the second case is derived from the trailer\u2019s offtracking. In the following, \u201cpath of the car\u2019\u2019 and \u201cpath of the trailer\u201d refer to the trajectory of the center of the respective axle. We now consider Figure 1 where the lead car in a twoaxle system is traveling counterclockwise around a circular path of radius r . We want to show that the trailer exponentially converges to a steady-state circular path with the same center (when the vehicle travels clockwise, the derivation is similar). Before we attempt this, coordinates must be assigned to the system. The center of the car\u2019s axle, A, is assigned to be the origin of an z - y moving frame. A fixed reference frame is attached to the center, C, of the circle", " The stable position has the trailer at point D with ADC a right triangle. If we restrict 141 5 ~ / 2 , i.e., where the trailer avoids the jack-knife positions, then 4 never reaches the unstable equilibrium. Under this assumption, we also have T > L. The case with r = L is unrealistic since this corresponds to R = 0 and d = -7r/2, i.e., the trailer is sitting at the center of the circle (see example section, case (c)). Theorem 5 FOT T > L, R ezponentially Converges to the steady state value R* = lim ~ ( a ) = & C G . ( 7 ) a-W Proof. Referring to Figure 1, the law of cosines on the triangle ABC gives R = (T' + L2 + 2 ~ L s i n 4 ) ~ ' ~ . (8) The derivative of equation (8) with respect to a is (9) From equation ( 8 ) , we have 4 = arcsin f 2 ? r n n > O , which can be used to write the left hand side of equation (9) as a function of R: - - R2 - rz + L2 JM dR dcu 4RL2 - _ = f ( R ) ' (10) The equilibrium points of the nonlinear equation (10) are Rei = d ~ ' - L' Rez = r f L . R,I corresponds t o the angle q5 = d8 of equation (4) and. Rt2 corresponds to the angle 4 = fm" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003601_s10846-012-9731-4-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003601_s10846-012-9731-4-Figure1-1.png", "caption": "Fig. 1 Earth fixed reference frame and body fixed reference frame", "texts": [ " In this paper, we present the motion model of an eight rotors helicopter whose blades lie on the same plane and are uniformly spaced in a circumference. The higher payload capacity and the possibility to continue operating despite the failure of a pair of rotors are the main advantages of this configuration. Also, a nonlinear controller is designed based on the sliding mode technique and evaluated through numerical simulations. 2 Mathematical Model 2.1 Kinematics Equations The rotorcraft used in this study has the form shown on Fig. 1. The dynamic model of this helicopter is basically the model of a rigid body evolving in 3D and subject to a main force and three moments. Let I = {Ix, Iy, Iz} denote an earth fixed reference frame as shown in Fig. 1. This system is a right-handed orthogonal axis-system with the origin at the helicopter\u2019s center of gravity at the beginning of the motion. Under simplifying conditions I is considered the inertial reference frame. On the other hand, let B = {Bx,By,Bz} be a body-fixed reference frame which is a right handed orthogonal system with the origin at the helicopter\u2019s center of mass. It is assumed that the axes of the B-frame coincide with the body principal axes of inertia. The orientation of the helicopter is given by a rotation R : B \u2192 I where R \u2208 SO(3) is an orthogonal rotation matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002763_s1063784208020096-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002763_s1063784208020096-Figure2-1.png", "caption": "Fig. 2. Friction tests by the (a) bushing-on-shaft scheme (shown is the surface area with deformation relief on which the microhardness was measured) and (b) end-seal scheme (part of the bushing from which specimens for transmission electron microscopy were cut out is shown). Arrows show the surface areas on which the microhardness was measured.", "texts": [ " Friction raises the temperature of the surface layer, and carbon atoms occupy lattice defects in the austenite. This may create microzones with an elevated content of carbon, form Mn\u2013C complexes, increase microstresses in the lattice, and eventually improve strength. Yet, the above information does not explain in full measure the intriguing tribological behavior of H13 steel; therefore, this steel remains an object of much research. Experiments were carried out on a 2168 UMT-1 setup under the conditions of dry friction for \u201cbushingon-shaft\u201d and \u201cend seal\u201d matings (Fig. 2). In both cases, bushings (test objects) made of H13 steel had an inner diameter of 31.1 mm, an outer diameter of 39.0 mm, and a height of 10.0 mm. Counterbodies were a shaft 31 mm in diameter made of 42KhM4F steel thermally treated to a microhardness of 56 HRC (in the first case) and a disk made of U10 hardened steel (62 HRC), against which the end face of the bushing was pressed 206 TECHNICAL PHYSICS Vol. 53 No. 2 2008 KOLUBAEV et al. (in the second case). Besides, 20-mm-high cylinders of diameter 15 and 20 mm were tested in the \u201cdisk\u2013pin\u201d scheme", " After friction tests, X-ray phase analysis was carried out on a DRON-UM1 diffractometer using the sliding beam technique, which made it possible to identify the structure of a layer up to 5 \u00b5 m thick. The fine structure and phase composition of Hadfield steel were examined by scanning and diffraction electron microscopy methods (thin foil and replica techniques) using Philips SEM 515 and \u00c9M-125K electron microscopes. Foils were prepared by electrolytic thinning of plates cut from a piece of the bushing parallel to the friction surface (Fig. 2b). To keep the defect structure, thinning was accomplished on the side opposite to the friction surface. The structure and phase composition of the wear surface and wear particles were examined. As-prepared Hadfield steel had a homogeneous structure, as revealed by metallographic analysis and X-ray diffraction analysis (Fig. 3, curve 1 ). After friction tests at a pressure of 0.8 MPa and a slip velocity of 0.3 m/s, noticeable changes in the phase composition of the surface layer were not observed (Fig", " Thus, X-ray diffraction analysis and electron microscopy studies of the Hadfield steel friction surface performed by scanning and diffraction electron microscopy methods indicate that dry friction over the steel surface gives rise to a thin layer containing \u03b3 iron and 208 TECHNICAL PHYSICS Vol. 53 No. 2 2008 KOLUBAEV et al. MnFe 2 O 4 and (MnFe) 2 O 3 oxides. The underlying layer is nanocrystalline and represents iron-based \u03b3 solid solution. The character of Hadfield steel deformation at friction can be judged from the deformation relief (Fig. 6) on the end face of the bushings in the bushing-on-shaft test scheme (the area of the end face where the deformation relief was analyzed is shown in Fig. 2a). The tests were carried out at a slip velocity of 0.02 m/s. The end faces of the bushings were carefully polished. Low test pressures (from 1 to 4 MPa) could not cause such a deformation under static conditions. At friction, however, slip bands typical of H13 steel deformation are observed at large depths (2\u20133 mm). The deformation relief at such depths can be explained only under the assumption of elastic wave excitation (see Introduction). These waves are excited when the rubbing elements seize up at contact spots and the friction process loses stability, as indicated by sound generation", " 2 2008 EFFECT OF ELASTIC EXCITATIONS 209 the friction unit. The latter vibrations show up as acoustic waves perceived by the man or as the low-frequency vibrations of the friction unit. It was noted [17] that the friction-induced increase in the hardness of the H13 surface layer is related to deformation. It is of interest to correlate the depth of deformation hardening with the hardness distribution in the strained layer. The microhardness was measured on the rough (relief) end face and on the longitudinal cross section (see Fig. 2b). In both cases, the microhardness values were the same, which means that the defect substructure on the end face and inside of the bushing is also the same. Indeed, the electron microscopic depth profiling of the material structure [13] gives the defect distribution similar to that observed on the end face of the bushings (Fig. 6). Figure 7 demonstrates the variation of the microhardness on the cross section with distance from the friction surface. As the pressure in the friction unit grows, the thickness of the deformed layer determined from these curves increases insignificantly" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001596_icsmc.1996.571368-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001596_icsmc.1996.571368-Figure5-1.png", "caption": "Fig. 5: Representation of Joint Angle", "texts": [ " When the ZMP exists within the domain of the support surface, the contact between the ground and the support leg is stable. where p z m p denotes a position of ZMP. S denotes a domain of the support surface. This - 1496 - condition indicates that no rotation around the edges of the foot occurs. 0 Boundary Condition for Continuous Walking For continuous Walking, the boundary conditions of reference trajectory are given where T is the period of one step. This condition represents the continuity of joint angles. The places of joint angles are shown in Fig.5. 0 Free Leg Condition The free leg should not be contact to the ground during it moves. collision between free leg a i d ground. The waist plate is parallel to the ground. 4 Dynamic Equation of Biped Locomotion Robot We calculate the torque of each actuator to generate natural motion. The natural motion needs less energy and skillfully uses dynamic effect. The dynamic equation of the biped locomotion robot is given M ( e ) e + q e , e) + G(e) = T (6) where 8 is a joint variable vector, T is a joint to'rque vector" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003721_icmech.2011.5971317-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003721_icmech.2011.5971317-Figure4-1.png", "caption": "Fig. 4 Free body diagram of the moving platform", "texts": [ " 0i )2 ]} -Q)ui Q)vi o;} +[ro/i x ( lui + Idi) rold\u00b7Oi + Cs (ro/i -ro)\u00b7 0i + Cu ro/i . 0i}[Ci x 0d1i (Ci \u00b70;)] (36) (37) Details for Sj' Sdj and SUi are given in the Appendix I. In order to derive Equations (36) and (37) the rules below have been used: axb=ab; (a\u00b7b)c=(caT)b; (38) where a is the skew symmetric matrix associated with the vector a = [ax ay az]T. In order to determine Facti' we need to use the equations of motion for the platform which are derived in the next section. B. Dynamics of the moving Plaiform The free body diagram of the moving platform is illustrated in Fig. 4. The vectors F ext and Mext are respectively the external force and moment in frame {P}, and can be expressed in frame {W} by the rotation transformation. Considering Fig. 4, the force equilibrium equation can be obtained as follows: \u2022. 6 mpXg -mpG-RFext + LFj =0 i\ufffdl (39) where m p is the mass of the platform and the payload. Xg is the linear acceleration of the mass centre of both the moving platform and the payload, which can be obtained as: (40) where r is the mass centre position vector of the moving platform (including payload) in the base frame. Substituting Equations (35) and (40) into Equation (39) and using the rules (38), gives: 6 .. 6 (mpl3 + LQJX-(mpr + LQjqJa+mp[rox(roxr)-G) i=1 i=1 6 6 + LVj = RFat + LFactjnj i=1 i=1 where 13 denotes the 3 x 3 identity matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002196_j.cma.2004.07.031-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002196_j.cma.2004.07.031-Figure2-1.png", "caption": "Fig. 2. Illustration of chosen point for local synthesis: (i) t2 tangent to the path of contact on gear tooth surface; (ii) eq and es are the unit vectors of principal directions; (iii) g2 is the parameter of orientation of t2 with respect to es.", "texts": [ " The algorithm of TCA may be formulated as follows: (i) Meshing of tooth surfaces R1 and R2 being in point tangency is considered. (ii) The coincidence of position vectors and surface unit normals at the point of tangency M and in the neighborhood of M (Fig. 1) has to be provided at any instant. (iii) In the case wherein the development of TCA is complemented with local synthesis, the location of the mean contact point M and information about certain parameters of synthesis (such as 2a and angle g2) has to be provided in addition (Fig. 2). (1) A gear drive with tooth surfaces being in point tangency is considered. (2) The basic machine tool settings applied for pinion and gear generations are known. (3) However, a TCA computer program for simulation of meshing of the gear drive is not available. (4) The location of the mean contact point M used for development of TCA is not known either. The goal is the development of a TCA computer program with the restrictions mentioned above. It is obvious that achievement of such a goal requires: (i) derivation of tooth surfaces R1 and R2 generated by applied machine-tool settings; (ii) determination of guess values for the mean contact point M and the location of M; (iii) development of TCA for simulation of meshing of generated surfaces R1 and R2", " To achieve the convergence of the system of non-linear equations to the expected solution (real contact point), the researcher has to provide a guess solution close enough to the exact solution, to initiate the search. Such a guess solution is provided by a set of guess values for the unknowns of the system. If the set of guess values has not been carefully determined, the numerical algorithm may terminate far from the expected root corresponding to the real contact point of the pinion and gear tooth surfaces. However, wherein the algorithm of local synthesis has been used ahead designing of the gear drive, the mean contact point is chosen on the gear tooth surface (see Fig. 2) and the pinion tooth surface is determined applying the desired conditions of meshing. Then, the surface parameters at the mean contact point become known in the beginning of the process of computations for TCA. We consider the case of design of a gear drive for the conditions that differ from those mentioned above: (i) the local synthesis has not been applied and the mean contact point has not been assigned ahead in the process of synthesis of the gear drive; (ii) the researcher is provided only with the machine-tool settings applied for generation of the gears; (iii) however the development of TCA is required" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.11-1.png", "caption": "Fig. 4.11 Mills, a A water-driven mill (Lu and Hua 2000), b An animal-driven mill (Lu and Hua 2000)", "texts": [ " This device is a planar mechanism consisting of three members (1, 2, and 3), two revolute joints (JRx and JRy), and one gear joint (JG). Therefore, NL = 3, CpRx = 2, NJRx = 1, CpRy = 2, NJRy = 1, CpG = 1, and NJG = 1. Based on Eq. (3.1), the number of degrees of freedom, Fp, of this mechanism is: Fp \u00bc 3 NL 1\u00f0 \u00de NJRxCpRx \u00fe NJRyCpRy \u00fe NJGCpG \u00bc 3\u00f0 \u00de 3 1\u00f0 \u00de 1\u00f0 \u00de 2\u00f0 \u00de \u00fe 1\u00f0 \u00de 2\u00f0 \u00de \u00fe 1\u00f0 \u00de 1\u00f0 \u00de\u00bd \u00bc 6 5 \u00bc 1 A mill is also a food-processing device to remove the chaff of grains. According to different power sources, it needs to use a gear train to transfer the transmission direction. Figure 4.11a shows a water-driven mill that was driven by a vertical 74 4 Ancient Chinese Machinery water wheel to produce an output rotation in the vertical direction through a gear mechanism (Lu and Hua 2000). Figure 4.11b shows a horizontal animal-driven mill that was driven by animals to produce an output rotation in the same direction through a simple gear train (Lu and Hua 2000). The book Nong Shu\u300a\u8fb2\u66f8\u300b (Wang 1968) has a detailed introduction of a waterdriven and a cow-driven paddle blade machines that use gears to transmit power. Furthermore, the cow-driven paddle blade machine can also be seen in paintings of the Tang Dynasty (AD 618\u2013907). The books Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b (Pan 1998) and Nong Zheng Quan Shu\u300a\u8fb2\u653f\u5168\u66f8\u300b (Xu 1968) also have discussions about this device" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure12-1.png", "caption": "Fig. 12. Bearing contact and contact stresses for the pinion (left) and gear (right) of helical gear drive of design A1 at the instantaneous contact point 9 when errors of alignment \u0394H2=\u0394V2=0.025\u00b0 occur.", "texts": [ " Elements C3D8I [11] of first order (enhanced by incompatiblemodes to improve their bending behavior) have been used to form the finite-element mesh. The total number of elements is 59372 with 67572 nodes. The material is steel with the properties of Young's module E=2.068\u22c5105 MPa and Poisson's ratio 0.29. A torque of 1600 Nm has been applied to the pinion. Figs. 12, 13, and 14 show the bearing contact and contact stresses for the pinion and the gear of a helical gear drive of design A1, A2 and A3, respectively, when errors of alignment \u0394H2=\u0394V2=0.025\u00b0 occur. An area of high contact stresses is observed in Fig. 12 due to a linealtype contact. Such area of high contact stresses is avoided for cases of design A2 and A3 where the contact is localized. Fig. 15 represents the evolution of contact and bending stresses for the pinion of a helical gear drive for the following cases of design: (i) conventional design (case A1), (ii) partial crowning (case A2), and (iii) total crowning (case A3). For all cases, errors of alignment \u0394H2=\u0394V2=0.025\u00b0 have been considered. Conventional design yields very high contact stresses due to the theoretical lineal-type contact shifted to edge contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001711_rob.10081-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001711_rob.10081-Figure2-1.png", "caption": "Figure 2. (a) Coordinate frames for medical robot calibration, and (b) the relationships among all transformations.", "texts": [ " In this paper, a method of base and tool calibration is developed for our medical parallel manipulator system. The calibration is carried out with an op- tical position sensor, OPTOTRAK 3020 (product of Northern Digital Inc., Canada). An error model for the base and tool transformation was first constructed. The pose measurement technology with OPTOTRAK 3020 was then described. Lastly, the simulation and experiment results were presented to demonstrate the effectiveness of the method. The parallel manipulator with an end-effector attached to its mobile platform can be abstracted as a model shown in Figure 2. In the model, a hexapod has legs mounted on the base plate at ball joints B1 to B6 , arranged in pairs, B1 B6 , B2 B3 and B4 B5 . The set of all six legs is arranged symmetrically on the base, on a circle with a radius rb . For the six joints A1 to A6 on the mobile platform, the geometric configuration is similar to that of base platform. Two coordinate frames are set up for the parallel manipulator. The fixed frame B Xb ,Yb ,Zb is located in the center of the base platform. The mobile frame A Xa ,Ya ,Za is located in the center of mobile platform" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003663_tmag.2012.2221134-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003663_tmag.2012.2221134-Figure3-1.png", "caption": "Fig. 3. Top and side view of the division of the corner segment of the rectangular coil.", "texts": [ " Since all the corner segments have the same calculation method, Segment is selected as an example. Fig. 2 shows the model of Segment and a new local coordinate system. The local coordinate system is denoted with the superscript , and the expressions of the orientation transformation matrix [5], [7] between the two coordinate systems are shown as follows. (The rotation angles are: To Segment , , , and . To Segment , , , and . To Segment , , , and . To Segment , , , and . Where , , and are the rotations about the -, -, and -axes, respectively.) (9) (10) As shown in Fig. 3, the Segment is divided into parts by using the composite numerical integral rule, the force and torque exerted on each part can be calculated analytically by using the Newton-Leibniz formula. Therefore, each part is divided by using a cubical mesh, and every mesh element can be considered as a rectangular bracket. The calculation model of a rectangular bracket in Segment is shown in Fig. 4, and the force and torque in Segment can be calculated as follows: (11) (12) where (13) (14) (15) and where is the volume of the Segment of the coil, is the projection of the Segment on the plane, the vector is the origin point of the local coordinate system in the global coordinate system, is the upper limit of the integral" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003759_10426914.2014.930963-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003759_10426914.2014.930963-Figure1-1.png", "caption": "FIGURE 1.\u2014Finite element model, showing (a) the geometry and (b) the mesh.", "texts": [ " The focus is to predict the resulting microstructure and particularly the grain size distribution in the build. The thermal model is to calculate the 3D transienttemperature distribution arising from laser deposition of multilayered Inconel 718 powder during a single-line build on a mild steel substrate with the process parameters defined in Table 1. The deposition process followed a continuous and unidirectional movement of the laser beam, such that at the end of one layer, the laser beam has to start at the beginning of the next layer. The physical mapping of the model as shown in Fig. 1(a) constitutes a 10-layer wall of Inconel 718, centrally built on the mild steel substrate of 25 25 12mm3. The wall width is approximately 2.31mm and height of approximately 5.58mm, with each of the 10 layers in the wall height assumed of equal, 0.558mm height. Also indicated in Fig. 1(a) is the adopted coordinate system, in which the origin is fixed at the center of the substrate top surface. The FE mesh shown in Fig. 1(b) illustrates the descretization of the geometry into the elemental form. The mesh was designed such that the clad wall and the region around the clad wall were assigned the fine mesh, and the regions away from the clad were assigned comparatively coarser mesh. Between the deposited clad and the substrate, perfect thermal bonding was modeled owing to the strong metallurgical bond and insignificant porosity formed at optimal parameters. Calculation of the temperature distribution was based on the solution to heat conduction equation" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001806_j.electacta.2003.08.024-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001806_j.electacta.2003.08.024-Figure8-1.png", "caption": "Fig. 8. Electrochemical stability of NiPCNF/CCE (prepared by two-step sol\u2013gel method) arising from repetitive potential over the range of \u22120.25 to 1 V after preparation (a) and (b\u2013e) 25, 50, 100 and 200th cycles, respectively, potential scan rate is 100 mV s\u22121.", "texts": [ " Since the modified CCE had several major advantages, such as high sensitivity, low detection limit, good stability at wide pH range for long time and fast response to sulfide oxidation, it can be used as an amperometric sensor in flow or chromatographic systems. Since much attention should be paid to the stability of CMEs, the stability of the NiPCNF-modified CCE was tested by cyclic voltammetry. The peak height and peak potential of the surface immobilized film by cycling the electrode potential over the range 0.2\u20131 V have remained nearly unchanged, and the amount of degradation after 200 cycles in electrolyte solution with scan rate 100 mV s\u22121 was less than 5% (Fig. 8). However, the storage stability of the CMEs was very good as the electrodes were found to have reserved their initial activity for more than 3 months when kept at ambient conditions. Only a 4% leakage was found when the electrode was immersed in 0.1 M phosphate buffer (pH 7) for 48 h. The high stability of the modified electrode is related to the chemical and mechanical stability of the silicate matrix, the limited wetting section controlled by methyl group, the strong adsorption of NiPCNF on graphite powder and the possible interaction between the NiPCNF and silanol groups" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5-1.png", "caption": "Fig. 5 . 6 . Transien t behavio r of temperatur e gradient .", "texts": [ " Futur e perspective s for rapi d solidificatio n laser processin g 292 Reference s 294 1. Introduction The interaction between a laser beam and a metal or alloy surface is controlled by a number of variables including the wavelength of the radiation, the incident power density, and the available interaction time. For the case of a continuous, convectively cooled, high-power C 0 2 laser with a wavelength of 10.6 jum the laser-material interaction as a function of incident power density and available interaction time is as shown in fig. 5.1. A particular combination of power density and interaction time defines a specific operational regime within the \"interaction spectrum\", and each operational regime results in the occurrence of a unique materials-processing effect. In order of increasing power density, the various processing effects include transformation hardening (Hella and Gnanamathu 1976, Breinan et al. 1976a), bulk surface alloying and cladding (Gnanamuthu and Locke 1976), deep penetration welding (Brown and Banas 1971, Breinan et al. 1975) and the LASERGLAZE\u2122 effect (Breinan et al. 1976b,c), drilling of holes and metal removal effects (Voorhis 1964), and laser shock-hardening (Fairand et al. 1972, 1974). In fig. 5.1, it may be noted that the materials-processing effects, or operational regimes, are clustered along a diagonal running from \"high power density-short interaction time\" to \"low power density-long interaction time\". This is a consequence of several factors. First, the very high power densities necessary for explosive material vaporization effects, such as those producing shock hardening and drilling, are obtained with pulsed lasers and thus are available only for short times. Repeated pulses generally are not additive", " Also, the quantities of energy necessary to generate the various thermal effects ranging from heating to \"red heat\" up to vaporization do not differ in energy consumed by more than two orders of magnitude. Thus, it is not primarily the quantity of energy applied, but the rate and power density at which it is applied, which gives rise to the specific materials-processing effect desired. Since both power density and interaction time span six or seven orders of magnitude, the diagonal is the primary area of interest. A study of fig. 5.1 should make this clear, along with the fact that, since the range of power densities extends far above that produced by most common thermal sources, even the long interaction time laser processes are in fact quite rapid, with interaction times rarely approaching 0.1 s. The LASERGLAZE\u2122 process was conceived to utilize the high power densities available from focused laser beams in conjunction with short interaction times to effectively limit thermal effects to a shallow surface layer (Breinan et al", " (5-9) T(x,t) = dT/dt = Y ( \u00b1\\X/1 E^XA^t)^Y_L_SL\\X/2 e-[ xA\u0302 yY^Y \u2022Althoug h th e mathematic s of thi s analysi s d o no t includ e actua l melting , th e abov e descriptio n is stil l accurat e in term s of th e temperatur e histor y of th e meltin g process . 244 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Rear first necessary to establish the position of the interface as a function of time. This was accomplished by selecting, in the time interval \u00f4 ' - \u00f4 (during which solidification occurs), a number of discrete points, ti9 and at each point solving eq. (5.6) iteratively for the depth, si9 at which the temperature equals r m e l t . This procedure is illustrated schematically in fig. 5.2. Fig. 5.2 shows the temperature history at different depths in the material. The upper curve shows how the temperature at the surface starts at the initial temperature T0, begins to melt at time / a , and reaches a temperature of Tmax at time \u00f4 when energy input ceases. The surface temperature then falls until it reaches 7 m e l t at time \u00f4 ' at which time solidification is complete. The lower curve of fig. 5.2 shows the temperature history at depth d. The time \u00f4 at which the temperature at this depth reaches Tmch defines the required heating time. The middle curve shows the temperature history at an intermediate depth st which melts at time tb and solidifies at time It is seen that solidification occurs during the time interval \u00f4 ' - \u00f4 over which the surface temperature varies from Tmax to !Tm e l t. Fig. 5.3 shows temperature profiles in the material at selected times, in effect, a cross-plot of fig. 5.2. The upper curve illustrates the temperature profile at time \u00f4 when the material at the surface has reached a temperature of r m a x and the material at depth d has just melted. The middle curve shows the temperature profile at a subsequent time t{ when the material has Fig . 5.2. Variatio n of temperatur e with tim e at selected mel t depths . T m a x > \\ ^ - S U R F A C E, D E P TH = 0 X X ^ O < D E P TH S i planar front growth. On the other hand, increasing the cooling rate, or gradient-rate product, since T=GR, gives rise to shorter diffusion paths and finer structures. In other words, the ratio G/R controls the character of the microstructure, whereas the product GR determines the scale of the microstructure. Fig. 5.11 shows some examples of microstructural changes in (100) oriented superalloy single crystals, after various laser surface melting treatments. As indicated, a relatively deep penetration \"homogenizing\" pass is applied to the surface prior to the application of one or more superimposed laserglazing passes. Without such an homogenizing treatment the glazed layers exhibit incomplete dissolution of MC carbide particles, and other refractory constituents in the initial microstructure. In all cases, laserglazing produces epitaxial growth in the resolidified layers, accompanied by a marked refinement in the scale of the microstructure. Within a given recast layer, the scale of the dendritic structure remains reasonably constant, although it undergoes obvious discontinuous changes with varying melt depth. This is to be expected, since fig. 5.7 shows that the cooling rate, which controls the scale of the microstructure, is relatively constant, after an initial transient stage. Close examination of the glazed layers under higher magnification also reveals significant changes in the character of the microstructure within a given melt zone. For example, fig. 5.12 shows a very thin layer of plane-front solidified material in contact with the melt/substrate interface. Moreover, with increasing distance from this interface, the structure becomes cellular (one-dimensional dendritic), cellular-dendritic, and finally fully dendritic. Such changes are clearly in accord with the calculated high initial G/R ratio, and its rapid fall-off as solidification proceeds towards the free surface, fig. 5.9. The second pass in fig. 5.12 shows the cellular growth extends to the free surface, which is indicative of a persistently high G/R ratio in this high cooling rate regime of solidification. Fig. 5.12 shows that the region encompassing the second pass, including a thin heat-affected zone (HAZ) in the underlying first pass does not etch-up as well as the rest of the material. The reason for this is that the cooling rate is fast enough to prevent precipitation of \u00e3 ' particles only in the second pass and its associated HAZ. Apparently, in the HAZ, the elimination of the \u00e3 ' particles is a consequence of much faster kinetics for the solution of the \u00e3 ' phase than for its precipitation. The region including the HAZ and the second pass exhibits a striking difference in size, distribution and morphology of MC carbides. In the second pass, the carbides occur as small platelets, unidirectionally aligned within the cellular boundaries. On the other hand, in the first pass, the more massive carbide platelets are distrib- Rapid solidification laser processing 257 258 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Kear Rapid solidification laser processing 259 uted in an irregular manner, following the tortuous paths defined by the interstices of a fully-developed dendritic structure (fig. 5.13). The step change in the scale of the carbides is going from the first pass to the second pass is to be expected, since their formation is governed by the degree of segregation, and scale of the interdendritic interstices, both of which diminish with increasing cooling rate. In laserglazing, the crystalline substrate necessarily is in intimate contact with the melt. This raises the question as to whether the presence of favorable nucleation sites for crystallization would prevent the undercooling necessary to achieve an amorphous structure. Test experiments on a low melting point eutectic alloy (Pd-4.2Cu-5.1Si) demonstrated that, under appropriate conditions of fast cooling, this alloy can be made amorphous by laserglazing. In this instance, the melted layer ( - 0 . 1 8 mm maximum in 260 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Kear thickness (was obtained with an incident power density of 6X 106 W/cm 2 and an interaction time of 3 x l 0 ~ 5 s. As shown in fig. 5.14, within the melted region, there are no discernible microstructural features, in contrast to the eutectic structure in the substrate. One manifestation of the noncrystalline amorphous nature of the material is the symmetrical pattern of curved shear bands formed around hardness indentations, fig. 5.14d. Another manifestation is the vein-like character of the fracture surface, fig. 5.14c. Confirmatory evidence was obtained by TEM; the thin foils had a speckled appearance and the electron diffraction pattern showed diffuse rings, fig. 5.14b. Similar tests carried out on low melting point TLP-type eutectic alloys gave no clear indication of an amorphous transition by laserglazing, even in Rapid solidification laser processing 261 thin sections ( ~ 0.025 mm) that had cooled at high rates. More typically, the result of laserglazing these alloys was the formation of either an ultra-fine dendritic structure, with varying degrees of phase decomposition, or an extremely fine eutectic structure. Examples of these two types of behavior were found in the three boron-rich nickel-base alloys shown in fig. 5.15. Alloy (b) has the preferred composition for TLP-21, an interlayer composition used for diffusion bonding of Udimet 700. Alloys (a) and (c) are, respectively, low and high boron modifications of this multicomponent alloy. As indicated in fig. 5.15, increasing the boron in this series of alloys increases the volume fraction of y + N i 3 B eutectic, at the expense of primary \u00e3. Alloy (c) contains a mixture of two primary phases (\u00e3 + M 3 B 2 ) , whereas alloys (a) and (b) contain only one primary phase (\u00e3). All three alloys responded to laserglazing by forming featureless regions, at least under the optical microscope. Fig. 5.16 shows a series of overlapping passes in alloy (a), whereas fig. 5.17 shows a series of parallel passes with varying interaction time in alloy (c). The most sharply distinguishing feature of these two examples is the extensive cracking in alloy (c), and the absence of cracking in (a). This has nothing to do with variations in laser melting parameters, but merely reflects the different strengths and ductilities of the substrates and laser melted regions. Both the substrate and laser melted regions are very hard in alloy (c), whereas they are much softer in alloy (a). Thus, cracking is avoided, or at least reduced, in (a) because of the ability of the material to undergo plastic deformation in response to the thermal 262 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Kear c m / s . (d) To p surfac e showin g cracking . fig. 5.15(a) (VH N of melte d regio n = 600 k g / m m 2 ) . Rapid solidification laser processing 263 strains developed during quenching. In (c), cracking typically took the form of a single longitudinal mid-rib crack, with many short transverse cracks, fig. 5.17d. Alloy (b) also showed extensive cracking, which is consistent with the presence in this alloy of a large volume fraction of the hard, brittle \u00e3 + N i 3 B eutectic, comparable with that in alloy (c). Although the microstructures of the laser melted regions in these alloys appeared to have no structure, close examination by SEM and TEM techniques showed that this was not the case. On the contrary, alloys (a) and (b) were composed of an ultra-fine dendritic structure, fig. 5.18a, whereas alloy (c) possessed a remarkable ultra-fine filamentary eutectic structure, fig. 5.18b. A general refinement in these structures was noted with decreasing thickness of the melt zone, as would be expected in view of the higher cooling rates. Under polarized light, with the material in the as-polished condition, a columnar grain structure became visible in alloy (c), fig. 5,19. Using this technique, it was shown that the superposition of two or more melting passes resulted in epitaxial growth, albeit with a thin transition layer of what appeared to be a spheroidized structure. A similar transition microstructure also occurs quite naturally at the interfaces between the melt zone and its substrate. In alloys (a) and (b), the transition zone was quite wide, reflecting the wide melting range of TLP-21 (1060\u00b0C solidus-1200\u00b0C liquidus). Selective melting of the eutectic, leaving the dendrites unmelted, can be seen in the transition zone of alloy (a) in fig. 5.16. Laserglazing experiments performed on eutectic superalloys yield a broad spectrum of microstructures, which differ mainly in degree, or scale, rather 264 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Kear than in kind. Under high cooling rates, the microstructure is typically composed of a fairly uniform distribution of MC carbide particles embedded in a solid solution matrix phase, similar to that found in splat quenched material. Under more moderate cooling rates, the structure is distinctly dendritic, with the MC carbide phase concentrated exclusively in the interdendritic interstices. These two representative types of microstructures are shown for a CoTaC-type eutectic alloy in fig. 5.20. In the laser melted pass at 3 kW-51 cm/s, fig. 5.20a, the MC carbide phase occurs as discrete particles having a platelet morphology, whereas in the laser melted pass at the lower cooling rate (3 kW-12.7 cm/s) fig. 5.20b, the carbide phase has a filamentary morphology. The very fine scale of the filamentary eutectic structure can be appreciated by reference to fig. 5.20c, which shows the transition zone between the melted layer and its substrate; the latter was solidified under carefully controlled plane front conditions. This abrupt change in microstructure is illustrative of the sensitivity of the microstructure in this alloy to solidification conditions. It is well known that a high ratio of temperature gradient to solidification rate, (G/R), is a prerequisite for coupled growth in this multicomponent, monovariant eutectic alloy. Another noteworthy feature with respect to the response of these alloys to laserglazing was the absence of cracking, both in the melts and in the substrate heat affected zones", " Apparently, in these alloys, the solid solution matrix phase is sufficiently ductile as to ensure the necessary plastic accommodation in both surface melt layer and substrate during cooling from the melt. Rapid solidification laser processing 265 of Ta C carbide s varie s with loca l solidificatio n conditions . In contrast to the behavior of the carbide eutectic alloys, laser melting of the \u00e3 /\u00e3 ' -\u00e4 eutectic did not give a well organized, fine-scale lamellar eutectic structure. In this case, the typical result was the development of a fine dendritic structure, fig. 5.21a, with some precipitation of \u00e3 ' and \u00e4, but particularly the \u00e4 phase. Moreover, cracking was observed in the laser melted regions, especially in the deeper melts, but not in the substrate. Evidently in this case, plastic deformation occurs quite freely in the substrate during fast cooling, and evidence for this is shown in fig. 5.21b. On the other hand, deformation is inhibited in the laser melted regions because of precipitation of \u00e3 ' and \u00e4, which sharply increases the strength of the material. Laserglazed \u00e3 ' precipitation hardened superalloys invariably exhibit dendritic growth. Direct evidence has been obtained by SEM observations on 266 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Rear the external surface along the center line of the melt, where, due to inadequate melt feeding, the dendritic structure stood out in sharp relief. Observations made in this way showed that the scale of the dendritic structure decreased with increasing cooling rate, or decreasing laser melt depth, as would be expected, fig. 5.22. Comparable structures were observed in transverse metallographic sections; moreover, strong indications were found for regrowth of certain, if not all, of the partially-consumed substrate grains residing at the original melt/substrate interface. In monocrystalline material, such oriented overgrowth, or epitaxial growth, appeared to be particularly favored on a cube oriented substrate, apparently because the normal to the substrate coincides with a fast-growing dendrite direction; namely (001). This is shown for PWA 1418L in fig. 5.11. The rather dramatic refinement in the scale of the dendritic structure following the first melting pass at 4 kW-3.5 cm/s is quite obvious in this micrograph. A further refinement in structure occurs in the two additional overlapping surface melting passes just visible at the top of the micrograph. When misoriented grains are present in the epitaxial zone, fig. 5.11 indicates that these tend to be eliminated by faster growth of the more favorably oriented cube-oriented grains. Misoriented grains are frequently nucleated in the vicinity of \u00e3 / \u00e3 ' eutectic located at the melt/substrate interface. Examination of the various interfaces in the laser melted material, fig. 5.11b, shows that in the first pass the structure develops by cellular growth, and as the gradient falls off this degenerates into cellular dendritic and finally dendritic growth. In the second and third passes, the cellular dendritic mode of solidification is predominant. The relationship of these structures to the heat flow considerations developed in section 1, has been explained in detail above. Rapid solidification laser processing 267 Most alloy steels in the normal heat-treated condition contain a fine dispersion of one or more carbides", " K ear J^SAJO 3I3UTS aq; 2\u00f5\u00ec\u00c2\u00e8\u00f4\u00f1\u00e1\u00f4 'ASojoqdjoui ajupuap ui saSireqo SSOJDE snonupuoo ziv spireq dqs Rapid solidification laser processing 269 glazing experiments included 440C, M-50, M-2, and 4350. The primary goal was to determine the influence of cooling rate on measured Vickers hardness in the glazed material, including both melt and heat affected zones. In the glazed condition, alloy 440C exhibited a dendritic structure of Cr-stabilized ferrite, interspersed with thin sheets of carbide in the interdendritic region (fig. 5.25). The melt zone was associated with a broad heat-affected zone (HAZ) in the substrate. The dark-etching band in the substrate appeared to define the lower limit of microstructural changes in the HAZ. The measured hardness in the melt zone (dendritic structure) was HV ~ 470 kg/mm 2 . This is to be compared with HV ~ 825 kg/mm 2 for the carbidestrengthened martensitic substrate. So in this case the effect of glazing was to produce softening of the material. On the other hand, the region of the HAZ just below the melt interface was somewhat harder (HV ~ 900 270 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Kear Rapid solidification laser processing 271 kg/mm 2 ) than the substrate. It appears, therefore, that laser heat treatment, rather than melting, is the approach to take to further harden this particular material. Alloy M-50 also showed evidence of dendritic growth in the melt zone (fig. 5.26), albeit in a form more difficult to detect than in alloy 440C. Moreover, in marked contrast to the behavior of alloy 440C, M-2 shows some improvement in hardness in the melt zone compared with the substrate: HV ~ 850 versus 800 kg/mm 2 , respectively. The heat affected zone also showed a small increase in hardness. Since the original carbide particles in the substrate are still visible in the HAZ (fig. 5.26), it seems likely that the high hardness of this zone is caused by the formation of fine martensite, not resolvable under the optical microscope. A similar situation exists in the melt zone, except that the fine martensite forms within the dendritic structure, probably interspersed with fine carbides. It is noteworthy that the original coarse carbide particles readily dissolve in the melt during glazing. In double or multiple passes, a clear indication was obtained of the formation of martensite (or bainite) on a coarse scale, accompanied by some reduction in hardness. In complete contrast to 440C and M-50, alloy M-2 showed no indications of a dendritic structure. On the contrary, the melt zone appeared to be composed of a fine-grained, two-phase structure (fig. 5.27). Hardness measurements showed this two-phase structure to be softer (HV ~ 600 kg/mm 2 ) than the substrate (HV ~1000 kg/mm 2 ) , at least in the region of a single pass. In the HAZ associated with a double pass, hardness values as high as HV ~ 900 kg/mm 2 were recorded, demonstrating that the strength in the Rapid solidification laser processing 273 melt zone can be recovered by a post-glazing heat treatment. Possibly, this occurs as a result of the formation of tempered martensite. Recently it has been shown that the as-glazed, two-phase structure is composed of ferrite and austenite, but not martensite", " Illustrative of the significant changes that can be induced by glazing of such materials is the behavior of spheroidized annealed alloy 4350 (HV ~ 450 kg/mm 2 ). Laserglazing of the material produces a dramatic harden- 274 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Rear ing, with the maximum hardness corresponding to the thinnest glazing passes or, in other words, the fastest cooling rates. Typical hardness values range from 800 to 850 kg/mm 2 , depending on cooling rate. In the HAZs associated with double or multiple passes (fig. 5.28) the hardness is much reduced compared with that in the as-glazed material, but still higher than that of the annealed substrate. There is thus significant evidence that rapid chilling of alloys by laserglazing gives rise to a variety of interesting and potentially useful metallurgical microstructures. In addition, consideration of these structures and the means by which they are produced has highlighted the laser as a potentially important tool for future materials processing applications. Although the laserglaze process has been found to be capable of producing rapidly chilled microstructures, its applications are limited by the small section thickness required to achieve high cooling rates", " In the section to follow, the experimental details of rapid solidification processing by laserglaze and layerglaze will be discussed, along with a prognosis about future application of these Directed Energy Processing techniques. 4. Processing 4.1. Surface melting and alloying (laserglaze processing) The nature of the interaction of a high power laser beam with a material surface has been discussed extensively in previous sections of this book. It depends primarily on the absorbed power density and interaction time, and the variety of interactions obtainable as a function of these two parameters has been illustrated in fig. 5.1. The combination of these two factors serves to define operational regimes for various materials processing techniques. At Rapid solidification laser processing 275 very high power densities of ~ 1 0 9 W/cm 2 , attainable currently with only pulsed laser equipment, nearly instantaneous surface vaporization occurs on interaction of the beam with the material If pulse duration is kept to ~10~ 7 s, typically involving an energy input of the order of 10 2 J /cm 2 , interaction is limited to the surface and the rapid expansion of the vaporized metal produces an effect similar to a blast wave (Fairand et al", " As a consequence of the high cooling rate, ultra-microcrystalline or amorphous microstructures have been obtained, as documented above. 276 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Kear Typical apparatus for laserglaze processing has involved use of continuous, multikolowatt C 0 2 lasers, although the effect is dependent on power density and can thus be achieved at power levels below 1 kW. Both Gaussian and unstable resonator output beams have been used. A typical experimental setup is schematically illustrated in fig. 5.29, and pictured in action in fig. 5.30. In fig. 5.29, a nominal 7.5 cm diameter beam from the laser is directed toward and focused upon the workpiece by reflective optics. In a typical test, a 46 cm focal length mirror would be used to provide an effective minimum spot diameter of 0.05 cm at the workpiece. At 3.0 kW, these optics would provide a maximum incident power density of approximately 1.5 X 106 W/cm 2 , a power density equivalent to that provided by a black body thermal radiative source at 22 800\u00b0C. This high power density is essential for localizing the energy input at the material surface, and further promotes effective coupling of the laser energy with the material, despite the initially high reflectivity of metallic surfaces to the 10.6 \u00ec\u00e9 \u00e7 wavelength of carbon dioxide laser radiation. The 3 kW power level is a convenient one, in that it promotes effective beam coupling, but does not create significant plasma generation problems. As noted in fig. 5.29, plasma suppression is accomplished by means of an inert gas shield, which further prevents atmospheric contamination of the melt. Cooling due to the inert gas flow was estimated to be negligible, in comparison with the heat-sinking effects of the unheated substrate material. Rapid solidification laser processing 111 278 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Rear A range of laserglaze melt depths may be achieved by varying the translational speed of the workpiece under the focused beam. Linear speeds of from 150 to greater than 6000 cm/min are attained by using a variable speed rotating disk with specimens located at a fixed radius on the disk surface", " Clearly, the precooling of the material becomes more important the lower its melting temperature. A condensed, or \"summarized\" version of the thermal calculations on melt depth and cooling rate, which were discussed above is presented in figs. 5.31 and 5.32. These two figures represent a set of convenient \"working Rapid solidification laser processing 279 figures\" which can be used to estimate first, melt depth from absorbed power and interaction time, and then cooling rate from melt depth and power density, as follows: Fig. 5.31 illustrates the transient surface melting characteristics for nickel. The solid lines indicate melt depth versus interaction time for various power densities. Interaction time is defined as the time required for the incident laser beam to traverse one spot diameter, and is computed as the ratio of spot diameter to beam sweep speed, D/V. The period is initiated from a uniform initial temperature of 21 \u00b0C and thus includes the time during which the material is heated up to and through the melting point. Subsequent to the onset of melting, the advance of the melt interface was found to be approximately linear with time. The dashed lines in fig. 5.31 indicate constant specific energy inputs to the material and are computed as the products of the absorbed specific power and the interaction time. It can be seen that the specific energy required to obtain a given melt depth decreases as power density is increased and interaction time is decreased. The reason for this, of course, is that at higher power densities less time is available for heat conduction into the solid, i.e., the energy is more concentrated in the melt. Thus, increased melting efficiency is not the only benefit of higher power densities; the steeper temperature gradients in the material also enhance more rapid cooling. Fig. 5.32 shows the effect of melt depth on average cooling rate for selected values of power density. It can be seen that there is a maximum cooling rate for a given absorbed power density corresponding to the Fig . 5.31. Transien t surfac e meltin g characteristic s of nickel . 1 0 0 - A B S O R B ED S P E C I F IC P O W ER W / c m2 ^ > < ' A B S O R B ED E N E R GY J / c m 2 x ^*< 200

TI exp( PO 1 So the maximum value of T,can be decided by TI which is set beforehand and by far smaller tension than T,. T, is the driving force of the pulley, and the torque that generates the tension over the maximum value of T, is not transmitted by slipping[3]. - 2244 - It is constructed as shown in Fig.7 @) and Fig.8. The wire drawn out from its winding pulley is hooked around the other pulley that is rotation free. This pulley is pulled by the spring for applying the tension on the wire. And the compressive force of coil spring, which is accumulated by turning the worm gear, has been applied on pulley by the link in this tensioner unit. 3 3 Float differential torque sensor It is useful to obtain torque information, which works in each axis in order to realize the advanced and three-dimensional motion control. As a torque sensor, \"Float differential torque sensor\" shown in Fig.9 is introduced. It is easy to maintain this sensor and the additional equipment. The motor is supported rotation freely from the base by ball bearings, and it is connected by the hard spring between the motor and base. By measuring the strain gauge mounted on this spring, the reaction torque of the motor is detected. Generally the strain gauge is applied to the output itself in order to measure the torque of the actuator. However this sensor has high reliability and generality, because it removes the wiring of collector ring or strain gauge from the output, which infinity rotates[4]. Harmonic gear is used in the actuator unit, so this torque sensor is adopted as the flexspline is supported rotation freely from the pitch shaft as Fig.10 shows. 3.4 Basic experiments The operation test of this prototype unit is carried out. This unit is position controlled by returning the value of sum or difference of two potentiometers which are set in the pitch and yaw axis to each motor driver. It has been confirmed that there are no problems such as the interference for this unit and that it normally operates. For the float differential torque sensor, it is confirmed that it has the sufficient linearity and its deviation is little in Fig.11. The external force is applied to the unit that is position controlled as performance test of M-Drive. A pair of outputs of torque sensors is in Fig.12. The left part shows an aspect under the permission torque, and then this joint unit acts as usual servo system. On the other hand, there is the leveling off in the right part, and it is a cause that the supeffluous torque does not arise by slipping. External force[kgfl Fig.11 Experiment of the float differential torque sensor -5 O; I J 0 2 4 6 8 Time[sec] -sensor A -sensor B Fig.12 Experiment of M-Drive -2245- 3.6 Improve the joint unit Dimembn Weight Torque Angle velocity 3.6.1 Consideration to the three-dimensional motion There is the case that only one in the pair of wheel contacts the ground by the body shape, because each joint does not have degree of freedom of roll motion. The suspension mechanism is added in each wheel in order to prevent this problem. And the frame rigidity is improved by establishing the top board at the uni t in order to stand the three-dimensional motion like 2 0 0 ~ 1 9 0 ~ 1 8 0 ~ 170~150~14511~~1(-46%) 2.5 kg 2 kg (-20%) 5 kglin 4.1 kglin 8 rpm 9.6 rpm 3.6.2 Improved tensoner The wire tensioner is independent composition in the primary model. The joint unit becomes smaller and lighter so that it is conbined with the motor uni t in the improved model. It is composed of the link with a free pulley and a ring around the motor. These are tied together with a torsion spring. And there are the different number of holes in the ring and the motor base. The wire tension is adjusted by the combination of the hole where the pin As a result of these improvements, it becomes about -20% in the weight and about -46% in the volume in comparing primary model. Table 2 Improvement of specification Primary Model Improved Model 4. Development of the three-dimensional Active Cord Mechanism: ACM-R2 4.1 System constitution ACM-R2 consists of 14 joint units which are straight-chained. It has ability for the propulsion at 1 m/s and the compensation for the weight of 5 units levelly. It has totally 28 degrees of freedom. Angle and torque of each joint are measured. It is possible to make self-contained system in the future, because there is space for mounting batteries, wireless LAN, etc. on the body. It has 2 motor drivers (TITECH Robot driver 2)[5], 2 amplifiers for the strain gauge and a microcomputer (HITACHI H8/3048F 16MHz). No. of unit 14 (28 degrees of freedom) Demension 2430x150~145 mm Weight 30 kg Promotion speed - 2246 - Each actuator controls its position by the motor driver, however each joint controls their torque at a local loop by returning the value of the torque sensor to the motor driver as a feedback value of the position. The processing by the microcomputer is DA converted for motor drivers (2ch), AD converted from angle or torque sensors (4ch) and serial communication to the host computer, which is in the last joint unit. The processingof the motion plan of serpentine motion, etc. is carried out in the host PC. 4.2 Fundamental operation 4.2.1 Torque control Torque control at the local loop has been implemented and is confirmed that i t can be controlled without causing abnormal vibration. And when the external force is applied to joints in a stationary state, it is also confirmed that the joint bends in the direction in order to avoid it 4.2.2 Position control Position control has been implemented by commanding the torque order in proportion to the difference in real joint angle and target one to each actuator. There are small vibrations in some joints in this control mode. The following causes are considered: That control period of the position loop is late, that the resolution of the AD conversion of the joint angle is low and noise. The vibrations are disposed of in raising the communication speed between the host PC and microcomputers on each joint, and redoing the wiring to endure the noise for these problems. There is no problem for the operation by these improvements, as long as the accuracy of the position is not so required in the present state. The experiment of ACMR-2 lifting its head as a sickle neck is carried out by manual control. And, the propulsion using control method, which makes each joint angle to change in sine wave like, is carried out as well as the conventional mechanical model. 5. Conclusions The ACM with three-dimensional motor capacity is discussed in this paper. It has various functionalities, and it is made good use by ACM possessing the ability of three-dimensional motion. Then, ACM-R2 that is the mechanical model with the three-dimensional capacity is actual made. It is a high performance model so that i t has M-Drive (torque limiter) and Float differential torque sensor. It is confirmed effectively operating of these mechanisms, and the experiment of fundamental operation is carried out. As a future work, It will be realized that manipulation and locomotion for adapting the body shape to the surroundings in order to keep the stability without overtuming. And the proposed new propulsions are to be verified by the real machine. It will be concretely examined control methods which utilize the torque information in order to achieve these. Acknowledgment This research is supported by The Grant-in Aid for COE Research Project of Super Mechano-Systems by the Minstry of Educaton, Scince,Sport and Culture. References [I] Shigeo Hirose : \u201cBiologically Inspired Robots (Snake-like Lo- comotor and Manipulator)\u201d, Oxford University Press, 1993 [2] Gen ENDO, Keiji TOGAWA ,Shigeo HIROSE : \u201cStudy on self-contained and Terrain Adaptive Active Cord Mechanism\u201d,in Proc. of IEEE/RSJ International Conference on Inteligent Robots and Systems, pp1399-1405,1999 [3] S.Hirose, Richard Chu : \u201cDevelopment of a Lightweight Torque Limiting M-Drive Acuator for Hyper-Redundant Manipulator Float Arm\u201d, in Proc. IEEE International Conference on Robotics and Automation, pp2831-2836,1999 [4] S.Hirose, K.Kato : \u201cDevelopment of the Float Differntial Torque Sensor\u201d, in Proc. of JSME Conference on Robotics and Mechatronics, IC1 2-6, 1998 (in Japanese) [5] E.F.Fukushima, T.Tsumaki,S.Hirose : \u201cDevelopment of a PWM DC Motor Servo Driver Circuit\u201d,in Proc. of RSJ95,pp1153-1154,1995 (in Japanese) - 2247 -" ] }, { "image_filename": "designv10_13_0001554_s0094-114x(98)00070-6-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001554_s0094-114x(98)00070-6-Figure5-1.png", "caption": "Fig. 5. Mobile is an isosceles triangle.", "texts": [ " The angle between any two lines of the star frame is also 1208. Its three lines pass through three vertices. The mechanism is singular when this mobile rotates together with the star frame to the position where the three lines of the star frame are parallel with the three sides of the base, respectively. The circumcircle radius of the base is in unit length. C1B3B5 is the mobile. P-C1B3B5 is the star frame. When PC1vvA5A3, PB3vvA1A3 and PB5vvA3A5, the mechanism is singular. Without loss of generality, take the position shown in Fig. 5, the center point P is just over A1. The coordinates of points A1, A3, A5, B3, B5 are the same as those in Example 1. The coordinates of point C1 are (1, 0, 0.866025)T. Thus, the Plu\u00c8 cker coordinates of lines A1C1 and A5C1 are $7 0:152882; 0; 0:988245; 0; \u00ff0:855845; 0 ; $8 0:907072; 0; 0:420974; 0; 0:364574; 0 : 29 The other four lines A1B3, A3B3, A3B5 and A5B5 are the same as $3, $4, $5, $6 in Eq. (15), respectively. Thus, the Jacobian matrix consists of J1 T $7 $8 $3 $4 $5 $6 : The determinant of the matrix is det J1 \u00ff2:7 10\u00ff7: That means, the mechanism is singular" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003341_icma.2010.5589079-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003341_icma.2010.5589079-Figure1-1.png", "caption": "Fig. 1. The new-style wheelchair robot. (a) Initial configuration of the wheelchair robot. (b) Terminal configuration of the wheelchair robot.", "texts": [ " Finally, the tip-over stability analysis and simulation for stair-climbing of the robot under the influence of passenger\u2019s attitude and action are performed with Force-Angle measure. A. The New-Style Wheelchair Robot The mechanism of the new-style wheelchair robot W 978-1-4244-5141-8/10/$26.00 \u00a9 2010 IEEE 1387 consists of a supporting frame, a chair fixed on the top of the supporting frame and two variable-geometry-tracked mechanisms installed at the flanks of the supporting frame symmetrically, as shown in Fig. 1. In the variable-geometrymechanisms, two back flippers are driven synchronously to realize mechanism transformation, two front flippers are driven synchronously to realize active control of track tension, two pairs of planetary wheels are attached at the tip of the flippers and the two back planetary wheels are also used as driving wheels which can be driven independently to realize moving and steering of the robot; some road wheels, guide wheels and idlers are installed to assist the mechanism to work" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002286_ac00275a028-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002286_ac00275a028-Figure1-1.png", "caption": "Figure 1. Main parts of the externally buffered enzyme electrode: a, oxygen electrode; b, ff gauze with immobilized enzymes; c, Pt coil (cathode); d, nylon nets; e, dlalysis membrane; f, in going buffer stream; g, buffer effluent; h, buffer reservoir; iI PID controller; j, reference potential; k, recorder; I , electrolysis current; F, buffer flow.", "texts": [ "4 mg of glucose oxidase was immobilized on each net. Assays for Glucose, Gluconic Acid, and Solvents. Enzymatic methods were used to measure glucose and gluconic acid contents of the samples. Glucose was determined by means of GLOX (Kabi AB, Uppsala, Sweden). Gluconic acid was assayed by using the corresponding enzymatic test kit (no 428 191) from Boehringer Mannheim (measurements were made at 340 nm). Solvents in the butanol medium were determined by means of a Varian Vista gas chromatograph. Instrumentation, Figure 1 shows schematically the construction of the glucose electrode. Onto the membrane of an oxygen electrode constructed according to Johnson et al. (11) was placed a platinum net with immobilized glucose oxidase and catalase. A dialysis membrane separated the enzyme chamber from the outer solution. A 20-mm Pt wire (diameter 2 mm) immersed in the sample solution served as cathode of the electrolytic circuit. Between the enzyme and the membrane and between the enzyme and the oxygen sensor were inserted nylon net (15 mesh, Monyl HD, ZBF, Zurich, Switzerland) spacers to ensure good flow characteristics of the external buffer", " It is of utmost importance that the external buffer does not contain dissolved gases to such an extent that they form bubbles in the measuring chamber. The . . . . . 1 - 100 A P 6 . ' I - BO I i t I ' I \\ it - 60 h < 3 - - 40 'I ::: ri ' I f-t I A I ' ,/Jt . 20 l Time (h) T i m e ( m i d Figure 2. Time-response curves in phosphate buffer of (A) the oxygen-stabilized glucose electrode wlthout the buffer flow system and (B) the oxygen-stabilized glucose electrode built according to the external buffer principle (Figure 1) wlth F = 0.23 mL/min. Each glucose addltlon is (A) 0.5 g/L and (B) 5.0 g/L (arrows). samples were kept at 30 \"C and the external buffer was deaerated by vacuum suction and kept at 40 \"C. This deaeration method functions for short experiments but is not recommendable for long-term use due to the fact that the buffer oxygen tension increases. For long-term experiments it is better to make use of the fact that air has a lower solubility at higher temperatures. In this case, the buffer was kept air saturated at 60 \"C (where oxygen has a solubility of just over half that at 25 \"C) which gave a very stable dissolved oxygen tension", " After the oxygen electrode signal was balanced against the reference voltage to give zero electrolysis current, glucose additions were made to the sample. When response curves were drawn, recalculation was made to account for sample dilution by additions of glucose stock solution. Overnight storage for reuse on the following day was achieved by immersing the electrode in fresh, glucose-free buffer at 30 \"C and having intermittent buffer flow for 15 min every 2 h. Description of the Glucose Electrode System. Figure 1 shows the main components of the system. As glucose from the sample solution enters the enzyme chamber, the immobilized enzyme (b) catalyzes its conversion to gluconic acid and hydrogen peroxide. This reaction consumes oxygen. The oxygen depletion is sensed by the galvanic probe (a) and the signal decrease obtained as a differential potential vs. a fixed reference potential 6). The potential difference is kept at zero by the action of a PID-controller (i) which governs the generation of oxygen by electrolysis at the Pt gauze (b)", " As can also be seen in Figure 3, the response curves are sometimes divided into two linear portions with different slopes. This phenomenon does not always occur and is thus attributed to flow characteristics of the individual electrodes, which by necessity differ somewhat from one copy to the other since the enzyme chamber is rebuilt for each new electrode. Characteristics of the Enzyme Chamber. The enzymes needed for the electrode reaction are immobilized in a Pt gauze which is situated so that it is flushed with the external buffer flow F (Figure 1). Reaction products and most of the incoming glucoseare thus washed away and leave the system through the outlet tubing. Outgoing amounts of metabolites can be measured and, together with knowledge of the buffer flow rate, the total enzyme reaction rate can be estimated. An example is given in Figure 4. At the given flow rate and an outer glucose concentration of 40 g/L, the total enzyme reaction rate is approximately 0.1 pmol/min. About 0.4 mg of glucose oxidase is immobilized in an electrode. Since the original, soluble enzyme is of activity 180 U/mg, the amount immobilized is of activity 72 U and gives a total reaction rate in the soluble state of 72 pmol/min" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003544_tcst.2012.2221091-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003544_tcst.2012.2221091-Figure6-1.png", "caption": "Fig. 6. Hybrid automaton sample trajectory. The aircraft starts in recovery mode with q = L , switches to hover when (\u03be ,\u03bc) \u2208 Bh(\u03be Heq ,\u03bcHeq ) and to transition when \u03be \u2208 B\u03b50(v X\u2192L (0)). In the end, the aircraft switches to level when (\u03be ,\u03bc) \u2208 Bl(\u03be Leq ,\u03bcLeq ).", "texts": [ " These considerations are encoded in the following definition of the guard map: G(H, X) = B\u03b50(v q1\u2192q2 (0)) G(X, L) = Bl(\u03be Leq ,\u03bcLeq ) G(L, X) = B\u03b50(v q1\u2192q2 (0)) G(X, H ) = Bh(\u03be Heq ,\u03bcHeq) G(H, R) = R 8\\Bh(\u03be Heq ,\u03bcHeq ) G(L, R) = R 8\\Bl(\u03be Leq ,\u03bcLeq ) G(X, R) = R 8\\B\u03b5(v q1\u2192q2 (t)) G(R, H ) = Bh(\u03be Heq ,\u03bcHeq ) where \u03b50 > 0 is the maximum allowed error on the initial state of a transition maneuver, B (\u03be Leq ,\u03bcLeq ) \u2282 B (\u03be Leq ,\u03bcLeq ) \u2282 BL(\u03be Leq ,\u03bcLeq ) and similarly Bh(\u03be Heq , \u03bcHeq ) \u2282 Bh(\u03be Heq ,\u03bcHeq) \u2282 BH (\u03be Heq ,\u03bcHeq), with , \u2208 R and h, h \u2208 R.The parameters h, h, , and are chosen so as to prevent chattering during switching events, which is always possible by choosing h < h and < sufficiently apart from each other. Fig. 6 depicts these sets for a sample trajectory, from the recovery to the level operating mode. 6) Reset Map: For each (q1, q2) \u2208 E and (\u03be, \u03bc) \u2208 G(q1, q2), the reset map R : E \u00d7 R 6 \u00d7 U \u2192 R 6 identifies the jump of the state variable \u03be during the operating mode transition from q1 to q2. For this particular application, the reset map is the trivial map R({q1, q2}, \u03be, \u03bc) = \u03be for any {q1, q2} \u2208 E as there are no impulsive state changes, only the employed local controller is modified when switching operating modes" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003721_icmech.2011.5971317-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003721_icmech.2011.5971317-Figure3-1.png", "caption": "Fig. 3 Free body diagram of one pod", "texts": [ " Acceleration of the mass centres of different parts of each pod Each pod contains two parts: an upper part, which is attached to the spherical joint, and a lower part which IS attached to the universal joint. Considering Ldi and LUi as the mass centre positlon vectors of the lower and upper parts of the ith pod with reference to the fixed pod frame, respectively; the accelerations of the mass centres of the lower and upper parts of the ith pod can be expressed as follows: Ldi = ali x Ldi +ro/i x (roli x Ldi) (25) LUi = ali XLui +ro/i x(roli xLui)+2roli XiiBi +i;Bi (26) A. Dynamics of Each Pod Considering a single pod consisting of two upper and lower parts (Fig. 3), the equilibrium equation of moments about the centre point of the lower joint can be written as follows: Mi +liBi xFi + (mULui +mdLd;)xG-muLui x LUi -mdLdi x Ldi -(lUi + Idi)a/i -rou x (lUi + Idi)rou -Cs(ro/i -ro)-Curoli =0 (27) where md and mu are masses of the lower and upper parts of each pod, respectively; Cu and Cs are respectively the viscous friction coefficients in universal and spherical joints and G is the vector of gravity acceleration. Fi and Mi are the reaction force and moment of the ith pod in the base frame, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003164_icfcc.2009.48-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003164_icfcc.2009.48-Figure1-1.png", "caption": "Figure 1. Main Board of Versatile mobile charger", "texts": [ " New instructions required to facilitate the mobile charger robot will be presented in Section IV, followed by conclusion of the work in Section V. II. VERSATILE MOVEABLE DOCKING CHARGER Keeping a large swarm of robot fully charged and running smoothly would be difficult without a mobile charging station. Multiple docking stations on the charger robot are desirable to support large swarms while versatility is important to address different scenario of charging. The versatile mobile charger robot main board is shown in Fig. 1. The robot is equipped with six infrared diodes and phototransistors for broadcasting and communication between the mobile charger and other swarm robots. Infrared and phototransistors of occupied docking station will be disabled during active charging. This behavior as shown in Fig. 2 prevent mobile robot from docking to occupied charger stations. 978-0-7695-3591-3/09 $25.00 \u00a9 2009 IEEE DOI 10.1109/ICFCC.2009.48 127 In the event of receiving request message from inactive robots, charger robot will move only if none of its docking station is occupied" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002231_robot.2003.1242095-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002231_robot.2003.1242095-Figure3-1.png", "caption": "Fig. 3: Link frames of one leg.", "texts": [ " We define frame Fo fned with the base and frame FP fixed with the mobile platform (fig. 2). Their origins are A, and P respectively. Their axes (xo, yo, a) and (xp, yp,, zp) are parallel. The base frames of the legs are defined by the frames FA,, Fm and FA, (fig. 2 ) , whose origins are A,, Q and A3 respectively. The zAi axes are This work has been supported by the project MAX of the p r o p ROBEA of the department S n C ofthe French CNRS. along the prismatic joint axes. The Khalil and Kleinfinger notations [ 5 ] , are used to describe the geometry of the system (fig. 3). The following notations are used: L (3x1) vector of the motorized joint variables: L = h , qn 4131T; \"V, (3x1) vector of the linear velocity of the origin of the The derivative of L and 'Vo with respect to the time are denoted L and 'Vu respectively. platform 0-7803-7736-2/03/$17.00 2003 IEEE 3272 The following kinematic models are presented in [6]: i) The inverse kinematic model of the robot: Where 'J; is the inverse Jacobian mabix of the Orthoglide, which is always regular in the working space", " The general form of the inverse dynamic model of a leg i, is written as (see appendix): Where: HI is the inverse dynamic model of leg i, when its terminal point is kee. Ti =H,(q,,4,,iii)+'JT Of, ~ ( 5 ) ri is composed of the independent torqueslforces of the joints of the leg i, where Tli and Ta are zero: r, =[r,, r2i rljIT =[r,; o 0IT (6) (7) Using equation ( 5 ) the forces fi can he written as: Off, = -H , ( %Ai,q,)+'JiT ri H, ( q , , q , , & ) = ' J ~ H, (qj,4,,iif) (8) Where: He is the inverse dynamic model with respect to the position Cartesian space at point P (fig.3) [7][8]. We show that [6]: Off, = -H, (q~,q~,q,)+'J~,:,,,r, (9) Where J:,:,i, represents the i' column of the inverse transpose Jacobian matrix of the robot. The Newton-Euler equation of the platform is written as (no rotation): With: 'g OFp = 'Vi: M, -M, 'g 'g=[O g o ] T , g=9.~1m.s-' (10) Acceleration of gravity, referred to kame Fo: M, Mass of the platform; OF, Total external forces on the platform. given by: From equations (9) and (lo), the dynamic model is 1 rmbOt =' '~,+C[~,(q,,q~,ii~ )I] (11) Jp i iil Different methods can he used to calculate Hj(qj,qi,qj)[9][10][1 I]", " Thus the equation (1 1) can be written as: rnsat = D,,,,, K,bd (12) K,,,, is the vector of the standard dynamic parameters of the Orthoglide: Lo, =[MP K : KT KT]T D,,,,, = [D' D, D, D,] K, =[Ma,j FS,~ Fv,, x:]' (13) (14) K, is the vector of the standard dynamic parameters of the leg i, such that: (15) xi = [ x T ' '_ x f ] r (16) Where: - Ma,, is the inertia of the rotor of motor i referred to the joint side; - Fvli is the viscous friction parameter; - Fsli is the coulomh friction parameter; Taking into account the three legs and the platform, we obtain that the parameters MX3Ri (i = 1, 2, 3) are grouped with the mass of the platform and with the parameters: MIR~I, z z m , XX1F.i and %Ri: -xi is the vector of the inertial parameters of link i. I 1 1 The standard inertial parameters of the link j (i = 1 to D4, D, D4, M, =M, +-MX,,, +-MX,,, +-MX,,, 1 5 , fig. 3) ofthe leg i are collected in the (10x1) vector: Ma,,, =Ma,, --MX,, x,, = [ ~ , , ~ , , ~ , , ~ , , i Y z j j ~ , , ~ j , ~ j , ~ , , M , , ] ' ( 1 7 ) D4i Where: - mi,, .. ., ZZ,, are the elements of the inertia matrix; - MX,,, MY,,, MZii define the first moments of link ji; - M,, is the mass of link ji. z4,, = ZZ,,, -D4, MX,, Mm, =MI,, --MX,,, 1 Thus, K,,, is a (160x1) vector and D,o,, IS a Dd, (3x160) matrix. 4.1 Base dynamic parameters of the robot The base dynamic parameters represent the minimum number of parameters from which the dynamic model can be calculated", " ZZZR~, MXzi, MYzR~, XXm, XYm, XZm, Y Z m , ZZm, MXm, MY,,,, M&, Since, the prismatic joint of leg 3 is along gravity, there are 15 base parameters for leg 3, the grouped inertia Malm does not eliminate MIR3 (Whose effect on the force of motor 3 will be constant and equal to -g.MIRl). The grouped relations are (the index R indicates that some parameters are grouped with that one): Ma,, =Ma, ,+M,i+M,i+M,i+M,i+M, , ZZ, = ZZZi + YY,i + YY4i + D:, M,; + YY,, MY,,=MY,,+MZ,i+MZ,i+MZ,i XX,,, = XX,, -YY,i +XX,{ -YY,, - Dii M,, XU,, = XU,, +XU,; XZ,, = XZ,, -Dai MZ,; +XZ,i YZ,,, = YZ,, +YZ,; (18) ZZ,,, = ZZ,, +ZZ,, +D:i Mai MX,,, = MX,, +MX,, +D,j M,i MY,,, =MY,, +MY,, MI,, =M,,+M,,+M,,+M,,+M,, Dqi is the distance between the axes of q,, and qai (fig.3). To understand the physical meaning of these grouped parameters, let us consider that the center of mass of links 3, and 7, is in the middle of OliOni and 07i08i respectively. Thus: (20) MX ,i -D4i -M,:, MX,, = -M,j Dd 2 2 Using equations (18) and (20) into (19), we obtain: (21) 1 1 2 2 Ma,, =Ma,i+M,j+M,,+-M,i+-M,, 1 1 2 2 MI,, =M,,+M,,+-M,,+-M,, From equation (21), we show that: -The masses Ma, are grouped entirely with the platform; - The masses MI, and M,, are divided by two: one half is grouped with the platform and the other with Malb and also with MIRl when i = 3", ", \"Identification of the dynamic parameters of a closed loop robot\", Proc. IEEE Int. Conf on Robotics and Automation, Nagoya, mai 1995, pp. 3045-3050. [lSIGautier M., Khalil W., \"Exciting trajectories for inertial parameters identification\", The Int. J. of Robotics Research, Vol. l l(4). 1992,pp. 362-375. Appendix : Dynamic model of a leg Each leg has a planar parallelogram closed loop. The inverse dynamic model of the equivalent tree structure is obtained by cutting the revolute joint qgi (i = 1, 2, 3), figure 3: r, = H , (q,&ii,) (38) Leg i is isolated from the platform, so we can consider the variables qii, q,; and q3i to he independent. In the complete model of the robot, only qji is active and the torques r,; and r3i are zero. Let the vector q., be composed of the independent joints and the vector qp, he composed of the passive joints of leg i: q., =[41, q2i %;IT qp, 95; %IT (39) q4, =Y,~, q,: =-q2,--. qTi = q a , qsi =-q3i (40) The constraint equations of the loop are: II: 2 The dynamic model of the leg is obtained from Th, and the constraint equations by [9]: r, = ~ , ( q , ~ , i i , ) r, = [r,; r2> r,JT = G: r , Jq,, JP" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001929_0956-5663(95)96793-x-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001929_0956-5663(95)96793-x-Figure5-1.png", "caption": "Fig. 5. Schematic presentation of different scanning techniques using microtips to visualise or manipulate molecular systems. (a) Conventional scanning tunneling microscope (STM). Also indicated is its use as a spectroscopic tool by monitoring current~voltage curves (scanning tunneling spectroscopy, STS). In the example shown here, the change in the bias polarity changes drastically the contour response above a charged surface atom. (b) Scanning microscopy (SFM) operated in the contact, non-contact or zero force mode. More sophisticated SFMs monitor in addition the friction forces in the film plane. (c) Scanning thermal microscope to monitor local heat production. (d) Scanning capacitive microscope to monitor capacities at zero Faraday current. (e) Scanning ion microscope to monitor local variations of ionic currents through a micropipette. (f) Scanning near field optical microscope to monitor local variations of optical properties by utilising the coaxial guide of a light beam with different frequencies in a metal-coated glass fibre with inner diameters down to the 50 nanometre range. A variety of additional SXM microscopes and combinations thereof are currently being developed and optimised to investigate biomolecular", "texts": [ " Polarons can also be formed in materials with non-degenerate ground-state (not shown here). Bipolarons are interacting polarons, which may form, if the density of polarons at one molecule in molecular materials is high (G6pel 1990, G6pel et al. 1994). W. G6pel physisorbed Biosensors & Bioelectronics chemisorbed isolated These techniques make use of various spatial variations, e.g., in electron densities attributed to different energetic states, in attractive or repulsive forces perpendicular or parallel to the surface, in ion currents, heats, optical or magnetic properties (Fig. 5). For further details on SXM approaches, see Michel, 1994 for a survey on experimental approaches to investigate interfaces, see G6pel, 1990, Henzler 1991, Bonett 1993. Unfortunately, some commonly used and powerful techniques for the detailed structural analysis of macromolecules (including in particular 2DFT-NMR or X-ray crystallography) are not (yet) sensitive enough to analyse thin film structures at the interface with the required resolution down to the molecular scale (Nicolini 1994). 3.3 Tests The preparation steps mentioned in Section 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002273_1077546304042047-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002273_1077546304042047-Figure1-1.png", "caption": "Figure 1. Leaf spring con gurations (Heisler, 1999).", "texts": [ " The energy created due to this movement is momentarily stored in the spring it is then released again due to the elasticity of the spring material, and in expanding this energy the spring rebounds. This causes the vehicle to bounce many times before the equilibrium is restored. If the body were rigidly connected to the axle, the kinetic energy created by a bump would be imparted directly to the body creating high impact forces at the chassis. The shock absorbers, on the other hand, are responsible for dissipating part of this energy through friction. Leaf springs are classified according to the design (Heisler, 1999), as shown in Figure 1. The fully elliptic spring goes back to the days of coaches, but it is now used for commercial vehicles. The three-quarter-elliptic suspension provides a soft but more rigidly supported version. The half- or semi-elliptic spring is today by far the most commonly used leaf spring. It is used for car rear suspensions, and for both front and rear van and lorry suspensions. The quarter-elliptic spring is used in small sport cars. Transverse semi-elliptic springs have been used to form bottom, top, or both transverse link-arms for independent suspension for front and rear suspension" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002901_0278364909348762-Figure19-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002901_0278364909348762-Figure19-1.png", "caption": "Fig. 19. Configuration series in the switching mode of Segm=1112.", "texts": [ " The simulation resulted in visualizing the trajectory of G by the two curves of 6 and 5 (reverse direction) in the right part of Figure 18(a). The figure clarifies that the trajectory 5 means a sway back motion. If the switching program has intelligence in coding such that primary and secondary Jk are exchanged in a timely manner, the configurations 2)\u20135) in Figure 22 become redundant since 1) can skip directly to 6) without traveling so much. The switch in this mode is imaginable by looking at the sheet of Figure 19 from behind, but the locomotion environment is ascending. Therefore, configurations are generated by flipping horizontally those in Figure 19. The joint Jh rotates one way without changing its rotation direction in contrast to the mode in Segm=1111, 2111. The trajectory of G is referred to the curve 3 (reverse direction) in the right part of Figure 21(a). The curve has a gentle form but shows quite a lot of sway back. Incidentally, the curves in the right part of Figure 21(b) are observed in Segm=1212, 2122. Its left part trajectories are observed in Segm=1122, 2212. The behaviors of this mode become clear by using Figure 16 (Segm=1111) since only the environment changes from ascending to descending" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002145_iros.2000.895302-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002145_iros.2000.895302-Figure3-1.png", "caption": "Fig. 3 New propulsion modes", "texts": [], "surrounding_texts": [ "To begin with, the prototype of the joint unit is made in order to develop the ACM mechanical model that realizes three-dimensional and various functions The joint unit has 2 degrees of freedom and can do pitch and yaw motion. Its dimension is 20Ox190x180mm, and i t is over 2.5kg including all parts. There are two motors in the joint unit, and pitch and yaw motions are performed by the coupring the outputs. The workspace is maximized by offsetting pitch and yaw axis. And, this uni t has new mechanisms called \"M-Drive\" and \"Float differential torque sensor\". The former is to prevent the mechanical destruction by excessive load, and the latter is the detection mechanism of torque at each drive axis. And the making of the self-containd system is possible in the future, so that there is room for such as control computer, motor driver, and battery. -2243- This unit has 2 passive wheels on the both side for obtaining the frictional property for the glide propulsion. Thus, it is easy to slip in the direction along the trunk, and it is difficult to slip in the direction which is orthogonalized with it. Though the interference of wheels and the effect of the slip angle are considered because of the curvature discreteness, placing the axle in the midpoint of each joint has reduced these effects. Table 1 Specifications of the prototype unit Actuator Dimension Weight Torque Angular velocity Workspace . - . 20W DC Motor x2 (Coupled) 200x 260 / 260 deg 90x180 mm 2.5 kg 5 kgfm 8 rpm (yaw / pitch) 3.1 Wire type differential mechanism It is necessary that the actuator unit is high output mass ratio, because large moment affects the root when the neck is lifted. As the solution, the differential mechanism using the harmonic gear is introduced. This mechanism is lightweight because it is composed of not bevel gears but wire and pulley. The harmonic gear is a differential system which has one input and two output parts. One output is attached to pitch shaft and the other is attached the pulley. 2 sets of these are placed on a pitch shaft. The wire and pulley configuration is shown in Fig.6, and the endpoint of the wire is fixed in the yaw pulley. The rotation in the pitch axis is carried out in the case that two pulley outputs are same directions in viewing from the pitch shaft, and the yaw axial motion is carried out when the pulley outputs are is reverse-directions, This actuator unit is adopted the coupled drive which is the method of maximizing output performance by cooperatively utilizing as possible all actuators that are installed. 3.2 Torque limiting mechanism M-Drive\" The ACM is hyper-redundant serial link system. The principal problem of existing systems is the inability to withstand unexpected external forces due to excessive moments at its root joints, so the torque limiter is necessary. Though usual torque limiter is bulky, it can be realized by adding simple parts in the wire drive system. The basic principle of M-Drive can be explained from the expression of the fiction transmission between the string and the pulley. In Fig. 7 (a), let T , and T, ( TI c T,) are the string's tension, ,U is the friction coefficient between the string and the pulley, and 8 is the winding angle of strings. The condition in which the slip occurs is the following. T, >TI exp( PO 1 So the maximum value of T,can be decided by TI which is set beforehand and by far smaller tension than T,. T, is the driving force of the pulley, and the torque that generates the tension over the maximum value of T, is not transmitted by slipping[3]. - 2244 - It is constructed as shown in Fig.7 @) and Fig.8. The wire drawn out from its winding pulley is hooked around the other pulley that is rotation free. This pulley is pulled by the spring for applying the tension on the wire. And the compressive force of coil spring, which is accumulated by turning the worm gear, has been applied on pulley by the link in this tensioner unit. 3 3 Float differential torque sensor It is useful to obtain torque information, which works in each axis in order to realize the advanced and three-dimensional motion control. As a torque sensor, \"Float differential torque sensor\" shown in Fig.9 is introduced. It is easy to maintain this sensor and the additional equipment. The motor is supported rotation freely from the base by ball bearings, and it is connected by the hard spring between the motor and base. By measuring the strain gauge mounted on this spring, the reaction torque of the motor is detected. Generally the strain gauge is applied to the output itself in order to measure the torque of the actuator. However this sensor has high reliability and generality, because it removes the wiring of collector ring or strain gauge from the output, which infinity rotates[4]. Harmonic gear is used in the actuator unit, so this torque sensor is adopted as the flexspline is supported rotation freely from the pitch shaft as Fig.10 shows. 3.4 Basic experiments The operation test of this prototype unit is carried out. This unit is position controlled by returning the value of sum or difference of two potentiometers which are set in the pitch and yaw axis to each motor driver. It has been confirmed that there are no problems such as the interference for this unit and that it normally operates. For the float differential torque sensor, it is confirmed that it has the sufficient linearity and its deviation is little in Fig.11. The external force is applied to the unit that is position controlled as performance test of M-Drive. A pair of outputs of torque sensors is in Fig.12. The left part shows an aspect under the permission torque, and then this joint unit acts as usual servo system. On the other hand, there is the leveling off in the right part, and it is a cause that the supeffluous torque does not arise by slipping. External force[kgfl Fig.11 Experiment of the float differential torque sensor -5 O; I J 0 2 4 6 8 Time[sec] -sensor A -sensor B Fig.12 Experiment of M-Drive -2245- 3.6 Improve the joint unit Dimembn Weight Torque Angle velocity 3.6.1 Consideration to the three-dimensional motion There is the case that only one in the pair of wheel contacts the ground by the body shape, because each joint does not have degree of freedom of roll motion. The suspension mechanism is added in each wheel in order to prevent this problem. And the frame rigidity is improved by establishing the top board at the uni t in order to stand the three-dimensional motion like 2 0 0 ~ 1 9 0 ~ 1 8 0 ~ 170~150~14511~~1(-46%) 2.5 kg 2 kg (-20%) 5 kglin 4.1 kglin 8 rpm 9.6 rpm 3.6.2 Improved tensoner The wire tensioner is independent composition in the primary model. The joint unit becomes smaller and lighter so that it is conbined with the motor uni t in the improved model. It is composed of the link with a free pulley and a ring around the motor. These are tied together with a torsion spring. And there are the different number of holes in the ring and the motor base. The wire tension is adjusted by the combination of the hole where the pin As a result of these improvements, it becomes about -20% in the weight and about -46% in the volume in comparing primary model. Table 2 Improvement of specification Primary Model Improved Model 4. Development of the three-dimensional Active Cord Mechanism: ACM-R2 4.1 System constitution ACM-R2 consists of 14 joint units which are straight-chained. It has ability for the propulsion at 1 m/s and the compensation for the weight of 5 units levelly. It has totally 28 degrees of freedom. Angle and torque of each joint are measured. It is possible to make self-contained system in the future, because there is space for mounting batteries, wireless LAN, etc. on the body. It has 2 motor drivers (TITECH Robot driver 2)[5], 2 amplifiers for the strain gauge and a microcomputer (HITACHI H8/3048F 16MHz). No. of unit 14 (28 degrees of freedom) Demension 2430x150~145 mm Weight 30 kg Promotion speed - 2246 - Each actuator controls its position by the motor driver, however each joint controls their torque at a local loop by returning the value of the torque sensor to the motor driver as a feedback value of the position. The processing by the microcomputer is DA converted for motor drivers (2ch), AD converted from angle or torque sensors (4ch) and serial communication to the host computer, which is in the last joint unit. The processingof the motion plan of serpentine motion, etc. is carried out in the host PC. 4.2 Fundamental operation 4.2.1 Torque control Torque control at the local loop has been implemented and is confirmed that i t can be controlled without causing abnormal vibration. And when the external force is applied to joints in a stationary state, it is also confirmed that the joint bends in the direction in order to avoid it 4.2.2 Position control Position control has been implemented by commanding the torque order in proportion to the difference in real joint angle and target one to each actuator. There are small vibrations in some joints in this control mode. The following causes are considered: That control period of the position loop is late, that the resolution of the AD conversion of the joint angle is low and noise. The vibrations are disposed of in raising the communication speed between the host PC and microcomputers on each joint, and redoing the wiring to endure the noise for these problems. There is no problem for the operation by these improvements, as long as the accuracy of the position is not so required in the present state. The experiment of ACMR-2 lifting its head as a sickle neck is carried out by manual control. And, the propulsion using control method, which makes each joint angle to change in sine wave like, is carried out as well as the conventional mechanical model. 5. Conclusions The ACM with three-dimensional motor capacity is discussed in this paper. It has various functionalities, and it is made good use by ACM possessing the ability of three-dimensional motion. Then, ACM-R2 that is the mechanical model with the three-dimensional capacity is actual made. It is a high performance model so that i t has M-Drive (torque limiter) and Float differential torque sensor. It is confirmed effectively operating of these mechanisms, and the experiment of fundamental operation is carried out. As a future work, It will be realized that manipulation and locomotion for adapting the body shape to the surroundings in order to keep the stability without overtuming. And the proposed new propulsions are to be verified by the real machine. It will be concretely examined control methods which utilize the torque information in order to achieve these. Acknowledgment This research is supported by The Grant-in Aid for COE Research Project of Super Mechano-Systems by the Minstry of Educaton, Scince,Sport and Culture. References [I] Shigeo Hirose : \u201cBiologically Inspired Robots (Snake-like Lo- comotor and Manipulator)\u201d, Oxford University Press, 1993 [2] Gen ENDO, Keiji TOGAWA ,Shigeo HIROSE : \u201cStudy on self-contained and Terrain Adaptive Active Cord Mechanism\u201d,in Proc. of IEEE/RSJ International Conference on Inteligent Robots and Systems, pp1399-1405,1999 [3] S.Hirose, Richard Chu : \u201cDevelopment of a Lightweight Torque Limiting M-Drive Acuator for Hyper-Redundant Manipulator Float Arm\u201d, in Proc. IEEE International Conference on Robotics and Automation, pp2831-2836,1999 [4] S.Hirose, K.Kato : \u201cDevelopment of the Float Differntial Torque Sensor\u201d, in Proc. of JSME Conference on Robotics and Mechatronics, IC1 2-6, 1998 (in Japanese) [5] E.F.Fukushima, T.Tsumaki,S.Hirose : \u201cDevelopment of a PWM DC Motor Servo Driver Circuit\u201d,in Proc. of RSJ95,pp1153-1154,1995 (in Japanese) - 2247 -" ] }, { "image_filename": "designv10_13_0002081_s0303-2647(03)00118-7-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002081_s0303-2647(03)00118-7-Figure4-1.png", "caption": "Fig. 4. Stability of the model\u2019s steady walking. Eq. (1) was solved from various initial conditions with the periodic constraint trajectory \u03b6\u0304std(t) without perturbation. Every point on (a) and (b) represents the model\u2019s initial condition. The symbol \u201c\u00d7\u201d represents the state point on the limit cycle. Depending on the initial condition, the model showed either maintained walking, falling down forward, or falling down backward. For every initial condition, the walking duration was recorded. (a) The gray scale represents the walking duration which depends on the initial condition on the \u03b8\u2013\u03b8\u0307 plane. More light the gray, shorter the walking duration. Each stick picture represents the solution whose initial condition is indicated by the arrow. (b) The basin of attraction of the limit cycle corresponding to the steady walking. The white region represents the set of initial conditions from which the model can keep walking more than 10 gait cycles. The gray and black regions represent the set of initial conditions from which the walker falls down backward and forward, respectively.", "texts": [ " We confirmed that these waveforms of \u03be were similar to those of the experimental data, at least qualitatively. The ground reaction forces and the joint torques also showed similarity to the experimental data (e.g. Winter, 1995). We denote the limit cycle oscillation with period T0 as \u03b3 , and corresponding periodic solution on \u03b3 as \u03be\u0304(t)(= \u03be\u0304(t + T0)) as shown in the six traces on the middle panel of Fig. 3. The time profile of the variable x, which is monotonically increasing in Fig. 3, can be regarded as periodic by taking modulo. Fig. 4 shows the appropriate initial conditions with which the model can keep walking over a long period. The model\u2019s behavior was examined by solving Eq. (1) from various initial conditions on the \u03b8\u2013\u03b8\u0307 plane. More precisely, set of the initial conditions was taken as: D = {\u03be|\u03b8 \u2208 [4.5, 5.0], x = 0.0, y = 1.040, \u03b8\u0307 \u2208 [\u22123.0, 6.0], x\u0307 = 0.888, y\u0307 = 0.224}. The initial conditions other than \u03b8 and \u03b8\u0307 were set exactly on the limit cycle at t = 0, i.e. \u03be\u0304(0). Depending on the initial condition, the model showed either maintained walk- ing, fell down forward, or fell down backward, where we regarded the walker to fall down if the angle of HAT-segment from horizontal, \u03b8, went out of the interval (\u03c0, 2\u03c0). For every initial condition, the walking duration, i.e. the time intervals from the beginning of each simulation until the model falls down, was recorded. The gray scale in Fig. 4a represents how the walking duration depends on the initial conditions on the \u03b8\u2013\u03b8\u0307 plane. More light the gray, shorter the walking duration. Each stick picture represents the solution whose initial condition is indicated by the arrow. The black region represent the walking duration more than 6 s. Fig. 4b shows the basin of attraction of \u03b3 . The white region of Fig. 4b represents the set of initial conditions from which the model can keep walking more than 10 gait cycles. The gray and black regions represent the set of initial conditions from which the walker falls down backward and forward, respectively. Confirming that various initial conditions in the white region give the stable walking along \u03b3 for 100 cycles, we concluded that this white region practically represents (a subset of) the basin of attraction of \u03b3 . Fig. 5 shows the stability of the limit cycle \u03b3 against the perturbation with various conditions (see Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure10.1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure10.1-1.png", "caption": "Fig. 10.1 An original crossbow a Original illustration (Mao 2001) b Real object (photoed in Beijing Capital Museum)", "texts": [ " There are three main types including the original crossbow (Hsiao 2013), Chu State repeating crossbow (Hsiao and Yan 2012a), and Zhuge repeating crossbow (Hsiao and Yan 2012a). Ancient Chinese crossbows were used to shoot bolts to attack long-distance targets by utilizing the elasticity of the bow and bowstring. The shooting process of a crossbow includes four steps: bowstring pulling, bolt setting, bowstring releasing, and bolt shooting. The original crossbow consists mainly of the frame (member 1, KF), a bow (member 2, KCB), a bowstring (member 3, KT), and the trigger mechanism. Figure 10.1a shows the mechanism structure of an original crossbow in the book Wu Bei Zhi \u300a\u6b66\u5099\u5fd7\u300b(Mao 2001). The frame (member 1, KF) is made from firm K.-H. Hsiao and H.-S. Yan, Mechanisms in Ancient Chinese Books with Illustrations, History of Mechanism and Machine Science 23, DOI: 10.1007/978-3-319-02009-9_10, Springer International Publishing Switzerland 2014 219 wood in which a hole, nut, and bolt channel are drilled for installing the trigger mechanism, bow, and bolt, respectively. The bow (member 2, KCB) is a composite member made from several pieces of different types of wood on which lacquer is applied to prevent corrosion", " Most of them are made from bronze, and each part is interchangeable because the size of the parts is very accurate. In the late Spring-Autumn Period (770\u2013476 BC), the original crossbow had been gradually developed and was used extensively after the Warring Period (475\u2013221 BC). For more 2,000 years, the original crossbow has been a standard weapon of the ancient Chinese army. The earliest object of the original crossbow with the trigger mechanism was excavated in Qufu City of Shandong Province (\u5c71 \u6771\u7701\u66f2\u961c\u5e02) in China, and it can be dated back to 600 BC (Zhong 2008). 220 10 Crossbows Figure 10.1b shows a bronze trigger mechanism from an excavation site of Changan City (\u9577\u5b89\u57ce) in the West Han Dynasty (\u897f\u6f22, 206 BC\u2013AD 8), now Xian City in Shanxi Province (\u965d\u897f\u7701\u897f\u5b89\u5e02). In view of the structures, the development of the original crossbow can be divided in time into two stages: before and after the Han Dynasty (206 BC\u2013AD 220). Before the Han Dynasty, the trigger mechanism did not have a Guo (\u90ed, a casing), so that the parts of the trigger mechanism were installed in the wooden frame directly. After the Han Dynasty, the original crossbow has two important design improvements", "6b6, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.6c5. Therefore, five specialized chains with identified frame, bow, bowstring, input link, percussion link, and connecting link are available as shown in Figs.10.6c1\u2013c5. However, the connecting link (KL) in Fig.10.6c2 and the percussion link (KPL) in Fig.10.6c4 are redundant during the shooting process. This means that the concepts in Figs.10.6c2 and c4 degenerate into five members, and these two specialized chains are not feasible. Step 4: The coordinate system is defined as shown Fig. 10.1a. The function of the trigger mechanism is to pull the input link to release the bowstring through the transmission of the percussion link and the connecting link. The uncertain joints may have multiple types to achieve the equivalent function. 1. Considering uncertain joints J1 and J2, each one has two possible types and they cannot be the same type simultaneously. When any one joint rotates about the z-axis, denoted as JRz, the other one is a cam joint, denoted as JA. 2. Considering uncertain joint J3, it has two possible types" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002337_tmag.2004.824774-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002337_tmag.2004.824774-Figure2-1.png", "caption": "Fig. 2. Definition of energy/coenergy density in PM: previous method 2.", "texts": [ " [5]\u2013[7] have performed extensive research and made some interesting observations. One method is to define the energy and the coenergy as [3], [6], [7] (1) Manuscript received July 1, 2003. The authors are with Ansoft Corporation, Pittsburgh, PA 15219 USA (e-mail: wfu@ansoft.com). Digital Object Identifier 10.1109/TMAG.2004.824774 (2) where the associated energy/coenergy density is shown in Fig. 1. The second method is to define the energy and the coenergy as [6], [7] (3) (4) where the associated energy/coenergy density is shown in Fig. 2. The disadvantages of these methods are: 1) the expressions of the energy/coenergy in PM and other materials are not uniform, i.e., the energy and coenergy do not obey the same relationship in both PM and other materials; 2) the computed force distributions from the energy formulation and from the coenergy formulation are different. The magnetic energy in a PM depends on its magnetizing history. During the magnetization process [5], the magnetic energy corresponding to a measurable quantity in a PM is stored as (5) where the shaded area is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003753_3.2815-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003753_3.2815-Figure3-1.png", "caption": "Fig. 3 Numerical results of one-strip approximation for a circular cylinder at M\u00b0\u00b0 = 4, 7 = 1.4 and their comparison with Belotserkovskii's results of two-strip approximation under the same conditions.", "texts": [ " 2, and therefore we can compare the results directly. It should be noted that the results of Ref. 2 are obtained by using a two-strip approximation, whereas ours are the one-strip approximations; hence some discrepancies are to be expected. It is interesting to notice that for an inaccurate guess of the initial condition we can still extend the integration beyond the sonic point without encountering numerical instabilities, though the sonic condition is not satisfied (the dashed-line curves in Fig. 3). With the usual computational scheme, it has been shown in Ref. 4 that, unless the initial condition for one-strip approximation can be guessed to at least six significant figures, the integration diverges before the sonic point is reached. Thus, the advantage of the present scheme is that it is stable near the sonic point. Although we have only carried out a simple example with one-strip approximations, it is believed that the situation is the same for higher approximations and for more complex geometrical configurations", " The scatter and minor inconsistencies in the plotted data are probably the result of efforts to traverse the balance in very small steps, which required that the traversing mechanism be operated very near its limit of accuracy. The region of main interest is that where the displacements are small such that the corresponding errors are also small. In this region the results are satisfactory and may be approximated by a linear relation between error and displacement. The linear relation indicates an error of 3 to 3.5% per 0.001-in. misalignment. Consideration of Fig. 3 indicates no obvious effect of Mach number. The variation among the several runs is believed to be primarily a result of variation in tunnel operation and equipment performance. If a Mach number effect is in fact present, it is unquestionably small. Similarly, a consideration of Fig. 4 indicates that any effect of Reynolds number is also small. Although the results vary somewhat with Reynolds and Mach numbers, there does not appear to be a consistent pattern in the variation. Some observations concerning the displacement and measurement errors may be pertinent at this point" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003983_978-3-642-55134-5-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003983_978-3-642-55134-5-Figure11-1.png", "caption": "Fig. 11. Optical micrographs taken at the time of initial contact (i) and successively though the alignment process (ii)(iv) showing the self-alignment of two robots", "texts": [ " Similar control schemes have been later presented [10]. Finally, compliance [11] between two or more docking microrobots can be used to further reduce the resulting control error. MicroStressBots are specifically well suited for compliant interaction because the USDAs can rotate if the motion on one of its sides is slightly obstructed. This mechanism is used used during turning, however also allows the robots to align during docking. Such self-alignment can be used to remove any residual control error. Fig. 11 shows mutual alignment of two MicroStressBots during docking. The self-alignment reduces final missalignment of the robots at the end of the assembly operation. Ultimately, independent multi-microrobot control is an important direction of future research. The scalability of the control scheme is of particular importance in order to enable control of future multi-robotic systems composed of large numbers of microrobots. For example, the SeSAT control scheme presented in [5] proposes a design methodology that can control n MicroStressBots with sublinear (O( \u221a n)) number of control voltage levels", " Untethered micro-scale end-effectors for advanced manufacturing on the micro scale will be advantageous for additive manufacturing operations in tight enclosed workspaces. The requirements of advanced manufacturing tasks are typically precise positioning and stable motion, needed for assembly and manipulation tasks. Therefore, the logical idea for a microrobot fitting the requirements is to exhibit incremental locomotion on a dry surface. Thus, a crawling micro-scale Magnetostrictive Asymmetric thin film Bimorph (\u03bcMAB) microrobot design has been proposed and investigated (Figure 11). Thismicro-scaleMagnetostrictiveAsymmetric thin filmBimorph (\u03bcMAB) microrobot [12, 13] consists of a magnetic film bonded to a nonmagnetic substrate. Due to the magnetostrictive phenomenon, stress is produced in the film when it\u2019s exposed to magnetic field. Bending occurs if one end of the two layer structures is clamped. Further, if the deflected end is in contact with some ground or face, a blocking force is produced which is able to provide mechanical work through the friction force it causes" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001450_cdc.1994.411345-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001450_cdc.1994.411345-Figure11-1.png", "caption": "Figure 11: Configuration of a car pulling three trailers with kingpin hitching.", "texts": [ " The third case (c) with LI = 0 and LZ = 2 = T as shown in Figure 10 is axle-to-axle hitching configuration that has been used widely in the literature. We see that the trailer has a large off-tracking to the right of the car's track. In an intersection, this would cause an intrusion beyond the pavement's edge. In comparing the three cases, the case with equal kingpin hitching yields the best results; the trailer follows more closely to the lead car's path than with the other two hitching configurations. We next used the interactive software package to drive a car pulling three trailers as shown in Figure 11. Figure 12 shows the trajectories of the centers of the four axles as the vehicle is driven through an obstacle field. The lengths of the hitches are all set t o 1.0, giving a total vehicle length of 7 units. The path swept out by the car and its trailers during motion is not much larger than that of a single car. This allows the system to travel quite easily through narrow passageways. From the actual off-tracking for the first and third trailers, as shown in Figure 13, a conservative bound for the first trailer is 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002030_s0022-460x(03)00277-3-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002030_s0022-460x(03)00277-3-Figure1-1.png", "caption": "Fig. 1. Analytical model of rotor sliding bearing system and its rubbing force.", "texts": [ " The transient response has been analyzed by Choy [14] and the effect of imbalance load and friction has been discussed. Considering the oil film force, Chu [15] has found that a rub-impact rotor system can exhibit very rich forms of motion, e.g., periodic, quasi-periodic and chaotic vibrations. All these works have helped research on the real rotor systems. But the coupling effect of the crack and the rubbing is the keystone of this paper. HWT is applied to reveal its characteristics in both time and frequency domains. Fig. 1 shows a simple Jeffcott rotor with transverse crack on its shaft in the inertial co-ordinates x y and rotating co-ordinates z x: The disk is located at the midspan of the shaft and the bearings at both ends are same, sliding ones. If \u00f0xd ; yd\u00de and \u00f0xb; yb\u00de represent the co-ordinates of the center of the disk and the journal, respectively. With constant angular velocity o; the equation of motion of the rotor sliding bearing system can be written as follows: md .xd \u00fe c\u00f0 \u2019xd \u2019xb\u00de \u00fe kx\u00f0xd xb\u00de \u00bc mdg \u00fe mdepo2 cos y; md " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001581_9.506234-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001581_9.506234-Figure3-1.png", "caption": "Fig. 3. attain parameter estimate values that are destabilizing for the nonadaptive system. The manifolds conditions close to the 8-axis and on the eigenspaces E\" and E\". Manifold W\" was obtained by simulation in reverse time. Stable (W ' ) and unstable ( W u ) invariant manifolds of unstable equilibria in S\"'. Solutions that converge to the unstable equilibria along 1.V' and W\" are determinei by simulations with initial", "texts": [ " With the following example we illustrate the fact that some solutions converge to S\"\". Example 6.1 (Example 5.1, C0ntinut.d): Let us return to (28) for which we determined that the set S\"\" is the interval (-&, A) on the &axis which implies that 6\"\" = (-a, a). Let us consider a point (x. e) = (0,de) in S\"\". With (52) and (50), we calculate the eigenspaces (75) of the matrix diag{A,(8), 0} corresponding to the eigenvalues XI and Xz, respectively. Therefore, there exist stable and unstable invariant manifolds, W\" arid W\", at each point in S\"\". These manifolds are shown in Fig. 3 for a set of points in the interval (0.6.1) c 6$.. Even though these points are unstable, solutions along W\" converge to them. The parameter estimate values tlhat they attain are destabilizing for the nonadaptive system. However, as we established in Theorem 5.1, the solutions corivergin5 to S\"\" have measure zero-almost all solutions converge to S\". This set, defined R24 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 41, NO. 6, JUNE 1996 in ( 5 3 , is the interval 6' = (a, +ea) on the &axis which corresponds to the stabilizing parameter estimate values for the nonadaptive system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003694_s12239-011-0034-8-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003694_s12239-011-0034-8-Figure1-1.png", "caption": "Figure 1. Column type EPS and PMSM rotor.", "texts": [ " In an EPS application, the magnetic saturation in the stator core and distortion of EMF is inevitable due to spatial and cost limitations(Lee, 2010). Imperfections of a low voltage inverter for EPS can be severe. This paper also analyzes torque ripple caused by the motor, deadtime effects, and current offset problems of the PMSM driver. The harmonic current distribution is calculated using finite element analysis, and the effective dead time compensation method is proposed. 2.1. Torque Ripple of PMSM for the EPS Figure 1 indicates a fabricated PMSM for the column type EPS system. The rotor configuration was skewed to reduce cogging torque. Segment type and ring type rotors are used for the purpose of this research. The specifications for a PMSM are listed in Table 1. Cogging torque and total harmonic distortion (THD) of a back-EMF required in the motor are less than 0.02 Nm and 0.7% respectively. If the rotor of a SPMSM is composed of segment-type permanent magnets, there is relatively low THD in the back-EMF (0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003142_s11740-009-0168-y-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003142_s11740-009-0168-y-Figure2-1.png", "caption": "Fig. 2 Test stand for identification of the static axial rigidity of the ball screw nut", "texts": [ " The axial rigidity of the ball screw nut can be determined as the ratio of the axial load and the resulting axial displacement of the nut. Through wear on the raceway of the nut, spindle and/or balls the rigidity of the ball screw reduces with the preloading of the nut, which causes positioning inaccuracies and an exchange of the ball screw in the machine tool. Before and after the fatigue tests with additived and nonadditived oils the axial rigidity of the ball screw nut was measured. For that, a rigidity test stand was designed (Fig. 2). The ball screw nut is integrated into a rigid support, which is fixed in axial direction with screws. Next to the nut, the torsion motion of the ball screw spindle is locked with a torsion prevention system consisting of two parts. This torsion prevention system is mounted on a support and can be moved in axial direction with guideways. The rigidity of the nut can be determined by measuring the displacement of the spindle relative to the nut and the axial load which is acting on the spindle through a hydraulic cylinder" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003846_cca.2012.6402345-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003846_cca.2012.6402345-Figure1-1.png", "caption": "Fig. 1. Passive rimless wheel model", "texts": [ ". INTRODUCTION A rimless spoked wheel, or simply, a rimless wheel (RW) shown in Fig. 1 has been investigated as the simplest model of passive dynamic walking [1]. This is an efficient, easy, flexible locomotion system that has both properties of wheels and legged robots. Until now, various applications have been considered such as active use [2][3], combined motion considering the phase difference [4][5], extension to 3D [6][7], improvement of the gait efficiency by adding feet [8][9], and efficiency analysis of 2-period gaits [10]. The stability inherent in a passive RW has also been studied", " (15) Let us assume that the transition function of the state error during the stance phase is specified as \u2206\u03b8\u0307 \u2212 i = Q\u0304\u2206\u03b8\u0307 + i . (16) Following Eqs. (10) and (14), the transition function, Q\u0304, is then solved as Q\u0304 = \u03b5 R\u0304 = cos \u03b1. (17) Therefore, we can find that the transition of the state error during the stance and collision phases are identical and are cos \u03b1. In the subsequent sections, we will investigate this result in more detail from the mechanical energy point of view. The dynamic equation of the RW shown in Fig. 1 is given by ml2\u03b8\u0308 \u2212 mgl sin \u03b8 = 0, (18) and its linearization around \u03b8 = \u03b8\u0307 = 0 becomes ml2\u03b8\u0308 \u2212 mgl\u03b8 = 0. (19) This can be arranged as \u03b8\u0308 = \u03c92\u03b8, (20) \u03c9 := \u221a g l . (21) The state space representation then becomes d dt [ \u03b8 \u03b8\u0307 ] = [ 0 1 \u03c92 0 ] [ \u03b8 \u03b8\u0307 ] . (22) In the following, we denote this as x\u0307 = Ax. The author investigated the inherent self-stabilization principle of a passive compass-gait by introducing the linearized mechanical energy and numerically showed the potentiality that the passive compass gait is stabilized not by means of the state variables but by means of the mechanical energy [13]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001472_6.2001-4179-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001472_6.2001-4179-Figure6-1.png", "caption": "Fig. 6 Attitude projection onto i/j \u2014 7 plane and attitude trajectory for command generation", "texts": [ " Equating terms give the desired relations as follows: \u2014 sin 9 \u2014 sin 7 cos a cos /3 \u2014 cos 7 sin j3 cos a sin \\L \u2014 cos 7 sin a cos n (40) sin 7 = cos {3 cos a sin 9 \u2014 sin /3 sin cos 9 \u2014 cos /3 sin a cos 0 cos 9 (41) cos#sin// = cos 7 cos /3 sin0 + tan 7 tan j3 (42) vCk = -K ek (37) Substituting (37) into (36) gives the closed-loop error dynamics ek+l = (A + BK) ek - ^A ek-i - FeWk - A& (38) The constant gain K G R6x3 is determined to place the closed-loop poles A of (38) at damped locations We choose (^,7) since piloting the aircraft in this hybrid axes is convenient; the ip determines the aircraft heading, and the 7 determines the vertical flight path (or climb rate) of the aircraft. Thus, we can make the flight attitude at any instant or flight attitude variation with time projected onto if} \u2014 7 plane in which the aircraft is attached to indicate the roll angle (Fig. 6). Giving the ^ \u2014 7 trajectory depends on 8 OF 11 AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 2001-4179 the controller, the aircraft performance, and maneuvers. These impose the bound of ip - 7 trajectory as shown in Fig. 6: maximum flight path angle 7ma;c is determined by SEP (specific excessive power) of the engine, and ^max is usually equal to n since it covers the entire horizontal (x \u2014 y) plane. Then the attitude trajectory to reach coordinates (V ;,7) of an arbitrary point on the inside the bound can be achieved by following elliptical (ij}c / jc) or circular (^c = 7C) path: ) (43) where (V^Tc) is the commanded attitude, r/rW is chosen in reference23 that starts and ends with zero angular rate and zero acceleration, and subscript T is a time to take to complete a rotation" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002346_bf02915922-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002346_bf02915922-Figure2-1.png", "caption": "Figure 2 Sensor array layout for study 1", "texts": [ " The basic measurement in both investigations was the time of flight of the bat between vertically oriented light beams and light sensors. Bat speeds reported here were calculated by dividing the distance between sensors by this time of flight. Experiment 1 Details In the first study, data were obtained from three array units\" of upward-looking light sensors illuminated by overhead sources. A schematic of one of the array units appears in Fig. 1 and a sketch of the three units in the system configuration appears in Fig. 2. The light source consisted of a 600 W incandescent bulb and three 1.2 m parabolic mirrors mounted 1.5 m above the sensors. This light arrangement produced three sheets of nearly parallel light rays, one sheet for each sensor array unit. The sensors were semiconductor-based photodetectors. In each unit (Fig. 1), sensor array T provided information on the location of the tip of the bat, while arrays S1 and $2 measured bat speed and provided information on bat angle in the horizontal plane. All sensors had 3", " For each bat, data for five swings by first one player and then the other (and then the third) were obtained. The production bats were used first in order to let the players become comfortable with the test environment. Measurements with the bare tube and then the tube with weights followed. This ordered, rather than random, sequence was adopted to minimize the time that the players were required to be in the laboratory. The results reported here are bat speeds for a point approximately 0.15 m from the bat tip measured by the middle array unit (Fig. 2). Individual and group averages and standard deviations appear in Table 2. Experiment 2 Details Seven 4.2 m W lasers provided the light for the second experiment. The lasers were positioned so that each illuminated a corresponding sensor mounted in a regulation-size home plate as shown in Fig. 3. The lasers were 2.4 m above the plate. Uncertainty in beam spacing was estimated to be + 0.2 mm about a nominal value of 50 mm. Semiconductor-based photodetectors like the ones in the first study were set in the home plate so that each receiving lens was approximately 6 mm below the plate surface and was aligned with the corresponding laser" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003784_s12613-013-0781-9-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003784_s12613-013-0781-9-Figure1-1.png", "caption": "Fig. 1. Dimension of the high-cycle smooth specimen.", "texts": [ " The (\u03b1 + \u03b2)/\u03b2 transformation temperature of LMD TC18 determined by metallographical method is (880 \u00b1 5)\u25e6C. The material received a stress-relieving treatment for 1 h at 750\u25e6C, followed by air cooling. Then, the alloy was annealed at 880\u25e6C for 1h, followed by furnace cooling to 750\u25e6C for another 2 h, and then air cooled. Finally, it was held at 580\u25e6C for a total aging time of 4 h and then air cooled. The long axis of the smooth bar specimens for the fatigue test was parallel to the T-orientation of the LMD TC18 titanium plate. As shown in Fig. 1, the smooth specimen was 70 mm long, with the diameter of 5 mm at the thinnest cross-section. The HCF tests were performed on a QBG-100 highcycle fatigue testing machine at room temperature under a load ratio of 0.1 with a frequency of 120-130 Hz. A sinusoidal cyclic axial load was applied. Tests were terminated either by failure or when 107 cycles were achieved. Fatigue strength was determined by staircase method, and then, the stress-strain (S-N) curve was obtained by grouping test method. The microstructure of the material was observed with an Olympus BX51M optical microscope (OM), a Camscan3400 scanning electron microscope (SEM), and an Apollo300 field emission SEM" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001704_cdc.1993.325328-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001704_cdc.1993.325328-Figure1-1.png", "caption": "Figure 1: Configuration Space of the Fire Truck", "texts": [], "surrounding_texts": [ "Lemma 2 (\"Averaging\" Transformation) Consider time-varying nonlinear system\nthe\nx = f(z,t) (12)\nwhere f is of period T , C', and where the if* entry of the vector f satisfies f i = O(Z)~'+' with k 2 1. Then there ezists a C' local change of coordinates x = y + Q(yl t ) under which (12) becomes\nY = f(Y)+f(Y,t)\nwhere f is the time average o f f and i i (y , t ) = O(y)2k+2 has period T .\nRemark Lemma 2 closely resembles Lemma 2.2 of [11], except now there is no dependence between the position and the order of an element fi of the vector f. Note that if we permute the vector z and hence the vectors f and y, the order of the element fi of the vector f of the previous result will no longer necessarily of order 2i + 1. In fact, if the element fi were of order 2k + 1, _the previous lemma would have asserted 5 to be order 2k+ 1 and fi to be order 2k + 2. The order of fi and f is then determined by the order of f i . However, a formal proof is still required.\nProof: The proof closely resembles a result described in [5]. We will divide f ( x , t ) into its time average, given by f(z), and the remainder f(z, t ) . We make the coordinate change:\n2 = Y + Q(Y, t )\nwith Q ( y , t ) specified later. We now solve for the dynamics of y.\na9 ( I + DuU)3i + at = k = f(Y + U) + f ( y + s,t)\nY = ( I + D,U)-' f ( Y + Q ) + j(y + U,t) - -7& ( Set = f ( y , t ) . As f l ( y , t ) has zero mean, Q is a bounded function of time. Furthermore, this implies that U is of higher order, thus the coordinate change is valid locally. Expanding the terms, we see:\nNow we will check the order of f i .\nAs the order of the element f i is 2k + 1, the elements of the corresponding row of Duf are of order 2k. The lowest order in @, as it is the time integral of f , is 3 from the case k = 1. We conclude that the first term is of order 2k+3. The same argument holds for the second term, as the element Qi is of order 2k + 1, the elements of the corresponding row of D u l is of order 2k. The product is then at least of order 2k + 3. 0.\nWith Lemma 2 in mind we will define the vectors z , f(z, t) E Rn-m-1.\nBy Lemma 2 there exists a locally valid averaging transformation. In spirit with the earlier notation, we will write the transformations maps z 4 E.\ni;o = Co(q + j;o(z, t)\nFurther, fjk0(3) is the time average of ffo(.Z,t) and ifo(Z,t) is of order 2k + 2. Now we will recall the case specific Lyapunov result from [Ill:\nLemma 3 (Case Specific Lyapunov Result) Consider time-varying nonlinear system the\nY = f ( Y ) + J ( Y , t ) (16)\nwhere y E Rn. Ij\nIIE(Y,~)II PiIIYI12('+i)\nf(Y) = A+(Y)\nfor all y in some open neighborhood of the origin and\nwhere A i s a square lower triangular matrix with ai, C. 0 for i = 1, ..., n and\n+ i ( Y ) = YiIIyII\"\nthen the origin of (16) is locally asymptotically stable.\nThe same kind of permutation argument can now be applied to Lemma 3 as was applied to Lemma 2, except in this case it would be wise to preserve the order within each chain in order to retain the the lower block diagonal structure of the matrix A. For our case, matrix A will then have lower block diagonal form (recall that the chains are decoupled except for the function p(z)) :\nwhere Aj E R R ~ X n ~ . The diagonal terms of the matrix A, are denoted by aik and are given by,\nsimilar to those in [Ill. As Olk< < 0, we may conclude local asymptotic stability.\nRemark 1: (Chained form systems) Corollary 2.1 of [I11 may be easily extended to the multiple input case. We may therefore conclude that the controls (7) will locally asymptotically stabilize the chained form system as well the power form.\nRemark 2: (Global Stability) As the chains are decoupled, we may can make the stability global by using saturation functions as described in Ill]. The example will incorporate this strategy. The controls with saturation functions incorporated are given by:\nvo = -YO + ( p ( z ) ) (cos(t) - sin(t)) U, = -y, + nh c~u(zih,)cos(ht) for 1 5 j 5 m (17)\nwith c: < 0 and with U : R 4 R, C3 and nondecreasing. The function is the identity map near the origin but never greater in\nh=l\n962\n11", "I\nmagnitude than some e > 0. Provided this e is small enough, the origin will be globally asymptotically stable.\nRemark 3: (Control of Dynamical Systems) These control laws may be adapted in order to regulate a class of mechanical systems. It has been shown in the literature [I, 10) that a large number of mechanical systems with nonholonomic velocity constraints may be written as:\nm\ni = C S i ( t ) U i , 4 = U. i=l\nThe first equation describes what is sometimes referred to as the kinematic system. We have developed controls laws U d ( ( , t ) which render ( = 0 globally asymptotically stable, solving the kinematic point stability problem for a class of mechanical systems. Since U d ( ( , t ) is a c' function of ( and t we we may apply the following control law in order to render the point ((,U) = (0,O) globally asymptotically stable:\nTo demonstrate that this control law stabilizes (O,O), examine the dynamics of the error of the input e = U - U d ( t , t ) :\ni = 4 - U((,t) = -e.\nNote that if we view the state of the system as (e,\u20ac), the equations will look like ( = g( ( )Ud( ( , t ) + g(()e. The linearly stable coordinates will then contain not only the terms due to w((, t ) as before, but also the entire vector e. In the center manifold, e = 0. Comequently the the equations for the dynamics on the center manifold are exactly the same as in the kinematic case, thus we may conclude stability.\n4 AnExample The stabilization method presented in this paper will be illustrated by a simple three-input example. The example we use. is the fire truck, or tiller truck shown in Figure (1). The kinematic equations were derived in [2] to have the following form:\neo Q 1 i\" e1 U1 +\nThe system has six states which are the Cartesian location of the center of the rear axle of the cab, (z,y); the steering angle of the front wheels relative to the cab's orientation, 40; the absolute cab orientation with respect to the horizontal axis of the inertial frame, Bo; the steering angle of the rear wheels with respect to the trailer body, 41; and the absolute trailer orientation, el. The constaqbs Lo and L1 correspond to physical parameters of the system. The three inputs ~ 1 , u2 and U S correspond to the driving velocity, the cab's steering velocity and the trailer's steering velocity, respectively.\nA modification of the transformation given in [2] puts the system directly into power form. In tho interest of brevity, we skip the steps leading to its derivation.\nYo = z tan do Yl = - L~ Cos3 eo\ntan $0 z:, = -taneO+z--Lo cos3 eo\nz:o = -y + - si441 - 00 i- 01) L~ cos d1 cos eo\nAway from the coordinate singularities 00 = 0 or 41 = 0, it may be verified that the system dynamics become:\nyo = vo y 1 = U1 zi2 = v2\nWe now present the simulation of the fire truck system. The simulation was performed on the system in power form with the states being stabilized to the origin from a given initial point by using the following control laws:\nvo = -yo + PO (cost - sint) v1 = -y1 + c1 p1 cost +- c2 p2 cos2t U2 = -y2 + c3 p3 cost . (19)\nThe C I , C Z , C ~ are constants and plrpz,p3,p4 are saturation functions designed to yield global stabilization results and defined as follows:\nP1 = +:o>, Pz = +:o), P3 = 4 4 0 ) 9\nwhere ~ ( z ) is a saturation function linear between (-E, E). The coordinates in power form were then transformed back into the original coordinates for analysis and a movie animation.\nFigure 2 shows the x-y p ot for a parallel parking maneuver, starting from an arbitrary i n i t h o i n t that illustrates the control law. The plot contains Lissajous figures.\nFigure 3 shows the trajectories of the body angles and y p e sition of the center of the rear axle of the cab for the same parallel parking maneuver. Through 8000 cycles, the y position slowly converges. The clipped clipped nature of 40 is due to the saturation functions of radius 0.5 used.\n5 Conclusion In summary, our contributions are the presentation of a transformation from most general chained form to power form and a\n963\n-1 --", "control law for a class of multiple input nonholonomic control systems without drift. In addition, we illustrated our results with an example from the literature, solving incidentally the parallel parking problem.\nIt is important to notice that the control laws presented here are smooth and, thus, are easily adapted to dynamical control systems. Examples of non-smooth laws with fast convergence rates my be found in [4, 81. The convergence in the coordinate directions for the law presented here can be modified by changing the coefficients of the control law.\nPossible future work includes finding a control law that asymptotically stabilizes to the origin an (m+l)-generator control system. We are also looking to enlarge the class of nonholonomic control systems which we may transform into chained form.\nAcknowledgements We are indebted to S.S. Saatry for suggesting the investigation of control laws for multiple input nonholonomic control systems.\nReferences [l) M. Reyhanoglu A. Bloch and N. H. McClamroch. Control\nand stabilization of nonholonomic caplygin dynamic systems. In IEEE Conference on Decision and Control, pages 1127 - 1132, Brighton, England, 1991. [2] L. Bushnell, D. Tilbury, and S. S. Saatry. Steering threeinput chained form nonholonomic systems using sinusoids: The fimtruck example. In European Controls Confernce, pages\n[3] J. Cam. Applications of Center Manifold Theory. SpringerVerlag, New York, 1981. [4] C. Canudis de Witt and 0. J. Sordalen. Exponential stabilization of mobile wheeled robots with nonholonomic constraints. In IEEE Conference on Decision and Control, pages 692-697, 1991. [5] J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifvrcations of Vector Fields. SpringerVerlag, New York, 1983. [6] A. Isidori. Nonlinear Control Systems. Springer-Verlag, second edition, 1989. [7] G. LafFerriere and H. J. Sussmann. Motion planning for controllable systems without drift. In IEEE International Conference on Robotics and Automation, pages 1148-1153, 1991. [SI R. M'Closkey and R. Murray. Nonholonomic convergence and exponential convergence: Some analysis tools. In IEEE Conference on Decision and Control, 1993. [9] R. Murray and S. Sastry. Steering nonholonomic systems in chained form. In IEEE Conference on Decision and Control, pages 1121 -1126, 1991.\nDynamics of Nonholonomic Systems. American Mathematical Society, Providence, Rhode Island, 1972. Volume 33 in Translations of Mathematical Monographs. [ll] A. Teel, R. Murray, and G. Walsh. Nonholonomic control systems: From steering to stabilization with sinusoids. In IEEE Conference on Decision and Control, pages 1603 - 1609, 1992. Also as Electronic Research Laboratory memo M92/28. [12] D. Tilbury, J-P. Laumond, R. Murray, S. Sastry, , and G. Walsh. Steering car-like robots with trailers using sinusoids. In IEEE International Conference on Robotics and Automation, pages 1993-1998, Nice, France, 1992.\n1432-1437, 1993.\n[lo] Ju. I. Neimark and N. A. Fufaev.\nTl" ] }, { "image_filename": "designv10_13_0002667_s1560354707020037-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002667_s1560354707020037-Figure2-1.png", "caption": "Fig. 2. Fig. 3.", "texts": [ " First note that the velocities of the points representing the contact point on the movable and the stationary surfaces are equal. This condition can be written as follows: r\u0307 = y\u0307 + \u03c9 \u00d7 y. (7) Here y is the vector drawn from the center of the stationary sphere to the contact point (Fig. 1). We have y = an, where a is the radius of the stationary sphere. From (7) one easily obtains n\u0307 = kn \u00d7 \u03c9, k = a a + b . (8) REGULAR AND CHAOTIC DYNAMICS Vol. 12 No. 2 2007 If a, b < 0, we have the outer rolling as shown in Fig. 1. If a < 0, b > 0, |a| > b and k = |a| |a|\u2212b > 0, we have the inner rolling of the ball over the sphere (Fig. 2), and if a > 0, b < 0, a < |b|, k = \u2212 a |b|\u2212a < 0, we have the outer rolling of the sphere over the ball (Fig. 3). Put a = \u221e, k = 1 for the case of the ball rolling over the plane and b = \u221e, k = 0 for a planar rolling over the sphere. Differentiate the constraint (3), by virtue of (8) we obtain (\u03c9\u0307,n) = 0. Hence, using the constraint itself we get the relations I\u03c9 + mr \u00d7 (\u03c9 \u00d7 r) = I\u03c9 + mb2\u03c9, I\u03c9\u0307 + mr \u00d7 (\u03c9\u0307 \u00d7 r) = I\u03c9\u0307 + mb2\u03c9\u0307. Therefore, J\u03c9\u0307 = J\u03c9 \u00d7 \u03c9 + \u03bbn + MQ, n\u0307 = kn \u00d7 \u03c9, J = I + mb2E, E = \u2016\u03b4ij\u2016, (9) where \u03bb = \u2212(J\u03c9 \u00d7 \u03c9,J\u22121n) + (MQ,J\u22121n) (n,J\u22121n) " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003272_tmag.2009.2024641-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003272_tmag.2009.2024641-Figure6-1.png", "caption": "Fig. 6. Flux density distribution due to .", "texts": [ " In the proposed method, a mesh with the same subdivision in the plane is used for the 2-D analysis of the motor. The meshes used for the 3-D eddy current analyses of the PM with Methods 1 and 2 are also the same as shown in Fig. 5. The widths and are 0.1 and 0.2 mm, respectively. For each model, the period of steady state is analyzed in steps of electrical angle of degrees. In this section, we investigate the method for determining the gap width in Method 2. The distribution of flux density generated by , obtained by subtracting the flux density for from that for , is shown in Fig. 6. The figure shows that the reluctance of the motor core should be determined by taking the whole region of the motor into account because flux due to flows throughout the motor. Fig. 7 shows the variation in the equivalent gap width due to the rotor position. should be determined for each rotor position. Fig. 8 shows the temporal variation in eddy current losses. The eddy current losses are normalized by the average for the full 3-D model without division. The loss determined using Method 1 is much larger than that determined by full 3-D analysis, and the loss oscillated following the harmonic components" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001362_s0022-0728(96)04974-1-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001362_s0022-0728(96)04974-1-Figure3-1.png", "caption": "Fig. 3. Cyclic vollammograms of the (A) rhodium-modified and (B) blank CCEs in the absence (1) and in the presence (2) of 0.25M 1-1202. 0.15M phosphate buffer solution, pH5.8, scan rate 20mVs-t", "texts": [ " Cyclic voltammetry and steady state response regions. The base cyclic voltammograms are restored when the electrolyte is changed to buffer without glucose. The dynamic response of the RhICCEIGOx electrode to a step change of glucose at -0 .15 V vs. SCE is shown in Fig. 5(A). The sensor is rather fast and the response time is close to 10 s in the initial stages of the calibration curve. Both steady state and cyclic voltammetric responses were unaffected by solution agitation. Hence, it could be as- Fig. 3 shows the cyclic voltammograms of the blank and rhodium-modified CCEs, in the presence and absence of hydrogen peroxide. Hydrogen peroxide oxidation on the blank CCE without rhodium, starts at potentials higher than 0.40 V vs. SCE while the reduction slowly sets in at about -0 .2 V. Oxidation of peroxide with a rhodium-modified electrode starts at 0.250V and cathodic currents corresponding to the reduction process are observed at potentials below 0.250 V. Hence, it is possible that hydrogen peroxide can be determined by reduction, at potentials close to 0V (and lower) at a rhodium-modified CCE" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003261_ems.2009.106-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003261_ems.2009.106-Figure1-1.png", "caption": "Figure 1. Twin rotor multi input multi output system", "texts": [ "00 \u00a9 2009 IEEE with feedforward inverse-model control and augmented ANFIS and feedback inverse-model control. II. EXPERIMENTAL SET-UP The twin-rotor multiple-input multiple-output (MIMO) system (TRMS) is a laboratory set-up developed by Feedback Instruments Limited [11] for control experiments. Its behaviour in certain aspects resembles that of a helicopter. For example, it possesses a strong cross-coupling between the collective (main rotor) and the tail rotor, like a helicopter. A schematic diagram of the TRMS used in this work is shown in Figure 1. It is driven by two DC motors. Its two propellers are perpendicular to each other and joined by a beam pivoted on its base that can rotate freely in the horizontal and vertical planes. The beam can thus be moved by changing the input voltage in order to control the rotational speed of the propellers. The system is equipped with a pendulum counterweight hanging from the beam, which is used for balancing the angular momentum in steady-state or with load. The system is balanced in such a way that when the motors are switched off, the main rotor end of the beam is lowered" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003824_tmag.2012.2237390-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003824_tmag.2012.2237390-Figure11-1.png", "caption": "Fig. 11. Prototype.", "texts": [ " As for , the analysis result shows an oscillation of 6 Hz. This is thought to be due to the shape of the stator. As shown in Fig. 2, the stator poles are arrayed as a hexagon. When the rotor moves in a circular motion, the transmission torque when the permanent magnets are in line with the vertex of the hexagon is not the same as when they are not in line with the vertex. Therefore periodical disturbance appeared in the dynamic characteristic. In this section, the dynamic characteristics of a prototype are compared with the analysis results. Fig. 11 shows the prototype of the actuator. The rotor is supported by a gimbal structure which has two degrees of freedom. Using this structure, the sensing problem is easily resolved. Rotary encoders are attached on both axes of the gimbal structure and the dynamic characteristics are measured. The same trajectories shown in Table II were set as the desired trajectory. Figs. 12 and 13 show the results of the experiment. First we will compare the experimental results with the desired values. For in Case 1, the actual trajectory does not agree with the desired trajectory in the wider rotation range, as can be observed in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001844_0956-716x(94)90284-4-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001844_0956-716x(94)90284-4-Figure2-1.png", "caption": "FIG. 2: Schematic drawing of the experimental set up. Incident beam has an angular distribution in the c3 -plane and a wavelength distribution.", "texts": [ " Since the volume fraction ofT' phase decreases with increasing temperature, 70vo1% at room temperature and 67vo1% at 1273K (5), the main peak fraction should decrease slightly with increasing temperatures. The constrained misfit 8 c in units of the unconstrained misfit 8 u is expected to follow the same way as at room temperature, since considerable relaxation at this temperature takes place only after a couple of hundred hours of annealing (11). Experimental Setup The neutron scattering data were obtained with the E-3 experimental setup of the Berlin Neutron Scattering Center at the Hahn-Meitner-Institut, Berlin. The schematic drawing of Figure 2 shows the experimental setup after primary 10' collimator, monochromator and 15' secondary collimator. A graphite monochromator with a take off angle of 65 \u00b0 leading to neutron wavelengths of ~'1 = 3\"64'10\"10 m (relative intensity 11 = 0.3), ~'2 = 1-82\"10\"10 m (I 2 = 1), ~'3 = 1-21\"10-1\u00b0 m (I 3 = 0.1) and ;~4 = 0\"9\"10-10 m (I 4 = 0.01) was used. The intensities of the different wavelengths have been measured by comparing the integral intensities of several reflections. Corrections of peak intensities are necessary if a superlattice reflex with ~'1 coincides with a matrix reflex obtained with g 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002273_1077546304042047-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002273_1077546304042047-Figure4-1.png", "caption": "Figure 4. Combined curvature of clamped blades (Heisler, 1999).", "texts": [ "comDownloaded from A leaf spring consists mainly of laminated steel leaves assembled and held together by means of a central bolt. The leaf spring is connected to the chassis through the spring eyes. Figure 3 shows a complete description of the components of the leaf spring as well as the assembled leaf spring. The spring leaves are made of cold drawn steel. When the springs are manufactured, each leaf or blade is curved, i.e. given a camber set. The greatest set is given to the smallest leaf, and the set is progressively reduced as the span increases, as shown in Figure 4. The leaf end may be formed in different shapes, as shown in Figure 5. A square end is the cheapest to produce but it causes concentration of the interleaf pressure, resulting in more friction. An end trimmed with a diamond point makes a better approximation of the uniform stress along the spring. Also, the pressure distribution is slightly improved. A tapered end approximates very closely the ideal uniform stress shape. Because of the flexibility of the tapered leaf ends, the pressure distribution in the bearing area is improved and the interleaf friction is reduced" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003061_bf01261876-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003061_bf01261876-Figure1-1.png", "caption": "Fig. 1. Illustrating the notation used in the problem.", "texts": [ " its mass and linear dimensions are assumed to be negligibly small in comparison with unity. It is free to move in space under the influence of the gravitational attractions of the primaries. In the limit, if the linear dimensions of the satellite are allowed to vanish, the problem reduces to the conventional restricted problem. Let P be the location of a typical element of mass # of the satellite. Then ~ # = M where ~ is always understood to mean summation over all elements of mass of the satellite. Figure 1 illustrates the allocation of vectors as follows: Then Also OP =Q, O = r , a - - f f __ ~ s = 1 and 2. P Os = Mrs, ~ # 6 = 0, etc. = Ir l A and Qs is the unit vector parallel to Qs etc. ATTITUDE STABILITY OF A RIGID BODY 19 3. Equations of Mot ion Assuming that the mass M of the satellite is negligible in comparison with unity, and that its linear dimensions are also negligible in comparison with rl and r2, the equation of motion of G can be written in the form i~+ 20~ x ~ + t~ x (t~ x r) m(_~ m__ z ) = - rl + r3 r 2 9 (3" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002391_elan.200302858-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002391_elan.200302858-Figure1-1.png", "caption": "Fig. 1. Cyclic voltammograms of 1 mM 2-thiouracil at A) unmodified carbon paste, and B) CoPc-modified carbon paste electrodes. Electrolyte was 0.05 M phosphate buffer (pH 7.0); sweep rate was 100 mV s 1.", "texts": [], "surrounding_texts": [ "Keywords: 2-Thiouracil, 2-Thiobarbituric acid, Cobalt Phthalocyanine, Carbon-paste electrode\nThe chemical modification of electrodes is a growing field of interest in analytical chemistry [1 \u00b1 3]. One of the most important properties of chemically modified electrodes (CMEs) has been their ability to catalyze the electrooxidation of analyte species that exhibit high overvoltages at unmodified surfaces. The major effect of the modifier consists of lowering the potential required for the electrolysis of the catalyzed redox system and increasing the rate of electrochemical processes and therefore, increasing sensitivity and selectivity.\nIt has been shown in recent years that some of the transition metal complexes act as redox mediators and can catalyze the oxidation of organic compounds. Promising advances towards improved selectivity of carbon based electrochemical sensors have been achieved through judicious surface modification of the electrodes with these complexes [4, 5]. Cobalt phthalocyanine (CoPc) and its derivatives have been shown to act as effective electrocatalysts towards a wide range of redox systems. Electrodes modified with these compounds have shown great promise for the voltammetric [6 \u00b110] and potentiometric [11, 12] determination of many organic and biologically interesting compounds, mainly with regard to the possibility of decreasing the effective oxidation or reduction potentials of these compounds.\nSulfhydryl compounds are known to undergo electrochemical oxidation at solid electrodes, but their oxidation\noccurs at relatively high potentials [13, 14]. Several types of CMEs have been designed and characterized for the electrocatalytic oxidation of sulfuhydryl compounds, like cysteine and its derivatives [15 \u00b1 18], Glutathione [15, 19], sulfide ion [11], 2-mercaptoethanol [19 \u00b1 21], and other sulfhydryl compounds [14, 20, 21].\nThe purpose of the present work was to study the electrochemical behavior of 2-thiobarbituric acid and 2- thiouracil at the carbon-paste electrode modified with CoPc. Among the thiols and disulfides, thiouracils and thiopurines have attracted special interests. Thiouracils are minor components of transfer RNA,which have anti-herpes virus activities and have been used for treatment of hyperthyroidism in men. Thiopurines are usually used in cancer therapy [22 \u00b1 26]. Results of some studies show that some derivatives of 2-thiouracil, such as propylthiouracil, which was used as antithyroid drugs, produced thyroid cancers in human and in some animals such as, mice, rats and hamsters [27]. In this paper, we report the detail and systematic investigation for the catalytic mechanism of oxidation of these compounds at the CPE modified with CoPc, by using cyclic voltammetry and obtaining Tafel plots. This modified electrode was further successfully applied for the selective and sensitive determination of minor amounts of 2-thiobarbituric acid and 2-thiouracil by voltammetric measurements in the presence of some other biologically thiols such as cysteine, glutathione and thioglycolic acid in the complex matrix of human serum samples.\nElectroanalysis 2004, 16, No. 11 \u00b9 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/elan.200302858", "Cobalt phthalocyanine (CoPc) was obtained from Fluka. 2- Thiouracil, 2-thiobarbituric acid, graphite powder, and spectroscopic mineral oil (Nujol) were purchased from Merck, and used as received. All other chemicals were of analytical reagent grade from Merck. All aqueous solutions were prepared with doubly distilled deionized water.\nStock solutions of sulfhydryl compounds were freshly prepared as required in 0.05 M phosphate buffer at the desired pH (3 \u00b1 9) and protected from light during investigation. Voltammetric experiments were carried out in buffered solutions of thiol compound, deoxygenated by pure nitrogen (99.999%).\nVoltammetric experiments were performed with a Metrohm Computrace Voltammetric Analyzer Model 757 VA. A conventional three-electrode system was used with a carbon-paste working electrode (unmodified or modified with CoPc), a saturated Ag/AgCl reference electrode, and a Pt wire as the counter electrode. A digital pH/mV/Ion meter (CyberScan model 2500) was used for the preparing of the buffer solutions, which were used as the supporting electrolyte in voltammetric investigations.\nThe unmodified carbon-paste electrode was prepared by thorough hand mixing graphite powder with appropriate amount of mineral oil (Nujol) in a mortar and pestle [4]. A portion of the composite mixture was packed into the end of a Pyrex glass tube (ca. 2 mm i.d.). Electrical contact was made by forcing a copper wire down the glass tube and into the back of the composite. Modified electrode was prepared by mixing unmodified composite with CoPc (2% w/w) and then homogenized by dissolving in dichloromethane. The mixture was stirred in a magnetic stirrer till all the solvent evaporates. The modified composite mixture was then air dried for 24 h and used in the same way as unmodified electrode.\nCobalt phthalocyanine (CoPc) has shown great promise for reducing the overpotential required for the electrochemical oxidation of many organic compounds [28, 29]. Cyclic voltammograms were recorded using both unmodified and modified CPEs in buffered solutions of sulfhydryl compounds saturated with nitrogen. The catalytic function of the CoPc-modified electrode is demonstrated in Figures 1B and 2B by cyclic voltammograms of 1 mM 2-thiouracil and 2- thiobarbituric acid solutions (pH 7.0), which were obtained at the surface of the CoPc-modified CPE, respectively. Under the same experimental conditions, the direct oxidation of these thiol compounds at the unmodified CPE showed very weak anodic waves with a peak potential that was not defined. By using CoPc modified electrode, a well-\nElectroanalysis 2004, 16, No. 11 \u00b9 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim", "defined anodic wave can be obtained for each compound in the potential range examined, with peak potential at about 460 and 633 mV for 2-thiouracil and 2-thiobarbituric acid, respectively. The oxidation of these thiols at the modified electrode, gives rise to typical electrocatalytic responses with anodic peak currents that are greatly enhanced over those observed for the unmodified electrode.\nThe plot of the experimental anodic peak currents (ip, a) versus the square root of sweep rate (v1/2), obtained from cyclic voltammograms of the oxidation of both thiol compounds at the CoPc modified electrode within the range of 20 \u00b1 120 mV s 1 (Figure 3). The linear dependence of ip versus v1/2, as shown in Figure 3, indicates that the oxidation of these compounds at the surface of the modified electrode is indeed diffusion controlled and the rate-limiting adsorption steps and also specific surface adsorptions can be neglected. The plot of the current function (ip/cv1/2) versus v1/ 2 shows a negative slope for both thiols reveals that the oxidation of these compounds occurs in a catalytic fashion at the surface of the modified electrode.\nValues of na (where is the transfer coefficient and na is the number of electrons involved in the rate-determining step) were calculated for the irreversible oxidation of thio compounds according to the equation na 0.048/(Ep \u00b1Ep/2), whereEp/2 is the potential corresponding to ip/2. For both thiol, the values of na at the modified electrode were between 0.4 \u00b10.5 in the investigated potential sweep range (20 \u00b1 100 mV s 1) and various pH values. The results indeed suggest a one-electron transfer process in the rate-determining step for the electrocatalytic oxidation of thiols (assuming that the is about 0.5 for these irreversible systems).\nIn the elucidation of the mechanism for the ratedetermining step of a multi-steps reaction, the Tafel slope\nplays a prominent role. The results of polarization studies for both thiols were obtained in various pHs and in the range of potential sweep rate within 20 \u00b1 100 mV s 1. Figure 4 shows typical polarization curves at the CoPc-modified CPE in 0.001 M solutions of both thiol with pH 7.0. The slope of Tafel plots was in the range of 121 \u00b1 138 mV.decade 1 for the applied range of sweep rate. This could indicate that oneelectron oxidation of thiol is the rate-determining step.\nFor 2-thiobarbituric acid, no cathodic peaks were observed on the reverse scan within the investigated potential and pH range (Figure 5). But, in the case of 2-thiouracil, a cathodic peak was obtained in potentials more negative than 0.0 mV in acidic conditions (peaks a and b in Figure 6). It seems that this cathodic peak may correspond to reduction of the disulfide formed by the oxidation of thiol. As can be seen in Figure 6, by increasing the pH of the buffered solutions, the potential of this cathodic peak shifts to more negative values. At pHs greater than 5, only the oxidation wave of thiol is observed. Figure 7 shows the variation of cathodic peak current with v1/2 for the reduction of disulphide that produced from the anodic oxidation of 2- thiouracil at pH 3.0. The linearity with the square root of potential scan rate and zero intercept indicates that it corresponds to the diffusion controlled cathodic current in the reverse scan. Zagal and co-workers have already observed such behavior for catalytic electrooxidation of 2- mercaptoethanol on a graphite electrode modified with perchlorinated iron phthalocyanine [30]. It is not clear why the cathodic peak disappears at higher pHs, and further work is necessary to explain this behavior.\nThe graph of anodic half-peak potential versus pH showed that the maximum peak current shifts to more negative potentials by increasing pH (Figure 8). Such a\nElectroanalysis 2004, 16, No. 11 \u00b9 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim" ] }, { "image_filename": "designv10_13_0002240_j.precisioneng.2002.12.001-Figure15-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002240_j.precisioneng.2002.12.001-Figure15-1.png", "caption": "Fig. 15. Positions and motions of ball and groove far field points.", "texts": [ " If we displace the sphere into and along the cone\u2019s axis of symmetry the compression about the resulting circular contact will be uniform. Subsequent displacement perpendicular to the axis of symmetry will lead to variations in compression about the contact. As reaction force depends upon the compression of material, we expect the force per unit length of contact arc will vary about the ball\u2013groove contact. A common metric used to describe material compression between contacting elements is the distance of approach, \u03b4n, between two far field points [12]. Fig. 15 shows the distance of approach (as \u03b4n(\u03b8ri)) between far field points, SIi and Gi(\u03b8ri), in a cross-section through a joint cut at \u03b8ri. The distance of approach in a cross-section is a function of the axial (\u03b4 \u21c0 SIiz) and radial (\u03b4 \u21c0 r (\u03b8ri)) displacement of the SIi relative to the JCSi. Eq. (A.2) provides the axial and radial displacements as a function of ball displacement.[ \u03b4r(\u03b8ri) r\u0302 \u03b4SIiz k\u0302 ] = [ (\u03b42 SIix + \u03b42 SIiy )0.5 cos[\u03b8ri \u2212 atan(\u03b4SIiy/\u03b4SIix)] r\u0302 \u03b4SIiz k\u0302 ] (A.2) Using Fig. 15 and Eq. (A.2) we can produce the relationship for \u03b4n(\u03b8ri) given in Eq. (A.3). \u21c0 \u03b4 n (\u03b8ri) = { \u2212(\u03b42 SIix + \u03b42 SIiy) 0.5 cosphantom ( \u03b4SIiy \u03b4SIix ) [ \u03b8ri \u2212 atan ( \u03b4SIiy \u03b4SIix )] cos(\u03b8c)+ \u03b4SIiz sin(\u03b8c) } n\u0302 (A.3) A.4. Step 4: modeling interface forces as a function of \u03b4n For solid ball\u2013groove joints that experience elastic contact deformation, one may use classical line contact solutions to relate the distance of approach to the force per unit length of contact, f \u21c0 n (\u03b8ri) [15,17]. A more general, flexible approach is needed to model a wide range of contact situations" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002947_tac.1978.1101892-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002947_tac.1978.1101892-Figure8-1.png", "caption": "Fig. 8. Nyquist plots for Nashner\u2018s model including transport lag.", "texts": [ " These plots show that the system without transport lags is stable for &,= 10 with 85 0 such that Ix(to) - X,j < R 1 2 + I X ( t ) - X,I < -dist(X,,aS\"}, V t 2 t o X = A , @ , 8 ) z + W ( z , e = -nqz, (78) C: L (76) KRSTIC: INVARIANT MANIFOLDS AND ASYMPTOTIC PROPERTIES 825 4, 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002901_0278364909348762-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002901_0278364909348762-Figure3-1.png", "caption": "Fig. 3. Kinetic model of the hybrid robot in the use of (a) walking and (b) rolling.", "texts": [ " The introduction of legs to a wheeled robot might also lead it to be hybrid, of course. In either introduction, two legs are fixed at the knee axes with an offset that is necessary to prevent the legs from touching together in W-type. Note that the actuators remain, even when we attach the wheel (see Figure 2). Then no additional motors are needed. The arm behaves as a link of a serial manipulator in L-type and as a spoke of a wheel in W-type. Schematic models including parameters and constants are shown in Figure 3. To serve as a hybrid robot, each leg is necessary to be longer than the knee joint rim radius. Therefore, r R l (1) The legs attached to the same wheel move in the same plane when 2r l. However, when 2r l legs must have a cranked at Afyon Kocatepe Universitesi on May 15, 2014ijr.sagepub.comDownloaded from form so that they do not bump together and swing within a limited angular range to avoid a meeting of leg alignment. This implies that the leg does not allow cyclic rotation. In practical use as a hybrid robot, l might be limited within l 4r ", " These definitions are common in Wtype. However, the leg connected to the lower Jk has no role in supporting the robot weight. The leg posture function is important to make the robot move in L-type, but not in the process of sitting or standing for switching the locomotion type. In turn, it is necessary to minimize the power to achieve the switch with smoothness. In this section, we consider kinetics related to torque at joints Jh and Jk in order to make the robot stand or sit at a certain height H . By referring to Figure 3(a), we have Th Wdh W r cos r l sin (16) Tk Wdk Wl sin (17) H r sin r l cos (18) where H is defined in the range R H r l (19) However, the configuration to make the robot stand at the height H is not unique. For instance, there are two stationary configurations of I and II shown in Figure 8(a) making the sum of motor torque of Jh and Jk same. This is clear because the distance a2 is equal to the sum of a1 and 2b1. The same thing can be said about the three cases marked with I, II, and III in Figure 8(b) because of a1 b1 b1 a2 b2 b2 a3 b3 b3" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure11.26-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure11.26-1.png", "caption": "Fig. 11.26 Structural sketch of the fabric reeling device", "texts": [ " It consists of the frame (member 1, KF), a warp beam (member 2, KU1), a cloth beam (member 3, KU2), and a fabric belt (member 4, KT). The fabric belt includes the warps and the fabric. The warp beam is connected to the frame with a revolute joint JRx. The fabric belt is 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) 277 connected to the warp beam and the cloth beam with wrapping joints JW. The cloth beam is connected to the frame with a revolute joint JRx. It is a Type I mechanism with a clear structure. Figure 11.26 shows the structural sketch of the fabric reeling device. Figure 11.27 shows an imitation of the original illustration in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b. Figure 11.28 shows a real object of the type of TTTH for the foot-operated slanting loom. Ti Hua Ji (\u63d0\u82b1\u6a5f, a drawloom for pattern-weaving), also known as Hua Ji (\u82b1\u6a5f), or Zhi Ji (\u7e54\u6a5f), is a large weaving device that can produce cloth with complex patterns as shown in Fig. 11.29 (Wang 1991; Pan 1998). The foot-operated slanting loom, mentioned in Sect", " In this situation, the weft pressing device usually consists of the frame, a weight link, a connecting link, and a reed comb as shown in Fig. 11.25k. The linkage with weight helps the weaver to press the weft effectively and comfortably. Fabric Reeling Device The function of the fabric reeling device is to keep the warps tight and collect the fabric in which warps and wefts are interwoven. The fabric reeling device in the drawloom for pattern-weaving consists of four members and four joints, the same as the one in the foot-operated slanting loom in Sect. 11.3. Figure 11.26 shows the structural sketch of the fabric reeling device. Fig. 11.39 Imitation illustration of a drawloom for pattern-weaving (Hsiao and Yan 2011) As a result, Fig. 11.39 shows an imitation of the original illustration in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b. Figure 11.40 shows a real object of the drawloom for pattern-weaving. Ancient Chinese textile devices use rigid links and flexible members extensively. Through the transmission of links, a variety of types of motions have been generated and applied into different textile processes" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001450_cdc.1994.411345-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001450_cdc.1994.411345-Figure7-1.png", "caption": "Figure 7: An upper bound on the off-tracking of the trailer is computed when the lead car changes its path from an arc of a circle of radius T t o a straight line.", "texts": [ " For a 2 7, equation (12) gives the bound with the initial off-tracking of the kingpin hitch Figure 6 shows that the bound z1 from equation (14) is always greaterthan the bound zz from (15). Therefore, we use the first bound as the maximum distance the kingpin hitch and the trailer swing off the car's path. 0 Theorem 9 If the lead car of a two-azle system with equal length kingpin hitching changes from an arc of a circle of radius r to a straight line, then an upper bound on the off-tracking of the trailer, z , is where a is the arc length traveled by the lead car from the instant the car switches to the circle and X := r / L . Proof. The proof refers to Figure 7. We assume the car travels counterclockwise around the circle, then switches to the straight line a t the origin 0. The trailer is a t point D at the switching time, and at point B when the car has moved a distance L. The kingpin hitch is at point E initially and follows the straight line path of the car. From Lemma 6, we know that R 5 '1. Therefore, the trailer will swing into the circle during this maneuver. In contrast to the previous theorem, we calculate the maximum bound on the off-tracking of the trailer as our upper bound (the kingpin off-tracking is actually zero for this case)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001375_1.2834123-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001375_1.2834123-Figure1-1.png", "caption": "Fig. 1 Test linear bearing", "texts": [ " Third, we explain theoretically the rate of increase of the overall sound pressure level to the linear velocity of the carriage. Fourth, to explain the main peaks which appeared in the sound spectra, we examine the modes of the carriage and derive the frequency expressions for the natural vibrations of an LGT recirculating linear ball bearing having arbitrary contact angle. Finally, we discuss the relationship be tween the main peak and the natural vibration of the carriage. 2.1 Test Linear Bearings. The test linear bearings used in the sound measurement are LGT recirculating linear ball bearings shown in Fig. 1. One test linear bearing consists of one profile rail and one carriage with recirculating balls. Preloads of test linear bearings are light or medium. Table 1 shows the test linear bearing specification. All test linear bearings were lubricated with mineral oil (ISO VG56). 2.2 Drive Unit and Measuring System. Figure 2 shows the drive unit which was developed for sound and vibration measurement of linear motion rolling bearings (Ohta and Kajita, 1996). The drive unit consists of a motor, a coupling, support bearings, a sliding screw, sliding guides, a pusher, and a con crete bed" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003827_j.proeng.2012.07.149-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003827_j.proeng.2012.07.149-Figure8-1.png", "caption": "Figure 8 shows the construction of an improved inner diameter sensor. The sensor consists of two photo reflectors (GENIXTEK Co. Ltd., TPR-105F), an electronic circuit board, an acrylic board to adjust their height, four chip resistors, two plastic sheets and air supply port. Compared with the previous sensor, this sensor has the electric circuits using the chip resistor in order to decrease the electrical lines from the sensor. In the case of the improved sensor, electric lines connected to the sensor are decreased from 8 to 4 lines. As a result of this improvement, it is possible to unite the electric lines and air supply port into the bulkhead. In addition, in order to set the sensor in the middle point of the artificial muscle, two butterfly shaped thin plastic films are used so as to hold the sensor in the center of the tube, as shown in Fig.8. Each plastic sheet has two incisions with the width of 8mm around the photo reflector so as not to prevent the measurement of the inner diameter.", "texts": [], "surrounding_texts": [ "Figures 5 (a) and (b) show the experimental setup and the relation between output value from the sensor and the axial displacement of the rubber artificial muscle with inner diameter sensor, respectively. In the experiment, the longitudinal displacement of the muscle as a true value measured by the potentiometer (Sakae Tsushin Kogyo Co. Ltd., 18FLPA50) as shown in Fig.5 (a). The supplied pressure to the rubber artificial muscle was given from 0 to 500 kPa and from 500 to 0 kPa every 50kPa. Then, both the sensor output (A/D value) and the displacement of the muscle were measured. The measuring process mentioned above was repeated five times. In Fig.5 (b), the output value shows the sum of the difference from the initial value of each photo-reflector through an A/D converter. The initial value of the sensor is defined as zero when no pressure was applied to the rubber artificial muscle. From Fig.5 (b), it can be seen that the relation between the axial displacement and the output from the inner diameter sensor has no hysteresis and reproducible even if there is nonlinear relationship. This nonlinear relationship depends on the characteristics of the rubber artificial muscle and the photo-reflector. As a result as shown in Fig.5 (b), the following approximate equation between the displacement y [mm] and the sensor value x [A/D value] can be obtained. x106.086x101.091x103.235x103.878x101.477x102.003y 2243648510613 (2) In the approximation, we used the six degree of function in order to get suitable approximate value of the axial displacement from the sensor output. In the position control of the rubber artificial muscle, this approximate equation was used in the position control of the artificial muscle. In order to estimate the validity of the proposed measuring method using the tested sensor, Figs.6 (a) and (b) show two types of characteristics about the axial displacement of rubber artificial muscle. Figure 6 (a) shows the relation between the supplied pressure and the axial displacement of the rubber artificial muscle. Figure 6 (b) shows the relation between the sensor output and the axial displacement of the muscle. From Fig.6 (a), we can see that the hysteresis is large. Especially, there is a larger difference in a decompressed process. This phenomenon depends on the characteristics of the typical rubber artificial muscle. From Fig.6 (b), we can find that there is no hysteresis. It means that it is possible to realize position control system of the rubber artificial muscle for axial direction using the tested sensor with a compact sensor arrangement. In order to confirm the validity of measuring value using the tested sensor, Figure 7 shows the relation between the actual displacement of the rubber artificial muscle measured with the potentiometer and the estimated displacement calculated by using the output from the inner diameter sensor and Eq.(2). In Fig.7, symbols and the blue line show the experimental results and the ideal case that both the measured and actual displacement are same, respectively, As a result, we can confirm that the estimated displacement agrees well with the actual displacement. At the point of larger displacement in Fig.7, it can be seen that there is a little error. We think that this error is caused by the nonlinear characteristics of the photo-reflector. We found that the standard deviation of the error is 0.4 mm and the maximum estimated error is less than 2.0 mm. However, the sensor has a little problem that the sensor may not be able to measure the inner diameter exactly when the disturbance force is acted at the end of the muscle. Therefore, the compensation of the error in the case of acting the disturbance force to the muscle should be executed. In addition, the making the inlet compact is executed so as to unite the inlet of the air supply and the electrical signal lines for the sensor. 3. Improved inner diameter sensor 3.1. Single type inner diameter sensor In order to compensate the measuring error for the inclination of the sensor, an inner diameter sensor that has 4 photo reflectors to measure the inclined angle of the sensor board is proposed. Figure 10 shows the model of the improved inner diameter sensor, we call it \u201cDouble type\u201d for short. Each electric board in the double type sensor has two photo reflectors that are set on the parallel with a distance of W as shown in Fig.10. From the geometrical arrangement of the photo reflectors, the inclined angle of the board and the inner diameter of the muscle d can be obtained by following equations. Fig.10. Model for compensation using double type inner diameter sensor Wrr uu 211tan (3) Wrr dd 122tan (4) 221 (5) 221 uuu rrr (6) 221 ddd rrr (7) costrrd du (8) where r and t mean the distance between the tube of the muscle and each photo reflector and thickness of the inner diameter sensor, respectively. The subscripts of 1 and 2 show the location in the sensor as shown in Fig.10. Figure 11 shows the construction of the double type inner diameter sensor. The sensor consists of four photo reflectors (GENIXTEK Co. Ltd., TPR-105F), two electronic circuit boards, acrylic plates to adjust their height, six chip resistors and two plastic sheets. In order decrease the electric lines from the sensor, there is three through holes between two electric circuit boards. As a result, electric lines from the sensor can be decreased 6 lines even if two additional photo reflectors are added. In addition, by redesigned the bulkhead, the air supply port and electric lines for the sensor are united in one end of the muscle. The size of the inner diameter sensor is same as previous one as shown in Fig. 3. That is 9 mm x 40 mm x 8 mm. The inner diameter sensor can be produced with low cost. The cost of the sensor is less than 3 US dollars. In addition, the cost including the measuring system with a micro-computer (Renesas Electronic Co. Ltd., H8/3664) is about 20 US dolloers. Fig. 11. Modified inner diameter sensor Figure 12 shows the relation between the calculated inner diameter using the double type inner diameter sensor and the axial displacement of the rubber artificial muscle. In the experiment, the supplied pressure is given as a same method of previous experiment as shown in Fig.9. The inner diameter of the muscle is calculated by Equation (3) to (8) using low-cost micro-computer (Renesus electronics Co. Ltd., H8/3664). In the micro-computer, the program to calculate the distance between the tube and the photo reflector using the sensor output from each photo reflector is installed. The measuring process was repeated three times. From Fig.12, it can be seen that the repeatability of the sensor output using the double type sensor is superior to the result using the single type. Figure 13 shows the schematic diagram of a position control system using the rubber artificial muscle with the built-in inner diameter sensor. The control system consists of the rubber artificial muscle with the built-in inner diameter sensor, a potentiometer for the desired position, a microcomputer and a small-sized quasi-servo valve which consists of a switching valve and a PWM valve [6]. Fig. 13. Schematic diagram of control system The position control is done as follows. First, the micro-computer gets the voltages from the potentiometer for the desired value and the inner diameter sensor through the A/D converter. The displacement of the muscle is calculated by the approximate equation mentioned above. The deviation from the desired position is also calculated. As a control method, we apply the On/Off control scheme and the proportional control scheme as shown in Eq. (3) to the system. eKu p (9) Where e, Kp and u show the position error, the proportional gain and the input duty ratio for the PWM control valve in the quasi-servo valve, respectively. The sampling period for On/Off control is 2.6ms and the sampling period for P control is 2.8ms. The PWM period is 5ms. Figure 14 shows the transient response of the axial displacement of follow-up control that used the proportional control mentioned above. In Fig.14, the red, blue and green lines show the desired position, the calculated displacement using the sensor and the actual displacement measured by the potentiometer, respectively. From Fig.14, it can be seen that the tracking performance of the displacement is relatively good even if the simple control scheme was used. In addition, the error of the axial displacement of the muscle is small, that is less than \u00b12 mm." ] }, { "image_filename": "designv10_13_0003619_065002-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003619_065002-Figure1-1.png", "caption": "Figure 1. Polymer micromagnet fabrication process and microscopy images. (a) Magnetic polymer composite and sacrificial layers were deposited by spin-coating onto silicon wafer; the composite was patterned using UV photolithography followed by a chemical development step to remove excess composite material. (b) SEM image of single 40 \u03bcm thick magnet, scale bar = 100 \u03bcm; (c) SEM image of patterned micromagnet array. (d, e) Optical microscopy images of patterned micromagnets before and after dissolving sacrificial layer. Scale bars in (c)\u2013(e) = 250 \u03bcm.", "texts": [ "9%) concentrations by mass fraction (volume) in microcentrifuge tubes. To avoid settling of the magnetic particles and attain a uniform dispersion, samples were mixed by vortexing (Vortex Genie 2, Scientific Industries) at 3000 rpm for 30 min immediately prior to use. Unless otherwise stated, particle concentrations are given by fractional mass percentage in the text. Micromagnetic structures were fabricated on silicon wafers covered with a sacrificial layer (Omnicoat, MicroChem) using the process shown in figure 1(a). The sacrificial layer was applied by spin-coating at 500 rpm for 5 s, followed by 3000 rpm for 30 s, and baking at 200 \u25e6C for 1 min, in accordance with the manufacturer\u2019s instructions. After the wafer cooled to room temperature, the mixed magnetic composite material was applied to the surface by spin-coating at 500 rpm for 5 s (ramp rate of 100 rpm s\u22121) followed by 30 s at 1000, 2000, 3000 or 4000 rpm (ramp rate of 300 rpm s\u22121). This was followed by pre-exposure bake, UV exposure, postexposure bake and development steps that were all conducted according to the manufacturer\u2019s recommendations for pure SU-8 unless otherwise specified", " Despite the multiple spin-coating and patterning steps, scanning white-light interferometry showed the top surfaces to be flat within 1 \u03bcm; profilometry data for the micromagnet in figure 4( f ) is shown in figure 4(g). The hybrid magnetic structures are also biocompatible and chemically resistant because the magnetic microparticles are completely encapsulated inside an inert SU-8 layer. Complete internalization of particles cannot be guaranteed when using any photopatternable composite and singlelayer deposition/patterning (figure 1(a)), because particles are immobilized in the composite during the pre-exposure-bake processing step prior to patterning. When the geometry is then defined by UV lithography, it is statistically likely that some particles will fall on the boundary of the UV-exposed area and will remain partially-imbedded in the material sidewalls when the composite is developed. The hybrid fabrication method encapsulates the composite regions in pure SU-8, which has been shown elsewhere to have excellent chemical resistance [30] and biocompatibility [31]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003878_j.robot.2013.08.005-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003878_j.robot.2013.08.005-Figure12-1.png", "caption": "Fig. 12. Example assembly task in SE(2). A componentwith four holes is positioned over a target with four pegs, and lowered into place.", "texts": [ " In other caseswemay be interested only in planar motion in SE(2), or even simply X\u2013Y positioning in R2 (see Fig. 27). In all cases the above method still applies; \u03c1(\u00b7) and \u03b1(\u00b7) are simply defined for the degrees of freedomwe are interested in. 4.4. An example in SE(2) This section applies the probabilistic assembly model to a pick and place operation in SE(2). While this is the same operation used to assemble most of our system\u2019s components (see Section 5), it is also a common task in industry. For this reason, we have chosen a SCARA type robot manipulator to illustrate this example. Fig. 12 shows a robot manipulator grasping a component with four holes. The component is positioned over a target with four pegs, and lowered into place. For the purposes of this example, it is assumed that positioning error in the robot\u2019s vertical axis, q4, does not substantially effect the success of an assembly process. Further, it is assumed that the joint axes q1 \u00b7 \u00b7 \u00b7 q4 are parallel and closely aligned with the workspace z axis. Therefore, we can consider the assembly operation simply as a placement task in SE(2)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002387_elan.1140010210-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002387_elan.1140010210-Figure1-1.png", "caption": "FIGURE 1. Expanded view of t h e flow cell: (A) carbon fiber; (6) mercury; (C) epoxy; (D) Teflon tape; (E) copper wire; (F) inlet; (G) outlet.", "texts": [ " The electrode was modified by potentiostatic platiniration carried out for 15 min ;it ;I potential of -0.18 V. The 5-ml platinization solution contained 165 nig hydrogen hexach1c)ropLatinate hydrate, 7.5 mg glucose oxidase, and 3 mg lead nitrate; the solution pl I was adjusted t o 3.5 with sodium hydroxide. After the codeposition o f glucose oxidase and platinum particles, the electrode was dipped for 1 hr in a stirred 0.1 M phosphate buffer ( p H 6.8). The modified electrode was then inserted into a T-shaped glass connecter that served as the body o f the flow cell (Fig. 1). A Teflon tube (1.2 mm i d . ) was placed on the opposite side to serve as the solution inlet. Teflon tapes sealed around the working electrode and tlie inlet tube. The cell outlet W;IS clipped i n ;I downstream reservoir (5-nil beaker) containing the reference and auxiliary electrodes. Solution flow through the cell w;~s governed by gr:ivity. Measurements were made 30-40 niin after the working potent;.al ( +0.80 or +0.85 V ) W;IS applied, to allow decay o f transient currents; the blank solution was tlowing slowly (0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001450_cdc.1994.411345-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001450_cdc.1994.411345-Figure2-1.png", "caption": "Figure 2: The phase portrait of 4. The two equilibrium points are (stable) and dez (unstable). The arrows indicate the direction Q moves when near an equilibrium point.", "texts": [ " To determine the stability of the system ( 5 ) , we use the Liapunov linearization method [8] to linearize equation (5) about the equilibrium point E {&I, & z } : _ - This gives the autonomous linear equation (6) dr r d a - = -,cos& z , where z := d-& is the linearized variable. The linearized system has the solution When 4e = &I, COB&I 2 0 and & 5 0. Thus, r converges exponentially to zero, or I$ converges to exponentially. Therefore, the equilibrium point +=I is locally exponentially stable. When 4. = &z, C O S + ~ Z 5 0 and 2 2 0. Thus, z diverges exponentially away from zero, or 4 diverges away from +=z exponentially. Therefore, the equilibrium point &Z is locally unstable. This is illustrated in the phase portrait in Figure 2. Since the linearized system (6) is locally exponentially stable in a neighborhood of the equilibrium point 4, = X we can conclude that the nonlinear system ( 5 ) is also locally exponentially stable in a neighborhood of del. 0 Figure 3 shows the stable and unstable equilibrium positions for this vehicle. The stable position has the trailer at point D with ADC a right triangle. If we restrict 141 5 ~ / 2 , i.e., where the trailer avoids the jack-knife positions, then 4 never reaches the unstable equilibrium" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002980_978-3-642-01153-5-Figure1.9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002980_978-3-642-01153-5-Figure1.9-1.png", "caption": "Figure 1.9.1 Sketch map for setting rotor motion equation", "texts": [ " AC Machine Systems 42 If P is the pole-pair number of the electric machine, is the electric angle by which the rotor d -axis leads ahead of the stator coordinates system axis (i.e. rotor position angle), then there is / P If according to generator convention, positive electro-magnetic torque is considered as braking torque, then the electro-magnetic torque can be written as T 2e PT Li i (1.9.8) When the rotor motion equation of the electric machine is set up, the generator is considered as a standard, such as in Fig. 1.9.1. Here, mT is the mechanical torque of the prime mover which is consistent with rotor general rotation direction; eT is the electro-magnetic breaking torque; surplus torque m eT T is the accelerating torque, and the rotor motion equation can be set up as d d m eJ T T t (1.9.9) where J is rotary inertia; is mechanical angular speed; d dt is angular acceleration. If the mechanical angle between rotor d -axis and phase a axis is expressed by , then d dt , thus formula (1.9.9) becomes 2 2 d d m eJ T T t (1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001647_s1567-5394(01)00144-x-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001647_s1567-5394(01)00144-x-Figure4-1.png", "caption": "Fig. 4. Schematic representation of hypothesis made on the interaction between the hydrophobic lined channel of catalase and the hydrophobic (non-EP) or hydrophilic (EP) GC electrode surface.", "texts": [ " Analysis by scanning tunneling microscopy of catalase adsorption on highly oriented pyrolytic graphite has led to the conclusion that anodization of graphite creates carboxyl groups, which react with the amine of the polypeptide chain to fix catalase onto the surface [8]. According to this last work, it may be suggested that EP provokes adsorption of catalase in an orientation which prevents electron transfer. Moreover, EP modifies the GC surface from hydrophobic to hydrophilic properties [9]. The con- nection of the hydrophobic channel of catalase might consequently be more difficult with the EP electrode than with the non-EP electrode as schematised in Fig. 4. When catalase was adsorbed on non-EP electrodes from DMSO solution, the current increase that was obtained can no longer be explained by Scheme I. In this case it is postulated that a direct electron transfer between catalase and the GC electrode occurs, which catalyses the direct electrochemical reduction of oxygen. [1] E. Horozova, Z. Jordanowa, V. Bogdanovskaya, Enzymatic and electro- chemical reactions of catalase immobilized on carbon materials, Z. Naturforsch. 50 (1995) 499\u2013504. [2] E. Horozova, N" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.6-1.png", "caption": "Fig. 9.6 A chain conveyor cylinder wheel (\u9ad8\u8f49\u7b52\u8eca) a Original illustration (Wang 1991), b Structural sketch of human-driven, c Structural sketch of animal-driven", "texts": [ " Its power comes from human or animals. The structure of the device is similar to Fan Che (\u7ffb\u8eca, a paddle blade machine), and its water lifting component is identical to Tong Che (\u7b52\u8eca, a cylinder wheel). Its structure contains a wooden board, two wheels in the higher and lower positions, a chain connected by ropes and bamboo cylinders, and the members designed for the power source (not shown in the 9.2 Water Lifting Devices 195 196 9 Flexible Connecting Mechanisms 9.2 Water Lifting Devices 197 illustration), as shown in Fig. 9.6a (Wang 1991). If the device is powered by human, the upper turning shaft needs to add more pedals to pedal (the same as Fan Che); if powered by animals, the device needs to add an extra pair of vertical and horizontal gears, and it would then have a similar structure as Niu Zhuan Fan Che (\u725b\u8f49\u7ffb\u8eca, a cow-driven paddle blade machine). Human-driven Gao Zhuan Tong Che is a mechanism with four members and four joints, including the frame (member 1, KF), an upper wheel (member 2, KK1), a lower wheel (member 3, KK2), and a chain (member 4, KC). The upper wheel is 198 9 Flexible Connecting Mechanisms connected to the frame with a revolute joint JRx. The chain is connected to the upper and lower wheels with wrapping joints JW. The lower wheel is connected to the frame with a revolute joint JRx. Figure 9.6b shows the structural sketch. Animal-driven Gao Zhuan Tong Che is a mechanism with five members and six joints, including the frame (member 1, KF), a horizontal gear with a vertical shaft (member 2, KG), an upper wheel with a vertical gear (member 3, KK1), a lower wheel (member 4, KK2), and a chain (member 5, KC). The horizontal gear is connected to the frame and the upper wheel with a revolute joint JRy and a gear joint JG, respectively. The other adjacent relationships are identical to the ones in human-driven device. Figure 9.6c shows the structural sketch. 9.2.5 Shui Zhuan Gao Che (\u6c34\u8f49\u9ad8\u8eca, A Water-Driven Chain Conveyor Water Lifting Device) Shui Zhuan Gao Che (\u6c34\u8f49\u9ad8\u8eca, a water-driven chain conveyor water lifting device) is a Tong Che (\u7b52\u8eca, a cylinder wheel) but driven by water as shown in Fig. 9.7a (Wang 1991) (the horizontal water wheel and the gear train are not shown in the illustration). Its structure is similar to the animal-driven Gao Zhuan Tong Che but with an additional horizontal water wheel. Figure 9.7b shows the structural sketch" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003523_j.bios.2011.02.021-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003523_j.bios.2011.02.021-Figure1-1.png", "caption": "Fig. 1. (a) Configuration of edge-plane microsensor. The diameter (\u00d8) of all three wires is shown on the left, while the size of the inner and outer diameter of the encasing polyethylene tube is shown on the right. SEM images of the \u2018electrochemical rebuilt surface\u2019 of the Au working electrode, without (b) and with (c) Pt nanoparticle deposit.", "texts": [ " bias potential for H2O2 and glucose were calculated using linear regression analysis between four concentrations points of analyte (100, 200, 300, and 400 M for H2O2 and 1, 2, 3, and 4 mM of glucose, respectively). The apparent Michaelis\u2013Menten constant (Kapp m ) of GOx-based glucose sensors was obtained using the Hill equation (n = 1), (Hale et al., 1991) with the help of Origin 8.0 plotting software. All experiments were repeated in triplicate and the data are presented as mean \u00b1 S.D. 3. Results and discussion 3.1. Edge-plane microsensor geometry The configuration of the edge-plane microsensor geometry is shown in Fig. 1a. Using microelectrodes in microfluidics configurations, our previous research indicated that distances varying from microns to millimeters range between the working, counter and reference electrodes show minimal (less than 5%) effect in sensor performance (Qiang et al., 2010). Accordingly, for the as cut, edge-plane sensors, inter-electrode distance variability resulted in a similar standard deviation range for H2O2 sensitivity (i.e. less than 5%). Surprisingly, even though such edge-plane sensor contains a working electrode with diameter of ca", "8 V bias, the Au surface gets oxidized and the gold ons form a soluble complex with OH\u2212, to be re-deposited in the h Pt nanoparticle (NPs) edge-plane sensors for H2O2 detection. (b) Corresponding ing rate, with (i) and (iii) showing microelectrode behavior. negative \u22121.0 V bias interval. During both positive and negative intervals, the generation of oxygen and hydrogen micro-bubbles template the Au re-deposition towards nano-/micro-porous morphology (Huang et al., 2009a). As this electrochemical rebuilding proceeds, the nanoporous structure advances deeper into the Au electrode. Fig. 1b illustrates a representative surface morphology as obtained by scanning electron microscopy (SEM), with pore size in the range of 100\u2013500 nm, as previously reported (Huang et al., 2009a). In order to improve stability and increase electrocatalytic activity, the surface of nanoporous Au working electrode was decorated with Pt nanoparticles by electroplating in 10 mM H2PtCl6 at \u22120.05 V for 60 s (Qiang et al., 2010). Fig. 1c shows the surface morphology of the Pt-coated nanoporous Au working electrode. By comparing the SEM micrographs of Fig. 1(b and c), Pt nanoparticles cover effectively the nanoporous Au surface, albeit decreasing slightly its pore size. In order to confirm the effect of Pt nanoparticles on the microelectrode behavior of the working electrode, the CV curves of the microsensors based on as cut (i) edge plane, nanoporous Au (NPG) (ii) and NPG with Pt nanoparticles are shown in Fig. 2b, when tested in 10 mM K3Fe(CN)6 and 1 M KCl at a scan rate of 10 mV/s. The introduction of Au nanoporosity, increased significantly the curve F kgrou v Fig. 1 s b t t 0 i t s i I b r H e a h w s t v a c n b s 3 e e s r t s m m b v s 3 e H t h H i h ig. 3. Edge-plane H2O2 sensor performance: (a) H2O2 sensitivity (left ordinate), bac ersus applied potential (against the built-in Ag/AgCl reference electrode, shown in eparation during forward and backwards scans due to appreciale increase in its surface area, while at the same time retaining the ypical steady-state diffusion current of the as cut Au microelecrode (i) (Huang et al., 2009b). However, the redox currents above .3 V and below 0.05 V show deviations from the sigmoidal shape, ndicative of inherent instability of NPG. Upon nano-Pt decoration, he sigmoidal steady state behavior is recovered over the entire canned range, which is attributable to the extreme electrochemcal stability of Pt and crucial for subsequent sensor applications. n accordance with the SEM results of Fig. 1(b and c), the spacing etween the forward and backwards scans decreased slightly as a esult of decreased porosity following nano-Pt deposition. Fig. 2a illustrates the sensitivities of these three electrodes to 2O2 (at 0.6 V vs. Ag/AgCl reference). The initial sensitivity of NPG lectrode (ii) increased by 374 fold (86.1 nA mM\u22121) vs. that of the s-cut edge plane Au electrode (i) (i.e. 0.23 nA mM\u22121). However, ere it is important to mention that the aforementioned NPG value as obtained immediately after its electrochemical re-building tep, and its sensitivity steadily decreased after each test (i" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure14-1.png", "caption": "Fig. 14. Bearing contact and contact stresses for the pinion (left) and gear (right) of helical gear drive of design A3 at the instantaneous contact point 9 when errors of alignment \u0394H2=\u0394V2=0.025\u00b0 occur.", "texts": [], "surrounding_texts": [ "As previously mentioned, pointing and undercutting of the shaver tooth surfaces have to be avoided. Pointing of the shaver means that the width of the topland becomes very small or equal to zero. Undercutting occurs when the generating tool removes part of the active surface of the gear teeth. Analytically, undercutting can be predicted by the appearance of singular points on the generated surface. Undercutting is avoided by considering the approach proposed by F.L. Litvin and represented in detail in [10]. Undercutting can be avoided by choosing an appropriate number of teeth. Larger pressure angles are in favor of avoidance of undercutting. Pointing is avoided by increasing the number of teeth of the shaver and the proper control of the helix angle, the pressure angle and the crossing angle. Fig. 7. Face width of the to-be-shaved gear and the shaver: (a) 3D 5. Computerized simulation of meshing and contact 5.1. Applied coordinate systems Fig. 8 represents the applied coordinate systems for tooth contact analysis (TCA) of a helical gear drive comprising a pinion of new geometry obtained by plunge shaving and a conventional helical gear. The following errors of alignment are considered: (i) axial displacement of the pinion, \u0394A1, (ii) axial displacement of the gear, \u0394A2, (iii) gear horizontal positioning shaft error, \u0394H2, and (iv) gear vertical positioning shaft error, \u0394V2. Coordinate systems S1 and S2 are movable coordinate systems rigidly connected to the modified shaved helical pinion and a conventional helical gear, respectively. Angles \u03d51 and \u03d52 are the angles of rotation of the pinion and the gear, respectively. Table 2 shows details of coordinate transformation from S1 to S2. 5.2. Discussion of results obtained A helical gear drive with main design parameters shown in Table 3 will be considered for tooth contact analysis and later for finite element analysis. Three cases of design, with design characteristics shown in Table 4, will be considered. Case of design A1 represents the conventional design of a helical gear drivewith lineal-type contact. The results of tooth contact analysis of the mentioned design of a helical gear drive when (a) no errors of alignment occur, (b) errors \u0394H2=\u0394V2=0.01\u00b0 occur, and (c) errors \u0394H2=\u0394V2=0.025\u00b0 occur are shown through Fig. 9(a), (b) and (c), respectively. For the conventional design of a helical gear drive, the bearing contact is lineal-type, it is not localized, and when errors of alignment occur, the contact pattern is shifted to the edge of the surface. view of the to-be-shaved gear; and (b) 3D view of the shaver. Fig. 9(d) represents the function of transmission errors for referred configurations of case of designA1. A piecewise almost linear function of transmission errors (see Fig. 9(d)), responsible of the noise and vibration of the gear drive is obtained when errors of alignment are present. Case of design A2 represent the application of partial crowning in longitudinal and profile direction by considering the theoretical generation by a rack cutter with generating surface divided in nine zones as shown in Fig. 1(a). The results of tooth contact analysis of the mentioned design of amodified helical gear drivewith partial crowning when (a) no errors of alignment occur, (b) errors \u0394H2=\u0394V2=0.01\u00b0 occur, and (c) errors \u0394H2=\u0394V2=0.025\u00b0 occur are shown through Fig. 10(a), (b) and (c), respectively. Themain advantages of application of partial crowning for modification of the geometry of a helical gear drive are obtained from the combination of the advantages of lineal and localized contacts.We can summarize the advantages as follows: (i) the bearing contact is localized when errors of alignment occur, and (ii) the smaller errors of alignment occur, the larger contact pattern is obtained, and lower contact stresses are expected. A very favorable function of transmission errors of low level is obtained for referred configurations of case of design A2 (see Fig. 10(d)). Case of design A3 represent the application of total parabolic crowning in longitudinal and profile direction. Total crowning means that the whole surface is crowned so that zones 2, 4, 5, 6 and 8 in Fig. 1 do not exist. The results of tooth contact analysis of mentioned case of design of a modified helical gear drive for same configurations than for the previous case of design are shown in Fig. 11. When total parabolic crowning is applied in longitudinal and profile directions, the bearing contact is localized and the gear drive is not sensitive to the appearance of errors of alignment. A parabolic function of transmission errors is obtained for all three cases of design. Based on the results of TCA, designs A2 and A3 with partial and total crowning, respectively, fulfill the requirements of gear drives of low noise and vibration levels, high endurance, and increased service life. In this stage, finite element analysis of both gear drives is fundamental to select the better approach for modification of the geometry of a helical gear drive. 6. Stress analysis This section covers stress analysis and investigation of formation of the bearing contact for modified helical gears finished by plunge shaving. The performed stress analysis is based on the finite-element method and application of a general purpose computer program [11]. The development of finite-element models of modified helical involute gears has been accomplished according to the ideas represented in [12]. Application of finite element analysis enables investigation of the formation of the bearing contact and the determination of contact and bending stresses for the whole cycle of meshing. Finite element models of three pairs of contacting teeth are used to study the influence of the load sharing on the bearing contact on the pinion and gear tooth surfaces. The main design parameters of the gear drive and cases of design investigated are shown in Tables 3 and 4. Elements C3D8I [11] of first order (enhanced by incompatiblemodes to improve their bending behavior) have been used to form the finite-element mesh. The total number of elements is 59372 with 67572 nodes. The material is steel with the properties of Young's module E=2.068\u22c5105 MPa and Poisson's ratio 0.29. A torque of 1600 Nm has been applied to the pinion. Figs. 12, 13, and 14 show the bearing contact and contact stresses for the pinion and the gear of a helical gear drive of design A1, A2 and A3, respectively, when errors of alignment \u0394H2=\u0394V2=0.025\u00b0 occur. An area of high contact stresses is observed in Fig. 12 due to a linealtype contact. Such area of high contact stresses is avoided for cases of design A2 and A3 where the contact is localized. Fig. 15 represents the evolution of contact and bending stresses for the pinion of a helical gear drive for the following cases of design: (i) conventional design (case A1), (ii) partial crowning (case A2), and (iii) total crowning (case A3). For all cases, errors of alignment \u0394H2=\u0394V2=0.025\u00b0 have been considered. Conventional design yields very high contact stresses due to the theoretical lineal-type contact shifted to edge contact. Modified helical gear drive represented in cases A2 and A3 show a smooth evolution of contact stresses due to the localization of the bearing contact, with the approach based on partial crowning of the pinion tooth surfaces yielding the lower contact stresses. The level of bending stresses is almost the same for all three cases of design as shown in Fig. 15(b). Fig. 16 shows the evolution of contact stresses for the pinion of cases of design A2 (Fig. 16(a)) and case of design A3 (Fig. 16(b)) for different values of errors of alignment. As shown in Fig. 16(a) for case of design A2, the lower the misalignment is, the lower contact stresses are obtained, increasing the endurance and life expectation of the gear drive. On the contrary, case of design A3 yield similar results of contact stresses no matterwhat thevaluesofmisalignments are. Therefore, bothapproached work properly for modified helical gear drives finished by plunging, having the approach based on partial crowning the possibility to reduce contact stresses even more when low errors of alignment occur. 7. Conclusions The results of the performed research allow the following conclusions to be drawn: (1) A modified geometry of helical gear drives finished by plunge shaving has been proposed and investigated. The geometry of the shaver tooth surfaces that will shave the helical pinion and apply the proposed surface modifications has been developed. (2) Geometric characteristics of the proposed shaver has been discussed. The necessary face width of the shaver and the con- ditions for avoidance of pointing and undercutting have been studied. (3) A numerical example of design of a modified helical gear drive has been represented. Three cases of design have been studied. Tooth contact analysis and stress analysis for the mentioned three cases of design,when different levels of errors of alignment are present, have been performed and the results compared. (4) Partial crowning of the pinion tooth surface has been proposed as the optimal design for a helical gear drive, yielding the lower contact stresses and transmission errors when errors of alignment occur. Acknowledgments The authors express their deep gratitude to Yamaha Motor Company and the Spanish Ministry of Science and Innovation (Project Ref. DPI2007-63950) for the financial support of respective research projects and to the latter for the support received through the Spanish National Program ofMobility of Human Resources, Reference PR20080331. References [1] D.P. Townsend, Dudley's Gear Handbook, 2nd EditionMcGraw-Hill, Inc., New York, 1991. [2] F.L. Litvin, Q. Fan, D. Vecchiato, A. Demenego, R.F. Handschuh, T.M. Sep, Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving, Computer Methods in Applied Mechanics and Engineering 190 (39) (2001) 5037\u20135055. [3] I. Moriwaki, M. Fujita, Effect of cutter performance on finished tooth form in gear shaving, Journal of Mechanical Design, Transactions of the ASME 116 (3) (1994) 701\u2013705. [4] D.H. Kim, Simulation of plunge shaving operation for spur and helical gear, and tooth contact analysis of finished gear drive, Proceedings of the ASME Design Engineering Technical Conference, vol. 4 A, 2003, pp. 247\u2013256. [5] S.P. Radzevich, Design of shaving cutter for plunge shaving a topologically modified involute pinion, Journal of Mechanical Design, Transactions of the ASME 125 (3) (2003) 632\u2013639. [6] S.P. Radzevich, Computation of parameters of a form grinding wheel for grinding of shaving cutter for plunge shaving of topologically modified involute pinion, Journal ofManufacturing Science and Engineering, Transactions of the ASME127 (4) (2005) 819\u2013828. [7] R.H. Hsu, Z.-H. Fong, Theoretical and practical investigations regarding the influence of the serration's geometry and position on the tooth surface roughness by shaving with plunge gear cutter, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220 (2) (2006) 223\u2013242. [8] S. Nakada, I. Moriwaki, Effect of preshaved form and cutter performance in plunge cut shaving, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007, vol. 7, 2008, pp. 39\u201346. [9] F.L. Litvin, I. Gonzalez-Perez, A. Fuentes, K. Hayasaka, K. Yukishima, Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis, Mathematical and Computer Modelling 42 (9\u201310) (2005) 1063\u20131078. [10] F.L. Litvin, A. Fuentes, Gear Geometry and Applied Theory, 2nd EditionCambridge University Press, New York (USA), 2004. [11] I. Hibbit, Karlsson & Sirensen, ABAQUS/Standard User's Manual, 1800 Main Street, Pantucket, RI 20860-4847, 1998. [12] J. Argyris, A. Fuentes, F.L. Litvin, Computerized integrated approach for design and stress analysis of spiral bevel gears, Computer Methods in Applied Mechanics and Engineering 191 (2002) 1057\u20131095." ] }, { "image_filename": "designv10_13_0001563_jsvi.1998.9999-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001563_jsvi.1998.9999-Figure2-1.png", "caption": "Figure 2. Spherical bearing kinematics and coordinate system: (a) front view, (b) enlarged side view.", "texts": [ " The spherical roller-type bearing has a fully crowned contour on its contact dimension. The radius of curvature of this contour will typically approach that of the inner and outer raceway curvature radii but not reach them [8]. Hence, theoretically both ball- and roller-type spherical bearings start with point/elliptical contact areas (except under heavy loading) and the contact angle a is a function of the load condition. The mean bearing translational displacements qm which are accompanied by mean load values Fm as shown in Figure 2 are given by the relative rigid body motions between the inner and outer rings. Note that angular displacements about the x and y axes need not be considered here since, due to the self-aligning nature of the spherical bearing, they are not opposed by moment loads. The total bearing displacement vector is given as q= qm + qa(t), where qa(t) is the fluctuation about the mean point qm. In general, for small preloads and/or relatively large time dependent values of qa(t), the bearing stiffness is time dependent and non-linear", " The specific objectives of this study are as follows: (1) to develop a new bearing stiffness matrix which is suitable for the analysis of vibration transmission through either ball or roller-type spherical bearings; (2) to develop an experimental technique to measure spherical bearing direct and cross-coupling stiffness coefficients as a function of axial and radial mean loads (preloads); (3) to verify the proposed stiffness model by comparing its predictions with experimental measurements; and (4) to relate the stiffness matrix values to various kinematic and design parameters, specifically unloaded contact angle and radial clearance, through parametric studies using the bearing stiffness matrix model. Consider the self-aligning double-row rolling element bearing shown in Figure 2. The relationships between the mean forces Fm = {Fxm, Fym, Fzm}T transmitted through the bearing and the resulting mean bearing displacements qm = {qxm, qym, qzm}T will be derived. From the bearing displacements the resultant elastic deformation d(Ci j ) of the jth rolling element of the ith row located at angle Ci j from the x-axis can be determined. Assuming the outer ring is fixed, in Figure 3 one has: d(Ci j )=6A(Ci j )\u2212A0 0 A(Ci j )qA0 A(Ci j )EA07 , A(Ci j )=z(di zj )2 + (di rj )2 , di zj =A0 sin (ai 0)+ qzm \u2212Pe , di rj =A0 cos (ai 0)+ qxm cos (Ci j )+ qym sin (Ci j )\u2212 rL " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.16-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.16-1.png", "caption": "Fig. 6.16 Throwers (\u6a91). a Original illustration (Mao 2001). b Structural sketch", "texts": [ " The colliding device is a mechanism with three members and two joints, including the frame (member 124 6 Roller Devices 6.5 War Weapons 125 1, KF), a rope (member 3, KT), and a colliding rod (member 4, KL). The rope is connected to the frame and the colliding rod with thread joints JT. Figure 6.15c shows the structural sketch of the colliding device. Lei (\u6a91, a thrower) also known as Lei (\u96f7), is a heavy object for throwing to attack soldiers under and outside the city walls. It has many different types as shown in Fig. 6.16a (Mao 2001). It is a mechanism with three members and two joints, including a wooden link (member 1, KL), a roller (member 2, KO), and a rope (member 3, KT). The link is connected to the roller and the rope with a revolute joint JRx and a thread joint JT, respectively. Figure 6.16b shows the structural sketch. Lang Ya Pai (\u72fc\u7259\u62cd, a thrower) has the same function as Lei (\u6a91) as shown in Fig. 6.17a (Mao 2001). It increases the area of the spiked surface and is installed on a pulley to easily manipulate. It is a mechanism with four members and three joints, including the frame (member 1, KF), a pulley (member 2, KU), a rope (member 3, KT), and a spiky link (member 4, KB). The pulley is connected to the frame with a revolute joint JRx. The rope is connected to the pulley and the spiked link with a wrapping joint JW and a thread joint JT, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003850_j.jmbbm.2013.05.009-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003850_j.jmbbm.2013.05.009-Figure4-1.png", "caption": "Fig. 4 \u2013 Morphological evolution of a cylindrical mucosa\u2013submuc internal pressure is set as \u03a0\u00bc 0:033.", "texts": [ " 4(a\u2013e), where the geometric and physical parameters are taken as A\u00bc 90, B\u00bc 90:5, C\u00bc 200, \u03bcm=\u03bcs \u00bc 1000 and \u03a0 \u00bc 0:033. In real biological organs, the ratio between the osa system with the growth of the mucosal layer, where the elastic moduli of mucosa and submucosa may vary in a broad range. For example, it was taken in the range of 1\u2013314 by Hrousis et al. (2002). When other representative geometric and material parameters are used in the calculation, the morphological evolution induced by the volumetric growth is similar to that in Fig. 4. The deformation process shown in Fig. 4 can be divided into three stages. In the first stage, the cylindrical tube grows in an axisymmetric manner and keeps the cylindrical symmetry. With the growth of the mucosa, the circumferential compressive stress becomes higher and higher. In the second stage, the first bifurcation occurs and the system buckles into a non-axisymmetric morphology when the compressive stress reaches a critical condition. A sinusoidal wrinkling pattern forms on the inner surface (Figs. 4b and c), as predicted by the above theoretical analysis. With further growth of the mucosa, the wavy wrinkles become deeper and deeper, leading to a finger-like pattern (Fig. 4d). If the mucosa is much stiffer than the submucosa, the system may undergo a secondary bifurcation during postbuckling, entering into the third stage. One wrinkle grows in amplitude at the expense of the amplitudes of its two neighbors. The second bifurcation creates a period-doubling morphology (Fig. 4e) and, in turn, a pitchfork-like pattern (Fig. 4f). This wrinkle-to-fold transition releases a part of the elastic strain energy of the system. By comparing the postbuckling processes with and without internal pressure, it can be found that the morphology evolutions for the two cases are quite similar (Li et al., 2001b). However, both the first and second bifurcations are delayed due to the presence of an internal pressure, demonstrating its stabilizing role in the buckling process. In this subsection, we examine the effects of surface tension on the critical condition and the circumferential mode number of surface wrinkling" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.7-1.png", "caption": "Fig. 9.7 A water-driven chain conveyor water lifting device (\u6c34\u8f49\u9ad8\u8eca) a Original illustration (Wang 1991), b Structural sketch", "texts": [ " Animal-driven Gao Zhuan Tong Che is a mechanism with five members and six joints, including the frame (member 1, KF), a horizontal gear with a vertical shaft (member 2, KG), an upper wheel with a vertical gear (member 3, KK1), a lower wheel (member 4, KK2), and a chain (member 5, KC). The horizontal gear is connected to the frame and the upper wheel with a revolute joint JRy and a gear joint JG, respectively. The other adjacent relationships are identical to the ones in human-driven device. Figure 9.6c shows the structural sketch. 9.2.5 Shui Zhuan Gao Che (\u6c34\u8f49\u9ad8\u8eca, A Water-Driven Chain Conveyor Water Lifting Device) Shui Zhuan Gao Che (\u6c34\u8f49\u9ad8\u8eca, a water-driven chain conveyor water lifting device) is a Tong Che (\u7b52\u8eca, a cylinder wheel) but driven by water as shown in Fig. 9.7a (Wang 1991) (the horizontal water wheel and the gear train are not shown in the illustration). Its structure is similar to the animal-driven Gao Zhuan Tong Che but with an additional horizontal water wheel. Figure 9.7b shows the structural sketch. 9.2 Water Lifting Devices 199 There are four handiwork devices with flexible members, including Ru Shui and Ru Jing (\u5165\u6c34, \u5165\u4e95, human pulleying devices), Zao Jing (\u947f\u4e95, a cow-driven well-drilling rope drive),Mo Chuang (\u78e8\u5e8a, a rope drive grinding device), and Zha You Ji (\u69a8\u6cb9\u6a5f, an oil pressing device). Each of these devices is described below: 9.3.1 Ru Shui, Ru Jing (\u5165\u6c34, \u5165\u4e95, Human Pulleying Devices) In the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b, Ru Shui and Ru Jing devices (human pulleying devices for water and well) are used to collect pearls, gems, coal, or precious minerals under water or from a well as shown in Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003010_09544100jaero571-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003010_09544100jaero571-Figure5-1.png", "caption": "Fig. 5 Trajectory of the aircraft", "texts": [ " Climb from 30 to 60 m at a rate of 12 m/s. 2. Accelerate to 42 m/s. 3. Perform a 180\u25e6 turn of radius 200 m (at a roll angle of 43\u25e6). 4. Perform a 180\u25e6 roll. 5. Perform a 180\u25e6 turn of radius 200 m (at a roll angle of 43\u25e6). 6. Resume level flight. 7. Perform two successive 270\u25e6 turns of radius 110 m (at a roll angle of 60\u25e6). Proc. IMechE Vol. 224 Part G: J. Aerospace Engineering JAERO571 at COLORADO STATE UNIV LIBRARIES on July 22, 2015pig.sagepub.comDownloaded from The trajectory of the aircraft is shown in Fig. 5. Figure 6 shows the time histories of the airspeed and altitude, and of their references, together with the thrust. Figure 7 shows the time histories of the Euler angles and their corresponding references. The time histories of the flap deflection angles are shown in Fig. 8. Note that the maximum available thrust is 180 N, while the maximum deflection for the flaps is 0.313 rad. It is observed that the aircraft follows the desired trajectory with zero tracking error for the JAERO571 Proc. IMechE Vol" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001431_s0168-874x(99)00076-1-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001431_s0168-874x(99)00076-1-Figure1-1.png", "caption": "Fig. 1. Geometry of the FE model, (a) 3-D view, (b) top view.", "texts": [ " and helical angle a, subject to either a tension or compression load F and/or a twisting moment M along the spring symmetric axis. Consider a transverse section taken perpendicular to the wire centre line. This section is circular and the resultant moments and forces on it are the same as on any other section, also the stress distributions in the overall cross-sections and the warping and distortion of all cross-sections will be identical. In other words, the problem may be reduced to an analysis of a typical in\"nitesimal slice of the coil as shown in Fig. 1. Due to the symmetry of the cross-section shape and loading, only half of the coil slice needs to be analysed. Three-dimensional solid brick elements have been used for the structural discretization. This element is de\"ned by eight nodes having three degrees of freedom on each, i.e. translations in the x, y, and z directions. Using the present approach only one element division is required in the wire axial direction to consider the helical e!ect (see Fig. 2). Precise boundary conditions are maintained by using the constraint equations which relate the displacements of the corresponding nodes on the wire cross-sections of the model, as will be discussed in the following section", "sin(h 4 #dh 4 ) 0 sin(h 4 #dh 4 ) cos(h 4 #dh 4 ) 0 0 0 1DA u x u y u z B#A !2r sin(dh 4 /2)sin(h#h 4 #(dh 4 /2)) 2r sin(dh 4 /2)cos(h#h 4 #(dh 4 /2)) dz 4 B (4) where u x , u y , u z and u@ x , u@ y , u@ z are the displacement components of node n and its corresponding node n@ in the Cartesian coordinate system, respectively. The sector angle h 4 and the sector length z 4 are the angle and distance measured in h and z directions of the global cylindrical coordinate system between the two corresponding nodes, respectively (see Fig. 1), and the relationship between them is z 4 \"R . h 4 tan a (5) where R . is the mean coil radius, and a is the helical angle measured at the wire centre line. dh 4 and dz s can be expressed in terms of the spring twist angle *U and elongation *\u00b8, respectively, as dh 4 \" *U n h 4 2n , (6) dz 4 \" *\u00b8 n h 4 2n , (7) where n is the number of coils in spring. The two corresponding radial edge lines L and L@, shown in Fig. 1 are initially straight and perpendicular to the spring central axis. They should remain straight and perpendicular to the spring central axis after deformation. Also, the corresponding nodes on these corresponding radial lines are on helically symmetric boundaries, hence should obey the helical symmetric relationship as formulated above. Degree of freedom constraints, to eliminate rigid body movement, were also introduced on these nodes. The rotation of line L is set to be zero and consequently the rotation of line L@ is set to be equal to dh 4 " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003528_045008-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003528_045008-Figure5-1.png", "caption": "Figure 5. Illustration of the two-camera set-up used to obtain 3D coordinates of SBFA. The coordinate system used in this figure is the same as in figure 4.", "texts": [ " Each syringe was pressurized by a separate Harvard pump 11 Elite. The coordinate system used to define the orientation of the SBFA in space is shown in figure 4. In this figure, X\u2032, Y \u2032 and Z\u2032 define an absolute coordinate system fixed to the lab stand. 8X and 8Y correspond to the projection of the angle 8, respectively, onto the X\u2032\u2013Z\u2032 and Y \u2032\u2013Z\u2032 planes. 8tip corresponds to the angle tangent to the tip of the SBFA. To capture the orientation of the SBFA in space, a camera along the X\u2032 axis and a camera along the Y \u2032 axis were set up as illustrated in figure 5. These two views correspond to the orientation of the SBFA projected on the X\u2032\u2013Z\u2032 and Y \u2032\u2013Z\u2032 planes. Figure 6 shows an SBFA prototype. A pin with a small red bead was fixed to the SBFA tip to easily track the SBFA displacements. Images taken by the two cameras were post-processed by using commercial software (Vision Builder by National Instrument), which enabled us to obtain the positions of the root of the SBFA, the tip of the SBFA and the angle formed by the pin (see 8tip in figure 6). 8Y-tip corresponds to 8tip projected onto the Y \u2032\u2013Z\u2032 plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003498_0022-2569(71)90044-9-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003498_0022-2569(71)90044-9-Figure8-1.png", "caption": "Figure 8. Construct ion of the cam disk during the return motion in the case of zero acceleration.", "texts": [ " Likewise, the line perpendicular to AoBoto through Btto is intersected by the perpendicular to AoBoto thrOUgh A o at Rt0, and then the line TttoRto intersects AoBtlo at the center of curvature, A~lo. From this, the radii of curvature pl and pro can be measured. Lay-out of the cam disk for the return portion in the case of zero acceleration Now the cam profile ought also to be constructed at some point during the return motion where the cam disk and final driven lever f move in directions opposite to one other. It is immaterial which directLn of absolute rotation is considered. In Fig. 8, it has been assumed that the cam disk turns counterclockwise with speed oJa, and the second-component mechanism turns clockwise. A further assumption that has been made, is to take position x = 0-5, that is to say, it is assumed that the inflection point in the velocity occurs in the position where the overall acceleration is Ao = 0. Equation (15) is thereby reduced to: Al . i . = - - A . . it 2. (47) The following values thus are true: ~ol = 90\u00b0; e t t = 105\u00b0; io5 = --1\"832; itt~ = +2\"615; it5 = --0\"701; mt~ = +35; qb,5 = CoQs = 31; qbz5 = 29.5 Arts. i)~ 1\"82 \u00d7 0\"701 ~ Ats . . . . 0'342 (49) itt.~ 2\"615 Ats.q~t= 0.342\u00d729.5 z = --5.95. (50) rn~5 = dt 50 In Fig. 8, one now turns the line CoC, which is the output link f , from its initial position CoC1 through tom = 105 \u00b0 into position CoCs, and this causes BoB' to be turned from BoBI to BoB5 through an angle ~tt.~ = 46 \u00b0. The cam-roll lever is consequently also rotated from BoBt to BoBs through ~tts. The rotation of Bs around Ao by the amount -\u00a2t.~ = --90 \u00b0 leads to a point B* on the cam profile and similar rotation of Bo by - 9 0 \u00b0 leads to point Bos (Fig. 8). Since the transmission ratio it is negative, the relative pole Q.~ must lie between Ao and Bos. Its distance from Bo.~ is qbts = 29.5. The straight line QsB~ is a normal to the cam profile and the line ts if drawn perpendicular to it is thus tangent to the profile. The slide-turn vector mes has a negative sign, and consequently, it must turn counterclockwise around Bo.~ with its arrowhead at Ao perpendicular to AoB,,.~, because the cam-roll lever BoBs, rotates clockwise. From its terminus Ts* one drops a * * is joined to pointAo" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.15-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.15-1.png", "caption": "Fig. 9.15 A cotton loosing device (\u5f48\u68c9) a Original illustration (Pan 1998), b Structural sketch", "texts": [ "4 Tan Mian (\u5f48\u68c9, A Cotton Loosening Device) After Mu Mian Jiao Che (\u6728\u68c9\u652a\u8eca) or Gan Mian Che (\u8d95\u68c9\u8eca) gins out the cotton cores and seeds, Tan Mian (\u5f48\u68c9, a cotton loosening device) can be used to loosen the cotton. After this step, the processed cotton would be ready for use to 208 9 Flexible Connecting Mechanisms manufacture blankets or jackets. In the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b(Pan 1998), Tan Mian contains a wooden rod to which a leather string (or a thread) is tied on both ends. Another rope is tied to the middle of the wooden rod, and the other end of the rope is tied to a bamboo that is fixed on the wall as shown in Fig. 9.15a. The operator plucks the leather string and swings the wooden rod to enhance the effects of loosening cotton by the elasticity of the leather string and bamboo. 9.4 Textile Devices 209 Although the leather string (or a thread) is tied to the wooden rod by both sides, they are still in an adjacent relationship between the two members, so one set is sufficient for analysis. Thus, the device is a mechanism with five members and five joints, including the wall or ground as the frame (member 1, KF), a wooden rod (member 2, KL), a leather string (member 3, KT1), a rope (member 4, KT2), and a bamboo (member 5, KBB). The wooden rod is connected to the frame by direct contact, denoted as JPxzRyz . The leather string is connected to the wooden rod with a thread joint JT. The rope is connected to the wooden rod and the bamboo with thread joints JT. The bamboo is connected to the frame with a bamboo joint JBB. Figure 9.15b shows the structural sketch. 9.4.5 Shou Yao Fang Che, Wei Che (\u624b\u6416\u7d21\u8eca, \u7def\u8eca, Hand-Operated Spinning Devices) After Tan Mian (\u5f48\u68c9, a cotton loosening device) looses cotton, and the cotton is twisted into long strips on a wooden board; or after the silk worm cocoon is processed for reeling, adjusting, or other procedures, the processed cotton or silk is ready to be spun into yarn by devices such as Shou Yao Fang Che (\u624b\u6416\u7d21\u8eca, a hand-operated spinning device) or Wei Che (\u7def\u8eca, a hand-operated spinning device) as shown in Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002861_robot.2008.4543833-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002861_robot.2008.4543833-Figure7-1.png", "caption": "Fig. 7. Basic geometry of the crane.", "texts": [], "surrounding_texts": [ "The user can specify the target position of the crane-tip in a number of different ways. One way is to use the mouse to click on the top right camera view. This will result in a position in the vertical plane. The second method is to use an ordinary joystick to move a pointer in the virtual environment. A 2-axis joystick is used and two buttons are used to simulate a third axis for full 3D motion. When the user presses a button, the current position of the pointer is sent to the control system. The crane motion that is required to move the crane tip from the current crane position to the target point is then calculated. The motion can be calculated to be optimal with regard to e.g. speed or energy efficiency. In the following section we describe a simple motion-planning algorithm which can be calculated on-line. If several subsequent target points are specified, the target points become waypoints on a target trajectory. The crane tip will then visit each waypoint in order. The next step is to transfer more responsibility from the operator to the control system. This means that certain tasks or processes are automated and performed autonomously by the system. As an example of an activity where the computer has increased responsibility, a simple collision-avoidance algorithm has been implemented in the CraneVE software. When collision avoidance is enabled, the system performs collision detection between the user-specified trajectory and the objects in the scene. If the user specified trajectory is blocked by an object, a new trajectory is calculated such that the crane tip passes above the object and avoids the collision. The collision avoidance algorithm is explained in Figure 6." ] }, { "image_filename": "designv10_13_0001450_cdc.1994.411345-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001450_cdc.1994.411345-Figure3-1.png", "caption": "Figure 3: The trailer exponentially converges to a circle of radius R, passing through point D. The unstable equilibrium occurs when the trailer is at point E.", "texts": [ " Therefore, the equilibrium point +=I is locally exponentially stable. When 4. = &z, C O S + ~ Z 5 0 and 2 2 0. Thus, z diverges exponentially away from zero, or 4 diverges away from +=z exponentially. Therefore, the equilibrium point &Z is locally unstable. This is illustrated in the phase portrait in Figure 2. Since the linearized system (6) is locally exponentially stable in a neighborhood of the equilibrium point 4, = X we can conclude that the nonlinear system ( 5 ) is also locally exponentially stable in a neighborhood of del. 0 Figure 3 shows the stable and unstable equilibrium positions for this vehicle. The stable position has the trailer at point D with ADC a right triangle. If we restrict 141 5 ~ / 2 , i.e., where the trailer avoids the jack-knife positions, then 4 never reaches the unstable equilibrium. Under this assumption, we also have T > L. The case with r = L is unrealistic since this corresponds to R = 0 and d = -7r/2, i.e., the trailer is sitting at the center of the circle (see example section, case (c)). Theorem 5 FOT T > L, R ezponentially Converges to the steady state value R* = lim ~ ( a ) = & C G " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003809_ccdc.2012.6244555-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003809_ccdc.2012.6244555-Figure1-1.png", "caption": "Figure 1. Tilt rotor showing the motor thrust and tilt angles of the two rotors with reference and body frames [4].", "texts": [ " The Tilt-rotor has two rotors mounted on the two sides of its airframe, which can be tilted to provide lift and forward thrust. Some examples of Tilt-rotor aircraft are the Arizona State University\u2019s HARVee [1], Compigne University\u2019s BIROTAN [4], large scale versions like Boeing\u2019s V22 Osprey [2] and Bell\u2019s Eagle Eye [1]. One clear advantage of the Tilt-rotor, with respect to other multi-rotors, is that it requires only two motors, allowing a reduction in weight, volume and energy consumption. Moreover, with the help of two rotors it can move faster than a fixed-wing airplane. The two rotors (rotor 1 and 2 as shown in Figure 1) rotate in opposite directions, canceling the reaction torque which is generated due to their motion, and this keeps the UAV stable. The control aspects of a Tilt-rotor include altitude control, forward motion and pitch control, lateral motion and roll control and, yaw control. Altitude control is achieved by varying the speed of both rotors simultaneously. Changing the {Arindam Bhanja Chowdhury, Anil Kulhare} are with the Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India {bhanja", " They are expressed as Fxb = fR sin(\u03b1R) + fL sin(\u03b1L), (2) Fzb = fR cos(\u03b1R) + fL cos(\u03b1L), (3) where fR, fL are the thrust exerted by the right and left rotors and \u03b1R and \u03b1L are their respective tilt angles with the positive zb axis. There is no translational force in the yb direction. So the body force vector (Fb) is given as Fb = [Fxb, 0, Fzb] T (4) Torques applied to the body expressed in the E-frame for changing \u03c6, \u03b8, \u03c8 are given by \u03c4\u03c6, \u03c4\u03b8, \u03c4\u03c8 respectively. Their expressions are \u03c4 = \u23a1 \u23a3 \u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8 \u23a4 \u23a6 = \u23a1 \u23a3 [fL cos(\u03b1L)\u2212 fR cos(\u03b1R)]l [fL sin(\u03b1L) + fR sin(\u03b1R)]h [fL sin(\u03b1L)\u2212 fR sin(\u03b1R)]l \u23a4 \u23a6 , (5) where l is the distance of each rotor from point O, and h is the vertical distance of the COG from O, as shown in Figure 1. C. Equations of motion The translational kinetic energy of the system is given as Ttrans = 1 2 mx\u03072 + 1 2 my\u03072 + 1 2 mz\u03072, (6) where m is the mass of the system. The body angular velocity [6] [\u03c9\u03c6, \u03c9\u03b8, \u03c9\u03c8] T of the system is given by\u23a1 \u23a3 \u03c9\u03c6 \u03c9\u03b8 \u03c9\u03c8 \u23a4 \u23a6 = (RTR\u0307)\u2228 = \u23a1 \u23a3 (\u03c6\u0307\u2212 \u03c8\u0307s\u03b8) (\u03b8\u0307c\u03c6+ \u03c8\u0307c\u03b8s\u03c6) (\u03c8\u0307c\u03b8c\u03c6\u2212 \u03b8\u0307s\u03c6) \u23a4 \u23a6 , where (..)\u2228 means converting the skew symmetric matrix RTR\u0307 into vector form. The kinetic energy due to rotation is given as Trot = 1 2 Ixx(\u03c6\u0307\u2212 \u03c8\u0307s\u03b8)2 + 1 2 Iyy(\u03b8\u0307c\u03c6+ \u03c8\u0307c\u03b8s\u03c6)2 + Izz 1 2 (\u03c8\u0307c\u03b8c\u03c6 \u2212 \u03b8\u0307s\u03c6)2, (7) where Ixx, Iyy, Izz are the moments of inertia about the xb, yb, zb axes respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure11.7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure11.7-1.png", "caption": "Fig. 11.7 Atlas of feasible designs of the guide silk mechanism", "texts": [], "surrounding_texts": [ "Sao Che (\u7e45\u8eca, a foot-operated silk-reeling mechanism), also called Zao Che (\u7e70 \u8eca), is used to extract and coil silk. Figure 11.1 shows the original illustration of Sao Che (Wang 1969). It consists of a cocoon cooking pot, several guide eyes, Gu (\u9f13, a pulley with an eccentric lug), one or two guide links, a belt, Ren Zhou (\u8ee0\u8ef8, a reel with a crank), a treadle, and one or two connecting links. Silk is extracted from cocoons in the cooking pot and passes through the guide eyes and the rack in the cooking pot. By the motion of the guide link(s), silk is coiled around the reel. There is a vertical pulley that has an eccentric lug on the top. One end of a belt circles around the reel, and the other end is covered on the pulley. The lug of the pulley is connected to the guide link. The operator pedals the treadle to generate the rotation of the reel through the motion of one or two connecting links. At the same time, the K.-H. Hsiao and K.-S. Yan, Mechanisms in Ancient Chinese Books with Illustrations, History of Mechanism and Machine Science 23, DOI: 10.1007/978-3-319-02009-9_11, Springer International Publishing Switzerland 2014 243 reel drives the pulley by the belt. The pulley moves one or two guide links to guide the silk. The individual fibers of silk are pulled from the cocoons in the heated water, passing through guiding eyes and over the rack before being laid down on the reel. Because of the function of the guide link(s), the silk string oscillates from side to side and forms even layers on the reel (Jia 1968; Chen 1984). The foot-operated silk-reeling mechanism can be divided by the function into two sub-mechanisms: the treadle crank mechanism and the guide silk mechanism (Hsiao et al. 2010). Each of them is presented as follows: Treadle Crank Mechanism The treadle crank mechanism includes the frame (member 1, KF), a treadle (member 2, KTr), a reel with a crank (member 3, KCR), and one or two connecting links (member 4, KL1, and member 5, KL2). Since there are many uncertain portions in the illustration, it is difficult to clarify how the oscillating motion of the treadle transfers to the rotation of the reel. Thus, this sub-mechanism is a Type III mechanism with uncertain numbers and types of members and joints. A rectangular coordinate system is defined as shown in Fig. 11.1. The z-axis is determined by the direction of the shaft of the reel, and the x and y axes are defined as the horizontal and vertical directions of the frame, respectively. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction design of the treadle crank mechanism is presented as follows: Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a planar mechanism with four members (members 1\u20134) or five members (members 1\u20135). 244 11 Complex Textile Devices 2. The treadle (KTr) is a binary link and connected to the frame (KF) with a revolute joint (JRz). 3. The reel (KCR) is a binary link and connected to the frame (KF) with a revolute joint (JRz). 4. There must be a binary link as the connecting link that is connected to the treadle (KTr) and/or the reel (KCR) with revolute joints (JRz). Step 2. Since this device is a mechanism with four or five members, the corre- sponding atlas of generalized kinematic chains with four and five members are shown in Fig. 11.2. Step 3. There must be a pair of binary links as the treadle and the connecting link, or the connecting link and the reel. Therefore, only those three generalized kinematic chains shown in Figs. 11.2a, d and f are qualified for the process of specialization. All feasible specialized chains are identified as follows: 11.1 Shao Che (\u7e45\u8eca, A Foot-Operated Silk-Reeling Mechanism) 245 Frame (KF) Since there must be a link as the frame (KF) and a pair of binary links is connected to the frame, the frame is identified as follows: 1. For the generalized kinematic chain shown in Fig. 11.2a, the assignment of the frame generates one result as shown in Fig. 11.3a1. 2. For the generalized kinematic chain shown in Fig. 11.2d, the assignment of the frame generates one result as shown in Fig. 11.3a2. 3. For the generalized kinematic chain shown in Fig. 11.2f, the assignment of the frame generates one result as shown in Fig. 11.3a3. 246 11 Complex Textile Devices Therefore, three specialized chains with identified frame are available as shown in Figs. 11.3a1\u2013a3. Treadle (KTr) Since there must be a binary link as the treadle (KTr) that is connected to the frame (KF) with a revolute joint (JRz), the treadle is identified as follows: 1. For the case shown in Fig. 11.3a1, the assignment of the treadle generates one result as shown in Fig. 11.3b1. 2. For the case shown in Fig. 11.3a2, the assignment of the treadle generates one result as shown in Fig. 11.3b2. 3. For the case shown in Fig. 11.3a3, the assignment of the treadle generates two results as shown in Figs. 11.3b3 and b4. Therefore, four specialized chains with identified frame and treadle are avail- able as shown in Figs. 11.3b1\u2013b4. Reel with a crank (KCR) Since there must be a binary link as a reel (KCR) that is connected to the frame (KF) with a revolute joint (JRz), the reel is identified as follows: 1. For the case shown in Fig. 11.3b1, the assignment of the reel generates one result as shown in Fig. 11.3c1. 2. For the case shown in Fig. 11.3b2, the assignment of the reel generates one result as shown in Fig. 11.3c2. 3. For the case shown in Fig. 11.3b3, the assignment of the reel generates one result as shown in Fig. 11.3c3. 4. For the case shown in Fig. 11.3b4, the assignment of the reel generates one result as shown in Fig. 11.3c4. Therefore, four specialized chains with identified frame, treadle, and reel are available as shown in Figs. 11.3c1\u2013c4. Connecting link 1 and connecting link 2 (KL1 and KL2) Since there must be a binary link as connecting link 1 (KL1) that is connected to the treadle (KTr) and/or the reel (KCR) with revolute joints (JRz), and the remaining link should be connecting link 2 (KL2), connecting link 1 and connecting link 2 are identified as follows: 1. For the case shown in Fig. 11.3c1, the assignment of connecting link 1 gen- erates one result as shown in Fig. 11.3d1. Figure 11.3d1 is completed for the process of specialization, and all members and joints are certain. 2. For the case shown in Fig. 11.3c2, the assignment of connecting link 1, con- necting link 2, and uncertain joint J1 generates one result as shown Fig. 11.3d2. 3. For the case shown in Fig. 11.3c3, the assignment of connecting link 1, con- necting link 2, and uncertain joints J2, J3, J4, generates one result as shown Fig. 11.3d3. 11.1 Shao Che (\u7e45\u8eca, A Foot-Operated Silk-Reeling Mechanism) 247 4. For the case shown in Fig. 11.3c4, the assignment of connecting link 1, con- necting link 2, and uncertain joints J5, J6, J7, generates one result as shown Fig. 11.3d4. Therefore, four specialized chains with identified frame, treadle, reel, con- necting link 1, and connecting link 2 are available as shown in Figs. 11.3d1\u2013d4. Step 4. The coordinate system is defined as shown in Fig. 11.1. The function of the treadle crank mechanism is to generate the rotation of the crank from the oscillating motion of the treadle. The uncertain joints may have multiple types to achieve the equivalent function. Since the device is planar, the uncertain joints must be planar joints. 1. Considering uncertain joints J1, J2, and J5, each joint has one possible type: connecting link 1 rotates about the z-axis with respect to connecting link 2, denoted as JRz. 2. Considering uncertain joints J3 and J4, each joint has two possible types and they can not be the same type simultaneously. When any one rotates about the z-axis, denoted as JRz, the other one rotates not only about the z-axis but also translates along the x-axis, denoted as JPxRz . 3. Considering uncertain joints J6 and J7, each joint has two possible types and they can not be the same type simultaneously. When any one rotates about the z-axis, denoted as JRz, the other one rotates not only about the z-axis but also translates along the x-axis, denoted as JPxRz . By assigning all possible types of uncertain joints J1(JRz), J2(JRz), J3(JRz and JPxRz ), J4(JRz and JPxRz ), J5(JRz), J6(JRz and JPxRz ), and J7(JRz and JPxRz ) to the specialized chains shown in Figs. 11.3d2\u2013d4, five specialized chains with particular joints as shown in Figs. 11.3e1\u2013e5 are obtained. Step 5. Based on Eq. (3.1), the number of degrees of freedom of Fig. 11.3e1 is 2. This means that the motion is not constrained. By removing such a chain, five feasible specialized chains with particular joints are available as shown in Figs. 11.3d1 and e2\u2013e5. Figures 11.4a\u2013e show the corresponding 3D solid models of the feasible designs. Guide Silk Mechanism The guild silk mechanism consists of the frame (member 1, KF), a reel with a crank (member 3, KCR), a belt (member 6, KT), a cylinder with an eccentric lug (member 7, KWC), and one or two guide links (member 8 KGL1, and member 9 KGL2). Since there are many uncertain portions in the illustration, it is difficult to clarify how the guide links guide the silk string to form even layers. Thus, this submechanism is a Type III mechanism with uncertain numbers and types of members and joints. A coordinate system is defined as shown in Fig. 11.1. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction design of the guide silk mechanism is presented as follows: 248 11 Complex Textile Devices Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a planar mechanism with five members (members 1, 3, and 6\u20138) or six members (members 1, 3, 6\u20139). 2. The reel with a crank (KCR) is a binary link and connected to the frame (KF) with a revolute joint (JRz). 3. The belt (KT) is a binary link and connected to the reel (KCR) and the cylinder (KWC) with wrapping joints (JW). 4. The cylinder with an eccentric lug (KWC) is a ternary link and con- nected to the frame (KF) and guide link 1 (KGL1) with a revolute joint (JRy) and an uncertain joint, respectively. 5. One guide link is connected to the frame (KF) with an uncertain joint. 11.1 Shao Che (\u7e45\u8eca, A Foot-Operated Silk-Reeling Mechanism) 249 Step 2. Since this device is a mechanism with five or six members, the corre- sponding generalized kinematic chains are shown in Figs. 11.2d\u2013i and 11.5. Step 3. There must be a pair of binary links as the reel and the belt. The pair of binary links must be connected to a multiple link as the frame and a ternary link as the cylinder, respectively. Therefore, only those three generalized kinematic chains shown in Figs. 11.2f, 11.5b and f are qualified for the process of specialization. All feasible specialized chains are obtained as follows: Frame (KF) Since there must be a multiple link as the frame (KF) and a pair of binary links is connected to the frame, the frame is identified as follows: 1. For the generalized kinematic chain shown in Fig. 11.2f, the assignment of the frame generates one result as shown in Fig. 11.6a1. 2. For the generalized kinematic chain shown in Fig. 11.5b, the assignment of the frame generates one result as shown in Fig. 11.6a2. (e) (f) (g) (h) (i) (j) (k) (l) (a) (d) (b) (c) Fig. 11.5 Atlas of (6, 7) and (6, 8) generalized kinematic chains. a N = 6, J = 7, b N = 6, J = 7, c N = 6, J = 7, d N = 6, J = 8, e N = 6, J = 8, f N = 6, J = 8, g N = 6, J = 8, h N = 6, J = 8, i N = 6, J = 8, j N = 6, J = 8, k N = 6, J = 8, l N = 6, J = 8 250 11 Complex Textile Devices 3. For the generalized kinematic chain shown in Fig. 11.5f, the assignment of the frame generates two results as shown in Figs. 11.6a3 and a4. Therefore, four specialized chains with identified frame are available as shown in Figs. 11.6a1\u2013a4. 11.1 Shao Che (\u7e45\u8eca, A Foot-Operated Silk-Reeling Mechanism) 251 Reel and Belt (KCR and KT) There must be a pair of binary links as the reel (KCR) and the belt (KT), and the reel is connected to the frame and the belt with a revolute joint (JRz) and a wrapping joint (JW), respectively. Therefore, the reel and the belt are identified as follows: 1. For the case shown in Fig. 11.6a1, the assignment of the reel and the belt generates one result as shown in Fig. 11.6b1. 2. For the case shown in Fig. 11.6a2, the assignment of the reel and the belt generates one result as shown in Fig. 11.6b2. 3. For the case shown in Fig. 11.6 a3, the assignment of the reel and the belt generates one result as shown in Fig. 11.6b3. 4. For the case shown in Fig. 11.6a4, the assignment of the reel and the belt generates one result as shown in Fig. 11.6b4. Therefore, four specialized chains with identified frame, reel, and belt are available as shown in Figs. 11.6b1\u2013b4. Cylinder with an eccentric lug (KWC) There must be a ternary link as the cylinder (KWC), and the cylinder is connected to the frame and the belt with a revolute joint (JRy) and a wrapping joint (JW), respectively. Therefore, the cylinder is identified as follows: 1. For the case shown in Fig. 11.6b1, the assignment of the cylinder generates one result as shown Fig. 11.6c1. 2. For the case shown in Fig. 11.6b2, the assignment of the cylinder generates one result as shown in Fig. 11.6c2. 3. For the case shown in Fig. 11.6b3, the assignment of the cylinder generates one result as shown in Fig. 11.6c3. 4. For the case shown in Fig. 11.6 b4, since there is no ternary link as the cylinder that is connected to the frame and the belt, Fig. 11.6 b4 is not qualified for the process of specialization. Therefore, three specialized chains with identified frame, reel, belt, and cylinder are available as shown in Figs. 11.6c1\u2013c3. Guide link 1 and guide link 2 (KGL1 and KGL2) Since guide link 1 (KGL1) must be connected to the cylinder, and the remaining link should be guide link 2 (KGL2), guide link 1 and guide link 2 are identified as follows: 1. For the case shown in Fig. 11.6c1, the assignment of guide link 1 and uncertain joints J8 and J9 generates one result as shown in Fig. 11.6d1. 2. For the case shown in Fig. 11.6c2, the assignment of guide link 1, guide link 2, and uncertain joints J10, J11, and J12 generates one result as shown in Fig. 11.6d2. 3. For the case shown in Fig. 11.6c3, the assignment of guide link 1, guide link 2, and uncertain joints J13, J14, J15, and J16 generates one result as shown in Fig. 11.6d3. 252 11 Complex Textile Devices Therefore, three specialized chains with identified frame, reel, belt, cylinder, guide link 1, and guide link 2 are available as shown in Figs. 11.6d1\u2013d3. Step 4. The coordinate system is defined as shown in Fig. 11.1. The function of the guide silk mechanism is to transfer the rotation of the cylinder to the reciprocating motion of the guide link and make the silk broad bands on the reel. The uncertain joints may have multiple types to achieve the equivalent function. Since the device is planar, the uncertain joints must be planar joints. 1. Considering uncertain joints J8 and J9, each joint has two possible types and they can not be the same type simultaneously. When any one rotates about the y-axis, denoted as JRy, the other one not only rotates about the y-axis but also translates along the z-axis, denoted as JPzRy 2. Considering uncertain joint J10, it has one possible type: guide link 1 rotates about the y-axis with respect to the cylinder, denoted as JRy. 3. Considering uncertain joints J11 and J12, each joint has two possible types: the first one rotates about the y-axis, denoted as JRy; and the other translates along the z-axis, denoted as JPz. 4. Considering uncertain joints J13 and J14, each joint has two possible types and they can not be the same type simultaneously. When any one rotates about the y-axis, denoted as JRy, the other one not only rotates about the y-axis but also translates along the z-axis, denoted as JPzRy. 5. Considering uncertain joints J15 and J16, each joint has two possible types and they can not be the same type simultaneously. When any one of the joints rotates about the y-axis, denoted as JRy, the other one not only rotates about the y-axis but also translates along the z-axis, denoted as JPzRy. By assigning all possible types of uncertain joints J8(JRy and JPzRy), J9(JRy and JPzRy), J10(JRy), J11(JRy and JPz), J12(JRy and JPz), J13(JRy and JPzRy), J14(JRy and JPzRy), J15(JRy and JPzRy) and J16(JRy and JPzRy) to the specialized chains shown in Figs. 11.6d1\u2013d3, 10 specialized chains with particular joints as shown in Figs. 11.6e1\u2013e10 are obtained. Step 5. Since a mechanismwith double sliders has the drawback of the transmission and was rare in ancient China, it does not meet the ancient technological standards. By removing the one shown in Fig. 11.6e6, nine feasible specialized chains with particular joints are obtained as shown in Figs. 11.6e1\u2013e5, e7\u2013e10. Figures 11.7a\u2013i show the corresponding 3D solid models of the feasible designs. Figure 11.8 shows an imitation illustration of the foot-operated silk-reeling mechanism in the book Nong Shu\u300a\u8fb2\u66f8\u300b. 11.1 Shao Che (\u7e45\u8eca, A Foot-Operated Silk-Reeling Mechanism) 253 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) Fang Che (\u7d21\u8eca, a spinning device) is used for yarn spinning. By different power sources and applied mechanical members, the spinning devices can be divided into three types: Shou Yao Fang Che (\u624b\u6416\u7d21\u8eca, a hand-operated spinning device), Jiao Ta Fang Che (\u8173\u8e0f\u7d21\u8eca, a foot-operated spinning device), and Pi Dai Chuan Dong Fang Che (\u76ae\u5e36\u50b3\u52d5\u7d21\u8eca, a belt drive spinning device). The hand-operated spinning device has been introduced in Sect. 9.4. The other two types are introduced as follows: 11.2.1 Jiao Ta Fang Che (\u8173\u8e0f\u7d21\u8eca, A Foot-Operated Spinning Device) Jiao Ta Fang Che (\u8173\u8e0f\u7d21\u8eca, a foot-operated spinning device) is driven by the operator\u2019s foot instead of hands to rotate the large pulley in the device. Freeing the 254 11 Complex Textile Devices operator\u2019s hands lets the yarn spinning be more efficient and also enhances the quality of yarns. The foot-operated spinning device has been known under many different names on a variety of specific books, including Mu Mian Xian Jia (\u6728\u68c9 \u7dda\u67b6), Xiao Fang Che (\u5c0f\u7d21\u8eca), and Mu Mian Fang Che (\u6728\u68c9\u7d21\u8eca) as shown in Fig. 11.9 (Wang 1991; Sun and Sun 1966). Its function is to twist and combine silk, cotton threads, or hemp fibers into yarns, and to coil the yarns around the spindle. Figure 11.9a shows the foot-operated spinning device in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b(Sun and Sun 1966). The weaver pedals the treadle to spin a large pulley, and the power through the thread on the large pulley drives the two spindles to rotate (Chen 1984; Zhang et al. 2004). By the spinner\u2019s twisting, four single-strand yarns merge into two double-strand yarns that coil around the spindles. It basically consists of the frame (member 1 KF), a treadle (member 2, KTr), a large pulley (member 3, KU), a thread (member 4, KT), and several spindles (member 5, KS). Due to the unclear illustrations, there may be a connecting link (member 6, KL) used for transmitting power from the treadle (Hsiao and Yan 2010) to the large pulley, making the large pulley rotate. Therefore, the foot-operated spinning device is a Type III mechanism with uncertain numbers and types of members and joints. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction design of the foot-operated spinning device is presented as follows: 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 255 Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a mechanism with five (members 1\u20135) or six members (members 1\u20136). 2. The treadle (KTr) is a binary link and connected to the frame (KF) with an uncertain joint. 3. The treadle (KTr) is connected to the connecting link (KL) or the large pulley (KU) with an uncertain joint. 4. The large pulley (KU) is a ternary link and connected to the frame (KF) and the thread (KT) with a revolute joint (JRz) and a wrapping joint (JW), respectively. 256 11 Complex Textile Devices 5. The spindle (KS) is a binary link and connected to the frame (KF) and the thread (KT) with a revolute joint (JRz) and a wrapping joint (JW), respectively. Step 2. Since this device is a mechanism with five or six members, the corre- sponding atlas of generalized kinematic chains with five and six members are shown in Figs. 11.2d\u2013i and Fig. 11.5. Step 3. There must be at least three binary links as the treadle, the thread, and the spindle. There must be only one pair of ternary links as the frame and the large pulley. Therefore, only those three generalized kinematic chains shown in Fig. 11.2f and Figs. 11.5a, b are qualified for the process of specialization. All feasible specialized chains are identified as follows: Frame (KF) Since there must be a ternary link as the frame (KF) and a pair of binary links that is connected to the frame, the frame is identified as follows: 1. For the generalized kinematic chain shown in Fig. 11.2f, the assignment of the frame generates one result as shown in Fig. 11.10a1. 2. For the generalized kinematic chain shown in Fig. 11.5a, the assignment of the frame generates one result as shown in Fig. 11.10a2. 3. For the generalized kinematic chain shown in Fig. 11.5b, the assignment of the frame generates one result as shown in Fig. 11.10a3. Therefore, three specialized chains with identified frame are available as shown in Figs. 11.10a1\u2013a3. Treadle (KTr) Since there must be a binary link as the treadle (KTr) that is connected to the frame (KF) with an uncertain joint, the treadle is identified as follows: 1. For the case shown in Fig. 11.10a1, the assignment of the treadle and the uncertain joint generates two results as shown in Figs. 11.10b1 and b2. 2. For the case shown in Fig. 11.10a2, the assignment of the treadle and the uncertain joint generates two results as shown in Figs. 11.10b3 and b4. 3. For the case shown in Fig. 11.3a3, the assignment of the treadle and the uncertain joint generates one result as shown in Fig. 11.10b5. Therefore, five specialized chains with identified frame and treadle are avail- able as shown in Figs. 11.10b1\u2013b5. Pulley (KU) There must be a ternary link as the pulley (KU) and the pulley is connected to the frame (KF) with a revolute joint (JRz). Therefore, the pulley is identified as follows: 1. For the case shown in Fig. 11.10b1, the assignment of the pulley and the uncertain joint generates one result as shown in Fig. 11.10c1. 2. For the case shown in Fig. 11.10b2, the assignment of the pulley generates one result as shown in Fig. 11.10c2. 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 257 3. For the case shown in Fig. 11.10b3, the assignment of the pulley and the uncertain joint generates one result as shown in Fig. 11.10c3. 4. For the case shown in Fig. 11.10b4, the assignment of the pulley generates one result as shown in Fig. 11.10c4. 5. For the case shown in Fig. 11.10b5, the assignment of the pulley generates one result as shown in Fig. 11.10c5. Therefore, five specialized chains with identified frame, treadle, and pulley are available as shown in Figs. 11.10c1\u2013c5. 258 11 Complex Textile Devices Thread (KT) There must be a binary link as the thread (KT) that is connected to the pulley (KU) with a wrapping joint (JW) and is not connected to the frame (KF) or treadle (KTr). Therefore, the thread is identified as follows: 1. For the case shown in Fig. 11.10c1, the assignment of the thread generates one result as shown in Fig. 11.10d1. 2. For the case shown in Fig. 11.10c2, no binary link that is neither connected to the frame nor the treadle can be assigned to the thread. 3. For the case shown in Fig. 11.10c3, the assignment of the thread generates one result as shown in Fig. 11.10d2. 4. For the case shown in Fig. 11.10c4, the assignment of the thread generates one result as shown in Fig. 11.10d3. 5. For the case shown in Fig. 11.10c5, the assignment of the thread generates one result as shown in Fig. 11.10d4. Therefore, four specialized chains with identified frame, treadle, pulley, and thread are available, as shown in Figs. 11.10d1\u2013d4. Spindle and connecting link (KS and KL) There must be a binary link as the spindle that is connected to the thread (KT) and the frame (KF) with a wrapping joint (JW) and a revolute joint (JRz), respectively. The remaining link should be the connecting link (KL). Therefore, the spindle and the connecting link are identified as follows: 1. For the case shown in Fig. 11.10d1, the assignment of the spindle generates one result as shown in Fig. 11.10e1. 2. For the case shown in Fig. 11.10d2, no binary link that is connected to the frame and the thread can be assigned to the spindle. 3. For the case shown in Fig. 11.10d3, no binary link that is connected to the frame and the thread can be assigned to the spindle. 4. For the case shown in Fig. 11.10d4, the assignment of the spindle, the con- necting link, and the uncertain joints generates one result as shown in Fig. 11.10e2. Therefore, two specialized chains with identified frame, treadle, pulley, thread, spindle, and connecting link are available as shown in Figs. 11.10e1 and e2. Step 4. The coordinate system is defined as shown in Fig. 11.9a. The function of the foot-operated spinning device is to transfer the oscillating motion of the treadle to the rotation of the pulley. The uncertain joints may have multiple types to achieve the equivalent function. 1. Considering uncertain joints J1 and J6, each joint has two possible types and they can not be the same type simultaneously. When any one is a spherical joint JRxyz, the other one not only rotates about the x and y axes but also translate along the z-axis, denoted as JPzRxy. 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 259 2. Considering uncertain joint J5, it has four possible types. Firstly, the treadle is connected to the frame with a revolute joint JRx. Secondly, the treadle not only rotates about the x-axis but also translates along the z-axis, denoted as JPzRx. Thirdly, the treadle not only rotates about the x and y axes but also translates along the z-axis, denoted as JPzRxy. Forthly, the treadle is connected to the frame with a spherical joint JRxyz. 3. Considering uncertain joint J8, it has two possible types: firstly, the connecting link is connected to the treadle with a revolute joint JRxz; secondly, the con- necting link is connected to the treadle with a spherical joint JRxyz. 4. Considering uncertain joint J9, it has two possible types: firstly, the connecting link is connected to the pulley with a revolute joint JRxz; secondly, the connecting link is connected to the pulley with a revolute joint JRz. By assigning all possible types of uncertain joints J1(JRxyz and JPzRxy), J5(JRx, J Pz Rx, JPzRxy, and JRxyz), J6(JRxyz and JPzRxy), J8(JRxz and JRxyz), and J9(JRxz and JRz) to the specialized chains shown in Figs. 11.10e1 and e2, except some rigid chains, 13 specialized chains with particular joints are obtained as shown in Figs. 11.11a\u2013m. Step 5. Considering the motions and functions of the mechanism, each specialized chain with particular joints is particularized to obtain the atlas of feasible designs that meet the ancient technological standards. Figures 11.12a\u2013m show the corresponding 3D solid models of the feasible designs. Figure 11.13 shows an imitation illustration of the foot-operated spinning device in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b. 11.2.2 Pi Dai Chuan Dong Fang Che (\u76ae\u5e36\u50b3\u52d5\u7d21\u8eca, Belt Drive Spinning Devices) In the Song and Yuan dynasties (AD 960\u20131368), the most advanced spinning device is Da Fang Che (\u5927\u7d21\u8eca, a large spinning device). This device was first used for twisting hemp threads, and then used for silk processing. The book Nong Shu\u300a\u8fb2\u66f8\u300b(Wang 1991) has records about Da Fang Che (\u5927\u7d21\u8eca) and Shui Zhuan Da Fang Che (\u6c34\u8f49\u5927\u7d21\u8eca, a water-driven spinning device). Both devices have the same basic structures and are a kind of application of the belt drive, as shown in Fig. 11.14. Since there are many uncertain portions in the illustration, it is difficult to identify the actual numbers of its members as well as the combinations and transmission process among the members. Therefore, the belt drive spinning device is a Type III mechanism with uncertain numbers and types of members and joints. Figure 11.15a shows an existing reconstruction concept for the belt drive spinning device that helps to clarify the structure of this device (Zhang et al. 2004). The belt drive spinning device consists of the frame, two pulleys, a belt, several spindles, a yarn circle with a wooden wheel, and yarns. The driving pulley on the 260 11 Complex Textile Devices left side is operated by a person, animal, or water. The power passes through the belt to spin the yarn circle and the spindles, to complete twisting and coiling the threads. By its function, the belt drive spinning device can be divided into three sub-mechanisms: the pulley and belt drive, the spinning and spindle drive, and the pulley and yarn circle drive. Each mechanism is presented as follows. Pulley and Belt Drive Mechanism The pulley and belt drive mechanism consists of the frame (member 1, KF), a driving pulley (member 2, KU1), a driven pulley (member 3, KU2), and a belt (member 4, KT1). The driving pulley is connected to the frame with a revolute joint JRz. The belt is connected to the driving and the driven pulleys with wrapping joints JW. The driven pulley is connected to the frame with a revolute joint JRz. Figure 11.16a shows the structural sketch. 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 261 Spinning and Spindle Drive Mechanism The spinning and spindle drive mechanism consists of the frame (member 1, KF), a yarn circle with a wooden wheel (member 5, KS1), several spindles (member 6, KS2), and yarns (member 7, KT2). The yarn circle is connected to the frame with a revolute joint JRx. The spindle is connected to the frame with a revolute joint JRz. 262 11 Complex Textile Devices 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 263 264 11 Complex Textile Devices The yarn is connected to the yarn circle and the spindle with wrapping joints JW. Figure 11.16b shows the structural sketch. Pulley and Yarn Circle Drive Mechanism The relevant data for the pulley and yarn circle drive mechanism is brief. The existing reconstruction concept for the belt drive spinning device shown in Fig. 11.15a is not clear as well. Therefore, the pulley and yarn circle drive mechanism has two possible structures. Each of them is presented as follows. The first possible structure consists of the frame (member 1, KF), a small pulley on the same shaft with the driven pulley (member 3, KU2), a yarn circle with a wooden wheel (member 5, KS1), and a thread (member 8, KT3). On the shaft of the driven pulley, another extra small pulley is added to coordinate with the wooden wheel. The small pulley is used to drive the wooden wheel through the thread, thereby driving the yarn circle. The small pulley is connected to the frame with a revolute joint JRz. The thread is connected to the small pulley and the wooden wheel with wrapping joints JW. The wooden wheel is connected to the frame with a revolute joint JRx. Figure 11.16c1 shows the structural sketch of the first pulley and yarn circle drive mechanism. Figure 11.15b shows the first reconstruction design. The second possible structure is based on the existing reconstruction concept, Fig. 11.15a. It consists of the frame (member 1, KF), a yarn circle with a wooden wheel (member 5, KS1), a thread (member 8, KT3), and a new added independent pulley (member 9, KU3). The belt directly rubs the newly added independent pulley. Through the thread, the yarn circle is driven to spin. The independent pulley is connected to the frame with a revolute joint JRz. The thread is connected to the independent pulley and the wooden wheel with wrapping joints JW. The wooden wheel is connected to the frame with a revolute joint JRx. Figure 11.16c2 shows the structural sketch of the second pulley and yarn circle drive mechanism. 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 265 Figure 11.15c shows the second reconstruction design. However, only using the friction between the belt and the independent pulley, the power seems to be not enough to drive the yarn circle. 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) Xie Zhi Ji (\u659c\u7e54\u6a5f, a foot-operated slanting loom) is a typical weaving device, in which links are united with treadles and threads to weave the cloth. The basic purpose of the weaving device is to hold the warps under tension to facilitate the interweaving of the wefts. Since this device has been well-developed with broad applications in ancient China, it was popular and illustrated in many Chinese literatures with different names, such as Yao Ji (\u8170\u6a5f), Bu Ji (\u5e03\u6a5f), and Wo Ji (\u81e5 \u6a5f), etc., Fig. 11.17 (Wang 1991; Pan 1998). The weaving process includes four steps: shed forming, shuttle throwing, weft pressing, and fabric reeling (Chen 1984). The foot-operated slanting loom has three sub-mechanisms to finish the weaving process including a heddle raising device, a weft pressing device, and a fabric reeling device. Figure 11.18 shows the types and the essential parts of the slanting looms (Hsiao et al. 2011). The warps, the longitudinal yarns, are rolled onto a warp beam. The warps are passed through the eye holds of the heddles, that hang vertically from the heddle rods. The heddle rack comprises the upper heddle rod and the lower heddle rod to which a series of threads, namely heddles, are attached. The weaver pedals the treadle to generate the rising or falling motion of the heddle rack through the transmission of the scale link and the threads in the heddle rasing device. When the heddle rack raises or lowers the heddles, that raises or lowers the warps, the shed is created. The early heddle raising devices had only the upper heddle rod and the warps were raised by the heddles directly. The weft yarn is inserted through the shed by a small carrier tool namely the shuttle. The shuttle is pointed at each end to allow passage through the shed. A single crossing of the shuttle from one side of the mechanism to the other is known as a pick. After the shuttle moves across the mechanism, the weft yarn is laid down and also passes through a reed comb. In each picking operation, the reed comb presses each weft yarn against the portion of the fabric that has already been formed in the weft pressing device. With each weaving operation, the newly constructed fabric must be reeled on the cloth beam in the fabric reeling device. At the same time, the warps must be released from the warp beam. Obviously, the members of the fabric reeling device include the frame, a cloth beam, a warp beam, and a fabric belt. The fabric belt consists of the warps and the fabric. Sorted by the numbers of the treadle and the heddle rack, the foot-operated slanting loom can be classified into the following main four types: 1. Two-treadle single-heddle-rack (TTSH) Figure 11.18a shows the type of two-treadle single-heddle-rack, denoted as 266 11 Complex Textile Devices TTSH. It consists of the frame, two treadles, a heddle rack, a scale link, a reed comb, a warp beam, a cloth beam, and threads for transmitting motions between members. In this case, thread 1, the upper heddle rod, the heddles, the lower heddle rod, and thread 1\u20131 can be regarded as the same member that is connected to the scale link and treadle 1. 2. Single-treadle single-heddle-rack (STSH) The type of single-treadle single-heddle-rack has two different kinds, denoted 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) 267 268 11 Complex Textile Devices as STSH. For the design shown in Fig. 11.18a without thread 2 and treadle 2, it belongs to the type of STSH-1 as shown in Fig. 11.18b. In the case, thread 1, the upper heddle rod, the heddles, the lower heddle rod, and thread 1\u20131 can be regarded as the same member that is connected to the scale link and treadle 1. For the design shown in Fig. 11.18a without thread 1\u20131 and treadle 1, it belongs to the type of STSH-2 as shown in Fig. 11.18c. In the case, thread 1, the upper heddle rod, the heddles and the lower heddle rod can be regarded as the same member that is connected to the scale link and the warps. The warps are fixed that can be regarded as the frame. 3. Single-treadle half-heddle-rack (STHH) For the design shown in Fig. 11.18c without the lower heddle rod, it belongs to the type of single-treadle half-heddle-rack, denoted as STHH as shown in Fig. 11.18d. In the case, thread 1, the upper heddle rod and the heddles can be regarded as the same member that is connected to the scale link and the warps. The warps are fixed that can be regarded as the frame. 4. Two-treadle two-heddle-rack (TTTH). By adding another heddle rack to thread 2 as shown in Fig. 11.18a, it belongs to the type of two-treadle two-heddle-rack, denoted as TTTH as shown in Fig. 11.18e. According to the function, the foot-operated slanting loom can be divided into three sub-mechanisms: the heddle raising device, the weft pressing device, and the fabric reeling device. Each of them is presented as follows: Heddle Raising Device The quality of the fabric depends on the shed by the heddle raising device. It plays an important part in the slanting loom. The simplest type of the heddle raising device is STSH-1 that comprises four members including the frame, a treadle, a thread with a heddle rack, and a scale link. The types of STSH-2 and STHH comprise five members including the frame, a treadle, a thread, a scale link, and another thread with a heddle rack or a heddle rod. The TTSH type comprises six members including the frame, two treadles, a scale link, a thread, and the other thread with a heddle rack. The TTTH type also comprises six members including the frame, two treadles, two threads with heddle racks, and a scale link. The structures of the TTSH and the TTTH types are the same from the viewpoint of mechanisms. Since there are many uncertain portions in the illustrations, such as the uncertain numbers of the treadles and the threads, the heddle raising device is a Type III mechanism with uncertain numbers and types of members and joints. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction design of heddle raising device is presented as follows: Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a planar or spatial mechanism with four members (members 1\u20134), five members (members 1\u20135), or six members (members 1\u20136). 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) 269 2. Treadle 1 (KTr1) is a binary link and connected to the frame (KF) with an uncertain joint. 3. Thread 1 (KT1) is a binary link and connected to the treadle (KTr) and the scale link (KSL) with thread joints (JT). 4. The scale link (KSL) is connected to the frame (KF) with an uncertain joint. 5. Thread 2 (KT2) is a binary link and connected to the scale link (KSL) and treadle 2 (KTr2) with thread joints (JT). For the STSH-2 and STHH types, one thread is connected to the scale link (KSL) and the frame (KF) with a thread joint (JT) and a prismatic joint (JPyz), respectively. 6. Treadle 2 (KTr2) is a binary link and connected to the frame (KF) with an uncertain joint. Step 2. Since this device is a mechanism with four, five, or six members, the corresponding atlas of generalized kinematic chains with four, five, and six members are shown in Fig. 11.2 and Fig. 11.5. Step 3. There must be a pair of binary links as the treadle and the thread. When the number of members is five, the pair of binary links must be connected to a ternary link as the scale link. When the number of members is six, there must be two pairs of binary links as two treadles and two threads. Therefore, only those three generalized kinematic chains shown in Figs. 11.2a, f and Fig. 11.5b are qualified for the process of specialization. All feasible specialized chains are identified as follows: Frame (KF) Since there must be a link as the frame (KF) and one or two pairs of binary links are connected to the frame, the frame is identified as follows: 1. For the generalized kinematic chain shown in Fig. 11.2a, the assignment of the frame generates one result as shown in Fig. 11.19a1. 2. For the generalized kinematic chain shown in Fig. 11.2f, the assignment of the frame generates one result as shown in Fig. 11.19a2. 3. For the generalized kinematic chain shown in Fig. 11.5b, the assignment of the frame generates one result as shown in Fig. 11.19a3. Therefore, three specialized chains with identified frame are available as shown in Figs. 11.19a1\u2013a3. Treadle 1 and thread 1 (KTr1 and KT1) Since there must be a pair of binary links as treadle 1 and thread 1, and treadle 1 must be connected to the frame (KF) and thread 1(KT1) with an uncertain joint (J1) and a thread joint (JT), respectively, treadle 1 and thread 1 are identified as follows: 1. For the case shown in Fig. 11.19a1, the assignment of treadle 1, thread 1, and uncertain joint J1 generates one result as shown in Fig. 11.19b1. 2. For the case shown in Fig. 11.19a2, the assignment of treadle 1, thread 1, and uncertain joint J1 generates one result as shown in Fig. 11.19b2. 270 11 Complex Textile Devices 3. For the case shown in Fig. 11.19a3, the assignment of treadle 1, thread 1, and uncertain joint J1 generates one result as shown in Fig. 11.19b3. Therefore, three specialized chains with identified frame, treadle 1, and thread 1 are available as shown in Figs. 11.19b1\u2013b3. 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) 271 Scale link (KSL) Since the scale link must be connected to thread 1 (KT1) and the frame (KF) with a thread joint (JT) and an uncertain joint (J2), respectively, the scale link is identified as follows: 1. For the case shown in Fig. 11.19b1, the assignment of the scale link and uncertain joint J2 generates one result as shown in Fig. 11.19c1. 2. For the case shown in Fig. 11.19b2, the assignment of the scale link and uncertain joint J2 generates one result as shown in Fig. 11.19c2. 3. For the case shown in Fig. 11.19b3, the assignment of the scale link and uncertain joint J2 generates one result as shown in Fig. 11.19c3. Therefore, three specialized chains with identified frame, treadle 1, thread 1, and scale link are available as shown in Figs. 11.19c1\u2013c3. Treadle 2 and thread 2 (KTr2 and KT2) Since thread 2 (KT2) must be connected to the scale link (KSL) with a thread joint, and the remaining link is treadle 2 (KTr2), treadle 2 and thread 2 are identified as follows: 1. For the case shown in Fig. 11.19c2, the assignment of thread 2 generates one result as shown in Fig. 11.19d1. 2. For the case shown in Fig. 11.19c3, the assignment of treadle 2, thread 2, and uncertain joint J3 generates one result as shown in Fig. 11.19d2. Therefore, two specialized chains with identified frame, treadle 1, thread 1, scale link, thread 2, and treadle 2 are available as shown in Figs. 11.19d1 and d2. Step 4. The coordinate system is defined as shown in Fig. 11.17a. The function of the heddle raising device is to generate the rising or falling motion of the heddle rack through the oscillating motion of the treadle. The uncertain joints may have multiple types to achieve the equivalent function. 1. Considering uncertain joints J1 and J3, each of them has three possible types: the first one rotates about the x-axis with respect to the frame, denoted as JRx; the second rotates about the z-axis with respect to the frame, denoted as JRz; the third translates along the y-axis with respect to the frame, denoted as JPy. 2. Considering uncertain joint J2, it has two possible types: the scale link rotates about the x-axis with respect to the frame, denoted as JRx; and the scale link rotates about the z-axis with respect to the frame, denoted as JRz. 3. When the scale link is connected to the frame with a revolute joint JRz, treadle 1 and treadle 2 are not suitable to be connected to the frame with prismatic joints JPy, due to the arrangement of the treadles. By assigning all possible types of uncertain joints J1(JRx, JRz, and JPy), J2(JRx and JRz), and J3(JRx, JRz, and JPy) to the specialized chains as shown in Figs. 11.19c1, d1, and d2, 19 feasible specialized chains with particular joints are obtained as shown in Figs. 11.20a\u2013s. 272 11 Complex Textile Devices Step 5. Considering the motions and functions of the mechanism, each specialized chain with particular joints is particularized to obtain the atlas of feasible designs that meet the ancient technological standards. Figures 11.21a\u2013s show the corresponding 3D solid models of the feasible designs. Weft Pressing Device With each picking operation, the reed comb presses each weft yarn against the portion of the fabric in the weft pressing device. The simplest type of the weft pressing device comprises two members including the frame and a reed comb. A bamboo or a linkage is used in the device to facilitate the pressing. The bamboo with its elasticity makes the reed comb go back to the original position after pressing. The members of the device with a bamboo comprise the frame, a reed comb, and a bamboo. The linkage with weight helps the weaver to press the weft yarn effectively and comfortably. The members of the device with a linkage comprise the frame, a reed comb, and one or two connecting links. From the descriptions and illustrations in the existing literatures, the number of members of 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) 273 the weft pressing device is two, three or four and the types of some joints are uncertain. Therefore, this device is a Type III mechanism with uncertain numbers and types of members and joints. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction design of the weft pressing device is presented as follows: Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a planar or spatial mechanismwith twomembers (members 1 and 7), three members (members 1, 7\u20138), or four members (members 1, 7\u20139). 2. The reel comb (KRC) is a binary link and connected to the frame (KF) or the bamboo (KBB) with an uncertain joint. 274 11 Complex Textile Devices 3. One bamboo (KBB) is a binary link and connected to the frame (KF) and the reel comb (KRC) with a bamboo joint (JBB) and an uncertain joint, respectively, in generalized kinematic chains with three members only. 4. One connecting link is a binary link and connected to the frame (KF) with an uncertain joint in a closed chain. Step 2. Since this device is a mechanism with two, three, or four members, the corresponding atlas of generalized kinematic chains with two, three, and four members are shown in Figs. 11.2a\u2013c and Fig. 11.22. Step 3. There must be a pair of binary links as the reed comb and the frame or the reed comb and the bamboo. Therefore, only those four generalized kinematic chains shown in Fig. 11.2a and Figs. 11.22a\u2013c are qualified for the process of specialization. All feasible specialized chains are identified as follows: Frame (KF) Since there must be a link as the frame (KF), the frame is identified as follows: 1. For the generalized kinematic chain shown in Fig. 11.22a, the assignment of the frame generates one result as shown in Fig. 11.23a1. 2. For the generalized kinematic chain shown in Fig. 11.22b, the assignment of the frame generates two results as shown in Figs. 11.23a2 and a3. 3. For the generalized kinematic chain shown in Fig. 11.22c, the assignment of the frame generates one result as shown in Fig. 11.23a4. 4. For the generalized kinematic chain shown in Fig. 11.2a, the assignment of the frame generates one result as shown in Fig. 11.23a5. Therefore, five specialized chains with identified frame are available as shown in Figs. 11.23a1\u2013a5. Reed comb (KRC) Since the reed comb must be connected to the frame (KF) or the bamboo (KBB) with an uncertain joint, the reed comb is identified as follows: 1. For the case shown in Fig. 11.23a1, the assignment of the reed comb and uncertain joint J4 generates one result as shown in Fig. 11.23b1. 2. For the case shown in Fig. 11.23a2, the assignment of the reed comb and uncertain joint J5 generates two results as shown in Figs. 11.23b2 and b3. 3. For the case shown in Fig. 11.23a3, the assignment of the reed comb and uncertain joint J5 generates one result as shown in Fig. 11.23b4. 4. For the case shown in Fig. 11.23a4, the assignment of the reed comb and uncertain joint J6 generates one result as shown in Fig. 11.23b5. 5. For the case shown in Fig. 11.23a5, the assignment of the reed comb and uncertain joint J7 generates one result as shown in Fig. 11.23b6. Therefore, six specialized chains with identified frame and reel comb are available as shown in Figs. 11.23b1\u2013b6. Bamboo (KBB) Since the bamboo must be connected to the frame (KF) and the reed comb (KRC) with a bamboo joint (JBB) and an uncertain joint in generalized kinematic chains with three members, the bamboo is identified as follows: 1. For the case shown in Fig. 11.23b2, no link that is connected to the frame and the reed comb can be assigned as the bamboo. 2. For the case shown in Fig. 11.23b3, the assignment of the bamboo generates one result as shown in Fig. 11.23c1. 3. For the case shown in Fig. 11.23b4, no link that is connected to the frame and the reed comb can be assigned as the bamboo. 4. For the case shown in Fig. 11.23b5, the assignment of the bamboo and uncertain joint J8 generates one result as shown in Fig. 11.23c2. Therefore, two specialized chains with identified frame, reed comb, and bam- boo are available as shown in Figs. 11.23c1 and c2. 276 11 Complex Textile Devices Connecting link 1 and connecting link 2 (KL1 and KL2) Since connecting link 1 must be connected to the frame (KF) with an uncertain joint in a closed chain and the remaining link is connecting link 2, connecting link 1 and connecting link 2 are identified as follows: 1. For the case shown in Fig. 11.23b5, the assignment of connecting link 1 and uncertain joints J9 and J10 generates one result as shown in Fig. 11.23d1. 2. For the case shown in Fig. 11.23b6, the assignment of connecting link 1, connecting link 2, and uncertain joints J11, J12, and J13 generates one result as shown in Fig. 11.23d2. Therefore, two specialized chains with identified frame, reed link, bamboo, connecting link 1, and connecting link 2 are available as shown in Figs. 11.23d1 and d2. Step 4. The coordinate system is defined as shown in Fig. 11.17a. The function of the weft pressing device is to operate the reed comb to press the weft yarn to avoid the loose structure of the textile. The uncertain joints may have multiple types to achieve the equivalent function. Since the device is planar, the uncertain joints must be planar joints. 1. Considering uncertain joints J4, J5, J6, and J7, each of them has two possible types: a revolute joint JRx or a thread joint JT. 2. Considering uncertain joint J8, it has one possible type: the reed comb is connected to the bamboo with a revolute joint JRx. 3. Considering uncertain joints J9 and J10, each has two possible types and they can not be the same type simultaneously. When any one is a revolute joint JRx, the other not only rotates about the x-axis but also translates along the z-axis, denoted as JPzRx. 4. Consider uncertain joints J11, J12, and J13, each has one possible type: it rotates about the x-axis, denoted as JRx. By assigning the possible types of uncertain joints J4, J5, J6, and J7(JRx and JT), J8 (JRx), J9 and J10(JRx and JPzRx), J11, J12, and J13(JRx) to the specialized chains shown in Figs. 11.23b1, c1, c2, d1, and d2, 12 specialized chains with particular joints are obtained as shown in Figs. 11.24a\u2013l. Step 5. Considering the motions and functions of the mechanism, each specialized chain with particular joints is particularized to obtain the atlas of feasible designs that meet the ancient technological standards. Figures 11.25a\u2013l show the corresponding 3D solid models of the feasible designs. Fabric Reeling Device The fabric reeling device is designed to keep the warps tight, and collects the fabric in which warps and wefts are interwoven. It consists of the frame (member 1, KF), a warp beam (member 2, KU1), a cloth beam (member 3, KU2), and a fabric belt (member 4, KT). The fabric belt includes the warps and the fabric. The warp beam is connected to the frame with a revolute joint JRx. The fabric belt is 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) 277 connected to the warp beam and the cloth beam with wrapping joints JW. The cloth beam is connected to the frame with a revolute joint JRx. It is a Type I mechanism with a clear structure. Figure 11.26 shows the structural sketch of the fabric reeling device. Figure 11.27 shows an imitation of the original illustration in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b. Figure 11.28 shows a real object of the type of TTTH for the foot-operated slanting loom." ] }, { "image_filename": "designv10_13_0003071_tmag.2008.2001660-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003071_tmag.2008.2001660-Figure1-1.png", "caption": "Fig. 1. Proposed single phase switched reluctance motor rotor shape.", "texts": [ " To solve this problem, some researchers have introduced an epoxy molded rotor which has a cylindrical rotor shape. This molded rotor also shows good performance at high speeds but its manufacturing process is more complex and expensive than a conventional SRM rotor because at least one or two more processes have to be appended onto the original manufacturing process. This paper presents a novel switched reluctance motor rotor shape which has ribs between the rotor salient poles on the rotor outer surface. Fig. 1 shows the proposed rotor shape, which is an aerodynamically cylindrical rotor that is magnetically identical to a conventional rotor because the ribs are magnetically saturated while the stator teeth are facing them. Using this rotor, the windage loss can be reduced dramatically at high speed. Fig. 2 shows the single phase SRM driving circuit. Because the proposed rotor has ribs between the rotor salient poles, these ribs must be saturated while the stator poles overlap the ribs in order for the rotor to get reluctance torques" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure19-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure19-1.png", "caption": "Figure 19. 5 Degree Of Freedom (DOF) Robotic Arm.", "texts": [ "0 kg, not including any Bits. The approximate size of the Ground Station is 14.3 cm x 14.3 cm x 9.6 cm. The Bits and Bit Sleeves are arranged in a close packed formation with the minimum of 19 or 31 bits (depending on requirement). The mass of the cache with the bits but no rocks is approxmiately 2.1 kg. Robotic arm The 1 m Robotic Arm is a five degree of freedom system with similar kinematics to the MER Instrument Deployment Device. The five axes include Azimuth, Elevation, Elbow, Wrist and Turret degrees of freedom (Figure 19). The Robotic Arm has been designed only to a level of detail appropriate to obtain a relatively accurate estimate of the mass required. Each joint was initially sized to be able to support the load of the turret mounted instruments (APXS, M\u00f6ssbauer, Microscopic Imager) and the drill, at Earth gravity. In addition, since the Robotic Arm may be used to remove the Sample Cache from the rover and place it on the ground, the mass of a fully loaded Sample Cache was used to design the joints. The arm joints were designed to meet the maximum loads under rover slip conditions" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003537_icra.2012.6224823-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003537_icra.2012.6224823-Figure3-1.png", "caption": "Fig. 3. Schematic of the five link planar biped model", "texts": [ " The most elegant one is by using virtual holonomic constraints [6] to relate the joints in one leg to one parameter that describes the position of the swing foot with respect to the hip. In essence, one would constrain the motion of the high order model to a lower order one, but still take into account the kinetic and potential energies of all links in the system. Alternatively, one could also use a constraint optimization method which minimizes, for example, energy consumption with (16) as constraint. In this section, the FPI algorithm is applied in an example to a model of a five link biped. This model is shown in Fig. 3. The model consists of five point masses and contains two lower legs, two upper legs and a torso. We derive the equations of motion as in (1) and implement these in a numerical simulation. We can now use (4), (5) and (8) in the FPI algorithm to find the desired configuration \u03b8FPI from (16) and track this using PD feedback controllers. As we have seen before, there is no unique configuration from which the biped evolves to the balanced standing configuration, so we enforce the stance leg to be always fully stretched: \u03b8FPI,2 = 0 and the torso to be always perpendicular to the ground: \u03b8FPI,3 = \u2212\u03d5" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001563_jsvi.1998.9999-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001563_jsvi.1998.9999-Figure4-1.png", "caption": "Figure 4. Experimental test set-up. (a) Self-aligning bearing with rigid masses of known inertia properties; (b) axial excitation; (c) radial excitation. Parameter values: m1 =3\u00b7366 kg, I1xx =0\u00b70114 kg m2, I1yy =0\u00b70114 kg m2, L1 =0\u00b70298 m, m2 =3\u00b7133 kg, I2xx =0\u00b70113 kg m2, I2yy =0\u00b70113 kg m2, L2 =0\u00b70364 m.", "texts": [ " Note that the above formulation for the stiffness matrix is valid independently of angular misalignment about the x- and y-axis as defined in Figures 2 and 3 since the spherical bearing does not produce moment loads. The stiffness matrix is effectively defined with respect to a reference frame oriented with the unloaded inner raceway. In order to examine the validity of the theoretically developed bearing stiffness model, an experimental test has been devised. Consider using the bearing to connect two rigid bodies as denoted in Figure 4. Here, r1 =[r1x r1y r1z u1x u1y ]T and r2 =[r2x r2y r2z u2x u2y ]T denote the displacement of each rigid body form the static equilibrium position. Rotation about the z-axis for both rigid bodies is not considered as these axes are collocated with the bearing axial direction. The origin of the bearing co-ordinate system in both rigid body reference frames is given by s1 =[0 0 L1 0 0]T and s2 =[0 0 \u2212L2 0 0]T, respectively. Neglecting rotational motion of each rigid body about the z-axis, the entire system has 10 degrees of freedom", " More generally, since the radial co-ordinate pair, x and y, can always be defined such that the resultant radial preload is oriented in the positive x direction, once values of kxx , kyy , kzz and kxz are obtained in this co-ordinate frame, a simple linear transformation can be used to obtain values for all six of the potentially non-zero stiffness and cross-coupling stiffness coefficients kxx , kyy , kzz , kxz , kxy and kyz for any other co-ordinate orientation. An example study was undertaken using the system depicted in Figure 4. It was verified beforehand that the test masses are indeed rigid for the frequency range of interest. However, the rigidity of the bearing interface fixture relative to the bearing, particularly the inner stub, is an issue. The test setup is flexibly suspended and axial and/or radial preloads are applied across the bearing, again using flexible couplings with stiffness coefficients several orders of magnitude below those of the bearing. Note that the preloads must consist of equal forces of opposite direction applied along vectors which pass through the bearing pivot point to maintain static stability" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001486_s0921-8890(01)00171-3-Figure18-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001486_s0921-8890(01)00171-3-Figure18-1.png", "caption": "Fig. 18. The system evolution when the clusters are initialized on different sides of the minimum, with the larger cluster at a higher g value than the smaller.", "texts": [ " 16, we plot the evolution of a pair of clusters when initiated on the decreasing region of g. In this case, Cluster 1 will grow, absorbing Cluster 2, and eventually resulting in a single cluster of all the pucks. This is commensurate with the results of Section 3. If we instead put the clusters initially on the increasing region of g, the situation radically changes (see Fig. 17). Since the larger cluster now has the larger g value, it tends to lose pucks to the smaller cluster. Thus, the two clusters approach each other in size, and eventually become equal in size. Fig. 18 illustrates the system evolution when the clusters are initialized on different sides of the minimum with the larger cluster at a higher g value than the smaller cluster. In this case, the larger cluster will lose pucks to the smaller cluster. Since the slopes are equal, the loss of pucks is directly proportional to the relative loss of g. Thus, the larger cluster cannot \u201ccatch up\u201d in g to the smaller. The result is that the process will continue until the initially smaller cluster passes the minimum of g and begins rising in g to meet the initially larger cluster" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002516_1-4020-4611-1_2-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002516_1-4020-4611-1_2-Figure3-1.png", "caption": "Figure 3. First fiber optic chemical sensor (from ref. [17]; used for sensing oxygen). Alos shown is a cross-sedction of the fiber bundle used. 6: light source; 9: photodectectors; 16: chemically sensitive layer.", "texts": [ " In 1974, Hesse 17 described a fiber optic chemical sensor for oxygen and this appears to have been the first FOCS at all. An oxygen-sensitive chemistry was placed in front of a fiber optic light guide through which exciting light was guided. The fluorescence emitted is guided back through either the same fiber, or through the other fibers of a bundle. The system is based on measurement of either fluorescence intensity or fluorescence decay time, both of which are affected by oxygen. A schematic of the design is shown in Fig. 3. We believe that the paper on optical affinity sensors for individual metabolites by Schultz & Sims 18 was a milestone paper in optical waveguide Fiber Optic Chemical Sensors and Biosensors 20 biosensing in that the fundamental principles of affinity sensors were outlined for the first time and in that optical affinity sensing was recognized as a viable alternative to radioisotope techniques. The determination of glucose via concanavalin served as an example. In these sensors, the intrinsic absorption of the analyte is measured directly" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003322_j.actaastro.2011.02.010-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003322_j.actaastro.2011.02.010-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of pressure-balanced needle-type gas regulating system: 1-gas bottle; 2-swith valve; 3-reducing valve; 4-servo valve; 5-gas generator; 6-channel of control valve; 7-throat of gas generator; 8-valve head; 9-chamber of valve head; 10-valve stem; 11-nozzle of control valve; 12-second combustor.", "texts": [ " In the first mode, the pressure in gas generator chamber is regulated by controlling the displacement of needle valve to obtain an appropriate throat area of gas generator. This mode, named area-regulated mode, is actuated by an electromechanical actuator. In Ref. [24], two types of area-regulated needle valves were presented. The second mode is called pressure-balanced mode, actuated by a pneumatic actuator. In this mode, the pressure in gas generator chamber is regulated by changing the pressure in valve head chamber. In this paper, a pressure-balanced gas regulating system is deployed, and its schematic diagram is shown in Fig. 2. The working principle of the system is as follows. When the need for gas flow increases, the servo valve (4) is controlled to make the gas enter into the valve head chamber (9) from a high-pressure gas bottle (1) through switch valve (2) and reducing valve (3). Pressure in the valve head chamber (9) is increased and upsets the force balance of the valve head (8), which then moves forward (as left in Fig. 2) along the valve stem (10), reducing the throat area (7) of gas generator (5) and increasing pressure in the gas generator (5). Since burning rate of solid propellant in the gas generator is proportional to chamber pressure, more burning gases get generated and increase flow rate through the channel of control valve (6). In contrast, when the servo valve (4) pushes the gas leaves the valve head chamber (9), pressure in the chamber valve head (9) is reduced, and so do pressure in the gas generator (5) and flow rate through the gas control valve", " (9), the transfer function among the displacement xv, the pressure pr and the pressure pv can be written as D ~xv\u00f0s\u00de \u00bc K3 T3s\u00fe1 D ~pr\u00f0s\u00de K4 T3s\u00fe1 D ~pv\u00f0s\u00de \u00f013\u00de where D ~pv\u00f0s\u00de \u00bc Dpv\u00f0s\u00de pv max K3 \u00bc Ar0 pr0\u00f0@Ar=@xv\u00de9xv \u00bc xv0 pr max xv min K4 \u00bc Av pr0\u00f0@Ar=@xv\u00de9xv \u00bc xv0 pv max xv min T3 \u00bc b pr0\u00f0@Ar=@xv\u00de9xv \u00bc xv0 The transfer function between the pressure pr and the pressure pv can be obtained by combining Eq. (11) with Eq. (13), and written as D ~pr\u00f0s\u00de \u00bc K5 T2 4 s2\u00fe2xT4s\u00fe1 D ~pv\u00f0s\u00de \u00f014\u00de where T4 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T3T1 1 K2K3 s , 2xT4 \u00bc T1\u00feT3 1 K2K3 , K5 \u00bc K2K4 1 K2K3 : As can be seen in Fig. 2, the pneumatic servo system, including a gas bottle, a switch valve, a needle valve head, a servo valve and some pipes, is able to regulate pressure in the valve head chamber. And the pressure in the chamber pv is determined by the interaction of charge/ discharge, movement of the valve and leakage of the gas. The leakage process of the gas through the annular clearance between the valve head and valve stem is very complex, making it difficult to establish an accurate mathematical model, thus a leakage model is then introduced [26]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001428_0094-114x(94)00048-p-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001428_0094-114x(94)00048-p-Figure2-1.png", "caption": "Fig. 2. Typical spur gear pair mesh mode shapes: (a) primary mesh mode (r = l) with A 1 = 1.61803 and A,I = l; (b) secondary mesh mode (r = 2) with A 2 = 0.61803 and An., = 0,23067.", "texts": [ "00 \u00d7 108 N/m t, = 10203.7 rad/s KaH. = 6.00 x 108 N/m Ks.. . = 1.50 x 10 s N/m K~tu~ = 6.71 x I08 N-m/rad 332 G. WESLEY BLANKENSHIP and RAJENDRA SINGH The spur gear case (\u00a2b = 0\u00b0) is considered first with both x = 0 and/~ = 0. Only two modes are of interest: torsional-0: and lateral-y. Bending-0x, rocking-0y and axial-z modes do not contribute to A,r under these conditions and Ao~r = 0. In most parallel axis gear pairs %y > 0.1 and the system is characterized by mode shapes similar to those shown in Fig. 2 given %y = 2.0. In order to clearly define the dynamic behavior, a few new terms are defined. Any mode having A~r = 1 or A0e = 1 is denoted as a primary normal or bending mesh mode, respectively. All other modes having non-zero A,r or A0+r are denoted as secondary normal or bending mesh modes, respectively. Dynamic force transmissibility 333 ) and A2( - ) versus %,; (b) In the example case shown in Fig. 2, torsional and lateral displacements add directly to form a primary mesh mode (A,~ = 1) at Aj = 1.61803. However, the r --- 2 modal displacements 0. and y tend to cancel, thus diminishing the combined relative normal mesh displacement A,2 = 0.23607 creating a secondary mesh mode at A2 = 0.61803. The eigenvalues Aj and A2 are dictated entirely by bearing stiffness ratio %y as shown in Fig. 3(a). A purely torsional model predicts a single mode at AI = 1. The effect of bearing flexibility is always to increase A~/> w/2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001450_cdc.1994.411345-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001450_cdc.1994.411345-Figure5-1.png", "caption": "Figure 5: An upper bound on the off-track-ig of the trailer and kingpin hitch i s computed when the lead car changes its path from a straight line DO to an arc of a circle of radius r .", "texts": [ " 0 The main result of this paper consists of the next two theorems which assume L := L1 = La for the kingpin hitching, and compute an upper bound on the off-tracking of the trailer and kingpin hitch when the car changes from a straight line t o an arc of a circle of radius r and vice versa. The bounds are computed with respect to the distance traveled by the lead car. Theorem 8 If the lead car of a two-azle system with equal length kingpin hitching changes from a straight line to an arc of a circle of radius T , then an upper bound on the off-tmcking of the trailer, E , and the off-tracking of the kingpin hitch, z , is where a is the arc length tmveled by the lead car from the instant the car switches to the circle and X := r /L . Proof. The proof refers to Figure 5. We assume the car travels from the right to the origin 0 along a straight line of length 2L, then at 0 switches to the arc of a circle of radius r . The kingpin hitch is at a distance L from the origin (point D) initially, and at point E when the car switches to the circle. The trailer is at a distance 2L from the origin initially, and a t point B at the switching time. From Lemma 6, we know that R 5 TI and r1 2 r , therefore f 5 z , i.e., we need to compute an upper bound on the off-tracking of the kingpin hitch" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001863_1131322-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001863_1131322-Figure1-1.png", "caption": "FIG. 1.-Interpretive and free-body diagrams of a model of an infant's upper extremity. The upper diagram shows the limb positioned in an inertial (X - Y - Z) coordinate system with a positive torque defined (M). The upper extremity is modeled as three interconnected rigid segments (S1 hand, S2 forearm, and S3 upper arm) with frictionless joints (J1 wrist, J2 elbow, and J3 shoulder). At each instant in time during a reach, a moving local plane (P) is calculated so that the plane contains the x, y, z coordinates of each of the three joint centers (J1, J2, J3). The planar torques at the wrist, elbow, and shoulder are calculated with respect to the respective joint axes (Zi, Z', Z') that pass through each joint and are perpendicular to the moving local plane (P). In the lower portion of the figure is a free-body diagram of the upper extremity. Depicted are forces related to the hand, forearm, and upper-arm segment weights (W1, W2, W3) acting their respective center of mass, and the wrist, elbow, and shoulder joint reaction forces (F1, F2, F3) and torques (M1, M2, M3).", "texts": [ " Accepting that limitation, researchers then have a tractable problem, and rigid-body equations of motion can be used to quantify limb dynamics. To do a rigid-body analysis of a limb's dynamics, a free-body diagram is first constructed, isolating the segment (link) of interest with all the external applied forces drawn on the diagram (Likins, 1973). In the This content downloaded from 137.99.31.134 on Mon, 27 Jun 2016 09:08:51 UTC All use subject to http://about.jstor.org/terms Zernicke and Schneider 985 upper portion of Figure 1, we show a schematic of an infant's upper extremity, consisting of three segments (S1, hand; S2, forearm; and S3, upper arm) connected by \"frictionless\" joints (J1, wrist; J2, elbow; and J3, shoulder). Previously we published the mathematical details and equations of motion for this three-segment model (Schneider & Zernicke, 1990), and, thus, here we only present the basic elements of the model we have used to study both adult and infant limb dynamics. The three-segment upper extremity moves in an inertial reference frame (X - Y - Z) that is oriented with respect to gravity, acting in the vertical direction (Fig. 1). We record the three-dimensional coordinates (x, y, z) of the wrist (J1), elbow (J2), and shoulder (J3) and-at each instant in timecompute a \"moving-local plane\" (P) that always contains the coordinates of the wrist, elbow, and shoulder (J1, J2, J3). In the moving-local plane, free-body diagrams are constructed, as illustrated in the lower portion of Figure 1. For each of the three segments, there is a force related to each segment's weight (W1, W2, W3) acting through each segment's center of mass, and at each joint, there are equal and opposite joint reaction forces (F1, F2, F3). For example at the wrist joint, F1 is the joint reaction force of the hand acting on the distal end of the forearm segment, while -F1 is the equal and oppo- This content downloaded from 137.99.31.134 on Mon, 27 Jun 2016 09:08:51 UTC All use subject to http://about.jstor.org/terms 986 Child Development site effect of the forearm acting on the hand", " For three of the seven subjects in the primary study, electromyograms for upperextremity muscles (biceps brachii, triceps brachii, anterior deltoid, and posterior deltoid) were recorded. A three-dimensional analysis of movement kinematics and a planar analysis of limb dynamics were completed for both the primary and pilot studies. Data Analysis Three-dimensional joint coordinates were recorded, linear and angular displacement-time data were smoothed, and first, second, and third derivatives were calculated. We modeled the upper limb as three interconnected rigid links (hand, forearm, upper arm) with frictionless joints at the shoulder, elbow, and wrist (Fig. 1) and used the joint three-dimensional coordinates to determine the inclination angles and time derivatives (angular accelerations and velocities) for the hand, forearm, and upper arm. With estimates of segmental masses, centerof-mass locations, and moments of inertia the two-dimensional dynamics were calculated for the limb in a moving-local plane containing the wrist, elbow, and shoulder joints (Fig. 1). At each joint, torques were calculated about axes that were normal to the moving-local plane and that passed through the joints (mathematical details in Schneider et al., 1989; and Schneider & Zernicke, 1990; also see Fig. 1). Changes in Limb Dynamics with Practice During the practice trials of our primary study, movement times decreased significantly. From the slowest to the fastest trial, an average decrease of 36% in movement time was achieved, with the slowest trial equaling about 1 sec and the fastest trial 0.6 sec. The major decrease in movement time was accomplished in the first 25 practice trials, as we observed an exponential decrease in movement time with practice. As subjects became faster during practice, hand paths became more parabolic in This content downloaded from 137" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001714_rnc.604-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001714_rnc.604-Figure7-1.png", "caption": "Figure 7. Incident waves de\"nitions.", "texts": [ " Robust Nonlinear Control 2001; 11:1239}1256 The dynamic positioning system cannot directly compensate \"rst order motions, since they have high-frequency components which would require an enormous power to be attenuated. The best that can be done is to minimize these motions, heading the FPSO in such a way that the waves do not induce large \"rst-order motions. The only task left for the controller is to reduce slow-drift oscillations in surge, sway and yaw directions, and also eliminate static o!sets induced by mean drift moment in yaw direction. Mean drift forces and moments are given by X ( )\"2 S( )D ( , ) d , i\"1, 2 or 6 (16) where is the wave incidence angle relative to the ship (Figure 7), S( ) is the wave spectrum and D( , ) are the drift coe$cients of the hull, taking into account the interaction between current and waves (wave drift damping), following Aranha [6]. Copyright 2001 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 2001; 11:1239}1256 The estimation of wave spectrum still presents practical and theoretical problems. In addition, sudden variations of the environmental conditions can occasionally occur. So, the controller must guarantee stability and performance requirements under some uncertainty on the intensity and direction of incident waves" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure8.5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure8.5-1.png", "caption": "Fig. 8.5 A donkey-driven cylinder wheel (\u9a62\u8f49\u7b52\u8eca), a Original illustration (Wang 1991) b Structural sketch", "texts": [ " 174 8 Gear and Cam Mechanisms There are four water lifting devices with gears including Lv Zhuan Tong Che (\u9a62\u8f49 \u7b52\u8eca, a donkey-driven cylinder wheel), Niu Zhuan Fan Che (\u725b\u8f49\u7ffb\u8eca, a cowdriven paddle blade machine), Shui Zhuan Fan Che (\u6c34\u8f49\u7ffb\u8eca, a water-driven paddle blade machine), and Feng Zhuan Fan Che (\u98a8\u8f49\u7ffb\u8eca, a wind-driven paddle blade machine). Each of these devices is a Type I mechanism with a clear structure and is described below: 8.2.1 Lv Zhuan Tong Che (\u9a62\u8f49\u7b52\u8eca, A Donkey-Driven Cylinder Wheel) Lv Zhuan Tong Che (\u9a62\u8f49\u7b52\u8eca, a donkey-driven cylinder wheel) in the book Nong Shu\u300a\u8fb2\u66f8\u300b, as shown in Fig. 8.5a (Wang 1991), has the same function of scooping water as Tong Che (\u7b52\u8eca, a cylinder wheel) that was described in Sect. 6.4. Since Tong Che is required to install near the turbulent current, if there is no such an area, Lv Zhuan Tong Che can be another option. Besides the frame and the water wheel with a horizontal shaft, the device adds a set of the vertical and horizontal gears. During operation, the horizontal gear rotated by animals, drives the vertical gear and water wheel to rotate to scoop water", " The vertical gear is connected to the water wheel with a horizontal shaft as an assembly. It is a mechanism with three members and three joints, including the frame (member 1, KF), a horizontal gear with a vertical shaft (member 2, KG1), and a vertical gear with a water wheel and a horizontal shaft (member 3, KG2). The horizontal gear is connected to the frame with a revolute joint, denoted as JRy. The vertical gear is connected to the frame with a revolute joint, denoted as JRx. The meshing activity between the gears can be considered as a gear joint JG. Figure 8.5b shows the structural sketch. 175 8.2.2 Niu Zhuan Fan Che (\u725b\u8f49\u7ffb\u8eca, A Cow-Driven Paddle Blade Machine) Niu Zhuan Fan Che (\u725b\u8f49\u7ffb\u8eca, a cow-driven paddle blade machine) consists of two parts including a gear train and a chain transmission mechanism as shown in Fig. 8.6a (Pan 1998). It has the same function as Fan Che (\u7ffb\u8eca, a paddle blade machine). Animals rotate the large horizontal gear, and the motion is transmitted from the gear train to the upper sprocket on the long shaft, the chain, and the lower sprocket" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002736_j.jmatprotec.2008.03.065-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002736_j.jmatprotec.2008.03.065-Figure7-1.png", "caption": "Fig. 7 \u2013 The section profile of (3) is the same as the section profile (2) in the middle transverse plane.", "texts": [ " Edge contact causes a serious concentration of stress and a significant decrease in the lifetime of the gear drive. The crowning modification can be applied on either (1) or (2). Here, (2) is selected and the crowning strategy is illustrated as shown in Fig. 6, where a form grinding wheel is driven by a parabolic motion with respect to the generated gear. The surface of revolution of the form grinding wheel is denoted by (3) and is the same as the section profile of (2) in the middle transverse plane. As shown in Fig. 7, the section profile of (2) in the middle transverse plane is a curve denoted by (2) and represented by r\u2217 2 = {x2( 1), y2( 1), 0, 1}T (27) A coordinate system S3 (x3, y3, z3) is applied to connect rigidly to (3) and x3 is the axis of revolution. The profile (2) is used to be the axial section profile of (3). By rotating (2) about the axis of revolution, x3, with parameter 3, the position vector of (3) can be obtained as follows: r3( 3, 1) = \u23a1 \u23a2\u23a2\u23a2\u23a3 x2( 1) cos 3[r2 + + y2( 1)] sin 3[r2 + + y2( 1)] 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 (28) By driving the form grinding wheel to move with a parabolic motion with respect to the generated gear, the tooth face (2), which is not a crowned one, is transformed into a crowned tooth face, which is denoted by (4)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003957_iros.2011.6094783-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003957_iros.2011.6094783-Figure7-1.png", "caption": "Fig. 7 Virtual wall and correction force.", "texts": [ " The perception-assist is performed considering xzmp. C. Stairs-ascending assist In this paper, it is assumed that users are elderly persons and a user ascends/descends stairs one step at a time. In the stairs-ascending assist, the robot judges whether the user trips over a step or can keep the balance. If any problems are found in the user\u2019s motion, the robot tries to modify the user\u2019s motion. To judge whether the user stumbles on a step, the virtual wall area is generated in front of the step as shown in Fig. 7(a). If the user\u2019s foot enters the virtual wall area, the robot tries to modify the user\u2019s motion to prevent the user from stumbling on the step. In the perception-assist, the robot generates the additional motion modification force along the virtual wall in addition to the power-assist force to avoid the collision with the step. The additional motor torque generated by the effect of the additional motion modification force (i.e., the perception-assist torque) is written as follows. vir virk virh fJ T , , \u00bb \u00bc \u00ba \u00ab \u00ac \u00aa W W (11) where Wh,vir is the additional hip joint torque, Wk,vir is the additional knee joint torque, J is Jacobian matrix and fvir is the additional motion modification force vector generated along the virtual wall", " To prevent the user from falling down and cancel the undesired effect of the ZMP change caused by the additional motion modification force vector, the ankle joint torque is generated. Wcancel which is the torque to cancel the effect of the change of ZMP is calculated as follows. viraswcancel fr u ,W (12) where rsw,a is the vector from the ankle joint of the supporting leg to the ankle joint of the swing leg. After the user\u2019s foot is lifted over the step, the user puts own foot on the step. Then, the robot generates the additional motion modification force vector as shown in Fig. 7(b) if it is necessary so that the user can overcome the next step. This additional motion modification force vector is generated in order to prevent the user\u2019s foot from entering the virtual wall area of next step. The robot repeats these perception-assists so that the user can ascend stairs safely. D. Stairs-descending assist In general, the case that an elderly person descends stairs has high possibility of falling down compared with the case that an elderly person ascends stairs. Next, the stairs-descending assist is discussed" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002641_robot.2005.1570507-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002641_robot.2005.1570507-Figure2-1.png", "caption": "Fig. 2. Coordinate system and free-body diagram of the trirotor rotorcraft", "texts": [ " The results show that the controller performs very well in practice. II. MODELLING OF THE TRIROTOR In this section we present the model of a three-rotor rotorcraft using a Lagrangian approach. The generalized coordinates describing the rotorcraft position and orientation are q = (x y z \u03c8 \u03b8 \u03c6)T where (x, y, z) denote the position of the center of mass of the three-rotor aircraft to the frame I, and (\u03c8, \u03b8, \u03c6) are the three Euler angles (yaw, pitch and roll angles) and represent the orientation of the rotorcraft (see figure 2). Therefore, the model partitions 0-7803-8914-X/05/$20.00 \u00a92005 IEEE. 2612 naturally into translational and rotational coordinates is \u03be = (x y z) \u2208 R 3 (1) \u03b7 = (\u03c8 \u03b8 \u03c6) \u2208 R 3 The translational kinetic energy of the rotorcraft is Ttra = 1 2 m . \u03be T . \u03be (2) where m denotes the mass of the rotorcraft. The rotational kinetic energy is Trot = 1 2 . \u03b7 T J . \u03b7 (3) The matrix J acts as the inertial matrix for the full rotational kinetic energy of the rotorcraft expressed directly in terms of the generalized coordinates \u03b7" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002690_j.compstruct.2007.04.025-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002690_j.compstruct.2007.04.025-Figure1-1.png", "caption": "Fig. 1. Kelvin\u2013Voigt material model.", "texts": [ " In real applications, it is often only possible to partly cover the structure with a damping layer. In order to study this, the influence of gaps in the damping layer is investigated using a 2D finite element model. Significant influence is observed for badly located gaps. To model the damping properties of the material, a Kelvin\u2013Voigt visco-elastic material model, see e.g. [18], has been introduced in both the semi-analytical and the finite element model. The model can be illustrated as a spring and damper in parallel connection, see Fig. 1. In the Kelvin\u2013Voigt model the normal stress component, r, and shear stress component, s, respectively, are taken to be given as r \u00bc E \u00fe c_ ; s \u00bc Gc\u00fe j_c \u00f01\u00de where and c denote the corresponding normal and shear strain components, respectively, and c and j the damping factors. A dot (\u00c6) denotes strain rates. The Kelvin\u2013Voigt model only describes a creeping phase, where the strains under a prescribed load grows from zero to a limited-value given by the elastic strain. The model is thereby not capable of modeling a relaxation behaviour in the material during a prescribed deformation, but since the system in this case is excited with a harmonic load, the effect of relaxation is not relevant" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.10-1.png", "caption": "Fig. 9.10 A rope drive grinding device (\u78e8\u5e8a) a Original illustration (Pan 1998), b Structural sketch", "texts": [ " The large pulley is connected to the frame with a revolute joint JRy. The rope is connected to the large and small pulleys with wrapping joints JW. The small pulley is connected to the frame with a revolute joint JRz. It is a Type I mechanism with a clear structure. Figure 9.9b shows the structural sketch. 9.3.3 Mo Chuang (\u78e8\u5e8a, A Rope Drive Grinding Device) In the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b, Mo Chuang (\u78e8\u5e8a, a rope drive grinding device) transmits power and motions by ropes or belts for jade processing as shown in Fig. 9.10a (Pan 1998). A grinding wheel is installed in the middle of the device\u2019s horizontal shaft, both sides of which are installed in bearings. On both sides of the grinding wheel, a rope is nailed to the shaft with its upper part. Each rope is coiled around the shaft several times in the opposite direction. The lower parts of the two ropes are installed on two treadles. When the operator pedals the treadles, the grinding wheel would rotate in an oscillating way, thereby grinding jade stones. Since Mo Chuang is symmetrical, one side of the device is sufficient for analysis", " It is a mechanism with four members and four joints, including the frame (member 1, KF), a treadle (member 2, KTr), a rope (member 3, KT), and a turning 202 9 Flexible Connecting Mechanisms shaft with a grinding wheel (member 4, KU). The treadle is connected to the frame with a revolute joint JRx. The rope is connected to the treadle and the turning shaft with a thread joint JT and a wrapping joint JW, respectively. The turning shaft is connected to the frame with a revolute joint JRx. It is a Type I mechanism with a clear structure. Figure 9.10b shows the structural sketch. 9.3.4 Zha You Ji (\u69a8\u6cb9\u6a5f, An Oil Pressing Device) Zha You Ji (\u69a8\u6cb9\u6a5f, an oil pressing device) in the book Tian Gong Kai Wu\u300a\u5929\u5de5 \u958b\u7269\u300bconsists of two parts including the hollow timber and the ramming device as shown in Fig. 9.11a (Pan 1998). The timber used for making an oil press must be an armful in diameter and hollowed in the center. The best raw material for the hollowed out timber is camphor wood. The hollow is formed by scooping out the wood with a curved chisel, so that the hollowed space becomes a flat trench with rounded ends" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001885_1.1518502-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001885_1.1518502-Figure5-1.png", "caption": "Fig. 5 Co-ordinate systems for contact definition", "texts": [ " In the following, a conjugated modification in one direction is applied to the modified tooth flank. 2.5 Contact Analysis. The contact simulation is based on BER 2002 .asmedigitalcollection.asme.org/ on 01/28/20 the theory of the continuous tangency of contacting surfaces and achieved by the simultaneous generation of the main contact surfaces, such as the convex surface of the pinion and the concave surface of the gear flank. The contacting surfaces are described in a fixed co-ordinate system, Ss ~Fig. 5! satisfying the meshing Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F equations. Ideal surfaces have a common point in contact position ~Eq. ~8!! and the unitary normal vectors of the surfaces at this point are co-linear ~Eq. ~9!!. rs1~ t1 ,w1 ,c1 ,f1!2rs2~ t2 ,w2 ,c2 ,f2!50 (8) ns1~ t1 ,w1 ,c1 ,f1!1ns2~ t2 ,w2 ,c2 ,f2!50 (9) Equations ~8! and ~9! supply six independent scalar equations. As far as the unitary normal vectors are used, the number of meshing equations for pinion and gear tooth surface generation are also considered as being capable of simulating contact with any kind of machine-settings", " As only the kinematics of solid bodies is considered in this study, contact simulation is replaced by a geometric approximation of contact ellipses, considered with a theoretical offset tooth surface. In practice, the method is based on the determination of the distance between the tooth surfaces in contact. Note that the distances between contacting surfaces are small and the surfaces are convex. Consequently, surface distance calculation is approximated by determining the radius vectors. More specifically, for a given contact position, the tooth surfaces are fixed and presented in co-ordinate system Ss ~Fig. 5!. In the vicinity of contact point Ps j , successive cutting planes perpendicular to axis zs are considered ~Fig. 6!. In each plane, two points are defined in such a way that distance uPs1 jPs2 j \u00af u equals 10mm and the length of their location vectors equals urs1 ju5urs2 ju. 2.7 Presentation of Results and Computing Conditions. The tooth surfaces are considered as rigid body and kinematics simulation is also considered. But in order to give a first approximation of contact patterns useful for modification of machining parameters, a geometrical analysis was made" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003568_s00502-013-0133-5-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003568_s00502-013-0133-5-Figure8-1.png", "caption": "Fig. 8. Parameters for planning motion in the sagittal plane [4]", "texts": [ " 6 it can be observed that the CoM is passing through acceleration and deceleration phases in such a way that the given ZMP reference is achieved. Similarly in Fig. 7 the CoM is forming a sinelike curve to satisfy the ZMP reference. In this section planning motion for the sagittal plane (axes x, y) is accomplished, considering only the phase of double support, and considering that the transition between the foot support is instantaneous. To accomplish this task are required some parameters, they determine the configuration of walking proces, as shown in Fig. 8. The trajectory of the tip of the swing limb is denoted by the vector Xa : (xa(t), ya(t)), where (xa(t), ya(t)) is the coordinate of the swing limb tip position with the origin of the coordinate system located at the tip of the supporting limb (see Fig. 8). We use a third and fifth degree polynomial functions for the xa and ya separately. They are shown in the following: xa = a0 + a1 \u00b7 t + a2(k) \u00b7 t2 + a3(k) \u00b7 t3 ya = b0 + b1 \u00b7 t + b2(k) \u00b7 t2 + b3(k) \u00b7 t3 +b4(k) \u00b7 t4 + b5(k) \u00b7 t5 \u23ab\u23aa\u23ac \u23aa\u23ad 0 < t \u2264 Ts (14) Then, we develop the constraint equations that can be used for solving the coefficients, ai and bj (i = 0 . . . 3 and j = 0 . . . 5). We cast the gait patterns in terms of four basic quantities: step length SL, step period for the Single support phase (SSP) TS , maximum clearance of the swing limb Hm and its location Sm" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.10-1.png", "caption": "Fig. 4.10 A water-driven grinder, a Original illustration (Wang 1968), b Structural sketch, c Chain", "texts": [ " Gear mechanisms for power transmissions were primarily used in changing the speed and/or direction of the power source such as human power, animal power, wind power, or water power to produce the required output work. Such designs were often seen in water-driven agricultural machines that did not require high accuracy and speed. Consequently, wood was used as material, and the shape of the teeth was insignificant. They were similar to the pin gears of today. In what follows, some applied examples of ancient Chinese gear mechanisms for power transmissions are presented. Figure 4.10a shows a water-driven grinder that was widely used during the Northern and Southern Dynasties (AD 386\u2013589) (Liu 1962). It is a food-processing device to grind grain. In the device, water rotates the vertical water wheel with a long shaft, that sets two other vertical gears. The direction of the power is changed to vertical by a gear train to drive the two output grinders rotating simultaneously. Since each of the two gear trains has the same allocation, using only one set is sufficient for analysis" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002250_bf00469465-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002250_bf00469465-Figure1-1.png", "caption": "Fig. 1. Cross-section through the sensing chemistry of the fiber optic lactate sensor. P plexiglass support; D dialyzing membrane; E enzyme solution; 0 O-ring; LG light guide. The arrows indicate the diffusional processes involved (L lactate; A acetate). The directions of the exciting light (exc) and fluorescence (flu) are also shown. The platelet has an outer diameter of 20 mm, the diameter of the cavity is 4 mm", "texts": [ " Fluorescence spectra were run on an Aminco SPF 500 spectrofluorometer (equipped with a 250 Watt xenon arc lamp) in 1 x I cm rectangular quartz cells. The flow-through cell was machined from stainless steel and had a chamber volume of approximately 20 I~1. The buffer and lactate solutions were pumped through the cell at a typical flow-rate of 1.2 ml rain -a. A cross section through the flow-through cell and the alignment of the fiber have been given previously [12]. All measurements were performed at 24 _+ 1 ~ and in air-saturated 0.1 tool/1 citrate buffers, because phosphate is known to be an inhibitor of LMO [21. Figure 1 shows a cross-section through the sensing part. It consists of a plexiglass disk (20 mm o.d., 1.5 mm thickness) with a cavity in its center (4 mm in diameter, 350 pm deep, volume 4.4 H1). LMO (1 mg) was dissolved in 50 pl o f distilled water and the solution was placed in the cavity of the plexiglass disk. The whole disk was covered with the dialyzing membrane which was fixed with a rubber O-ring. Cuprophane is not permeable to the enzyme, but allows the substrate (lactate) to diffuse to the enzyme" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003258_memsys.2011.5734353-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003258_memsys.2011.5734353-Figure1-1.png", "caption": "Figure 1: Fabrication and design of the dual sensor. (a) fabrication and functionalization of the sensor on contact lens; (b) images of contact lens with integrated sensors.", "texts": [ " One method for interference compensation is a dual sensor structure where only one sensor responds to glucose while both respond equally to the interferences [5]. We have fabricated such a dual microscale sensor on a contact lens and demonstrate that it can be successfully used for sensing low concentrations of glucose in the presence of interfering chemicals. Sensor design and sensing principles The dual sensor is designed with two working electrodes (WE), two conjoint counter electrodes (CE), and one common reference electrode (RE) (Figure 1(b)). The reaction of interest occurs at the WE; CE acts as the current drain; RE provides a stable reference potential; the bare area between WE and CE works as a platform for enzyme immobilization. The shape of concentric rings minimizes the resistance between WE and CE. In addition, CE (75 \u03bcm) is designed wider than WE (50 \u03bcm) to ensure that the current signal is strictly determined by conditions at the WE, as voltage will drop mainly on WE. The common RE is designed as a bar between the primary sensor and the control sensor, having an area of about 1 mm2", "5 mm2) are used to make electrical connections between an external potentiostat and the sensor for testing. All the electrode structures are designed on the edge of the contact lens, leaving the central area clear in order not to block visual path for future wireless design. The main reactions for amperometric sensing scheme used in our sensor are as follows: 2 2 2 + - 2 2 2 Glucose Oxidase 2 D-Glucose + O H O + D-Gluconolactone D-Gluconolactone + H H O 2H + O + 2e O D-Gluconic Acid \u23af\u23af\u23af\u23af\u23af\u2192 \u2192 \u2192 The last reaction occurs on the electrode surface and produces the sensing current. As shown in Figure 1(a), the fabrication process started with a transparent polyethylene terephthalate (PET) wafer, which was cut to the standard 4-inch wafer shape using a CO2 laser cutter and cleaned with acetone, isopropyl alcohol 978-1-4244-9634-1/11/$26.00 \u00a92011 IEEE 25 MEMS 2011, Cancun, MEXICO, January 23-27, 2011 (IPA) and deionized (DI) water in sequence. After it was spin-coated with an approximately 6 \u03bcm layer of photoresist (AZ4620), the wafer was soft baked for 20 min at 65 OC, and then the photoresist was exposed and developed", " In the next step three metal layers Ti(10 nm)/Pd(20 nm)/Pt(100 nm) were evaporated in sequence without breaking vacuum. The additive layer of Pd between Ti and Pt here is significant, as Pd works as a metal diffusion barrier layer and also increases signal stability [6]. After lift-off in acetone for 10 minutes, and cleaning with IPA and DI water, the plastic wafer was dried with nitrogen gas, and then cut to small pieces with a diameter of 1 cm. Subsequently, the small sensor was heat molded to the shape of a contact lens with electrodes on the outside surface, as shown in Figure 1(b). In order to test the sensor\u2019s functionality under controllable conditions that resemble the eye surface, we designed and fabricated a polydimethylsiloxane (PDMS) model that mimics a human eye (Figure 2(a)). By carefully reconstructing the curvature of the cornea, and the tear duct and drain system, we were able to test the sensor functionality in thin liquid layers similar to those of tear film. The PDMS eye model was fabricated using a double molding procedure, starting with a 25 mm diameter glass sphere which has a curvature similar to that of a human eye", "5 mm was then precisely inserted into the final mold to create two liquid inlets and one outlet connecting the backside of the eye model and the internal sidewall of the faux eyelid, simulating the geometry of the tear ducts and drains of a real human eye. After molding the sensor to the lens shape, the pads were connected to electrical wires using silver conductive epoxy and then isolated with non-conductive epoxy. After rinsing thoroughly with DI water and drying with N2, one sensor (the control sensor) was covered with a piece of parafilm, and the other sensor (the primary sensor) was left open for the following surface treatment, as shown in Figure 1(a). A 20 \u03bcL glucose oxidase (GOD) solution with a concentration of 10 mg/mL was dropped onto the open area for the primary sensor. Then the dual sensor was suspended vertically above a titanium isopropoxide (TI) solution (97%) in a sealed dish for 6 hours, allowing the vapors to create a TI/GOD sol-gel membrane. TI was applied here in order to improve the immobilization efficiency of GOD for the sensor, just as reported [7]. The TI/GOD sol-gel film is very efficient in preventing GOD from detaching from the film due to the large number and the strong connection of hydroxyl groups in TI" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003272_tmag.2009.2024641-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003272_tmag.2009.2024641-Figure9-1.png", "caption": "Fig. 9. Distributions of average eddy current loss densities determined using (a) full 3-D analysis, (b) Method 1, (c) Method 2 without consideration of , and (d) Method 2 with consideration of .", "texts": [ " This was due to the overestimation of the eddy current due to the neglecting of the reduction in the variation in flux densities due to . On the other hand, the loss determined using Method 2 without consideration of was less than that determined by full 3-D analysis owing to the overestimation of the reduction in the variation in the flux density due to . When the PM is divided into five segments, these errors decrease because the eddy current in the PM is less. The loss determined using Method 2 with consideration of is in good agreement with that determined by full 3-D analysis. Fig. 9 shows the distributions of the average eddy current loss densities determined using the various methods. The figure shows that the distribution determined using Method 2 with consideration of coincides with the distribution determined by full 3-D analysis. The average eddy current losses obtained using various methods are compared in Fig. 10. The eddy current losses are normalized by the average for the full 3-D model without division. When both and are considered, the eddy current loss is in good agreement with that determined by full 3-D analysis in every case" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002867_icma.2009.5246352-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002867_icma.2009.5246352-Figure9-1.png", "caption": "Fig. 9. Assist force amplified gravity compensation device", "texts": [ " 2 B - 2 sm-, r 1 2 where K denotes the spring constant. From this, the gener alized moment exerted on the joint shaft is driven as 8U(B) 2r22h2 K . B B r22h2 K . T = - --- = - sm - cos - = - sm B. 8B ri 2 2 ri Therefore, by the same discussion as the previous section , if the spring constant K is taken to K = mgt (r1)2 (11) h2 r2 the proposed mechanism works as a gravity compensation system . From (11), the moment generated by this gravity compensation system can be amplified arbitrarily by increas ing the gear ratio r2 / rl . Fig.9 shows the developed assist force amplified gravity compensation device . The length of the link body, mass properties and spring constants of the equipment are listed in Table.III. Here, it should be noticed that the roller is attached to the linear slider 1. Since the large torques is exerted on the gear, if there is no support by the rollers, the system becomes rickety. This implies that the system will get to large and heavy to generate the large compensation force by this mechanism. This device is for the inverted pendulum, but it can be extended to the multi link version in the same way as the previous section by using the timing belt" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001384_978-94-017-2925-3-Figure20.9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001384_978-94-017-2925-3-Figure20.9-1.png", "caption": "Fig. 20.9. Blow molding.", "texts": [ " In addition, some RUBBER-RELATED POLYMERS 605 equipment manufacturers, resin suppliers, and others are interested in special fields of blow molding such as the production of large tanks, bag and box con tainers, large toy cars and animals, beverage cases, and the like. In principle, all blow-molding systems require that a molten tube or parison of polymer be delivered to an open mold. The mold closes on the parison and air pressure is applied to force it against the inside surfaces. The solidified part is ejected from the mold and trimmed if necessary (Fig. 20.9). Although injec tion-molding machines may be used to supply the molten parison, most pro ducers utilize extruders for this purpose. In some designs, the extruder feeds an accumulator which in tum forms the parison. This permits continuous operation of the extruder even though the parison extrusion is intermittent. In other de signs, several molds are placed on a rotary table and are automatically presented under the extrusion head to receive the parison at the proper time. Continuous extrusion of tubing to be received by molds on a belt or wheel is another tech nique that is used widely in the United States" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure18-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure18-1.png", "caption": "Fig. 18. Gear contact pattern estimation for the second example: nominal condition and modified assembly error values (shaded: HFM; black solid line: geometric estimation).", "texts": [], "surrounding_texts": [ "We have presented a geometric approach to the estimation of the contact pattern of a hypoid gear drive. The method does not seek for contact pressures and does not directly consider material properties since it only deals with geometric properties of the pinion and gear surfaces. However, with the proposed approach, tooth, gear body, shaft and housing deformations as well as load sharing are approximately taken into account by properly selecting the marking compound thickness and topography. As explained in Section 5.4, the marking compound thickness and topography are the outcome of a procedure where the estimated contact pattern matches a (reliable) reference contact pattern computed considering real operating conditions. The procedure has been tested with an accurate contact analysis tool (HFM) and the comparisons have shown that the estimated contact pattern shape is very reliable. The computational load of the proposed procedure is very low compared to FEM approaches. For this reason the geometric approach can be profitably employed in an automatic contact pattern sensitivity test and/or optimization procedures." ] }, { "image_filename": "designv10_13_0002376_02701367.1985.10608448-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002376_02701367.1985.10608448-Figure4-1.png", "caption": "Figure 4-Depiction of the mean vertical (F,) and mediolateral (FJ forces for ail subjects for both feet at six instants of time during the stride and swing phases. The times shown for each position (+9 were recorded for one subject (shown above). The timing varied slightly among subjects. Forces less than .1 BW are not shown.", "texts": [ " Figure 3a indicates a total F, force (left + right) of approximately .7 BW occurred .5 s before impact. 2.0 0.5 0.0 .50 f C. -.25h / \u2019 -.5 -.4 -.3 -.2 - . I 0 .1 Time (s) Figure 3-Mean force time curves for ail subjects for both feet (shaded area denotes standard error). Forces are shown in units of body weight (BW): (a) vertical forces (FJ, (b) medioiaterai forces (FJ, and (c) anteroposterior forces (F,). During that time the left foot remained in contact with the ground, but off the force plate, as the batter prepared to stride forward (Figure 4a). Although no left F, forces were recorded during this brief interval, in all probability the sum of the right and left F, forces was approximately 1 BW. Once the left foot was lifted off the ground, right F, forces increased to 1 BW for the remainder of the stride. Any small deviations from this value were due to the downward acceleration of the batter\u2019s center of gravity. After completion of the stride, total F, forces increased to a maximum of 2 BW at contact. The right mediolateral forces (F,) were exerted laterally, away from the batter (negative X direction), and were responsible for initiating movement of the body toward the pitched ball (Figures 3b and 4a-f)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003850_j.jmbbm.2013.05.009-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003850_j.jmbbm.2013.05.009-Figure1-1.png", "caption": "Fig. 1 \u2013 A growing bilayer tissue in a cylindrical lumen: (a) initial configuration and (b) current configuration.", "texts": [ " In this paper, therefore, we consider an isotropic and hyperelastic cylinder containing a mucosal layer and a submucosal layer, which grow either in a fixed tube or without any external constraint. Usually, mucosae are much stiffer than submucosae. Therefore, we assume that the elastic modulus of the mucosa is higher than that of the submucosa. The volumetric growth model originally established by Rodriguez et al. (1994) is employed to analyze growth-induced deformation. In the cylindrical coordinate system, the position of a representative material point at the initial configuration X\u00bc \u00f0R;\u0398;Z\u00de transforms to x\u00bc \u00f0r; \u03b8; z\u00de at the current configuration due to tissue growth, as shown in Fig. 1. The bilayer tube has the initial inner radius A, the interface radius B, and the outer radius C. Thus, the initial thicknesses of the mucosal layer and the submucosal layer are Hm \u00bc B\u2212A and Hs \u00bcC\u2212B, respectively. Here and in the sequel, the subscripts m and s denote the quantities defined in the mucosa and submucosa, respectively. Consider the case of axisymmetric growth, which would lead to axisymmetric deformation, i.e. r\u00bc r\u00f0R\u00de. In the current configuration, the inner, interfacial and outer radii become a, b and c, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002131_j.finel.2004.04.007-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002131_j.finel.2004.04.007-Figure2-1.png", "caption": "Fig. 2. Generating rack in a meshing position during the gear generation process.", "texts": [ " This is especially the case if the gear transmission is of the anti-backlash type, since the elimination of backlash introduces an additional degree of freedom between the gear pair, and the effect of this is not known. Therefore, the aim of the present work is to investigate the transmission error in anti-backlash conical involute gear transmissions. The finite element (FE) method is used, and to reduce the total computation time needed to solve the non-linear contact problems, a global\u2013local FE meshing method is adopted, which yields a dense FE mesh in the contact regions and a coarse mesh in the rest of teeth. An involute gear may be defined by its meshing with a rack with straight-lined flanks. Fig. 2 shows the generation of a conical involute gear with helix angle and cone angle by a generating rack (or tool). The operation is similar to that required to generate a helical gear, but instead of being parallel to the axis of the gear, the generating rack is inclined to the axis by the cone angle. The generating rack in Fig. 2 has pressure angle n\u2212in the normal plane and pressure angles t+ and t\u2212 in the transverse plane. According to [7], the relation between these angles is tan tj = tan n cos i sec i \u2212 j sin i tan i = tan n cos sec \u2212 j sin tan , (1) where i = \u2212(\u22121)i , i = \u2212(\u22121)i . (2,3) The subscript i is equal to 1 for gear 1 (pinion) and 2 for gear 2 (gear). During the cycle of contact, the successive positions of the straight-lined flanks will describe two involute helicoids. One coordinate system for every tooth n of every gear i is used" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.8-1.png", "caption": "Fig. 6.8 An Archimedean screw (\u9f8d\u5c3e) a original illustration (Shi 1981). b Structural sketch", "texts": [ " Its components are a tilted hollow external cylinder and a center shaft with screw threads. When the center shaft spins, its screw threads can draw water up to the shore. Figures 6.8a1\u2013a4 show the geometric graphics of some parts, and Fig. 6.8a5 shows the graphic after its installation (Shi 1981). It is a mechanism with two members and one joint, including an external cylinder as the frame (member1, KF) and a center shaft as the moving link (member 2, KL). The center shaft is connected to the frame with a revolute joint JRz. Figure 6.8b shows the structural sketch. 6.4 Water Lifting Devices 117 There are 11 war weapons with roller members that can be divided by function into three types: reconnaissance, attack, and defense. Among these devices, Chao Che (\u5de2\u8eca, an investigating wagon) and Wang Lo Che (\u671b\u6a13\u8eca, an investigating wagon) are devices for reconnaissance. Hao Qiao (\u58d5\u6a4b, a moat bridge), Yang Feng Che (\u63da\u98a8\u8eca, a winnowing device), Fen Wen Che (\u8f52\u8f40\u8eca, a digging wagon), Yun Ti (\u96f2\u68af, a tower ladder wagon), Pao Che (\u7832\u8eca, a ballista wagon), and Zhuang Che (\u649e\u8eca, a colliding wagon) are for attack" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002980_978-3-642-01153-5-Figure1.10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002980_978-3-642-01153-5-Figure1.10-1.png", "caption": "Figure 1.10.1 Sketch map of single phase induction machine circuit (a) Stator connection; (b) Rotor loops", "texts": [ " Normally, symmetric component method is used for researching the single phase electric machine; in this method, the above factors would bring about many inconveniences, and bigger error would be caused. Adopting the Multi-Loop Analysis method for researching the single phase electric machine, writing equations and calculating parameters can be realized according to actual loops, and the effects of many factors can be considered more comprehensively. This method is suitable particularly for the condition with stronger space harmonics of air-gap magnetic field and special winding connection. In the following, the Multi-Loop Method is used to research the single phase electric machine. Figure 1.10.1(a) is the stator connection sketch of a single phase induction machine. Here, m and a represent main phase winding and auxiliary phase 1 Circuit Analysis of AC Machines\u2014Multi-Loop Model and Parameters 45 winding, respectively, C is series capacitor. Figure 1.10.1(b) is the sketch of the rotor loops of a single phase induction machine. When parameter calculation and performance analysis of single phase induction machine are carried out, the stator phase windings can be considered as stator loops. At the same time, it is needed to calculate the inductances of stator single coil, then by combining them the inductances of stator phase winding are obtained. In the following, firstly the inductances related to air-gap main magnetic field are researched, sum of the inductances caused by the main magnetic field and leakage one are the inductances of stator phase winding", " If several different connection types of the main phase and auxiliary phase windings exist, then respective AC Machine Systems 50 calculations are needed based on actual connection. If the single coil inductance is calculated firstly, in spite of coil connection mode it is very convenient to calculate the inductances of windings, branches, or certain several coils connected, if needed, in terms of the obtained single coil inductances. The reason why the above method is adopted is to illustrate its concrete usage. The rotor circuit of the single phase induction machine is shown in Fig. 1.10.1(b). When the inductances of the rotor loops of the single phase induction machine are researched, the formulas (1.5.14) and (1.5.17) of the rotor damper loop inductances of the salient pole synchronous machine can be cited. But, the air-gap permeance of the single phase induction machine has only the constant term 0 / 2 (harmonic terms 2 4 0 ) owing to uniform air-gap of the single phase induction machine, i.e., only when 2 0l k j , there are values in the two formulas, hence the self inductance of rotor - thi loop is 2 2 02 2 2 1 sin 2 r r i k w l kL P k (1", "19), and (1.10.20) are substituted into the flux-linkage equation (1.10.24), then the voltage equations (1.10.21), (1.10.22), and (1.10.23) are brought in, a group of equations will be obtained in which the amplitudes of the sine parts and cosine parts are unknown quantities, including each harmonic sine function and cosine function of t . Pay attention to the fact that the rotor loop of the induction machine is short circuit ( 0)nu , the electric source of stator winding is fundamental voltage (refer to Fig. 1.10.1(a)), then 0 0cos sinmu u U t U t (1.10.25) 0 0 0 0 0 0 0 0 0 0 1cos sin ( cos sin )d cos sin sin cos a C a a a a u u u U t U t I t I t t C I IU t U t t t C C (1.10.26) 1 Circuit Analysis of AC Machines\u2014Multi-Loop Model and Parameters 55 It is enough to analyze only according to a certain loop equation of rotor, because the amplitude of each loop current of the rotor is the same, and the phase angle difference of the adjacent loops is also the same. As for the current of another loop of the rotor, it is not difficult to be calculated based on equation (1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001468_s0956-5663(97)00122-x-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001468_s0956-5663(97)00122-x-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the screen-printed biosensor (a) cutaway view of the tip of the electrode, (b) electrode body from above. I, PVC; 2, Ag strip; 3, carbon layer,\" 4, Ag/AgCl reference electrode; 5, working electrode; 6, insulation layer; 7, enzyme and mediator layer,\" 8, outer membrane layer.", "texts": [ " A model S-600M screen printer (Ever Bright Printing Machine Ltd., Hong Kong) was used to print the electrodes. Cyclic voltammetry and chronoamperometry were performed using an EG&G Potentiostat/Galvanostat Model 273A (Princeton Applied Research, USA) connected to a Gateway-2000 computer (South Dakota, USA) to record the voltammograms. The base electrodes were produced by screenprinting in the form of a lanar, two-electrode electrochemical cell. The arrangement of the components is indicated in Fig. 1. Sensors were screen-printed in groups of 45 onto clear polyvinyl chloride. The conducting tracks consisted of silver ink. A graphite pad was deposited onto the conducting tracks. The reference electrode was made by applying a crescent consisting of silver ink mixed with finely ground silver chloride in the ratio 0.2 g AgC1 per gram of ink, onto the end of a graphite pad. The insulation shroud was then applied, leaving terminals and active surfaces exposed. Glucose oxidase and 1,1'-ferrocenedimethanol were dissolved in distilled water to give an appropriate concentration so that when 1 /xl was dropped onto the working area of the electrode it gave the desired final amounts" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003716_j.jsv.2010.12.015-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003716_j.jsv.2010.12.015-Figure1-1.png", "caption": "Fig. 1. Geometry of a typical cylindrical helical spring.", "texts": [ " After verifying the results obtained in this study and given by other models, the first five natural frequencies for clamped\u2013clamped springs with three different cross-sections and the first three natural frequencies for clamped\u2013free springs of rectangular cross-section have been presented. The effects of the aspect ratio for the elliptic cross-section, the number of active turns, the helix pitch angle and the ratio of the radii of cylinder to minor axes of wire cross-section on the free vibration frequencies have also been investigated. For the system as shown in Fig. 1, the local coordinate reference frame x, Z and s (principle normal in, bi-normal iZ and tangent t to the general helix) is used. The arc length along the curved is denoted by s. If x and Z are principal axes of the cross-section, kx is zero and kZ and ks are the curvature and tortuosity of the helix [20]. The parametric relationships of a cylindrical helix are h\u00bc Rtana, c\u00bc \u00f0R2\u00feh2\u00de 1=2, ks \u00bc h=c2 \u00bc \u00f01=R\u00desinacosa, kZ \u00bc R=c2 \u00bc \u00f01=R\u00decos2a, ds\u00bc cdb, where h is the step for unit angle of the helix, R is the centerline radius of the helix, a is the pitch angle and db\u00bc ds=c is the infinitesimal angular element" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure5.8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure5.8-1.png", "caption": "Fig. 5.8 A water-driven mill, a Original illustration (Lu and Hua 2000) b Structural sketch c Chain", "texts": [ "2 Reconstruction Design Methodology 97 This section presents the procedure of classification and reconstruction designs of ancient mechanisms. Three different types of mechanisms with illustrations are presented as examples, including mechanisms with clear structures (Type I), mechanisms with uncertain types of joints (Type II), and mechanisms with uncertain numbers and types of members and joints (Type III). 5.3.1 Example 1: Shui Long (\u6c34\u7931, A Water-Driven Mill) Shui Long (\u6c34\u7931, a water-driven mill) is a grain processing device that uses a gear train to drive the mill, as shown in Fig. 5.8a (Lu and Hua 2000). It consists of a vertical water wheel, a horizontal shaft, a vertical gear, and a mill gear. 98 5 Reconstruction Design Methodology The horizontal shaft that connects to the vertical water wheel and gear with no relative motion is considered as the same member. When water drives the vertical water wheel to spin, the horizontal shaft and vertical gear also spin. Through gear transmission, the mill gear is operated to remove the chaff of grains. Based on the written description and the illustration, the numbers and types of all members and joints in the water-driven mill can be identified" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001885_1.1518502-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001885_1.1518502-Figure4-1.png", "caption": "Fig. 4 \u201ea\u2026 Co-ordinate systems for crown gear generation \u201eb\u2026 Co-ordinate systems for pinion generation \u201ec\u2026 Co-ordinate systems for gear generation", "texts": [ " is described in the coordinate system Sb1, the generating point P of the cutter edge is 762 \u00d5 Vol. 124, DECEMBER 2002 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 represented by the radius vector rb1(t). The co-ordinate system Sb1 is rotated around axis zt1 with the sum of angles n and k. Angle n is a basic angle when the cutter edge plane is directed towards the instantaneous axis I of rotation ~Fig. 2!. The auxiliary co-ordinate system, St1, is rigidly connected to the co-ordinate system Sh1 of the head cutter ~i51 in Fig. 4~a!!. The radius of the head-cutter is Rh15uOt1Oh1 \u00af u. The co-ordinate system Sh1 performs a rotation w1 about axis zu1. The auxiliary co-ordinate system Su1 is rigidly connected to another auxiliary co-ordinate system, Sv1. The machine distance, M d15uOu1Ov1 \u00af u Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F links the two co-ordinate systems. Co-ordinate system Sv1 rotates about axis zc1, wa1 being the current rotation angle. The coordinate system Sc1 is attached to the generating crown gear. Angles w1 and wa1 are related by Eq. ~1! where p1 and r1 are respectively the radius of the rolling circle and the base circle. w1 wa1 5 r1 p1 (1) The generating crown gear gives the tooth surface ~Fig. 4~b!! and the co-ordinate system Sc1 rotates about axis zm by an angle of rotation c1 . Pinion co-ordinate system S1 rotates simultaneously about axis zw1, with angle ca1. The installation position of coordinate system Sw1, in relation with co-ordinate system Sm , is determined by pitch angle d1 , measured clockwise. The relation between these two angles, c1 , ca1, is given in Eq. ~2!. The instantaneous axis of rotation is the axis ym . c1 ca1 5sind1 (2) rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 2.2 Gear Generation. Index 2 related to the gear. The gear cutter edge geometry is presented in the co-ordinate system Sb2 ~Fig. 3~c!!. The generation of the resulting crown gear surface is achieved in a similar way to that of the pinion ~i52 in Fig. 4~a!!. The generating crown gear generates the tooth surface ~Fig. 4~c!! and the co-ordinate system Sc2 rotates about axis zm by angle of rotation c2 . Gear co-ordinate system S2 rotates simultaneously about axis zw2, with angle ca2. The installation position of Sw2, with respect to Sm , is determined by pitch angle d2, measured counter-wise. The relation between these two angles, c2 , ca2, is given by Eq. ~3!. The instantaneous axis of rotation is the ym axis. c2 ca2 5sind2 (3) 2.3 Obtaining Tooth Surfaces. During matrix transformations and calculations, the surfaces of the generating gear are represented in coordinate system Sci by the radius vector rci (w i ,t i)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002853_s11012-006-9037-3-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002853_s11012-006-9037-3-Figure2-1.png", "caption": "Fig. 2 Model used in the kinematic analysis", "texts": [ " Section 8 gives an example trajectory tracking problem. Section 9 gives the conclusions drawn from the results of this work. The kinematics analysis of the SPM relates the lengths of the prismatic legs to the position and orientation of the moving platform [5]. FK analysis relates the position and orientation of the top platform to the leg lengths, whereas IK analysis relates leg lengths to the position and orientation of the top platform, as described in the introduction. Architecture of the SPM used in inverse kinematics analysis is given in Fig. 2. IK equations are used to generate data for training the neural network. Coordinates of the vertices of the top platform are given with respect to the reference system on the base with a rotation matrix R and a translation vector t. In order to find the rotation matrix R, the order of the rotations of the top platform need to be known. If the reference frame on the top platform first rotates about the x axis through an angle of \u03b3 degrees, then about the y axis through an angle of \u03b2 degrees, and finally about the z-axis through an angle of \u03b1 degrees, using Euler angles, R, the matrix of rotation, is defined as R = (RxRyRz) T , (1) where Rx is the matrix of rotation about the x-axis, Ry is the matrix of rotation about the y-axis and Rz is the matrix of rotation about the z-axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003601_s10846-012-9731-4-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003601_s10846-012-9731-4-Figure2-1.png", "caption": "Fig. 2 Detail of forces acting on the helicopter", "texts": [ " Moreover, since no coupling terms appear in Eq. 5 the vehicle dynamics can be partitioned into translational dynamics and rotational dynamics [7]. Also, the last property helps to analyse the generalized forces acting on the vehicle in two groups, the first group composed of translational forces and the second related to the rotational torques of motion as described below. The force that a rotor produces is commonly called thrust. The direction of the vector thrust is ideally always perpendicular, upwards the rotor disc. According to Fig. 2 it follows that this vector takes the form FB = \u239b \u239d 0 0 u \u239e \u23a0 (6) where u = \u22118 i=1 | fi| = \u22118 i=1 ki\u03c9 2 i is the lift force exerted by each motor Mi in free air, whit \u03c9i denoting the angular velocity of the rotor and k > 0 being a parameter depending on the density of the air, the radius, shape, pitch angle of the blade and other factors (see [8] for details). The nonconservative torques acting on the helicopter, denoted as \u03c4\u03b7 = [\u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8 ]T , are caused from the action of the lift forces induced by the eight rotors around the x and y axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003539_1.4025602-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003539_1.4025602-Figure1-1.png", "caption": "Fig. 1 Basic tapered roller bearing geometry, relative race displacements, and total roller race geometrical interference", "texts": [ " The word analytical is used for describing the fact that no numerical iterations and rolling element load summation are required for calculating the bearing loads and moments. Also, the contact stiffness will be defined for ball bearing (BB), tapered roller bearing (TRB), cylindrical roller bearing (CRB), and spherical roller bearing (SRB), so that the suggested approach can be widely used and programmed in any FEA or MBS tool for describing any rolling element bearing type. Without repeating the results described in Ref. [1], the main points are summarized below. Figure 1 shows a TRB whose inner ring (IR also called cone) and outer ring (OR also called cup) centers are represented by the points I and O, respectively. The half-included cup angle is a and is negative when point I is located to the left of point O (as in Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 15, 2013; final manuscript received September 20, 2013; published online November 13, 2013. Assoc. Editor: Dong Zhu. Journal of Tribology JANUARY 2014, Vol. 136 / 011105-1Copyright VC 2014 by ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Fig. 1). Alternatively, the angle a is positive when point I is located to the right of point O. A similar sketch to Fig. 1 could be shown for an angular contact ball bearing where a is the initial contact angle, negative when the IR race center I is on the left of the outer race center O. Cone and cup mean radii are Ri and Ro while the roller has an effective length L and a mean diameter D. The two sketches show the relative position of the cone and cup, before and after displacements of the point I relative to O. The relative race displacements dx, dy, and dz are defined in such a way that when dy and dz are nil, the IR is centered in the OR and then dx equal to zero corresponds to the IR race just touching the rolling element, itself just touching the OR race" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.9-1.png", "caption": "Fig. 6.9 Reconnaissance devices. a An investigating wagon (\u5de2\u8eca) (Mao 2001). b Structural sketch of roller device. c Structural sketch of pulley device. d An investigating wagon (\u671b\u6a13\u8eca) (Mao 2001)", "texts": [ " Hao Qiao (\u58d5\u6a4b, a moat bridge), Yang Feng Che (\u63da\u98a8\u8eca, a winnowing device), Fen Wen Che (\u8f52\u8f40\u8eca, a digging wagon), Yun Ti (\u96f2\u68af, a tower ladder wagon), Pao Che (\u7832\u8eca, a ballista wagon), and Zhuang Che (\u649e\u8eca, a colliding wagon) are for attack. Lei (\u6a91, a thrower), Lang Ya Pai (\u72fc\u7259\u62cd, a thrower), and Man (\u5e54, a shield wagon) are for defense. Each device is a Type I mechanism with a clear structure and is described below: Military strategists in ancient China considered the reconnaissance of enemies\u2019 positions as an important task. Chao Che (\u5de2\u8eca, an investigating wagon) is the 118 6 Roller Devices most representative device for the task as shown in Fig. 6.9a (Mao 2001). The device can be tracked to the Spring\u2013Autumn Period (770\u2013476 BC) (Lu 2003). In the device, Ban Wu (\u677f\u5c4b, a wooden cab that can rise and fall), made from solid wood and covered with raw cowhide to prevent the attacks from enemies. It can hold two scouts. When the scouts enter the wooden cab, the cab is raised by using a pulley so that they can see the status of the enemies. The device has wheels so that other soldiers can move it around on the battlefield and the scouts on the cab can look out and search for enemies. 6.5 War Weapons 119 Chao Che can be divided into two parts: the roller device and the pulley device. The roller device is a mechanism with two members and one joint, including a wagon body as the frame (member 1, KF) and wheels on the frame as the roller member (member 2, KO). The wheel is connected to the frame with a revolute joint JRz. Figure 6.9b shows the structural sketch. The pulley device is a mechanism with four members and three joints, including the frame (member 1, KF), a pulley (member 3, KU), a rope (member 4, KT), and a Ban Wu (member 5, KB). The pulley is connected to the frame with a revolute joint JRz. The rope is connected to the pulley and the Ban Wu with a wrapping joint JW and a thread joint JT, respectively. Figure 6.9c shows the structural sketch. In the book Wu Bei Zhi\u300a\u6b66\u5099\u5fd7\u300b, there is another type of reconnaissance device known as Wang Lo Che (\u671b\u6a13\u8eca, an investigating wagon) as shown in Fig. 6.9d (Mao 2001). The device has the same function as Chao Che, but without the pulley and the rope. It only has a roller device, and its Ban Wu is set on a standing rod (as the frame). Thus, the scouts need to climb up to the Ban Wu on their own. Figure 6.9b shows the structural sketch. In the Shang Dynasty (1600\u20131100 BC), entrenchments had been used outside the city walls for defense. Soldiers needed to pass over the entrenchments in order to attack the city. Hao Qiao (\u58d5\u6a4b, a moat bridge) is a device to assist soldiers to cross the entrenchments as shown in Fig. 6.10a (Mao 2001). It is a mechanism with two members and one joint, including a bridge body as the frame (member 1, KF) and wheels on the frame as the roller members (member 2, KO). The wheel is connected to the frame with a revolute joint JRz" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002492_s0022-5193(89)80155-9-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002492_s0022-5193(89)80155-9-Figure11-1.png", "caption": "FIG. 11. (a) Body curvature by activation of ventral longitudinal elements with spring constants 1 (straight), 2 (half circle) and 6 (circle). (b) The transition from skeleton forming a single circle [outer skeleton, same as in (a)] to a skeleton coiled twice around itself (inner skeleton) is achieved by activation of all circular elements (spring constant = 8). The segments seem to penetrate each other, due to the lateral view.", "texts": [ " This general form includes the simple case of a sequence of cubes [Fig. l(a)] as well as the more refined shape shown in Fig. l(b), which has been adapted to the relaxed state of a leech. We have several reasons for using our geometrical simplification: (i) It reflects the segmental structure of many annelids. (ii) It is much simpler to compute deformations of quadrilateral than of, for example, cylindrical objects. (iii) (iv) Variation of the length of the edges allows for a high flexibility of the body (see Fig. 11). The straight edges of our segments correspond to parts of the muscular system which can be activated separately (cf. Stuart, 1970; Ort et aL, 1974). In each segment there are 4 edges representing longitudinal and 8 edges representing circular muscles. In the model, we call these \"elastic elements\". The 4 lateral edges from the latter group can also incorporate the effects of the dorsoventral muscles. So far, only the oblique muscles have not been directly modelled. Depending on the shape of the body, they may either support the longitudinal or the circular muscles and maintain the pressure (Mann, 1962)", " It w o u l d ce r t a in ly be o f in te res t to m e a s u r e wh ich With increasing volume the internal pressure increases sharply at first, levels off, and then decays again, as is expected from the derivative o f the energy functional eqn (2.4) (see also Appendix). The shapes are similar to those shown in Figs l (a) and 9(a). 5.3. B E N D I N G B Y A C T I V A T I O N O F L O N G I T U D I N A L E L E M E N T S This section demonstrates the flexibility o f a skeleton composed of 21 segments, or 21 finite elements, in technical terms. For the first time, the contribution of the main muscle groups to bending can be assessed. Figure 11 shows the shapes of the skeleton with activation o f ventral longitudinal elements increased with factors 2 and 6. Next, all circular elements are activated. For example, an 8-fold increase makes the worm coil twice around its own axis and increases the angle between 2 midbody segments from 18 \u00b0 to 35 \u00b0 (Figs 11 and 12). Changes in curvature are rapid at first, but decline with increasing activation, independent o f the type o f elements causing this change (Fig. 12). These observations can be summarized by the \"volume-rule\": Whenever elastic elements are activated, they tend to shorten, and therefore transfer, internal volume P r e s s u r e a n d e n e r g y v e r s u s v o l u m e v o 0-7 0\"525 0\"35 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002777_s10846-008-9284-8-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002777_s10846-008-9284-8-Figure9-1.png", "caption": "Fig. 9 Test bed power supply", "texts": [ " All electric helicopters have high power consumption. During hovering, the electric motor of the helicopter used needs about 50 A current of 24 V. Normally in these helicopters, LiPo (Lithium Polymer) batteries are used that have high capacity and the ability to sustain such currents. With this consumption and with a high capacity LiPo battery, the helicopter can perform hovering for only about 15 min. To overcome this limitation, the test bed is provided with constant power supply of 24 V that gives continuous current to the helicopter (Fig. 9). Power is supplied through wires that do not block the movement of the helicopter or the flying stand. This setup assures continuous experiments without the need of recharging the battery or changing it with a charged one. 2.3 Ground Control Station For the autonomous navigation of the helicopter, the use of a computer who serves as the operator is necessary. This computer manages the signals from the sensors and calculates the appropriate control signals in order to efficiently control the helicopter" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002131_j.finel.2004.04.007-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002131_j.finel.2004.04.007-Figure3-1.png", "caption": "Fig. 3. Gears 1 and 2 and their rigidly connected local coordinate systems (a) and the relation between a global and a local coordinate system (b).", "texts": [ " rai(winj ) = raIi + (rafi \u2212 ra0i)winj /bi. (14) The interval of the surface parameter winj may be defined by 0 winj bi. (15) The unit normal vector to the involute helicoids may be defined by n\u0302inj ( inj ) = rinj inj \u00d7 rinj winj\u2223\u2223\u2223\u2223 rinj inj \u00d7 rinj winj \u2223\u2223\u2223\u2223 = [\u2212j cos n cos sec tj sin( inj \u2212 j tj ) j cos n cos sec tj cos( inj \u2212 j tj ) \u2212 sin i sin n \u2212 j cos sin i cos n ] . (16) Only gears mounted on parallel axes will be considered. The derivations will be based on Litvin\u2019s vector approach [30]. Fig. 3a shows the teeth of gears one and two and their rigidly connected coordinate systems. The two global parameters 1 and 2 define the rotations of the gears. A global coordinate system (frame) Sri (see Fig. 3b) is introduced for each gear. This coordinate system is located at the same position as Oin and is oriented such that the xirzir -plane coincides with the axial plane of the two gears and the zir -axis coincides with the zin-axis. The coordinate transformation from Sin to Sir is represented by the matrix equation rrinj ( inj , winj , in) = Mriinrinj = [ ri cos( inj+ in)+(ri( inj \u2212 i(winj )) \u2212 jsij (winj )/2) cos tj sin( inj+ in \u2212 j tj ) ri sin( inj+ in) \u2212 (ri( inj \u2212 i(winj )) \u2212 jsij (winj )/2) cos tj cos( inj+ in \u2212 j tj ) winj ] , (17) where Mriin = [cos in \u2212 sin in 0 sin in cos in 0 0 0 1 ] . (18) We determine from Fig. 3a and b that in( i) = i + (\u22121)i in, (19) where i = 2 /zi is the angular pitch. Finally, we have n\u0302rinj ( inj , in) = Mriinn\u0302inj = [\u2212j cos n cos sec tj sin( inj + in \u2212 j tj ) j cos n cos sec tj cos( inj + in \u2212 j tj ) \u2212 sin i sin n \u2212 j cos sin i cos n ] . (20) The contacting gear tooth surfaces must be in continuous tangency, which can be obtained if the following relations obtain: rr1 nj ( 1nj , w1nj , 1n) = Mr1r2rr2 lj ( 2lj , w2lj , 2l) + [a 0 e ]T, n\u0302r1 nj ( 1nj , 1n) = \u2212Mr1r2n\u0302r2 lj ( 2lj , 2l), (21,22) where a is the distance between the gear axes and e is the axial distance between Or2 and Or1, which will take on negative values if the zr1-position of Or2 is negative. The index l is based on the coordinate systems configuration in Fig. 3a and is defined by l = { n if j = +1, n + 1 if j = \u22121. (23) The matrix Mr1r2 is the rotational transformation matrix from coordinate system Sr2 to Sr1. This may be defined by Mr1r2 = [\u22121 0 0 0 \u22121 0 0 0 1 ] . (24) The matrix equation (22) indicates that 1nj + 1n = 2lj + 2l . (25) Substitution of this expression into (21) gives us cos( 1nj + 1n \u2212 j tj ) = cos( 2lj + 2l \u2212 j tj ) = (r1 + r2) cos tj /a. (26) We conclude from this expression that inj + in = cj = const. (27) Substituting this expression in (17) gives us the surface of action rrinj ( in, winj ) = [ ri cos(cj ) + (ri(cj \u2212 in \u2212 i(winj )) \u2212 jsij (winj )/2) cos tj sin(cj \u2212 j tj ) ri sin(cj ) \u2212 (ri(cj \u2212 in \u2212 i(winj )) \u2212 jsij (winj )/2) cos tj cos(cj \u2212 j tj ) winj ] ", " However, by assuming that j = k = tot/2 we can determine an approximated total interference (or backlash): tot(e) = 2 cos t+ cos t\u2212((r1 + r2)(inv t+ + inv t\u2212 \u2212 inv wt+ \u2212 inv wt\u2212) + 2((x01 + x02)m + e tan ) tan n cos sec )/(cos t+ + cos t\u2212). (46) This expression gives the exact total interference if tj = tk . Since lubricant is present between the meshing gear flanks, the frictional forces are neglected since they are low compared with the normal forces. As a result, the contact force Fri nj acts only along the normal to the contacting surface, i.e. Fri nj = F ri xnj F ri ynj F ri znj = \u2212F ri nj n\u0302 ri nj = F ri nj [ \u2212 cos ij sin wtj \u2212j cos ij cos wtj j sin ij ] , (47) where F ri nj = |Fri nj |. (48) According to Fig. 3 and expression (23), F r1 nj = F r2 lj . (49) Fig. 5 shows a model of an anti-backlash conical involute gear transmission. When the gear transmission is in its initial position, the axial distance e is equal to e0, the gap g is equal to g0 and the spring, which has stiffness ksp, has been preloaded with the force Fsp0. Gear 1 is free to move in its axial direction, but is blocked when gap g is equal to zero. As a result, e e0 \u2212 g0. The preloaded spring eliminates backlash at rotation reversals, where low torques are transmitted, and, by allowing for axial compensation movements, avoids high peaks in friction torques due to deviations from ideal gear geometries, mounting errors and unfavourable deformations" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002356_bf02451562-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002356_bf02451562-Figure4-1.png", "caption": "Fig. 4. - Frenet coordinates provide a natural way of describing orthoclinal growth rings on tubular coiled seashell surfaces. Equation (5), for the shell aperture which ties in the (r v3)-plane, is a simple vectorial addition; r = Y - b cos 0 e~ + b sin 0 e~.", "texts": [ " By analogy with eq. (3), seashel-like surfaces with orthoclinal growth rings may now be writ ten in terms of the new Frene t coordinates as follows: (5) r (0, r = Y(r + exp [ar b cos 0 r + b sin 0 e3), and this applies for any second-order ~(clockspring, trajectory given in ref. (9. Reading this equation from right to left, we should imagine a circular generating C. iLLERT curve of initial radius b, lying in the (e2, e~)-plane (which is always perpendicular to the principal growth direction el as in fig. 4) and dilating exponentially as-it translates along the trajectory Y. Other not necessarily exponential scale factors are possible, but it is essential that they act equally on the ~ and r axes simultaneously otherwise the generating curve would be squashed or deformed throughout the growth process. Bronsvoort et al. (~) initially modelled simple helices (using eq. (5) with a = 0), overlooking the possibility of dilating generating curves, but have since produced the beatiful images appearing in fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002172_978-1-4613-9030-5_43-Figure43.2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002172_978-1-4613-9030-5_43-Figure43.2-1.png", "caption": "Figure 43.2: TIle model used here (left) and a proposed model (right) combining pelvic list, lateral trunk bending, and ankle eversion, as seen from the front. Note that the addition of lateral trunk bending allows pelvic list without destabilizing the system sig nificantly. (Reprinted with permiSSIOn from Yamaguchi & Zajac, IEEE Trans. Biomed. Eng. 37. \u00a9 1990 - IEEE.)", "texts": [ " Some breakdown of the trunk into segments would also be desirable. Transverse rotations of the shoulder could be included for added realism. and the motions of the upper trunk could be separated from the motion of the pelvis. The analyst could then model pelvic list without com promising the position of the center of mass of the head. arms. and trunk (HAT). If the pelvis is in cluded as part of a single-segment HAT. pelvic list equals \"HAT list\", which causes the moment ex erted by gravity to increase in a highly unstable fashion (Figure 43.2). Furthermore. calculating musculotendon forces at the hip requires accurate relative orientations of the femur and pelvis. If pel vic list cannot be modeled for stability reasons. accuracy is compromised in the musculotendon force-length-velocity computations. A better model of the HAT would include a 2 DOF \"sacral-pelvic\" joint in the lumbar region al lowing sagittal-plane flexiOn/extension and lateral bending in the frontal plane between the upper trunk and pelvis. plus an additional degree of freedom in the mid-thoracic region (near 17)", " Ankle inversion/eversion (#6) is considered to be an energy-conserving measure, which in con junction with pelvic list allows the position of the body's center of mass to swing transversely over the stance foot. Item #7, transverse pelvic rota tion, allows the step length to be increased, which is another method by which energy is conserved (Inman et al., 1981). The inclusion of a 2 DOF sacral-pelvic joint (items #8 and #9) separates the motions of the up per and lower trunk. In particular, lateral bending of the trunk would allow the pelvis to list without severely increasing the frontal-plane gravitational moment of the trunk about the supporting hip (Figure 43.2). Thus, vertical fluctuations of the body's center of mass and the stresses on the lateral hip muscles (abductors) could be mini mized simultaneously. Remaining items add realism and contribute somewhat to energy savings during normal gait. Adding swing-side hip abduction/adduction (#10) would allow the swing leg to extend in the direc tion of forward progression even if the pelvis were rotating transversely. The addition of this DOF would also decouple lateral leg motions from lateral motions of the trunk" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001824_aero.2004.1367684-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001824_aero.2004.1367684-Figure2-1.png", "caption": "Figure 2 - Annulus sections and vdawn", "texts": [ " The following sections describe these steps. Wbeel Rim Identification and Classification411 points of interest on the wheel rim are first identified. Points of interest lie in a region between the inner wheel rim diameter r,, and the outer wheel rim diameter rwhrel (see Figure 1). For rimless wheels or tires, rwhe,, corresponds to the outer tire diameter and r, is chosen to he slightly less than rwheel. Points of interest in the annular region are divided into two regions corresponding to the left and right half of the wheel (see Figure 2). This is done since terrain entry generally occurs in one half of the wheel, and terrain exit occurs in the other. Thus the algorithm searches for one terrain interface in each region. LeA and right wheel halves are determined with respect to the vector vdown. The vector vdo*R, is a unit vector perpendicular to the pitch angle of the vehicle (e.g., on flat terrain, vd,, is parallel to the gravity vector). Pixel Intensity Computation-The average grayscale intensity is computed for every row of pixels in and SI.,^ (see Figure 2). A row contains multiple pixels and is perpendicular to vd, For each row the summed intensity is computed as the sum of each individual pixel's intensity. Two arrays of summed row intensities are thus formed. Terrain Interface Identification4 one-dimensional spatial Gaussian filter is employed to smooth the intensity arrays and reduce the effects of noise. Here the summed row intensities are weighted by the numher of pixels in a row to minimize the influence of noise in low pixel-count rows. A Gaussian distribution is approximated by a binomial distribution" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001632_j.jmmm.2003.12.520-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001632_j.jmmm.2003.12.520-Figure1-1.png", "caption": "Fig. 1. Schematic of 5.75:1 magnetic gear.", "texts": [ " Magnetic gears are an alternative technology which may offer significant advantages, such as, reduced maintenance and improved reliability, inherent overload protection, and physical isolation between input and output shafts. However, despite these advantages magnetic gearing has received relatively little attention to date, probably because of the relative complexity and poor torque density of the magnetic circuits which have been proposed [1,2]. Therefore, for applications in which mechanical gearing cannot be accommodated, direct electrical drives are employed. The paper describes a magnetic gear topology, Fig. 1, which combines a significantly higher torque transmission capability, and a very high efficiency. onding author. Tel.: +44-114-222-5812; fax: +44- 96. address: k.atallah@sheffield.ac.uk (K. Atallah). $ - see front matter r 2003 Elsevier B.V. All rights reserved. /j.jmmm.2003.12.520 Fundamental to the operation of the magnetic gear is the modulation of the magnetic fields produced by either the high- or low-speed rotor permanent magnets, by the steel pole pieces, which results in space harmonics having the same number of poles as the other rotor permanent magnets [3]", " ka0; is different to the velocity of the rotor, which carries the permanent magnets. Therefore, in order to transmit torque at a different speed, the number of pole pairs of the other permanent magnet rotor must be equal to the number of pole pairs of a space harmonic for which ka0: Fig. 2 shows the variation of the radial component of flux density due to the high-speed rotor permanent magnets in the airgap adjacent to the low-speed rotor, and Fig. 3 shows its corresponding space harmonic spectrum, for the 5.75:1 magnetic gear, shown in Fig. 1. Clearly, the presence of the stationary steel pole-pieces results in a number of asynchronous space harmonics, one of which having the same number of poles as the number of poles of the permanent magnets of the other rotor. Fig. 4 shows the variation of the maximum torque on low-speed rotor with the radial thickness of the steel pole pieces, when the diameter of the airgap adjacent to the low-speed rotor and the magnet volumes of high- and mitted torque (low speed), at different input shaft (high speed) ) low-speed rotors are kept constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002574_pime_proc_1987_201_098_02-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002574_pime_proc_1987_201_098_02-Figure4-1.png", "caption": "Fig. 4 Diagrammatic representation of the pressure distribution in an EHD film between circumferentially ground discs (a) Longitudinal section, A $ 1.0: h approximately constant; p approximately Hertzian", "texts": [ "sagepub.comDownloaded from Pressure cell measurements: Bair and Winer (6) Disc machine: 0 5 mm, V 12 mm width discs (3) The effect will now be considered of reducing the ratio A of the nominal film thickness h, to the combined surface roughness r~ from the large values associated with \u2018smooth surface\u2019 behaviour to the order of unity. At the high spots of the two surfaces there will be a local thinning of the film resulting in local increases in shear rate and pressure, as shown diagrammatically in Fig. 4. Thus the traction force will be dominated by the shear stress developed in these regions of high pressure and shear rate. Referring to the map in Fig. 1, the effective value of the abscissca aofi will be governed by the pressure at the high spots where the traction is developed. This will have the effect of moving the operating point in the map to larger values of a, j. Thus a contact which, with smooth surfaces, may be operating in Slide-roll ratio AU/O regime 11, with rough surfaces (A small) may be effectively operating in regime 111 or even IV", " 96 in reference (S)] in which K (= 1/R) in the Hertz formulae for circular contacts is replaced by an equivalent curvature K , (= l / R , ) for elliptical contacts defined by K , = (ti' * X\")1/2 (9) where K' and K\" are the principal relative curvatures of the two contacting surfaces. For two circumferentially ground discs, each of radius R, K' = R/2 and K\" = ~ $ 2 , where K , is the mean asperity curvature derived from a profilometer trace taken across the width of the disc. The value of os is derived from the same trace, whereupon equation (8) can be rewritten as where C is a factor that depends upon the ratio K'/K\" and can be obtained from Fig. 4.4 of reference (8). Digitizing the profilometer trace of the rough ground surface in Fig. 6c at a sampling interval of 2 pm gave the following values : R , = 0.95 pm; K' = R/2 = 20 mm; u = 4 2 R , = 1.34 pm; K\" = tiJ2 = 45 pm, gives K , = 0.95 mm K'/K'' = 440 for which C = 0.6 Substituting in equation (9) gives an asperity pressure pa = 3.3 GPa Note that the value of K , obtained from a profilometer trace is sensitive to sampling interval. Hence, even though the calculated asperity pressure pa varies as K : / ~ , the result of this calculation must be treated with reserve" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002059_1.2008299-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002059_1.2008299-Figure4-1.png", "caption": "Fig. 4. A ball spinning counterclockwise when dropped vertically onto the strings of a horizontal racquet will bounce to the left. If the racquet is tilted to the right, the ball will bounce almost vertically. If the racquet is tilted to the left, the ball will bounce even further to the left.", "texts": [ " About 80 such impacts were filmed and 39 of the \u201cbest\u201d impacts were analyzed based on the fact that the ball was incident within 10\u00b0 of the normal, the line drawn on the ball remained centered so that the ball spin could be measured accurately, and the ball landed near the middle of the strings. Two series of measurements were made for bounces off the strings, one where the racquet was deliberately tilted to the right at angles up to 10\u00b0 away from the horizontal, and one where the racquet was deliberately tilted to the left, as shown in Fig. 4. The direction of the ball spin was not changed, but in the first case the ball was incident with backspin and in the second case the ball was incident with topspin. In the first case the ball bounced almost vertically. In the second case the ball bounced at angles up to about 40\u00b0 away from the vertical. The bounce angle is determined by the combined effects due to spin and tilt. In both cases the ball tended to deflect to the left due to its spin, but in the first case the tilt of the racquet acted to deflect the ball back to the right so that the resulting bounce was almost vertical, while in the second case the tilt exaggerated the deflection to the left. The situation represented by Fig. 4 when rotated by 90\u00b0 can present a difficult problem for an inexperienced tennis player because a player who tilts the racquet in the wrong direction is likely to make a large error. Even an experienced player can misjudge the required tilt angle. To position the strings underneath the falling ball, the racquet was maneuvered slowly in a horizontal plane and at about 0.8 m/s vertically upward. The vertical motion was unintentional, but it had the effect of imparting additional vertical velocity to the ball, above that due to the bounce itself" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002777_s10846-008-9284-8-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002777_s10846-008-9284-8-Figure5-1.png", "caption": "Fig. 5 Coordinate frames attached to revolute joints", "texts": [ " Using this equations, position and orientation of the helicopter (end-effector) can be calculated. The flying stand (Figs. 3 and 4) has five revolute joints. Each joint rotates around an axis and the synthesis of all rotations provides the final position of the endeffector, which in our case is the place where the helicopter is mounted on the stand. In Fig. 4, a right side view of the stand is presented. Based on this view, the coordinate frames attached to the center of each revolute joint are presented in Fig. 5. As it can be derived from Figs. 4 and 5, dimensions presented in Fig. 5 are not the actual ones, but a relevant clear view of each frame is presented, since in the stand the distance between these frames is very small. Frame 5 is the frame of the end effector. Parameters L1, L2, L3, L4, L5 are known system constants that represent the length of each link, while parameters \u03b81, \u03b82, \u03b83, \u03b84, \u03b85 represent the rotation angle of each joint. Angles \u03b83, \u03b84, \u03b85 correspond to the yaw, roll and pitch angles of the helicopter, respectively. The stand allows full rotation of the yaw angle while it constraints roll and pitch angles between \u221240\u25e6 and 40\u25e6" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001563_jsvi.1998.9999-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001563_jsvi.1998.9999-Figure3-1.png", "caption": "Figure 3. Elastic deformation of rolling element for non-constant contact angle ai j .", "texts": [ " The specific objectives of this study are as follows: (1) to develop a new bearing stiffness matrix which is suitable for the analysis of vibration transmission through either ball or roller-type spherical bearings; (2) to develop an experimental technique to measure spherical bearing direct and cross-coupling stiffness coefficients as a function of axial and radial mean loads (preloads); (3) to verify the proposed stiffness model by comparing its predictions with experimental measurements; and (4) to relate the stiffness matrix values to various kinematic and design parameters, specifically unloaded contact angle and radial clearance, through parametric studies using the bearing stiffness matrix model. Consider the self-aligning double-row rolling element bearing shown in Figure 2. The relationships between the mean forces Fm = {Fxm, Fym, Fzm}T transmitted through the bearing and the resulting mean bearing displacements qm = {qxm, qym, qzm}T will be derived. From the bearing displacements the resultant elastic deformation d(Ci j ) of the jth rolling element of the ith row located at angle Ci j from the x-axis can be determined. Assuming the outer ring is fixed, in Figure 3 one has: d(Ci j )=6A(Ci j )\u2212A0 0 A(Ci j )qA0 A(Ci j )EA07 , A(Ci j )=z(di zj )2 + (di rj )2 , di zj =A0 sin (ai 0)+ qzm \u2212Pe , di rj =A0 cos (ai 0)+ qxm cos (Ci j )+ qym sin (Ci j )\u2212 rL . (1a\u2013d) Here, A0 and A are the unloaded and loaded relative distances between the inner (ain ) and outer (aout ) raceway groove curvature centers. Note that A0 = ri , the radius of the locus of inner raceway groove curvature centers. The unloaded contact angle is denoted by ai 0 and radial clearance and axial endplay are denoted by rL and Pe , respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.35-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.35-1.png", "caption": "Fig. 5.35. Stabilit y Criterio n for Layerglaze \u2122 proces s feedstoc k interactio n zone .", "texts": [ " The location of the feedstock, at this stage, turned out to be the most critical parameter. With the impingement angle of the wire feed at 30\u00b0, it was determined that most satisfactory transfer occurred when the wire contacted the arbor at the exact edge of the molten pool. If the wire is Rapid solidification laser processing 285 displaced into the pool, significant drop transfer results, whereas if the wire is displaced away from the pool, incomplete melting occurs. The maximum tolerance on the wire position is approximately two wire diameters, as illustrated in fig. 5.35. Structures produced using wire feed. Initial parametric studies were conducted using stainless steel wire feed and a stainless steel substrate as a model system for the wire feed process. Wire diameter was 0.089 cm and the goal of the tests was to establish the most uniform possible deposition for the wire feed process. A typical series of tests, in which the arbor advance rate was the variable under study is shown in fig. 5.36. The macroetched cross sections of the five-layer deposits showed that the slower rate resulted in the formation of the most uniform deposits", " With only the larger size fractions, the feeder is able to achieve free flow, but the flow is nonuniform and cannot be adequately controlled. From the standpoint of powder utilization, it should be noted that use of as wide a range of sizes as possible is desirable to improve the yield factor. Initial development of the powder feed process served to confirm that the criticality of alignment in the interaction zone between the beam, the arbor, and the feedstock is identical to that determined for wire, as depicted in fig. 5.35. The location of the stable region is the same, and in the unstable region the appearance of the deposit changed significantly, and is appreciably different from that of the wire deposit. In the unstable region, the powder injected directly into the beam would melt and spatter. Also, optical breakdown of the beam would result from the seeding effect of the misplaced powder. When operating in the stable region, the deposit surface is very smooth and uniform. A typical sample of effective deposition is shown in fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002323_7.1044-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002323_7.1044-Figure1-1.png", "caption": "Fig. 1 . Elastic spacecraft model", "texts": [ " Optimal openloop control law has been derived in [7, 81 by solving the two-point boundary value problem. These published works [4-81 are based on the assumption that the system dynamics is completely known and there is no disturbance torque acting on the vehicle. In a real situation, the modeling errors exist and unknown disturbance torque is continuously acting on the spacecraft. Thus, the question of the control of an elastic spacecraft in the presence of uncertainty is of considerable importance. We present an approach to control of a flexible spacecraft beam-tip body configuration (see Fig. 1). For simplicity, it is assumed that the tip body is a point mass. Of course, the approach here is applicable to nonlinear models having tip body with inertia. The connecting structure is idealized as a long slender beam capable of transverse bending in two orthogonal planes. Control moments are applied along three orthogonal axes of the spacecraft. In addition, the control forces and moments act along the axes y , , z , at the tip of the beam. The unknown disturbance torques are allowed to act on the space vehicle", " The stabilizer uses only modal velocity feedback for vibration damping. In case of collocated actuators and sensors, robust stabilization of the elastic modes is accomplished similar to [14, 151. I1 presents the mathematical model and the control problem. The attitude controller is designed in Section 111. Section IV derives the vibration stabilizer, and simulation results are obtained in Section V. The organization of this paper is as follows. Section It. THE MATHEMATICAL MODEL AND CONTROL PROBLEM The elastic spacecraft model is shown in Fig. 1. A right-handed coordinate system xo, yo, zo (denoted as So) is fixed to the spacecraft which is centered at its mass center. The orientation of the spacecraft is described with reference to an inertial coordinate system x1 , yl , zI (denoted as SI) . The coordinate system S, is a translation of the frame So to the attachment point 0. The transformation from the inertial frame S1 to the frame So is brought about by an Euler sequence (e,, 0 2 , 8,) of rotations about the axis x,, and rotated axes y , and z,, respectively, in a standard way [2]", " The choice of such basis functions to approximate the transverse vibrations of the beam is reasonable [2, 161. Define r i z = wherep = (p l , ..., pJT, q = ( q l , ..., q,l)T. Let U = (U,, u2, u ~ ) ~ be the control moment and Td = ( T d l , Td2 , Td3)T be the unknown bounded disturbance torque acting on the space vehicle along axes xo, yo, zo, respectively. For vibration stabilization control force F = ( F , , F2)T and moment GT = ( G T I , Gf2)T are applied along axes y , , z1 , respectively. the model shown in Fig. 1 has been given in [2]. The equations of motion are given by (readers may refer to [2] for the details) The complete derivation of the equations of motion of Go(F, G T ) + Td + U + N l ( 8 , o , i , V , b ) ] ( 3 ) = [ Bl F + B2 GT + N 2 ( 8 , 6 , i , V , o ) where N I , N , are nonlinear functions of the indicated arguments, the stiffness matrix K is r El KI = - L diag(A:, ..., At) [$ ] , M22 E R\"\"\" M22 M22 = The matrix M22 is a positive definite symmetric matrix and A, are the roots of cos hA cos A + 1 = 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002268_j.compbiomed.2006.06.007-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002268_j.compbiomed.2006.06.007-Figure6-1.png", "caption": "Fig. 6. The batter\u2019s view of a slider thrown by a right-handed pitcher: the ball is coming out of the page. The red dot signals the batter that the pitch is a slider. Copyright , 2004, Bahill, from http://www.sie.arizona.edu/sysengr/slides/ used with permission.", "texts": [ " As the angle between the spin axis and the direction of motion decreases, the magnitude of deflection decreases, but the direction of deflection remains the same. If the spin axis is coincident with the direction of motion, as for the backup slider, the ball spins like a bullet and undergoes no deflection.3 Therefore, the slider is usually thrown so that the axis of rotation is pointed up and to the left (from the perspective of a right-handed pitcher). This causes the ball to drop and curve from the right to the left. Rotation about this axis allows some batters to see a red dot at the spin axis on the top-right-side of the ball (see Fig. 6). Bahill et al. [11] show pictures of this spinning red dot. Seeing this red dot is important, because if the batter can see this red dot, then he will know that the pitch is a slider and he can therefore better predict its trajectory. We questioned 15 former major league hitters; eight remembered seeing this dot, but two said it was black or dark gray rather than red. For the backup slider, the spin causes no horizontal deflection and the batter might see a red dot in the middle of the ball. This section has equations, but it can be skipped without loss of continuity" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003548_elan.201100681-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003548_elan.201100681-Figure2-1.png", "caption": "Fig. 2. General view of the conductometric transducer and its interdigitated microelectrodes.", "texts": [ "de 1089 Dynamic light scattering (Zetasizer Nano-ZS, Malvern Instruments) was used to determine the zeta potential of coated nanoparticles and their size distribution. The measured values of zeta potential of the uncoated and coated AuNPs are presented in Table 1. When the outermost layer is a polycation (PAH), a positive zeta potential is observed whereas when urease is the outermost layer, a negative potential is observed showing the successful immobilisation of urease (pie=5.9). The conductometric transducers, consisting of two identical pairs of gold interdigitated thin film electrodes (Figure 2) (thickness: 150 nm), were fabricated by vacuum deposition on a ceramic substrate (5 30 mm) at the Lashkaryov Institute of Semiconductor Physics (Kiev, Ukraine). A 50 nm-thick intermediate chromium layer was used for better gold adhesion. The dimension of each interdigital space and digit was 20 mm and the length of the digits was about 1.0 mm. The sensitive area of each pair of electrodes was about 1 mm2 [2]. Microelectrodes were placed in a glass cell filled with 5 mL of a 5 mM phosphate buffer pH 7" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure2-1.png", "caption": "Fig. 2 Singular configurations of the mechanism related to the boundary lines of Eq. (2) and shown in the diagram of Fig. 1: (a) between types A and B; (b) between types B and C; (c) between B and the area of no closure", "texts": [ "org/about-asme/terms-of-use Thus, introducing the parameters U and W as U \u00bc l r and W \u00bc e r (1) the types A, B and C of the mechanism can be represented through three different areas of the diagram of Fig. 1. In particular, the three boundary lines of the diagram of U versus W can be expressed in the following forms: U \u00bc W\u00fe 1 U \u00bc 1 W U \u00bc W 1 (2) which divide the plane of the diagram in four areas. Each of them corresponds to the type A, B or C of an offset slider-crank/rocker mechanism, while the grey area corresponds to the no closure condition. The singular configurations of the mechanism for the boundary lines of Eqs. (2) are sketched in Fig. 2 according to what reported in the diagram of Fig. 1. Moreover, the centered slider-crank mechanisms are obtained for W\u00bc 0, while U\u00bc 1 and W\u00bc 0 give the Scott-Russell mechanism for which l \u00bcr and e\u00bc 0. Referring to the kinematic sketch of Fig. 3, the position analysis of a slider-crank/rocker mechanism ABC is carried out by developing the following closure equation: r\u00fe l \u00bc m\u00fe e (3) Vectors r, l, m and e are given in the fixed frame F\u00f0O;X;Y\u00de by r \u00bc r cos d sin d\u00bd T l \u00bc l cos u sin u\u00bd T m \u00bc \u00f0r cos d\u00fe l cos u\u00de 0\u00bd T e \u00bc e 0 1\u00bd T (4) where r and l are the crank and coupler lengths, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002222_095440605x31436-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002222_095440605x31436-Figure5-1.png", "caption": "Fig. 5 Hybrid planar\u2013planar 6R1P mechanism with two d.o.f. Fig. 6 Hybrid planar\u2013planar 6R1P DM mechanism", "texts": [ " Hence any bond between any couple of bodies has a dimension that is less than or equal to 3. However, the third kind of new DM seven-link mechanism with one prismatic pair is obtained when two sets of joint axes in two planar 4R-chain loops are not parallel to each other. In the first step, a hybrid type mechanism is formed from two planar 4R loops A-B-C-D and G-F-E-D supposing that the motion planes belonging to each chain are not parallel. It is called a hybrid planar\u2013planar 6R1P mechanism as shown in Fig. 5. Two original 4R chains have four adjacent parallel joint axes. Without loss of generality, the revolute joints at D in each chain are arranged to be intersecting. After that, these two revolute joints are removed and one prismatic joint is added at D, direction of which is perpendicular to the two planes and moreover link AD in the A-B-C-D chain and link DG in the G-F-ED chain are omitted, respectively. As a consequence, a hybrid A-B-C-D-E-F-G 6R1P chain with two finite d.o.f. is synthesized (Fig. 5). The chain is a hybridization of two planar 3R1P chains A-B-C-D and G-F-E-D with a merging of the two parallel P pairs in only one P pair. Through a special imbrication of the same two planar 3R1P chains, a new hybrid planar\u2013planar A-G-B-F-C-E-D 6R1P chain with DM is further synthesized. This mechanism has the same geometrical arrangement of joint axes as that of Fig. 5 but the links are modified and its mobility is quite different. In other terms, the hybrid planar\u2013planar 6R1P mechanism of Fig. 5 can be considered as a hybridization of two planar slider-crank chains with one common prismatic pair and two distinct sets of three adjacent parallel revolute joint axes. These two chains are the planar slider-crank chains A-BC-D and G-F-E-D. If the prismatic pair at D is ignored temporarily and link 3 and link 4 are welded together, then two mechanical generators of planar gliding subgroups in this 6R-chain loop can be recognized. The first generator is associated to the subgroup fG(u)g of planar gliding perpendicular to u, whose generator is made up of three parallel revolute joints with axes (A,u), (B,u), and (C,u)", " but generally the global or finite relative motion cannot happen. The true d.o.f. is zero except for the special case of symmetrical arrangement of paradoxical chain of Bricard form. The translation motion Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C23403 # IMechE 2005 at The University of Iowa Libraries on May 29, 2015pic.sagepub.comDownloaded from between link 7 and link 3 is parallel to w and is directly realized by adding one prismatic pair at D to make a hybrid planar\u2013planar 6R1P chain as shown in Fig. 5. This is not a truly spatial chain because an opened sub-chain that generates the full group fDg of displacements with its six dimensions cannot be found. The opened sub-chain with six R pairs generates a five-dimensional bond instead of a six-dimensional bond because three serial R generate fG(u)g, three serial R generate fG(v)g, and the six R pairs generate the product fG(u)gfG(v)g with fG(u)g > fG(v)g \u00bc fT(w)g. The opened chain 6R1P obtained from the closed-loop chain by splitting the body 4 in two parts also generates the five-dimensional bond fG(u)gfG(v)g, with passive two d", " Using set theory notations, it can be written as {L(7,5)} $ {T(w)}< {1=G(v)} No sub-chain is a generator of another subgroup of displacements except the possible generation of the improper subgroup fDg by a sequence of six R pairs. In fact, in the singular pose, fR(A,u)g fR(G,v)gfR(B,u)gfR(F,v)gfR(C,u)gfR(E,v)g = fDg. As a matter of fact a product of six one-dimensional subgroups cannot be six-dimensional if the linear span of the twists that represent allowed infinitesimal displacements is not six-dimensional. From the analysis of Fig. 5 mechanism, it follows that the vector space of twists is five-dimensional. Hence, locally in the singular pose, fL(7,5)g \u00bc T(w)g < f1/G(v)g. The bond fL(7,5)g has a bifurcation towards two distinct planar working modes starting from the singular pose. However, any mechanism working in each of its two possible planar working modes destroys the local linear dependency of the six R twists. After any working the mechanism becomes a truly spatial 6R1P linkage, i.e. includes a generator of fDg and therefore the bond fL(7,5)g can become an one-dimensional manifold in fDg" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure5.9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure5.9-1.png", "caption": "Fig. 5.9 An iron roller, a Original illustration (Pan 1998) b Structural sketch c Chain d Atlas of possible designs", "texts": [ "8b and c show its corresponding structural sketch and chain, respectively. 5.3 Examples of Reconstruction Designs 99 5.3.2 Example 2: Tie Nian Cao (\u9435\u78be\u69fd, An Iron Roller) Tie Nian Cao (\u9435\u78be\u69fd, an iron roller) from the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b \u7269\u300bis used mainly for grinding cinnabar ore to produce the raw material for red color dye. When producing the dye, people place the ore into the grinding groove and push the rod to drive the roller and then grind the ore into powder. Furthermore, the powder is put into a jar and soaked in clean water, as shown in Fig. 5.9a (Pan 1998). This device consists of a pushing rod, a vertical rod, a roller, and a grinding groove. There is no relative motion between the pushing rod and the vertical rod, so that they can be considered as the same member. Since the ore needs to be ground into powder, the grinding groove was made into a V shape to help the roller\u2018s grinding. Based on the written description and the illustration, the device has a clear number of members, but its two joints, J\u03b1 between the vertical rod and the frame, and J\u03b2 between the roller and the grinding groove, can not be identified", " Considering the types and the directions of motion of the vertical rod, uncertain joint J\u03b1 has two possible types: the vertical rod rotates about the z-axis with respect to the frame, denoted as JRz; and the vertical rod not only rotates about the z-axis but also translates along the y-axis with respect to the frame, denoted as J Py Rz . Considering the types and the directions of motion of the roller, uncertain joint J\u03b2 also has two possible types: the relative motion between the roller and the grinding groove is pure rolling without slipping, denoted as JO; and, the relative motion between them is a combination of rolling and slipping, denoted as JPxO . By assigning the possible types of uncertain joints J\u03b1 and J\u03b2 into the sketch shown in Fig. 5.9b, four results as shown in Figs. 5.9d1\u2013d4 are obtained. Based on Eq. (3.1), the number of degrees of freedom for the mechanism obtained in Fig. 5.9d2 is 0. By removing such a design, three feasible designs are available as shown in Figs. 5.9d1, d3, and d4. 5.3.3 Example 3: Yang Shan (\u98b6\u6247, A Winnowing Device) Yang Shan (\u98b6\u6247, a winnowing device) is also called Feng Che Shan (\u98a8\u8eca\u6247) or Yang Shan (\u63da\u6247, the same sound but different in the first Chinese character). It is a device for winnowing husks and dust from the grains" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003544_tcst.2012.2221091-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003544_tcst.2012.2221091-Figure3-1.png", "caption": "Fig. 3. 2-D representation of aircraft.", "texts": [ " The reference frame {B} is fixed at the aircraft\u2019s center of gravity and it is identified by the set of unitary vectors {iB , jB,kB}, where iB is directed toward the aircraft nose and lies on the aircraft\u2019s symmetry plane, jB is perpendicular to the aircraft\u2019s symmetry plane, and kB completes the right-handed set. For the sake of simplicity, we assume that iB is coincident with the wing\u2019s zero-lift line and aligned with the thrust vector. This configuration of references frames is depicted in Fig. 3. Having defined the reference frames, one obtains the aircraft equations of motion from the application of the Newton\u2019s second law to a rigid body, resulting in (see [20]) mv\u0307 = f \u2212 m\u03c9 \u00d7 v (2a) I\u03c9\u0307 = \u03b7 \u2212 \u03c9 \u00d7 (I\u03c9) (2b) p\u0307 = R v (2c) R\u0307 = \u2212S(\u03c9)R (2d) where v = [u v w] denotes the velocity of {B} w.r.t. {I } expressed in {B}, \u03c9 = [p q r ] denotes the angular velocity of {B} w.r.t. {I } expressed in {B}, p = [x y z] denotes the position of {B} w.r.t. {I } expressed in {I }, R \u2208 SO (3a) and (3b) denotes the rotation matrix from {I } to {B}, f \u2208 R 3 and \u03b7 \u2208 R 3 denote the external forces and torques acting on the aircraft, respectively, m denotes the aircraft\u2019s mass and I \u2208 R 3\u00d73 denotes its tensor of inertia" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001965_9.159588-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001965_9.159588-Figure1-1.png", "caption": "Fig. 1. A one-link rigid robot with flexible joint.", "texts": [ " x1 = qd - 4, x2 = qd - 4 3 x3 rd - 7, xq rd - 7 where qd, qd, rd, id denote a given desired trajectory for corresponding states of the system. Then, if the final value of the desired trajectory is an equilibrium point of the system, it is easy to show that all the above results hold for the error system with its states defined above. Therefore, similar results on the tracking problem can be achieved by properly formulating the tracking problem into a stability problem. V. ILLUSTRATIVE XAMPLE To illustrate the design procedure, consider a single rigid link connected to an actuator through a flexible joint, as shown in Fig. 1. Ignoring damping for simplicity, the equations of motion given in [14] are Jlql + MgLsin(q,) + Z ( q l - q2) = 0 J242 - a 4 1 - q 2 ) = U where M and 1 are the mass and length of the link, respectively, Z is the stiffness of the linear torsional spring, .I1 is the inertia of the link, J, is the total inertia reflected to the end of the motor shaft, and the torque output of the motor U is the control. 1441 All the parameters are assumed to be bounded by known constant upper and lower bounds as J , I J , s T , - J 2 < J 2 < 5 ; , - Z s Z s Z , a s M g L < Z " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003506_j.jphotochem.2011.10.021-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003506_j.jphotochem.2011.10.021-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of flow injection CL system. (a) Phenol solution or sample solution; (b) MnDP solution; (c) sodium hydroxide solution; (d) luminol solution; ( W p", "texts": [ " The solvents were removed after the reaction and the products were washed with distilled water for three times and dried in vacuum. m.p. > 300 \u25e6C; 1HNMR: paramagnetic; IR (KBr, cm\u22121): 2925 (m, C\u2013H), 1716 (s, C O), 1592 (m), 1449 (m), 1382 (m), 1266 (w), 1227 (w), 1026 (s, C\u2013O), 978 (m), 850 (w), 753 (m), 698 (m); ESI+\u2013MS (35 eV, m/z): 563 [M+H]+, 504 [M+H\u2013CH2CO2H]+, 445 [M+H\u20132CH2CO2H]+; UV\u2013vis (DMF, nm), max (relative intensities): 365.3 (1.00), 456.4 (0.893), 542.8 (0.158). 2.4. Experimental procedures The flow injection analysis manifold, consisted of two peristaltic pumps (as shown in Fig. 1), was used throughout this study. One peristaltic pump (three channels) was used to deliver phenol (or sample solution), manganese (III) deuteroporphyrin and NaOH solutions at a flow rate of 2.5 mL min\u22121 (per tube). The other pump (two channels) was used to deliver luminol and H2O2 solutions at a flow rate of 2.0 mL min\u22121 (per tube). Polytetrafluoroethylene tube (0.8 mm i.d.) was used to connect all components in the flow system. The flow cell located in front of the detection window of the photomultiplier tube (PMT) was a coil of glass tubing (1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001409_12.388828-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001409_12.388828-Figure4-1.png", "caption": "Figure 4: Experimental Setup.", "texts": [ " The resulting vibration signals were then analyzed using the continuous wavelet transform with a Daubechies level 4 (DB4) wavelet basis function. This was done to ensure that the separated vibration signals were viable as input for a wavelet-based diagnostic algorithm such as the normalized energy metric.9 The results presented in this paper are thought to be representative of typical planet gear damage. Downloaded From: http://proceedings.spiedigitallibrary.org/ on 07/14/2015 Terms of Use: http://spiedl.org/terms 3.1 Experimental Setup The experimental setup for conducting the separation and diagnostic tests is displayed in Figure 4. The test rig shown in Figure 4a consists of an electric drive motor which serves as input to a planetary gearbox. This motor is capable of 3 HP and 1750 RPM. Instrumentation for the rig consists of accelerometers, a tachometer on the input shaft, and a one-per-rev pulse generator and torque sensor on the output shaft. The planetary gearbox used in the experiiiients is shown iii Figure 4h. Properties of the gearbox are listed in Table 1. The tests were run with au input speed of 1500 RPM and a nominal load of 110 in\u2014lb. 3.2 Experimental Results For the gearbox under consideration. flRt'a'i.j, I and thus multiple sensors were used to increase the number of planet teeth captured, not to increase robustness. Accelerometers I, 2 and 3 were located at annulus teeth 1, 55, and 37. respectively. Thus. P1 = I. P = 55, and P3 a = 37 The data collection window width for each sensor was set at 5 tooth meshes" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003878_j.robot.2013.08.005-Figure19-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003878_j.robot.2013.08.005-Figure19-1.png", "caption": "Fig. 19. Cutaway drawing of the grasper (Part Type 13) attached to a structural part (Part Type 2). Details of grasper operation can be seen in Supplemental Videos 1 and 2.", "texts": [ " The vertical motor can be assembled onto vertical track towers by another manipulator. The sliding protocol is similar, but not interchangeable, to that of the horizontal motor. The gearing and slide components required a different mechanical design than those of the horizontal motor, in order to withstand high torsional loads generated from lifting cantilevered weights. The design of the end-effector (or \u2018\u2018grasper\u2019\u2019) is similar to that reported in [29]. A single end-effector is used for grasping components and to tighten and un-tighten the threaded fasteners (see Fig. 19). The grasper is integral to the design of the entire system, since it effects theway parts are picked up, how they are connected to each other, and how parts must be brought into place during assembly. Furthermore, the grasper should be easy to fabricate, and if possible well-suited for miniaturization (such as the MEMS and micro-devices in [51\u201353] or the chemically actuated gripper in [54]). The end-effector consists of a spring loaded tool-piece with a slot and internal thread. For grasping a part, the internal thread of the toolmateswith the threaded tension pin on a component" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002273_1077546304042047-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002273_1077546304042047-Figure5-1.png", "caption": "Figure 5. Leaf spring ends (Society of Automotive Engineers, 1985).", "texts": [ " The leaf spring is connected to the chassis through the spring eyes. Figure 3 shows a complete description of the components of the leaf spring as well as the assembled leaf spring. The spring leaves are made of cold drawn steel. When the springs are manufactured, each leaf or blade is curved, i.e. given a camber set. The greatest set is given to the smallest leaf, and the set is progressively reduced as the span increases, as shown in Figure 4. The leaf end may be formed in different shapes, as shown in Figure 5. A square end is the cheapest to produce but it causes concentration of the interleaf pressure, resulting in more friction. An end trimmed with a diamond point makes a better approximation of the uniform stress along the spring. Also, the pressure distribution is slightly improved. A tapered end approximates very closely the ideal uniform stress shape. Because of the flexibility of the tapered leaf ends, the pressure distribution in the bearing area is improved and the interleaf friction is reduced" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001742_ac0498765-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001742_ac0498765-Figure1-1.png", "caption": "Figure 1. Schematic representation work principle of the glucose biosensor based on proton transfer through an aqueous-organic gel microinterface: (a) organic phase; (b) microhole membrane; (c) aqueous phase.", "texts": [ " 18, September 15, 2004 5547 Published on Web 08/06/2004 The use of ITIES to analyze glucose could at a first glance seem to be an impossible task since glucose is a neutral molecule and a detection system based on ITIES relies on the transfer of charged ions through the liquid-liquid interface. However, glucose oxidase (GOx) catalyzes the oxidation of \u00e2-D-glucose by oxygen to D-gluconolactone,19 which subsequently hydrolyzes spontaneously to gluconic acid; simultaneously, the reduction of oxygen to hydrogen peroxide occurs, as exemplified in Figure 1. This model is consistent with the \u201cping-pong\u201d mechanism described in the literature, where the \u00e2-D-glucose oxidation induces enzyme reduction, while the natural acceptor O2 acts as a twoelectron oxidant,20 This is followed by the proton transfer through the liquid-gel interface in a process similar to that described by Osakai et al.5 and more recently by Pereira et al.,21 who reported a Zn(II) amperometric sensor based on the assisted ion transfer through gellified \u00b5ITIES. In this paper, an amperometric glucose sensor, based in a gellified \u00b5ITIES is described" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.3-1.png", "caption": "Fig. 4.3 A drill device, a Real object (Hommel 1937), b Structural sketch, c Chain", "texts": [ " When the lower ruler is set, moving the bronze levers would cause the upper ruler to become parallel to the lower ruler. Figures 4.2b and c show the corresponding structural sketch and chain, respectively. This device is a planar mechanism consisting of four members (1, 2, 3, and 4) and four revolute joints (JRz; joints a, b, c, and d). Therefore, NL = 4, CpRz = 2, and NJRz = 4. Based on Eq. (3.1), the number of degrees of freedom, Fp, of this mechanism is: 4.2 Linkage Mechanisms 65 A drill device is a carpenter\u2019s tool used to drill holes in ancient China. Figure 4.3a shows the mode of handling the drill device (Hommel 1937). It consists of the frame (member 1, KF), an input link (member 2, KL1), a long thread 1 (member 3, KT1), a bitstock (member 4, KL2), and a short thread 2 (member 5, KT2). The input link and the bitstock are made of Chinese black wood. The two threads are made of hemp. The steel bit is driven into a square wooden block and the block is inserted at the bottom of the bitstock. A brass sleeve is covered on the upper bitstock and used as a handgrip" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002736_j.jmatprotec.2008.03.065-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002736_j.jmatprotec.2008.03.065-Figure1-1.png", "caption": "Fig. 1 \u2013 The tooth face 2 of output gear is determined by the tooth face 1 of input gear and the relation 2 ( 1).", "texts": [ " Contact points are ocalized at the middle transverse plane. The dimensions of he contact ellipses can be controlled by the parameter of arabolic motion of the form grinding wheel. . Mathematical model .1. Constraint equation of input and output rotation ngles xternal gear drives with parallel axes are widely used in ndustry for transmitting rotational motion between two parllel and opposite rotating shafts. The relationship between he rotation angle of the input gear and that of output gear ust obey a certain function. As shown in Fig. 1, coordinate ystems S1 (x1, y1, z1) and S2 (x2, y2, z2) are connected rigidly o the input and output gears, respectively. Axes z1 and z2 re coincided with the input and output shafts, respectively. lanes x1 \u2212 y1 and x2 \u2212 y3 are the middle transverse planes of he input and output gears, respectively. When the coordinate ystem S1 (x1, y1, z1) rotates counterclockwise about axis z1 ith angle 1, the tooth face 1 of the input gear pushes the ooth face 2 of the output gear, so that the coordinate sysem S2 (x2, y2, z2) rotates clockwise about axis z2 with angle 2", "\u23a7\u23aa\u23a8 \u23aa\u23a9 E1 = (\u2202r1/\u2202 1) \u00b7 (\u2202r1/\u2202 1) F1 = (\u2202r1/\u2202 1) \u00b7 (\u2202r1/\u2202v) G1 = (\u2202r1/\u2202v) \u00b7 (\u2202r1/\u2202v) (18) Second, the basic quantities of the second kind of (1) are determined.\u23a7\u23aa\u23a8 \u23aa\u23a9 L1 = n1 \u00b7 (\u22022r1/\u2202 2 1) M1 = n1 \u00b7 (\u22022r1/\u2202 1\u2202v) N1 = n1 \u00b7 (\u22022r1/\u2202v2) (19) Then, the primary principal direction and curvature can be obtained as\u23a7\u23a8 \u23a9 e (1) I = \u2202r1 \u2202 1 / \u221a E1 (1) I = L1/E1 (20) and the secondary principal direction and curvature are obtained as\u23a7\u23a8 \u23a9 e (1) II = n1 \u00d7 e (1) I (1) II = ( E1N1 \u2212 2F1M1 + G1L1 E1G1 \u2212 F2 1 ) \u2212 (1) I (21) 2.3. Mathematical model of the tooth face of the output gear 2.3.1. Generation of the tooth face As shown in Fig. 1, when the input gear rotates with angular parameter 1, the output gear is constrained to rotate with (14), which is rewritten here as follows: 2( 1) = A\u22121BYT + ( N1 N2 ) 1 (22) s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 3\u201313 8 j o u r n a l o f m a t e r i a l s p r o c e s Now, the tooth face (1) of the input gear is regarded as the generating surface of the tooth face (2) of the output gear. In S2, (1) forms a family of surfaces {\u2211(1) 1 } , the position vec- tor of which can be determined by the following coordinate transformation equations: { r2( 1, v, 1) = M21( 1)r1( 1, v) M21( 1) = Rz( 2( 1)) \u00b7 Ty(\u2212r1 \u2212 r2) \u00b7 Rz( 1) (23) Based on the theory of gearing (Litvin, 1989), the necessary condition for the existence of the envelope to {\u2211(1) 1 } is f ( 1, v, 1) = n1 \u00b7 v (12) 1 = 0 (24) Solving for 1 from Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002468_j.jmatprotec.2005.02.202-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002468_j.jmatprotec.2005.02.202-Figure6-1.png", "caption": "Fig. 6. Model of the ABB 4400/60 robot in the second analysed position of its arms.", "texts": [], "surrounding_texts": [ "In the case of the model presented on Figs. 5 and 6 accepted parameters are shown on Table 1 (inertial) and Table 2 (elastic-damping parameters). Figs. 7 and 8 present parts of the robot model and corresponding dialog windows of the GRAFSIM program, where user can put geometrical data such as attachment co-ordinates of elastic-damping elements in local co-ordinate systems of inertial elements as well as angles between these syst c a c c e" ] }, { "image_filename": "designv10_13_0001981_ias.1988.25099-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001981_ias.1988.25099-Figure1-1.png", "caption": "Figure 1. Definitions of the elecmcal angles.", "texts": [ " with: j = r : rotor quantities j = s : stator quantities j = h : airgap quantities j = m : mechanic rotor quantity (position) i = r : rotor flux synchronous reference frame i = s : stationary reference frame linked to phase a of the i = t : stator flux synchronous reference frame i = h : air gap flux reference frame i = m: rotating reference frame linked to the rotor shaft i = i : arbitrary synchronous reference frame i = a : synchronous reference frame linked to arbitrary flux stator windings vector The angles are defined in Fig. 1 and are in electrical degrees. 88CH2565-0/88/0000-0450S01 .OO 0 1988 IEEE In order to link the d-axis di of the reference frame to a flux vector one usually states that the q component of this flux vector equals zero. For example, in the classical theory of field oriented controllers one states that the q component of the rotor flux equals zero: Yiq = 0 which automatically implies that the reference frame is fixed to the rotor flux !& and hence superscript 'i' equals k'. As a result the classical field oriented controllers derived from these equations use the rotor flux as a reference vector", " The flux initialization routine spends most of the time calculating the square route functions. For a final eight bit precision this may be as short as 17 ps. One c;tn conclude that the UFO algorithn~ has no additional hnrdwarti costs compared to other field orientation schemes which use a DSP. The total calculation time (approximately 120 ps) is so short that high speed applications are possible with no significant deterioration of the current commands. A picture of the DSP board with 4k by lhbit PROM memory and the TMS32010 signal processor is shown in Fig. 1 0 . Conclusions From these examples i t is evident that the LJFO controller is applicable in al l existing field oriented controller schemes due to the generality of its reference frame. In case of direct field orientation the UFO controller leads to the philosophy that the decoupler should operate in that reference frame where the the corresponding flux is sensed i.e. stator flux, whenever stator flux is sensed (directly or by using the stator voltage equations) and airgap flux, whenever airgap flux is sensed (Hall sensors or center tab windings)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure9-1.png", "caption": "Fig. 9. Path of contact on the two members.", "texts": [ " For a given value u1 of the pinion rotation angle, the corresponding rigid rotation of the gear u2 is determined by the tooth pair that produces the greatest transmission error value: u2\u00f0u1\u00de \u00bc u1 N1 N2 \u00femax k Du2 u1 \u00fe k 2p N1 \u00f026\u00de with k 2 Zju1i 6 u1 \u00fe k 2p N1 6 u1o : The path of contact over the pinion and gear tooth surface is given by the union of the tangency points over a complete mesh cycle. The values u1\u00f0u1\u00de; v1\u00f0u1\u00de; u2\u00f0u1\u00de, v2\u00f0u1\u00de are mapped on eCf 1 and eCf 2 to obtain the path of contact on the two mating member surfaces, as depicted in Fig. 9. We present here a geometric approach to estimate the contact pattern extension over the mating surfaces. The approach mimics the experimental contact pattern inspection adopted in industry practice. An offset surface is superimposed on the gear tooth surface that represents the marking compound surface. We initially \u2018\u2018tune\u201d the marking compound shape and thickness to match the geometric contact pattern to a reference one obtained by a run of HFM [9]. We will show that the results continue to match even after significant changes of the ease-off topography and/or introduction of misalignments" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001907_1.1302299-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001907_1.1302299-Figure2-1.png", "caption": "Fig. 2. Loaded sphere version of the tippe top. The center of mass G is off center ~O! by distance a. Space-fixed axes are XYZ with Z vertical ~X and Y can be chosen arbitrarily and are not shown!, and body-fixed axes are 123 with 3 along the symmetry axis ~1 and 2 can be chosen arbitrarily and are", "texts": [ " \u00a9 2000 American Association of Physics Teachers. I. INTRODUCTION The behavior of the tippe top has fascinated physicists for over a century.1\u201330 Textbook discussions are, however, still quite rare and brief.26,28,29 Figure 1 shows schematically the small wooden commercial model readily available. ~Appendix A gives the specifications of the model in our possession.! This type was introduced in Denmark a half century ago. In the nineteenth century loaded ~eccentric! spheres of various kinds were used2\u20134 ~Fig. 2!. Here we discuss some aspects of the motion of such tippe tops, but the results are in fact more general, and apply to any symmetric top with a spherical peg in contact with a horizontal plane. It has been established,33 both experimentally5,12,18,21 and theoretically,3,6,7,27,34 that a full explanation of the steady rising of the center of gravity of both ordinary and tippe tops requires sliding friction.35 There are regimes, however, where sliding can be neglected and the top rolls and pivots, e", " The paper is organized as follows: The translational and rotational equations of motion are given in Sec. II, followed by three sections giving the derivations of the three constants of the motion, and then a discussion. There are also two appendices, one on the frictionless case, and another giving some data for the tippe top in our possession. For our purposes the older model tippe top is slightly more convenient, i.e., a loaded ~eccentric! sphere. The center of mass is off center by a distance a\u2014see Fig. 2. There are no qualitative differences in the behaviors of the tops of Figs. 1 and 2, and the minor differences are easily explained.7,16 Figure 2 shows the geometry. As is standard in rigid body theory, we use two sets of axes: space-fixed axes ~XYZ! with Z vertical, and body-fixed axes ~123! with 3 along the top symmetry axis and origin at the center of mass ~G!. The only angle of interest49 to us is u, the angle between the Z and 3 axes. Its rate of change, u\u0307 , gives the tipping rate. 821jp/ \u00a9 2000 American Association of Physics Teachers license or copyright; see http://ajp.aapt.org/authors/copyright_permission The translational and rotational equations of motion for the top are M v\u03075Ftotal[F1w, ~1", " is perpendicular to the page and outward, such that 18 28 3 is a right-handed system. 822C. G. Gray and B. G. Nickel license or copyright; see http://ajp.aapt.org/authors/copyright_permission where r25r28 2 1r3 25R21a222Ra cos u. The expression for the energy is thus 1 2 @I11M ~R21a222Ra cos u!#v18 2 1 1 2 I1v28 2 1 1 2 M @~R cos u2a !v282R sin uv3#21 1 2 I3v3 2 1Mga~12cos u!5E . ~6! This gives one relation among v18 , v28 , and v3 . The two nonobvious constants of the motion to which we now turn will give us two more relations for these three components of v. We notice from Fig. 2 that the torque about G in the r direction vanishes, i.e., t\u2022r50. From ~2! we then have L\u0307\u2022r50. ~7! As we shall prove shortly, L\u2022 r\u030750, ~8! so that we then have obviously d dt ~L\u2022r!50, ~9! i.e., L\u2022r is a constant of the motion, L\u2022r5const. ~10! To establish ~8!, we first express r\u0307 in a convenient form. From the definition r5Rz\u03022a 3\u0302 we have r\u030752a 3\u0307\u0302 . But for a rotating rigid body, for the body-fixed vector 3\u0302 we have 3\u0307\u0302 5v3 3\u0302 . Hence we get51 r\u030752av3 3\u0302 . ~11! From ~11! and ~5! we have L\u2022 r\u030752a~I1v1DIv33\u0302 !\u2022~v3 3\u0302 !. ~12! The terms v\u2022(v3 3\u0302) and 3\u0302\u2022(v3 3\u0302) vanish since (v3 3\u0302) is perpendicular to both v and 3\u0302, which establishes ~8!. The constant of the motion ~10! is obviously the scalar product of L and r, as was first pointed out by O\u2019Brien and Synge.13 This constant is not, as sometimes stated,19,31 the component of L along r, i.e., L\u2022 r\u0302 . Since L\u2022r5L\u2022 r\u0302r , where r[uru, and r obviously varies during the motion ~see Fig. 2!, it is clear that L\u2022 r\u0302 is not a constant of the motion. Jellett34 first found this constant @in a form close to ~14! given below# by an approximate argument for the case that there is slipping. It was Routh40 who first showed that ~10! is an exact constant of the motion whether or not there is slipping! Since constants of the motion are unusual for dissipative systems, we sketch another derivation which brings out more clearly why ~10! is also valid if slipping occurs. Examining Fig. 4 we note that only the component F18 of F normal to the plane of the figure contributes to the torque components tz5F18a' and t35F18r' ", " is the second relation among v18 , v28 , and v3 , ~6! being the first. We now find another one. As we shall see, the Routh constant, like the Jellett constant, is a kinetic quantity and does not involve the gravitational strength g @unlike the total energy ~6!#. Unlike the Jellett constant ~14!, it is quadratic in the angular velocities and involves rotational kinetic energy. To derive it, we start by eliminating the reaction force F between the two equations of motion ~1! and ~2!: L\u030752r3~M v\u03072w!. ~15! Inspection of Fig. 2 shows that r3w is perpendicular to the ZO3 plane ~the plane of the figure!, and therefore has no 823C. G. Gray and B. G. Nickel license or copyright; see http://ajp.aapt.org/authors/copyright_permission 3-component. Hence taking the scalar product of ~15! with 3\u0302 eliminates w: L\u030735M v\u03073r\u2022 3\u03025M 3\u03023 v\u0307\u2022r, ~16! where we have used the cyclic property of A3B\u2022C. From v5v3r, we have v\u03075v\u03073r1v3 r\u0307. Using ~11! and the standard decomposition of A3(B3C), we find 3\u03023 v\u03075r3v\u03072rv\u030731av3v3 3\u0302 . ~17! From ~17! we get 3\u03023 v\u0307\u2022r5r3~v\u0307\u2022r", " where we have again used r5Rz\u03022a 3\u0302 to get the last term in ~20!. Substituting v\u0307\u2022r from ~20! into ~18!, and the result into ~16!, and replacing L\u03073 by I3v\u03073 on the left-hand side ~LHS! gives I3v\u0307352M DI I1 r3 2v\u030732M DI I1 Rr3v3v\u2022~ 3\u03023 z\u0302 !2Mr2v\u03073 1MaRv3v\u2022~ 3\u03023 z\u0302 !. ~21! We now manipulate ~21! as follows. ~i! We multiply both sides by v3 in order to obtain the energy rate of change (d/dt) 1 2 I3v3 2 on the LHS. ~ii! On the right-hand side ~RHS! we note that 3\u03023 z\u030252sin uu\u0302, where u\u0302 is a unit vector perpendicular to the plane of Fig. 2, pointing outward. We then note that v\u2022 u\u0302[u\u0307 . Replacing r2 in the third term on the RHS by r25r3 21r' 2 , where r3 is the component of r along 3\u0302 and r' the remaining part perpendicular to 3\u0302, and canceling the resulting r3 2 term against part of the first term gives I3v3v\u0307352M I3 I1 r3 2v3v\u030732M S I3 I1 21 DRr3v3 2u\u0307 sin u 2Mr' 2 v3v\u030731MaRv3 2u\u0307 sin u . ~22! From the second term on the RHS of ~22!, we obtain two terms from the two terms in (I3 /I121). When we replace r3 by (R cos u2a) in the second term, from the 21 we obtain a term which cancels the last term in ~22", " Since there are X, Y and 1, 2 rotational symmetries in the problem, f and c will contain arbitrary reference values. 50For a masterful account of nonholonomic constraints, see J. G. Papastavridis, Tensor Calculus and Analytical Dynamics ~CRC Press, Boca Raton, FL, 1999!. 51Note that r\u0307\u00dev. The correct relation is r\u03075v2 r\u0307C , where rC is the vector from the origin of an arbitrary set of space fixed axes to the moving point C. Using r\u0307C5vO5v3Rz\u0302 , since point C is always directly under point O ~see Fig. 2!, and v5v3r, we again get ~11!. 52Isaeva ~Ref. 19! states \u2018\u2018The projection of the angular momentum about the point of contact on a principal axis of inertia is a constant.\u2019\u2019 We are unable to confirm this claim. The angular momentum about contact point C, LC , is related to that about G, LG[L, by LC5L1Mr3v. Because LC\u2022r5L\u2022r, we have LC\u2022r5const as another version of the Jellet constant ~10!. This gives LCZ2(a/R)LC35const, where LCZ5LC3 cos u 1LC28 sinu. Hence LC3 and LC28 are related. However, the individual quantities L\u0307C18 , L\u0307C28 , and L\u0307C3 can be calculated from L\u0307C @using an equation of motion ~Ref", " ~29!.# Here tC is the torque about C, and r\u0307C the velocity of the contact point as traced out on the horizontal surface ~see Ref. 51!. 53See, for example, Osgood ~Ref. 45, p. 456!, Synge and Griffith ~Ref. 44, pp. 328, 388! Goldstein ~Ref. 42, pp. 75, 76, 215, 216, or Chataev ~Ref. 28, pp. 130, 136, 210!. 54D. J. McGill and J. G. Papastavridis, \u2018\u2018Comments on \u2018Comments on Fixed Points in Torque-Angular Momentum Relations,\u2019 \u2019\u2019 Am. J. Phys. 55, 470\u2013 471 ~1987!. 55The normal force is given by @see Fig. 2 or Eq. ~1!# Fz5Mg1M v\u0307z . Since v\u0307z5 z\u0308 and z5R2a cos u, we have v\u0307z5a sin uu\u03081a cos uu\u03072. From u\u03072 5 f (u) we obtain u\u03085 f 8(u)/2, so that Fz as a function of u is Fz(u) 5Mg1Ma( 1 2 sin uf8(u)1cos uf(u)). 56We choose X,Y axes as in Fig. 4. Fx[F18 can be obtained from @see the argument above Eq. ~13!# FxR sin u5t35I3v\u03073 . From ~31! we get v\u030735 2KR f\u0307 3 / f 3 2. Evaluating f\u0307 3 from ~32! then yields expression ~38! for Fx given in the text. To obtain Fy we start with t5L\u0307, so that t\u2022 1\u030285L\u0307\u2022 1\u03028 5(d/dt)(L\u2022 1\u03028)2L\u2022 1\u0307\u030285I1v\u0307182L\u2022 1\u0307\u03028" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003498_0022-2569(71)90044-9-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003498_0022-2569(71)90044-9-Figure1-1.png", "caption": "Figure 1. Tandem mechanism, consisting of a cam mechanism coupled to a four-bar linkage.", "texts": [ " It can be shown by simple methods that for each motion relationship, there is, in the case of oscillating output levers, a definite curve for the roller center, which depends on the transmission angle[3]. Contrary to the case when the output roller has a linear path, it is not possible to increase the transmission angle (and thereby the quality of transmission of motion) arbitrarily by increasing the size of the cam disk. The transmission angle/z lies, in the case that the cam disk is driving, between the normal n to the cam profile and the center line of the cam-roll lever (Fig. 1). Since the normal, however, also determines the transmission ratio of the cam drive, the construc- tion of the first derivative of the law of motion, which contains the transmission angle as a parameter, must be used as a starting point. As shown in Fig. 5, one first draws the locus q for the range of the positive transmission ratio and the locus q' for the range of the negative transmission ratio. A fixed link length dl = 50 has been assumed. Initially, this will be discussed for the point Q," ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002497_nme.1620230607-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002497_nme.1620230607-Figure2-1.png", "caption": "Figure 2. Geometry of the hyperboloidal spring", "texts": [ " In this calculation the result has sufficient accuracy when one circle of the coil is divided into twelve pieces in using the transfer matrix method. It can be seen that the present result shows very good agreement with Sawanobori and Fukushima's results,14 and that the effect of the rotatory moment of inertia is significantly small. Hence one circle of the coil is divided into twelve pieces and the rotatory inertia term is omitted in the following calculation. As an example of irregularly shaped springs, consider the spring of hyperboloidal shape, as in Figure 2, where R , is the centre radius of the spring which is chosen as the reference radius ( is . R , = Rl), and R, is the end radius. In this spring, the radius R of the N'th roll from an end is (20) R = R , + (R , - R l ) ( l - 2N/N), where N is the number of windings at the considered point and N is the number of effective windings between two ends. 7 x 6 5 x 4 3 2.2 1 1.0 1. 4 1.8 Rz 1R i a = 4. 8 , R i I d =l O. O , N = 6. 5 Fi gu re 3 . N on -d im en si on al n at ur al f re qu en ci es v er - su s R ,/ R , fo r h yp er bo lo id al s pr in gs 6 5 4 4 3 2 1 4 , 5 6 7 8 N Q = 4 " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003126_s11768-010-8038-x-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003126_s11768-010-8038-x-Figure2-1.png", "caption": "Fig. 2 Planar two-link manipulator.", "texts": [ " Remark 2 Three RBF networks are used to emulate the inertia matrix, centripetal matrix and gravitational vector of the robot directly. Nonlinear robot function f(x) estimate in [6] is not necessary. Chattering caused by switch gain can be decreased effectively. Remark 3 In this paper, the closed-loop system of nlink robot manipulator is proved to be uniformly ultimately bounded (UUB) by the help of the GL matrix and operator. 6 Simulation tests For the simulation studies we consider a two-link robot manipulator as Fig.2, whose dynamics are described by M(q)q\u0308 + Vm(q, q\u0307)q\u0307 + G(q) = \u03c4, (57) where M(q) = [ p1 + p2 + 2p3 cos q2 p2 + p3 cos q2 p2 + p3 cos q2 p2 ] , Vm(q, q\u0307) = [\u2212p3q\u03072 sin q2 \u2212p3(q\u03071 + q\u03072) sin q2 p3q\u03071 sin q2 0 ] , G(q) = [ p4 cos q1 + p5 cos(q1 + q2) p5 cos(q1 + q2) ] . We get equation (57) from [8], and the meaning of p1 \u223c p5 are described as follows: p1 = m1l 2 c1 + m2l 2 1 + I1, p2 = m2l 2 c2 + I2, p3 = m2l1lc2, p4 = m1lc2 + m2l1, p5 = m2lc2, where mi and li are the mass and length of link i, lci is the distance from joint (i \u2212 1) to the centre of mass of link i, and Ii is the moment of inertia of link i" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.6-1.png", "caption": "Fig. 4.6 A bronze trigger mechanism, a Real object (Xu 2007), b Original illustration (Mao 2001), c Structural sketch, d Chain", "texts": [ " A follower is connected to the frame with a revolute joint or a prismatic joint (JP). It is usually driven to move with varying speeds in a non-continuous and irregular motion. Figures 4.5a and b 4.2 Linkage Mechanisms 69 show the structural sketch of a simple cam mechanism and its corresponding chain, respectively. Cam mechanisms had been used fairly early in ancient China. About 600 BC, the trigger mechanism of the crossbowwas an intricate cam-shaped swing arm. Hence, the invention of the cam may be traced back to the Spring-Autumn and Warring Periods (770\u2013222 BC). Figure 4.6a shows a bronze trigger mechanism found in the excavation site ofChanganCity (\u9577\u5b89\u57ce) of theQinDynasty (221\u2013206 BC) (\u79e6\u671d), now Xian City in Shanxi Province (\u965d\u897f\u7701\u897f\u5b89\u5e02). Figures 4.6b\u2013d show the corresponding original illustration, structural sketch, and chain of the trigger mechanism, respectively. (a) (b) JA JR KF (1) KA (2) KAf (3) JR JA JP JRa b c 1 2 3 JR Cam Follower Fig. 4.5 A simple cam mechanism 70 4 Ancient Chinese Machinery Cam mechanisms also appeared in water-driven pestles. The publication Huan Zi Xin Lun\u300a\u6853\u5b50\u65b0\u8ad6\u300bduring the latter part of the West Han Dynasty (206 BC\u2013 AD 8) records a water-driven pestle that \u201c\u2026used water to pestle\u2026\u201d \u300e\u2026\u5f79\u6c34\u800c \u8202\u2026\u300f (Huan 1967)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001403_0021-9673(96)84622-x-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001403_0021-9673(96)84622-x-Figure3-1.png", "caption": "Fig. 3. Drawing of a microdialysis probe, with its tip magnified: 1, inlet tubing; 2, outlet tubing; 3, plastic head; 4, outer cannula; 5, inner cannula; 6, glue; 7, laser-drilled hole; 8, acceptor phase; 9, membrane. From Ref. [161.", "texts": [ " The Internal Minimal disturbance of bioprocess No replacement possible; prone to fouling; relatively long response time External Replacement possible; relatively fast Risk of disturbing bioprocess probe can be used for sampling of low-molecularmass analytes, such as glucose, in complex solutions for at least two weeks without exchanging the membrane. The applicability of a miniaturized version of such an internal dialysis unit has been reported in a number of papers. The technique, called microdialysis, was originally developed for sampling of drugs from blood and tissues of animals and humans and typically uses a probe as shown in Fig. 3. The probe contains an inner and an outer cannula and a tubular membrane at the tip. Acceptor phase is pumped down through the inner cannula, passes through two holes into the outer cannula and is pumped upwards again. In the probe tip, the acceptor phase is led along the membrane and here the dialysis process takes place; the acceptor phase which contains the analyte(s) - - the dialysate - - is finally pumped out of the probe into an injection loop, from whence it is introduced into an analytical system [15]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002046_robot.1997.606793-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002046_robot.1997.606793-Figure1-1.png", "caption": "Figure 1: Hilare with its trailer", "texts": [ " In the following experimentation we only use proprioceptive sensors: the *The author is partially supported by Alcatel-Espace. tThe author is also with LGMT INSA, Toulouse. odometer (based on optical encoders on dedicated wheels) gives the position ( z r , y,.) and the direction 0,. of the robot w.r.t. a starting configuration; an angular encoder gives the absolute direction 'p of the trailer w.r.t. the direction of the robot. The trailer is hooked up on the top of Hilare, on the vertical axis passing through the middle point of the driving wheel axle (see Figure 1). The distance between the driving wheels is denoted by d. The distance between the middle point of the wheels of both the trailer and the robot is denoted by e . The absolute coordinates of the trailer will be denoted by (Q, yt, 4). 0-7803-361 2-7-4/97 $5.00 0 1997 IEEE 3306 The control system is [6]: [ ; I u 1 + [ 0i + 0 0 1 where w1 and v2 are the respective velocities of the two driving wheels, w = $(vl+v2) is the linear velocity of the robot and w = f ( v 1 - v2) is its angular velocity. computing of the corresponding trajectory) runs also on the workstation; the trajectory is then sent to an on-board computer; it is the input of a module that computes the control laws u1 and u2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002464_iet-cta:20050518-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002464_iet-cta:20050518-Figure3-1.png", "caption": "Fig. 3 Diagram showing the thrust and CG offset scheme in pitch plane", "texts": [ " No disturbance was considered along the roll axis (i.e. w3 \u00bc 0) because only the pitch and yaw motions of the vehicle were of interest. Thrust (Tc) generated from both engines acts along the roll axis (Z-axis). Now consider the worst case, where the thrust +X (+Yaw) 1\u03b4 2\u03b44\u03b4 3\u03b4 Nozzle Nozzle + For push - For pull 90o90o +Y (+Pitch) Fig. 2 Bottom view of four actuators to obtain effective nozzle deflection for pitch motion 305 offset (x1) and the CG offset (y1) are in opposite directions, as shown in Fig. 3. From this, it was observed that along with the control moment 2TClC, one extra moment was generated along the ZX plane because of the small auxiliary control arm length (x1\u00fe y1) along X-axis. Thus, the disturbance moment due to thrust offset (x1) and CG offset (y1) along the pitch (ZX ) plane can be expressed as M1 \u00bc TC\u00f0x1 \u00fe y1\u00de \u00fe TC\u00f0x1 \u00fe y1\u00de \u00bc 2TC\u00f0x1 \u00fe y1\u00de Therefore w1 \u00bc M1 IYY \u00f08a\u00de Similarly, to calculate the disturbance due to thrust offset and CG offset along the yaw plane, consider the case where thrust offset is x2 and CG offset is y2, as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001876_s0142-9612(01)00151-x-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001876_s0142-9612(01)00151-x-Figure2-1.png", "caption": "Fig. 2. Plasma was recirculated through the minidialyser and returned to the reservoir. Ultrafiltrate was collected and the plasma volume was kept constant by the addition of the dialysate (50mm sodium phosphate buffer pH 7.4) to the plasma reservoir via pump 3. Radioactivity present in the ultrafiltrate and in plasma was measured as described in the Methods section. Dialysis conditions for b2-M and lysozyme were as shown in Table 3.", "texts": [ "14mNaCl with 4 changes until no radioactivity was present in the dialysate. Labeling of each protein was confirmed by sodium dodecyl sulphate-polyacrylamide gel electrophoresis (SDS-PAGE), followed by autoradiography (Fig. 1). The characteristics of each protein are shown in Table 2. 2.3. In vitro study The transport kinetics of [3H] b2-M and [3H] lysozyme during the simulated hemodialysis of human plasma (collected from healthy volunteers) and their interaction with the membrane under study were evaluated as shown in Table 3 and Fig. 2. The volume of plasma under experimentation was adjusted according to the surface area of the minimodules so as to imitate the conditions used with a standard module. In all experiments plasma was recirculated at 371C for 180min for experiments with [3H] b2-M and for 120min for experiments with [3H] lysozyme. In the course of these simulated hemodialysis sessions, samples were taken from the plasma at 0, 5, 10, 20, 30, 60, 90, 120 and/or 180min and the radioactive content determined in a liquid scintillation counter (Packard Minaxi b)", " The total protein content of the plasma at the end of each dialysis session on the different membranes was determined using the Lowry technique [26]. 3.1. The effect of simulated hemodialysis on plasma b2-M levels Normal human plasma from healthy volunteers was spiked with 30 mg [3H] b2-M per ml plasma, a concentration corresponding to the average concentration found in patients developing amyloidosis on dialysis [20,27]. Three milliliters spiked plasma were circulated for 3 h over each of the minimodules as shown in Fig. 2 and the radioactivity present in plasma was determined at the times indicated. It is apparent (Fig. 3) that already after 12min there is a steep decline (50%) in [3H] b2-M levels in the plasma passed over AN69XT, AN69ST, PS and PMMA BK, and this decrease reaches 90% after 60min. On the contrary in the plasma passed over cuprophan, the decrease never exceeds 15% even after 60min. At the end of the 180min period of simulated hemodialysis residual [3H] b2-M levels for AN69XT, AN69ST, PS and PMMA BK are all around 1", " As regards their adsorption capacity to AN69XT it was also found that the labeled lysozyme adsorbed to the same extent as unlabeled lysozyme regardless of whether its specific activity was 3000 cpm/ mg, 27 000 cpm/mg or 99 000 cpm/mg (results not shown). A similar observation was made for b2-M with specific activities of 1600 cpm/mg, 16 000 cpm/mg and 42 000 cpm/mg. These results strongly suggest that the radiolabeling procedure did not alter the adsorptive capacities of these two proteins. To assess the clearance of these proteins from human plasma, a microscale hemodialysis device was therefore developed to mimic in vitro the standard size module and conditions used routinely in a clinical setting (Fig. 2). In the case of b2-M, a simulated hemodialysis session on a micro scale revealed that of the five membranes studied, only cuprophan was not effective in lowering plasma b2-M levels. This result confirms those of earlier studies which showed that this cellulose derived membrane is impermeable to b2-M due to its dense symmetrical structure which does not permit the easy diffusion or convection of proteins through the membrane [30,31]. One additional characteristic of the cuprophan membrane which renders it impermeable to b2-M is its cut-off limit 1 kDa [32]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure1.14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure1.14-1.png", "caption": "Figure 1.14-The hysteresis loop traversal during operation of a flyback Converter. From W.A. Martin, Proc., Power Electronics Conf.(l987)", "texts": [], "surrounding_texts": [ "In the design of transformers for inverters, the worst case scenario is used with regard to transient voltages that may increase the input voltage. Knowing the maximum and minimum voltages will help in the design process. Another Circuit Push-pull Feed forward Flyback Advantages Medium to high power Efficient core use Ripple and noise low Medium power Low cost Ripple and noise low Lowest cost Few components Disadvantages More components Core use inefficient Ripple and noise high Regulation poor Output power limited \u00ab100 Watts) operational problem that must be considered in the design of push-pull con verters is the possibility of D.C. imbalance in the two arms of the circuit. For this reason, full bridge converters are used for most high-power applications even though they have twice as many power semiconductor switches. The voltage stress is only on the DC Bus voltage, not twice the value. In addition, a DC blocking capacitor can be added to the full bridge where it cannot in a push-pull circuit. 1.6-THE HYSTERESIS LOOPS FOR POWER MATERIALS Since this book is involved with the application and choice of magnetic components in power electronics, it is important to relate the action and prop erties of the magnetic materials in the transformers and inductors in the cir cuits we have been studying. What produces the voltage is not the alternation but the rate of change of the flux. As the current and voltage wave-forms change during operation, the magnetic components go through the hysteresis loop characteristic of the magnetic material. In some cases only part of the hysteresis loop is traversed. The operation of a power transformer or choke can be designed to have a bipolar drive as in the push-pull type or unipolar (forward or flyback mode). In the bipolar case, the course of the induction or the excursion is in both directions so that the magnetization is reversed. The In the unipolar case, the induction is unidirectional and the magnetization is not reversed. In Figure 1.12b, for the forward converter, a slow-rise capacitor or ringing choke has been added to reset the core. In the case of the flyback converter, (Figure 1.12c), the offset ofthe ac induction loop is due to the DC usually present in flyback converter. In certain instances in power electronics, the limits of induction are from the remanent to a higher induction. The loop traversed is a minor loop in the first quadrant similar to the one shown in Fig ure 1.13. In this case, the B used in the induction equation is still Lffi/2 even though the magnetization is not reversed. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 13 Whereas the ~B and thus the corresponding voltage are smaller in a unipolar than in the bipolar drive, the construction and operation are much simpler and more economical. The hysteresis loop traversals for flyback, forward and push-pull converters are shown in Figures 1.14, 1.15, and 1.16 . In the use of ferrites as flyback transformers for television receivers, the voltage and cur rent waveforms are not sinusoidal but saw-tooth or flyback shape. This per mits the electron beam to sweep across the TV screen with its visual signal and when it comes to the end, it would rapidly return or fly back to the start ing horizontal sweep position to present the next lower line of information. In this case, the transformer operation is unipolar. The basis of the modem elec tronic switching power supply is the action of the transistor as a switch. Early transistors were not built to carry much power and thus, as was the case for early ferrite inductors and transformers, they were used mainly in telecommu nication applications at low power levels. The first power electronic compo nent was the inverter that is a device that takes a DC input and produces an ac output in a manner other than the usual rotary generator. A transformer may be incorporated in the device to give the required voltage. The device can be mechanical such as a vibrator or chopper or it can be of the solid state variety using a transistor. The word, oscillator, may sometimes be confused for an inverter but in the oscillator, the frequencies may be higher and the power levels lower. The second important item, a DC converter, takes the DC of one voltage and converts it to DC at another voltage. One might call it a DC trans former. The intermediate step in a converter is that of an inverter namely the conversion of DC to AC. Of course, the additional step is rectification to D.C. The input to a converter can sometimes be a low frequency (50-60 Hz.) which is rectified, inverted, transformed, and then again rectified. The advantage over a conventional transformer is that the transformation is much more effi cient at the higher frequency. 1. 7-SWITCHING POWER SUPPLIES The complete switching power supply may consist of several auxiliary sections in addition to the power transformer. If ac is the input, it must first go through a noise filter to keep out unwanted transients. It is then rectified be fore entering the power transformer where it is first inverted to a square wave of the higher frequency (or pulse repetition rate) and then transformed to the desired output voltage. The transistor is driven by an auxiliary timing trans former or driver. After passing through the power transformer, the secondary voltage is again rectified. It then passes through a voltage regulator to main tain the voltage limits in the required range. Often this is done in a feedback circuit which controls the on-off ratio of the switching transistor. This 14 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 15 B t Bmax B ~B ----~~~---...... L ~'4--_---L-B H technique is called \"pulse width modulation\" or PWM and is widely used. An example of such a circuit is shown in Figure 1.17. Switching power supplies have efficiencies on the order of 80-90% compared to those of linear power supplies that may range from 30-50%. The switching supplies are, therefore, lighter and smaller than their counterparts. A typical switching power supply is shown schematically in Figure 1.18 (Magnetics 1984). 1.8-FERRORESONANT CONVERTERS In a previous section, we have discussed the use of pulse width modula tion (PWM) as a means of regulating a high frequency power supply. This method using square wave produces high switching loss because of all the odd harmonics produced by the square wave. There are several other control mechanisms which we will discuss One is the use of a resonant or ferroreso nant converter. The other is the use of a magnetic amplifier. There are many instances of resonance as it relates to low level linear fer rite components. In such cases a series or parallel combination of an inductor and capacitor acted as an LC circuit for frequency control in low level filters. The term resonance (more properly, ferroresonance) here has more of a connotation of resistance to changes in the input voltage and current by stor ing energy in the resonant circuit. As a matter of fact the first uses of ferro resonance was in the construction of a constant-voltage 60 Hz. transformer by Sola. In power supplies, an important use of the ferroresonant transformer is as a regulator. The early 60Hz transformers have given rise to the high-frequency type, which as noted earlier, may be even more useful at the highest frequencies than the conventional switching transformer design. As a high-frequency power inductor, the ferroresonant transformer has a quite different function. For one thing, the magnetic circuit is non-linear and because of the high currents and fields, operation is close to saturation. Most often when used as a power inductor, it is necessary to insert an air gap or spacer to avoid saturation. Figure 1.19 shows a simple ferroresonant regulator that consists of a lin ear inductor, Lh a non-linear saturating inductor, L2 and a capacitor, C, in parallel with L2\u2022 The latter two components form the ferroresonant circuit that controls the input voltage. The input energy is stored in L, and the resonant circuit acts to pass a uniform voltage to the load. Although the linear trans former may be of the typical power ferrite found in transformers, the saturat ing transformer is quite different. In addition to the usual attributes of power ferrites, it should possess a rather square hysteresis loop. The squareness ratio, BIBs should be over 85%. The permeability over the linear portion ofthe loop APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 17 18 MAGNETIC COMPONENTS FOR POWER ELECTRONICS should be as high as possible with the saturation permeability quite low (Jl = 20-30) By combining the ferroresonant regulator with a high frequency inverter, a ferroresonant converter can be constructed as shown in Figure] .20 Then, with the addition of a rectifier in front, a switching power supply can be made. See Figure 1.21. McLyman(1969) has shown how a high frequency ferroresonant trans former, tuned to about 20 KHz. can be used to stabilize high frequency inverters. With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for en ergy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 19 To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10\u2022 There are applications in which a high-frequency inverters is needed with low harmonic distortion. In a resonant inverter, a square-wave is produced by the switch network. The square wave has many odd harmonics that produces distortion and high switching loss. When the square wave is fed into the reso nant tank circuit that is tuned to the fundamental frequency, a pure sine wave is produced that is then rectified and filtered. By changing the frequency closer or further from the resonant frequency, the voltage and current at the load can be controlled. A resonant inverter circuit with two switches is shown in Figure 1.22.With the addition of a rectifier and low pass filter network, a resonant converter circuit is formed. See Figure 1.23. 1.9-S0FT SWITCHING IN COMMON TOPOLOGIES The reduced switching loss is the chief advantage of a resonant converter brought about by either zero-current switching (ZCS) or zero-voltage switch ing (ZVS). These fall under the heading of soft switching that can also 20 MAGNETIC COMPONENTS FOR POWER ELECTRONICS be applied to other topologies. The switching using the resonant inverter is done at the zero crossing points of the sinusoidal current or voltage wave forms and thus reduce the semiconductor switching loss allowing operation at higher frequencies. In a buck converter, zero-current switching can be imple mented by insertion of a quasi-resonant switch cell in place of the PWM switch cell as shown in Figure 1.24 . It is also possible to insert a ZVS switch cell into a buck converter as shown in Figure 1.25. A Zero Voltage Switching Circuit using an active-clamp snubber network in a forward and flyback con verter is shown in Figure 1.2. SUMMARY This chapter has reviewed the various circuits that are commonly used in power electronics. The hysteresis loop traversals of the magnetic components were correlated with the three topologies for unipolar and bipolar cases. The magnetic functions of the magnetic components involved in the operation a switching power supply will be discussed in Chapter 2. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 21 22 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 23 References Severns, R. P. and Bloom, G. E.,(1984) Modern DC-to-DC Switchmode Con verter Circuits, EJ Bloom Associates, San Rafael, CA Bracke, L.P.M.,(1983) Electronic Components and Applications, Vo1.5, #3 June 1983,p171 Bracke L.P.M.(1982) and Geerlings, F.C., High Frequency Power Trans former and Choke Design, Part I, NY Philips Gloeilampenfabrieken, Eindhoven, Netherlands Erickson, R.W. and Maximovic, D., (2001)Fundamentals of Power Electron ics, Second Edition Kluwer Academic Publishers, Boston, Dordrecht Magnetics (2000) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Martin, W.A.(1987), Proceedings, Power Electronics Conference (1987) Chapter 2 MAIN CONSIDERATIONS FOR MAGNETIC COMPONENT CHOICE INTRODUCTION After having reviewed the applications and topologies for the various power electronic circuits in Chapter 1, we can now proceed to investigate the main considerations that are made in choosing the appropriate magnetic com ponent. In this chapter, these considerations are related to the function of the component in the circuit. They include a general review of material properties and the core shapes and sizes. The final size will be determined by the design considerations and the input and output variables. Lastly, the question of cost will come into play depending on the market that the component and the fm ished product is aimed. 2.1-CONSIDERA TIONS BASED ON COMPONENT FUNCTION At the end of Chapter 1, we listed the various magnetic functions that are used in a switching power supply. They are; 1. Power Transformer 2. Power Inductor or Choke 3. In-line or Differential-Mode Choke 4. Common-mode Choke 5. EMI Suppression Core 6. Pulse Transformer for Transistor Firing 7. Magnetic Amplifier Core 8. Power Factor Correction Core In choosing the best magnetic component for these functions, we use a proc ess similar to that employed for low-level components except that the neces sary parameters are somewhat different. The choice will be determined by: 1. The type of converter circuit used. 2. Frequency of the circuit. 26 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 3. Power requirements. 4. The regulation needed (percentage variation of output voltage permitted) 5. Cost of the component. 6. Efficiency required. 7. Input and output voltages The components for each of these functions will be considered separately as their requirements are somewhat different. The cores selected to meet these requirements will be discussed with regard to; 1. Core material 2. Core configuration which includes associated hardware (bobbins, clamps, surface-mount connections etc.) 3. Size of the core 4. Winding Parameters- (number of turns, wire size) This chapter will review these requirements in general for the various func tions and in much more detail in the following chapters. 2.2-MAGNETIC COMPONENT CHOICES Having limited the choice of material somewhat to only power and power-related applications, there are still a large variety of components that can be used. These include; 1. Soft ferrite cores 2. Powdered metal toroids (and some E-cores) 3. Magnetic metal strip cores (Tape cores, laminations, cut-cores) 4. Amorphous metal strip wound tape-cores 5. Nanocrystalline material strip-wound tape cores F or the last two materials, there are several variations of material available but the core shape (a toroidal tape-wound core) is set by the physical attributes of the material (brittleness). These properties also may limit the size of the core particularly with respect to the inside diameter. The choice for the various components for each function will be discussed separately. 2.3-COMPONENTS FOR POWER TRANSFORMERS In power transformer functions, a large induction swing may be trav ersed calling for a core with highest effective permeability derived from the best core material and shape. A high saturation material with low losses under CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 27 the operating conditions is desirable. While a toroid gives the highest effec tive permeability for a specific material, it is costly to wind. An ungapped ferrite E-core or other power shape is preferable for noncritical applications. For lower frequency power applications (line or mains frequency) laminated strip of iron or SiFe is commonly used. For somewhat higher frequency power applications, tape cores of thin strip SiFe, high permeability NiFe (80 Per malloy) high saturation NiFe (50 Permalloy) or CoFe (Supermendur) can be used. For high frequency operation, the workhorse of the power electronics components is the ferrite core that is available in many materials, shapes and sizes. Recently, some inroads have been made with the new amorphous and nanocrystalline materials. Power transformers have one requirement in common, that is that the material saturation be as high as possible consistent with other factors such as core loss. As we shall see later, at very low frequencies, the materials are satu ration-driven as eddy current losses are moderately low. These materials such as iron, low-carbon steel and heavy gage silicon iron will not be discussed in this book since they do not enter into the field of power electronics. At high frequencies, the materials are core-loss-driven so that materials such as fer rites are generally used. For medium high frequencies, materials such as thin gage silicon iron, amorphous materials and the new nanocrystalline materials are available. We normally make this choice on the basis of frequency of op eration. Vendors usually provide guidelines as to what materials are suitable for the various frequency ranges. The core losses are often given as a function of frequency. Although vendors generally list power materials separately, the user often has a choice of several available materials varying according to losses, frequency and sometimes, cost. Since power ferrites operate at the highest possible induction, we find, as we would expect, that they have the highest saturation of the ferrites consistent with maintenance of acceptable losses at the operating frequency. For frequencies up to about 1 MHz., Mn-Zn ferrites are the most widely used materials. Above this frequency, NiZn fer rites may be chosen because of their higher resistivities. Since ferrite cores make up the largest proportion of high frequency power transformers, the considerations for their choice will be discussed first. 2.4- FERRITE POWER TRANSFORMERS Having mentioned that ferrite cores are the major components for power electronics we will discuss them first. Switching power supplies and ferrite expansion went hand in hand. To explain why ferrites were made to order for these applications, we must understand the implications of going to higher frequency operation. Ferrites have low saturation compared with most common metallic magnetic materials (such as iron) and also have much lower 28 MAGNETIC COMPONENTS FOR POWER ELECTRONICS permeabilities than materials such as 80% NiFe. The low saturation of ferrites comes about from the fact that the large oxygen ions in the spinel lattice con tribute no moment and so dilute the magnetic metal ions. This situation is compared to a metal such as iron where there is no such dilution. In addition, because of the anti ferromagnetic interaction, not all the magnetic ions con tribute to the net moment in ferrites but only those with uncompensated spins. The first use of ferrite material in a power application was to provide the time-dependent magnetic deflection of the electron beam in a television receiver. The two ferrite components used were the deflection yoke and the flyback transformer. This application remains the largest in tons of soft ferrite used. Another early use of power ferrites was in matching line to load in ultra sonic generators and radio transmitters. Ferrites were not considered for line power inputs because at the lower frequencies (50-60 HZ.),they wereeco nomically unattractive (lower Bsat and higher cost than electrical steels). How ever, today's ferrites are employed as noise filters in power lines on the input to all types of electronic equipment. The potential for using ferrites at high frequencies was always there but the auxiliary circuit components (mostly semiconductors) were not yet developed. In addition, earlier there was no great market or stimulus for high frequency power supplies. One envisaged use was in high frequency fluorescent lighting at about 3000 Hz. This idea was suggested in the early 1950's but the need for setting up line power at these frequencies was never fulfilled. (See Haver 1976) In the 1970's, the rapid growth of ferrites for use at high power levels oc curred shortly after the similar growth of power semiconductors that could switch at very high frequencies. This design specifically required moderate cost magnetic components with low losses at higher frequencies and elevated power levels. Thus the age of the switched mode power supply (SMPS) was born. Coincidentally, the rapid growth of computers and microprocessors has required small, efficient power supplies that could be constructed with power ferrite components. The computer and allied markets are certainly providing much of the present day impetus for today's power ferrite development. The matching of SMPS component needs with ferrite properties is explained in the following two sections. 2.4.1- Frequency-Voltage Considerations A changing electric current in a winding provides a corresponding change in a magnetizing field which sets up a resultant varying magnetic in duction in a magnetic material. This changing flux will induce a voltage in another (secondary) winding. The general case of a voltage produced by a changing (not necessarily alternating) magnetic flux is given by Faraday's equation namely; CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 29 E = -N dcjl/dt = -N d(BA)/ dt [2.1] For a sine wave, the induced voltage is given by: E = 4.4BNAfxlO-8 [2.2] where:cjl = Magnetic flux, maxwells E = induced voltage, volts B = maximum induction, Gausses N = number of turns in winding A = cross section of magnetic material, cm2 f = frequency in Hz. For a square wave, the coefficient is 4.0 instead of 4.44. If we, for the present, minimize the effects of complicating problems such as core losses and temperature rise (which we will discuss later), we can use this important induction equation to examine the use of the variables in the most preliminary design. To obtain a given voltage with the most efficient arrangement, the tradeoffs can be as follows; 1. Increasing B by using a material with high induction such as 50% Co-Fe. This material is used in aircraft and space application where space and weight are important. However, there is a material limitation on how high the B can go. Ferrites may have saturation of 4-5,000 gausses. The highest RT saturation of about 23,000 gausses is found in 50% Co-Fe, so that there is a possible 4:1 or 5:1 advantage here for metals. See Table 2.1. 2. N can be increased which leads to higher wire resistance losses. Also, there is a maximum number of turns that can be wound around a core with a window or bobbin area. Using small wire size allows more turns, but the increased resistance (due to the increased length to cross sectional area) limits the useable current through the wire. 3. A can be increased. In addition to higher core losses, the larger cross-section requires a longer length of wire per tum leading to higher copper losses and a larger and heavier device. The larger cross section in a poor thermal conductor such as a ferrite also creates the problem of how to remove the heat produced in a large core. If the heat isn't removed, the temperature rise lowers the saturation induction, Bs of the ferrite. Under these conditions, if the induction-swing, ~B, is large enough, the core may actually saturate and the current in the winding can become very large possibly causing catastrophic failure. This can damage the core, the winding and other components. 4. f can be increased. Here the effect can be quite dramatic depending on the frequency dependence of core losses. For instance, in going from a 60-Hz power supply to 100KHz supply, the factor is 1666. This coupled 30 MAGNETIC COMPONENTS FOR POWER ELECTRONICS with a 4: 1 reduction in going from high B metals to low B ferrite still leaves 400+:1 advantage. This permits a great reduction in the size & weight of the transformer, which reduces wire and core losses. In a high frequency power supply, increasing the frequency can exacerbate the thermal runaway problem if the exponent of frequency dependence is higher than that for flux density. We will deal with this subject with later in this chapter. NiFe (50% Ni, 50% Fe) NiFe (79% Ni, 4% Mo, Balance Fe) NiFe Powder (81% Ni, 2% Mo, Balance Fe) Fe Powder Ferrites Amorphous Metal Alloy(Iron-Based) Amorphous Metal Alloy (Co-based) Nanocrystalline Materials (Iron-based) 2.4.2-Frequency-Loss Considerations 15,000 7,500 8,000 8,900 4,000-5,000 15,000 7,000 12,000-16,000 We have shown that by increasing the frequency of a transformer, we can produce the desired voltage requirement at a greatly increased efficiency. However, we have neglected one consideration, that is, the increased losses that occur when we increase the frequency of operation. The additional losses incurred in the frequency increase are mainly eddy current losses caused by the internal circular current loops that are formed under ac excitation. The eddy current losses of a material can be represented by the equation: Pe = KBm2Fd2/ P [2.3] where: P e = Eddy Current losses, watts K = a constant depending on the shape of the component Bm = max induction, Gausses f= frequency, Hz d = thickness-narrowest dimension perpendicular to flux, cm p = resistivity, ohm-cm Again there is a trade-off for lower P e. B can be lowered which means larger A to get the same voltage. Frequency, f, can be lowered which again means CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 31 larger components. The thickness, d, can be made smaller, such as in thin metallic tapes, wire or powder. There are physical limitations to this variable, and also the high cost of rolling metal to very thin gauges. The other measure we can take is to increase the resistivity. (See Table 2.2.) A comparison will demonstrate the advantage of ferrites. The resistiv ity for metals such as Permalloy or Si-Fe is about 50 x 10-6 ohm-cm. The re sistivity of even the lowest resistivity ferrite is about 100 ohm-cm. The dif ference then is about 2 million to 1. Since the effect of the frequency on the losses is a square dependence and that of resistance only a linear one, the net effect on frequency is about 1400 to 1. Thus, losses to the 60 Hz operation, for the same size core, extend to 84,000 Hz, close to the 100 KHz we postu lated for the voltage calculation. Granted this calculation is simplified, having omitted wire losses and loss differences due to B variations, but the order of magnitude is probably reasonable. In actual cases, 60 Hz power supplies op erate at efficiencies of about 50%, whereas the ferrite high frequency switch ing power supplies operate at 80-90%. Table 2.2 Resistivities of Ferrites and Metallic Magnetic Materials Material Zn Ferrite Cu Ferrite Fe Ferrite Mn Ferrite NiZn Ferrite Mg Ferrite Co Ferrite MnZn Ferrite Yttrium Iron Garnet Iron Silicon Iron Nickel Iron Resistivitity, n -cm 102 105 4 X 10-3 104 106 107 107 102_103 1010_1012 9.6 X 10-6 50 X 10-6 45x10-6 We must include another consideration in the comparison. We have men tioned the poor thermal conductivity of ferrite and ceramics in general. Aside from the difficulty of firing very dense, large, ceramic parts without produc ing cracks, there is also the previously mentioned problem of heat transfer. Because of this limitation, ferrite switching power supplies have not been made larger than about 10 KW. This is in comparison to the over 100 KW supplies that are made of metallic materials. However, since the large mar kets in power supplies are for home computers or microprocessors, and since these are well within the operational size of ferrites, there is no real size problem here. A comparison of magnetic properties of ferrites with other 2.4.3-Choosing the Best Ferrite Power Transformer Material A material slated for a power application must meet certain special requirements. Although ferrites in general have low saturations, we must, at least, provide the highest available variety consistent with loss considerations. This is mostly a matter of chemistry. Along with this consideration is the need for a high Curie point. This generally means maintaining a high saturation at CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 33 some temperature above ambient which approaches actual operational tem perature. In addition to the saturation requirement, the material must possess low core losses at the operating frequency and temperature. The transformer losses, which include both the core loss and the winding loss, will heat the ferrite causing a reduction in the saturation to a value lower than that at room temperature. If this fact is not taken into account, the core may saturate at the higher temperature with disastrous results. A runaway heating situation could develop leading to catastrophic failure. Many ferrite suppliers have redes igned their materials such that the core losses will actually minimize at higher operating temperatures preventing further heating of the cores. The negative temperature coefficient of core loss at temperatures approaching the operating temperature helps compensate for the positive temperature coefficient of the winding losses in the same region. Roess(l982) has shown that the minimum in the core loss versus temperature occurs at about the position of the secon dary permeability maximum. Thus, if the chemistry of the ferrite can be de signed to have the secondary permeability maximum at the temperature of device operation of the transformer as described above, the core losses will also be lowest at that temperature. However, we must consider that this is only a local minimum. Having the minimum at 75-1 OO\u00b0C.is a tremendous aid to the designer in avoiding thermal runaway, but still requires careful design work as the core loss increases above this minimum and the capacity for thermal runaway is still very real. Some smaller portable devices such as lab top computers operate intermittently at low ambient temperatures so materials with core loss minimum temperatures near room temperature may be used. 2.4.4-Power Ferrite Core Shapes Power ferrites come in a variety of shapes. Although pot-cores were the ferrite shapes of choice in telecommunication ferrites, several required or preferred features for this application are not as critical in power usage. These include: 1. Shielding 2. Adjustability In addition, pot cores are more costly and power ferrites must compete with other alternative materials. Therefore, shapes such as E cores, U cores, and PQ cores are more applicable to power application. Other shapes including solid center post pot cores can be used. The following chapter describes the types of shapes available. The shape of the core has a bearing on the ampli tude permeability since the inductance is given by; L = .41tJ.lN2/IA [2.4] 34 MAGNETIC COMPONENTS FOR POWER ELECTRONICS where: I = length of the winding, cm. A = Cross sectional area, cm2 L = Amplitude Permeability Therefore, the longer the section on which the winding is placed and the shorter the height of the winding, the higher the inductance. 2.4.S-Component Processing after Assembly After the ferrite component is wound, there are additional process steps that may affect the choice of component. These include; 1. Encapsulation 2. Soldering 3. Clamping 4. Winding 5. Gluing 6. Coating Encapsulation, coating, gluing and clamping all put stresses on the core that may affect the magnetic properties. Some materials are more sensi tive to stresses than others even though the properties are superior. Winding also stresses the core. Toroidal winding is costlier than bobbin winding. In modern printed circuit design, wave soldering is often used to attach compo nents and leads to the board. Proper component choice will minimize the ef fect of the soldering temperature. 2.4.6-High Frequency Applications Special attention must be paid if the frequencies of power supplies extend past 100 KHz and even to the 1 MHz region. First, the size of the core may be reduced significantly. Second, the core material must be modified to lower the core losses at these frequencies. The maximum flux density or B level used which, at lower frequencies, may have extended to 2000-2500 gausses may have to be reduced to something on the order of 500-600 gausses to attain the lower losses. The increase in frequency with smaller size and better efficiency may more than offset the lower saturation used. We will dis cuss designs at these higher frequencies at a later point in this chapter. Ven dors design instructions are based on allowing the flux density to drop to lower values at higher frequencies in order to keep the core loss constant at 100 mW/cm3. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 35 2oS-METAL STRIP POWER TRANSFORMERS In our discussion in Section 2.4.1, we found that a great advantage of some of the metal strip magnetic components was their high saturation, (Si Fe, Ni-Fe, and Co-Fe). However, as we examined the core losses in Section 2.4.2, we also found that due to their low resistivity, the usefulness of these materials was diminished. Reducing the thickness or gage of these materials allowed them to operate at somewhat higher frequencies. For the 80% Ni-Fe, with a lower saturation, the very high permeability also reduced high frequency losses especially in thinner gages. The Ni-Fe alloys had an addi tional advantage of being able to be reduced to an extremely thin gage (0.0005\") Provided that the frequency is not too high, this material can be used in the form of tape cores, laminations an also cut cores. The advantages and disadvantages of Si-Fe and Co-Fe are given in Table 2.5. The compara ble listings for Ni-Fe are given in Table 2.6. One general advantage of the metallic strip cores is that they can handle higher power levels than the ferrite cores. Aside from their higher saturations, their higher thermal conductivities allow them to dissipate heat more efficiently. 206o-AMORPHOUS METAL STRIP CORES A newer line of metal strip materials other than those described in the previous section are the amorphous metal alloys. The iron-based alloys have the high saturation for use as power transformers. Their resistivities are higher 36 MAGNETIC COMPONENTS FOR POWER ELECTRONICS than the crystalline magnetic alloys and they can be annealed for either low frequency or higher frequency operation. However, they are magnetostrictive and are only used at lower frequencies. The Co-based materials have almost zero magnetostriction which gives them a high permeability and lower losses. The advantages and disadvantages of the amorphous materials are given in Table 2.7. In Figure 3.34 are shown the real and imaginary values of the com plex permeability. Roess gives one advantage of ferrites over the amorphous materials in that they can only be produced in toroidal tape-wound cores. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 37 2.7. -NANOCRYSTALLINE-BASED POWER TRANSFORMERS The newest of the soft magnetic strip power materials are the nano crystalline. These materials were developed as an extension of the amorphous metal materials and are made by a similar process except that the material is annealed to produce a very fine grain size on the order of 10 nanometers. The iron based material has high saturation and permeability. The latter is due to almost zero magnetostriction similar to the Co-based amorphous alloys 2.8-COST CONSIDERATION FOR MAGNETIC COMPONENTS Aside from the technical performance of the magnetic component, some consideration must be given to the comparative cost of the component. The final cost is determined by several factors; 1. Cost of raw materials 2. Cost of core fabrication 3. Cost of winding Some of the advantages of a ferrite core are the low raw material and fabrication costs. Thin gage metals (SiFe, amorphous and nanocrystalline) have relatively high fabrication costs. For winding costs, toroids are the most 38 MAGNETIC COMPONENTS FOR POWER ELECTRONICS expensive, then pot cores and finally, E-cores. Figure 2.1 gives the trans former cost utility in maxwells per dollar as a function of frequency. The pre dominance of ferrites especially at higher frequencies is evident. 2.9-COMPETITIVE HIGH FREQUENCY POWER MATERIALS Roess( 1987) has recently emphasized that a great virtue of ferrite power material is their adaptability, and even at higher power frequencies. He compares the losses of several competing power materials for the higher fre quency operation. Trafoperm is a NiFe strip material. Vitrovac is an amor phous metal strip material and Siferrit is of course, a ferrite. The results are given in Figure 2.2 . Up to 100 KHz., the amorphous metal materials have lower losses than the ferrite especially the thinner gage type which remains lowest even at the higher frequencies. Roess points out that despite this disad vantage, a ferrite core is still the magnetic component of choice because of its much lower cost and its adaptability to be produced in many different shapes. The strip, on the other hand, has limitations on the shapes in which it can formed as shown in Figure 2.3. The new nanocrystalline materials were de veloped after this study. A new fine-grained rapidly solidified nanocrystalline (not amorphous) strip material was introduced by Hitachi Ltd. It has much higher saturation (13,500 Gausses), higher permeability (16,000 at 100 KHz.) than ferrites and very low losses at 100KHz. Although these properties compare favorably to ferrites, it remains to be seen if the price and performance will allow it to compete with ferrites. In addition, the nanocrystalline cores have the same lack of fabrication versatility as other strip-wound cores 2.10-DESIGN CONSIDERATIONS IN COMPONENT CHOICE Aside from the items previously mentioned in choosing a mag netic component for power electronics, there are additional considerations based on the other design requirements. These include; 1. Space, Volume and Weight Restrictions 2. Ambient Temperature-Heat removal 3. Environmental-Corrosion, Radiation, Vibration and Shock 4. Reliability-Lifetime 5. Regulation- Voltage variation 6. Safety considerations CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 39 2.11- FERRITES VS METALLIC MAGNETIC MATERIALS There have been many comparisons of ferrites with other magnetic materials for power applications. The author (Goldman 1984) listed other metallic materials that were used for SMPS's. Goldman (1995) compared metal strip, powder cores and ferrites for various applications including power. Bosley (1994) presented a rather extensive study of the different mate rials for transformers and inductors versus frequency where the maximum flux was limited by saturation or core losses. The useable flux density under these limitations is given in Figure 2.4. For frequencies above 100 KHz., the MnZn and NiZn ferrites had the highest values. The performance factor in 40 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Tesla-hertz vs frequency is shown in a figure in next chapter. Here again, above 100 KHz., the two ferrites were the highest. The economic trade-off for these materials is given in Figure 2.1 which charts the maxwells of flux per dollar as a function of frequency for the competing materials. Bosley (1994) also listed the advantages and disadvantages of the competing materials for SMPS transformers. Table 2.5 show these for SiFe and Permendur, Table 2.6 for the NiFe alloys, Table 2.7 for the amorphous alloys and Table 2.4 for fer rites. Snelling C 1996) presents a plot of the power loss density of power fer rite, Co-Fe amorphous metal strip and the Vitrovac 6030 nanocrystalline ma terial vs frequency in figure in next chapter. The relative advantages in core loss depend on the frequency and flux density. The previous comparisons did not include the nanocrystalline materials that gained recognition shortly after the Bosley article even though Y oshizawa (1988) reported on them earlier. The frequency dependence of the permeability and loss factor of a nanocrys talline material was compared (Herzer 1997)along with those for a Co-based amorphous material and a MnZn ferrite. The permeability is higher and the loss factor is lowest for the nanocrystalline material. In addition the saturation induction was measured for the same materials (Herzer 1997). The nano crystalline material has the advantage there. It remains to be seen whether the pricing of the nanocrystalline can be low enough to compete with the rela tively inexpensive ferrite materials. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 41 2.12-0UTPUT POWER INDUCTORS Power Inductors differ from the low-level inductors that we have dealt with in telecommunication applications. They are not used in LC circuits for frequency control. In power inductors, use is made of their ability to store large amounts of power in their magnetic field. As such, they can limit the amount of ac voltage and current. When this is done in the presence of a high D.C. current, the inductor, usually in combination with a capacitor, serves as a smoothing choke to remove the ac ripple in a D.C. supply. This is often done in the output circuit ofthe supply after rectification. Since there are large D.C. and smaller superimposed a.c. currents, they usually need gaps to prevent saturation. In addition to the increase in current and possible catastrophic fail ure at saturation, the incremental permeability drops close to zero and there fore, the required inductance specification is not met. With the gap, the mag netization curve is skewed to avoid saturation (See Figure 4.11). With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for energy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10 , In some power inductor applications, as in the common mode choke, the magnetic core must sense the small difference between 2 magnetic cur rents and a high permeability toroid or ungapped shape must be employed. In some other of these inductor functions, the full power of the circuit passes through the magnetic component and some feature must be added to keep the core from saturating. The same is true for some energy-storage functions where a high DC current is present. In these two cases, either a core with a discreet gap (ferrite E core) or a distributed gap toroid (iron powder core) is warranted. 2.12.I-Ferrite vs Metallic Powder Inductors Earlier in this chapter, we compared ferrite power transformer materi als with their counterparts in metallic materials. For ferrite power inductors, the materials are mostly the same as the transformer materials. However in the case for metallic materials, the materials for power inductors are different than those used for power transformers. Whereas gapped ferrite cores are used for many power inductor applications, in the case of the metallic cores, the gap is a distributed one as found in powder cores. Bosley (1994) who did the analysis on SMPS transformer materials compared the materials for SMPS inductors in the same paper. The materials evaluated were; 42 MAGNETIC COMPONENTS FOR POWER ELECTRONICS I.NiFe Powder Cores- Molypermalloy and Hi_Flux Cores 2.Sendust Powder Cores- Kool-Mu and MSS cores 3.Amorphous Choke Cores 4.Powdered Iron Cores 5.Gapped Ferrite Cores 6, Metal Strip Cut Cores Some of these materials were used for low level telecommunications applica tions. For power applications at high power levels, the materials may be somewhat different. Bosley (1994) listed the advantages and disadvantages of the above mentioned materials for power inductor applications. Table 2.8 lists these for NiFe powder cores, Table 2.9 for Sendust (FeAISi) powder cores. Table 2.10 for amorphous metal choke cores, Table 2.11 for powdered iron cores, Table 2.12 for gapped ferrite cores and Table 2.13 for cut cores. Since power inductor often must operate under high D.C. bias conditions, the effec tive permeability for these materials are given. The DC bias curves for several of these materials are shown in Figure 2.5. Again, the nanocrystalline materi als were not considered. Bosley also listed the core losses of the various in ductor materials compared to ferrites in Table 2.14. Although the ferrites are lower in losses than the others listed. Bosley notes that, with a medium to large gap, there may be increased losses due to fringing flux This may in crease ac copper losses near the gap. Nanocrystalline materials were not con sidered here as well. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 43 44 MAGNETIC COMPONENTS FOR POWER ELECTRONICS CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 45 Pauly (1996) reviewed the selection of a high-frequency core material for power line filters. He compared various powder core materials and gapped ferrites with respect to volume, sound level and cost. All cores were 1.84 inch toroids except the gapped ferrite which wa a gapped EC70/70G . The induc tors were 4.0 mHo Ripple current was a 40 KHz. triangular Wave with peak to-peak level of 33% of rated current. Output power was theoretical. Table 2.15 summarizes the results. The losses of the MPP, MSS (Sendust) and Hi Flux cores were much lower than that of the powdered iron but the cost was dramatically lower. Best performance was found in the MPP cores. Table 2.16 is the author's opinion in the ranking of the cores as to the suitability of the various cores for a given application. In general smaller cores may be oper ated at higher frequencies and flux levels. 46 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2.13- POWER FACTOR CORRECTION CORES In some new ac input lines for switching power supplies, a \"front end\" boost pre-regulator is used to obtain an essentially Unity Power Factor or UPF. The circuit for this function is shown in Figure 2.6. An external logic circuit serves to control the duty cycle of the main switch, Q 1 to raise the in put voltage, Vi to the output voltage, Vo. Higher peak ac flux densities are present than in conventional output chokes so core losses are quite important here. If the wrong core or material is used, core losses will increase and the possibility of thermal failure may occur. As in the case of the output choke, the materials used are the various types of powder cores (iron, molyperm, high flux NiFe, Sendust) or a gapped ferrite. However, special considerations of the losses must be taken into account with iron powder cores so that larger cores and lower loss materials must be used. A_C. IIIVT + Cl \u2022 D.C. CIlITM Fgure 2.6- A front-end boost preregulator for Power Factor Correction (PFC), (From B. Car sten, Application Note, Micrometals (2001) 2.14 -MAGNETIC AMPLIFIER CORES In cases of multiple outputs in switching power supplies, their may be an imbalance in the output voltages. In cases where the regulation must be controlled very precisely, one solution is the use of a magnetic amplifier CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 47 regulator circuit. The circuit for a forward converter with a 5V and 12V. ou put is given in Figure 2.7 . The 5V output uses PWM feedback circuitry to regulate. The 12 V output uses the magnetic amplifier or saturable-core reac tor to regulate. The materials used for the mag amp must have high square ness or B/Bs ratios, low coercive force for small reset current and low core loss for small temperature rise. Components for this function are Square-loop NiFe tape cores, Co-based amorphous metal cores and square loop ferrite toroids. We have considered the use of square loop ferrites previously in conjunction with the ferroresonant transformer design. The advantages and disadvantages of the square permalloy are shown in Table 1.17.Those of the cobalt-based amorphous metal material are given in Table 1.18 and the corresponding ones for the square-loop ferrite are given in Table 1.19. 48 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2.tS-PULSE TRANSFORMERS There are instances when the transistor switch supplying the square wave is triggered or fired by an external source or pulse generator. Ferrite cores, especially small toroids, are widely used in pulse transformers. This application requires transmission of a square wave with little distortion. The shape of a typical square wave voltage pulse is shown in Figure 2.8. During the time that the voltage pulse is on, the current is ramping up as is the flux CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 49 density. In the case of a square wave, the ~B is given in terms of the applied voltage, E, and the pulse width, T. For a specific core area and number of turns, the equation is; B = ET xI0-8/NAe [2.5] From the value of ~B , the corresponding value of H, the magnetizing field can be determined from the vendor's curves on the material properties. From this value of H, and the Ie of the trial core, the excitation current can be deter mined from; H =.4 nNIp//e [2.6] IfE, T, N are given and a AB is assumed, the effective dimensions of the core can then be given as; IJAe = O.4nN\\ m x1081ET~H [2.7] The cores corresponding to various values of IJAe are listed by the vendor. The pulse permeability is given by; ~p = ETlIp [2.8] The pulse transformers used in digital data processing circuits will usually have ~B's on the order of 100 Gausses and are always little toroids inserted in small TO-5 cans for use on PC boards. Higher power pulse transformers may use pot cores or E cores that may be gapped to prevent saturation. All of the frequency related problems encountered in wide-band transformers are pres ent in the pulse transformer, but here, it is evidenced by pulse attenuation (droop). As in the previous case, the permeability should be as high as possi ble, but when high pulse repetition rates or fast rise times are used, perme ability concerns may be compromised for lower losses. Permeabilities of about 5-7000 are frequently used for small ferrite toroids. 2.16-COMPONENTS FOR EMI SUPPRESSION Before our discussion of the actual components used for EMI sup pression, it is useful to look at the circuitry involved along with the currents both intentional and unintentional. The latter, of course are the EM! interfer ence or noise currents. Basically, there are two types of EMI currents, namely the common-mode and the differential currents. These are contained in a pair of wires leading to and from the load. The first of these is the differential cur- 50 MAGNETIC COMPONENTS FOR POWER ELECTRONICS rents whose current flow is the same as in ordinary intended or designed cir cuitry as shown in Figure 2.9. The differential EMI currents then flow in the same direction as the intended currents. If a current probe is placed around the pair of conductors, no current flow will be detected for either the intentional or unintentional (EMI) currents. In the case of the common-mode EMI cur rents, they flow in the same direction in both conductors. Now, while the dif ferential intended currents will cancel, the non-intentional (EMI) currents will not and there will be a current indicated with a probe. Another way of de scribing the two types of current flow is shown in Figure 2.9 that shows the voltages producing the currents. In the differential case, the voltage is be tween the high voltage line and the neutral line while in the common-mode case, it is the voltage between both the high voltage and neutral lines to ground. The components for EMI suppression extend from very small beads to rather large cable clamp cores. Some and even slug-type cores toroids are used in the coil type of suppressor 2.16.1-Materials For EMI Suppression Until recently, the materials available for EMI suppression applica tions essentially were of two types. The most widely were and still are soft ferrites and the other less widely used one would be powder cores. Recently, amorphous and nanocrystalline cores have been used for the same purpose. Although sometimes the principal operational frequency of the circuit may be quite low (line or mains frequency, 50-60 Hertz), it is not primarily that fre quency which is designed for in EMI suppression. It is rather the interference or disturbance frequency that mostly determines the choice of material used although the effect of the lower frequency (DC) must be dealt with in the de sign of the EMI filter. This interference frequency frequency can be high fre quency ac or square or other digital waveform in the high Kilohertz or Mega hertz region. The secondary consideration would be the operational frequency in that the material must pass the lower frequency with sufficient inductance. This means that, at low frequencies, the material must behave as a fairly good inductor but at high frequencies, it must be quite lossy. The frequencies in volved in this application preclude any of the conventional metallic strip ma terials. Other possible new materials which will be listed later are the High Flux NiFe powder cores and the Sendust (Fe-AI-Si) powder cores. 2.16.2-Amorphous-Nanocrystalline Materials- EMI Suppression One of the earliest uses of the amorphous material was for a choke coil that Toshiba called the \"Spike-killer\". Presumably, only the cores are sold. The Fe-based amorphous materials used are under license from Allied's CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 51 l Metglas\u00ae Division (now Honeywell) . Vacuumschmelze does market a Cobased amorphous materials for EMI suppression applications. It is designated Vitrovac 6025 and is essentially a zero magnetostriction material. As an out growth of the amorphous materials, the iron-based nanocrystalline materials are the newest ones available and they have been used for EMI suppression. Their high permeabilities and low magnetostrictions made it very useful as a" ] }, { "image_filename": "designv10_13_0002015_s0263574705001670-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002015_s0263574705001670-Figure1-1.png", "caption": "Fig. 1. Parallel manipulator with prismatic actuators.", "texts": [ " Sorli et al24 conducted the dynamic modelling for Turin parallel manipulator, though the mechanism has three identical legs, it has 6-DOF. However, to the best of our knowledge, there is no efficient dynamic modelling approach available for parallel manipulator. II. INVERSE KINEMATIC MODELLING Let Ox0y0z0(T0) be a fixed Cartesian frame. A spatial manipulator with three degrees of freedom is moving with respect to this frame; the mechanism consists of four kinematical chains, including three variable length legs with identical topology and one passive constraining leg, all connecting the fixed base to a moving platform (Fig. 1). In this 3-DOF parallel mechanism, a kinematical chain, associated with one of the three identical active legs, was introduced between the base and the moving platform. It consists of a fixed Hook joint, characterized by the angular velocity \u03c9A 10 = \u03d5\u0307A 10 and the angular acceleration \u03b5A 10 = \u03d5\u0308A 10, and a moving link of length l2, mass m2 and tensor of inertia J\u03022, which has a relative rotation with the angle \u03d5A 21, so that \u03c9A 21 = \u03d5\u0307A 21, \u03b5 A 21 = \u03d5\u0308A 21. An actuated prismatic joint is as well as a moving link to the A3x A 3 yA 3 zA 3 (T A 3 ) frame, having a relative displacement \u03bbA 32, velocity vA 32 = \u03bb\u0307A 32 and acceleration \u03b3 A 32 = \u03bb\u0308A 32", " It consists of a prismatic joint attached to the base and a moving link of length l1 and mass m1, having a purely vertical displacement \u03bbD 10, velocity vD 10 = \u03bb\u0307D 10 and acceleration \u03b3 D 10 = \u03bb\u0308D 10. A Hook joint is attached to the moving platform. The moving platform is an equilateral triangle with edge l, mass m4 and tensor of inertia J\u03024. Rotations of the moving platform are defined by the angles \u03d5D 21 and \u03d5D 32 in the local coordinates (Fig. 2). The orientation of the joints A, B, C on the fixed platform (Fig. 1) is given by \u03b1A = 0, \u03b1B = 2\u03c0 3 \u03b1C = \u22122\u03c0 3 . (1) For convenience, the independent coordinates of the platform have been chosen as zG 0 , \u03b11, \u03b12, where zG 0 is the height of the platform and \u03b11, \u03b12 are the angles of the Hook joint. Assuming the passive leg D on the OD1D2D3 path, the passing matrices are derived: d10 = e\u0302, d21 = d \u03d5 21a1, d32 = d \u03d5 32a2. (2) Now, considering the OA1A2A3A4 track of the limb A, the transfer matrices are given by a10 = a \u03d5 10a1a A \u03b1 , a21 = a \u03d5 21a\u03b2a2, a32 = a1, (3) Where:25 a1 = 0 0 \u22121 0 1 0 1 0 0 , a2 = 0 0 \u22121 \u22121 0 0 0 1 0 , aA \u03b1 = cos \u03b1A sin \u03b1A 0 \u2212 sin \u03b1A cos \u03b1A 0 0 0 1 a\u03b2 = cos \u03b2 sin \u03b2 0 \u2212 sin \u03b2 cos \u03b2 0 0 0 1 , a \u03d5 k,k\u22121 = cos \u03d5A k,k\u22121 sin \u03d5A k,k\u22121 0 \u2212 sin \u03d5A k,k\u22121 cos \u03d5A k,k\u22121 0 0 0 1 (4) ak0 = k\u220f j=1 ak\u2212j+1, k\u2212j , (k = 1, 2, 3)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure11.15-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure11.15-1.png", "caption": "Fig. 11.15 Reconstruction designs of the belt drive spinning device. a An existing reconstruction concept (Zhang et al. 2004), b The first reconstruction design, c The second reconstruction design", "texts": [ " The book Nong Shu\u300a\u8fb2\u66f8\u300b(Wang 1991) has records about Da Fang Che (\u5927\u7d21\u8eca) and Shui Zhuan Da Fang Che (\u6c34\u8f49\u5927\u7d21\u8eca, a water-driven spinning device). Both devices have the same basic structures and are a kind of application of the belt drive, as shown in Fig. 11.14. Since there are many uncertain portions in the illustration, it is difficult to identify the actual numbers of its members as well as the combinations and transmission process among the members. Therefore, the belt drive spinning device is a Type III mechanism with uncertain numbers and types of members and joints. Figure 11.15a shows an existing reconstruction concept for the belt drive spinning device that helps to clarify the structure of this device (Zhang et al. 2004). The belt drive spinning device consists of the frame, two pulleys, a belt, several spindles, a yarn circle with a wooden wheel, and yarns. The driving pulley on the 260 11 Complex Textile Devices left side is operated by a person, animal, or water. The power passes through the belt to spin the yarn circle and the spindles, to complete twisting and coiling the threads", " The yarn circle is connected to the frame with a revolute joint JRx. The spindle is connected to the frame with a revolute joint JRz. 262 11 Complex Textile Devices 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 263 264 11 Complex Textile Devices The yarn is connected to the yarn circle and the spindle with wrapping joints JW. Figure 11.16b shows the structural sketch. Pulley and Yarn Circle Drive Mechanism The relevant data for the pulley and yarn circle drive mechanism is brief. The existing reconstruction concept for the belt drive spinning device shown in Fig. 11.15a is not clear as well. Therefore, the pulley and yarn circle drive mechanism has two possible structures. Each of them is presented as follows. The first possible structure consists of the frame (member 1, KF), a small pulley on the same shaft with the driven pulley (member 3, KU2), a yarn circle with a wooden wheel (member 5, KS1), and a thread (member 8, KT3). On the shaft of the driven pulley, another extra small pulley is added to coordinate with the wooden wheel. The small pulley is used to drive the wooden wheel through the thread, thereby driving the yarn circle. The small pulley is connected to the frame with a revolute joint JRz. The thread is connected to the small pulley and the wooden wheel with wrapping joints JW. The wooden wheel is connected to the frame with a revolute joint JRx. Figure 11.16c1 shows the structural sketch of the first pulley and yarn circle drive mechanism. Figure 11.15b shows the first reconstruction design. The second possible structure is based on the existing reconstruction concept, Fig. 11.15a. It consists of the frame (member 1, KF), a yarn circle with a wooden wheel (member 5, KS1), a thread (member 8, KT3), and a new added independent pulley (member 9, KU3). The belt directly rubs the newly added independent pulley. Through the thread, the yarn circle is driven to spin. The independent pulley is connected to the frame with a revolute joint JRz. The thread is connected to the independent pulley and the wooden wheel with wrapping joints JW. The wooden wheel is connected to the frame with a revolute joint JRx. Figure 11.16c2 shows the structural sketch of the second pulley and yarn circle drive mechanism. 11.2 Fang Che (\u7d21\u8eca, A Spinning Device) 265 Figure 11.15c shows the second reconstruction design. However, only using the friction between the belt and the independent pulley, the power seems to be not enough to drive the yarn circle. 11.3 Xie Zhi Ji (\u659c\u7e54\u6a5f, A Foot-Operated Slanting Loom) Xie Zhi Ji (\u659c\u7e54\u6a5f, a foot-operated slanting loom) is a typical weaving device, in which links are united with treadles and threads to weave the cloth. The basic purpose of the weaving device is to hold the warps under tension to facilitate the interweaving of the wefts. Since this device has been well-developed with broad applications in ancient China, it was popular and illustrated in many Chinese literatures with different names, such as Yao Ji (\u8170\u6a5f), Bu Ji (\u5e03\u6a5f), and Wo Ji (\u81e5 \u6a5f), etc" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003824_tmag.2012.2237390-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003824_tmag.2012.2237390-Figure3-1.png", "caption": "Fig. 3. Basic structure of the outer rotor spherical actuator.", "texts": [ " The proposed outer rotor spherical actuator consists of a stator and a rotor. In the rotor, as shown in Fig. 1, four rows of identically polarized, small spherical shell-shaped permanent magnets are placed around the Z-axis. The rows are arranged so that along the Z-axis, the N and S poles alternatively appear every 22.5 degrees. Components of the stator are shown in Fig. 2. The stator has 24 electromagnetic poles (EM poles) with 310 turn concentrated windings, which are arrayed around the Z-axis at even intervals. Fig. 3 shows the assembled structure. Generally, outer rotor motors can produce a higher torque than that of inner rotor motors of the same size. By employing this structure, high output torque can be achieved in spite of the small size. In previous research [9]\u2013[11], a simple model that uses air core coils was theoretically derived. However, as the core of Manuscript received November 04, 2012; revised December 27, 2012; accepted December 28, 2012. Date of current version May 07, 2013. Corresponding author: K" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure10-1.png", "caption": "Figure 10. Drill removes a bit from the Bit Carousel.", "texts": [ " This architecture as mentioned earlier has been developed specifically to reduce the risk associated with core acquisition and aching. Another approach developed by NASA JPL, on the other hand, focused on reducing the mass of the returned cache [10, 11]. The system components of the proposed architecture are shown in Figure 9 and include: 1. Drill 2. Sample Cache 3. Bit Carousel 4. 5 DOF Robotic Arm 5. Rock Abrasion and Brushing Tool (RABBit) The core acquisition and caching sequence takes only 4 steps as follow: 1. Drill docks with the Bit Carousel and acquires a new Bit (Figure 10). 2. Robotic Arm preloads the Drill against a target rock. The Drill commences its core acquisition operation: it drills to a target depth, breaks off and captures the core, and retracts the bit from the hole (Figure 11). 3. Robotic Arm positions the core bit in front of the camera (PanCam, HazCam etc.) and verifies the presence of the core inside the bit (Figure 12). 4. The Drill docks with the Cache. The bit with the core inside is initially inserted into the sleeve within the Cache and then screws in, creating a Hermetic seal (Figure 13)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002787_robot.2008.4543695-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002787_robot.2008.4543695-Figure3-1.png", "caption": "Fig. 3. Transforming a straight line segment path into a pivoting sequence. The pivoting sequence is planned using rotation of the endpoints of the supporting edge (left). During the regular sequence, rotations of same angles are repeated before adjustment sequence that positions the line segment at the endpoint.", "texts": [ " Let us first analyze the effective strategy used by the robot to perform an elementary pivoting motion. The robot starts inclining the box to realize a single contact point between the box and the floor. The contact point is a corner of the box. Then the robot performs a vertical rotation of the box centered at that corner. Then it sets the object horizontally along the box edge. Such an edge is said to be the supporting edge. Therefore we model the problem of 3D box pivoting as the problem of pivoting a 2D segment around its endpoints (see Fig. 3). Such a modeling does not reduce the scope of the general problem1. The computation of the pivoting sequence along a straight line segment is illustrated in Fig. 3. Let l be the length of the segment corresponding to the \u201csupporting edge\u201d and L the length of the straight line segment of the path to follow. Considering the constraint of the reachable area of robot arms, we introduce an angle \u03b2 such that the robot is able to perform an elementary pivoting motion of total angle 2\u03b2. After initializing the process by a pivoting of angle \u03b2, we then apply n times the elementary pivoting motion of angle 2\u03b2, n being defined as the greater integer verifying L > nl sin\u03b2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001897_ip-epa:20030365-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001897_ip-epa:20030365-Figure2-1.png", "caption": "Fig. 2 Cross-sectional geometry of test motor", "texts": [ " Then, with the spatial linearity property of the forces, the frequency response defines the forces for a specific whirling radius for the studied whirling frequency range. The spatial linearity property of the forces is used in this study. Analytically, the spatial linearity is shown to be valid for small values of eccentricity [5] and also numerically [14] it is shown to be valid at least until 40% eccentricities. The test machine is a 15kW four-pole cage induction motor. The main parameters of the motor are given in Table 1 and the cross-sectional geometry is shown in Fig. 2. The test motor was equipped with radial magnetic bearings to measure the forces and to generate the eccentric motions of the rotor. Only the radial bearings were installed, because the electrical machine itself acts as an axial bearing. The radial bearings were ordinary eight-pole heteropolar bearings with bias-current linearisation. Magnetic-bearing operation and the parameters of this particular bearing type are listed by Lantto [15]. The calibration of the active magnetic bearings and the measurements were done following the procedure presented in [6]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002131_j.finel.2004.04.007-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002131_j.finel.2004.04.007-Figure7-1.png", "caption": "Fig. 7. Contact region on gear flank.", "texts": [ " Linear constraint equations (ANSYS: CEINTF), which are based on the shape functions of the elements of the global model, are used to relate the nodes in a contact region to the nodes of the global model at the common interface. Finally, the degrees of freedom of the coupled FE meshes are reduced by static condensation (ANSYS: MATRIX50). Therefore, the global\u2013local approach with dense/coarse-meshed regions will not actually speed up the contact simulations in this work, but the static condensation (the process of reducing the degrees of freedom by substitution), and thereby reduce the total computation time needed to solve the non-linear contact problems. Fig. 7 shows a right tooth flank and its plane of action. For reasonable loads, the elastic deformation of the gears will be small. Therefore, the contact regions are assumed to be symmetric around the plane of action. In an arbitrary meshing position, which is defined by the global rotation angle i , the two outer points that define a contact region in an arbitrary transverse plane that is defined by the parameter winj is first approximated with the two vectors rriUnj = rrinj ( inj ( i), winj , ij ( i)) \u2212 aregb\u0302rij , rriLnj = rrinj ( inj ( i), winj , ij ( i)) + aregb\u0302rij , (57) where the parameter areg is the semi-width of the contact region and b\u0302rij = a\u0302riw,j \u00d7 a\u0302ri ,j /| a\u0302riw,j \u00d7 a\u0302ri ,j | = [\u2212 cos wtj j sin wtj 0 ]T (58) is a unit normal vector to the plane of action" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003411_iros.2011.6094663-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003411_iros.2011.6094663-Figure6-1.png", "caption": "Fig. 6. Two tangent lines l12 and l23 pass p1 and p2 respectively.", "texts": [ " Inter-section Constraints For Grasping Model 1, in the general situation where no two sections of the OctArm share the same circle, the section circles have to satisfy the following: \u2022 the section 1\u2019s circle is tangent to the section 2\u2019s circle at point p1, which is also the end point of section 1, and \u2022 the section 2\u2019s circle is tangent to the section 3\u2019s circle at point p2, which is also the end point of section 2. p1 and p2 are both on section 2\u2019s circle. Let l12 and l23 be the tangent lines going through p1 and p2 respectively, as shown in Fig. 6. They must satisfy the following two constraints: \u2022 Constraint 1: the tangent lines l12 and l23 must be coplanar. \u2022 Constraint 2: the tangent lines l12 and l23 must be on the same circle. Define two vectors along l12 and l23 respectively as the following: l12 = y1 \u00d7 (p1 \u2212 c1) (4) and l23 = y3 \u00d7 (p2 \u2212 c3) (5) where y1 and y3 are the unit vectors of the y axes of section 1 and section 3 respectively, which also represent plane normals of the two sections respectively; c1 and c3 are the position vectors of the centers of section 1\u2019s and section 3\u2019s circles respectively; p1 and p2 are the position vectors of p1 and p2 respectively, all in the robot\u2019s base frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001379_87.701355-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001379_87.701355-Figure2-1.png", "caption": "Fig. 2. The sliding surface and its associated boundary layer for the cases (a) the bang-bang compensator, (b) the saturation compensator, and (c) the smooth compensator.", "texts": [ " Since the trajectories of (11) are globally uniformly ultimately bounded and since only at the origin when , the trajectories of the system in (11) converge onto the sliding surface and are globally asymptotically stable. This concludes the proof. Remark 2: The time-varying nature of the proposed compensator guarantees the asymptotic stability of the closedloop system. This can be interpreted from the viewpoint of the sliding surface and its associated boundary layer. The bang-bang compensator has no boundary layer, as shown in Fig. 2(a), and therefore it can ensure asymptotic stability. The saturation compensator, shown in Fig. 2(b), has a boundary layer and therefore performance is enhanced at the expense of asymptotic stability. The proposed compensator, shown in Fig. 2(c), has a time-varying boundary layer whose thickness depends on and and approaches zero as time Therefore asymptotic stability can be ensured without sacrificing system performance. Remark 3: It is worthwhile to point out that the timevarying hyperbolic tangent compensator does not behave like a bang-bang compensator in the limit as . This can be explained as follows. From the proof of the theorem we know that the trajectories of are globally uniformly ultimately bounded and therefore as time becomes large, approaches a ball of radius centered at the origin" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003800_s40430-014-0133-3-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003800_s40430-014-0133-3-Figure11-1.png", "caption": "Fig. 11 Test bench 2 with AC motor, planetary gearbox and a magnetic particle break", "texts": [ " This is because in the latter only basic algebraic functions are implemented; whereas in the dynamic model, functions are calculated from the solution of the equations of motion using the HHT algorithm. \u2022 Both models are qualitative, i.e., they do not quantify the magnitude or level of failure because it depends on several parameters such as the torque transmitted, amplitude of gearmesh stiffness and damping, among others. This section presents the results from two test benches, T.B. 1 (Fig. 10) and T.B. 2 (Fig. 11). Both T.B. use the same planetary gearbox, whose parameters and frequency calculations are given in Tables 3 and 4, respectively. The only difference between both T.B. is the method used to produce the resistant torque; T.B. 1 has a DC generator that dissipates energy through a resistance bank and T. B. 2 has a magnetic particle break controlled by an input current. The seeded failure is shown in Fig. 12, there are defects affecting one tooth flank of one planet gear. The failure is modeled by a decrease in the tooth stiffness, which is due to the decrease of its width, thus affecting the gearmesh stiffness functions of the dynamic model" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002482_tmech.2006.882994-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002482_tmech.2006.882994-Figure3-1.png", "caption": "Fig. 3. Body frame and inertial frame.", "texts": [ " GPS information was available once per second and other sensory information were sampled every 10 ms. Although the complete dynamics of the Kiteplane are extensively complex, a simple rigid body model can provide useful information. In order to concentrate on the dynamics to be controlled during nominal conditions, Section III considers the case without wind disturbances. Let the body frame be a Cartesian coordinate system that is attached to the airplane with the origin located at the center of gravity (Fig. 3). The X-axis is aligned with the front of the body and the Z-axis is oriented downward when the airplane is on the ground. The Y-axis is defined using a right-hand coordinate system. Let the inertial frame be a Cartesian coordinate system that is fixed to the ground. The X-axis and the Y-axis of the inertial frame are aligned to the east and the north, respectively. The Zaxis is the perpendicular direction oriented upward. The velocity of the airplane is denoted as V CG and let UB, VB, and WB represent the components of V CG with respect to the body frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001375_1.2834123-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001375_1.2834123-Figure9-1.png", "caption": "Fig. 9 Coordinates for carriage", "texts": [ " In a preloaded LGT recirculating linear ball bearing without external force, the normal force is applied to each con tact point of the raceways and the balls in the load zone, and the normal elastic deformation occurs at each contact point. Thus each contact point has the characteristics of a spring. Since the springs exist in interval s of loaded balls, they are named \"discrete normal springs.\" The carriage is supported by the discrete normal springs that exist in the load zone of each circuit of the recirculating balls. The discrete normal spring constant is denoted by K as shown in Fig. 9. While the LGT recirculating linear ball bearing is driven at constant velocity, each contact point of the raceways and the balls change at every moment. Moreover, the total number of the balls in the load zone varies. As a result, location and number of the discrete normal springs change, and the spring constants K also vary at every moment. These changes should be considered for theoretical analysis on the rigid-body natural vibration of the carriage. However, it is very difficult to consider these changes from a theoretical point of view", " 4>, 6 and i// are the angular displacements of the carriage around the x-, y-, z-axis, respectively, a is the distance from the origin o to the contact point of the upper circuits of the recirculating balls of the car riage and the distributed normal spring in the direction parallel to the z-axis. b is the distance from the origin o to the contact point of the lower circuits of the recirculating balls of the car riage and the distributed normal spring in the direction parallel to the z-axis. c is the distance from the origin o to the contact point of the carriage and distributed normal spring in the direc tion parallel to the ji-axis. The other symbols are as in Fig. 9. When the carriage supported by the distributed normal springs vibrates in rigid body mode, the kinetic energy E^ can be ex pressed as: EK = \\Ma'^ + |Mt)2 + \\j,^'^ + \\jy'e^ + yjij'^. (16) The potential energy Ep can be given by: 1 r'''2 Ep = - k \\ [[(u \u2014 acf) + lijj) cos a 2 Jo + (-V - c(f) + 19) s ina}^ -I- [{u \u2014 a4> - lift) cos a + {-V - c4i - 16) sin a]^ -I- {{u \u2014 b(f) + lip) cos a + {v + c ~ W) sin aY + [(u \u2014 b(j) \u2014 lifi) cos a + (i) -I- c 0 + W) sin a}^ + {(-M + a4> - lip) cos a -t- {-V + c(p + 16) sin a}^ + {(-M + a(/) + l^) cos a + (-1) + c(f> - 19) sin a}^ + [(\u2014u + b4> \u2014 lip) cos a + {v - c4> \u2014 16) sin a}^ + { ( - \u00ab + b(j) + lip) cos a + (v - c4> + 16) sin a)^]dl k\\ 2u% - 2(j>u(a + b)lL + (t>Ha^ + fo')/i, + - i / ' ' [ c o s = a + 2k{a \u2014 b)c4>^li sin a cos a + k(2v% + 2c^\\ + - 6^ sin^ a" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002222_095440605x31436-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002222_095440605x31436-Figure1-1.png", "caption": "Fig. 1 Hybrid planar\u2013spherical 7R mechanism with two d.o.f.", "texts": [ " In terms of general Grubler\u2013Kutzbach formula, these DM mechanisms generally have one global d.o.f. Any computer animation software, such as Working Model 3D [16], can confirm their constrained motion. However, in these DM mechanisms, the relative motion set between two specific links is not a one-dimensional manifold but the union of two one-dimensional manifolds. For further confirmation in the sequel, a group-theoretical approach will be used to discuss or illustrate the discontinuous mobility of these mechanisms. A hybrid planar\u2013spherical 7R mechanism is shown in Fig. 1. First, take one planar 4R-chain loop A-BC-D with four parallel axes z1, z2, z3 and z4 and one spherical 4R-chain loop G-F-E-D with four concurrent joint axes z1 0, z20, z30, and z4 0 at a point O. z1, z2, z3, and z4 are determined by (A,u), (B,u), (C,u), and (D,u) and z1 0, z2 0, z3 0, and z4 0 are determined by (O,uz1 0), (O,u0 z2 ), . . ., etc. Intentionally make coaxial two separate revolute joints. Then the common axis is determined either by (D,u) or by (O,uz4 0). For simplicity and convenience, let revolute joint axes (A,u) and (G,uz1 0) intersect. Meanwhile, one of the two coaxial revolute joints must be removed at D and link AD in the planar chain and link DG in the spherical chain in order to synthesize a hybrid A-BC-D-E-F-G 7R mechanism with two d.o.f. Furthermore, Fig. 2 introduces a new DM 7R chain, which is derived from the previous continuously movable hybrid mechanism. The DM chain of Fig. 2 has the same geometric arrangement of joint axes as the 7R chain in Fig. 1. However, with a little different process cited earlier, all link lengths and link twists from any two adjacent revolute axes can be constructed by determining the normal distance between two skew lines [17], z1 and z1 0, z10 and z2, z2 and z2 0, z20 and z3, z3 and z3 0, z30 and z4 0, and z4 0 and z1. Thus the synthesized mechanism is a hybrid planar\u2013spherical A-G-B-F-C-E-D 7R mechanism with discontinuous mobility. A hybrid planar\u2013spherical 7R chain in Fig. 1 exhibits two possible motion modes, planar and spherical motions, when the distance between joints A C23403 # IMechE 2005 Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science at The University of Iowa Libraries on May 29, 2015pic.sagepub.comDownloaded from and D is fixed. In this situation, two motions are respectively independent; that is, planar motions do not affect spherical motions at the same time. If removing or ignoring the revolute pair D in this chain loop, a planar\u2013spherical 6R mechanism with one d.o.f. can be recognized. This mechanism includes a mechanical generator of the subgroup fG(u)g of planar gliding perpendicular to u. The generator is made of three revolute pairs at A, B, and C with three axes parallel to u. The mechanism of Fig. 1 also includes a mechanical generator of the subgroup fS(O)g of spherical rotations about O. This generator consists of three revolute pairs G, F, and E with converging axes at O. At the same time, motion of link 3 relative to link 7 has to be planar and spherical and therefore is represented by the intersection set fG(u)g > fS(O)g \u00bc fR(O,u)g. Hence, the mobility of this 6R chain is generally continuous with one d.o.f. of finite motion. This type of overconstrained mobility, which can be explained by the intersection of two displacement subgroups is said to be exceptional; see reference [13]. Furthermore, when the pair at D in Fig. 2 is also removed, the resulting kinematic chain with 6R has the same arrangement of joint axes as that of the aforementioned 6R exceptional chain. The infinitesimal, local, or instantaneous mobility still has one d.o.f. but generally finite relative motion cannot happen. The true d.o.f. is zero except for the special case of symmetrical arrangement of paradoxical chain of Bricard form. To sum up, the kinematic chain of Fig. 1 has two global d.o.f., which can readily be explained as follows. When any one pair among the seven revolute pairs is locked, the resulting mechanism has one d.o.f. For example, if the revolute pair in A is locked, then a planar\u2013spherical 6R linkage with one d.o.f. As a matter of fact in any resulting linkage, a regular generator of planar motion and a regular generator of spherical motion is obtained. \u2018Regular\u2019 means without superfluous passive mobility in the generation of planar motion and spherical motion", " Using set theory notations, it can be written as {L(7,5)} $ {R(D,u)}< {1=S(O)} No sub-chain is a generator of another subgroup of displacements except the possible generation of the improper subgroup fDg by a sequence of six R pairs. In fact, locally in the singular pose, fR(A,u)gfR(G,uZ2 )gfR(B,u)gfR(F,uZ4 )gfR(C,u)g fR(E,uZ6 )g = fDg. As a matter of fact a product of six one-dimensional subgroups cannot be sixdimensional if the linear span of the twists that represent allowed infinitesimal displacements is not six-dimensional. From the analysis of Fig. 1 mechanism, it is known that the vector space of twists is five-dimensional. Hence, locally in the singular pose, fL(7,5)g \u00bc fR(D,u)g < f1/S(O)g. The bond fL(7,5)g has a bifurcation towards two working modes starting from the singular pose. However, any mechanism working in each of its two possible modes destroys the local linear dependency of the six R twists. After any working, the mechanism becomes a truly spatial 7R linkage, i.e. includes a generator of the six-dimensional group fDg and therefore the bond fL(7,5)g can become an one-dimensional manifold in fDg" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001885_1.1518502-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001885_1.1518502-Figure3-1.png", "caption": "Fig. 3 \u201ea\u2026 Cutter edge variations for tooth height direction correction \u201eb\u2026 Cutter edge geometry for pinion generation \u201ec\u2026 Cutter edge geometry for gear generation", "texts": [ "org/ on 01/28/20 are considered in two directions on the gear tooth surface either along the length of the pinion tooth, or along its height. Varying the radius of the head cutter carries out tooth length corrections ~Fig. 2!. Thus the curvature of the longitudinal shape of the convex side of the generating crown gear is modified. The curvature increases while the radius is reduced. This also changes machining distance ~Fig. 1!. A curved cutter edge is then introduced, as opposed to the originally straight-line cutter edge, in order to modify the height of the tooth surface ~Fig. 3~a!!. Due to the remaining conjugated points, the contact between a base tooth surface ~gear tooth surface! and a corrected tooth surface ~pinion tooth surface! in length direction or in height direction supports zero kinematics error. Regarding tooth length correction, the contact areas are located across the surface. On the contrary, for tooth height corrections, longitudinal contact areas appear. The conjugated line contact area becomes a point contact area if the tooth surface is modified in both directions and only one conjugated point ~mean point", " Above certain extreme values, the rotation of the cutter edge can cause a kinematics jump @15#, thus rotation limits are also presented to prevent this. 002 by ASME DECEMBER 2002, Vol. 124 \u00d5 761 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F The purpose of this paper is to take into account influences of actual cutting parameters and make comparisons of various machine-setting modifications in order to achieve contact optimization and to define a flexible design method for epicycloidal Klingelnberg spiral bevel gears. 2.1 Pinion Generation. Index 1 related to the pinion. The geometry of the cutter edge ~Fig. 3~b!! is described in the coordinate system Sb1, the generating point P of the cutter edge is 762 \u00d5 Vol. 124, DECEMBER 2002 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 represented by the radius vector rb1(t). The co-ordinate system Sb1 is rotated around axis zt1 with the sum of angles n and k. Angle n is a basic angle when the cutter edge plane is directed towards the instantaneous axis I of rotation ~Fig. 2!. The auxiliary co-ordinate system, St1, is rigidly connected to the co-ordinate system Sh1 of the head cutter ~i51 in Fig", " Pinion co-ordinate system S1 rotates simultaneously about axis zw1, with angle ca1. The installation position of coordinate system Sw1, in relation with co-ordinate system Sm , is determined by pitch angle d1 , measured clockwise. The relation between these two angles, c1 , ca1, is given in Eq. ~2!. The instantaneous axis of rotation is the axis ym . c1 ca1 5sind1 (2) rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 2.2 Gear Generation. Index 2 related to the gear. The gear cutter edge geometry is presented in the co-ordinate system Sb2 ~Fig. 3~c!!. The generation of the resulting crown gear surface is achieved in a similar way to that of the pinion ~i52 in Fig. 4~a!!. The generating crown gear generates the tooth surface ~Fig. 4~c!! and the co-ordinate system Sc2 rotates about axis zm by angle of rotation c2 . Gear co-ordinate system S2 rotates simultaneously about axis zw2, with angle ca2. The installation position of Sw2, with respect to Sm , is determined by pitch angle d2, measured counter-wise. The relation between these two angles, c2 , ca2, is given by Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.20-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.20-1.png", "caption": "Fig. 7.20 Simulation illustration of a horizontal-wheel water-driven wind box (Hsiao et al. 2010)", "texts": [], "surrounding_texts": [ "There are four devices with linkage mechanisms that can not be classified under the above mentioned three types, including Feng Xiang (\u98a8\u7bb1, a wind box), Shui Pai (\u6c34\u6392, a water-driven), Shui Ji Mian Luo (\u6c34\u64ca\u9eab\u7f85, a water-driven flour bolter), and Tie Nian Cao (\u9435\u78be\u69fd, an iron roller). Each of them is described below: 7.4.1 Feng Xiang (\u98a8\u7bb1, A Wind Box) Feng Xiang (\u98a8\u7bb1, a wind box) is a common device for blast metallurgy in ancient China as shown in Fig. 7.15a (Pan 1998). The operator pushes the piston of the device to increase air pressure, thereby opening and closing the valve. It can provide successively higher wind pressure and wind volume to enhance the intensity of the metal and increase production. Feng Xiang is a planar mechanism with two members and one joint, including a box as the frame (member 1, KF) and a pushing rod outside the box with the piston inside. The pushing rod is connected to the piston as an assembly (member 2, KP). 7.3 Grain Processing Devices 155 The piston is connected to the frame with a prismatic joint JPx. It is a Type I mechanism with a clear structure. Figure 7.15b shows the structural sketch. 7.4.2 Shui Pai (\u6c34\u6392, A Water-Driven Wind Box) Nong Shu\u300a\u8fb2\u66f8\u300b(Wang 1991) shows another device for blast metallurgy in ancient China namely Wo Lun Shi Shui Pai (\u81e5\u8f2a\u5f0f\u6c34\u6392, a horizontal-wheel water-driven wind box) as shown in Fig. 7.16. The function of the device is to transmit water power through its linkage mechanism for wind blasting. The structure and the transmission process are explained as follows: A vertical shaft contains the upper and lower horizontal wheels. One half of the lower wheel is installed under the water, and both wheels are fixed to the shaft. The upper wheel is encircled by a rope. The rope also passes around the wooden cylinder with a crank. The connected link is attached to the crank and the left bar. The horizontal shaft is connected to the left and right bars as an assembly. The long rod is connected to the right bar and the wooden fan of the blast furnace. When flowing water spins the lower wheel, through the drive of the vertical shaft, the upper wheel spins as well. The motion is transmitted via the thick rope to the wooden cylinder with a crank. The crank drives the connecting link and the left bar of the horizontal shaft. The right bar pushes the long rod to generate the oscillating motion of the wooden fan for blasting wind into the box (Liu 1962). There are many illogical or unclear parts in the illustration of the device, such as the rope (member 3) on the wooden cylinder (member 4) is too thick, the crank (member 4) is located in the wrong position, the connecting link (member 5) has unclear joints on both ends, and the long rod (member 7) passes over the left bar (member 6). Figure 7.17 shows the result of the reconstruction design by Liu Xianzhou (\u5289\u4ed9\u6d32, AD 1890\u20131975) (Liu 1962). Although some of the unclear structure 156 7 Linkage Mechanisms have been solved, such as, making the diameter of the rope thinner, adjusting the position of the crank, solving the problem of the long rod passing over the left bar, and assigning the two revolute joints on both ends of the connecting link. However, for the connecting link, how the two assigned revolute joints can transform the rotating motion of the crank into the oscillating motion of the left bar is still unclear. According to the classifying method described in Chap. 5, the device is a Type II mechanism with uncertain types of joints. The rectangular coordinate system is defined as shown in Fig. 7.17. The x-axis is defined as the direction of the axle of the horizontal shaft, the y-axis is defined as the direction of the diameter of the horizontal shaft, and the z-axis is based on the right-hand rule. The device can be divided into three parts: a rope and pulley mechanism, a spatial crank and rocker mechanism, and a planar double rocker mechanism (Hsiao et al. 2010). Each of them is explained below: 1. The rope and pulley mechanism includes the frame (member 1, KF), a vertical shaft with the upper and lower wheels (member 2, KU1), a rope (member 3, KT), and a wooden cylinder with a crank (member 4, KU2). The vertical shaft is connected to the frame (KF) and the rope (KT) with a revolute joint JRy and a wrapping joint JW, respectively. The wooden cylinder (KU2) is connected to the rope (KT) and the frame (KF) with a wrapping joint JW and a revolute joint JRy, respectively. Figure 7.18a shows the structural sketch. 2. The spatial crank and rocker mechanism includes the frame (member 1, KF), a wooden cylinder with a crank (member 4, KU2), a connecting link (member 5, KL1), and a horizontal shaft with the left and right bars (member 6, KL2). The wooden cylinder (KU2) is connected to the frame (KF) with a revolute joint JRy. The connecting link (KL1) is connected to the wooden cylinder (KU2) and the horizontal shaft (KL2) with uncertain joints J\u03b1 and J\u03b2, respectively. The 7.4 Other Devices 157 horizontal shaft (KL2) is connected to the frame (KF) with a revolute joint JRx. Figure 7.18b shows the structural sketch. 3. The planar double rock mechanism includes the frame (member 1, KF), a horizontal shaft with the left and right bars (member 6, KL2), a long rod (member 7, KL3), and a wooden fan as the output link (member 8, KL4). The horizontal shaft (KL2) is connected to the frame (KF) and the long rod (KL3) with revolute joints JRx. The wooden fan (KL4) is connected to the long rod (KL3) and the frame (KF) with revolute joints JRx. Figure 7.18c shows the structural sketch. The function of the spatial crank and rocker mechanism is to transform the rotating motion of the crank (member 4, KU2), through the drive of the connecting link (member 5, KL1), to the oscillating motion of the horizontal shaft (member 6, KL2). The two joints on both ends of the connecting link have multiple possible types that could achieve the function mentioned above. Considering the types and the directions of motion of the connecting link and the crank, uncertain joint J\u03b1 has three possible types: the first one is that the connecting link is connected to the crank with a revolute joint JRxy; the second one is that the connecting link is connected to the crank with a spherical joint JRxyz; and the last one is that the connecting link is connected to the crank with a joint JPzRxy. Considering the types and the directions of motion of the connecting link and the left bar, uncertain joint J\u03b2 has three possible types: the first is that the connecting link is connected to the left bar with a revolute joint JRxy; the second is that the connecting link is 158 7 Linkage Mechanisms connected to the left bar with a spherical joint JRxyz; and the third is that the connecting link is connected to the left bar with a joint JPzRxy. By assigning the possible joints J\u03b1(JRxy\u3001JRxyz\u3001 JPzRxy) and J\u03b2(JRxy\u3001JRxyz\u3001 JPzRxy) into the structural sketch shown in Fig. 7.18b, nine results are obtained. However, when joints J\u03b1 and J\u03b2 are of the same type JRxy simultaneously, the device would fail to move. By removing such a case, eight feasible designs of the horizontal-wheel water-driven wind box are obtained as shown in Figs. 7.19a\u2013h. Figures 7.20 and 7.21 show the simulation illustration and the prototype of the horizontal-wheel water-driven wind box according to the design shown in Fig. 7.19g. 7.4.3 Shui Ji Mian Luo (\u6c34\u64ca\u9eab\u7f85, A Water-Driven Flour Bolter) Shui Ji Mian Luo (\u6c34\u64ca\u9eab\u7f85, a water-driven flour bolter), as shown in Fig. 7.22a (Wang 1991), has the same function as Mian Luo (\u9eab\u7f85) described in Sect. 7.3. 7.4 Other Devices 159 160 7 Linkage Mechanisms The structure of Shui Ji Mian Luo is similar to the horizontal-wheel water-driven wind box, but it replaces the long rod, wooden fan, and blast furnace on the horizontal-wheel water-driven wind box into the connecting link with a floursieving screen, rope, and box, respectively. It is a Type II mechanism with uncertain types of joints. This device can be divided into three parts: a rope and pulley mechanism, a spatial crank and rocker mechanism, and a connecting link and rope mechanism. Shui Ji Mian Luo sieves grains through the reciprocating motion of the connecting link with a flour-sieving screen (member 7). Figures 7.22b1\u2013b8 show the feasible designs of the water-driven flour bolter. 7.4 Other Devices 161 7.4.4 Tie Nian Cao (\u9435\u78be\u69fd, An Iron Roller) Tie Nian Cao (\u9435\u78be\u69fd, an iron roller), as shown in Fig. 7.23a, is mainly used to grind cinnabar ore. People use the device to grind ore into powder for the red color dye (Pan 1998). The reconstruction design of Tie Nian Cao is described in Sect. 5.3. It is a (3, 3) planar mechanism and is a Type II mechanism with uncertain types of joints. Figures 7.23b1\u2013b3 show the feasible designs of the iron roller." ] }, { "image_filename": "designv10_13_0002307_s00542-006-0303-z-Figure14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002307_s00542-006-0303-z-Figure14-1.png", "caption": "Fig. 14 A planar structure for assembling a microcube", "texts": [ " The plates were completely coated with polyimide film since longer lengths of polyimide film result in larger bending angles. Figure 12 shows the side profile of several plates connected by polyimide hinges after 90 min heating at 500 C. The measured bending angles h1 \u2013 h6 are shown in Fig. 13. The results show that the bending angles are almost the same regardless of the number of plates. The average bending angle is 35.2 and the standard deviation is 2.6 . By utilizing the properties of the polyimide hinges ascertained by these experiments, microcubes were assembled to demonstrate this self-assembly method. Figure 14 shows a schematic view of a planar structure for assembling a microcube, which consists of five movable plates and a fixed plate connected by polyimide hinges. It was heated for 90 min at 500 C in a furnace to produce 90 C rotation of each plate. Furthermore, the assembly process was observed using the experimental set up shown in Fig. 15. For visualization, the hinged structure was heated locally using a far infrared heater so that a CCD camera could be set up in close proximity to the structure" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002781_e2008-00637-7-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002781_e2008-00637-7-Figure1-1.png", "caption": "Fig. 1. The construction scheme of the three-ball swimmer: the balls are spinning around the in-plane axes so that the angular velocities \u03c91 + \u03c92 + \u03c93=0. A simulation snapshot on the right hand side illustrates the raspberry model implementation of the swimmer.", "texts": [ " One should note, however, that on the nanometer and micrometer scale the thermal fluctuations are expected to compete with the propulsion mechanisms and, therefore, the interplay between the swimming and dissipation processes is of great interest [20\u201325]. In this work, we report on general dynamic properties of a microswimmer at finite temperatures. For our study we chose a simple model swimmer, consisting of three spheres with their centers comprising an equilateral triangle. The distances between the spheres are fixed. a e-mail: lobaskin@tum.de To impose propulsion, we make the spheres spin via applied constant torque. We arrange the torque directions as shown in Fig. 1a so that the net torque is always zero. This constraint mimics the rotation due to internal degrees of freedom, as it would be in case of a microorganism swimming. At the same time, the algorithm allows us to keep control over the amount of supplied energy. The dynamics of the three-ball animals was modeled numerically using a hybrid molecular dynamics/ Lattice Boltzmann (LB) simulation method [26,27]. The spheres were modeled with the raspberry setup (a tethered network of small Lennard-Jones (LJ) beads wrapped around a big bead) [27]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003279_cbo9780511778025.003-Figure2.3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003279_cbo9780511778025.003-Figure2.3-1.png", "caption": "Figure 2.3. A fixed-time impulsive rendezvous trajectory.", "texts": [ "1017/CBO9780511778025.003 Downloaded from http:/www.cambridge.org/core. University of Liverpool Library, on 25 Dec 2016 at 07:34:25, subject to the Cambridge Core terms of use, available at occurs. In the latter case, the rendezvous actually occurs before the final time, and the spacecraft coasts along the final orbit until the final time is reached. To determine when a terminal coast will result in a trajectory that has a lower fuel cost, consider the two-impulse fixed-time rendezvous trajectory shown in Figure 2.3. In the two-body problem, if the terminal radii ro and rf are specified along with the transfer time \u03c4 \u2261 tf \u2212 to, the solution to Lambert\u2019s Problem [10] [11] provides the terminal velocity vectors v+o (after the initial impulse) and v\u2212f (before the final impulse) on the transfer orbit. Because the velocity vectors are known on the initial orbit (v\u2212o before the first impulse) and on the final orbit (v+f after the final impulse), the required velocity changes can be determined as vo = v+o \u2212 v\u2212o (2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003721_icmech.2011.5971317-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003721_icmech.2011.5971317-Figure2-1.png", "caption": "Fig. 2 Kinematic model of the universal joint", "texts": [ " The velocity of the th platform connection point L; can be obtained by taking the derivative with respect to time on both sides of Equation (5), which yields: L; = COli X lin; + i;n; (9) The acceleration of the ith platform connection point L; can be determined by taking the second order derivative with respect to time on both sides of Equation (5), which yields: L; = ali x lin; + COli x (COli x l;n;) + 2COli x i;n; + i;n; (10) where a Ii is the angular acceleration of the th pod. C. Angular Velocities and Accelerations of the Pods . .. Our knowledge of I; and I; shows that we still cannot solve Equation (9) for COli and Equation (10) for ali' since 3x3 systems of the linear equations that result from the expanding Equations (9) and (10) are not full rank. Therefore, in order to determine co Ii and a Ii , we need to use the kinematic model of the universal joint (Fig. 2). In the dynamic equations of references [5-15], the assumption that the angular velocity and acceleration of each pod are perpendicular to the direction of the same pod (i.e. COli' n; = 0 and ali' n; = 0 ) sounds inaccurate. This is simplifying approximation and may be true only at the instant when there is no rotation about the axial direction. An exact solution can be obtained by considering the rotational degree of freedom of the pods around the axial direction. The unit vectors u;, v; and c; indicate the kinematic model of the universal joint, and the unit vectors n;, v; and c; indicate the fixed pod frame. The unit vector u; along the fixed axis of the universal joint can be obtained from the geometry of the mechanism. The unit vector v; along the other revolute joint axis of the universal joint rotates in a plane normal to u;, and it is also normal to n;. The unit vector c; is normal to the two axes of rotation of the universal joint and the unit vector c; is nonnal to the vectors Bi and Vi . As shown in Fig. 2, the angular velocity of the lh pod can be resolved into two components along the two axes ui and Vi of the universal joint, and can be defmed as: the component of au along the direction of the pod. The vector ani can be expressed as: ani = {Bi x Li - Bi X [rou x (rou x liBi) + 2ro/i x iiBi ]}/li (22) Equaling Equations (17) and (21), and taking the dot product on the two sides of the resulting equation with ui, (11) gives: components of roli along the revolute joint axes ui and Vi' and can be expressed as: Wui = -(Li -iiBi) " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001488_jf970354i-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001488_jf970354i-Figure1-1.png", "caption": "Figure 1. Plot representing the construction and assembly of the double-membrane tubular potentiometric detector sensitive to iodide: (A) the shielded cable is attached to a silver plate; (B) the membrane is glued to the silver disk with a silver-based epoxy resin; (C) the membranes are housed in a double-perspex cylinder, 3 mm apart, and a hole is drilled at the membrane center; (D) the sensor module is set in a rectangular perspex block for incorporation in the FIA system.", "texts": [ " Construction and Evaluation of the Tubular Potentiometric Detector. The iodide-sensitive potentiometric detectors were constructed as previously mentioned (Couto et al., 1997), using two homogeneous crystalline membranes 3 mm apart. The sensor for membrane preparation consisted of a mixture (1:1) of silver iodide/silver sulfide. The membranes were prepared by pressing 0.25 g of the pulverized sensor at 19 000 kg cm-2, producing a disk with 10 mm diameter and 0.4 mm thickness. For detector construction (Figure 1), a rectangular silver plate (2 \u00d7 4 mm) was soldered to the inner conductor of a shielded electric cable and glued with conductive silver epoxy resin to a square membrane. After this dried, each membrane was placed in the rectangular cavity (3 \u00d7 4.5 \u00d7 7.5 mm) of a perspex cylinder and filled with a nonconductive epoxy resin. After hardening, the set was drilled (0.8 mm channel) through the center of the two membranes. The surface of the sensor membrane was restored, whenever the slope diminished, by polishing with a damp cotton thread with aluminum oxide (Buehler 40-6603-030-016) followed by conditioning for a few hours in a 1 \u00d7 10-3 M potassium iodide solution" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001554_s0094-114x(98)00070-6-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001554_s0094-114x(98)00070-6-Figure7-1.png", "caption": "Fig. 7. Both plates are non-regular.", "texts": [ " But the angles between the three lines passing through the three vertices should be successively equal to the corresponding exterior angles of the stationary triangle. The mechanism is singular when the three lines of the star frame are parallel to the three sides of the base, respectively. Triangle A1A3A5 is non-regular. The angles are A1=458, A3=758, A5=608. The moving triangle is B1B3B5. The star frame passing through the three vertices inside the moving triangle is set, making the angles B1PB3=1358, B3PB5=1058, and B5PB1=1208. The mobile is located as shown in Fig. 7. Without loss of generality, the point P lies just over point A1. These points' coordinates are A1 1; 0; 0 T; A3 0; 1; 0 T; A5 \u00ff0:577350; 0; 0 T; B1 1:2; 0; 1 T; B3 0:5; 0:5; 1 T; B5 0:5; \u00ff0:866025; 1 T: Then the Plu\u00c8 cker linear coordinates of the six lines associated with the six links are $1 0:196116; 0; 0:980581; 0; \u00ff0:980581; 0 ; $2 0:871525; 0; 0:490351; 0; 0:283104; 0 ; $3 \u00ff0:408248; 0:408248; 0:816497; 0; \u00ff0:816497; 0:408248 ; $4 0:408248; \u00ff0:408248; 0:816497; 0:816497; 0; \u00ff0:408248 ; $5 0:229851; \u00ff0:857814; 0:459701; 0:459701; 0; \u00ff0:229851 ; $6 0:631480; \u00ff0:507613; 0:586142; 0; 0:338410; 0:293070 : The Jacobian matrix of the six screws with zero pitch is J3= [$1 $2 $3 $4 $5 $6]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003752_001872086300500106-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003752_001872086300500106-Figure4-1.png", "caption": "Fig. 4. Free-body diagram isolating elements and showing forces and torques on each element.", "texts": [ "comDownloaded from 62 - February, 1963 H U M A N F A C T O R S Substitution of the above equations into the equation for A-, leads to arm-hand gravity center, relative to the elbow axis. .. A, = SE = Ok * [(SE,) i+(SEy)j]+ +& *{&*[(SE,)i+(SEy)j]) A, = SE = -[O(J'Ey)+(e)2(SE,)]i+ These in turn are added vectorially to the elbow acceleration components : + [WE*) -(@2(sEy)lJ7 A,, = +A,,+A,,, (19) A, = Auy+Acey (20) which lead to inertial forces of the forearm-hand combination. Sf,, = -(Wc/981.0)Ac, (21) Sfcy = -(Wc/981.0)Ac,, (22) From the free body diagram (Fig. 4) it is evident that Rex = -ffccx (23) Bey = -qcy+ Pc (24) and approach simplifies programming. The graphical representation of the acceleration analysis is found in Fig. 3. To continue the force analysis, the values from equations (1 1) and (12) are used to determine the components of inertial force at the center of gravity of the upper arm. Sfux = -(W,/981) A-,,(Sc.g.,/SE) (13) Sfuy = -(W,/981)Auy(S~.g.,/SE) (14) A similar procedure is followed with the forearm-hand. Components of the distance from the elbow axis to the center of gravity of the forearm-hand combination are expressed as EG,, = (EG,) sin(bi (15) EG, = - (EG," ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003930_cjme.2012.01.071-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003930_cjme.2012.01.071-Figure1-1.png", "caption": "Fig. 1. Coordinate systems for angular contact ball bearings", "texts": [ ", the centrifugal force or the gyroscopic moment due to the orbital circulation of the ball about the centerline of the bearing. Anyway, the centrifugal force and the gyroscopic moment can be conveniently imposed onto the balls if necessary. In terms of the specific operating condition, the global coordinate system for motion and force/moment balance analysis of the ball bearing and the local coordinate systems for relative slip and tractive action between its components are diagrammatically represented in Fig. 1. A local coordinate system is separately presented in Fig. 2 to illustrate the definition of rolling contact problem and the mathematical method to solve it. All these are right-hand coordinate systems and are summarized in Table. The rolling contact of elastic bodies with friction is extremely complicated. One task of rolling contact analysis is to find the intrinsic coupling mechanism that connects the relative motions of two contacting bodies with the interactions imposed by one another. Part I: Theoretical Formulation \u00b774\u00b7 CHEN Wenhua, et al: Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Table" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001486_s0921-8890(01)00171-3-Figure21-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001486_s0921-8890(01)00171-3-Figure21-1.png", "caption": "Fig. 21. The behavior of a two-cluster system initialized on the increasing part of g. As before, the system forms a stable configuration of two clusters of the same size.", "texts": [ " In this subsection, we assume that the magnitude of the slope of region 1 is smaller than that of region 2. Fig. 20 illustrates the behavior of the system of two clusters both initialized on the decreasing side of g. In this case, the system has two possible stable outcomes. In the first, the pucks are completely absorbed by the larger cluster, yielding one final culster (Fig. 20(a)). In the second case (Fig. 20(b)), the slope of the second region is sufficient for the g value of the larger cluster to \u201ccatch up\u201d to that of the smaller cluster, yielding a stable configuration. Fig. 21 illustrates the behavior of a system of two clusters initially in the increasing region of g. As before, this system forms a stable configuration of two clusters with the same size. In Fig. 22, we give the evolution behavior of the system of two clusters initially on different sides of the minimum in g in which the larger cluster has a smaller g value than the smaller. This produces two different results depending on the relative slopes and positions of the clusters. In the first behavior, the slope on the increasing side is large enough that the g value of the larger cluster \u201ccatches up\u201d to that of the smaller" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002468_j.jmatprotec.2005.02.202-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002468_j.jmatprotec.2005.02.202-Figure5-1.png", "caption": "Fig. 5. Discrete phenomenological model of the robot with the points of coincidence distances from the mass centres of the inertial elements in the first working position.", "texts": [], "surrounding_texts": [ "f these programs is GRAFSIM, which was implemented in E-mail address: grzegorz.wszolek@polsl.pl. The ABB 4400/60 is a compact robot with medium to heavy handling capacity. It can handle loads up to 60 kg, or 924-0136/$ \u2013 see front matter \u00a9 2005 Elsevier B.V. All rights reserved. oi:10.1016/j.jmatprotec.2005.02.202 up to 45 kg at very high speeds. It can be used for material handling, machine tending, grinding, polishing, scaling, gluing, assembly, spraying and cutting. In the manufacturing industry, there are a lot of tasks involving transfer of parts and components to and out from machine tools and other machinery. In the food and beverage industry, products are to be picked, packed into cases and the cases to be palletized. In warehouses and in post terminals, there are parcels to be packed into containers. Robots are well suited for all of these tasks. They can relieve humans from tedious tasks or replace special built machinery, which is inflexible if new or redesigned parts are to be handled [9]. Fig. 1 presents a picture of a mentioned ABB 4400/60 robot, and Figs. 2 and 3 present movement possibilities and its main dimensions. Two positions of the robot arms were accepted for numerical analysis and are presented on Figs. 5 and 6. There are constraints in the robot joints, which, in an accepted model, are represented by damping-elastic elements (11\u201316), characterised by stiffness and linear and angular suppression. In the robot model, two kinematic excitations (7,8) were considered. They come from ground tremblings, where the robot is situated and from the work of different 1. Phenomenological model of a mechanical system has been accepted in the following form: system (Figs. 5 and 6) is considered as two-dimensional with: \u2022 six inertial elements (Fig. 4), such as: - robot basis, - column of the robot, - arm, - counterbalance, - connecting rod, - mount of the gripper; \u2022 seven elastic-damping elements (Figs. 5 and 6); \u2022 two kinematic and one dynamic excitations (Figs. 5 and 6). 2. Masses and inertial elements moments of inertia of the accepted model of the system (Table 1), the linear and angular elasticity of the elastic elements and the linear and angular suppressions of the damping elements (Table 2). 3. The local co-ordinate systems of inertial elements, elasticdamping elements and kinematic and dynamic excitations (Figs. 5 and 6). 4 5 . The attachment co-ordinates of elastic-damping elements in local co-ordinate systems of inertial elements, with which they are incident and angles between co-ordinate systems of elastic-damping elements and inertial elements (Figs. 5 and 6). . Attachment co-ordinates of dynamic excitation in local co-ordinate system of inertial element, with which it is in- cident and angles between co-ordinate system of dynamic excitation and that inertial element. 6. Angles among kinematic excitations co-ordinate systems and elastic-damping elements. 7. Numbers of all elements of modelled dynamic system in following order: - inertial elements, - kinematic excitations, - elastic-damping elements, - dynamic excitations. 8. Rotation movements of the robot in relation to the one, four and six axes have been rejected (Figs. 5 and 6) (robot can move only in relation to the two, three, five axes)." ] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure1-1.png", "caption": "Fig. 1. Tool surface (for tooth convex side).", "texts": [ " In this paper we follow the recently introduced invariant approach [16] and we briefly review the main steps here. In the Euclidean space E3 e we define the generating tool as a regular surface Re and we indicate its generic point by Pe\u00f0n; h\u00de, with \u00f0n; h\u00de 2 A R2. Let Oe be a fixed point on the rotation axis of the tool, then it is possible to associate each point Pe of E3 e to a position vector pe 2 R3 as follows: pe\u00f0n; h\u00de \u00bc Pe\u00f0n; h\u00de Oe: \u00f01\u00de By definition the normal vector me to Re is given by me\u00f0n; h\u00de \u00bc pe;n pe;h: \u00f02\u00de Fig. 1 shows the generating tool surface Re together with the defined quantities. For a more detailed description of the tool surface, see for instance [11]. We define another Euclidean space E3 g and a 1 The tuning process is automatic. one-parameter family of surfaces Ug whose envelope Cg we are interested in. It is given by a sequence of surfaces Rg\u00f0/\u00de isomorphic to Re. If Pg represents the generic point on Ug , then the associated position vector pg is given by pg \u00bc Pg Og ; \u00f03\u00de where Og is a point on a fixed rotation axis in E3 g " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001384_978-94-017-2925-3-Figure5.8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001384_978-94-017-2925-3-Figure5.8-1.png", "caption": "Fig. 5.8. Gehman low-temperature testing apparatus (ASTM 01053). A-torsion head, B torsion wire, C-clamp stud, D-movable protractor, E-specimen rack, F-specimen.", "texts": [], "surrounding_texts": [ "When rubber is forced to deform faster than its relaxation time permits, it breaks. Extremely high speed would be required to produce a brittle fracture at room temperature, but as the temperature is lowered, a point is reached at which a specimen breaks under a given deformation at a given speed. In ASTM 0746 (Vol. 9.02), specimens 1.9 mm (0.075 in.) thick are bent sharply by impact with a striker arm moving at 6 to 7 feet per second. When multiple specimens are used, care must be taken that the breaking energy is not high enough to slow the striker arm below 6 feet per second after the impact. Otherwise, too low a brittle temperature would be indicated. As with any low-temperature test, either a gaseous or liquid heat-transfer medium may be used if it has been shown to give equivalent results on speci mens of a material having similar composition to that of the test material. This means that a liquid medium should not corrode or swell the rubber and that the rubber should not crystallize in the range of test temperatures. The longer times required for thermal equilibrium in the gaseous medium would promote more crystallization than would the liquid medium. Low-temperature stiffening and low-temperature embrittlement do not cor relate well enough with each other to permit either index to be inferred from PHYSICAL TESTING OF VULCANIZATES 157 the other. The choice of test to be run must be made on the basis of anticipated service conditions. Brittle fracture is visually distinguishable from tensile fail ure in that the failure surfaces have a glassy rather than a ragged appearance." ] }, { "image_filename": "designv10_13_0002198_j.aca.2006.04.068-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002198_j.aca.2006.04.068-Figure1-1.png", "caption": "Fig. 1. Schematic of the needle-type enzyme sensor system (A, B) and images of the detector region (C\u2013E). (1) Needle-type hollow container, (2) round-shaped holes, (3) immobilized enzyme membrane, (4) optic fiber probe, (5) ruthenium complex, (6) excitation LED light source, (7) spectrometer, (8) personal computer.", "texts": [ " Changes in the glucose concentrations can be monitored by varying the frequency in the radio band over a range, optimized to measure the impact of glucose on the impedance pattern. However, most sensor systems are designed for humans or livestock, and such sensors have rarely been used in fish. For application as fish, sensors need to be fairly strong, as fish might resist blood collection. In addition, since testing should be conducted at the fish farm i m i c i c T s fl g s e m e m c m 2 2 n y p P t ( c 0.1 M phosphate-buffered solution (PBS; pH 7.0), titrated and stored for \u226512 h to prepare standard glucose solutions. Fig. 1 shows a schematic of the needle-type enzyme sensor and images of the detector region. The sensor consists of a needle-type hollow container, immobilized enzyme membrane and optic fiber probe with ruthenium complex. The sensor assembly is described below. The hole at the tip of a commercially available 18-gauge needle (diameter: 1.2 mm; Terumo, Tokyo, Japan) was blocked using epoxy resin (Toagosei Co., Tokyo, Japan). Next, 4 \u00d7 1.0 mm holes were made on one side of the needle, and 4 \u00d7 0.8 mm holes were made on the opposite side (Fig. 1A and E). Glucose oxidase (1 mg) was dissolved in 200 l of 0.1 M PBS (pH 7.8), and 25 l of the resulting solution was mixed with 80 mg of AWP. Next, a dialysis membrane soaked in distilled water was evenly spread over a glass plate without bubbles and then completely dried. The above-mentioned enzyme and AWP mixture was evenly applied and rubbed into the dialysis membrane. After drying for 1 h in the dark, the membrane was p b a m w i e 2 i c l t t i U ( 2 L ( J a t p r l t e f possible, portability is an important issue", " Tokyo, Japan). All other reagents used for experiments were ommercial- or laboratory-grade. Glucose was dissolved in laced under a fluorescent lamp for 1 h to prepare an immoilized enzyme membrane. AWP is a photosensitive polymer, nd hardens with time to immobilize the enzyme. The resulting embrane was cut into 8 mm \u00d7 3 mm strips, soaked in distilled ater again and then dried on filter paper. Due to differences n drying shrinkage between the dialysis membrane and AWP, ach strip curled and formed a tube (Fig. 1A (3)). .2.3. Needle-type enzyme sensor A tube-shaped immobilized enzyme membrane was inserted nto the tip of the needle-type hollow container (Fig. 1C). The ontainer was soaked in 0.1 M PBS (pH 7.0) so that the immobiized enzyme membrane would swell and adhere to the needleype hollow container. The container was also lightly tapped o eliminate air bubbles. Next, the optic fiber probe includng a ruthenium complex (FOXY-AL300: Ocean Optics, FL, SA) was inserted inside the immobilized enzyme membrane Fig. 1D) to set up the needle-type glucose sensor. .2.4. Oxygen measurement system An excitation light-emitting diode (LED) light source (USBS-450; Ocean Optics, FL, USA), UBS2000 spectrometer Ocean Optics) and VT900 personal computer (NEC, Tokyo, apan) are connected to the needle-type enzyme sensor to set up glucose determination system. The optic fiber probe includes he ruthenium complex at the tip. Since the distal end of the robe tip comprises a thin layer of hydrophobic sol\u2013gel mateial, ruthenium complex is trapped in the sol\u2013gel matrix" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003557_ica-130421-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003557_ica-130421-Figure1-1.png", "caption": "Fig. 1. A 2-DOF rigid-link robotic manipulator.", "texts": [ " If \u03c1min is found and used in the design of the H\u221e controller, then the closed-loop system will have increased robustness. The Hamiltonian matrix H = [ A \u2212(2r \u2212 1 \u03c12 )BB T \u2212Q \u2212AT ] (97) provides a criterion for the existence of a solution of the Riccati equation Eq. (74) and for finding \u03c1min. A necessary condition for the solution of the algebraic Riccati equation to be a positive semi-definite symmetric matrix is thatH has no imaginary eigenvalues [10]. The performance of the proposed flatness-based adaptive fuzzy MIMO controller was tested in the benchmark problem of the 2-DOF rigid-link robotic manipulator (Fig. 1). The differentially flat model of the robot and its transformation to the Brunovksy form has been analyzed in Section 4. The state feedback gain was K\u2208R2\u00d74. The basis functions used in the estimation of fi(x, t), i = 1, 2 and gij(x, t), i = 1, 2, j = 1, 2 were \u03bcAj (x\u0302) = e( x\u0302\u2212cj \u03c3 )2 , j = 1, . . . , 3. Since there are four inputs x1, x\u03071 and x2, x\u03072 and the associated universes of discourse consist of 3 fuzzy sets, for the approximation of functions fi(x, t) i = 1, 2, there will be 81 fuzzy rules of the form: Rl : IF x1 is Al 1 AND x\u03071 is Al 2 AND x3 is Al 3 AND x\u03073 is Al 4 THEN f\u0302 l i is bl (98) The aggregate output of the neuro-fuzzy approxima- tor (rule-base) is f\u0302i(x, t) = \u221181 l=1f\u0302 l i \u220f4 i=1\u03bc l Ai (xi) \u221181 l=1 \u220f4 i=1\u03bc l Ai (xi) " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003016_s00202-010-0180-4-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003016_s00202-010-0180-4-Figure2-1.png", "caption": "Fig. 2 Experimental planar robot manipulator with two directly driven links", "texts": [ " It is seen that the proposed control law does not involve fractional-power func- tions of certain state variable, and no singularity occurs in the proposed scheme. Beside its simplicity in implementation compared with the previous terminal SMCs, the proposed scheme has the terminal time t f as an explicit parameter for the designer\u2019s convenience. 4 Application to a two-link manipulator 4.1 System description Consider the position control of a two-link revolute-joint manipulator subject to an uncertain payload. For a two-link robot manipulator moving in the vertical plane as shown in Fig. 2, the dynamic equation is given by [ M11 M12 M21 M22 ] [ q\u03081 q\u03082 ] + [ B11 B12 B21 B22 ] [ q\u03071 q\u03072 ] + [ g1 g2 ] = [ u1 u2 ] + [ d1 d2 ] (15) in which M11 = m 1 2 1c + I 1 + Im1 + ( m 2 + m2 + m p ) 2 1 + m 2 2 2c + I 2 + Im2 + IM2 + m p 2 2 + 2 ( m 2 2c + m p 2 ) 1 cos q2, M12 = M21 = m 2 2 2c + I 2 + Im2 + m p 2 2 + ( m 2 2c + m p 2 ) 1 cos q2, M22 = m 2 2 2c + I 2 + Im2 + m p 2 2, B11 = \u22122 ( m 2 2c + m p 2 ) 1q\u03072 sin q2, B12 = \u2212 ( m 2 2c + m p 2 ) 1q\u03072 sin q2, B21 = ( m 2 2c + m p 2 ) 1q\u03071 sin q2, B22 = 0, g2 = g(m 2 2c + m p 2)cos(q1 + q2), g1 = g [ (m 1 1c + m 2 1 + m2 1 + m p 1) cos q1 +(m 2 2c + m p 2)cos(q1 + q2) ] Here, m i is the mass of link i , I i is its moment of inertia about mass centre, i denotes the length of link i , ic is the distance between the joint i and the mass centre of link i , Imi is the rotor moment of inertia of motor i , IM2 is the stator moment of inertia of motor 2, m2 is the mass of motor 2, g is the gravitation constant, and m p denotes the mass of an uncertain payload" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure3-1.png", "caption": "Figure 3. The BigTooth concept allows easy ejection of unwanted cores and hence allows reuse of the same bit.", "texts": [ " This core break off approach is also robust to anomalous cores, which is another SAC requirement. Enabling Technology: BigTooth Bit All drill bits utilize a cutter configuration which allows for easier removal of the rock core from the drill bit in the event that the core is unwanted, but the drill bit needs to be reused. The BigTooth bit concept uses a number of tungsten carbide cutters at the end of the bit as normal. One of these cutters is slightly larger than the others, cutting more of the core than the other cutters (Figure 3). This geometry results in a slightly smaller diameter core than if all the cutters were the same size, and aligned similarly. The result is that when the Breakoff Tube is aligned in one orientation, the core is captured by the BigTooth cutter. Rotating 180 degrees from the captured orientation allows the core to have more clearance to be ejected from the Bit than if all the cutters had the same geometry. In order to eject the core from the bit, the drill first positions the bit along the gravity vector and the Breakoff Tube is rotated back to the drilling position to provide the maximum clearance" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002468_j.jmatprotec.2005.02.202-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002468_j.jmatprotec.2005.02.202-Figure2-1.png", "caption": "Fig. 2. ABB 4400/60 robot with axes showing its movement possibilities.", "texts": [], "surrounding_texts": [ "f these programs is GRAFSIM, which was implemented in E-mail address: grzegorz.wszolek@polsl.pl. The ABB 4400/60 is a compact robot with medium to heavy handling capacity. It can handle loads up to 60 kg, or 924-0136/$ \u2013 see front matter \u00a9 2005 Elsevier B.V. All rights reserved. oi:10.1016/j.jmatprotec.2005.02.202 up to 45 kg at very high speeds. It can be used for material handling, machine tending, grinding, polishing, scaling, gluing, assembly, spraying and cutting. In the manufacturing industry, there are a lot of tasks involving transfer of parts and components to and out from machine tools and other machinery. In the food and beverage industry, products are to be picked, packed into cases and the cases to be palletized. In warehouses and in post terminals, there are parcels to be packed into containers. Robots are well suited for all of these tasks. They can relieve humans from tedious tasks or replace special built machinery, which is inflexible if new or redesigned parts are to be handled [9]. Fig. 1 presents a picture of a mentioned ABB 4400/60 robot, and Figs. 2 and 3 present movement possibilities and its main dimensions. Two positions of the robot arms were accepted for numerical analysis and are presented on Figs. 5 and 6. There are constraints in the robot joints, which, in an accepted model, are represented by damping-elastic elements (11\u201316), characterised by stiffness and linear and angular suppression. In the robot model, two kinematic excitations (7,8) were considered. They come from ground tremblings, where the robot is situated and from the work of different 1. Phenomenological model of a mechanical system has been accepted in the following form: system (Figs. 5 and 6) is considered as two-dimensional with: \u2022 six inertial elements (Fig. 4), such as: - robot basis, - column of the robot, - arm, - counterbalance, - connecting rod, - mount of the gripper; \u2022 seven elastic-damping elements (Figs. 5 and 6); \u2022 two kinematic and one dynamic excitations (Figs. 5 and 6). 2. Masses and inertial elements moments of inertia of the accepted model of the system (Table 1), the linear and angular elasticity of the elastic elements and the linear and angular suppressions of the damping elements (Table 2). 3. The local co-ordinate systems of inertial elements, elasticdamping elements and kinematic and dynamic excitations (Figs. 5 and 6). 4 5 . The attachment co-ordinates of elastic-damping elements in local co-ordinate systems of inertial elements, with which they are incident and angles between co-ordinate systems of elastic-damping elements and inertial elements (Figs. 5 and 6). . Attachment co-ordinates of dynamic excitation in local co-ordinate system of inertial element, with which it is in- cident and angles between co-ordinate system of dynamic excitation and that inertial element. 6. Angles among kinematic excitations co-ordinate systems and elastic-damping elements. 7. Numbers of all elements of modelled dynamic system in following order: - inertial elements, - kinematic excitations, - elastic-damping elements, - dynamic excitations. 8. Rotation movements of the robot in relation to the one, four and six axes have been rejected (Figs. 5 and 6) (robot can move only in relation to the two, three, five axes)." ] }, { "image_filename": "designv10_13_0002736_j.jmatprotec.2008.03.065-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002736_j.jmatprotec.2008.03.065-Figure12-1.png", "caption": "Fig. 12 \u2013 Contact path and contact ellipses plotted on the solid model of tooth of input gear, where (A) is the direction of rotation and (B) the sequence of contact.", "texts": [], "surrounding_texts": [ "10 j o u r n a l o f m a t e r i a l s p r o c e s s i n g\nby the following equations: { r\n(1) f \u2212 r (4) f = 0\nn (1) f \u2212 n (4) f\n= 0 (35)\nwhere\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 r (1) f = r (1) f ( 1, v, \u01311) = Mf 1(\u01311)r1( 1, v) r (4) f = r (4) f ( 3, 1, \u01314) = Mf 4(\u01314)r4( 3, 1) n (1) f = n (1) f ( 1, v, \u01311) = Lf 1(\u01311)n1( 1, v)\nn (4) f = n (4) f ( 3, 1, \u01314) = Lf 4(\u01314)n4( 3, 1)\nThe first vector equation in Eq. (35) contains three independent nonlinear algebraic equations, but the second vector equation in Eq. (35) contains two independent ones, as |n(1)\nf | =\n|n(4) f | = 1. Eq (35) forms a system of equations with five independent nonlinear algebraic equations. By regarding the parameter \u01311 as an independent variable, based on the theory of existence of implicit functions, the other five parameters can be solved as implicit functions as follows:\n{\u01314(\u01311), 1(\u01311), v(\u01311), 3(\u01311), 1(\u01311)} (36)\nAfter obtaining \u01314 (\u01311), the actual transmission error is defined by\n\u01314 = \u01314(\u01311) \u2212 ( N1\nN2\n) \u01311 (37)\nWhether there are assembly errors or not, the tangent conditions in Eq. (35) are applicable. The influence of assembly errors on meshing can be analyzed by conducting the assembly errors into the coordinate transformation matrices Mf1 (\u01311) and Mf4 (\u01314). As shown in Fig. 9, center distance error c, axial distance error a, vertical angular error , and horizontal angular error h are considered. The coordinate\nt e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 3\u201313\ntransformation matrices Mf1 (\u01311) and Mf4 (\u01314) are determined by the following successive multiplication of matrices: { Mf 1(\u01311) = Ry(\u2212 h) \u00b7 Rx(\u2212 v) \u00b7 Tz( a) \u00b7 Rz(\u01311)\nMf 4(\u01314) = Ty(C + c) \u00b7 Rz(\u2212\u01314) (38)\n3.2. Contact ellipse\nAs the contacting surfaces are elastic bodies rather than rigid ones, the contact point will expand as a small elastic deformation area under load. Based on the theory of gearing (Litvin, 1989), the elastic deformation region on the common tangent plane is an elliptical area by expanding the surfaces to a second order Taylor series. The instantaneous elliptical area is called the contact ellipse, the dimensions and orientation of which can be determined by the principal curvatures and directions of the meshing surfaces. The principal curvatures and directions of contacting surfaces (4) and (1) have already been obtained in the previous sections. Thus, the length of the major axis 2a and the length of the minor axis 2b of the contact ellipse are determined by 2a = \u221a\u2223\u2223\u2223 \u03c2\nA\n\u2223\u2223\u2223, 2b = 2 \u221a\u2223\u2223\u2223 \u03c2 B \u2223\u2223\u2223 (39)\nwhere\u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 A = 1 4 { (4) \u02d9 \u2212 (1) \u02d9 \u2212 \u221a g2 4 \u2212 2g4g1 cos 2 (41) + g2 1} B = 1 4 { (4) \u02d9 \u2212 (1) \u02d9 + \u221a g2 4 \u2212 2g4g1 cos 2 (41) + g2 1} (4) \u02d9 = (4) I + (4) II , (1) \u02d9 = (1) I + (1) II\ng4 = (4) I \u2212 (4) II , g1 = (1) I \u2212 (1) II\nThe angle (41) measured counterclockwise from the principal direction e\n(1) I,f to the principal direction e (4) I,f is determined by\n(41) = tan\u22121\n( e\n(4) I,f \u00b7 e (1) II,f\ne (4) I,f \u00b7 e (1) I,f\n) (40)\nThe angle \u02db measured counterclockwise from the principal direction e\n(4) I,f\nto the minor axis of the contact ellipse is determined by the following equations:\u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 cos 2\u02db = g4 \u2212 g1 cos 2 (41)\u221a g2 4 \u2212 2g4g1 cos 2 (41) + g2 1\nsin 2\u02db = g1 sin 2 (41)\u221a g2\n4 \u2212 2g4g1 cos 2 (41) + g2 1\n(41)\n4. Numerical analysis\n4.1. Comparison of the actual transmission error to the pre-designed function of transmission error\nTo prove that the proposed gear drive is able to reconstruct the pre-designed function of transmission error, the actual transmission error, \u01314, is compared numerically with the pre-designed function of transmission error, 2. The setting of parameters for numerical analysis is shown in Table 1.", "No. Parameter description Symbol Unit Setting\n1 Module m mm 10 2 Pressure angle \u02db \u25e6 20 3 Number of teeth of input gear N1 \u2013 18 4 Number of teeth of output gear N2 \u2013 18 5 Radius of form grinding wheel mm 15 6 Magnitude of transmission error \u03b5 Arc-sec 20 7 Period of cycle of meshing T rad 2 /N1 8 Shape parameter \u0131 rad T/4 9 Shape parameter rad T/2\n10 Shape parameter Arc-sec/rad 0 11 Elastic approach \u03c2 mm 0.6E\u22122 12 Parabolic parameter kg 1/mm 0.5E\u22123\nF o\nI m A p o a i s t s t o t p f\n4\nF n\ninput gear tooth faces, respectively. On the output gear tooth face, the contact points move from top to bottom; on the input gear tooth face, the contact points move from bottom to top. If no assembly error is considered, the contact points are exactly\nig. 10 \u2013 The middle curve of \u01314 coincides with the curve f 2.\nt should be noted that the unit of the magnitude of transission error, \u03b5, is Arc-sec and one degree equals to 3600 rc-sec. Numerical results of \u01314 are calculated by the comuter program established based on the mathematical model f tooth contact analysis. Three periods of cycle of meshing re considered. As shown in Fig. 10, numerical results of \u01314 n three periods of cycle of meshing are represented by three olid curves. Numerical values of the pre-designed function of ransmission error, 2, is represented by the solid curve with quares. It can be found that the curve of 2 coincides with he middle curve of \u01314. The numerical results of \u01314, which is btained from the tooth contact analysis, are perfectly equal to he numerical values of 2. This evidence shows that the proosed gear drive is capable of reconstructing the pre-designed ourth order polynomial function of transmission error.\n.2. Analysis of contact ellipses\nrom the results of tooth contact analysis, the instantaeous contact points and contact ellipses can be determined.\nthe direction of rotation and (B) the sequence of contact.\nFigs. 11 and 12 show the contact ellipses on the output and", "12 j o u r n a l o f m a t e r i a l s p r o c e s s i n g\nr\nDC.\nat the middle transverse plane. The bearing contact, which is formed by the set of contact ellipses, is localized at the central part of the tooth face. The lengths of the major and minor axes of the contact ellipses with respect to the rotation angular poison of the input gear are listed in Table 2. As the angle is increased, the length of the major axis is monotonously increased, but the length of the minor axis is not monotonously increased. This is because the tooth face of the output gear has been crowned by a form grinding wheel which is provided with a parabolic motion with respect to the output gear. If there is no crowning modification, the input and output gear tooth faces will be in line contact and the major axis will become a straight line across the tooth face. In this case, the gear derive becomes very sensitive to angular misalignment.\n4.3. Influence analysis of varying the parabolic parameter of the form grinding wheel\nThe form grinding wheel used to crown the output gear tooth face is provided with a parabolic motion with parameter kg. It is worth mention that the purpose of applying the grinding wheel is to crown the tooth rather than to change the pre-designed function of transmission error. Therefore, the variation in kg can not cause any variation in the function of transmission error. This statement is verified numerically. By varying kg and observing the numerical results of transmission error, it is found that the variation of kg indeed does not cause any variation in transmission error. This is because the axial profile of the form grinding wheel is the same as the section profile of the non-crowned tooth face (2).\n(4)\nThe crowned tooth face is tangent to the non-crowned tooth face (2) along the profile (2), which is the section profile of (2) in the transverse plane and the axial profile of the form grinding wheel. When kg is decreased, as the\nt e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 3\u201313\nresults shown in Table 2, the length of the major axis is increased but the length of the minor axis is unchanged. The length of the minor axis is not a function of kg but a function of 2. In other words, as long as the type of 2 is determined, the length of minor axis is also determined. The length of major axis can be controlled by kg. The smaller kg, the longer the length of major axis. If kg is set to be zero, the crowned tooth face (4) will coincide with the non-crowned tooth face (2) and the crowning effect is disappeared.\n5. Conclusions\nThis paper describes a new cylindrical crown gear drive that is provided with a controllable fourth order polynomial function of transmission error. The new method can not only reduce the level of noise of the gear drive but also increase the strength of the tooth fillet. During the construction of the geometry of the tooth faces, the function of transmission error is firstly pre-set as a given function. The tooth face of the input gear is then chosen to be involute. Through a series of coordinate transformations and enveloping processes, the geometry of the tooth face of the output gear is generated. When the input gear meshes with the output gear, the gear drive can exactly reproduce the pre-designed fourth order polynomial function of transmission error. The proposed manufacturing process can be applied extensively to produce other new tooth faces by simply replacing the geometry of the input gear and controlling the type of function of transmission error. If the pre-designed function of transmission error is chosen as a second order polynomial, then, using the same procedures proposed in this paper, a gear drive that can exactly reproduce the pre-designed function of transmission error can also be constructed.\ne f e r e n c e s\nDe Donno, M., Litvin, F.L., 1999. Computerized design and generation of worm gear drives with stable bearing contact and low transmission errors. Trans. ASME J. Mech. Des. 121, 573\u2013578. Lee, C.K., Chen, C.K., 2004. Mathematical models, meshing analysis and transmission design for robust cylindrical gear set generated by double blade-disks with parabolic cutting edges. Proc. Inst. Mech. Eng. Part C. J. Mech. Eng. Sci. 218, 1539\u20131553. Litvin, F.L., Kim, D.H., 1997. Computerized design, generation and simulation of meshing of modified of modified involute spur gears with localized beaming contact and reduced level of transmission errors. Trans. ASME J. Mech. Des. 119, 96\u2013100. Litvin, F.L., Lu, J., 1995. Computerized design and generation of double circular-arc helical gear with low transmission errors. Comput. Methods Appl. Mech. Eng. 127, 57\u201386. Litvin, F.L., 1989. Theory of Gearing. NASA RP-1212, Washington,\nLitvin, F.L., Argentieri, G., De Donno, M., Hawkins, M., 2000. Computerized design, generation and simulation of meshing and contact of face worm-gear drives. Comput. Methods Appl. Mech. Eng. 189, 785\u2013801." ] }, { "image_filename": "designv10_13_0001840_20.539490-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001840_20.539490-Figure1-1.png", "caption": "Fig. 1 sintered NdFeB magnets. Configurations of the perpendicular magnetic gears with two 12-pole", "texts": [ " In general, magnetic gear transmission is understood to consist in motion or the transfer of motion through non-contacted gears. There are a number of advantages for using magnetic gears; for example, they can operate through a separation wall, transmit energy without any physical contact, and are free from the lubrication and extremely low vibration and noise-levels etc.. Therefore, it is quite suitable for using in vacuum and in clean room environments. In this investigation, we report the experimental studies of the magnetic coupling of perpendicular magnetic gear system as shown in Fig. 1 as functions of the number of poles, the area of the poles covered by the magnets, and the distance between the magnetic gears. Manuscript received March 7, 1996. 7899617, fax: (886-2) 7834187. This work was sponsored in part by the National Science Council of Y. D. Yao, email: phyao@gate.sinica.edu.tw, phone: (886-2) . the R.O.C. under Grant No. NSC85-2112-M-001-020. * also Department of Physics, National Chung Cheng University, Chiayi 621, Taiwan ROC. 11. EXPERIMENTAL Sintered NdFeB magnets with (BHmax) of 3 1.3 MGOe were chosen for fabricating magnetic gears for this study. The magnetization profiles with 8, 10, and 12 poles were used to study the variation of magnetic coupling. For example, Fig. 1 shows configurations of the perpendicular magnetic gears with twci 12-pole sintered NdFeB magnets. Each pole of the perpendicular magnetic gears was made of a piece of sintered NdFeB magnet with proper dimensions to cover the surface of an iron yoke of 2 mm thickness. The inner radii of the smaller edge are 14.5 mm, 18.5 nun, and 22..4 mm for 8, 10, and 12 poles, respectively. The distance H between the smaller and large edges of the magnets to cover the poles are varied from 10, 15, 20, to 30 mm", " The magnetic field distributions of the samples were measured by placing a Hall probe over the suiface of the magnets. A PV-900 Digital Torque Angle Measuring system was used to measure the torque of the rotating cone-shape magnet wheel. 111. RESULTS AND DISCUSSION The magnetic coupling between two perpendicular magnet separation distance d (distance between the nearest faces of gears with fixed number of poles is decreased quickly as the 0018-9464/96$05.00 0 1996 IEEE 5062 the gear as shown in Fig. 1) between gears is increased or the cover area of the poles by magnets is decreased. As an example, Fig. 2 shows the torque of magnetic coupling as a function of the separation distance for a 10-10 pole perpendicular magnetic gear system. The cover area of the poles by magnets is varied by changing the distance H between the small edge and large edge (H = 10, 15,20, or 30 m). For a different multi-pole magnetic coupling the magmtude of the torque is increased as the number of poles increases, when d is smaller than a critical separation distance, called d,, however it decreased with increasing the number of poles as the separation &stance is larger than d, For explanation, Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001441_2.5490-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001441_2.5490-Figure4-1.png", "caption": "Fig. 4 Mesh layout of turbine disks for FEA.", "texts": [ " This time is designated as the L0:1 life. According to Mahorter et al.,22 at the L0:1 life disk retirement policy recommends either the removal or reworking of the used disk. From Eq. (1) where X D L, the L0:1 life is calculated from the data of Fig. 3 according to the following: L0:1 D L\u00af exp \u00a1 6:9073 e (14) Stress Analysis and Life Prediction A NASTRAN linear static nite element analysis (FEA) was used to predict the maximum shear stresses \u00bf45 of the disks. The FEA model mesh of sections of disks A and B are shown in Fig. 4. Symmetry in the disks allowed for reduced model segments to be used for analysis. Hence, disk A was analyzed as a 60-deg segment and disk B as a 30-deg segment. Both disks were analyzed for stress and probabilityof failure for two load conditionsat 11,200 rpm. One conditionrelated to disk operation in the engine under full compressorblade (rim) loading.The second conditionrelated to the NAPC spin tests without compressor blade (rim) loading. These FEA maximum shear stress results for the disks are shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002356_bf02451562-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002356_bf02451562-Figure2-1.png", "caption": "Fig . 2. - a) This circle of radius b, wi th its cent re displaced a distance a along the x-axis and h down the z-axis, r ep resen t s the shell aper ture . I t is called the , = 314-2 rad/s\na Phase voltage and phase current b Field current (zero shown) and phase current\n8 CONCLUSIONS\nAssuming sinusoidal flux distributions and constant-field flux linkages, the performance equations have been derived for a cylindrical rotor generator without damper windings, connected to a bridge-rectifier load. Equations for the displacement angle and the commutation current, together with equations for the field current during the commutation and interlude intervals, allow the performance of the generator to be computed. The effective commutation inductance of the generator is related to the transient properties of the machine, and the effective inductance approaches the transient inductance at small loads. The performance equations have been extended to allow for bridge delay. The theoretical and practical performance of a small laboratory generator with bridge-rectifier load compare favourably.\nREFERENCES EASTON, V.: 'Excitation of large turbogenerators', Proc. IEE, 1964, 111, (5), pp. 1040-1048 CLADE, J. J.,and PERSOZ,H.: 'Calculation of dynamic behaviour of generators connected to a DC link', IEEE Trans., 1968,PAS-89, pp. 1553-1564 TIPIKIN, A. P.: 'Mathematical modelling of electromagnetic transient processes in synchronous generator with rectifier load',Izv. VUZ Elektromekh., 1966, pp. 1246- 1253 ADAMSON, C , and HINGORANI, N. G.: 'High voltage direct current power transmission' (Garraway, 1960) SHAEFFER, J.: 'Rectifier circuits\u2014theory and design' (Wiley, 1965) FRERIS, L. L.: 'An analysis of the three phase bridge convertor', Direct Current, 1963, 8, pp. 6-11 FITZGERALD, A. E., and KINGSLEY, C : 'Electric machinery' (McGraw-Hill, 1961)", "10 APPENDIXES Field equations:\n10.1 Cylindrical-rotor-generator equations Vf = rfif + pi//f\nArmature equations: = ~ L af i a cos 9 + ijg cos I 9 ) + i 2TT\n= r i a + p(\u2014Laaia \u2014 Labib \u2014\n: :::: as) fif cos 0)\nvb = rib + Pj\u2014LabJa ~~ Laaib ~ LabJc + Lafif / 2w\\ ) ^^ ^ ' ^ Specification of cylindrical-rotor laboratory\ncos (0 j [ generator\ni 5 kVA, 4 pole, 3 phase, 400 V, 50 Hz, 'sinewave1 machine with v c = r i c + pj\u2014 L a bi a \u2014 La^ib ~ L a a i c + L^if measured inductance constants:\ncos (\u2022\u2022?)! = 0-054, Laf = 0-395, Lff = 4-91 H\n1342 PROC. IEE, Vol.119, No. 9, SEPTEMBER 1972" ] }, { "image_filename": "designv10_13_0002691_j.jbiomech.2008.08.031-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002691_j.jbiomech.2008.08.031-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of the loading apparatus. The load is applied with a voice-coil actuator and the deformation is measured with a LVDT. The osteochondral sample is loaded against a glass slide. A side view of the chamber shows that the sectioned specimen is mounted with its cross-section nearly flush with the transparent chamber wall, to produces images as shown in Fig. 1.", "texts": [ ", Franklin Park, IL) was used to spray the cross-sectional surface with Verhoeff\u2019s stain to produce an optically textured surface (Narmoneva et al., 1999) (Fig. 1). Specimens were mounted into the loading apparatus along a line of action perpendicular to the articular surface and parallel to the cross-sectional surface. The textured cross-section of the sample was placed flush against the glass face of a specimen chamber to ensure that motion of the specimen relative to the camera was parallel to the image plane, and to minimize out-of-plane deformation. The specimen chamber was filled with PBS at room temperature (Fig. 2). Images of the joint cross-section were acquired before and during deformation using a video camera (Sony SSC-C50, Japan, 640 480 pixel resolution) mounted on a stereoscope (Olympus model SZ40, Olympus America, Melville, NY, 20\u201325mm/pixel). The articular surface of the osteochondral sample was loaded against the flat glass bottom of the chamber (Fig. 1) using a voice-coil force actuator (Model LA17-28-000A; BEI Kimco Magnetics Division, San Marcos, CA, 71 N peak force, 28 N stall force). An earlier study (Park et al", " The true extent of this limitation is difficult to assess, since there is currently no practical method of measuring accurate 3D strain fields in intact articular layers for comparison purposes. This limitation is inherent to all studies of cartilage mechanics where the tissue is excised or partially cut to measure its properties or strain distribution (Schinagl et al., 1997; Wang et al., 2002), and future studies may have to investigate this issue more closely. A more readily measurable experimental limitation is the assumption that the testing configuration constrained the articular layer from deforming out of the plane of the cross-section (Fig. 2). If this were true, then Ezz \u00bc 0 and no interstitial fluid could escape from the presumably well-sealed sectioned cartilage surface. Since it is well known that cartilage deformation is isochoric in the short-term loading response (Armstrong et al., 1984; Ateshian et al., 2007; Jurvelin et al., 1997), due to the nearincompressibility of the solid matrix and interstitial fluid (Bachrach et al., 1998), and the low permeability which prevents rapid fluid exudation, we would thus expect that Exx+Eyy+Ezz \u00bc 0 (under small strains), or equivalently here, Exx \u00bc Eyy" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002777_s10846-008-9284-8-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002777_s10846-008-9284-8-Figure2-1.png", "caption": "Fig. 2 The proposed experimental test bed", "texts": [ " Main parts and systems of the test bed are presented together with the way this test bed works. In Section 3, we present a simple fuzzy controller which was designed for validation and experimentation on the suggested test bed. In Section 4, experimental results are presented and remarked. At last, a conclusion is derived and future work on the subject is suggested. The laboratory test bed consists of three basic parts; a customized flying stand, a customized small helicopter and a control unit (Fig. 2). 2.1 Helicopter Flying Stand The flying stand is a mechanical construction able to hold the helicopter, allowing full movements (5 df) while protecting it from damaging and crashing. It is a customized construction based on the commercially available mechanism by Whiteman Industries, that it is used by inexperienced pilots for flight training. A small electric helicopter is mounted on the stand as shown in Figs. 2, 3 and 4. The stand is all aluminum construction with ball bearings to allow smooth and easy movements to the helicopter" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003272_tmag.2009.2024641-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003272_tmag.2009.2024641-Figure5-1.png", "caption": "Fig. 5. The 3-D meshes of the PM for (a) Method 1 and (b) Method 2.", "texts": [ " To investigate the effect of the division of the PM on the accuracy of the proposed method, we analyzed two models in which the PM is not divided and is equally divided into five segments in the thickness direction. In the full 3-D analysis, we analyze the half region of one segment of the PM. Fig. 4 shows the 3-D mesh without the division of the PM. In the proposed method, a mesh with the same subdivision in the plane is used for the 2-D analysis of the motor. The meshes used for the 3-D eddy current analyses of the PM with Methods 1 and 2 are also the same as shown in Fig. 5. The widths and are 0.1 and 0.2 mm, respectively. For each model, the period of steady state is analyzed in steps of electrical angle of degrees. In this section, we investigate the method for determining the gap width in Method 2. The distribution of flux density generated by , obtained by subtracting the flux density for from that for , is shown in Fig. 6. The figure shows that the reluctance of the motor core should be determined by taking the whole region of the motor into account because flux due to flows throughout the motor" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003814_j.electacta.2013.02.117-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003814_j.electacta.2013.02.117-Figure5-1.png", "caption": "Fig. 5. Platelet activation upon interaction of Hep and PU-Hep NPs with PRP for 30 min at 37 \u25e6C. Expression of the platelet activation marker anti-CD62P-FITC on platelets was given as % of platelet activation. Plasma incubated with saline as a negative control.", "texts": [ " It is known that negatively charged sulfate and sulfonate groups of heparin play a major role in the biocompatibility acticity of heparin, which may reduce the inflammatory potential of an external additive [34\u201336]. 3.5. Platelet activation Platelet activation upon interaction with samples is another major barrier in blood incompatibility and can lead to thrombotic complications under in vivo conditions [30]. The platelet activation was measured after incubating heparin and PU-Hep NPs in PRP for 30 min at 37 \u25e6C using flow cytometry. The data of platelet activa- icant difference between the PU-Hep NPs (0.46%) and the control plasma sample (0.34%) (Fig. 5). Little change in platelet activation C. Sun et al. / Electrochimica A 190 200 210 220 230 240 250 -40 -30 -20 -10 0 10 20 30 b a [q ]* 1 0 -4 /d eg .c m 2 .d m o l- 1 Wavelength/nm F t t [ 3 s p s n p t F P ig. 6. CD spectra of (a) pure GOx, and (b) GOx/(PU-Hep) in 0.1 M PBS (pH = 7.4) in he wavelength region of 185\u2013260 nm. hat occurred with the PU-Hep NPs was also attributed to heparin 34\u201336]. .6. Characterization of GOx/(PU-Hep) hybrids CD is quite a suitable tool for the estimation of the secondary tructure content of the proteins due to its high sensitivity to olypeptide backbone conformations [37]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.40-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.40-1.png", "caption": "Fig . 5.40. Layerglaze \u2122 fabricate d mode l turbin e disk (prefor m (a) an d machine d (b) part) . Fina l diameter : 13.2 cm.", "texts": [ " The visible distortion of the mandrel was evidence for considerable compressive stresses which the deposit imposed upon it. Subsequent structural analysis and mechanical testing of this preliminary part revealed that the laser-deposited material was free from major flaws, and had good structural integrity along with reasonable strength and ductility. An additional part was fabricated in order to demonstrate the capability to produce a significantly larger diameter part for a program which involved the spin testing of a scale model turbine disk. This part is shown in fig. 5.40 both in the as-fabricated condition, and following machining to a typical disk configuration. This part was fabricated from a combination of alloys, the bore section consisting of a Ni-8Al-12Mo-3Ta alloy (at%) (8-12-3) which was one of a family specifically developed for laserglaze fabrication, and the outer diameter consisting of a conventional superalloy, IN-718. The use of two different alloys served to demonstrate the feasibility of altering material composition within a single part. Surface layers" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003628_s12541-012-0132-1-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003628_s12541-012-0132-1-Figure2-1.png", "caption": "Fig. 2 The schematic of T.E. definition", "texts": [ " Manuscript received: July 1, 2011 / Accepted: November 24, 2011 \u00a9 KSPE and Springer 2012 The origin of the gear whine noise is the gear mesh, in which vibrations are excited, mainly due to the transmission error which is expressed as an angular deviation, or a linear deviation measured at the pitch point and calculated at successive positions of the pinion as it goes through the meshing cycle.7 From measured angle of rotation, the T.E. of a pair of gears can be expressed in terms of a linear discrepancy tangential to pitch circle. 2 12 1b bTE r r\u03b8 \u03b8= \u2212 (1) where \u03b8 is the angle of gear rotation, rb is the base radius. Subscripts 1 and 2 respectively denote the pinion and wheel. Fig. 2 is the schematic of T.E. definition. Two types of transmission error are commonly referred. The first is the manufactured transmission error, which is obtained for unloaded gear sets when rotated in single flank contact, and the second is loaded transmission error, which is similar in principle to manufactured transmission error but takes into account tooth deflections due to load. Two methods are currently implemented by using macrogeometric and micro-geometric modifications to reduce the gear noise and vibration responses of the system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002901_0278364909348762-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002901_0278364909348762-Figure2-1.png", "caption": "Fig. 2. Renovated mechanism of the PEOPLER-II.", "texts": [ " Accordingly, the robot is composed of four DOFs in total one arm set and one leg set for each side. In addition, we introduced wheels to the legged robot to make it a hybrid robot (Okada et al. 2006) so that it moves not only as an L-type but also as a W-type (see Figure 1(b)). The introduction of legs to a wheeled robot might also lead it to be hybrid, of course. In either introduction, two legs are fixed at the knee axes with an offset that is necessary to prevent the legs from touching together in W-type. Note that the actuators remain, even when we attach the wheel (see Figure 2). Then no additional motors are needed. The arm behaves as a link of a serial manipulator in L-type and as a spoke of a wheel in W-type. Schematic models including parameters and constants are shown in Figure 3. To serve as a hybrid robot, each leg is necessary to be longer than the knee joint rim radius. Therefore, r R l (1) The legs attached to the same wheel move in the same plane when 2r l. However, when 2r l legs must have a cranked at Afyon Kocatepe Universitesi on May 15, 2014ijr.sagepub" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003081_tmag.2008.2002690-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003081_tmag.2008.2002690-Figure1-1.png", "caption": "Fig. 1. Single-phase brushless DC motor.", "texts": [ " Performance curves of phase advance angle versus frequency for a conventional circuit do not work well when the harmonic components are considered. We therefore propose an improved circuit in which the phase advance angle is more accurate than that of a conventional circuit when the harmonic components are considered. Furthermore, the proposed circuit provides better performance. We present experimental results to verify the related theoretical analysis. Index Terms\u2014Automatic phase advance adjustment, single-phase BLDC motor. I. INTRODUCTION T HE single-phase brushless DC (BLDC) motor as shown in Fig. 1 has been widely used in the applications of fans of cooling systems, compressing motors of air conditioners, and CD-ROM spindle motors. In these applications, the phase advance concept has been proposed to increase the efficiency of the motor in former research works[1]\u2013[4]. The purpose of phase advance is to let the current climb first before the corresponding back electromotive force (EMF) goes into the smooth field; the greater the overlay range of the two smooth areas is, the better efficiency will be" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003220_s00170-011-3742-3-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003220_s00170-011-3742-3-Figure3-1.png", "caption": "Fig. 3 Nomenclature describing the various directions during LRM", "texts": [ " Energy dispersive X-ray spectrometer (EDS) attached with SEM was used to confirm the chemical composition on the transverse section of laser rapid manufactured porous structures. These samples were subjected to compression testing to evaluate their mechanical properties as per the American standard test method of compression testing of metallic materials at room temperature, ASTM standards [34]. These tests were conducted on a BiSS, India-made computerized servo-hydraulic 150 kN universal testing machine. Figure 3 presents the nomenclature used in the sample to indicate the various directions, associated with LRM of these samples. The relation between yield strength and porosity was evaluated. Vickers microhardness measurement was performed on the cross-section of the laser rapid manufactured porous structures using Leitz Mini load-2 microhardness tester with a load of 100 g, as per ASTM standards [35]. 3.1 Effect of processing parameters Since LRM involves a number of processing parameters, it is desirable to optimize the manufacturing parameters in a mutually coordinated manner to accomplish the fabrication of the components/structures" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.15-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.15-1.png", "caption": "Fig. 6.15 A colliding wagon (\u649e\u8eca). a Original illustration (Mao 2001). b Structural sketch of roller device. c Structural sketch of colliding device", "texts": [ "14c shows the structural sketch of the roller device. The ballista device is a mechanism with three members and two joints, including the frame (member 1, KF), a ballista rod (member 3, KL), and a rope (member 4, KT). The ballista rod is connected to the frame and the rope with a revolute joint JRz and a thread joint JT, respectively. Figure 6.14d shows the structural sketch of the ballista device. Zhuang Che (\u649e\u8eca, a colliding wagon), also known as Chong Che (\u6c96\u8eca), is a device to collide cities\u2019 gates and walls as shown in Fig. 6.15a (Mao 2001). Mozi (\u58a8\u5b50) (479\u2013381 BC) called the motion of the device as the character \u201cChong\u201d, meaning \u201ccolliding\u201d. It contains two parts: the roller device and the colliding 6.5 War Weapons 123 device. The roller device is a mechanism with two members and one joint, including the frame (member 1, KF) and wheels on the frame as the roller members (member 2, KO). Each wheel is connected to the frame with a revolute joint JRz. Figure 6.15b shows the structural sketch of the roller device. The colliding device is a mechanism with three members and two joints, including the frame (member 124 6 Roller Devices 6.5 War Weapons 125 1, KF), a rope (member 3, KT), and a colliding rod (member 4, KL). The rope is connected to the frame and the colliding rod with thread joints JT. Figure 6.15c shows the structural sketch of the colliding device. Lei (\u6a91, a thrower) also known as Lei (\u96f7), is a heavy object for throwing to attack soldiers under and outside the city walls. It has many different types as shown in Fig. 6.16a (Mao 2001). It is a mechanism with three members and two joints, including a wooden link (member 1, KL), a roller (member 2, KO), and a rope (member 3, KT). The link is connected to the roller and the rope with a revolute joint JRx and a thread joint JT, respectively. Figure 6" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure4.14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure4.14-1.png", "caption": "Figure 4.14-Various techniques of surface mounting of ferrite cores to printed circuit boards. From Huth, J.F III, Proc. Coil Winding Conf Sept. 3~-Oct. 3, 1986, 130", "texts": [ "S-SURF ACE-MOUNT DESIGN IN POWER FERRITES The use of surface mount design has been used for low power ferrite applications. The motivation was the development of PC board technology surface-mount design (SMD. As with the low profile cores, the application has been widespread mostly in the power ferrite application. The use of low profile ferrite cores can be complemented to a large degree by surface-mount technology. The two terminal mounting types used for power ferrites are the gullwing and the J-type terminals shown in Figure 4.14. The gull wing form is used when thin wire up to .18 mm in diameter is used. The J-type design is used in wire sizes greater than .8 mm. Surface mount design lends itself to high speed automatic component placement on the PC board. A surface mount bobbin with gullwing terminals is shown in Figure 4.15. The place ment on the PC board is also shown. 4.6-PLANAR TECHNOLOGY Continuing with the low-profile design tendency particularly with PC board mounting has led to a completely new generation of cores called planar cores" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003429_s12161-012-9468-5-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003429_s12161-012-9468-5-Figure1-1.png", "caption": "Fig. 1 Biosensor used in this work utilizing nanocomposite electrode", "texts": [ " The enzymatic\u2013spectrophotometric determinations were performed with DR 2800 spectrophotometer obtained from Hach Lange (D\u00fcsseldorf, Germany). Preparation of Nanocomposites The procedure developed by our research team described previously for nanocomposite electrodes was used for the nanocomposite fabrication (Mono\u0161\u00edk et al. 2012c). Briefly, nanocomposite mixture was prepared by mixing MWCNT with melted N-eicosane. Thus, the prepared mixture was transferred and spread on the surface of metallic contact. Finally, the layer of the nanocomposite was left to solidify, and the surface was smoothed on a sheet of paper (Fig. 1). Preparation of Biosensors The electrodes were carefully cleaned with Milli-Q water and ethanol. The immobilization of enzymes on the surface of the working electrodes was carried out by their sandwiching between chitosan layers (1 % w/w, aqueous solution). DP and GLD were dissolved in Milli-Q water before the deposition. The amounts of enzymes on the electrodes were optimized from 0.5 to 4 units for DP and from 2.7 to 8 units for GLD, respectively. Each layer was deposited after the previous one was dried" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001486_s0921-8890(01)00171-3-Figure17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001486_s0921-8890(01)00171-3-Figure17-1.png", "caption": "Fig. 17. The evolution of two clusters initiated on the increasing region of g. In this case, the clusters will evolve to the same size, equipartitioning the pucks.", "texts": [ " Let us suppose that we have a g made up of the juxtaposition of two linear regions which have the same magnitude of slope. Then we have three possible situations, with associated possible outcomes. In Fig. 16, we plot the evolution of a pair of clusters when initiated on the decreasing region of g. In this case, Cluster 1 will grow, absorbing Cluster 2, and eventually resulting in a single cluster of all the pucks. This is commensurate with the results of Section 3. If we instead put the clusters initially on the increasing region of g, the situation radically changes (see Fig. 17). Since the larger cluster now has the larger g value, it tends to lose pucks to the smaller cluster. Thus, the two clusters approach each other in size, and eventually become equal in size. Fig. 18 illustrates the system evolution when the clusters are initialized on different sides of the minimum with the larger cluster at a higher g value than the smaller cluster. In this case, the larger cluster will lose pucks to the smaller cluster. Since the slopes are equal, the loss of pucks is directly proportional to the relative loss of g" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002745_s0025654408030023-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002745_s0025654408030023-Figure1-1.png", "caption": "Fig. 1.", "texts": [ "OI: 10.3103/S0025654408030023 1. STATEMENT OF THE PROBLEM. EQUATIONS OF MOTION OF THE CELT The celt is a rigid body of ellipsoid shape (frequently, of half an ellipsoid shape). We assume that the body moves on an immovable horizontal plane XY which the celt is touching at point P (Fig. 1). We associate the celt with the principal axes of inertia x, y, z in which the triaxial ellipsoid of the celt surface is given by the equation \u03a6(r) \u2261 (\u2212x cos d + y sin d)2 a2 + (x sin d + y cos d)2 b2 + z2 c2 \u2212 1 = 0, (1.1) where r = OP = (x, y, z), d is the angle between the principal axis of inertia and the ellipsoid major axis, the ellipsoid principal axes are denoted by a, b, c, and a > b > c. The center of gravity G of the body of mass m is displaced with respect to the ellipsoid geometric center O along the z-axis by k (if k > 0, then point G lies on the negative part of the z-axis)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003952_978-1-4471-6275-9-Figure8.3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003952_978-1-4471-6275-9-Figure8.3-1.png", "caption": "Fig. 8.3 Checking whether the mobile vertex (yellow dot on the dark gray rough 2D mesh) is penetrating the fixed polygon (green dashed line on the light gray 2D mesh). Both of the green fixed triangles (dark dashed line and light dotted line) are inside the gray spatial cell (segmented by black radial lines). However, only the dark green triangle (dashed line) is intersected by the vector connecting the origin (red dot) to the mobile vertex. The signed radial distance between the dark green triangle and the vertex is calculated by subtracting the red vector (short vector) from the blue one (long vector) [13, 14] (Reprinted from Journal of Biomechanics, Vol. 42, Arbabi E, Boulic R, Thalmann D, Fast collision detection methods for joint surfaces, pp. 91\u201399, Copyright (2009), with permission from Elsevier)", "texts": [ " This method returns the pairs of penetrated mobile vertices and their corresponding penetrated fixed triangles. The method could be shown to be faster than many other general methods and also to be suitable for evaluating human joints. However, it also suffers from some weaknesses in accuracy and in processing stages. Later, Arbabi et al. proposed another method working by radial segmentation of the object\u2019s spatial occupancy [14]. The collision is found by comparing the position of the vertices and the polygons occupying the same radial segment (see Fig. 8.3) [14]. Generally, the method is inspired by the work done by Maciel et al. [18]. However, an important part of the method, i.e. the strategy used for creating and filling the table, is different from this work. The proposed new strategy not only makes the method return accurate collision answers (vs. the approximated answer of [18]), but also increases the speed of table updating significantly. Arbabi et al. also investigated the effect of the mapping function (to map from Cartesian coordinates to radial segments) on the processing time to check the importance of simplicity of the function versus uniformity of its output\u2019s distribution [14]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002966_tie.2007.907667-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002966_tie.2007.907667-Figure2-1.png", "caption": "Fig. 2. SA130 six-axis industrial manipulator.", "texts": [ " Assuming the training motion data have been appropriately clustered, the next step is to derive a set of basis functions for each cluster that are representative of the trajectories contained. We achieve this via a PCA of the trajectories contained within each cluster. A finite number of the most dominant principal components (typically four for our application) are then used as basis functions for linear interpolation. In this section, we describe the details of each step of our algorithm, focusing on the functional (square) blocks shown in Fig. 1. Our algorithm is presented for standard six-axis industrial manipulators of the topology shown in Fig. 2, but should be easily generalizable to other nonstandard topologies. For training motion data we seek a sufficiently large set of trajectories that have minimum torque, and at the same time as fast as possible without causing saturation in any of the actuators. For the minimum torque problem in which a fixed tf is given as input, it is intuitively clear (and also confirmed by extensive simulations) that for larger values of tf , the minimum torque profiles become increasingly flatter (and smoother)", " This is essentially identical to the procedure for determining the smallest tf while avoiding actuator saturation in the minimum torque motion case (Section III), and we adopt the same line search procedure. We note that the inverse dynamics calculations can be performed in real-time via any of the wellknown recursive algorithms. To demonstrate both the computational feasibility and performance gains of our methodology, we perform simulation experiments for the SA130 six-axis industrial manipulator of Fig. 2. We use the approximate kinematic and inertial specifications listed in Table I for our case study. The robot\u2019s feasible joint space and the torque limits are given in Table II. Partitioning the 6-D joint space into a grid, and generating optimal motions for arbitrary pairs of points on this grid, is computationally intractable. Extensive simulations on the other hand have revealed that the effective inertia strongly affects the shape and nature of the optimal trajectories; generally, we have observed that minimum torque motions tend to first \u201cfold in\u201d to a posture that minimizes the robot\u2019s effective inertia, moves the base links, then \u201cfolds out\u201d to the desired ending configuration" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001596_icsmc.1996.571368-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001596_icsmc.1996.571368-Figure4-1.png", "caption": "Fig. 4: Zero Moment Point (ZMP)", "texts": [ " I 2: Design of Biped Locomotion Robot 3 Conditions for Continuous Walking In this section, we consider the conditions for stable walking. Biped locomotion robots must be controlled under the possibility of falling down. Therefore the reference trajectory of biped locomotion robots must be generated without falling down. We must consider mmy kinds of conditions for Continuous walking without falling down as follows; e Conditions of Zero Moment Point(ZMP) The moment is generated by the floor reaction, force and torque. Figure 4 shows the concept of Zero Moment Point, where p is the point that T, = 0 and Tu = 0 , T,, Tu represent the moments around x axis and y axis generated by reaction force F,. and reaction torque T,. respectively. The point p is defined as the Zero Moment Point(ZMP). When the ZMP exists within the domain of the support surface, the contact between the ground and the support leg is stable. where p z m p denotes a position of ZMP. S denotes a domain of the support surface. This - 1496 - condition indicates that no rotation around the edges of the foot occurs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002560_j.triboint.2006.11.002-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002560_j.triboint.2006.11.002-Figure10-1.png", "caption": "Fig. 10. Twin-disc machine, contact area.", "texts": [], "surrounding_texts": [ "The lubrication system was modified to vary the lubricant flow rate. Fatigue life tests were carried out for different flow-rates and for a given set of operating conditions (see Table 3). The tests were conducted with artificially dented surfaces. The 250 mm dents were made using a Rockwell indentor (see Fig. 11a.). Dented surfaces were used in order to decrease the fatigue life (see Coulon et al. [18,19]). Previous work has shown a standard deviation of the dented fatigue life of 10%. In addition, most contacts in industrial applications are working under contaminated conditions and thus with dented surfaces. The damage develops on the dented disc around the dents or on the smooth disc. The aim is to generate cracks and spalls (see Fig. 11b) and to avoid scuffing. Tests were run using two different lubricants with similar base oil viscosities (oil A: 7mPa. s@80 1C; oil B: 6.3mPa. s@80 1C). These are commercial lubricants with a semi-synthetic base oil and different additive packages. The first oil is used for marine transmissions and the second one is for passenger car gearboxes. The absolute fatigue lives obtained are different, but the trends are similar (see Fig. 12). It can be seen that for a relative lubricant flowrate of 50%, the fatigue life is significantly shortened (almost divided by two). This shows that the rolling contact fatigue life depends strongly on the amount of lubricant. These results can be compared with studies done by Dawson [16], using the lambda ratio as the driving parameter. In a first approximation, the comparison is done, assuming that the lambda ratio is proportional to the lubricant flow-rate. Similar tendencies are obtained." ] }, { "image_filename": "designv10_13_0002516_1-4020-4611-1_2-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002516_1-4020-4611-1_2-Figure5-1.png", "caption": "Figure 5. Triple sensor for pH, oxygen and CO2 for monitoring the blood status during cardiopulmonary bypass (CDI Inc., 1986).", "texts": [ " copper(II) ion, may ever produce adequate return, unless the same instrument can sense several other species as well. While several optical chemical sensors and biosensors in use that do not rely on fiber optics, the commercialization of FOCS technology started slowly, probably because of the limitations imparted to optical sensing if O.S. Wolfbeis and B.M. Weidgans 35 combined with fiber optics. In 1984, CDI (later 3M) introduced their critical care monitoring system (GasStat 300) for oxygen, pH and CO2 for cardiopulmonary monitoring (see Fig. 5). The sensors employed are based on the work (papers and patents) of D. W. L\u00fcbbers et al., O. S. Wolfbeis et al., M. Yafuso, W. W. Miller and J. Tusa. The sensor head consists of a flow-through cell containing sensor spots and fiber optic cables attached to the cell in order to optically interrogate the sensor spots. The sensor exhibits excellent performance if properly calibrated. Fig. 5 shows the instrumental arrangement of the commercially most successful optical chemical sensor between 1984 and 2000. It is used in about 70% of all critical care operations in the US to monitor pH, pCO2 and pO2 in the cardiopulmonary bypass operations 35 . It contains 3 fluorescent spots, each sensitive for one parameter, in contact with blood. Fluorescence intensity is measured at two wavelengths and the signals are then submitted to internal referencing and data processing. Other medical products based on optical sensor technology include those of Cardiomed (System 4000), Puritan-Bennett, and one of Radiometer (Copenhagen) which has been withdrawn meanwhile" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003500_j.scient.2011.08.005-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003500_j.scient.2011.08.005-Figure2-1.png", "caption": "Figure 2: Schematic of a half-toroidal CVT including one roller and two disks.", "texts": [ " Akbarzadeh and Zohoor [11] found an optimized geometry with constant EHL oil temperature, input disk rotational velocity, and tilting angle of roller using Genetic Algorithm method. However, no research was conducted on discovering the best geometry for different values of these parameters yet. To solve this new optimization problem, a simplified model was selected. Oil film thickness and temperature was assumed to be constant, and energy loss in bearings of the rollers was neglected. Efficiency of half-toroidal CVT depends on geometry of the components and properties of EHL oil [10,12], so an analysis on geometry and dynamics of half-toroidal CVT must be performed. Figure 2 shows the schematic of half-toroidal CVT where r22 is the curvature radius of roller in contact point with the disk. r0, \u03b8 and \u03b3 are radius of curvature of disk, angle of a half-cone with center atO, and angle of rotation of the roller, respectively, and r1 and r3 are the distance between disk axis and contact points. As the input disk rotates, it forces the roller to rotate around axis OA, and similarly the rotation is transmitted to the output disk. By rotation of roller around the axis perpendicular to sketch plane and passing through O, \u03b3 changes and consequently speed ratio is altered" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003082_s0263574708004608-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003082_s0263574708004608-Figure2-1.png", "caption": "Fig. 2. The geometry of a screw.", "texts": [ " The two quantities associated with the screw axis are the rotation angle \u03b8 and the translation d. A screw is denoted by (d, \u03b8, L). A rigid body displacement is usually described as a rotation followed by a translation. There is a conversion between the conventional motion description, denoted by (R, t), and the corresponding screw description (d, \u03b8, L). According to the Rodrigues formula, we can describe R as a rotation through an angle \u03c6 and around a unit axis r that passes through the origin. As shown in Fig. 2, we have t = d u + (I \u2212 R) c. (4) Using the Rodrigues formula, R c = c + sin(\u03c6) r \u00d7 c + (1 \u2212 cos \u03c6) r \u00d7 ( r \u00d7 c), (5) and r \u00b7 c = 0, it follows that c = ( t \u2212 ( t \u00b7 r) r + cot(\u03c6/2) r \u00d7 t)/2. (6) Then, the screw translation d, the rotation angle \u03b8 , and the direction vector u can be determined as in ref. [7]. We can get the following equation from (2): RA = RXRBRT X, which is a similarity transformation since RX is an orthogonal matrix. Hence, an eigenvector v of RB corresponds to an eigenvector RX v of RA" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure6-1.png", "caption": "Fig. 6. Contact lines between shaver and the to-be-shaved gear on: (a) the surface of the to-be-shaved gear, and (b) the surface of the shaver.", "texts": [ " It has to allow shaving of the whole active surface of the gear teeth so that contact lines between the shaver and the gear have to cover the whole gear tooth surface. Avoidance of pointing and undercutting of the shaver teeth by appropriate basic geometric parameters is also required. Numerical determination of the contact lines between the shaver and the to-be-shaved gear, and the numerical determination of the minimum face width of the shaver will be represented below. 4.1. Determination of the face width of the shaver Fig. 6 shows the contact lines on the to-be-shaved gear (Fig. 6(a)) and on the shaver tooth surface (Fig. 6(b)), for a shaver with a facewidth equal to that of the to-be-shaved gear. The applied design parameters for the gear and shaver as shown in Table 1. As shown in Fig. 6, the to-be-shaved gear has two unshaved areas because contact lines between the shaver and the to-be-shaved gear tooth surfaces, for a shaver with a face-width equal to that of the gear, do not cover the whole active surface of the gear tooth surface. Consequently, the shaver has to be designed a little wider than the tobe-shaved gear to shave the whole surface of the gear. To obtain the contact lines on the gear and shaver tooth surfaces, the theory represented in [10] is used. It can be summarized as follows: (i) Lines of contact on the to-be-shaved gear surface are determined by simultaneous consideration of Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001510_robot.1994.350969-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001510_robot.1994.350969-Figure3-1.png", "caption": "Figure 3: The planar parallel manipulator equivalent to the Stewart Platform", "texts": [ " We have n, = nd = 2, p, = Pd = 1 and therefore Bz, B3 lie on a ruled surface of order 6. Therefore B1 lie on a surface of order 12, circularity 6 which has at most 12 real intersection points with a circle. Therefore the forward kinematic problem has at most 12 solutions except in the degenerate case where there are an infinity of solutions. 2.2 Second approach Let us denote IIl, I I 2 , II3 the three planes containing the circles C j . Let us consider U3 the projection of B3 on I I 1 and U2 the projection of B2 on I I 1 (figure 3 ) . As B3 moves on C3 U3 will move on a similar circle in II,. Let us consider now the triangle B1B3U3: the length of its edge B1 B3 is constant and the length of its edge U3B3 is also constant and equal to the distance between the plane TI1, IIz. As the edges U3B3, B1U3 2PcPd. form aright angle we deduce that the length IlV3B1II is also fixed. In a similar manner for the triangle B2 B1 U2 the length IIU2B1() is fixed and the length llVzU311 is constant. Therefore we get in the plane TI1 a triangle U3UzB1 whose edges have a constant length and whose vertices are connected to fixed points through three links of length r l , r-2, r3 which can rotate around the normal to the plane: we get a planar parallel manipulator" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure18-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure18-1.png", "caption": "Figure 18. Removing the Bits from the Cache", "texts": [ " Cache Ground Station and the Cache The Sample Cache with the installed Bit Sleeves is constrained by a Ground Station which includes a number of rollers, as well as a Pin Puller (Figure 16). The rollers constrain the Sample Cache radially, while the Pin Puller constrains it axially and rotationally. Once all of the Bit Sleeves are filled with Bits, the Pin Puller is actuated, and the rollers guide the Sample Cache as it is removed from the Ground Station to be placed on the ground (Figure 17). Upon core acqusition, bits with rock samples inside, are inserted into protective sleeves within the Cache. A hermetic seal is made between the bit neck and the top of the sleeve (Figure 18). Each bit within its protective sleeve can be removed from the cache, for repackaging by another handling system, e.g., on a lander or for distribution when returned to Earth. The current best estimated mass of the Sample Cache Ground Station and the Cache is approximately 2.0 kg, not including any Bits. The approximate size of the Ground Station is 14.3 cm x 14.3 cm x 9.6 cm. The Bits and Bit Sleeves are arranged in a close packed formation with the minimum of 19 or 31 bits (depending on requirement)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.2-1.png", "caption": "Fig. 7.2 Cutting devices. a A grass cutting device (\u9401) (Wang 1991), b A mulberry cutting device (\u6851\u593e) (Wang 1991), c Structural sketch", "texts": [ " The translation along the x-axis or z-axis is to enable them to more easily pestle grain from the corresponding direction. Figure 7.1e shows an imitation of the original illustration of a foot-operated pestle in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b. 138 7 Linkage Mechanisms 7.1 Levers 139 7.1.2 Si (\u9401, A Grass Cutting Device), Sang Jia (\u6851\u593e, A Mulberry Cutting Device) Si (\u9401, a grass cutting device) and Sang Jia (\u6851\u593e, a mulberry cutting device) are both cutting devices for processing forage as shown in Fig. 7.2a, b (Wang 1991). Si is used to cut grass to feed cows, and Sang Jia cuts mulberry to raise silk worms. Their components are similar and include a knife made from wrought iron and a wooden base. The tip of the knife is passed through by a thin rod that is connected to the base. The operator uses one hand to place the forage or mulberry under the knife, and the other hand presses the handle down to cut them up. It is a linkage mechanism with two members and one joint, including the base as the frame (member 1, KF) and a knife as the moving link (member 2, KL). The knife is connected to the frame with a revolute joint JRz. It is a Type I mechanism with a clear structure. Figure 7.2c shows the structural sketch. 7.1.3 Lian Jia (\u9023\u67b7, A Flail) To separate the seeds from their pods, grains may be simply hit with a Lian Jia (\u9023 \u67b7, a flail) after harvesting as shown in Fig. 7.3a (Wang 1991; Pan 1998). The seed pods are spread on the hard ground, and the flail is applied by swinging the handle. After the seeds have been flailed, the pods and leaves are blown off with a 140 7 Linkage Mechanisms 7.1 Levers 141 winnowing device. This is followed by sieving. Thus, the good seeds are made ready for storage in the barn" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002100_pime_proc_1989_203_096_02-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002100_pime_proc_1989_203_096_02-Figure12-1.png", "caption": "Fig. 12 Apparatus for measurement of film thickness using the optical interferometry technique", "texts": [ "252 the present work, although the range of conditions covered by them is small. 5 EXPERIMENTAL MEASUREMENTS OF FILM THICKNESS AND COMPARISON WITH THEORETICAL RESULTS 5.1 Experimental apparatus Experimental measurements of film thickness were made using a specially developed optical interferometry rig. The technique of film thickness measurement by optical interferometry was used by Kirk (18) and later developed and refined by Cameron and his co-workers [see, for example, Foord et al. (19)]. A sketch of the rig used in the present work is shown in Fig. 12. A steel ball of diameter 19.05 mm and with a superfinished surface of roughness 0.03 pm Ra is loaded against the lower flat surface of a glass disc 101 mm in diameter and 12.7 mm thick, with a surface roughness of approximately 0.01 pm Ra. The working surface of the disc has a chromium coating to give a reflectivity of around 18 per cent to improve fringe visibility, and the other flat surface has a coating of MgF, to reduce unwanted reflections. The ball is cemented to a light alloy conical chuck with epoxy resin and is supported on the outer races of three accurately positioned small ball bearings mounted in a lever arm through which a deadweight load can be applied" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003554_1350650110397261-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003554_1350650110397261-Figure1-1.png", "caption": "Fig. 1 Schematic view of the bearing assembly", "texts": [ " The friction torque was measured with a piezoelectric torque cell KISTLER 9339 A, ensuring high-accuracy measurements even when the friction torque generated in the bearing was very small compared to the measurement range available. The operating temperature was measured by seven thermocouples positioned in strategic locations in order to obtain the lubricant and bearing housing temperatures, so that the lubricant viscosity and the heat evacuated through the bearing housing could be calculated with reasonable precision. The thermocouples I\u2013V are shown in Fig. 1, and two of these thermocouples (VI and VII) are used to record the temperatures of the air flow surrounding bearing house and the room temperature, respectively. The rolling bearing assembly was submitted to continuous air-forced convection by two fans, evacuating the heat generated during bearing operation. In the torque tests, a 51107 thrust ball bearing was submitted to an axial load of 7000 N, rotational speeds between 100 and 5500 r/min and air-forced convection. The measurements were performed in three periods of 2 min for each operating condition with stabilized temperature due to the restrictions imposed by the torque cell [15]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002777_s10846-008-9284-8-Figure13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002777_s10846-008-9284-8-Figure13-1.png", "caption": "Fig. 13 Position error representation", "texts": [ " Although the flying stand permits roll angles from \u221240\u25e6 to 40\u25e6, the flight control system takes as input degrees from \u221290\u25e6 to 90\u25e6. The linguistic variables that represent the roll angle are: left big (LB), left (L), zero (ZERO), right (R), right big (RB), and their membership functions are shown in Fig. 14. The second input variable is the pitch angle of the helicopter. The linguistic variables for this input are: back big (BB), back (B), zero (ZERO), front (F), front big (FB), with membership functions also presented in Fig. 14. In Fig. 13, we show the representation of the position error input, which is defined as the difference between the current horizontal position and the target horizontal position (position error = current position \u2013 target position). Position error represents how far the helicopter is from the target point. Since for safety reasons we do not want the stand to rotate out of its limits (\u2212180\u25e6 to 180\u25e6), we set the range of the position error variable to be between \u2212180\u25e6 and 180\u25e6. The linguistic variables for these inputs are: negative big (NB), negative (N), zero (ZERO), positive (P), positive big (PB) (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002405_1.2043255-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002405_1.2043255-Figure2-1.png", "caption": "FIG. 2. Mechanical profilometry data for a small-scale wrinkles, one-dim one-dimensional trace, and d large-scale wrinkles, surface plot. ensional trace, b small-scale wrinkles, surface plot, c large-scale wrinkles,", "texts": [ " Therefore, the two-layer coating atop a stiff substrate is more susceptible to wrinkling when the top layer is above its Tg. Heating the sample to an even higher temperature, such as 130 \u00b0C, generates additional in-plane compressive stress in the PVA layer but would not change the critical stress required for wrinkling. Therefore, heating to a higher temperature would not change the wrinkling of the top layer. The wavelength of the largescale wrinkles predicted from Eqs. 16 \u2013 18 is about 420 m, which is close to the observed average wavelength of 460 m measured by mechanical profilometry Fig. 2 . In-plane stress owing to frustrated swelling develops when the top PVA layer absorbs atmospheric moisture. Table TABLE II. Thermomechanical properties of the PVA Tg K Modulus MPa Line expan PVA 343\u2013358 2\u20133 103 T Tg 1\u20132 102 T Tg 7\u201312 1\u20132 PEA 249\u2013430 4\u20135 10\u22122 at 20 \u00b0C, 0.5 10\u22122 at 100 \u00b0C T Tg 6. PET 343\u2013373 1\u20132 103 T Tg 5 102 T Tg 2\u2013 TABLE III. Analysis of the small-scale wrinkles gen Relative humidity % Equilibrium moisture contenta % Modulusa MPa Stress require for wrinkli MPa 100 60 80 \u22120. 79 15" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002273_1077546304042047-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002273_1077546304042047-Figure12-1.png", "caption": "Figure 12. Leaf spring model.", "texts": [ " The modal contact, restoring, and friction forces associated with the generalized modal coordinates of the leaf spring can be determined and introduced to the system dynamic equations of motion as generalized forces in the vector Qi e of equation (42). In this section, the vibration characteristics of the leaf spring obtained using the finiteelement method are compared with the results obtained using some of the simple methods discussed in the first part of this paper. To this end, we use a simple leaf spring model shown in Figure 12. The leaf spring consists of two leaves and can be classified as an elliptic leaf spring. This design of the leaf spring is known as a fully tapered leaf spring. In this design, the leaf thickness is not constant. The leaf thickness is designed to be continuously variable along the leaf centerline in order to achieve certain spring stiffness characteristics and, at the same time, to follow certain deformation modes under the expected loading conditions. This design has the advantage of eliminating the frictional contact between the leaves and hence improving the ride quality", " Another technique used to calculate the equivalent stiffness of the leaf spring is the standard procedure used by the Society of Automotive Engineers (1985). This procedure adopted the beam theory to calculate the equivalent stiffness of the leaf spring. Design formulae and correction factors that account for different leaf spring designs and geometries are available. Following this procedure, the leaf spring can be modeled as modified parabolic cantilever. According to this procedure, each leaf of the model shown in Figure 12 can be considered to contribute one half of the load support and rate. The stiffness of the cantilevered beam using the modified parabolic model can be calculated from k E 0t3 0 4l3 C (50) where E is the Young modulus of the leaf material, w0 is the leaf spring width, t0 is leaf base thickness, l is the leaf length, and Cv is the vertical load factor. The appropriate correction for the semi-elliptic leaf spring, Cv, was calculated and used to calculate the equivalent stiffness of the leaf spring" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002554_j.biosystems.2006.09.015-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002554_j.biosystems.2006.09.015-Figure2-1.png", "caption": "Fig. 2. A scheme of a curvature-increasing feedback. (A) A passively bent cell layer with its convex surface stretched and the concave one compressed. (B) Its expected response, namely the active expansion", "texts": [ " Bent arrows within a layer indicate the expected flow of cell material towards the convex side. the force that stimulated it. A succession of this kind of passive-active responses can propagate in a relay fashion through an entire collection of samples, and returns back to the first ones, keeping them in an extended state. For illustrating the curvature increasing (CI) feedback, let us consider a part of a cell layer bent by external forces. As a result of the bending, its convex side will be passively stretched while the concave side compressed (Fig. 2A). Now, if the layer\u2019s edges are firmly fixed (as it takes place usually), the expected HR reaction would be the active extension of the convex side and the active contraction of the concave one, both of which could be simultaneously accomplished by migration of cells from the concave to the convex side. Consequently, a bending initiated by an external force will be magnified due to the internal forces action (Fig. 2B). ll layer) with its part actively contracted and hence part passively calation-mediated) extension which relaxes/compresses part in the ach other for several times. (C) A passive horizontal extension of tion (B, dotted arrows), so that two mutually orthogonal zones of cell esses and dense lines the active ones. ky / Bio 3 l b t t t u e s b G 3 o c i I a n c i m w w s w g o F b a L.V. Beloussov, V.I. Grabovs . Models of shape formation We formulated HR hypothesis in an deliberately oose way, leaving much freedom for its specification y ascertaining the values of the implicated parameers" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003176_17452759.2011.613597-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003176_17452759.2011.613597-Figure1-1.png", "caption": "Figure 1. a) Real part b) Figure en 3D model c) Surface model.", "texts": [ " The formed parts are selected because their geometry and dimensions are optimal and they are manufactured with stainless steel material. Formed parts are processed into their near net shape without undergoing machining processes afterwards. The commercial parts were bought to obtain a replica using the Sidio Triple Advance digitalisation program and to compare the same geometrical features. The 3D scanning process used optical technology to obtain Cartesian coordinate data, which were processed to extract four real part surfaces. To obtain the digital surface or real part (Figure 1a), it is necessary to project a series of black and white vertical fringes onto the surface. Cameras measure deformations of the light lines that are reflected in the model. A dense cloud with 300,000 points is obtained for each model. SW RapidForm XO Redesign software joins the clouds to generate a surface with a tolerance of less than 25 microns (Figure 1b). The surface is turned into a 3D model (Figure 1c) and, finally, the 3D models are converted into STL format. 2.2 Experimental set-up and materials The experiments were carried out with the \u2018Concept Laser M3 Linear\u2019 recognised as a Laser Cusing (LC) process, which is the same as the SLM process. Experiments were conducted in a SLM machine with parameters set as shown in Table 2. The SLM system consisted of a 100 W diodepumped Nd:YAG laser with a nitrogen environment that reduces the oxygen in the building chamber and the oxidation of the part. According to the machine vendor information, the SLM machine technology has a precision of 15 microns in a volume building of 300x350x300 mm" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003511_iros.2013.6697013-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003511_iros.2013.6697013-Figure12-1.png", "caption": "Fig. 12. Snapshots of the OctArm automatically grasping and lifting an object while avoiding an obstacle", "texts": [ " Figure 11 shows the valid grasping configurations found for four objects by our analytical approach and based on the above OctArm parameter ranges: (a)\u2013(c) have only unique OctArm solutions respectively, and the types of solutions are indicated; (d)\u2013(f) show a cir that has three OctArm solutions of different types. Clearly, given a cir, the types and number of valid grasping configurations vary, but it is possible to have any type of grasping configuration among cases (1)\u2013 (6). Similarly, for two object circles cir1 and cir2, the types and number of valid grasping configurations vary, but a valid one can be of any of the cases (7)\u2013(10). Figure 12 shows the autonomous execution of the OctArm to reach a grasping configuration, grasp, and lift an object while avoiding another object. The target object was a box wrapped in a foam so that it has a large size and irregular shape, which was difficult for a conventional gripper to pick up. The objects were first detected automatically based on the RGB-D data obtained from the overhead Kinect camera, next the grasping configuration was automatically generated, and finally the path connecting the initial configuration of the arm to the grasping configuration was automatically generated, which also avoids the other object", " The final lift of the object (see Figure 13) shows that the grasp was a stable and forceclosure grasp. Figure 14 shows the OctArm automatically avoiding two objects before getting ready to reach a grasping configuration for one of the objects (i.e., the blue one). The attached video shows three operation cases. Case (1) is the autonomous grasping and lifting operation of the object in Figure 13, case (2) is the autonomous obstacle avoidance operation as shown in Figure 14, and case (3) is the autonomous operation of grasping and lifting an object while avoiding another object, as shown in Figure 12. The object In the grasping cases, it is interesting to note that the target object moved after the initial contact with the arm. The ability of the manipulator to deal with such moveable objects shows a significant advantage over rigid-link manipulators with grippers, which may not be able to properly grasp an object that is not fully static. It should be noted that the object was lifted about 2 inches off the surface, though this ability varies depending on the shape, size, and weight of the object being grasped" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001963_tcst.2002.804126-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001963_tcst.2002.804126-Figure1-1.png", "caption": "Fig. 1. Experimental setup.", "texts": [ " Position information is obtained from incremental encoders located on the motors, which have a resolution of 1 024 000 p/r for the first motor and 655 360 p/r for the second one. The accuracy for both motors is 30 arc/s. A motion control board based on a TMS320C31 32-bit floating point microprocessor from Texas Instruments, is used to execute in a PC Pentium II host computer. A vector field with a circular contour in task coordinates as a ( -limit) global attractor was chosen. The origin of the Cartesian frame is attached at the axis of rotation of the fist joint, while and denote the horizontal and vertical axes, respectively (see Fig. 1). The vector field was chosen to exhibit a behavior without abrupt changes in velocity and acceleration such that saturation of actuators were prevented. The mathematical expression of the desired velocity field is (28) where m is the circle diameter, m and m defines the circle center coordinates, ms , m , m , and ms is the desired tracking speed. Since the controller proposed in this paper was designed to track a desired velocity field in joint coordinates, a previous step has to be made, in order to translate the velocity field from Cartesian to joint coordinates" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001345_1.1349420-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001345_1.1349420-Figure2-1.png", "caption": "Fig. 2 Defect modeling and characteristic functions", "texts": [ " The mesh stiffness per unit contact length k(h ,t) accounts for contact, tooth bending, base compliance and the normal contact condition at any potential point of contact is introduced by the unit Heaviside function H(D(h ,t)) which is zero when contact is lost and equal to one otherwise. Upon assuming that no-load transmission error is not altered by defects of small dimensions ~compared to the tooth face!, the contributions of k localized tooth defects can be extracted from global deviations and the equivalent normal deviations defined in ~4! become: de~h ,t !5de ~0 !~h ,t !1( k ek~h ,t ! (5) where (0) refers to no-local-defect conditions ~as opposed to geometrical errors! and each local fault is modeled by a set of normal deviations at a given location on the base plane ~Fig. 2!. The SEPTEMBER 2001, Vol. 123 \u00d5 423 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use 424 \u00d5 Vol. 123, SEPT Downloaded From: http://mechanicaldesi distribution of deviations ek(h ,t) depends on both h ~along defect widths! and time in order to simulate the defect extent in the profile direction. After separation of space and time variables, it comes: ek~h ,t !5Pk~h!\u2022Fk~ t ! (6) Fk(t) which represents the defect morphology in the profile direction is a windowing function whose amplitude lies between 0 and 1 within the defect area and is set to zero outside ~Fig. 2!. Equation ~3! can be simplified for reasonably small defects so that mesh stiffness variations along defect widths Dk(t) can be neglected, i.e., k(h ,t).kk(t) for the kth defect. Keeping the notation of Eq. ~5!, it comes: $G~ t ,$x%!%5$G~ t ,$x%!%~0 !1( k kk~ t !\u2022Fk~ t !\u2022E Dk~ t ! H~D~h ,t !! \u2022Pk~h!\u2022$V~h ,t !%\u2022dh (7) Upon assuming that defects have a negligible influence on contact conditions outside the defective zones, a limit case of interest can be analytically tackled, i.e., when H(D(h ,t))51 at all points within the defect areas", " scheme and a unilateral contact algorithm @8# which, at each timestep, controls that there is no negative contact force and no penetration outside the calculated contact area. The mechanical system under consideration is depicted in Fig. 4 and Table 1. Spur and helical tooth profiles are modified by linear symmetric tip reliefs and realistic pitch error distributions on pinion and gear are EPTEMBER 2001 ldesign.asmedigitalcollection.asme.org/ on 01/27/20 introduced ~peak-to-peak amplitude: 22 mm on pinion and gear, maximum jump: 9 mm on pinion and gear!. For simplicity, any local tooth fault is assimilated to a parallelepiped when transferred in the base plane ~Fig. 2! so that both the defect depth Pk(h) and width Dk(t) are constant and Fk(t) is a rectangular windowing function. The defect location on tooth flank is characterized by xc ,zc , co-ordinates of the defect center on the base plane ~Fig. 2!. As demonstrated by Cahouet et al. @12#, simulated and measured accelerations are in good agreement and such a model is representative of the dynamic behavior of single-stage geared systems with local tooth faults. Extensive numerical simulations have been conducted in order to analyze the influence of the defect position, size and number as well as the performances of the detection methodology. Results are synthesized in Figs. 5 and 6. It is confirmed that the evolution of the cepstrum damage indicator d(t) versus defect depth Pk and width Dk follows a parabolic law in accordance with the analytical indications of section 1", " $F0% 5 nominal load vector $F( e\u0308*(t))% 5 inertial force vector due to no-load transmission error e*(t) $G(t ,$x%)% 5 non-linear second member generated by mounting errors and tooth shape deviations from ideal involutes @Ka# 5 shaft, coupling, bearing, . . . constant stiffness matrix 430 \u00d5 Vol. 123, SEPTEMBER 2001 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/20 @K(t ,$x%)# 5 time-varying possibly nonlinear gear stiffness matrix L 5 normalized defect extent in the profile direction ~Fig. 2! @M # ,@C# 5 mass, damping matrices Pk(h) 5 defect depth s(t),S(y), s\u0303 5 respectively time signal, Fourier transform and cepstrum xM ,zM 5 coordinates of a potential point of contact on the base plane ~Fig. 1! bb 5 base helix angle D(h ,t) 5 deflection at a point of contact de(h ,t)5e(h ,t)2maxt$e(h ,t)% 5 equivalent normal deviation @1# Alattass, M., 1994, \u2018\u2018Maintenance des machines tournantes. Signature des de\u0301- fauts d\u2019engrenages droits et he\u0301lico\u0131\u0308daux,\u2019\u2019 Ph.D. dissertation, INSA de Lyon, p" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001384_978-94-017-2925-3-Figure20.11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001384_978-94-017-2925-3-Figure20.11-1.png", "caption": "Fig. 20.11. Extrusion coating.", "texts": [ " The time to fail at a given pressure and temperature is recorded in the form of stress-life curves.65\u202266\u202267 By using various established techniques, one may es timate the pressure rating for a life expectancy of 20 years or more with rea sonable certainty. The extrusion coating of polyethylene on paper or other substrate is an impor tant segment of the polyethylene industry. In commercial practice, an extruder is used to feed polymer through a slit die somewhat similar to that required for chill-roll film (Fig. 20.11).68 The polymer melt is laid down continuously on the substrate and then chilled by contact with a polished roll. Linear speeds of 300 to 1000 feet per minute are common. Coatings may be 0.25 to 2 mils in thickness. Important substrates for polyethylene coating include kraft paper for multiwalled bags and paper board for milk cartons and other food containers.69 When applied to cellophane, polyethylene provides heat sealability, tear resis tance, moisture-barrier properties, and improved resistance to shelf-ageing" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure5-1.png", "caption": "Fig. 5 Analysis in the Gauss plane to determine the moving centrode of offset slider-crank/rocker mechanisms", "texts": [ " (15) or (17) can be expressed as Xa 1;2\u00bc6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2 e2\u00fe2er r 2 p and Xa 3;4\u00bc6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2 e2 2er r 2 p (18) Journal of Mechanisms and Robotics FEBRUARY 2012, Vol. 4 / 011003-3 Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Similarly, referring to Fig. 5, the implicit and then the explicit algebraic equations of the moving centrode k are obtained by considering the complex plane of Gauss as coincident with the moving plane of f \u00f0X; x; y\u00de that is attached to BC. Thus, the position complex vectors zI, zA and zC of the points I, A, and C can be expressed as zI \u00bc x\u00fe i y (19) zA \u00bc r zI zIk k and (20) zC \u00bc l (21) Consequently, the position complex vector zD is given by zD \u00bc zA e zI zC zI zCk k (22) which lets to express the vector zn in the form zn \u00bc zD zC\u00f0 \u00de zI zC\u00f0 \u00de (23) The implicit algebraic equation of the moving centrode is obtained by equating to zero the real part of zn, as reported below Re zn \u00bc 1 2 \u00f0zn \u00fe zn\u00de \u00bc 0 (24) Thus, substituting Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003702_s11071-010-9940-y-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003702_s11071-010-9940-y-Figure1-1.png", "caption": "Fig. 1 Schematic diagram showing relative positions of force elements F\u2217 acting on the airframe at relative distances l\u2217 from the CG-position (checkered circle); shown is the projection onto the (x, y)-plane", "texts": [ " Three further degrees of freedom, the vertical velocity Vz, roll velocity Wx and pitch velocity Wy , need to be included in order to accurately model asymmetric loading between the landing gears. The model used here was specifically developed in Ref. [7] to work efficiently with continuation software; the results in this paper are computed with the package AUTO [8]. Indeed, continuation methods and bifurcation analysis [9, 10] have proved effective in the study of flight dynamics, road vehicle dynamics and aircraft ground dynamics [11\u201313]. The equations of motion were derived by balancing either the forces or moments in each degree of freedom [14]. In Fig. 1 the relative positions and directions of the force elements that act on the aircraft are shown in a top-down view, the (x, y)-plane in the body coordinate system. This diagram can be used to derive the equations for Vx , Vy and Wz. The remaining equations are obtained by the same method but using different projections. The equations of motion for the translational and rotational velocities in the body-axis of the aircraft are given by the ordinary differential equations (1)\u2013(6). A dot notation is used to show the first derivative with respect to time of the translational velocities V\u2217 and angular velocities W\u2217", " 5 the thrust is varied in the range T \u2208 (12%,15.2%) which corresponds to FxT \u2208 (26 689 N,33 806 N). The orthogonal force elements on each of the nose, main-right and main-left tyres are denoted F\u2217N , F\u2217R and F\u2217L, respectively. The individual aerodynamic force and moment elements act at the aerodynamic centre of the aircraft and are denoted F\u2217A and M\u2217A, respectively. The thrust force is assumed to act parallel to the x-axis of the aircraft, and it is denoted FxT . The dimensions l\u2217 are shown to scale in Fig. 1 to give an idea of the relative lengths between components. The mathematical model presented and used here has been validated against an industry-standard multibody dynamics model. Full details of the component models for tyre forces and aerodynamic forces are given, along with details for the model\u2019s validation, in Ref. [7]. The lateral forces on the tyres depend nonlinearly on the vertical load on the tyre and its slip angle. For small slip angles, the relation between slip angle and lateral force is linear, but at higher slip angles the force generated by the tyre saturates before starting to decrease" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002012_s0967-0661(02)00063-1-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002012_s0967-0661(02)00063-1-Figure1-1.png", "caption": "Fig. 1. IRIS-T missile configuration.", "texts": [ " Critical issues for next-generation autopilots will not only be a fast response to the required acceleration demands or to provide extreme maneuverability while maintaining stability, but also to guarantee robustness over a wide range of mission profiles at all altitudes. Accelerating and decelerating flight conditions, changing mass and inertia properties, varying thrust characteristics, or uncertain effectiveness of the control surfaces are among the effects leading to a highly nonlinear behavior of the missile dynamics in the considered flight envelope. The Infra-Red Imaging System-Tail/thrust-vector controlled (IRIS-T missile) illustrated in Fig. 1 is a new short range air-to-air missile currently developed in a joint effort by Germany, Greece, Italy, Norway, and Sweden with BGT acting as prime contractor. Using combined aerodynamic and thrust vector control, the missile is optimized for close-in air-to-air combat. In order to deliver the desired maneuverability, the missile is capable of flying at high angles of attack and exhibits considerable lateral acceleration capabilities. Considering the rapidly changing, highly nonlinear dynamics involved, selecting the appropriate methodology for autopilot design is crucial for the success of the missile development" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003477_1350650111431790-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003477_1350650111431790-Figure5-1.png", "caption": "Figure 5. Shear deformation of layers when passing through a rolling contact with slip.12", "texts": [ " Therefore, an initially linear region of the traction curve around the origin has to be followed by a non-linear transition to sliding with a constant coefficient of friction. During the transition, there is a growing area of slip in the contact area where the limiting shear stress is reached (Figure 4). A contact lubricated by a fluid with purely elastic properties and a limiting shear stress strictly proportional to pressure would yield the same traction characteristics as a dry contact of solid bodies. It can simply be regarded as an elastic layer on top of the solid rolling elements (Figure 5). However, in contrast to Coulomb-type solid friction, in the case of a lubricant film, viscous relaxation substantially alters the shear stresses related to a specific amount of shear. Hence, the maximum traction shifts to higher slip values. Higher rolling speeds and therefore shorter passage times through the contact principally reduce the effect of relaxation. Therefore, in contrast to dry contacts with Coulomb type friction, there will be an influence of rolling speed. at UNIVERSITY OF WATERLOO on March 25, 2015pij" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002273_1077546304042047-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002273_1077546304042047-Figure11-1.png", "caption": "Figure 11. Flexible body coordinates.", "texts": [ " The method proposed in this investigation to model stiff leaf springs that experience small elastic deformation is based on the finite-element floating frame of reference formulation (Shabana, 1998). Using the assumption that there is no relative rigid body displacement between the leaves of the spring, the leaf spring can be modeled as one flexible body in the floating frame of reference formulation. The leaves are discretized using the finite-element method. The gross motion of the leaves is described by the displacement of the spring (body) coordinate system, as shown in Figure 11. The deformation of the leaves with respect to the body coordinate system is described using the finite-element nodal coordinates. The leaves of the spring at some sections can experience intermittent contacts and friction due to the relative displacements. Using the floating frame of reference formulation and assuming that the spring i consists of ni l leaves, and each leaf l is discretized using nil e elements, the global position vector of an arbitrary point on an element j of leaf l of the spring i can be written as ri jl Ri Ai ui jl j 1 2 nil e l 1 2 ni l (12) where Ri is the global position vector that defines the location of the origin of the spring body coordinate system, Ai is the transformation matrix that defines the orientation of the body coordinate system in the global inertial frame of reference, and ui jl , as shown in Figure 11, is the vector that defines the position of the arbitrary point on the leaf l with respect to the body coordinate system. This vector can be written as ui jl ui jl 0 ui jl f (13) at GEORGIAN COURT UNIV on December 11, 2014jvc.sagepub.comDownloaded from where ui jl 0 is the local position of the arbitrary point in the undeformed configuration, and ui jl f is the elastic deformation at the arbitrary point. Using the finite-element floating frame of reference formulation and the concept of the intermediate element coordinate system, the vector ui jl can be expressed in terms of the finite-element nodal coordinates of the spring as (Shabana, 1998) ui jl Ni jl qi 0 qi f (14) where qi 0 is the vector of nodal locations in the undeformed state, qi f is the vector of elastic nodal deformations of the spring, and Nijl is the appropriate shape function that can be defined using the procedure described in Shabana (1998)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002784_j.fss.2008.09.017-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002784_j.fss.2008.09.017-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the process.", "texts": [ " x3, u \u2208 are jacket and jacket inlet temperatures and the latter is considered as the manipulated variable. \u2208 M is the reaction rate vector, Kst \u2208 N\u00d7M is the stoichiometric coefficient matrix, H \u2208 1\u00d7M is the heat of reactions vector. Fr, Fj \u2208 are reactor and jacket flow rates, and Vr, Vj \u2208 are the reactor and jacket volumes, respectively. r, j \u2208 are parameters related to the physical properties of reactor and jacket fluids, Vr, Vj and heat transfer surface and coefficient. The schematic diagram of the process is shown in Fig. 1. Let n = N + 2 be the state space dimension. The natural set where the dynamical system (1)\u2013(3) is defined becomes n+ = { x \u2208 n : xi 0, i = 1, 2, . . . , n}. It is assumed that x1 is unavailable state vector, and x2 and x3 are measured. Also volumes of reactor and jacket, Vr and Vj, are assumed to be constant. Note that the actual manipulated variables are cold and hot water flow rates denoted by Fc and Fh. The jacket inlet temperature can be obtained through an energy balance around the mixing point of cold and hot water as given below:{ Fcxc,in + Fhxh,in = Fju Fc + Fh = Fj (4) where xc,in, xh,in \u2208 are temperatures of cold and hot waters, assumed to be constant, and Fj is also constant" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001843_1.2826131-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001843_1.2826131-Figure7-1.png", "caption": "Fig. 7 Coordinate systems applied for simuiation of meshing", "texts": [ " (r = c, t), or (\u00ab) as the envelope to the two parameter family of surfaces of the worm. Both approaches provide the same pinion (gear) tooth surface. The computerized simulation of meshing is based on the equations that provide continuous tangency of pinion and gear tooth surfaces. The simulation can be accomplished for aligned and misaligned gear drives. The computerized simu lation of contact is based on determination of the contact ellipse at each instant. Three coordinate systems, S , S^ and Sf are applied for investigation. Fig. 7. The fixed coordinate system Sf is rigidly connected to the housing of the gear drive. Fig. 1(a). The movable coordinate systems S^, and Sg are rigidly connected to the pinion and the gear, respectively. An auxiliary coordi nate system S,^ is applied for simulation of meshing when the gear axis is crossed or intersected with the pinion axis instead of being parallel, and when the shortest distance between the pinion and gear axes is changed. The misalignment angle Ay is decomposed into two components, Ay^ and Ay^ that represent the crossing angle and the intersection angle, re spectively", " Angle lAi^jl of ^hc compensating turn can be determined by using the equation (A<^2 X fj -I- Aq) \u2022 n = 0 (10) Here: A<^2 '*> the vector of the compensating angle of rotation of gear 2; n is the unit normal at the contact point: Fj is the position vector of the current point of the line of action; and Aq is the displacement of the contact point caused by misalignment. Determination of Linear Functions of Transmission Er rors. Three types of angular misalignment are considered: crossing of axes, intersection of axes, and an error of the lead angle of the pinion (or the gear). Using Eq. (10), we have determined the following equation of transmission errors for both types of helical gears considered above. where. N., b = - -r- tan A A02 = b(j)i tan a\u201e (11) AA\u201e AA\u201e sin A\u201e sin A (12) Here: A-y\u0302 is the crossing angle. Fig. l{b); Ay^ is the intersection angle. Fig. 7(c); AA ,\u0302 and AA ,\u0302 are the errors of the lead angles of the pinion and the gear, respectively. Influence of Change of Center Distance. The change of center distance of N.-W. gears and modified involute helical gears does not cause transmission errors but only the shift of the bearing contact (the path of contact). The shift can be evaluated as the change of the pressure angle determined as follows: {i) In the case of N.-W. gears we have [10, 16] sin a : ^E -y\u201e,+ y\u201e. (13) where y^,. (r = c, t) is the coordinate of the circle center corresponding to circular arc p," ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure13-1.png", "caption": "Fig. 13. Bearing contact and contact stresses for the pinion (left) and gear (right) of helical gear drive of design A2 at the instantaneous contact point 9 when errors of alignment \u0394H2=\u0394V2=0.025\u00b0 occur.", "texts": [], "surrounding_texts": [ "As previously mentioned, pointing and undercutting of the shaver tooth surfaces have to be avoided. Pointing of the shaver means that the width of the topland becomes very small or equal to zero. Undercutting occurs when the generating tool removes part of the active surface of the gear teeth. Analytically, undercutting can be predicted by the appearance of singular points on the generated surface. Undercutting is avoided by considering the approach proposed by F.L. Litvin and represented in detail in [10]. Undercutting can be avoided by choosing an appropriate number of teeth. Larger pressure angles are in favor of avoidance of undercutting. Pointing is avoided by increasing the number of teeth of the shaver and the proper control of the helix angle, the pressure angle and the crossing angle. Fig. 7. Face width of the to-be-shaved gear and the shaver: (a) 3D 5. Computerized simulation of meshing and contact 5.1. Applied coordinate systems Fig. 8 represents the applied coordinate systems for tooth contact analysis (TCA) of a helical gear drive comprising a pinion of new geometry obtained by plunge shaving and a conventional helical gear. The following errors of alignment are considered: (i) axial displacement of the pinion, \u0394A1, (ii) axial displacement of the gear, \u0394A2, (iii) gear horizontal positioning shaft error, \u0394H2, and (iv) gear vertical positioning shaft error, \u0394V2. Coordinate systems S1 and S2 are movable coordinate systems rigidly connected to the modified shaved helical pinion and a conventional helical gear, respectively. Angles \u03d51 and \u03d52 are the angles of rotation of the pinion and the gear, respectively. Table 2 shows details of coordinate transformation from S1 to S2. 5.2. Discussion of results obtained A helical gear drive with main design parameters shown in Table 3 will be considered for tooth contact analysis and later for finite element analysis. Three cases of design, with design characteristics shown in Table 4, will be considered. Case of design A1 represents the conventional design of a helical gear drivewith lineal-type contact. The results of tooth contact analysis of the mentioned design of a helical gear drive when (a) no errors of alignment occur, (b) errors \u0394H2=\u0394V2=0.01\u00b0 occur, and (c) errors \u0394H2=\u0394V2=0.025\u00b0 occur are shown through Fig. 9(a), (b) and (c), respectively. For the conventional design of a helical gear drive, the bearing contact is lineal-type, it is not localized, and when errors of alignment occur, the contact pattern is shifted to the edge of the surface. view of the to-be-shaved gear; and (b) 3D view of the shaver. Fig. 9(d) represents the function of transmission errors for referred configurations of case of designA1. A piecewise almost linear function of transmission errors (see Fig. 9(d)), responsible of the noise and vibration of the gear drive is obtained when errors of alignment are present. Case of design A2 represent the application of partial crowning in longitudinal and profile direction by considering the theoretical generation by a rack cutter with generating surface divided in nine zones as shown in Fig. 1(a). The results of tooth contact analysis of the mentioned design of amodified helical gear drivewith partial crowning when (a) no errors of alignment occur, (b) errors \u0394H2=\u0394V2=0.01\u00b0 occur, and (c) errors \u0394H2=\u0394V2=0.025\u00b0 occur are shown through Fig. 10(a), (b) and (c), respectively. Themain advantages of application of partial crowning for modification of the geometry of a helical gear drive are obtained from the combination of the advantages of lineal and localized contacts.We can summarize the advantages as follows: (i) the bearing contact is localized when errors of alignment occur, and (ii) the smaller errors of alignment occur, the larger contact pattern is obtained, and lower contact stresses are expected. A very favorable function of transmission errors of low level is obtained for referred configurations of case of design A2 (see Fig. 10(d)). Case of design A3 represent the application of total parabolic crowning in longitudinal and profile direction. Total crowning means that the whole surface is crowned so that zones 2, 4, 5, 6 and 8 in Fig. 1 do not exist. The results of tooth contact analysis of mentioned case of design of a modified helical gear drive for same configurations than for the previous case of design are shown in Fig. 11. When total parabolic crowning is applied in longitudinal and profile directions, the bearing contact is localized and the gear drive is not sensitive to the appearance of errors of alignment. A parabolic function of transmission errors is obtained for all three cases of design. Based on the results of TCA, designs A2 and A3 with partial and total crowning, respectively, fulfill the requirements of gear drives of low noise and vibration levels, high endurance, and increased service life. In this stage, finite element analysis of both gear drives is fundamental to select the better approach for modification of the geometry of a helical gear drive. 6. Stress analysis This section covers stress analysis and investigation of formation of the bearing contact for modified helical gears finished by plunge shaving. The performed stress analysis is based on the finite-element method and application of a general purpose computer program [11]. The development of finite-element models of modified helical involute gears has been accomplished according to the ideas represented in [12]. Application of finite element analysis enables investigation of the formation of the bearing contact and the determination of contact and bending stresses for the whole cycle of meshing. Finite element models of three pairs of contacting teeth are used to study the influence of the load sharing on the bearing contact on the pinion and gear tooth surfaces. The main design parameters of the gear drive and cases of design investigated are shown in Tables 3 and 4. Elements C3D8I [11] of first order (enhanced by incompatiblemodes to improve their bending behavior) have been used to form the finite-element mesh. The total number of elements is 59372 with 67572 nodes. The material is steel with the properties of Young's module E=2.068\u22c5105 MPa and Poisson's ratio 0.29. A torque of 1600 Nm has been applied to the pinion. Figs. 12, 13, and 14 show the bearing contact and contact stresses for the pinion and the gear of a helical gear drive of design A1, A2 and A3, respectively, when errors of alignment \u0394H2=\u0394V2=0.025\u00b0 occur. An area of high contact stresses is observed in Fig. 12 due to a linealtype contact. Such area of high contact stresses is avoided for cases of design A2 and A3 where the contact is localized. Fig. 15 represents the evolution of contact and bending stresses for the pinion of a helical gear drive for the following cases of design: (i) conventional design (case A1), (ii) partial crowning (case A2), and (iii) total crowning (case A3). For all cases, errors of alignment \u0394H2=\u0394V2=0.025\u00b0 have been considered. Conventional design yields very high contact stresses due to the theoretical lineal-type contact shifted to edge contact. Modified helical gear drive represented in cases A2 and A3 show a smooth evolution of contact stresses due to the localization of the bearing contact, with the approach based on partial crowning of the pinion tooth surfaces yielding the lower contact stresses. The level of bending stresses is almost the same for all three cases of design as shown in Fig. 15(b). Fig. 16 shows the evolution of contact stresses for the pinion of cases of design A2 (Fig. 16(a)) and case of design A3 (Fig. 16(b)) for different values of errors of alignment. As shown in Fig. 16(a) for case of design A2, the lower the misalignment is, the lower contact stresses are obtained, increasing the endurance and life expectation of the gear drive. On the contrary, case of design A3 yield similar results of contact stresses no matterwhat thevaluesofmisalignments are. Therefore, bothapproached work properly for modified helical gear drives finished by plunging, having the approach based on partial crowning the possibility to reduce contact stresses even more when low errors of alignment occur. 7. Conclusions The results of the performed research allow the following conclusions to be drawn: (1) A modified geometry of helical gear drives finished by plunge shaving has been proposed and investigated. The geometry of the shaver tooth surfaces that will shave the helical pinion and apply the proposed surface modifications has been developed. (2) Geometric characteristics of the proposed shaver has been discussed. The necessary face width of the shaver and the con- ditions for avoidance of pointing and undercutting have been studied. (3) A numerical example of design of a modified helical gear drive has been represented. Three cases of design have been studied. Tooth contact analysis and stress analysis for the mentioned three cases of design,when different levels of errors of alignment are present, have been performed and the results compared. (4) Partial crowning of the pinion tooth surface has been proposed as the optimal design for a helical gear drive, yielding the lower contact stresses and transmission errors when errors of alignment occur. Acknowledgments The authors express their deep gratitude to Yamaha Motor Company and the Spanish Ministry of Science and Innovation (Project Ref. DPI2007-63950) for the financial support of respective research projects and to the latter for the support received through the Spanish National Program ofMobility of Human Resources, Reference PR20080331. References [1] D.P. Townsend, Dudley's Gear Handbook, 2nd EditionMcGraw-Hill, Inc., New York, 1991. [2] F.L. Litvin, Q. Fan, D. Vecchiato, A. Demenego, R.F. Handschuh, T.M. Sep, Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving, Computer Methods in Applied Mechanics and Engineering 190 (39) (2001) 5037\u20135055. [3] I. Moriwaki, M. Fujita, Effect of cutter performance on finished tooth form in gear shaving, Journal of Mechanical Design, Transactions of the ASME 116 (3) (1994) 701\u2013705. [4] D.H. Kim, Simulation of plunge shaving operation for spur and helical gear, and tooth contact analysis of finished gear drive, Proceedings of the ASME Design Engineering Technical Conference, vol. 4 A, 2003, pp. 247\u2013256. [5] S.P. Radzevich, Design of shaving cutter for plunge shaving a topologically modified involute pinion, Journal of Mechanical Design, Transactions of the ASME 125 (3) (2003) 632\u2013639. [6] S.P. Radzevich, Computation of parameters of a form grinding wheel for grinding of shaving cutter for plunge shaving of topologically modified involute pinion, Journal ofManufacturing Science and Engineering, Transactions of the ASME127 (4) (2005) 819\u2013828. [7] R.H. Hsu, Z.-H. Fong, Theoretical and practical investigations regarding the influence of the serration's geometry and position on the tooth surface roughness by shaving with plunge gear cutter, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220 (2) (2006) 223\u2013242. [8] S. Nakada, I. Moriwaki, Effect of preshaved form and cutter performance in plunge cut shaving, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007, vol. 7, 2008, pp. 39\u201346. [9] F.L. Litvin, I. Gonzalez-Perez, A. Fuentes, K. Hayasaka, K. Yukishima, Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis, Mathematical and Computer Modelling 42 (9\u201310) (2005) 1063\u20131078. [10] F.L. Litvin, A. Fuentes, Gear Geometry and Applied Theory, 2nd EditionCambridge University Press, New York (USA), 2004. [11] I. Hibbit, Karlsson & Sirensen, ABAQUS/Standard User's Manual, 1800 Main Street, Pantucket, RI 20860-4847, 1998. [12] J. Argyris, A. Fuentes, F.L. Litvin, Computerized integrated approach for design and stress analysis of spiral bevel gears, Computer Methods in Applied Mechanics and Engineering 191 (2002) 1057\u20131095." ] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure1.15-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure1.15-1.png", "caption": "Figure 1.15- The hysteresis loop traversal during operation of a Forward Converter. From Martin (1987)", "texts": [], "surrounding_texts": [ "In the design of transformers for inverters, the worst case scenario is used with regard to transient voltages that may increase the input voltage. Knowing the maximum and minimum voltages will help in the design process. Another Circuit Push-pull Feed forward Flyback Advantages Medium to high power Efficient core use Ripple and noise low Medium power Low cost Ripple and noise low Lowest cost Few components Disadvantages More components Core use inefficient Ripple and noise high Regulation poor Output power limited \u00ab100 Watts) operational problem that must be considered in the design of push-pull con verters is the possibility of D.C. imbalance in the two arms of the circuit. For this reason, full bridge converters are used for most high-power applications even though they have twice as many power semiconductor switches. The voltage stress is only on the DC Bus voltage, not twice the value. In addition, a DC blocking capacitor can be added to the full bridge where it cannot in a push-pull circuit. 1.6-THE HYSTERESIS LOOPS FOR POWER MATERIALS Since this book is involved with the application and choice of magnetic components in power electronics, it is important to relate the action and prop erties of the magnetic materials in the transformers and inductors in the cir cuits we have been studying. What produces the voltage is not the alternation but the rate of change of the flux. As the current and voltage wave-forms change during operation, the magnetic components go through the hysteresis loop characteristic of the magnetic material. In some cases only part of the hysteresis loop is traversed. The operation of a power transformer or choke can be designed to have a bipolar drive as in the push-pull type or unipolar (forward or flyback mode). In the bipolar case, the course of the induction or the excursion is in both directions so that the magnetization is reversed. The In the unipolar case, the induction is unidirectional and the magnetization is not reversed. In Figure 1.12b, for the forward converter, a slow-rise capacitor or ringing choke has been added to reset the core. In the case of the flyback converter, (Figure 1.12c), the offset ofthe ac induction loop is due to the DC usually present in flyback converter. In certain instances in power electronics, the limits of induction are from the remanent to a higher induction. The loop traversed is a minor loop in the first quadrant similar to the one shown in Fig ure 1.13. In this case, the B used in the induction equation is still Lffi/2 even though the magnetization is not reversed. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 13 Whereas the ~B and thus the corresponding voltage are smaller in a unipolar than in the bipolar drive, the construction and operation are much simpler and more economical. The hysteresis loop traversals for flyback, forward and push-pull converters are shown in Figures 1.14, 1.15, and 1.16 . In the use of ferrites as flyback transformers for television receivers, the voltage and cur rent waveforms are not sinusoidal but saw-tooth or flyback shape. This per mits the electron beam to sweep across the TV screen with its visual signal and when it comes to the end, it would rapidly return or fly back to the start ing horizontal sweep position to present the next lower line of information. In this case, the transformer operation is unipolar. The basis of the modem elec tronic switching power supply is the action of the transistor as a switch. Early transistors were not built to carry much power and thus, as was the case for early ferrite inductors and transformers, they were used mainly in telecommu nication applications at low power levels. The first power electronic compo nent was the inverter that is a device that takes a DC input and produces an ac output in a manner other than the usual rotary generator. A transformer may be incorporated in the device to give the required voltage. The device can be mechanical such as a vibrator or chopper or it can be of the solid state variety using a transistor. The word, oscillator, may sometimes be confused for an inverter but in the oscillator, the frequencies may be higher and the power levels lower. The second important item, a DC converter, takes the DC of one voltage and converts it to DC at another voltage. One might call it a DC trans former. The intermediate step in a converter is that of an inverter namely the conversion of DC to AC. Of course, the additional step is rectification to D.C. The input to a converter can sometimes be a low frequency (50-60 Hz.) which is rectified, inverted, transformed, and then again rectified. The advantage over a conventional transformer is that the transformation is much more effi cient at the higher frequency. 1. 7-SWITCHING POWER SUPPLIES The complete switching power supply may consist of several auxiliary sections in addition to the power transformer. If ac is the input, it must first go through a noise filter to keep out unwanted transients. It is then rectified be fore entering the power transformer where it is first inverted to a square wave of the higher frequency (or pulse repetition rate) and then transformed to the desired output voltage. The transistor is driven by an auxiliary timing trans former or driver. After passing through the power transformer, the secondary voltage is again rectified. It then passes through a voltage regulator to main tain the voltage limits in the required range. Often this is done in a feedback circuit which controls the on-off ratio of the switching transistor. This 14 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 15 B t Bmax B ~B ----~~~---...... L ~'4--_---L-B H technique is called \"pulse width modulation\" or PWM and is widely used. An example of such a circuit is shown in Figure 1.17. Switching power supplies have efficiencies on the order of 80-90% compared to those of linear power supplies that may range from 30-50%. The switching supplies are, therefore, lighter and smaller than their counterparts. A typical switching power supply is shown schematically in Figure 1.18 (Magnetics 1984). 1.8-FERRORESONANT CONVERTERS In a previous section, we have discussed the use of pulse width modula tion (PWM) as a means of regulating a high frequency power supply. This method using square wave produces high switching loss because of all the odd harmonics produced by the square wave. There are several other control mechanisms which we will discuss One is the use of a resonant or ferroreso nant converter. The other is the use of a magnetic amplifier. There are many instances of resonance as it relates to low level linear fer rite components. In such cases a series or parallel combination of an inductor and capacitor acted as an LC circuit for frequency control in low level filters. The term resonance (more properly, ferroresonance) here has more of a connotation of resistance to changes in the input voltage and current by stor ing energy in the resonant circuit. As a matter of fact the first uses of ferro resonance was in the construction of a constant-voltage 60 Hz. transformer by Sola. In power supplies, an important use of the ferroresonant transformer is as a regulator. The early 60Hz transformers have given rise to the high-frequency type, which as noted earlier, may be even more useful at the highest frequencies than the conventional switching transformer design. As a high-frequency power inductor, the ferroresonant transformer has a quite different function. For one thing, the magnetic circuit is non-linear and because of the high currents and fields, operation is close to saturation. Most often when used as a power inductor, it is necessary to insert an air gap or spacer to avoid saturation. Figure 1.19 shows a simple ferroresonant regulator that consists of a lin ear inductor, Lh a non-linear saturating inductor, L2 and a capacitor, C, in parallel with L2\u2022 The latter two components form the ferroresonant circuit that controls the input voltage. The input energy is stored in L, and the resonant circuit acts to pass a uniform voltage to the load. Although the linear trans former may be of the typical power ferrite found in transformers, the saturat ing transformer is quite different. In addition to the usual attributes of power ferrites, it should possess a rather square hysteresis loop. The squareness ratio, BIBs should be over 85%. The permeability over the linear portion ofthe loop APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 17 18 MAGNETIC COMPONENTS FOR POWER ELECTRONICS should be as high as possible with the saturation permeability quite low (Jl = 20-30) By combining the ferroresonant regulator with a high frequency inverter, a ferroresonant converter can be constructed as shown in Figure] .20 Then, with the addition of a rectifier in front, a switching power supply can be made. See Figure 1.21. McLyman(1969) has shown how a high frequency ferroresonant trans former, tuned to about 20 KHz. can be used to stabilize high frequency inverters. With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for en ergy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 19 To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10\u2022 There are applications in which a high-frequency inverters is needed with low harmonic distortion. In a resonant inverter, a square-wave is produced by the switch network. The square wave has many odd harmonics that produces distortion and high switching loss. When the square wave is fed into the reso nant tank circuit that is tuned to the fundamental frequency, a pure sine wave is produced that is then rectified and filtered. By changing the frequency closer or further from the resonant frequency, the voltage and current at the load can be controlled. A resonant inverter circuit with two switches is shown in Figure 1.22.With the addition of a rectifier and low pass filter network, a resonant converter circuit is formed. See Figure 1.23. 1.9-S0FT SWITCHING IN COMMON TOPOLOGIES The reduced switching loss is the chief advantage of a resonant converter brought about by either zero-current switching (ZCS) or zero-voltage switch ing (ZVS). These fall under the heading of soft switching that can also 20 MAGNETIC COMPONENTS FOR POWER ELECTRONICS be applied to other topologies. The switching using the resonant inverter is done at the zero crossing points of the sinusoidal current or voltage wave forms and thus reduce the semiconductor switching loss allowing operation at higher frequencies. In a buck converter, zero-current switching can be imple mented by insertion of a quasi-resonant switch cell in place of the PWM switch cell as shown in Figure 1.24 . It is also possible to insert a ZVS switch cell into a buck converter as shown in Figure 1.25. A Zero Voltage Switching Circuit using an active-clamp snubber network in a forward and flyback con verter is shown in Figure 1.2. SUMMARY This chapter has reviewed the various circuits that are commonly used in power electronics. The hysteresis loop traversals of the magnetic components were correlated with the three topologies for unipolar and bipolar cases. The magnetic functions of the magnetic components involved in the operation a switching power supply will be discussed in Chapter 2. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 21 22 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 23 References Severns, R. P. and Bloom, G. E.,(1984) Modern DC-to-DC Switchmode Con verter Circuits, EJ Bloom Associates, San Rafael, CA Bracke, L.P.M.,(1983) Electronic Components and Applications, Vo1.5, #3 June 1983,p171 Bracke L.P.M.(1982) and Geerlings, F.C., High Frequency Power Trans former and Choke Design, Part I, NY Philips Gloeilampenfabrieken, Eindhoven, Netherlands Erickson, R.W. and Maximovic, D., (2001)Fundamentals of Power Electron ics, Second Edition Kluwer Academic Publishers, Boston, Dordrecht Magnetics (2000) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Martin, W.A.(1987), Proceedings, Power Electronics Conference (1987) Chapter 2 MAIN CONSIDERATIONS FOR MAGNETIC COMPONENT CHOICE INTRODUCTION After having reviewed the applications and topologies for the various power electronic circuits in Chapter 1, we can now proceed to investigate the main considerations that are made in choosing the appropriate magnetic com ponent. In this chapter, these considerations are related to the function of the component in the circuit. They include a general review of material properties and the core shapes and sizes. The final size will be determined by the design considerations and the input and output variables. Lastly, the question of cost will come into play depending on the market that the component and the fm ished product is aimed. 2.1-CONSIDERA TIONS BASED ON COMPONENT FUNCTION At the end of Chapter 1, we listed the various magnetic functions that are used in a switching power supply. They are; 1. Power Transformer 2. Power Inductor or Choke 3. In-line or Differential-Mode Choke 4. Common-mode Choke 5. EMI Suppression Core 6. Pulse Transformer for Transistor Firing 7. Magnetic Amplifier Core 8. Power Factor Correction Core In choosing the best magnetic component for these functions, we use a proc ess similar to that employed for low-level components except that the neces sary parameters are somewhat different. The choice will be determined by: 1. The type of converter circuit used. 2. Frequency of the circuit. 26 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 3. Power requirements. 4. The regulation needed (percentage variation of output voltage permitted) 5. Cost of the component. 6. Efficiency required. 7. Input and output voltages The components for each of these functions will be considered separately as their requirements are somewhat different. The cores selected to meet these requirements will be discussed with regard to; 1. Core material 2. Core configuration which includes associated hardware (bobbins, clamps, surface-mount connections etc.) 3. Size of the core 4. Winding Parameters- (number of turns, wire size) This chapter will review these requirements in general for the various func tions and in much more detail in the following chapters. 2.2-MAGNETIC COMPONENT CHOICES Having limited the choice of material somewhat to only power and power-related applications, there are still a large variety of components that can be used. These include; 1. Soft ferrite cores 2. Powdered metal toroids (and some E-cores) 3. Magnetic metal strip cores (Tape cores, laminations, cut-cores) 4. Amorphous metal strip wound tape-cores 5. Nanocrystalline material strip-wound tape cores F or the last two materials, there are several variations of material available but the core shape (a toroidal tape-wound core) is set by the physical attributes of the material (brittleness). These properties also may limit the size of the core particularly with respect to the inside diameter. The choice for the various components for each function will be discussed separately. 2.3-COMPONENTS FOR POWER TRANSFORMERS In power transformer functions, a large induction swing may be trav ersed calling for a core with highest effective permeability derived from the best core material and shape. A high saturation material with low losses under CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 27 the operating conditions is desirable. While a toroid gives the highest effec tive permeability for a specific material, it is costly to wind. An ungapped ferrite E-core or other power shape is preferable for noncritical applications. For lower frequency power applications (line or mains frequency) laminated strip of iron or SiFe is commonly used. For somewhat higher frequency power applications, tape cores of thin strip SiFe, high permeability NiFe (80 Per malloy) high saturation NiFe (50 Permalloy) or CoFe (Supermendur) can be used. For high frequency operation, the workhorse of the power electronics components is the ferrite core that is available in many materials, shapes and sizes. Recently, some inroads have been made with the new amorphous and nanocrystalline materials. Power transformers have one requirement in common, that is that the material saturation be as high as possible consistent with other factors such as core loss. As we shall see later, at very low frequencies, the materials are satu ration-driven as eddy current losses are moderately low. These materials such as iron, low-carbon steel and heavy gage silicon iron will not be discussed in this book since they do not enter into the field of power electronics. At high frequencies, the materials are core-loss-driven so that materials such as fer rites are generally used. For medium high frequencies, materials such as thin gage silicon iron, amorphous materials and the new nanocrystalline materials are available. We normally make this choice on the basis of frequency of op eration. Vendors usually provide guidelines as to what materials are suitable for the various frequency ranges. The core losses are often given as a function of frequency. Although vendors generally list power materials separately, the user often has a choice of several available materials varying according to losses, frequency and sometimes, cost. Since power ferrites operate at the highest possible induction, we find, as we would expect, that they have the highest saturation of the ferrites consistent with maintenance of acceptable losses at the operating frequency. For frequencies up to about 1 MHz., Mn-Zn ferrites are the most widely used materials. Above this frequency, NiZn fer rites may be chosen because of their higher resistivities. Since ferrite cores make up the largest proportion of high frequency power transformers, the considerations for their choice will be discussed first. 2.4- FERRITE POWER TRANSFORMERS Having mentioned that ferrite cores are the major components for power electronics we will discuss them first. Switching power supplies and ferrite expansion went hand in hand. To explain why ferrites were made to order for these applications, we must understand the implications of going to higher frequency operation. Ferrites have low saturation compared with most common metallic magnetic materials (such as iron) and also have much lower 28 MAGNETIC COMPONENTS FOR POWER ELECTRONICS permeabilities than materials such as 80% NiFe. The low saturation of ferrites comes about from the fact that the large oxygen ions in the spinel lattice con tribute no moment and so dilute the magnetic metal ions. This situation is compared to a metal such as iron where there is no such dilution. In addition, because of the anti ferromagnetic interaction, not all the magnetic ions con tribute to the net moment in ferrites but only those with uncompensated spins. The first use of ferrite material in a power application was to provide the time-dependent magnetic deflection of the electron beam in a television receiver. The two ferrite components used were the deflection yoke and the flyback transformer. This application remains the largest in tons of soft ferrite used. Another early use of power ferrites was in matching line to load in ultra sonic generators and radio transmitters. Ferrites were not considered for line power inputs because at the lower frequencies (50-60 HZ.),they wereeco nomically unattractive (lower Bsat and higher cost than electrical steels). How ever, today's ferrites are employed as noise filters in power lines on the input to all types of electronic equipment. The potential for using ferrites at high frequencies was always there but the auxiliary circuit components (mostly semiconductors) were not yet developed. In addition, earlier there was no great market or stimulus for high frequency power supplies. One envisaged use was in high frequency fluorescent lighting at about 3000 Hz. This idea was suggested in the early 1950's but the need for setting up line power at these frequencies was never fulfilled. (See Haver 1976) In the 1970's, the rapid growth of ferrites for use at high power levels oc curred shortly after the similar growth of power semiconductors that could switch at very high frequencies. This design specifically required moderate cost magnetic components with low losses at higher frequencies and elevated power levels. Thus the age of the switched mode power supply (SMPS) was born. Coincidentally, the rapid growth of computers and microprocessors has required small, efficient power supplies that could be constructed with power ferrite components. The computer and allied markets are certainly providing much of the present day impetus for today's power ferrite development. The matching of SMPS component needs with ferrite properties is explained in the following two sections. 2.4.1- Frequency-Voltage Considerations A changing electric current in a winding provides a corresponding change in a magnetizing field which sets up a resultant varying magnetic in duction in a magnetic material. This changing flux will induce a voltage in another (secondary) winding. The general case of a voltage produced by a changing (not necessarily alternating) magnetic flux is given by Faraday's equation namely; CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 29 E = -N dcjl/dt = -N d(BA)/ dt [2.1] For a sine wave, the induced voltage is given by: E = 4.4BNAfxlO-8 [2.2] where:cjl = Magnetic flux, maxwells E = induced voltage, volts B = maximum induction, Gausses N = number of turns in winding A = cross section of magnetic material, cm2 f = frequency in Hz. For a square wave, the coefficient is 4.0 instead of 4.44. If we, for the present, minimize the effects of complicating problems such as core losses and temperature rise (which we will discuss later), we can use this important induction equation to examine the use of the variables in the most preliminary design. To obtain a given voltage with the most efficient arrangement, the tradeoffs can be as follows; 1. Increasing B by using a material with high induction such as 50% Co-Fe. This material is used in aircraft and space application where space and weight are important. However, there is a material limitation on how high the B can go. Ferrites may have saturation of 4-5,000 gausses. The highest RT saturation of about 23,000 gausses is found in 50% Co-Fe, so that there is a possible 4:1 or 5:1 advantage here for metals. See Table 2.1. 2. N can be increased which leads to higher wire resistance losses. Also, there is a maximum number of turns that can be wound around a core with a window or bobbin area. Using small wire size allows more turns, but the increased resistance (due to the increased length to cross sectional area) limits the useable current through the wire. 3. A can be increased. In addition to higher core losses, the larger cross-section requires a longer length of wire per tum leading to higher copper losses and a larger and heavier device. The larger cross section in a poor thermal conductor such as a ferrite also creates the problem of how to remove the heat produced in a large core. If the heat isn't removed, the temperature rise lowers the saturation induction, Bs of the ferrite. Under these conditions, if the induction-swing, ~B, is large enough, the core may actually saturate and the current in the winding can become very large possibly causing catastrophic failure. This can damage the core, the winding and other components. 4. f can be increased. Here the effect can be quite dramatic depending on the frequency dependence of core losses. For instance, in going from a 60-Hz power supply to 100KHz supply, the factor is 1666. This coupled 30 MAGNETIC COMPONENTS FOR POWER ELECTRONICS with a 4: 1 reduction in going from high B metals to low B ferrite still leaves 400+:1 advantage. This permits a great reduction in the size & weight of the transformer, which reduces wire and core losses. In a high frequency power supply, increasing the frequency can exacerbate the thermal runaway problem if the exponent of frequency dependence is higher than that for flux density. We will deal with this subject with later in this chapter. NiFe (50% Ni, 50% Fe) NiFe (79% Ni, 4% Mo, Balance Fe) NiFe Powder (81% Ni, 2% Mo, Balance Fe) Fe Powder Ferrites Amorphous Metal Alloy(Iron-Based) Amorphous Metal Alloy (Co-based) Nanocrystalline Materials (Iron-based) 2.4.2-Frequency-Loss Considerations 15,000 7,500 8,000 8,900 4,000-5,000 15,000 7,000 12,000-16,000 We have shown that by increasing the frequency of a transformer, we can produce the desired voltage requirement at a greatly increased efficiency. However, we have neglected one consideration, that is, the increased losses that occur when we increase the frequency of operation. The additional losses incurred in the frequency increase are mainly eddy current losses caused by the internal circular current loops that are formed under ac excitation. The eddy current losses of a material can be represented by the equation: Pe = KBm2Fd2/ P [2.3] where: P e = Eddy Current losses, watts K = a constant depending on the shape of the component Bm = max induction, Gausses f= frequency, Hz d = thickness-narrowest dimension perpendicular to flux, cm p = resistivity, ohm-cm Again there is a trade-off for lower P e. B can be lowered which means larger A to get the same voltage. Frequency, f, can be lowered which again means CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 31 larger components. The thickness, d, can be made smaller, such as in thin metallic tapes, wire or powder. There are physical limitations to this variable, and also the high cost of rolling metal to very thin gauges. The other measure we can take is to increase the resistivity. (See Table 2.2.) A comparison will demonstrate the advantage of ferrites. The resistiv ity for metals such as Permalloy or Si-Fe is about 50 x 10-6 ohm-cm. The re sistivity of even the lowest resistivity ferrite is about 100 ohm-cm. The dif ference then is about 2 million to 1. Since the effect of the frequency on the losses is a square dependence and that of resistance only a linear one, the net effect on frequency is about 1400 to 1. Thus, losses to the 60 Hz operation, for the same size core, extend to 84,000 Hz, close to the 100 KHz we postu lated for the voltage calculation. Granted this calculation is simplified, having omitted wire losses and loss differences due to B variations, but the order of magnitude is probably reasonable. In actual cases, 60 Hz power supplies op erate at efficiencies of about 50%, whereas the ferrite high frequency switch ing power supplies operate at 80-90%. Table 2.2 Resistivities of Ferrites and Metallic Magnetic Materials Material Zn Ferrite Cu Ferrite Fe Ferrite Mn Ferrite NiZn Ferrite Mg Ferrite Co Ferrite MnZn Ferrite Yttrium Iron Garnet Iron Silicon Iron Nickel Iron Resistivitity, n -cm 102 105 4 X 10-3 104 106 107 107 102_103 1010_1012 9.6 X 10-6 50 X 10-6 45x10-6 We must include another consideration in the comparison. We have men tioned the poor thermal conductivity of ferrite and ceramics in general. Aside from the difficulty of firing very dense, large, ceramic parts without produc ing cracks, there is also the previously mentioned problem of heat transfer. Because of this limitation, ferrite switching power supplies have not been made larger than about 10 KW. This is in comparison to the over 100 KW supplies that are made of metallic materials. However, since the large mar kets in power supplies are for home computers or microprocessors, and since these are well within the operational size of ferrites, there is no real size problem here. A comparison of magnetic properties of ferrites with other 2.4.3-Choosing the Best Ferrite Power Transformer Material A material slated for a power application must meet certain special requirements. Although ferrites in general have low saturations, we must, at least, provide the highest available variety consistent with loss considerations. This is mostly a matter of chemistry. Along with this consideration is the need for a high Curie point. This generally means maintaining a high saturation at CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 33 some temperature above ambient which approaches actual operational tem perature. In addition to the saturation requirement, the material must possess low core losses at the operating frequency and temperature. The transformer losses, which include both the core loss and the winding loss, will heat the ferrite causing a reduction in the saturation to a value lower than that at room temperature. If this fact is not taken into account, the core may saturate at the higher temperature with disastrous results. A runaway heating situation could develop leading to catastrophic failure. Many ferrite suppliers have redes igned their materials such that the core losses will actually minimize at higher operating temperatures preventing further heating of the cores. The negative temperature coefficient of core loss at temperatures approaching the operating temperature helps compensate for the positive temperature coefficient of the winding losses in the same region. Roess(l982) has shown that the minimum in the core loss versus temperature occurs at about the position of the secon dary permeability maximum. Thus, if the chemistry of the ferrite can be de signed to have the secondary permeability maximum at the temperature of device operation of the transformer as described above, the core losses will also be lowest at that temperature. However, we must consider that this is only a local minimum. Having the minimum at 75-1 OO\u00b0C.is a tremendous aid to the designer in avoiding thermal runaway, but still requires careful design work as the core loss increases above this minimum and the capacity for thermal runaway is still very real. Some smaller portable devices such as lab top computers operate intermittently at low ambient temperatures so materials with core loss minimum temperatures near room temperature may be used. 2.4.4-Power Ferrite Core Shapes Power ferrites come in a variety of shapes. Although pot-cores were the ferrite shapes of choice in telecommunication ferrites, several required or preferred features for this application are not as critical in power usage. These include: 1. Shielding 2. Adjustability In addition, pot cores are more costly and power ferrites must compete with other alternative materials. Therefore, shapes such as E cores, U cores, and PQ cores are more applicable to power application. Other shapes including solid center post pot cores can be used. The following chapter describes the types of shapes available. The shape of the core has a bearing on the ampli tude permeability since the inductance is given by; L = .41tJ.lN2/IA [2.4] 34 MAGNETIC COMPONENTS FOR POWER ELECTRONICS where: I = length of the winding, cm. A = Cross sectional area, cm2 L = Amplitude Permeability Therefore, the longer the section on which the winding is placed and the shorter the height of the winding, the higher the inductance. 2.4.S-Component Processing after Assembly After the ferrite component is wound, there are additional process steps that may affect the choice of component. These include; 1. Encapsulation 2. Soldering 3. Clamping 4. Winding 5. Gluing 6. Coating Encapsulation, coating, gluing and clamping all put stresses on the core that may affect the magnetic properties. Some materials are more sensi tive to stresses than others even though the properties are superior. Winding also stresses the core. Toroidal winding is costlier than bobbin winding. In modern printed circuit design, wave soldering is often used to attach compo nents and leads to the board. Proper component choice will minimize the ef fect of the soldering temperature. 2.4.6-High Frequency Applications Special attention must be paid if the frequencies of power supplies extend past 100 KHz and even to the 1 MHz region. First, the size of the core may be reduced significantly. Second, the core material must be modified to lower the core losses at these frequencies. The maximum flux density or B level used which, at lower frequencies, may have extended to 2000-2500 gausses may have to be reduced to something on the order of 500-600 gausses to attain the lower losses. The increase in frequency with smaller size and better efficiency may more than offset the lower saturation used. We will dis cuss designs at these higher frequencies at a later point in this chapter. Ven dors design instructions are based on allowing the flux density to drop to lower values at higher frequencies in order to keep the core loss constant at 100 mW/cm3. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 35 2oS-METAL STRIP POWER TRANSFORMERS In our discussion in Section 2.4.1, we found that a great advantage of some of the metal strip magnetic components was their high saturation, (Si Fe, Ni-Fe, and Co-Fe). However, as we examined the core losses in Section 2.4.2, we also found that due to their low resistivity, the usefulness of these materials was diminished. Reducing the thickness or gage of these materials allowed them to operate at somewhat higher frequencies. For the 80% Ni-Fe, with a lower saturation, the very high permeability also reduced high frequency losses especially in thinner gages. The Ni-Fe alloys had an addi tional advantage of being able to be reduced to an extremely thin gage (0.0005\") Provided that the frequency is not too high, this material can be used in the form of tape cores, laminations an also cut cores. The advantages and disadvantages of Si-Fe and Co-Fe are given in Table 2.5. The compara ble listings for Ni-Fe are given in Table 2.6. One general advantage of the metallic strip cores is that they can handle higher power levels than the ferrite cores. Aside from their higher saturations, their higher thermal conductivities allow them to dissipate heat more efficiently. 206o-AMORPHOUS METAL STRIP CORES A newer line of metal strip materials other than those described in the previous section are the amorphous metal alloys. The iron-based alloys have the high saturation for use as power transformers. Their resistivities are higher 36 MAGNETIC COMPONENTS FOR POWER ELECTRONICS than the crystalline magnetic alloys and they can be annealed for either low frequency or higher frequency operation. However, they are magnetostrictive and are only used at lower frequencies. The Co-based materials have almost zero magnetostriction which gives them a high permeability and lower losses. The advantages and disadvantages of the amorphous materials are given in Table 2.7. In Figure 3.34 are shown the real and imaginary values of the com plex permeability. Roess gives one advantage of ferrites over the amorphous materials in that they can only be produced in toroidal tape-wound cores. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 37 2.7. -NANOCRYSTALLINE-BASED POWER TRANSFORMERS The newest of the soft magnetic strip power materials are the nano crystalline. These materials were developed as an extension of the amorphous metal materials and are made by a similar process except that the material is annealed to produce a very fine grain size on the order of 10 nanometers. The iron based material has high saturation and permeability. The latter is due to almost zero magnetostriction similar to the Co-based amorphous alloys 2.8-COST CONSIDERATION FOR MAGNETIC COMPONENTS Aside from the technical performance of the magnetic component, some consideration must be given to the comparative cost of the component. The final cost is determined by several factors; 1. Cost of raw materials 2. Cost of core fabrication 3. Cost of winding Some of the advantages of a ferrite core are the low raw material and fabrication costs. Thin gage metals (SiFe, amorphous and nanocrystalline) have relatively high fabrication costs. For winding costs, toroids are the most 38 MAGNETIC COMPONENTS FOR POWER ELECTRONICS expensive, then pot cores and finally, E-cores. Figure 2.1 gives the trans former cost utility in maxwells per dollar as a function of frequency. The pre dominance of ferrites especially at higher frequencies is evident. 2.9-COMPETITIVE HIGH FREQUENCY POWER MATERIALS Roess( 1987) has recently emphasized that a great virtue of ferrite power material is their adaptability, and even at higher power frequencies. He compares the losses of several competing power materials for the higher fre quency operation. Trafoperm is a NiFe strip material. Vitrovac is an amor phous metal strip material and Siferrit is of course, a ferrite. The results are given in Figure 2.2 . Up to 100 KHz., the amorphous metal materials have lower losses than the ferrite especially the thinner gage type which remains lowest even at the higher frequencies. Roess points out that despite this disad vantage, a ferrite core is still the magnetic component of choice because of its much lower cost and its adaptability to be produced in many different shapes. The strip, on the other hand, has limitations on the shapes in which it can formed as shown in Figure 2.3. The new nanocrystalline materials were de veloped after this study. A new fine-grained rapidly solidified nanocrystalline (not amorphous) strip material was introduced by Hitachi Ltd. It has much higher saturation (13,500 Gausses), higher permeability (16,000 at 100 KHz.) than ferrites and very low losses at 100KHz. Although these properties compare favorably to ferrites, it remains to be seen if the price and performance will allow it to compete with ferrites. In addition, the nanocrystalline cores have the same lack of fabrication versatility as other strip-wound cores 2.10-DESIGN CONSIDERATIONS IN COMPONENT CHOICE Aside from the items previously mentioned in choosing a mag netic component for power electronics, there are additional considerations based on the other design requirements. These include; 1. Space, Volume and Weight Restrictions 2. Ambient Temperature-Heat removal 3. Environmental-Corrosion, Radiation, Vibration and Shock 4. Reliability-Lifetime 5. Regulation- Voltage variation 6. Safety considerations CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 39 2.11- FERRITES VS METALLIC MAGNETIC MATERIALS There have been many comparisons of ferrites with other magnetic materials for power applications. The author (Goldman 1984) listed other metallic materials that were used for SMPS's. Goldman (1995) compared metal strip, powder cores and ferrites for various applications including power. Bosley (1994) presented a rather extensive study of the different mate rials for transformers and inductors versus frequency where the maximum flux was limited by saturation or core losses. The useable flux density under these limitations is given in Figure 2.4. For frequencies above 100 KHz., the MnZn and NiZn ferrites had the highest values. The performance factor in 40 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Tesla-hertz vs frequency is shown in a figure in next chapter. Here again, above 100 KHz., the two ferrites were the highest. The economic trade-off for these materials is given in Figure 2.1 which charts the maxwells of flux per dollar as a function of frequency for the competing materials. Bosley (1994) also listed the advantages and disadvantages of the competing materials for SMPS transformers. Table 2.5 show these for SiFe and Permendur, Table 2.6 for the NiFe alloys, Table 2.7 for the amorphous alloys and Table 2.4 for fer rites. Snelling C 1996) presents a plot of the power loss density of power fer rite, Co-Fe amorphous metal strip and the Vitrovac 6030 nanocrystalline ma terial vs frequency in figure in next chapter. The relative advantages in core loss depend on the frequency and flux density. The previous comparisons did not include the nanocrystalline materials that gained recognition shortly after the Bosley article even though Y oshizawa (1988) reported on them earlier. The frequency dependence of the permeability and loss factor of a nanocrys talline material was compared (Herzer 1997)along with those for a Co-based amorphous material and a MnZn ferrite. The permeability is higher and the loss factor is lowest for the nanocrystalline material. In addition the saturation induction was measured for the same materials (Herzer 1997). The nano crystalline material has the advantage there. It remains to be seen whether the pricing of the nanocrystalline can be low enough to compete with the rela tively inexpensive ferrite materials. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 41 2.12-0UTPUT POWER INDUCTORS Power Inductors differ from the low-level inductors that we have dealt with in telecommunication applications. They are not used in LC circuits for frequency control. In power inductors, use is made of their ability to store large amounts of power in their magnetic field. As such, they can limit the amount of ac voltage and current. When this is done in the presence of a high D.C. current, the inductor, usually in combination with a capacitor, serves as a smoothing choke to remove the ac ripple in a D.C. supply. This is often done in the output circuit ofthe supply after rectification. Since there are large D.C. and smaller superimposed a.c. currents, they usually need gaps to prevent saturation. In addition to the increase in current and possible catastrophic fail ure at saturation, the incremental permeability drops close to zero and there fore, the required inductance specification is not met. With the gap, the mag netization curve is skewed to avoid saturation (See Figure 4.11). With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for energy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10 , In some power inductor applications, as in the common mode choke, the magnetic core must sense the small difference between 2 magnetic cur rents and a high permeability toroid or ungapped shape must be employed. In some other of these inductor functions, the full power of the circuit passes through the magnetic component and some feature must be added to keep the core from saturating. The same is true for some energy-storage functions where a high DC current is present. In these two cases, either a core with a discreet gap (ferrite E core) or a distributed gap toroid (iron powder core) is warranted. 2.12.I-Ferrite vs Metallic Powder Inductors Earlier in this chapter, we compared ferrite power transformer materi als with their counterparts in metallic materials. For ferrite power inductors, the materials are mostly the same as the transformer materials. However in the case for metallic materials, the materials for power inductors are different than those used for power transformers. Whereas gapped ferrite cores are used for many power inductor applications, in the case of the metallic cores, the gap is a distributed one as found in powder cores. Bosley (1994) who did the analysis on SMPS transformer materials compared the materials for SMPS inductors in the same paper. The materials evaluated were; 42 MAGNETIC COMPONENTS FOR POWER ELECTRONICS I.NiFe Powder Cores- Molypermalloy and Hi_Flux Cores 2.Sendust Powder Cores- Kool-Mu and MSS cores 3.Amorphous Choke Cores 4.Powdered Iron Cores 5.Gapped Ferrite Cores 6, Metal Strip Cut Cores Some of these materials were used for low level telecommunications applica tions. For power applications at high power levels, the materials may be somewhat different. Bosley (1994) listed the advantages and disadvantages of the above mentioned materials for power inductor applications. Table 2.8 lists these for NiFe powder cores, Table 2.9 for Sendust (FeAISi) powder cores. Table 2.10 for amorphous metal choke cores, Table 2.11 for powdered iron cores, Table 2.12 for gapped ferrite cores and Table 2.13 for cut cores. Since power inductor often must operate under high D.C. bias conditions, the effec tive permeability for these materials are given. The DC bias curves for several of these materials are shown in Figure 2.5. Again, the nanocrystalline materi als were not considered. Bosley also listed the core losses of the various in ductor materials compared to ferrites in Table 2.14. Although the ferrites are lower in losses than the others listed. Bosley notes that, with a medium to large gap, there may be increased losses due to fringing flux This may in crease ac copper losses near the gap. Nanocrystalline materials were not con sidered here as well. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 43 44 MAGNETIC COMPONENTS FOR POWER ELECTRONICS CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 45 Pauly (1996) reviewed the selection of a high-frequency core material for power line filters. He compared various powder core materials and gapped ferrites with respect to volume, sound level and cost. All cores were 1.84 inch toroids except the gapped ferrite which wa a gapped EC70/70G . The induc tors were 4.0 mHo Ripple current was a 40 KHz. triangular Wave with peak to-peak level of 33% of rated current. Output power was theoretical. Table 2.15 summarizes the results. The losses of the MPP, MSS (Sendust) and Hi Flux cores were much lower than that of the powdered iron but the cost was dramatically lower. Best performance was found in the MPP cores. Table 2.16 is the author's opinion in the ranking of the cores as to the suitability of the various cores for a given application. In general smaller cores may be oper ated at higher frequencies and flux levels. 46 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2.13- POWER FACTOR CORRECTION CORES In some new ac input lines for switching power supplies, a \"front end\" boost pre-regulator is used to obtain an essentially Unity Power Factor or UPF. The circuit for this function is shown in Figure 2.6. An external logic circuit serves to control the duty cycle of the main switch, Q 1 to raise the in put voltage, Vi to the output voltage, Vo. Higher peak ac flux densities are present than in conventional output chokes so core losses are quite important here. If the wrong core or material is used, core losses will increase and the possibility of thermal failure may occur. As in the case of the output choke, the materials used are the various types of powder cores (iron, molyperm, high flux NiFe, Sendust) or a gapped ferrite. However, special considerations of the losses must be taken into account with iron powder cores so that larger cores and lower loss materials must be used. A_C. IIIVT + Cl \u2022 D.C. CIlITM Fgure 2.6- A front-end boost preregulator for Power Factor Correction (PFC), (From B. Car sten, Application Note, Micrometals (2001) 2.14 -MAGNETIC AMPLIFIER CORES In cases of multiple outputs in switching power supplies, their may be an imbalance in the output voltages. In cases where the regulation must be controlled very precisely, one solution is the use of a magnetic amplifier CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 47 regulator circuit. The circuit for a forward converter with a 5V and 12V. ou put is given in Figure 2.7 . The 5V output uses PWM feedback circuitry to regulate. The 12 V output uses the magnetic amplifier or saturable-core reac tor to regulate. The materials used for the mag amp must have high square ness or B/Bs ratios, low coercive force for small reset current and low core loss for small temperature rise. Components for this function are Square-loop NiFe tape cores, Co-based amorphous metal cores and square loop ferrite toroids. We have considered the use of square loop ferrites previously in conjunction with the ferroresonant transformer design. The advantages and disadvantages of the square permalloy are shown in Table 1.17.Those of the cobalt-based amorphous metal material are given in Table 1.18 and the corresponding ones for the square-loop ferrite are given in Table 1.19. 48 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2.tS-PULSE TRANSFORMERS There are instances when the transistor switch supplying the square wave is triggered or fired by an external source or pulse generator. Ferrite cores, especially small toroids, are widely used in pulse transformers. This application requires transmission of a square wave with little distortion. The shape of a typical square wave voltage pulse is shown in Figure 2.8. During the time that the voltage pulse is on, the current is ramping up as is the flux CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 49 density. In the case of a square wave, the ~B is given in terms of the applied voltage, E, and the pulse width, T. For a specific core area and number of turns, the equation is; B = ET xI0-8/NAe [2.5] From the value of ~B , the corresponding value of H, the magnetizing field can be determined from the vendor's curves on the material properties. From this value of H, and the Ie of the trial core, the excitation current can be deter mined from; H =.4 nNIp//e [2.6] IfE, T, N are given and a AB is assumed, the effective dimensions of the core can then be given as; IJAe = O.4nN\\ m x1081ET~H [2.7] The cores corresponding to various values of IJAe are listed by the vendor. The pulse permeability is given by; ~p = ETlIp [2.8] The pulse transformers used in digital data processing circuits will usually have ~B's on the order of 100 Gausses and are always little toroids inserted in small TO-5 cans for use on PC boards. Higher power pulse transformers may use pot cores or E cores that may be gapped to prevent saturation. All of the frequency related problems encountered in wide-band transformers are pres ent in the pulse transformer, but here, it is evidenced by pulse attenuation (droop). As in the previous case, the permeability should be as high as possi ble, but when high pulse repetition rates or fast rise times are used, perme ability concerns may be compromised for lower losses. Permeabilities of about 5-7000 are frequently used for small ferrite toroids. 2.16-COMPONENTS FOR EMI SUPPRESSION Before our discussion of the actual components used for EMI sup pression, it is useful to look at the circuitry involved along with the currents both intentional and unintentional. The latter, of course are the EM! interfer ence or noise currents. Basically, there are two types of EMI currents, namely the common-mode and the differential currents. These are contained in a pair of wires leading to and from the load. The first of these is the differential cur- 50 MAGNETIC COMPONENTS FOR POWER ELECTRONICS rents whose current flow is the same as in ordinary intended or designed cir cuitry as shown in Figure 2.9. The differential EMI currents then flow in the same direction as the intended currents. If a current probe is placed around the pair of conductors, no current flow will be detected for either the intentional or unintentional (EMI) currents. In the case of the common-mode EMI cur rents, they flow in the same direction in both conductors. Now, while the dif ferential intended currents will cancel, the non-intentional (EMI) currents will not and there will be a current indicated with a probe. Another way of de scribing the two types of current flow is shown in Figure 2.9 that shows the voltages producing the currents. In the differential case, the voltage is be tween the high voltage line and the neutral line while in the common-mode case, it is the voltage between both the high voltage and neutral lines to ground. The components for EMI suppression extend from very small beads to rather large cable clamp cores. Some and even slug-type cores toroids are used in the coil type of suppressor 2.16.1-Materials For EMI Suppression Until recently, the materials available for EMI suppression applica tions essentially were of two types. The most widely were and still are soft ferrites and the other less widely used one would be powder cores. Recently, amorphous and nanocrystalline cores have been used for the same purpose. Although sometimes the principal operational frequency of the circuit may be quite low (line or mains frequency, 50-60 Hertz), it is not primarily that fre quency which is designed for in EMI suppression. It is rather the interference or disturbance frequency that mostly determines the choice of material used although the effect of the lower frequency (DC) must be dealt with in the de sign of the EMI filter. This interference frequency frequency can be high fre quency ac or square or other digital waveform in the high Kilohertz or Mega hertz region. The secondary consideration would be the operational frequency in that the material must pass the lower frequency with sufficient inductance. This means that, at low frequencies, the material must behave as a fairly good inductor but at high frequencies, it must be quite lossy. The frequencies in volved in this application preclude any of the conventional metallic strip ma terials. Other possible new materials which will be listed later are the High Flux NiFe powder cores and the Sendust (Fe-AI-Si) powder cores. 2.16.2-Amorphous-Nanocrystalline Materials- EMI Suppression One of the earliest uses of the amorphous material was for a choke coil that Toshiba called the \"Spike-killer\". Presumably, only the cores are sold. The Fe-based amorphous materials used are under license from Allied's CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 51 l Metglas\u00ae Division (now Honeywell) . Vacuumschmelze does market a Cobased amorphous materials for EMI suppression applications. It is designated Vitrovac 6025 and is essentially a zero magnetostriction material. As an out growth of the amorphous materials, the iron-based nanocrystalline materials are the newest ones available and they have been used for EMI suppression. Their high permeabilities and low magnetostrictions made it very useful as a" ] }, { "image_filename": "designv10_13_0003154_1077546310362450-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003154_1077546310362450-Figure1-1.png", "caption": "Figure 1. Gear system with a single gear pair: (a) a 3D solid model and (b) a discrete physical representation.", "texts": [ " Undoubtedly, simultaneous considerations of timevarying stiffness and damping would be a more practical way to examine gear dynamics. Therefore, in this study a new approach to gear dynamic analysis is proposed, in which the time-varying lubrication effect is incorporated based on the elastohydrodynamic-lubrication and squeezed-film theories. The behavior of lubricant damping and its effects on the dynamic responses of spur gear pairs are also thoroughly discussed. A 3D geometric model of a geared transmission system with a single spur gear pair is shown in Figure 1(a). The theoretical model is illustrated in Figure 1(b), in which all components are assumed to deform with one degree of freedom. Thus, using Lagrange\u2019s principle, the vibration equations of motion for the geared system can be derived as (Lin et al., 1988): JM \u20acyM \u00fe CS1\u00f0 _yM _y1\u00de \u00fe KS1\u00f0yM y1\u00de \u00bc TM ; \u00f01\u00de J1 \u20acy1 \u00fe CS1\u00f0 _y1 _yM \u00de \u00fe KS1\u00f0y1 yM \u00de \u00fe Cg\u00f0t\u00derb1 \u00f0rb1 _y1 rb2 _y2\u00de \u00fe Kg\u00f0t\u00de\u00bdrb1\u00f0rb1y1 rb2y2\u00de \u00bc Tf 1\u00f0t\u00de; \u00f02\u00de J2 \u20acy2 \u00fe CS2\u00f0 _y2 _yL\u00de \u00fe KS2\u00f0y2 yL\u00de \u00fe Cg\u00f0t\u00derb2 \u00f0rb2 _y2 rb1 _y1\u00de \u00fe Kg\u00f0t\u00de\u00bdrb2\u00f0rb2y2 rb1y1\u00de \u00bc Tf 2\u00f0t\u00de; \u00f03\u00de JL \u20acyL \u00fe CS2\u00f0 _yL _y2\u00de \u00fe KS2\u00f0yL y2\u00de \u00bc TL; \u00f04\u00de where JM , J1, J2, and JL represent the polar inertia of mass for the input motor, driving and driven gears, and applied loading; CSi and KSi are the torsional damping factors and torsional stiffnesses of the input and output shafts in which i \u00bc 1; 2; Cg\u00f0t\u00de and Kg\u00f0t\u00de are the damping factor and stiffness of the meshed gear pair; yM , y1, y2, and yL are the angular displacements of the input shaft, driving gear, driven gears, and output shaft; rb1 and rb2 are the base circle radii of the driving and driven gears; TM and TL are the input and output torques; and Tf 1\u00f0t\u00de and Tf 2\u00f0t\u00de are the frictional torques on the driving and driven gears, respectively. Among these, Cg\u00f0t\u00de and Kg\u00f0t\u00de reflect the time-varying properties of the meshing stiffness and lubrication damping due to moving meshing points with gear rotation. First, the meshing stiffness, Kg\u00f0t\u00de, of a gear pair as shown in Figure 1(a) can be derived by including the three aspects of compliance which are (1) qt;i that accounts for the bending and compressive deformations of its gear teeth subject to the meshing force; (2) qb;i for tooth displacement due to being elastically supported on their gear bodies; and (3) qH ;i for the local Hertz deformations on the contacting tooth surfaces (Cornell, 1981; Huang and Liu, 2000). Therefore, the meshing stiffness, K12; i, of the ith tooth pair of mating gears, i \u00bc 1, 2, can be deduced as K1 2; i\u00f0t\u00de \u00bc \u00f0qt;i \u00fe qb;i \u00fe qH ;i\u00de 1: \u00f05\u00de By including all tooth pairs participating in meshing at a given instant, the total stiffness of the gear pair is Kg\u00f0t\u00de \u00bc XnT i\u00bc1 K12; i\u00f0t\u00de; \u00f06\u00de where nT is the number of the tooth pairs in the mesh, which is generally one or two for gear pairs with a low contact ratio" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001352_s0045-7949(98)00251-x-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001352_s0045-7949(98)00251-x-Figure5-1.png", "caption": "Fig. 5. Numerical model for determination of (seq)max and H.", "texts": [ " For the treated example the maximum contact pressure is equal to p0=1400 N mm\u00ff2. The frictional loading distribution q(x ) is calculated with use of the simple Coulomb friction law with q(x )=m p(x ), where m is the coe cient of friction between contacting cylinders. It is taken to be equal to m=0.04, which is the average value for gears with good lubrication [19]. The resulting maximum equivalent von Mises stress (seq)max and its position (depth H under the contact surface) are determined using the \u00aenite element model shown in Fig. 5. The \u00aenite element analysis of the model results in (seq)max=800 N mm\u00ff2 and H= 0.126 mm. In the model it is assumed that the embryonic crack is initiated along inclusion interfaces at the point of the maximum equivalent stress computed above, i.e. at depth H = 0.126 mm under the contact surface. For the case of fatigue crack initiation along inclusion interfaces the number of stress cycles Ni required for the crack initiation can then be determined with Eq. (9), where the computed maximum equivalent stress (seq)max=800 N mm\u00ff2 is used as the applied stress amplitude Dt to the grain [10]", " The results are presented in Figs. 6 and 7. From these computations it can be concluded that the number of stress cycles Ni required for the fatigue crack initiation decreases with increase of the inclusion radius R and its shear modulus Gv. Taking into account that the usual values for 2R/D lie in the interval from 0.01 to 0.1, the computed number of stress cycles Ni required for the fatigue crack initiation along inclusion interfaces is between 1.372 102 and 2.286 105 load cycles. The equivalent model shown in Fig. 5 is also used for the numerical simulations of the fatigue crack propagation. The local \u00aenite element discretization around the initial crack is shown in Fig. 8 (step 1), where the special fracture \u00aenite elements are used around the crack tip. During the \u00aenite element analysis, the stress intensity factor at the crack tip is computed at discrete crack extensions and is very small at the beginning, but later increases as the crack propagates through the material in the direction of the frictional contact loading (see Fig. 5). When the crack approaches the contact surface (Fig. 8, step 11), the value of the stress intensity factor is high, although still lower than the critical stress intensity factor of the material KIc=2620 N mm\u00ff3/2. Numerical simulations have shown that at the moment, when the crack reaches the contact surface, the stress intensity factor in the other crack tip (left) exceeds the critical value KIc. This implies that when the crack reaches the contact surface the uncontrolled crack growth occurs at the other crack tip, which results in tearing of the material and formation of the surface pit" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003411_iros.2011.6094663-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003411_iros.2011.6094663-Figure7-1.png", "caption": "Fig. 7. The tangent lines l12 and l23, normal lines l1 and l2, and section 2\u2019s circle are on the same plane; \u03b11 and \u03b12 are complementary.", "texts": [ " y1 can be further expressed in terms of \u03c61 as: y1 = R(z1, \u03c61)y0 (6) where R(z1, \u03c61) is the rotation matrix of the rotation about the z1 axis with angle \u03c61, and y0 is the (fixed) y axis of the base frame of the robot. c1 can be expressed in terms of \u03c61 and \u03ba1 as: c1 = R(z1, \u03c61)[\u2212 1 \u03ba1 , 0, 0]T (7) where [\u2212 1 \u03ba1 , 0, 0]T is the center position of section 1 expressed in section 1\u2019s frame. Now, for the case that l12 and l23 are not parallel, Con- straint 1 can be expressed as: (p2 \u2212 p1) \u00b7 (l12 \u00d7 l23) = 0 (8) Let \u03b11 be the angle between p2 \u2212 p1 and l12 and \u03b12 be the angle between p2 \u2212 p1 and l23, as shown in Fig. 7, such that2 sin(\u03b11) = \u2016l12 \u00d7 (p2 \u2212 p1)\u2016 \u2016l12\u2016\u2016p2 \u2212 p1\u2016 (9) and sin(\u03b12) = \u2016l23 \u00d7 (p2 \u2212 p1)\u2016 \u2016l23\u2016\u2016p2 \u2212 p1\u2016 (10) Then, to satisfy Constraint 2, \u03b11 and \u03b12 must be either equal or complementary (see Fig. 7), depending on the directions of l12 and l23; that is, the following equation must be satisfied: sin(\u03b11) = sin(\u03b12) (11) For the case that l12 and l23 are parallel, then Constraint 1 is satisfied since l12 \u00d7 l23 = 0 (12) and Constraint 2 can be expressed as: (p2 \u2212 p1) \u00b7 l12 = 0. (13) Since p1 and p2 are on section 1\u2019s circle and section 3\u2019s circle respectively, each can be expressed in terms of a scalar angle as derived below. Define a local coordinate system for section i\u2019s circle, as illustrated in Fig", " Next we need to solve for the plane, center, and radius of section 2\u2019s circle. In the case where two tangent lines l12 and l23 are parallel, the center c2 of section 2\u2019s circle is on the same line as p1 and p2, and thus, its position satisfies: c2 = (p1 + p2) 2 (18) In the case where l12 and l23 are not parallel, l12 and l23 determines the plane of the section 2. Line l1 through p1, perpendicular to l12, and on the plane of section 2 can be determined, and similarly line l2 through p2, perpendicular to l23, and on the plane of section 2 can be determined as shown in Fig. 7. Then the intersection point of l1 and l2 is the center c2 of section 2\u2019s circle. In both cases, The radius of section 2\u2019s circle is: r2 = \u2016p1 \u2212 c2\u2016 (19) From section 1\u2019s circle (for the specified values of \u03ba1 and \u03c61) and section 2\u2019s circle, as well as p1 and p2, which are end-points of section 1 and section 2 respectively, the unknown configuration parameters of section 1 and section 2: s1, \u03ba2, s2, and \u03c62 can be found easily [14]. They are valid if their values are within their respective ranges" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002397_j.mechmachtheory.2004.10.003-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002397_j.mechmachtheory.2004.10.003-Figure1-1.png", "caption": "Fig. 1. Geometric set up for the generation of spiral bevel gears.", "texts": [ " According to the notation introduced in Section 4, let a be the axis of the machine cradle (generating tool) and b the axis of the gear blank. As well known, during generation of a spiral bevel gear a and b can be skew axes. Points Oa and Ob are not taken in this case on the line of shortest distance, as suggested in Eq. (16), but, according to [14] and also to common practice, they are displaced with respect to such line. More precisely, point Oa is moved along a by the so-called sliding base DXB2 , while point Ob is moved along b by the machine center to back DXD2 , as shown in Fig. 1). Quantity DEM2 , still in Fig. 1, called blank offset, is indeed the shortest distance between axes a and b. In order to actually apply the proposed approach (i.e., for computational purposes) we need to define, in the linear space R3, a unique (fixed) reference frame S = (O;x,y,z), with unit vectors (i, j,k). It is worth noting that all computations will be performed using just this single reference system. We take full advantage of the fact that our analysis is based only on vectors and they always belong to the same linear space R3" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002887_1.5057008-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002887_1.5057008-Figure10-1.png", "caption": "Figure 10: Functional prototype of a combuster swirler made of In 718 manufactured by SLM", "texts": [ " A new repair approach consists of the following three steps: 1) The damaged section of the vane is removed completely. 2) A patch that fits into the prepared void is manufactured by SLM. 3) The patch is welded into the vane by LMD. This repair technique could also be used e.g. for engine casings. Individual patches can be manufactured by SLM for each individual damage or deterioration. If individual units or small quantities of a certain geometry are required, SLM is significantly faster and more cost-effective than e.g. precision casting. Figure 10 shows an example of a functional prototype made by SLM. This combustor swirler is made of In 718. Page 210 of 1009PICALO 2008 Conference Proceedings Figure 11 shows an example of a patch for the repair of a HPT NGV. In this case the geometric data of the NGV was acquired by computer tomography. Alternatively, 3D CAD data could be used if available. The materials under investigation for this application are Rene 80 and MAR-M 247. Both materials are susceptible to micro crack formation during SLM processing" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003220_s00170-011-3742-3-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003220_s00170-011-3742-3-Figure2-1.png", "caption": "Fig. 2 a Schematic arrangement of laser rapid manufacturing setup. b Photograph of laser rapid manufacturing setup with co-axial processing head in inset", "texts": [ " In our earlier work, the recursive ball deposition method was employed to fabricate the porous material of stainless steel AISI 316 L, and a porosity of around 28% was achieved, but these materials did not have adequate mechanical strength due to the oxidized non-uniform joints among successive balls [27]. This work is focused on cross-thin-wall fabrication method. 2.3 Experimental setup This study was carried out using an in-house integrated LRM system. It consisted of an indigenously developed 3.5-kW CW CO2 laser system [28], a co-axial powderfeeding nozzle with a volumetric controlled powder feeder [29] and a five-axis CNC laser workstation. Figure 2a and b presents the schematic arrangement and photograph of the experimental setup. The CO2 laser beam was transferred to a five-axis CNC laser workstation by steering the beam with the water-cooled gold coated plane copper mirrors. A concave mirror (radius of curvature=600 mm) at an inclination angle of about 22\u00ba was used to focus laser beam at the laser workstation, and a defocused beam of diameter about 1.2 mm was delivered at the fabrication point for LRM. Argon gas was used as shielding and carrier gas" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003255_1.3151805-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003255_1.3151805-Figure1-1.png", "caption": "Fig. 1 Generating mechanism for curvilinear gears", "texts": [ " The TCA has been utilized herein to investigate the kinematical error KE of the circular-arc curvilinear tooth gear drive meshing under ideal and error assembly conditions. The location and shape of contact ellipses of the mating gear and pinion can be also simulated by applying the TCA results and surface topology method 9 . Six examples are presented to show the relations among the radius of circular-arc tooth profile, radius of curvilinear tooth-trace, contact ratio, contact pattern, and KE of the gear pair under different assembly conditions. Figure 1 illustrates the generating mechanism, proposed by Liu 1 for cutting of curvilinear gears, where axis A-A represents the rotation axis of the gear blank, and axis B-B expresses the cutter spindle. The spindle of the face-mill cutter with radius Rab rotates about the axis B-B with an angular velocity t and translates with a linear velocity 1r1 to the right, where r1 is the pitch radius of AUGUST 2009, Vol. 131 / 081003-109 by ASME f Use: http://www.asme.org/about-asme/terms-of-use t i a c I a s e c F c 0 Downloaded From: he gear blank and 1 is the angular velocity of it" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003037_ipec.2010.5544591-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003037_ipec.2010.5544591-Figure3-1.png", "caption": "Fig. 3. Configuration of the variable-magnetic-force memory motor.", "texts": [ " Furthermore, the magnetic flux of the constant magnetized magnet becomes a base portion and the magnetic flux of the variable magnetized magnet is added as a changed portion. Therefore, the variation range of the total magnetic flux can be enlarged. If the polarity of the variable magnetized magnet is reversed especially, variation range of the total magnetic flux will be doubled. The rotor of the principle model, which has arranged the variable magnetized magnet and the constant magnetized magnet in parallel, is shown in Fig. 3. In this principle model, the variable magnetized magnet has been arranged to the radial direction between magnetic poles, and the constant magnetized magnet is arranged in the central part of the magnetic pole so that it can be located between variable magnetized magnets. The magnetization property of a permanent magnet is expressed in the equation (1).In order to change magnetic flux density irreversibly, the magnetic polarization J changes with an external magnetic field. JHB += 0\u03bc (1) where B is magnetic flux density (T), 0 is permeability of vacuum, H is magnetic field (A/m), J is magnetic polarization (T)", " Magnetic flux distribution at maximum linkage magnetic flux. Electic angle degrees M ag ne tic f lu x de ns it y ( T ) Fig. 5. Distribution of air-gap magnetic flux density at maximum linkage magnetic flux. Magnetic field analysis using the finite element method was performed for the novel motor to verify the change of the linkage magnetic flux by the permanent magnet. The model for analysis determined the principle model. The magnetization direction of the magnet in an analysis model is the same as Fig. 3. The magnetization direction of the constant magnetized magnet is the direction of daxis, and is the upward direction. The magnetization direction of the variable magnetized magnet is the rightangled to q-axis. Firstly, the N pole is formed at d-axis side to produce the maximum of linkage magnetic flux. The analysis results at this state are shown in Fig. 4 and Fig. 5. The magnetic flux distribution of Fig. 4 shows that magnetic flux increases by addition of the magnetic flux of the variable magnetized magnet and the constant magnetized magnet" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003142_s11740-009-0168-y-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003142_s11740-009-0168-y-Figure1-1.png", "caption": "Fig. 1 Ball screw test stand with motion profile", "texts": [ " Therefore, even in the mixed friction area the deviations of the lubrication film of a basis lubrication which is necessary for a full separation of the contact surfaces will be preceded and consequently simplified [3]. In order to investigate the effect of the lubrication additives on the performance of ball screws in machine tools under real operating conditions, a ball screw test stand has been designed within the CRC 442 at the laboratory for machine tools and production engineering (WZL) (Fig. 1). The test stand abstracts a z-axis of a machine tool with ball screws and guarantees a detailed investigation of the ball screw during continuous operation. Technical parameter of the test stand: \u2022 Rapid/normal speed of slide: 40/10 m/min \u2022 Slide mass: 250 kg \u2022 Acceleration/deceleration: 10 m/s2 \u2022 Ball screw dimension: 40 9 20 (preloaded over 4- point-contact) \u2022 Ball screw length: 1,000 mm \u2022 Bearing arrangement: fixed-free \u2022 Lubrication: oil lubrication with 0.5 cm3/h The ball screw spindle is driven by a servo motor with integrated encoder which has a maximum moment of round about 230 Nm" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure5-1.png", "caption": "Figure 5. Powder and Regolith Acquisition Bit (PRAB) Collection Positions.", "texts": [ " Enabling Technology: Powder and Regolith Bit The Powder and Regolith Acquisition Bit can be used to acquire rock cuttings during the drilling process as is accomplished by the Mars Science Laboratory (MSL) Powder Acquisition Drill (PAD) System [7]. The bit can also be used to acquire regolith. Once the bit acquires rock powder or planetary regolith, the sample can be either dispensed into an instrument inlet port, observation tray, or cached for earth return along with rock cores. The principle of the bit operation is very similar to that of the Core PreView bit in that there are slots within the breakoff tube (referred to as Inner Canister in this case) and the auger as shown in Figure 5. When the slots are aligned, the regolith or rock powder can flow into the inner cavity. When the slots are closed (the inner tube is rotated with respect to the outer auger) the powder inside the bit is retained. The main difference between the Core PreView bit and the Powder/Regolith Bit is that the former uses a coring bit while the latter uses a full faced bit which cuts the entire diameter of the hole. The PowderBit integrates a set of sieves in the collection slots of the Inner Canister. Currently, the Inner Canister has 3 slots: 1 with a 150 micron sieve, 1 with a 1 mm sieve, and one without any sieve (Open Slot), while the Outer Canister needs just one Open Slot" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001487_mssp.2001.1413-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001487_mssp.2001.1413-Figure2-1.png", "caption": "Figure 2. Defect modelling and characteristic functions.", "texts": [ " In these conditions, the equations of motion read as [M]Mx( N#[C]MxR N#[K a ]MxN#[K(t,MxN)]MxN\"MF 0 N#MF(e(H(t))N#MG(t,MxN)N (1) and the analytical expressions of the two quantities which largely control the geared system dynamic response to tooth defects are [K(t, MxN)]\"k 0P L(t) H(D(g, t)) dgM< 0 NM< 0 NT (2) MG(t,MxN)N\"k 0P L(t) H(D(g, t))de(g, t) dgM< 0 N (3) where \u00b8(t) is the nominal contact length at time t and H(D(g, t)) is the unit Heaviside function which is zero when contact is lost and equal to one otherwise. Contact de#ections D(g, t) and tooth shape deviations e(g, t) are related by D(g, t)\"M< 0 NTMxN!de(g, t) (4) with de(g, t)\"eH(t)!e(g, t), eH(t) being the maximum of e(g, t) at t which is zero for perfect tooth #anks. Each local fault is modelled by normal deviations e(g, t) at a given location on the base plane (Fig. 2) which depends on both g(along defect widths) and time in order to simulate the defect extents in the pro\"le direction. Focusing on the early detection of localised tooth defects, it can be assumed that (i) contact is kept in the defect area (H(D(g, t))\"1, i.e. small depth of defect compared to mesh de#ection), (ii) no-load transmission error is not modi\"ed by defects of small dimensions (defect width is less than tooth face width). Dynamic system (1) becomes linear and the excitation functions read as [K(t, MxN)]\"[K(t, MxN)] ND \"k 0 \u00b8(t)M< 0 NM< 0 NT (5) MG(t, MxN)N\"MG(t)N\"k 0 M< 0 NP D(t) e(g, t) dg (6) where the subscript ND refers to no-local-defect conditions (as opposed to geometrical errors) and D(t) is the instantaneous defect width along the contact line. By using the mean value theorem, equation (6) is transformed into MG(t)N\"k 0 D(t)e(gN , t)M< 0 N (7) where gN is the abscissa (measured on a line of contact) of a point inside the instantaneous defect width D(t). After separating space and time variables as e(g, t)\"P(g)F(t) (8) where F(t) represents the defect morphology in the pro\"le direction [a windowing function whose amplitude lies between 0 and 1 within the defect area and is set to zero outside (Fig. 2)], one gets the additional excitation term induced by a tooth fault: MG(t)N\"k 0 F(t)D(t)P(gN )M< 0 N. (9) Setting \u00b8(t)\"\u00b8 m (1#a/(t)) (10) with a, a small parameter representing the relative variation of contact length with time, stable solutions can be sought by using a perturbation method (straightforward expansion) i.e. MxN\"Mx 0 N#aMx 1 N#2. (11) Inserting equation (11) in the linear system associated with equation (1) leads to the main (zero) order di!erential system (higher-order terms are not considered for the sake of clarity): [M]Mx( 0 N#[C]MxR 0 N#[K a ]Mx 0 N#k 0 \u00b8 m M< 0 NM< 0 NTMx 0 N\"MF 0 N#k 0 F(t)D(t)P(gN )M< 0 N" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure4.6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure4.6-1.png", "caption": "Figure 4.6- Ferrite EC cores for power applications (Courtesy of Siemens-Matsushita, Data Book, Ferrites and Accessories, 1997)", "texts": [], "surrounding_texts": [ "Figure 3.34-Penneability versus frequency for various materials. Reprinted from Herzer, Handbook of Magnetic Materials Vol. 10, \u00a91997, pA55, with pennission from Elsevier Science. 3.4.2-Amorphous-Nanocrystalline Materials for EMI Suppression One of the earliest uses of the amorphous material described earlier was as a choke coil that Toshiba called the \"Spike-killer\". Presumably, only the cores are sold. The amorphous materials used are under license from Al lied's Metglas\u00ae Division. Vacuumschmelze does market a Co-based amor phous material for EMI suppression applications. It is designated Vitrovac 6025 and is essentially a zero magnetostriction material. The characteristics are shown in Table 3.3. As an outgrowth of the amorphous materials, the iron based nanocrystalline materials are the newest ones available and they have been used for EMI suppression. Their high permeabilities and low magne- MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 91 tostrictions made it very useful as a common-mode choke at relatively low frequencies. The earliest nanocrystalline soft magnetic alloy was made by Hitachi and names \"Finemet\". The properties of the Finemet nanocrystalline material are given in Table 3.4. The saturation is high but not in the Si-Fe class. The permeability is high but not in the 80 permalloy class. The magne tostriction is low and about the same as the Co-based amorphous material. The resistivity is the same as the amorphous alloys but many orders of mag nitude lower than ferrite. It is really the combination of most of the good at tributes that make it attractive. High permeability materials without the high resistivities are useful for the inductive or permeability portion of the imped ance and are limited to the lower frequencies. Vacuumschmelze has two nanocrystalline materials, Vitroperm 500F and 800F that they recommend for EMI suppression(common-mode chokes) along with their Co-based amorphous zero-magnetostriction material Vitrovac 6025. The permeability of the 800F is somewhat higher than the 500F. A comparison of the Co-based amorphous, the nanocrystalline material and a MnZn ferrite is given in Figure 9.35 The permeability is higher and the loss factor is lower for the metallic material than for the other materials. The in- The use of gapped ferrite cores as output chokes was discussed ear lier. in Section 3.1.10 . Another series of good material choices for the appli cation are the metal powder cores. Aside from output chokes, a recent and MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 93 related application is that of power factor correction (PFC) cores. For these applications, there are two main advantages of powder cores over ferrites. They are; 1. Their saturation flux densities are much higher ( as much as 2-3 times higher) 2. The gap is a distributed one while that of ferrite is discreet lead ing to high gap losses. A disadvantage of the powder core is the need for costly toroidal winding as they are mostly used as ring cores. Some metal powder E-cores are now available. Similar to the metal strip analog, the lowest loss, highest perme ability material of the powder cores are the 80% Ni variety which allows for operation at higher frequencies (especially in thin gage). The 50% Ni alloy has twice the saturation of the 2-81 Moly Permalloy (MPP) material but it has higher losses and is used for lower frequencies. The iron powder cores have the highest saturation and lowest cost but the highest losses. For EMI applications, while common-mode filters are mostly used in unbalanced circuits where the currents return to ground, the differential-mode filter is used primarily in balanced systems. Consequently, putting a ferrite toroid around both wires would not cause any flux change in the core and so not suppress the EM!. The solution in this case is to put suppressor cores on each of the wires. However, this means that the full ac (and D.C.) signals would pass through the suppressor core. While the common-mode ferrite core can be used in high current power filters, the differential-mode suppressor ferrite core is only used in low current power filters. With the differential mode or in-line filters, the core losses could be a problem (except for D.C.), the main problem would be core saturation. To prevent this, a core with low permeability is needed. Either a gapped ferrite core or a powder core can be used. 3.5.1-Iron Powder Cores The iron powder cores, unlike those listed for low level telecommuni cations applications are of the higher permeabilities (from 70-100 perm). They are usually of the hydrogen-reduced variety. Before discussing the mag netic properties of powder cores for EMI suppression, we must point out that, while permeability has been our criterion for EM! ferrite suppression ability, with powder cores, vendors do not specify impedance. Since the application of these cores involves high flux densities and often D.C. bias, the magnetic properties usually listed are; 94 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 1. Permeability versus Flux Density 2. Permeability versus DC Bias 3. Core Losses 4. Permeability versus Frequency 5. Permeability versus Temperature 6. D.C. Energy storage curves Another important property for an application as a D.C. choke is the variation of energy stored versus D.C. current. The energy storage criterion is given by Y2 U 2\u2022 For the iron powder cores, the high saturation of about 20,000 Gauss is suited for this application. Curves displaying the variation of permeability with flux density and DC bias for iron powder cores are shown in Figures 3.36 and 3.37. Permeability versus frequency is shown in Figure 3.38.Core loss and Energy storage curves are shown in Figures 3.39-3.40. MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 95 96 MAGNETIC COMPONENTS FOR POWER ELECTRONICS --- 710 100 ... - '10 .. 40 .. .. \u2022\u2022 t-- -, .... \" I-- ... A. C. iOIeIIly 810M0t I\"'U') I-- -65 MATERIAL , , , , A~ V' ,- -- / ~'\" -,- , -./ -..... , I. .... .. '10 zoo 100 100 1000 1iIOO'\" .- ,ocoo IOOCIO.... ICIIIIIIII 10100D 0\\., C. PlU'Q1' 8TOI'&OI \\'IlL\" ~I Figure 3.40- Energy storage curves for 85 penn iron powder cores. From Pyroferric MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 97 3.5.2-NiFe Powder Core Materials Nickel iron powder cores come in two varieties, the 2-81 MPP (Moly permalloy Powder) and the 50-50 Hi Flux Cores. The NiFe powder cores listed as High Flux cores are different from the MPP cores listed in the chap ter on low level applications of powder cores. These NiFe cores are 50% Nickel-50% Iron. The have about twice the saturation (l5,000)of the MPP cores and thus are much better for the present application. Cores of this mate rial are available in permeabilities of 200, 160, 147, 125, 60, 26 and 14. The variations of permeability with flux density and D.C. bias, frequency and temperature for different permeabilities of this material are shown given in Figures 3.41 and 3.42. Plots of permeability versus frequency and temperature are found in Figures 3.43 and 3.44.The core losses are given in Figure 3.45. As expected, the stability is inversely proportional to the permeability but the high frequency core losses are proportional to the frequency. Cost-wise the High Flux powder cores are more expensive than the iron powder cores, but somewhat less expensive than the MPP cores. 98 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 100 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 3.5.3- Sendust Powder Material The Sendust cores are marketed under the trade names of Kool-Mu and MSS materials. It is a new application of an old material having been de scribed by Matsumoto in 1936 and patented in 1940 (Matsumoto 1940). Sen dust is a ternary alloy containing about 6% aluminum and 9% silicon. Its at traction is that it is close to a zero anisotropy-zero magnetostriction material. Its brittleness and difficulty in producing it have limited its use in the past to recording head material due to its great hardness. When used in powder cores, its brittleness helps in the comminution process. The high saturation of this material (on the order of about 10,000 Gauss provides much more energy storage than MPP cores or gapped ferrites. The cores come in permeabilities of 60, 75, 90 and 125. Figures 3.46-3.49 show the permeability variations of different permeabilities of this material for flux density, D.C. bias, frequency and temperature. The core loss of the 125 perm material is given in Figure 3.50. The core losses are significantly lower than the iron powder cores. However, the Sendust cores are somewhat more expensive. Cores with O.D's from. 140 inches to 2.25 inches are available. MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 101 Permeability versus Frequency Curves, Kool MIJ 102 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Permeability versus Temperature Curves, Kool MIJ Core Loss Density Curves, Kool MIJ MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 103 References Buthker,C.(1986) and Harper, OJ., Transactions HFPC, 1986,186 Bozorth, R.M. (1951) Ferromagnetism, Van Nostrand New York Fair-Rite (1996) Fair-Rite Soft Ferrites, 13th Ed. Fair-Rite Products Corp. One Commercial Row, Wallkill, NY 12589 Goldman, A. (1985), Advances in Ceramics U, Proc 4th ICF, p.421 Goldman, A. (1995), J. Mat. Eng. And Performance 1,395 Herzer, G. (1997) Handbook of Magnetic Materials, Vol. 10, Elsevier Science B.V. Amsterdam, 418,444,454,455 Hitachi (1998) FINEMET FT-IKM-KN Series Core Page on Internet Product Guide Hilzinger, H.R. (1996)Soft Magnetic Materials '96, Feb.26-28, 1996, San Francisco, Gorham-Intertech Consulting, 411 U.S. Route One, Portland ME, 04105Magnetics (1987) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Honeywell (2000). Metglas@ Technical Bulletin, Metglas@ Products, 6 Eastman Rd. Parsippany NJ 07054 Magnetics (1995) Tape-Wound Cores Design Manual, TWC-400, Magnetics, Division of Spang and Co., Butler, PA 16001 Magnetics (1998) Powder Cores MPP Cores for Filter and Inductor Applica tions, Magnetics, Div. of Spang and Co. Butler, PA 16001 Magnetics (2000) Ferrite Core Catalog, FC601, Magnetic Div., Spang and Co, Butler, PA 16001 Makino, A. (1997),Hatanai, T., Naito, Y. Bitoh, T.,Inoue, A., and Masumoto, T., IEEE Trans. Mag. MAG33, 3793 Micrometals (1990) Micrometals Iron Powder Cores, EMI and Power Filters Micrometals, 1190 N. HawkCircle, Anaheim ,CA, 92807 MMPA (!996) Soft Ferrites, A User's Guide SFG-96 Parker, C. (1994) Presented at MMPA Soft Ferrite Users Conference, Feb. 24- 25, 1994, Rosemont ,IL Pyroferric(1984) Toroidal Cores for EMI and Power Filters, Pyroferric Inter national, 200 Madison St., Toledo, IL 62468 Roess, E.(1982), Transactions on Magnetics MAG 18,#6,Nov.1982 Smit,J.(1954) and Wijn,H.PJ. Advances in Electronics and Electron Physics, 2.,69 Snelling E.(1988) Soft Ferrites, Properties and Applications Butterworths, London Vacuumschmelze (1995) Vitrovac 500F-Vitroperm 6025, PK-004, Vac uumschmelze GMBH, Hanau, Germany Yoshizawa, Y (1988) Oguma, S. and Yamaguchi, K.,J. Appl. Phys.,64, 6044 Yoshizawa, Y (1989) and Yamaguchi, K., IEEE Trans. Mag. MAG25, 3324 Chapter 4 CORE SHAPES FOR POWER ELECTRONICS INTRODUCTION In the previous chapter, the inherent material properties of compo nents for power electronics were examined. In most cases these properties were measured on toroids because their magnetic cross-sectional area is con stant and they have an uninterrupted magnetic path. This makes for ease of interpretation of the measurements. However, while toroids are still used in some applications, designers of magnetic circuits (including those for power electronics) find it more practical to rely on many other shapes for technical and economic reasons. Because the shape of the component influences the performance of the device, modified component parameters including mate rial and shape considerations must be developed. This chapter will list the possibilities of core shapes used in power electronics. In addition, several new changes in the overall height to cross-section brought about by mounting on PC boards will be discussed. Since, very often the magnetic component is the largest on the board, the shape of the component takes on much more ill'por tance. 4.1-FERRITE CORE SHAPES Ferrite cores possess one advantage over other magnetic materials in that they come in a large variety of shapes. This feature is made possible by the part-forming process in which the ferrite powder is pressed in a die before sintering to final dimensions. The die can be complex as long as the pressed part can be ejected from the die. Some parts such as round-leg E-cores must be pressed with legs up which creates a need for a minor adjustment. A vari ety of ferrite shapes for power applications are shown in Figure 4.1 4.1.1 Pot Cores Pot cores are sometimes used ungapped in power applications with a solid center post since there is no need for the adjustor found in telecommuni cation applications. The shielding to protect a low-level telecommunication signal in LC circuits is not necessary. There may be some advantage to the shielding in that it does provide the lowest leakage inductance. Besides cost, MAGNETIC COMPONENTS FOR POWER ELECTRONICS 106 from the windings to escape. Since pot core dimensions all follow IEe stan dards, there is interchangeability between manufacturers. 4.1.2-Double Slab Cores In slab-sided solid center pot cores, a section of the core has been cut off on each side parallel to the axis of the center post. This opens the core considerably. These large spaces accommodate large wires and allow heat to be removed. In some respects, these cores resemble E-cores with rounded legs. See Figure 4.2 107 CORE SHAPES FOR POWER ELECTRONICS 4.1.3-RM Cores and PM Cores RM cores (See Figure 4.3) were originally developed for low power, telecommunications applications because of the improved packing density. They have since been made in larger sizes without the center hole. Their large wire slots are an advantage while still maintaining some shielding PM cores are large RM-shaped cores specifically for power applications. Zenger(1984) feels that the geometry and self-shielding of RM cores make them useful at high frequencies. Roess (1986) points out that the stray field from an E-42 core is 5 times higher than that of an RM core. With the trend towards in creased operating frequencies, he feels that there may be a backs wing to the RM cores in mains (line) applications. Since that time, the use of RM cores for power applications has grown significantly. Low-profile RM cores are available in the RM4, RM5, RM6, RM7, RM8, RmIO, RM12 and RM14 sizes . Surface mount bobbins are available in RM 4 Low Profile, RM5, RM6, and RM6LP. For power non-linear choke cores, Siemens offers special RM8 to MAGNETIC COMPONENTS FOR POWER ELECTRONICS 108 RM 14 cores with tapered center posts. PM (Pot-core Module) cores are used for transformers handling high powers, such as in pulse power transformers in radar transmitters, antenna matching networks, machine control systems, and energy-storage chokes in SMPS equipment. It offers a wide flux area with a minimum of turns, low leakage and stray capacitance. Because of the weight of these pot cores, they may not be suitable for mounting on PC boards. The numbering system of the RM cores is based on the grid system for holes on printed circuit boards. There are 10 grids to an inch (25.4mm) The RM number corresponds to the number of grids that a side of the square that contains the core. Thus an RM4 core would fit in an are of 4X4 grids (O.4X 0.4 inches) or about 10 x 10 mm. 4.1.4-E Cores These cores are the most common variety used in power transformer applications. As such they are used ungapped. There are some variations that we shall discuss here. Their usefulness is based on their simplicity. Initially, E- cores were made from metal laminations and the early ferrite E cores were made to the same dimensions and were called lamination sizes. However, as 109 CORE SHAPES FOR POWER ELECTRONICS the ferrite industry matured, E core designs especially useful for power ferrite applications were developed.( Figure 4.4). Many standard E-cores have bob bins that permit horizontal mounting. Some of the smaller sizes also are avail able in surface mount design with gull-wing terminals. 4.l.S-E-C Cores E-C cores are a modification of the simple E core. The center post is round similar to a pot core and since round center bobbins wind easier and are more compact than square center bobbins, this is an advantage. The length of a tum on the round bobbin is 11 percent shorter than the square bobbin that means lower winding losses. The legs of these cores have grooves to accom modate mounting bolts. (Figures 4.5 and 4.6) 4.1.6-ETD Cores ETD cores are similar to E-C cores. They have a constant cross sec tion for high output power per unit weight and simple snap-on clips for hold ing the two halves together. They also have a bobbins which provides for creepage for mains (line) isolation and have enough space for many terminals. Zenger( 1984) suggests that the constant cross section of the ETD is an im portant attribute for high frequency at\"~ high drive levels. (Figure 4.5) These cores are available only in the large s:z~;, and thus are not used with surface mount bobbins. 111 CORE SHAPES FOR POWER ELECTRONICS 4.1. 7-E-R Cores These cores combine high inductance and low overall height. They have a round center post and surface mount bobbins available with the smaller sizes. 4.1.8-EP Cores EP cores are a modification of a pot core but the overall shape is rec tangular. A large mating surface allows better grinding and lapping, preserv ing more of the material's permeability. The EP core is usually mounted on its side with the bobbin below it facilitating printed circuit mounting. The best advantage of this core is in high permeability material. Shielding is very good. Some sizes of E-P cores (EP7 and EP13) are available with surface-mount bobbins with gull-wing terminals. Figure 4.7 shows an assortment of EP cores with the mounting accessories. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 112 4.1.9-PQ Cores TDK says it stands for Power and Quality. These are one of the new est types of cores for power ferrites for switched mode power supplies. The lowest core losses in a transformer usually exist when the core losses equal the winding losses. The geometry in a PQ core is such as to best accomplish this requirement in a minimum volume. The clamp is also designed for a more efficient assembly. A more uniform cross sectional area is also achieved so that the flux density is uniform throughout the core so that the temperature will not vary much. See Figure 4.8. 4. 1. 10-Toroids Toroids are sometimes used as power shapes because they take full advantage of the material permeability. Since there is no gap, leakage is very low. The toroid's main disadvantage is the high cost of winding as compared to an E or pot core. (Figure 4.9). Engelman (1989) constructed a multi-toroid power transformer that provides digital control. 40 toroids were used. 113 CORE SHAPES FOR POWER ELECTRONICS Bates (1992) reported on a new SMP core technology combining new high frequency ferrite power materials as toroids in a matrix transformer that can deliver 2000 watts at 5V D.C. It has the advantage of being low profile, has low leakage inductance excellent winding isolation and higher thermal dissi pation due to increased surface area. 4.1.11-EFD Cores Probably the newest design in miniature power shapes is the EFD cores which stands for E- core with flat design. (See Figure 4.10) The center leg was flattened for the extra low profile needed for PC board mounting. Simple clips are available. As expected surface mount bobbins are available. Mulder (1990) has written an extensive application note on Design of Low Profile High Frequency Transformers. He finds an empirical relation between effective volume and the thermal resistance of a magnetic device with which a MAGNETIC COMPONENTS FOR POWER ELECTRONICS 114 CAD program can be constructed to develop the optimum range of EFD cores for the frequency band 100KHz to 1 MHz. 4.2-EFFECTIVE CORE PROPERTIES-POWER CORE SHAPES In Chapter 3, the inherent properties of the various power magnetic materials were listed. In most every case, the measurements reported were made on toroids or ungapped shapes. We know that most power shapes are gapped. Even the so-called \"ungapped\" cores have a gap in the mating sur faces. For gapped cores, the dimensions and magnetic properties must be modified to the effective parameters The toroid was described as a closed magnetic circuit with uniform cross section. Even in a toroid, however, the magnetic path length varies from the circumference formed by the ID and to that formed by the OD. The mean length is often taken as the circumference of the average diameter [ Ie = n( do + dj)/2]. Where there is a large variation between the OD and ID, the average 115 CORE SHAPES FOR POWER ELECTRONICS Figure 4.10- EFD Cores for Power Applications value is invalid and a more complex method involving integration of all the paths is necessary. The situation on other shaped components is usually not as simple. First, the circuit may have an air gap (intentional or that formed by mating surfaces). The permeability of the magnetic circuit will be; Jl e == JlJ{1+ JlJllm } [4.1] where; Jle == Effective permeability of gapped structure J.1o = permeability of the un gapped structure Ig == length of gap 1m = length of magnetic path It is very important for us to appreciate the impact of this relationship espe cially in high permeability materials. For example, let us take the case of an EP core of 10,000 permeability material with no intentional gap. A separation of only 1 micron(or .00004 inches} will reduce the effective permeability to about 6700. The effective permeability, Jle is actually the permeability of an equivalent ungapped structure having the same inductance and same dimensions. If there is a varying cross section of the component (such as a pot-core), then special methods are available for determining the effective length, Ie, the ef fective cross section, Ae, and effective volume, Ve, of these shapes by com bining the contributions of each varying section. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 116 4.2.1-Measurement of Effective Permeability The effective permeability can be measured by several different methods. Impedance Bridges which separate the inductive and resistive com ponents of an impedance are generally used for ferrites. The effective perme ability is given by; /-le = LJJ.41tN2Ae [4.2] 4.2.2-Inductance Factor, AL One characterization of the inductance of a component is the induc tance factor AL. It is defined as the inductance of the core in henries per tum or millihenries per 1000 turns. This factor for a specified core can be used to calculate the inductance for any other number of turns, but we must remember that since L varies as N2, so does AL. LN = ALN2/(l oooi for L in millihenries [4.3] LN = ALN2 for L in henries [4.4] The standard AL values for pot cores are chosen from the International Stan dards Organization R5 series of preferred numbers. In this system, the anti logs of .2, .4 .6 .8, 1.0 and their multiples of 10 are selected numbers. Thus common AL'S are 16, 25, 40, 63, 100,160,250, 400 and so on. Some compa nies include AL'S from the RIO series which include antilogs of .1, .5 and .9 and have AL'S of 125,315 and 800. 4.3-GAPPED CORES In low power transformer or inductor applications, gapped cores were used to control the inductance and to raise the Q of the core. Although many ferrite power cores are used in the \"ungapped\" state, either as an E core or pot core without any intentional gap, in some situations, the intentional gap can be quite useful even in power applications. These often occur when there is a threat of saturation that would allow the current in the coil to build up and overheat the core catastrophically. The gap can either be ground into the cen ter post or a non-magnetic spacer can be inserted in the space between the mating surfaces. The gapped core is extremely important in design of filter inductors or choke coils. We shall discuss this application later in this chapter. The basis of the gapped core is the shearing of the hysteresis loop shown in Figure 4.11a and 4.11b where 4.11a represents the ungapped and 4.l1b the 117 CORE SHAPES FOR POWER ELECTRONICS gapped core. The effective permeability, J.le, of a gapped core can be ex pressed in terms of the material or ungapped permeability, J..l, and the relative lengths of the gap, Ig, and magnetic path length, 1m : [4.5] With a very small or zero ratio of gap length to magnetic path length, the ef fective permeability is essentially the material permeability. However, when the permeability is high(lO,OOO), even a small gap may reduce the perme ability considerably. For a power material with a permeability of 2,000 and a gap factor of .001, the effective permeability will drop to 1/3 of its ungapped value. When each point of the magnetization curve is examined this way, the result is the sheared curve shown in Figure 4.11. Ito(1992) reported on the design of an ideal core that can decrease the eddy current loss in a coil by the use of the fringing flux in an air gap. The design includes a tapering of the core at the air gap. The reduction in temperature rise will depend on the oper ating frequency, the gap length and the wire diameter. 4.3.1-Prepolarized Cores Another variation of the gapped core is one that is prepolarized with a permanent magnet. If the transformer operates in the unipolar mode and the polarity of the magnet is opposite to the direction of the initial ac drive, the starting point for this induction change will not be the remanent induction as is usually the case but a point much lower down on the hysteresis loop and in MAGNETIC COMPONENTS FOR POWER ELECTRONICS 118 the opposite quadrant. The flux excursion will be much greater, possibly two or more times higher than the simple unipolar case. Magnetic biasing is old but the extension to this application has been described by Martin (1978) . To avoid eddy current losses, the magnet used may be a ferrite magnet often of the anisotropic variety. Shiraki (1978) reported a reverse-biased core for this purpose. Using a high-energy rare-earth cobalt magnet for the bias, he re duced the volume of the core 56% and the copper wire by a corresponding amount. Shiraki points out that the reverse-biased core has higher inductance near the normal saturation than the unbiased core. With this device, he more than doubled the volt-amp rating of the transformer. Nakamura (1982) re ported a 70% increase in the figure of merit namely the U 2. Thus, size and weight was reduced. The losses were not significantly higher under these conditions. Sibille (1982) also reported on several different geometries to im plement the prepolarized core. Prepolarized cores are especially useful in flyback and inductor appli cations with high DC components. Huth (1986) has described a clever way of biasing a core using orthogonal winding techniques. (See Figure 4.12 ). 119 CORE SHAPES FOR POWER ELECTRONICS 4.4-LOW-PROFILE FERRITE POWER CORES F or low power ferrite applications, the past 5-10 years have seen the introduction of low profile cores in several configurations. One reason for this change is explained in the section in which the permeability is maximizes by having the winding length large and the cross section small. This condition can be accomplished in a low profile or low height core. The other reason (also mentioned in Chapter 1) is the growing use of PC (printed circuit) boards on which to mount the magnetic cores. This method of attaching cores is even more important in the power ferrite area than in the low power tele communications area since PC technology is increasingly placing the power supply for a circuit on the same PC board as the other circuit components. The space between the boards is one half inch so the power ferrite core must be designed to fit in that space with the bobbin and mounting hardware. The availability of low profile cores has been discussed under the sections dealing with the various core shapes. A low-profile EFD core is shown in Figure 4.13. 4.S-SURF ACE-MOUNT DESIGN IN POWER FERRITES The use of surface mount design has been used for low power ferrite applications. The motivation was the development of PC board technology surface-mount design (SMD. As with the low profile cores, the application has been widespread mostly in the power ferrite application. The use of low profile ferrite cores can be complemented to a large degree by surface-mount technology. The two terminal mounting types used for power ferrites are the gullwing and the J-type terminals shown in Figure 4.14. The gull wing form is used when thin wire up to .18 mm in diameter is used. The J-type design is used in wire sizes greater than .8 mm. Surface mount design lends itself to high speed automatic component placement on the PC board. A surface mount bobbin with gullwing terminals is shown in Figure 4.15. The place ment on the PC board is also shown. 4.6-PLANAR TECHNOLOGY Continuing with the low-profile design tendency particularly with PC board mounting has led to a completely new generation of cores called planar cores. Huth(l986) reported on this earlier and now, most ferrite companies offer planar cores in several varieties. Some of the arrangements are shown in Figure 4.16. Either the E-E or E-I configuration is used. The I core is actu ally a plate completing the magnetic circuit. In many cases the windings are fabricated using printed circuit tracks or copper stampings separated by insu lating sheets or constructed from multilayer circuit boards.(See Figure 4.17 ) MAGNETIC COMPONENTS FOR POWER ELECTRONICS 120 121 CORE SHAPES FOR POWER ELECTRONICS In some cases, the windings are on the PC boards with the two sections of the core sandwiching the board. Philips (1998) claims the advantages of this ap proach as; 1. Low profile construction 2. Low leakage inductance and inter-winding capacitance. 3. Excellent repeatability of parasitic properties. 4. Ease of construction and assembly 5. Cost effective 6. Greater reliability 7. Excellent thermal characteristics-easy to heat sink. Yamaguchi(1992) performed a numerical analysis of power losses and in ductance of planar inductors. A rectangular conductor was sandwiched with magnetic substrates. He suggested that the air gap between two magnetic sub strates is an important factor governing the trade off between inductance and iron losses. Sasad (1992) examined the characteristics of planar indutors using NiZn ferrite substrates. A planar coil of meander type is embedded in one of the NiZn ferrite substrates and covered with another with a specified air gap. A buck converter ofthe 10 Watt class was constructed using the inductors with an efficiency as high as 85 percent and a switching frequency of 2 MHz.Varshney (1997) has described a monolithic module integrating all of the magnetic components of a 100 Watt I MHz. forward converter using a plasma-spray process for deposition of the ferrite which serves as the core. Mohandes (1994) used integrated PC boards and planar technology to im prove high frequency PWM (Pulse Width Modulated Converter) performance. Estrov (1986) has described a 1 MHz resonant converter power transformer using a new spiral winding with flat cores that solved eddy current losses, leakage inductance and other problems. He also used planar magnetics and low-profile cores to cut the height and improve converter efficiency from 20 KHz. to 1 MHz. Brown (1992) replaced the traditional copper wire with a winding from the PC board or stamped copper sheet and using a low-profile ferrite core improved the performance and manufacturability of HF power supplies. Huang (1995) described design techniques for planar windings with low resistance. Three representative pattern types were explored; circular, rectangular and spiral. Gregory (1989) has described the use of flexible cir cuits to work with new planar magnetic structures. He claims that printed cir cuit inductors reduce losses and increase packing density making them an ex cellent choice for high-frequency magnetics. Figure 4.18 shows a collection of low-profile and planar cores. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 122 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 124 4.7-INTEGRATED MAGNETICS Bloom (1994) has shown the application of planar-type \"integrated\" magnet ics wherein the transformer and inductor element can be combined on the same core with separate wing. An example of this technique is shown in Fig ure 4.19. The use of folded windings on printed circuit boards with flexible fold lines is shown in Figure 4.20. 125 CORE SHAPES FOR POWER ELECTRONICS 4.8- CORE SHAPES FOR METAL STRIP MATERIALS Metal strip materials as discussed here for power electronics applica tions include; 1. Thin gage Si-Fe alloys (0.001-0.004 inches) 2. NiFe Alloys (Permalloys) 3. CoFe Alloys (Supermendur) 4. Amorphous Alloys 5. Nanocrystalline Alloys The shapes of the into which these alloys are formed are; 1. Tape-Wound Cores 2. Tape-Wound Cut Cores 3. Stacked Laminations For the power electronic applications, stacked laminations are rarely used since the metal thicknesses of laminations are normally greater than those compatible with high frequency operation. In addition, with the amorphous and nanocrystalline materials, their hardnesses make it economically unat tractive to punch because of die wear. For lower frequencies and higher power, cut cores can be used successfully because of the lower winding costs of cut cores compared to tape-wound cores. That leaves the bulk of the usage of metal strip components for power electronics to tape wound cores. Unlike ferrites whose inherent magnetic properties for a single material are the same regardless of shape or size, core properties of a specific strip wound core are dependent on strip thickness. This condition arises from the lowering of high frequency Eddy Current losses as the strip thickness is decreased. In addition, the so-called \"stacking factor\" or ratio of volume of metal to volume of wound core must be accounted for in flux density consideration. 4.9 CORE SHAPES OF METAL POWDER COMPONENTS Metal powder core components of a specific base chemistry are clas sified according to permeability. The permeability of a particular material is determined by the physical properties including particle size, amount of insu lation and pressed density. There are two main shapes of metal powder core components. They are; I. Toroids 2. E-Cores MAGNETIC COMPONENTS FOR POWER ELECTRONICS 126 Although, traditionally, toroids have been the shape of choice since the low permeabilities of powder cores are additionally lowered by a gap. However, in recent years, there has been growing usage of the E-core design. Here again, the motivation has been the elimination of costly toroidal wind ing. SUMMARY This chapter has listed the shapes that are commonly used in compo nents for power electronics. The next chapter will discuss the techniques that are used to determine the optimum size of the component. As such the mater rial and component parameters will be integrated into the circuit requirements. References Bloom, 0.(1989) Powertechnics April 1989, 19 Estrov, A. (I 989) and Scott,!., PCIM, May 1989 Huth, J.F. III, (l986)Proc. Coil Winding Conf. Sept. 30-0ct. 2, 1986 Magnetics (1987) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Martin, W.A.(l978), Electronic Design, April 12,1978, 94 Nakamura, A.(l982) and Ohta, J.,Proc. Powercon 9,C5, 1 Shiraki, S.F.(1978), Electronic Design, ~ 86 Sibille,R. (1981), IEEE Trans. Magnetics, Mag.22 #5,Nov. 1981,3274 Sibille, R.( 1982), and Beuzelin, P., Power Conversion International, 1982, 46 Chapter 5 CORE SIZES-DESIGN CONSIDERATIONS IN POWER ELECTRONICS INTRODUCTION The last few chapters, the choices of components for power electron ics were considered based on the circuit topology, component function, mate rial and shape. This chapter will be concerned with the selection of the size of the core. First consideration will center on satisfying the electrical input re quirements with regard to input and output voltages and currents, followed by efficiencies, regulation, temperature-rise and safety requirements. The first section will concentrate on output transformers and output inductors, followed by common-mode chokes, EMI suppression cores and magnetic amplifier components. The appendices will deal with design examples for the various functions. S.l-DETERMINING SIZE OF THE TRANSFORMER CORE Years ago, transformers were designed by using cut-and-try methods involving many modifications and final optimization. Such techniques are time-consuming and ineffective procedure and although some use of them remains, many design aids have been established to assist the designer in at least a close fit to the required circuit with only some minor adjustment needed. Several schemes of sizing the core and completing the circuit design are presented in this chapter. The first approach is the use of the core area window area product that has been adopted by many manufacturers of power magnetic components. These vendors correlate the area products with certain core sizes and materials. Variations of the product area have been used by the manufacturers or authors in books. The next approach involves the use of other power specifications offered by the vendors. These may include the core losses for the cores (either per cc or gm), the core surface areas and the ther mal resistances. In many cases when not all the input and output conditions are specified, some reasonable assumptions will be made in the initial desig nation of the core size. Since no universal scheme for sizing the core has yet emerged, the variety of different methods will be discussed. 128 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 5.l.l-Initial Considerations in Designing a Power Transformer Core In the design of a core for a power transformer used in SMPS con verters, we must take into account the input current requirements to provide the ac field to drive the core to the proper B level. This will be determined by the following equation; H= .4nNIII [5.1] In strict operational terms, the NI of the primary winding will provide the flux variation to induce the necessary secondary voltage. This voltage is related to the operating conditions by the following equation; E = 4.44 BNAfx 10-8 [5.2] for sine wave with the coefficient changing to 4 for square wave. Although part of the dimensions (cross sectional area) of the magnetic core is related directly to the flux requirements imposed by the second equation, all the windings in a power core are contained inside the core. This includes the pri mary turns, Np, determined by the magnetizing current equation and the sec ondary turns, Ns, given by the induction equation. These windings are con tained either inside the window of the toroid or a U or E core or are on a bob bin surrounding the center post in a pot core. Consequently, the size of the window or bobbin winding space does directly affect the overall size of the core. Therefore, it is these two requirements that are related in the design de termining the shape and size of the core. In other words, the flux equation contains the cross sectional area of the core. The NI requirements must be met by a certain number of turns each having a certain capacity to carry a current I. Achieving a higher current may allow only a few turns with a larger cross sectional area per tum as opposed to a design carrying a larger number of turns with a smaller cross sectional area per tum. It is the product of the NI which is a measure of the total copper cross sectional area and which will determine the window area. Therefore, there are two areas that will at first determine the size of the core. One criterion used for years by design engineers is the product of these areas that is called the Area Product, Ap, (Magnetics 1987) described by; Ap = WaAc (cm4) [5.3] Where; Ap = Area Product Wa = Area of the window (cm2) Ac = Area of the window (cm2) Of course, the Ac is the area transverse to the flux and the Wa is the area transverse to the current flow. The area of the window is not completely us able because of the space between the wires and also the insulation thickness. Therefore, we introduce a copper-filling factor, K, which is the fraction of the CORE SIZES- DESIGN IN POWER ELECTRONICS 129 window containing the copper. The total cross sectional area of the copper is given by; Acu =NAw where; Aeu = area of copper (cm2) [5.4] Aw = Cross sectional area of the copper wire, cm2\u2022 Therefore, the copper filling factor, K, is; [5.5] N=KWjAw [5.6] If we multiply by Ae, we get; [5.7] Now, from Equation 2.2 for a square wave; [5.8] Setting the two equations equal and rearranging; WaAe = EAw x 108/4BfK [5.9] The area of the wire is related to its current- carrying capacity by one of sev eral analogous factors. Traditionally, electrical engineers have spoken of wire sizes in circular mils instead of cm2 (possibly because the number is quite small in cm2). A circular mil is the cross-sectional area of a wire whose di ameter is 1 mil or .001 inches. The area is then .7854 square mils or 5.0671 x 10-5 cm2 \u2022 Therefore, to convert from a Aw or possibly a Wa in cm2 to circular mils, divide the circular mils by this last number. If, as is a common practice, the current carrying capacity of the wire is given in terms of C in circular mils/ampere, the relevant equations are; C=AwfI Circular mils/ampere [5.10] Then; Aw=IC [5.11 ] The input power, Pi is Pi=EI [5.12] If we further define the efficiency; [5.13] Where; Po = Output power 130 MAGNETIC COMPONENTS FOR POWER ELECTRONICS We can then relate the output power, Po to the Area Product, Ap; VlaAc = PoCxl08/4BetK [S.14] If some assumptions are made about C (800-1000 circular mils/amp), e at about 80-90%, and K (about .2-.3) we can simpify the equation. Note that the K value is only the copper-filling factor only for the primary that normally occupies about SO% of the winding space. The rest is occupied by the secon dary winding. Based on these assumptions, we arrive at an equation relating Po to operating conditions with a single constant, k1; [S.1S] If the B level is set at 2000 Gausses, families of curves relating the output power, Po to the Area Product, WaAc, can be generated as shown in Figure S.I. The various cores having the corresponding WaAc values are also shown. The Po calculated from this equation is compared to the measured values in Table 18.2. The agreement is quite good. The WaAc ranges can also be corre lated to the temperature rise of the core in operation. The table below from Magnetics Catalog(2000) gives an approximation of the temperature rise that can be expected. CORE SIZES- DESIGN IN POWER ELECTRONICS 131 S.1.2-0ther Area Product Relationships McLyman (1982) points out a similar relationship between the area product, Ap, to the power handling capability as well as to several other important pa rameters used in transformer design. For current carrying capacity, a new constant, Kj is introduced making his equation; Ap = (Pt x 104/KrBmfKuKjY where: Kr = wave form coefficient = 4.00 for square wave [5.16] = 4.44 for sine wave Ku = window utilization factor as previous K Kj = current density coefficient related to copper losses x = exponent related to geometry (for pot cores, x = 1.2) Bm = Maximum induction in Teslas (Note the change from Gausses. (1 Tesla = 104 Gausses) 132 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 5.1.3-Voltage Regulation in Transformers McLyman(1982) has also developed a new criterion and design method for transformers and inductors where the so called \"regulation\" is an important consideration. Smith (198S) describes regulation as \"the variation in voltage from no load to full load expressed as a percentage\". Thus, regulation of S% means that S% of the input voltage is dropped across the series resis tances and reactances and the balance is transmitted to the load. McLyman (1982) combines the power handling ability and the regu lation by relating them to two constants, one a function of geometry and the other related to magnetic and electrical operating conditions. The equation is: [S.17] where Pt == apparent power a == regulation in percentage Kg == geometry coefficient Ke == electrical coeffecient The apparent power, Ph is the sum of the input power, Pi, and the output power, Po; [S.18] With a given efficiency, TJ , and in the typical D.C.-D.C Converter, the equa tion becomes; Pt == Po {..j2iq +..fi} [S.19] The geometry constant, Kg is given as; Kg == WaAc2K/ML T where ML T == Mean length per turn [S.20] Rather than using circular mils for the wire size, Aw and window area, Wa. these units are each given in cm2\u2022 The constant Ke or the electrical constant is given by; Ke == 0.14S K/fBm2xI0-4 [S.21] (B is in Teslas or Wb/m2) The current density, J, in Alcm2 is given by; [S.22] CORE SIZES- DESIGN IN POWER ELECTRONICS 133 McLyman gives an example of the Kg approach in the design of a transformer for a single-ended forward converter. It is shown in Appendix 2. This ap proach may appear long and and requires data which may not be in the manu facturers catalog. Fortunately, McClyman has supplied a compilation of the needed data in his books( 1982,1988) . Grossner (1983) has also called attention to the dependence of Po on the area product. He uses the same approach as previously discussed with several geometrical coefficients to approximate the output power, Po. Grossner is more concerned with the temperature rise in the calculation that is expressed as; where; resistance [5.23] C2 = a constant involving core and winding fractions and wire h = Coefficient of heat transfer e = Temperature rise ~ = Geometrical constant involving surface area, magnetic path length and wire length per turn Thus, Grossner concludes that the power level is more responsive to increases in frequency and flux density than to an increase in the temperature rise. In practice, f is defined by the circuit and B is limited by the core material. With Band f fixed, keeping a small size and a high power level are aided by oper ating at the highest possible temperature rise. Because circuits may be de signed to optimize different requirements, Grossner develops the parameters, gl - gs, which in some combination will lead to optimization of power, induc tance, and optimum power. Smith (1985) uses the area product as a design criteria, but reduces it to Normalized core dimensions so that any size core can be calculated. Another author using the WaAc approach is Pressman (1977). Here the tables of the supplier are used to approximate the core for the power level required. DeMaw (1981) approximates the temperature rise in a core as; Trise = SOP/Po [5.24] Where Po is not the output power as previously used but the power dissipation level within a specified core that will cause a 50\u00b0C temperature rise. Pt is the total power dissipated in an inductor including core loss and winding loss. The core loss data can be obtained from the manufacturing catalog while the winding losses can be estimated by formulae. 134 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Watson ( 1986) also uses the Area product and McLyman's Kg method but derives equations based on two kinds of current density, rms and instanta neous. This distinction is important for flyback transformers. Although the WaAc approach is merely a starting point in the design, many other factors may have to be considered in finalizing the design. With ferrites in power supplies some of these factors are as follows; I. Max temperature of the core \u00ab100\u00b0C.) 2. DC imbalance 3. Magnitude and linearity of magnetizing current 4. Magnitude of transient current 5. Under transient loading, need to limit Bm to avoid saturation 5.1.4-0ther Transformer Design Techniques Snelling( 1988) has divided the design of power transformers into several dif ferent categories. They are: I. Winding loss limited 2. Saturation limited 3. Regulation limited 4. Core loss limited 5. High frequency limited Items numbered 2-5 are discussed previously. Snelling has added the other two. He discusses them each separately, stating that, in general, they come into playas the frequency of operation increases. 5.1.4.1-Winding-Loss-limited Design This is almost the same situation we have been discussing using the WaAc approach or the wire current density approach. As in the previous cases, there is also some limit on the B level. However, here the only real source of dissipation is the winding loss and, depending on the size of the transformer, the treatment is only applicable to a frequency of about 5-10 KHz. The equa tion for the input power, Pi , Snelling(l988)gives as; Pi 2 = PwfB/lmk) [5.25] Where; m = Fractional increase in the resistivity of the copper over that at and; CORE SIZES- DESIGN IN POWER ELECTRONICS lw= mean length ofa tum of the winding F w = Winding factor ofthe copper 5.1.4.2-Regulation-Limited Design 135 In this category, the regulation can be a constraint on the winding loss listed above. Again, the winding loss is really the only source of dissipation, that is, the core loss, Pc is much smaller than P w at these frequencies. The voltage regulation, ,is given as [5.26] Then; Pi = (fB/almkl )xlOO [5.27] Since the core loss is negligible, we can ignore it and the output power is given by; Po = Pi-Pw = Pi[l- al100] = fBe2(a- .01a 2)/mkl xl00 [5.28] [5.29] B/ is limited by the saturation flux density of the material. The other pa rameters are given so that k\\ can be calculated. Snelling (1988 ) presents a table of the values of k\\ in his book for many power core sizes in so that the choice can be made. Most ferrite transformers are not regulation limited. 5.1.4.3-Saturation-Limited-Design As the flux density increases, the hysteresis curve will flatten out as saturation is approached. When this happens, the incremental permeability drops sharply. In this case, the impedance (or inductive reactance) becomes quite small and the current, therefore, increases. See Figure 5.2. The manu facturer will often give limit values for the maximum flux density that the designer should not exceed. Since the saturation drops at higher temperatures, the saturation value at the operating temperature should be examined in this regard. For operation at 100\u00b0C., the value of 3200 gausses would be a real maximum. The constant k\\ is still a valid constant for saturation-limited designs. Since the efficiencies at these lower frequencies are close to 100 percent, the output power, Po, can be considered the same as the input power, Pi- There fore; 136 MAGNETIC COMPONENTS FOR POWER ELECTRONICS [5.30] If the flux, <1>2, is used instead of B/, the factor k2 is used where k2 = k1A/. If core loss is included in the saturation limited case, the equation for the square wave drive becomes; Po={Pt-Pc)ll2k3FwI/2f Watts [5-31] where; Pt =Total Losses = P w + Pc [5-32] Pt is also listed in Snelling's (1988 )Table 9.3. At low frequencies, the core loss is less than half the total loss and so may be set to 0 especially because of the square root dependence. [5.33] Again, Snelling lists the values of k2 and k3 in Table 9.3 of his book (1988). In addition the value of Pt which is the sum of all the losse (winding and core) is also given in the same table. The permitted temperature rise in this table is 40\u00b0C. If the proposed temperature rise is different, the new value of Be or can be recalculated from the thermal resistance, ~. At low frequencies, where core loss is a small fraction of the total loss, the output power is proportional to f. If the operating variables such as fre quency, temperature rise and copper factor are assumed, the power handling values for a given core can be given. Most manufacturers provide such infor mation. The values of Po are similar to the ones derived earlier from the area product technique. 5.1.4.4 -Core-Loss-Limited Design Traditionally, design of a transformer is optimized by making the winding losses equal to the core losses. It has generally been taken as a de vice. Other calculations place the division as; [5.34] When n=2, the two losses are indeed equal. However at higher frequencies, the value of n is between 2 and 3. For core loss limited designs assuming the output power, Po, is equal to the input power, Pi, the equation for the core loss, Po, for a square wave is; CORE SIZES- DESIGN IN POWER ELECTRONICS 137 Po = [P.I(1 +2/n)] 112 x k3Fwl/2f ~p-p [5.35] where K3 is defined as before. With PI and k3 given in the table, the output power can be given in the case of a core-loss limited design. To check the flux density, the manufactur ers' graphs showing core loss as a function of frequency and flux density can be consulted. When PI is known, the core loss can be estimated from the pre vious equation or just set to 112 PI' From this core loss and the operating fre quency, the B value can be read off the graph. If there is a varying cross sec tional area of the core, the equation is modified as such for square wave; P (1+2/n)II2]/2fBF 112 = P A 1m I ]112 X A . = Ir owl wi w mm ~ [5.36] The values for ~ are also tabulated in Snellings Table 9.3. Based on the input design specifications, ~ and B can be calculated from the minimum area and a core can be chosen. For the division of losses, a value of 2.5 is typical. For a fully-wound transformer, Fw can be set at .5. With these assumptions, ~ can be written as; and ~ = O.845PoIfB for sine wave ~ = O.949PoIfB for square wave [5.37] [5.38] 138 MAGNETIC COMPONENTS FOR POWER ELECTRONICS The manufacturers' data is certainly a good way to check the core loss as sumptions. These design methods are useful in initially picking a core and modifications must be made if one or more condition is not met. S.1.S-Power Ferrite Design from Vendors' Catalogs The vendors of ferrite cores have proposed several different design schemes. The one used in the Magnetics Catalog( 1987) has been discussed. Design methods described by other ferrite vendors are: 5. 1.5. I-Philips-(Yageo) In the case of Philips catalog, the throughput power, Po, information is supplied in the form of graphs of the Po and output voltage, Vo for each type of converter. Such a graph is shown in Figure 5.3. In addition, the perform ance factor (f x BmroJ is graphed as a function of frequency for their power ferrite materials. A graph of this type is given in Figure 3.11. 5.1.5.2-Epcos (Siemens) Epcos lists the output powers for each power shape in several power materials and for each converter type. The output powers are given at a typi cal frequency and a cut-off frequency for each material. A portion of this table is given in Table 5.3. The material-specific values on which the table values are based were taken from the maximum temperature rise for each material given in Table 5.4 and the thermal resistance for each size and shape of core that is listed in Table 5.5. The total core losses are related to these factors by ; PV,tot == i1TlRtb [5.39] The values of output power are obtained from the following formula; Where PF = Performance factor P v == Specific Core Loss CORE SIZES- DESIGN IN POWER ELECTRONICS ~ T = Temperature Rise oK Rth = Thermal Resistance fcu = Winding Factor PCu = Wire Resistance. AN = Winding Cross-Sectional Area Ae = Core Cross-Sectional Area IN Winding length Ie = Effective Magnetic path length 139 The assumption is made that the temperature rise and the losses in the core are evenly distributed. The application area for flyback transformers were re stricted to 150 KHz .. The overtemperature, ~ T is the sum of the temperature rises resulting from the core and winding losses. The maximum flux densities were <200mT for flyback converters and <400mT for push-pull converters. 140 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Table S.3-Power handling capabilities of various shape cores & materials Power capacities Push-pull Single-ended Ryback converter converter converter C= 1 ' ) C=0,71 ' ) C =0,62 ' ) Core shapes Mate- Version ftyp fcuIDII P'rons P'rans P'rans P'rons Ptrans Ptrans rial (LP=Low (~) (fculDff) (ftypl (fcutoll) (ftyp) (fClJIOff) profile) kHz kHz W W W W W W EFD2511319 N59 Nonna! 750 1500 311 417 221 296 193 258 N49 500 1000 196 263 139 187 122 163 N67 100 300 175 280 124 199 109 173 N87 100 500 242 482 172 342 150 299 EFD3OI1519 N59 Nonna! 750 1500 401 343 285 244 249 213 N49 500 1000 253 544 180 386 157 337 N67 100 300 226 365 160 259 140 227 N87 100 500 312 630 221 447 193 390 U cores Ul511116 N27 Normal 25 150 31 81 22 58 20 50 .... U17/1217 N27 Normal 25 150 37 97 26 69 23 60 U2011617 N27 Normal 25 150 74 161 52 114 46 100 U25120113 N27 Normal i 25 150 198 432 141 306 123 268 UU93I15213O N27 Normal 25 150 2527 5508 1794 3910 1567 3415 1) NI.IT1III1eaI data are staIad in IICCOIIIanc8 with the publication \"Ellact althe ~ ~ on the ohape and dirnenaiOnS allnInsform- 8IBandchokes in_power supplies\", G. RoeepeI, Siemens AG M~ J. 01 Ms!11. and Magn. _189(1978) 1~ From Siemens (1998) Table S.4- Maximum Temperature Rise and Typical and Cut-off fre quencies for various ferrite power materials aTmax ftyp 'cutoff K kHz kHz N59 30 750 1500 N49 20 500 1000 N62 40 25 150 N27 30 25 100 N67 40 100 300 N87 50 100 500 N72 40 25 150 N41 30 25 100 CORE SIZES- DESIGN IN POWER ELECTRONICS 141 Thomson(1988) presents charts of average wattage for the various size and shape power cores listed according to inverter type. The frequencies are 25KHz(2000 Gausses), 100 KHz(1000 and 1200 Gausses). 5.1.5.4-TDK TDK lists the calculated output power under the specifications of each type of power core. These power levels are given at 50 and 100 KHz for their standard power materials. These power levels are given for the forward converter mode. TDK also gives the power losses for each power core. The conditions are 25 KHz(2000 Gausses) and 100 KHz(200&- Gausses). In an older catalog, the temperature rise was also plotted against the power loss for each core. See Figure 5.4. 142 MAGNETIC COMPONENTS FOR POWER ELECTRONICS I . .1. ~-'----'----i ,G' Note N11tTrvt ~ fMoptWfl 'o\\I1Ie/'Io lI\u00bb.J'Oh'IO GunMf q: 2OGI- _ffd of the transistor switch, using a feedback system from the output. The result is a regulated DC output, expressed as: [5.57] The off time of the transistor switch is related to the voltages by !off = (l-Eou/Eirunax)/f [5.58] For Einmin: fmin = (l-Eou/Einmin)/toff [5.59] If we assume the ripple current, i, through the indictor to be equal to 21 Omin, the inductance is; L = Eout!ortl Lli [5.60] The ferrite core to supply this inductance can be obtained by again calculating the U 2 product and using the charts such as the one shown in Figure 5.16. CORE SIZES- DESIGN IN POWER ELECTRONICS 153 From the intersection of the LI2 with one of the core lines, the appropriate AL can be read. In this case it is convenient to refer to the standard gapped cores available under each core's description. The number of turns can be calculated from; The wire size is chosen from the wire tables using a current density of 500 circular mils/amp. An example of this method from the Magnetics Catalog is shown in Appendix D. An approach given by Jongsma (1982a) and contained in the Philips Catalog is shown in Figure 5.16. The LI2 is plotted against the spacer thick ness or center leg gap-width for a series of different core shapes and sizes. When a core supplying the required Lf is chosen, reference is made to the data for the individual core chosen. 154 MAGNETIC COMPONENTS FOR POWER ELECTRONICS The specific graph of LJ2 versus spacer thickness for that core is given for various choke designs (depending on the IaJlo ratio). A graph of this type is shown in Figure 5.17. On the same graph, the curve of LJ2 versus AL for that particular core is given. For the particular LJ2 chosen, the intersection with the line for the converter is found. The working point must be below this line. A vertical can be dropped to the spacer thickness axis and from the tolerance on the spacer thickness, !>min and !>max can be chosen on the axis. These lines can be extended to the AL curve for the converter type. The two intersections when read across to AL (to right hand scale) will give the limits of AL. To avoid saturation Nmax is given by; [5.62] CORE SIZES- DESIGN IN POWER ELECTRONICS 155 To achieve Lmin, the Nmin is given by; [5.63] An integral number of turns is chosen. The winding procedure can be com pleted as outlined under transformers or if special considerations are needed, the design by Jongsma is recommended. 5.7.2-McLyman Treatment ofInductor Design Following a treatment similar to the one used for transformers, McLy man(1982) employs the Kg constant. The applicable expression is: a = (Energy)2/KgK., [5.64] j.!H A2 156 MAGNETIC COMPONENTS FOR POWER ELECTRONICS where a and Kg have been defined under the transformer calculation. The energy in an inductor is given by Energy = 112 U 2 [5.65] The Ke constant is varied somewhat from the transformer equation. It is rep resented by: [5.66] The area product approach can also be used for inductors: The fraction, Ku, of the available winding space that will be occupied by the copper is given by [5.68] where S) = conductor area/ wire area S2 = wound area/usable window area S3 = usable window area/window area S4 = usable window area/ usable window area + insulation The design of an inductor using McLyman's approach is given in Appendix 5. 5.7.3\"-Flyback Converter Design Previously, we stated that the design of a tlyback converter is similar to that of a power choke or inductor because in both cases, the energy is stored in the inductor during the current rise period and released when the current is turned off. If the converter is a simple non-isolating type (no trans former coupling as shown in Figure 18-6), the design (Jongsma 1982) is treated as a power inductor where; Lmin = 9 Omin vimaxf and: [5.69] 1m = Idcmax +21ac [5.70] = (Pel omax Vimin) + ( omax V imin/2tL) [5.71] With the calculated values of Imax and Lmin. the design can then be completed using the power inductor methods. If however, there is transformer coupling as shown in Figure 1.9, the turns ratio must be controlled to avoid damage to the semiconductor switches. Jongsma gives the limiting equations in this case as; CORE SIZES- DESIGN IN POWER ELECTRONICS 157 Ferrite DC Bias Core Selector Charts ,-I_ --1100 \",.~ _eo.. ..... ,- -. . ..... \" .. ,- C-4121J ........ Do4Mn -_. l - ~. L_ ~ -l! - - \u00a7 700 ... ~ 100 !. 100 i -JU .. 200 ,. '00 .en ....... .. ., .. .. . , .... , \u2022 \u2022 \u2022 I \u2022 l' .. ... . \u2022\u2022 LP (m4I11/OUIM) PQCoNe ... 1200 1100 poc.. - (I'Q 2IW2III ... -(l'Q1IIK) ~ (I'Q JIIIO) .. - - (I'Q UIIII) e-(l'QMIM) E ~ (I'Q t114II) a 100 \u00a7 700 A ... ... % 100 !. 100 -I \u2022 -... .. -'. 100 .I, . ...... . .. . ..J \u2022\u2022 .... ' \u2022 \u2022 , \u2022\u2022 t \u2022 \u2022 ..... , . UI (mllll/OUIM) Figure 5.15- A Graph showing the AL needed in a particular core to furnish a specific Le. From Magnetics Catalog (1989) 158 MAGNETIC COMPONENTS FOR POWER ELECTRONICS CORE SIZES- DESIGN IN POWER ELECTRONICS For VimaxNimin <2 r = 3/7 {VimaxNo+VF+VI0} [5-72] Where, VF = Voltage drop across the output choke and VR = Voltage drop across the rectifier 159 We see then that not only the characteristics of the magnetic devices must be considered but also the voltage drop and current distribution in many of the auxiliary circuit elements. Because of this, when completing the design of these and other magnetic components, the reader is advised to consult the many books, vendors' literature and various periodicals that deal with this subject. 160 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 5.S-SWINGING CHOKE We have spoken of the use of the air gap and the prepolarized cores as techniques in the design of power inductors. Another such design variation that is used to improve the regulation and efficiencies of choke is called the swinging choke or divided gap choke. This is described by Keroes( 1969), Martin(l982) and by Snelling(l988). The action is non-linear as shown in Figure 5.l8. The use of the stepped gap (Figure 5.l9) allows for a wide swing of D.C. currents or magnetic fields. At low D.C. levels, the ripple current is a large part of the total current so a high inductance is needed and is provided by the small gap. However as the D.C. level increases, the ferrite at the small gap will saturate and the large gap will take over, protecting the circuit and main core from saturation and overheating. Thus, a dual action is accom plished. CORE SIZES- DESIGN IN POWER ELECTRONICS 161 5.9-MAGNETIC AMPLIFIER-MULTI-OUTPUT DESIGN In a multi-output power converter, it is often important to control one or more of the outputs independently. One method of doing this is by using a core having a square-loop material as a magnetic amplifier. As pointed out by Snelling (1976), this delays the leading edge ofthe secondary circuit 'on' pulse by an amount depending on the re-set condition. The re-set condition determines the amount of volt-seconds needed to drive the core to saturation. When saturation occurs, the inductance falls to a low value and the energy transfer can commence. Appendix 5.1 Design Example ofMcLyman Kg Approach The following section is abstracted from Magnetic Core Selection for Trans formers and Inductors by Colonel Wm. T. McLyman, Marcel Dekker, New York, 1982 Single-Ended Forward Converter Design The following parameters are given: Input voltage (Vin) = 140 V min Output voltage(VoutF 10 V Output current (10) = 5.0 A 162 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Frequency(f) = 20 KHz Switching efficiency= 90% Regulation = 1.0% Ferrite toroid matl.= 5000Jl (Magnetics) The design steps used can be summarized as follows 1. Calculate output power which is equal to (Vout + V(diode drop\u00bbX (10) = (10 + 1)5 = 55 Watts 2. Calculate the apparent power using Equation 5.19 Pt = Po{..j2iq +.fi} = 55 {1.411.9 +1.41} = 164 10 % is added to the apparent power for the demagnetizing winding; P.(l.l) = 180 Watts 3. Calculate the electrical conditions assuming Bm =.2T and square wave (KF4.0) using Equation 5.20 K., = 3712 , 4. Calculate Kg = P.l2K.\" using Equation 5.21 Kg = 180/2(3712) =.0242 Kg is then recalculated for additional insulation because of the high voltage between primary & secondary windings. Kg= .03025 5. Select a toroid from McLyman's table (Table 11.5) with the comparable Kg and record the data regarding the toroid. Magnetics 52507, Kg = .0352 6. Calculate primary turns, Np, using Equation 2.2 using coefficient 4 for square wave in place of 4.44 for sine and using Teslas for the units for Bm (1 T =104 Gausses). Np = Vp x 104/ KrfBmAc = 140 x 104/4 x.2 x 2 x 104 x .393 = 222 Np = Nm (Demagnetizing winding) 7. Calculate primary current, Ip using a duty cycle, D, of .5 and a switching efficiency,,,, of .9. Ip = Po/DVp\" = 55/(.5 x 140 x .9) = .873 A. 1m = Ip x.l = .0873 A. 8. Calculate current density, J, from Equation 5.22. Use Ku (Window Utiliza tion Factor) =.4 J= 380 9. Calculate bare wire size Aw(B). For forward converter, Ip and 1m must be multiplied by .707 Aw(B) = Ip(.707)/J =(.873 x .707)/380 = .00162 CORE SIZES- DESIGN IN POWER ELECTRONICS 163 Aw(B) = Im(.707)/J =(.0873 x .707)/380 = .000162 10. Select wire size from table AWG #25 has bare area of.00162 J,lfiIcm = 1062 11. Calculate primary winding resistance, Rp Rp = (MLT)(N) x J,lfiIcm. = 3.3 x 1062 x223 x 10-6 = .7810 12. Calculate primary copper loss. Pp P p = (Ip x .707 i R, = (.873 x .707) x .781 = .297 Watts 13. Calculate secondary turns, Ns Vs =( Vo + Vd)ID = (10 + 1)/.9 = 22 Ns=Np VJVP = (223X22)/140 = 35 Turns 14. Calculate bare wire size, AW<:B) for secondary Aw(B) = 10(\u00b7707)/J = (5)(.707)1380 = .00930 cm2 15. Select wire size from table A WG Wire with area of .00823 cm2 J,lfiIcm = 209.5 16. Select secondary winding resistance Rs = (MLT)(NXJ,lfiIcm) = (3.3)(35X209) x 10-6 = .02420 17. Calculate secondary copper loss, P s Ps = (10 x .707i Rs = (5 x .707)2 .0242 = .302 Watts 18. Calculate transformer regulation a. = P cu x 100/(Po +P cu) where P cu = sum of primary and secondary copper losses = (.297 + .302) = .599 Watts = (.599 x 100)/ (55 + .599) = 1.08 % 19. Calculate core loss, P e from core loss curves and core weight. 164 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Pfe = (Milliwatts/gm) Wfe X 10-3 = (20)(12.1) X 10-3 = .242 Watts 20. Calculate Total Losses PI: = Peu + Pfe = (.599) + (.242) = .841 Watts 21. Calculate efficiency for transformer e=(Po xl00)/(Po +PI: ) = [(55) X 100]/(55 + .599) = 98.9% 22. Calculate WattslUnit Area from surface area of core. 'P = PI: 1 At = (.841 )/33.4 = .025 Watts/cm2 A value of.03 Watts/cm2 normally gives a 25\u00b0C. rise. APPENDIX 5.2 The following section is abstracted from the Magnetics Catalog FC405, pub lished by Magnetic, Division of Spang and Co., Butler PA 16001, 1987 Magnetics Inductor Design Method using Hanna Curves Example - The following example illustrates the use of a Hanna curve to find the core for a particular power inductor. Let L = .1 mH and IDe = 10 amperes. Find the core, the air gap and number of turns required. I. Calculate U 2 Le = (.1 x 10-3) x (10i = lOx 10-3 2. Refer to Hanna Curve in Figure 5.16. Assume (Ui/V = (from center of vertical scale). 5 X 10-4 3. Core Selection- Choose a core geometry, for example an E core, and se lect a size with the volume nearest to 20 cm3\u2022 Use P45021-EC. CORE SIZES- DESIGN IN POWER ELECTRONICS 165 Volume = 21.6 cm3,le=9.58cm,Wa=.351 x 106 circ.mils 4. Recalculate Le/V = 10 xlO-3/21.4 = 4.6 x 10-4 5. Determine Hand l.jle from the Hanna curve (P material),using recalcu lated value of LeN. H=18 and l.j/e = .006 6. Calculate N H =.4 NIII, N = HV.4 1= 13.7Turns-Use N=14 7. Calculate Wa needed. For loe = 10 amperes, use A W G # II wire. Wa = 9 X 103 cir. mils per turn Wa needed = Aw x NIK where Wa = core or bobbin window area Aw = cross sectional area of the wire N = number of turns K=winding (or space utilization) factor (K varies with the designer and operating conditions of the inductor. Typically, this factor is 0.4). Wa needed = (9 x 103) x (14/0.4) = 315 x 103 circ. mils 8. Compare Wa values Wa needed = 315 x 103 circ. mils Wa available in 45021-EC = 351 x 103 circ. mils At this point, the designer can use the core selected or repeat this process to select a smaller (or larger) core. 9. Gap calculation. If the P-45021-EC core is chosen, the air gap is calcu lated as follows. l.jle = .006, Ie = 9.58 cm. 19 = .006 x 9.58 = .057 cm.(.023 in.) APPENDIX 5.3 Magnetics Inductor Design for SwitclBng. Regulators The following is abstracted from Magnetics Catalog FC405, published by Magnetics, Division of Spang & Co.,Butler, PA 16001, 1987 Only two parameters ofthe design application must be known: (a) Inductance required with DC bias (b) DC current 166 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 1. Compute the product of U 2 where: L = inductance required with DC bias (millihenries) I = maximum DC output current = lomax + i 2. Locate the U 2 value on the Ferrite Core Selector charts such as the one shown in Figures 5.16. Follow the U 2 coordinate to the intersection with the first core size curve. Read the maximum nominal inductance, AL, on the Y axis. This represents the smallest core size and maximum AL at which satu ration will be avoided. 3. Any core size line that intersects the U 2 coordinate represents a workable core for the inductor if the core's AL value is less than the maximum value obtained on the chart. If possible, it is advisable to use the standard gapped cores because of their availability. These are indicated by dotted lines on the charts and can be found in the catalog. 4. Required inductance L, core size, and core nominal inductance (Ad are known. Calculate the number of turns using N ~ 10' ~ L AL where L is in millihenries. 5. Choose the wire size from the wire tables using 500 circular mils per amp. Example - Choose a core for a switching regulator with the following re quirements: Eo = 5 Volts eo =.5 Volts lomax = 6 amp lomin = 1 amp Einmin= 25 Volts Einmax= 35 Volts f=20KHz. 1. Calculate the off-time and minimum switching, fmin, of switch using equations 5.58 and 5.59. toff = (1-Eou/Einmax)/f toff = (1-5/35)/(20,000) = 4.3 x lO-5 sec. fmin = (1-Eou/Einmin)toff the transistor CORE SIZES- DESIGN IN POWER ELECTRONICS fmin = (1-5/25)/(4.3 x 10-5) = 18,700 Hz. 2. Let the maximum ripple current, i, through the inductor be Lli = 2Iomin Lli = 2(1) = 2 Amps 3. Calculate L using Equation 5.60. L = (Eout x !off)/ Lli L = 5(4.3 x 10-5)/2 = .107 millihenries 167 4. Calculate the value of the capacitance, C and maximum equivalent series resistance, ESR max C = il8fmin Lleo C = 2/8(18700)(.5) = 26.7 J.I. farads ESRmax = Lleo / Lli ESRmax = .5/2 = .25 ohms 5. The product ofLf = (.107) (8i = 6.9 millijoules. 6. Due to the many shapes available in ferrites, there can be several choices for the selection. Any core size that the U 2 coordinate intersects can be used if the maximum AL is not exceeded. Following the U 2 coordinate, the choices are: (a) 45224 EC 52 core, AL315 (b) 45015 E core, AL250 (c) 44229 solid center post core, AL315 (d) 43622 pot core, AL400 (e) 43230 PQ core, AL250 7. Given the AL, the number of turns the required inductance can be found for each core using Equation 5.61. AL Turns 250 21 315 19 400 17 8. Use #14 wire. 168 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPENDIX 5.4 MCL YMAN DESIGN -SWITCHING INDUCTOR - \"K<; APPROACH This section is abstracted from Magnetic Core Selection for Transformers and Inductors by Colonel Wm. T. McLyman, Marcel Dekker, New York, 1982 Design of a Buck Switching Inductor Given; Input Voltage, Vi = 28 +1- 6 V. Output Voltage, Vo = 20 V. Output Current Range, 10 = 5 - 0.5 A Frequency, f, = 20 KHz. Switching Efficiency, = 98% Regulation = 1.0% Ferrite Pot Core Step 1. Calculate time period, t, of operation t = lIf= 1I20x 103 = 50 X 10-6 s. Step 2. Calculate Minimum duty cycle Dmin = VoIVin(max) = 20/34(0.98) = .60 Step 3 Calculate maximum duty cycle Dmax = VoIVin(min) = 20/22(0.98) = .927 Step 4. Calculate Load Resistance at Minimum Load Current Ro = Vo/IO(min) = 20/0.5 = 40 Step 5. Calculate Minimum Required Inductance F or a Buck Converter Lmin = ~min)t(l-D)min)/2 =(40)(50xl0-6)(I-0.6)/2 = 400 x 10-6 H. Step 6. Calculate ~I in the Inductor M = tVin(maxP(min(l-D(min\u00bb1L = (50 xl 0-6)(34)(0.6)(1-0.6)/400 x 10-6 = 1.0 = 210(min) A. Step 7. Calculate Lel2 1= 100max) + ~1/2 = (5.0) + 1.0/2 = 5.5 A. U 2/2 = (400 x 10-6) (5.5f/2 = .00605 W-s. Step 8. Calculate Ke using Equation 5.66. Po = Yolo = (20)(5) =100 W. CORE SIZES- DESIGN IN POWER ELECTRONICS Assume Bm = .35 T (3500 Gausses) K.: = 0.145 PoB2 xl0-4 = 0.000178 Step 9. Calculate ~ ~ =(Energy)21K.: using Equation 5.64 = (0.00605i/(0.000 1781) = 0.213 169 Step 10. Select a comparable core geometry Kg from listing of pot cores (McLyman, 1982 ). Record all pertinent dimensional data. Pot core = B6561I, 36x22(Siemens) For this pot core, Kg = 0.221 G(window height) =1.46cm. Wtfe(weight ferrite) = 26 gm. MLT = 7.3 cm.,Ac = 2.01 cm2, Wa = 1.00 cm2 At(Surface area) = 45.24 cm2 Step II. Calculate current density (Correlation with Kg is derived in book (McLyman 1982) J = 2(Energy) x 104/BmKuAp Use K = 0.4 (window utilization factor) J= 2(0.00605) x 10R4F/(0.35)(0.4X2.01) = 430Alcm2 Step 12. Calculate bare wire size Aw(8) Aw(8) = loIJ =5/430 = .0116 Step 13. Select a wire size from the wire table. If area is not within 10%,take smaller size. Record wire data. AWG #17 with 0.01039 cm2 )lO/cm = 166 Aw = 0.0117 cm2 (with insulation) Step 14. Calculate the effective window area, Wa(eft) Wa(eft) = WaS3 For single section bobbin on pot core, S3 = 0.75 Wa(eft) = (1.00) (0.75) = 0.75 Step 15. Calculate number of turns N = Wa(eft) S2/Aw Typical value of S2 = 0.6 N = (0.75XO.6)/(0.0117) = 38 turns Step 16. Calculate gap required for inductance 19 = 0.4 N2 Ac xl 0-8/ L = (1.26)(38i(2.01) x 10-8/412 xlO-Q =0.089 cm. For fishpaper spacer, thickness is given in mils. 170 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 19 = 0.089 cm x 393.7 mils/cm = 35 mils Paper comes in 10 and 7 mils .One of each across entire pot core mating sur face doubles gap.(a gap each for skirt and centerpost) Therefore the total gap is 17 mils or 0.034x2.34 = 0.0864cm. Step 17-18. Recalculate new turns correcting for fringing flux (not shown here) N=34 Step 19. Calculate Winding Resistance R = (MLT)(N) 0 /cm x 10-6 = (7.3)(34XI66) X 10-6 = 0.0410 Step 20. Calculate Copper Loss, P cu Peo = eR = (5.5i(o.041) = 1.24 W. Step 21. Calculate Regulation, . a = P cu xlO0/(Po +P cu) =(1.24)(100)/(100+ 1.24) = 1.22% Step 22. Calculate total a.c. + d.c. flux density Bm = O.41tN(Ide +~I12) x 10-4/lg = (1.26)(34)(5.5) x 10-4/0.0864 =0.273T(2730G.) Step 23. Calculate a.c. flux density Bmae= 0.41tN(M/2) x 10-4/lg = (1.26X34)(O.5) x 104 /0.0864 = 0.0248 T Step 24. Calculate Core Loss Pfe. Use core loss curves for 0.0248 T. or 248 Gausses. Use the ferrite weight given before. Pfe = (mW/grnXWtfe) x 10-3 = (O.06X57)x 10-3 = 0.0034 W. Step 25. Calculate total loss Pt = Pcu + Pfe = (1.24) + (0.0034) = 1.2434 W. Step 26. Calculate the efficiency e = (Po)(100)/(Po + Pt)= (100)(100)/(100+1.2434) =98.8% Step 27 Calculate the Watts/unit area \\II = P /At = (1.2434)/45.24 = 0.0275 W/cm2 CORE SIZES- DESIGN IN POWER ELECTRONICS 171 The value of .03 W/cm2 corresponds to a temperature rise of25\u00b0C. APPENDIX 5.5 Design of Output Inductor using Metglas Amorphous Choke Cores The following is the design procedure suggested by Honeywell (pre viously Allied-Signal) for the design of a high frequency output inductor us ing Metglas amorphous choke cores. 1. Determine the Choke Ripple Current, AI- For continuous operation, the minimum DC current Iomin, must be equal to or greater than 112 the choke ripple current, ~I lomin =1>~1/2 ~I =/< 2 Iomin When the minimum DC current is not given, assume that ~I is 10- 20% oflomax. ~I = o. 2 lomax 2. Determine the critical inductance, Lmin Where and Dmin = Eo /(Eo-Epk) toffinax= 1- Dmin T = ton + toff= 1If ton = DT and toff= T-DT For average volt-seconds across inductor to equal zero, DT Epk = Eo (T-DT) Solving for D; 3. Determine the required energy; I pk = lomax + (~I12) 172 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 4. Determine the area product WaAc; WaAc= {2W /(BmaxKJ)} x 104 (cm4) Choose a core from the the Metglas Core Table 5. Calculate the number of turns and wire size N = {Lmin (nH)/ Ad 0.5 Aw=KWA/N 6. Calculate the ripple current, BM 7. Calculate the DC flux density, Boc Boc = 0.4 nNIoc x 104/lm Check for the maximum flux density, Bmax Bmax = Boc + Bt.l2 Teslas Check for percent permeability vs DC Bias(From ~ vs DC Graph) H = 0.4 nNIoc/lm Oersteds 8 . Losses and Temperature Rise p c( W) = P c( W /Kg) x wt.(Kg) Calculate copper loss R = (MLT) x (Rw) x (N) Calculate Total Loss CORE SIZES- DESIGN IN POWER ELECTRONICS Estimate Temperature Rise SA = {1t(OD)wouniI2} + {1t(OD)wound x (htcore +ODwound + ODcore) Appendix 5.6 Push-Pull Output Inductor Design Using a LPT E2000Q Core Nanocrystalline Core by Coremaster International Article ANl14 by Colonel Wm T. McLyman +0-_---...... , J Figure S.20-Push-Pull Converter with Single Output 1. Frequency 2. Output Voltage 3. Output current, max 4. Output current, min 5. Delta current 6. Input Voltage, maximum 7. Input Voltage, minimum 8. Regulation 9. Output Power IO.Operating Flux Density II.Window Utilization 12.Diode Voltage Drop f = 100 KHz. Vo = 5 V. lomax = 10 A IOmin = 2 A ~I =4A Vsimax = 9V Vsimin = 6V a = 1.0% Po = 50 W. BM =0.8T Ku = 0.4 Vd = 1 V Step No.1. Calculate the period, T T= lIf T = 11100,000 = 10. 10-6 L1. L...-+_--o+ 1 C2 .. J 173 174 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Step No. 2.Calculate the minimum duty ratio, Dmio Dmio = 5/9 = 0.555 Step No.3. Calculate the required inductance, L L = T. (Yo - Vd). (1- Dmio) L = 10. 10-6.6. (1-0.555) = 6,675 use 7 [~H] Step No.4. Calculate the peak current, Ipk Ipk = lomax +!J.. 112 Ipk= 10 + 4/2 = 12 A Step No.5. Calculate the energy-handling capability in watt-seconds, [w.s] Energy = L.I pk 2 /2 Energy = 7. 10-6.122 = 0.000504 [w.s] Step No.6. Calculate the electrical condition, Ke Ke = 0.145. Po. BM2. 10-4 Ke = 0.145.50.0.8 2.10-4 = 0.000464 Step No.7. Calculate the core geometry, Kg Kg = Ener~/ Ke. (l Kg = 0.0005042/0.000464.1.0 = 0.000547 [cm2 Step No.8. Select from the LPT data sheet a E2000Q core comparable in core geometry, Kg Core number Manufacturer Magnetic path length, MPL Core weight, W tfe Copper weight, Weu Mean length per tum (ML T) Iron area, Ac Window Area, Wa Area Product, A p GC70111 CMI 4.1 cm 4.3 g. 5.6 g. 2.7cm. 0.14 cm2 0.581 0.08132 cm4 CORE SIZES- DESIGN IN POWER ELECTRONICS 175 Core geometry, Kg Surface Area, At Permeability MilliHenries per 1000 turns Step No. 9.Calculate the rms current I =~12 + (81/2)2 nns max 0.00168 cm5 16.3 cm2 Il = 300 mH= 129 Step No.1 O.Calculate the current density, J,using a window utilization,Ku= 0.4 J = (2. Energy. 104)/ Ap. Bm .Ku J = (2 x 0.000504 x 104)/(0.08132 x 0.8 xO.4) =387 [A/cm2) Step No.ll Calculate the required permeability, L\\1l ~Il = (0.8 x 3.14 x 0.581 x.387 x 0.4) = 290 use 300 Step No.1 2. Calculate the number of turns N = 1000 ~ L(new) / ~(XX) N = 1000.JO.007 1 129 = 7.37 use 7 turns Step No. 13 Calculate the peak flux density, Bm Bm = (O.41tNIpk Ill: .1 04)IMPL Bm = (0.4 x3.14x 7 x 12x 300. 104)/4.06 = 0.779 [T] Step No.14. Calculate the required bare wire area, Aw(B). Aw(B) = Inn/J Aw(B)= 10.2/387 = 0.0264 [cm2] 176 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Step No.15. Select the wire size with the required area from the Wire Table. If the area is not within 10% of the required area, then go to the next smaller size. AWG= 13 Aw(B) = 0.0263[cm2] JJfl/cm = 65.5 Step No. 16. Check the ~I current density using the skin effect e. s = 6.621.fl .JI00,000 s = 6.621 .Jl 00,000 = 0.0209 [cm] Calculate the diameter of a #13 AWG D = ~4Aw(B/ Jr D= .J4xO.0263 13.14 = 0.183 [cm] Subtract 2 times the skin depth from the diameter and calculate the new area. Dn = D-2e Dn= 0.183 -2x 0.0209 = 0.141 [cm] A = nD 2/4 n n An = 3.14 xO.1412/4 = 0.0156 [cm2] Take the difference between Aw(B) and An. This will be the area for the M CUT rent. A~I = Aw(Br An A~I= 0.0263- 0.0156 = 0.0107 [cm2] Check the current density to see if it is close to the designcurrent density, J. J=~I1 AM J = 4/0.0107 = 374 [Alcm2] ~I current density = 374 DC current density = 387 Step No.17 .Calcuate the winding resistance, R R = MLT xN x (J.lnlcm) xlO\u00b76 Rv = 2.7 x 7 x 65.6 xl 0-<> = 0.00124 [Q] CORE SIZES- DESIGN IN POWER ELECTRONICS 177 Step No. 18. Calculate the copper loss, P cu P cu = Inns 2 R Pcu = 10.22 X 0.00124 = 0.124 = 0.129 [W] Step No. 19. Calculate the magnetizing force in Oersteds, H H = O.4n NIpklMPL H = 0.4 x 3.14 x 7x 12/4.06 = 25.98 [Oe] Step No. 20. Calculate the ac flux density in T, Bac Bac = (O.4nN x M12)x f..lr xl04IMPL Bac = O.4n x 7x 2 x 300 x 104/4.06 = 0.13 [T] Step No. 21 Calculate the regulation, a, for this design New regulation= Kg(requiredyKg(used)= 0.00547/0.00168 = 0.326 Step No. 22. Calculate the WattslKilogram, WIK WIK = 8.64 x 10-7 f 1.834 X Ba/\u00b71l2 WIK= 8.64 x 10-7 x 100,0001.834 X 0.132.JJ2 = 17.0[W] Step No. 23. Calculate the core loss, Pre Pre = (mW/g) Wre xlO-3 Pre = 17 x 4.3 xlO-3 = 0.0738 [W] Step No. 24. Calculate the total loss, P~ P~ = Pcu + Pre P~ = 0.129 0.0731 0.202 [W] Step No. 25. Calculate the watt density, \\}I \\}I = P~ 1 At \\}I = 0.202/16.3 = 0.0124 [W/cm2] Step No. 26. Calculate the temperature rise, Tr 178 MAGNETIC COMPONENTS FOR POWER ELECTRONICS T = 450 x qIl.826 r Tr = 450 X 0.0124\u00b0.826 = 1.98 [OC.] Step No. 27. Calculate the window utilization factor, Ku Ku = N SN Aw(B) Ku =7x Ix 0.0263/0.581=0.317 References Bracke, L.P.M.,(1983) Electronic Components and Applications, Vo1.5, #3 June 1983,p171 Bracke L.P.M.(1982) and Geerlings, F.C., High Frequency Power Trans former and Choke Design, Part I, NV Philips Gloeilampenfabrieken, Eindhoven, Netherlands Buthker,C.(1986) and Harper, D.l, Transactions HFPC, 1986,186 Carsten, B.(1986), PCIM,Nov.1986,34 De Maw,M.F .(1981 ),Ferromagnetic core Design and Applications Handbook, Prentice Hall, Englewood Cliffs, NJ, 1981 Grossner, N.R.(1983), Transformers for Electronic Circuits, McGraw-Hill Book Co., New York Hanna,C.R.,J.Am.(1927) I.E. E., 46,128, Hess, J.(1985) and Zenger, M., Advances in Ceramics, Vo1.l6 501 Hiramatsu, R.(1983) and Mullett, C.E.,Proc. Powercon 10,F2, I Hnatek,E.R.(l981), Design of Solid State Power Supplies, Van Nostrand Reinhold,New York IEC (19 ) Document 435,International Electrotechnical Commission Jongsma, J.(1982),High Frequency Ferrite Power Transformer and Choke Design, Part 3, Pilips Gloeilampenfabrieken, Eindhoven Netherlands Jongsma, J.(1982a) and Bracke, L.P.M. ibid Part 4 Magnetics (2000) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Magnetics (1984) Bulletin on Materials for SMPS Martin,H.,(1984), Proc. Powercon II, BI, 1 Martin, W.A.( 1978), Electronic Design, April 12,1978, 94 Martin, W .A.( 1986), Powertechnics Magazine,F eb.1986,p.19 Martin, W.A.(l982), Proc. Powercon 9 Martin,. W.A.( 1987), Proceedings,Power Electronics Conference (1987) McLyman, Col. W.T.(1969) JPL, Cal Inst. Tech. Report 2688-2 McLyman, CoI.W.T.,(1982), Transformer and Inductor Design Handbook, Marcel Dekker, New York CORE SIZES- DESIGN IN POWER ELECTRONICS McLyman, Col.W.T.(1982), Magnetic Core Selection for Transformers and Inductors, Marcel Dekker, New York McLyman, Col. W.T. (1990) KG Magnetics Magnetic Component Design Software Program 179 Pressman, A.(1977) Switching and Linear Power Supply Converter Design, Hayden Book Co., Rochelle Park, N.J. Philip Catalog,(1986) Book C5, Philips Components and Materials Div., 5600Md, Eindhoven, Netherlands Roddam, T.( 1963), Transistor Inverters and Converters, Iliffe, London and Van Nostrand Reinhold, New York Siemens (1986-7) Ferrites Data Book, Siemens AG, Bereich Bauelemente, Balanstrasse 73, 8000 Munich 80 Germany Smith, S.(1983), Magnetic Components, Van Nostrand Reinhold, New York Smith, S. (1983a) Power Conversion International, May 1983, 22 Snelling E.(1988) Soft Ferrites, Properties and Applications Butterworths, London Snelling, E(1989) presented at ICF5 Stijntjes,T.G.W.(1985), and Roelofsma, J.J., Advances in Ceramics, Vol 16, 493 Stijntjes, T.G.W.(1989) Presented at ICF5, Paper CI-0l TDK (1988) Catalog BLE-OOIF, June 1988, TDK, 13-1 Nihonbashi, Chuo-ku, Tokyo, lO3, Japan Thomson (1988) Soft Ferrites Catalog, Thomson LCC, Courbeville, Cedex, France VDE ( ) Document 0806 Watson, J.K.(1980) Applications of Magnetism, John Wiley and Sons, New York Watson, J.K.(1986) IEEE Trans Magnetics Wood, P.(1981) Switching Power Converters, Van Nostrand Reinhold, New York Zenger,M. (1984), Proceedings, Powercon 11(1984) APPENDIX 5.6 RECENT ARTICLES ON DESIGN OF FERRITES FOR POWER APPLICATIONS Baasch, T.L., Electronic Products, Oct. 1971,25 Bledsoe, C., Electronic Business, June 1,1984, 128 Bloom,E., IEEE Transactions on Magnetics,(1986), 141 Bosley, L.M. (1994) Magnetics Brochure. Brown, B.(1992) PCIM, July 1992) 46 Brown, J.F., Powetechnics. Dec. 1986, 17 Carlisle, B.H.(1985) Machine Design,Sept. 12, 53 180 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Cattermole,P.(1988) and Cohn,Z .. Proc. HFPC,1986, III Chen, D.Y., Solid State Power Conversion, Nov/Dec., 1978,50 Ciarcia, S.A,Byte,Nov.1981, 36 Cuk,S., Power Conversion International, 1981, 22 Dull,W., Kusko, A& Knutrud,T., EDN, Mar.5, 1975, 47 Engelman, R.( 1989)PCIM, ~ #7...J..1 Estrov, A(1989) PCIM, May, 1989 16 Estrov, A(1986) PCIM, August 1986, 14 Finger, C. W. (1986) Power Conversion International, 1986 Fluke,J.C.,Proc. Power Electronics Show, 1986, 128 Gatres B.( 1992) PCIM, il, #7 July 1992, 28 Harada, H. and Sakamoto, K., IEEE Translation Journal of Magnetics in Ja- pan, #7, Oct.1985 Hew, E., Power Conversion International, Jul.! Aug. 1982, 14 Hill, P.C., Proc. Powercon 2, 1975,243 Hiramatsu, R. (1983),and Mullett, C.E.,Proc. Powercon,lO, F2,1 Kamada, . (1985), and Suzuki, K., Advances in Ceramics,Vol. 16,507 Kepco (1986) Kepco Currents, Vol 1.#2 Kitagawa, T. and Mitsui, T.,IEEE Translation Journal of Magnetics in Japan, Sept, 1985 Konopinski, T. and Szuba, S. Electronic Design, 12,June 7, 1979,86 Margolin, B., Electronic Products, Mar.28, 1983, 53 Martin, H. (1984) Proc. Powercon, 11, B 1, I Martin, W.A Proc. Powercon 9, 1982, Middlebrook, R.D., Power Conversion International, Sept. 1983,20 Mochizuki, T. (1985) Sasaki, I. And Torii, M.,Advances in Ceramics, Vol. 16,487 Mohandes B.E.(1994) PCIM, July 1994, 8 Mullett, C.E.,Proc. Power Electronics Show, 1986,36 Sano, T. (1988), Morita, A and Matsukawa, A Proc. PCIM,July 1988, 19 Schlotterbeck, M.(1981 ),and Zenger,M., Proc. PCIM, 1981 ,37 Shiraki, S.F.(1980) Proc. Powercon,7,J4, I Smith, S., Power Conversion International, May 1983, 22 Stratford, J.M., EDN, Oct. 13,1983, 140 Sum, K.K.,Power Electronics,1986, 153 Triner, J.E.,Power Conversion International, Jan. 1981,69 Turnbull, J., Electronic Products, May, 15, 1972, 53 Ying X. and Zhi,Z.,IEEE Transactions on Magnetics,Feb.1985,148 Zenger,M.( 1984) Proc. Powercon, 11 (1984 Chapter 6 COMMERCIALL Y -A V AILABLE COMPONENTS FOR POWER ELECTRONICS INTRODUCTION In the previous two chapters, the component material and shape prop erties of components for power electronic systems were reviewed. This chap ter will list these components that are available commercially. 6.1- TDK FERRITE POWER ELECTRONIC COMPONENTS TDK offers a wide variety of materials and component shapes for power electronic applications. The materials will be considered first followed by the cores that are offered in the various materials. The specifications listed for each core as it applies to design will be reviewed. The catalog pages for material and representative listings of core properties are found in the Appen dix at the end ofthe chapter. 6.1.1-TDK Power Ferrite Materials TDK has 6 ferrite materials that can be used for power supply transformers and chokes. They are; 1.-PC40- an standard low frequency material in various E-type cores, (ETD, EC, EI, EE, EF, EP, and RM) 2.-PC44- a lower loss improved material in LP, PQ, EPC (low pro file) cores. 3.-PC50- a higher frequency material in PQ,EPC,EP, and RM cores Tables of magnetic properties are found in Table 6Al. These three materials have a minimum core loss temperature of about 1000 C. for continuous serv ice. Recently, TDK has also introduced 2 other materials that have a mini mum core loss temperature of 40-80 0 C. for small portable power supplies that operate intermittently and one that has a higher permeability. Another lower temperature material has a moderately high permeability. 4. PC45-has a minimum core loss temperature between 40-50 0 C. 5. PC46-has a minimum core loss temperature between 60-80 0 C. 182 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 6. DNSO-has a core loss minimum at SO\u00b0 C. and has a higher perme ability than the others. It is available in EPC, ER (high power), EEM cores and also in a special EER core whose design gives 13- 20% reduced loss. The properties of the above three materials are found in Table 6A2. Figure 6.1 shows the core loss vs T for several TDK power materials. For large high power reactor and transformer cores, TDK has, in ad dition to the previously cited PC40, another material PC22 with a slightly higher saturation value. The high power cores are available in T (Toroids), VV, EC, EIC, PQ, E, EI, PT and SP cores. In addition to the material specifications, TDK lists some design data for each core such as the effective parameters (Ae, Ie, and Ve). For ungapped cores, they list the calculated output power in Watts for 100 KHz.and SOO KHz. (PCSO). For gapped cores for chokes, the list the AL at 1 KHz.,O.S rnA and 100 T (1,000 Gausses).PQ cores have an NI limit for gapped cores and AL vs gap. Listed is also the temperature rise versus total loss an also core loss at 100 0 Cat 100 KHz. and 200 mT (2,000 Gausses). TDK Common-Mode Choke materials-TDK has three materials for common mode choke applications. They are HSS2,HSn and HS 10. Their permeabil ities are respectively SSOO, 7S00 and 10,000. They are available in T(Toroids), FT, FTR, ET and UU cores. Except for the V-V, they are all con tinuous-path (no mating surface) cores. Provided are the AL values and the effective parameters. Toroids are also available in the HSC2 high permeability material. TDK also offers Common-mode filters equivalent circuit model for Spice. See Table 6A3. TDK EM] Suppressor Materials-TDK lists 6 materials for EMI suppressor cores. They are HF30, HF40, HFSO, HFSS, HF60 and HF70. Their properties are given in Table 6A4 . From their resistivities, all except HF 60 are NiZn materials, while HS 60 is a MnZn material. These materials are available in multi-hole substrates, chip suppressors, beads, wire-wound-beads, cable clamps, and toroids. TDK also makes their own EMI filters. 6.2- PHILIPS (YAGEO) POWER FERRITE COMPONENTS Philips has 12 ferrite materials for power applications. Eleven ofthem are MnZn ferrites and one N iZn ferrite. The properties of these materials are listed in Table on page . The first 3 materials are used for line output trans formers for TV deflection yokes. The remaining 9 materials are arranged es sentially in order of their frequency of operation. 3CSI has a minimum core loss minimum at SO 0 C. 3C94 is an industrial use material. For 400 KHz. operation, 3C94 is a low loss high Bm material and 3C9 a very low loss mate rial. The 3F materials are for higher frequencies, 3F3 for 700 KHz, 3F35 for 1 MHz. and 3F4 for 3 MHz. A graph of the performance factor(PF) defined 184 MAGNETIC COMPONENTS FOR POWER ELECTRONICS earlier in Section 3.14 is given in Figure 6A6 for a 500 mW/cm3 limit for for 5 representative material grades. For selecting a core according to power out put, Table 6.1 lists the core sizes capable of handling the power ranges at 100 KHz. Table 6.1-Power Handling Capacities of Ferrite Cores-Philips Power throughput for different core types (at 100 kHz switching frequency) POWER RANGE CORE TYPE (W) <5 RM4; P11n; R14; EF12.6; Ul0 5 to 10 RM5; Pl418 10 to 20 RU6; E20; Pl8111; R23; U15; EF015 20 to 50 RM8; P22113; U20; RM10; ETD29; E25; R26110; EFD20 50 to 100 ETD29~ ETD34; EC35; EC41; RM12; P30/19; R2612O; EFD25 100 to 200 ETD34; ETD39; ETD44; EC41; EC52; RM14; P36I22; E30; R56; U25; U30; E42; EFD30 200 to 500 ET044; ETD49; E55; EC52; E42; P42129; U37 <500 E65;EC70;U93;U100 The individual core sheets list the AL ,J.le and Bsat at H = 250 Aim and T = 100 0 C. as well as the core loss at 25, 100 and 400 KHz. Gappe core data lists the AL ,J.le and the air gap. In addition , for RM cores, the core loss is given at IMHz. and 3 MHz. and planar E-cores at 30 and 10 mT respectively. Philips Common-Mode Choke materials-Philips offers 5 high perm materials that can be used for common-mode choke applications at lower frequencies. They are 3E25, 3e27, 3E26, 3E5 and 3E6 which range in permeabilities re- COMMERCIAL POWER MAGNETIC COMPONENTS 185 spectively from 6000, 6,000, 7,000, 10,000 and 12000.They are mostly avail able in beads, toroids and other common mode shapes. For higher frequencies SMD common-mode chokes are available in the NiZn material, 4S2. Philips EMf Suppressor Materials-Philips lists a variety of EMI suppression materials. They are listed in Table 6AIS . The 3E series are MnZn common mode choke materials. 3S 1 is also a rather high perm material that can not withstand a high DC bias and instead the lower perm 4S2 should be used. Two new materials,3S3 and 3S4 are MnZn with high resistivity. All of the remaining materials (4 series)are NiZn materials with high resistivities and lower perms. An impedance versus frequency plot for 3S4 is shown in Figure 6AS. 6.3- EPCOS POWER FERRITE COMPONENTS Epcos (formerly Siemens-Matsushita) has 10 different power materi als. For 100 KHz., there are N27,NS3 and N41; for 200 KHz. there are N62,N67\"N72, and N82; for SOO KHz. there is N87; for 300 Khz. to I MHz. and resonance converters, there are N49 and NS9. See Tables 6A17-19 anf Figure 6A6Just released at this book's publication is a new material N97 which listed best in class at 2S-400 KHz. The loss at 100 0 C. is 20% lower than that ofN87. It also claims a better DC bias property than N87. They also list a new material, N92 with which they claim it is possible to increase the rated current of output chokes by 10% against N87.At the same time, the losses at 1000 C. are comparable to N87. They also claim that their N49 mate rial has been improved to meet the needs of rising performance requiements of DC to DC converters. The aim was to reduce losses while increasing satu ration. At SOO KHz. the losses have been reduced by 30%. and saturation has been increased by 10%. The material data and The material data and core loss curves for all three materials are given in Tables 6.2-6.4 and Figures 6.2, 6.3, 6.S, 6.7 and 6.8 . In addition DC bias curves are given for N92 and N97 in Figures 6.4 and 6.6 . A table of transformer power capabilities at several frequencies is given for each core. Epcos lists performance factor, PF for 100 0 C. and 300 kW/m3 and a rather little cited property, the standardized hysteresis constant as a function of temperature. There is a very wide variety of core shapes. The RM cores are particularly featured in sizes from RM4 to RM 14. They are also available in low profile in this range. Other cores include EP, standard pot cores, E-cores including ELP and EFD. Some cores including the RM's are available with surface -mount accessories. Individual sheets for cores include AL ,/J.e and core loss at 100 KHz. and SOO KHz. and 100 0 C. at 200 mT and SO mT. respectively. Gapped core 186 MAGNETIC COMPONENTS FOR POWER ELECTRONICS data show the AL ,J.le and the air gap. Low profile and planar cores are avail able in a several sizes. Epcos Common-Mode Choke moterials-Epcos does not specifically list common-mode choke materials but they have 5 materials that have perme abilities of 6000 and higher (up to 15,000). They are T35,T37,T38 T42 and T46. The last one is only available in small ring cores. 'JDO ., -\"'7 ~~~ ____ ~ _____________________________________ - _- ~\"~'1~ I: ~ ~ ~------------~~~-~--------~----~--- COMMERCIAL POWER MAGNETIC COMPONENTS 187 Figure 6. 4- \u2022 Reversible Permeability of N97 compared with N87 COMMERCIAL POWER MAGNETIC COMPONENTS 189 6.4-MAGNETICS POWER FERRITE COMPONENTS Magnetics has 4 different power materials. One material, F, has a minimum core loss temperature at about 25 0 C and is meant for low frequen cies. K and P materials have core loss minimum temperatures at about 60 0 C at 100 and 500 KHz. R has the lowest core loss at 100 0 C for 100KHz and 500 KHz. K material has the lowest core loss at 700 KHz. See Table 6A5 The various materials are available in all the popular core shapes. In cluded in the power ferrite design information is a table of core cross section window area products for all the power cores. Graphs showing the same area product plotted against the output power allowing the core selection to be made for the various core shapes and sizes. Another table gives the power handling capabilities for different frequencies and core shapes for a forward converter. Output power is also plotted against temperature rise for different frequencies. The individual core size sheets list the core-window product area and the AL for ungapped cores . Using the common core-loss equation; Where PL = the core loss in mW/cm3 COMMERCIAL POWER MAGNETIC COMPONENTS 191 Magnetics Common-Mode Choke materials- Magnetics has 3 high penn~ ability materials for common mode choke operation. They are J, W and H materials whose permeabilities are 5,000, 10,000 and 15000 respectively. The latter is available only in toroids. The others can be had in most other core shapes. See Table 6A7 6.5 TOKIN POWER FERRITE COMPONENTS Tokin's power ferrite line is listed in Table 6A1O .Four materials are listed spanning the range from 100KHz. to 1 MHz. The core loss minimum temperature for the BHI and BH2 are in the range 90-100 0 C while that of BH40, the higher frequency materia~ is between 70-80 0 C. Properties of new material with somewhat higher saturation, BH3 is listed in Table 6Al1 com pared with BHI. Plots of core loss versus frequency and flux density at three temperatures are presented. 192 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Tokin Common-Mode Choke materials- Tokin has one material, BH5000 which has a higher permeability(5000) for lower frequency common-mode choke application. 6.6- FAIR-RITE POWER FERRITE COMPONENTS Fair-Rite Products has two materials for use as power trans formers, 77 material for 25 Khz. operation and 78 with a saturation of 5000 Gausses for 100 KHz. operation. The 75 material can be used at 25Khz. at 100 0 C. Power materials are available in EP, PQ, U, E and ETD cores. See Table 6A8 Fair-Rite Common-Mode Choke materiais- Fair-Rite lists one material 75 for their common-mode choke aplications. It has a permeability of 5000.Another material, 76 has a 10000 permeability and is recommended for frequencies up to 500 Khz. Fair-Rite EMI Suppressor Materials -Fair-Rite lists 5 materials for EMI suppression, 43, 44, 61,73 and 77. The 73 and 77 materials are MnZn for lower frequencies( <30 MHz.) while the other 3 are NiZn for higher frequencies (30-250 MHz.). The 61 material is the most stable with temperature. See Table 6A9. 6.7-FERRONICS POWER FERRITE COMPONENTS Ferronics Common-Mode Choke materials-Ferronics has 2 MnZn ferrite materials, B (5000) and T(lO,OOO) perm which can be used for common mode chokes at lower frequencies. See Table 6A23 Ferronics EMI Suppressor Materials- Ferronics has 3 NiZn materials that are used for EMI suppression, J, K, and P. The permeabilities are 850, 125 and 40 respectively. The latter two are perminvar materials that list the cau tion that the permeabilities and loss factors may be irreversibly increased if excited with a high magnetizing force. This factor should be considered when applying high DC or ac currents. J perm is recommended for frequencies from 5-500 MHz, K for above 20 Mhz. and P for above 80MHz. The materials are offered in toroids, multi-hole wide band cores and beads. The material prop erties are given in Table 6A23 . COMMERCIAL POWER MAGNETIC COMPONENTS 193 6.8-FDK POWER FERRITE COMPONENTS FDK lists 7 different power ferrite materials as shown in Table 6A25. The 6H series are high flux density materials for 25-100 KHz. operation. The higher the number after the 6H, the lower the losses. The minimum loss tem peratures vary from 40 0 C - 100 0 C. The 7H series are lower flux density materials for higher frequencies. The newest material 7H20 has half of the core loss of7H1O at I Mhz. and 100 0 C. The individual core data include the effective parameter, the window and core cross-sectional areas and the AL'S. See Fig 6A7-8 FDK Common-Mode Choke materials- FDK recommends two high perme ability materials, 2H07 and 2H1O with permeabilities of 7,000 and 10,000 respectively for common mode usage. 2H lOis recommended for frequencies lower than 500 KHz. FDK EMf Suppressor Materials-FDK lists 4 EMI suppressor materials, K32, L51, K 14, and K26. They are NiZn materials ranging in permeability from 700 to 40 over a range of increasing frequencies. Their properties are listed in Table 6A24. 6.9-A VX POWER FERRITE COMPONENTS The A VX ferrite product line is that of the former Thomson company. Their power ferrite component line is made from 8 materials listed in Table 6A26. The PWI materials are for the lower frequencies up to 32 KHz. proba bly for line output TV transformers. The PW2 materials operate at 100 KHz. The PW3 and PW4 materials run up to 500KHz. and the PW5 to 1.5 MHz. See Table 6A26. A JIX Common-Mode Choke materials-There are 3 high perm A VX materials that can serve as common mode chokes. They are A2, A3 and A4 with per meabilities of 10,000, 7500 and 6000 respectively. Their properties are given in Table 6A27 . 6.10-MMG-NEOSID POWER FERRITE MATERIALS MMG has six materials for power transformers and chokes, F47, F45, F44, F5, F5A and F5C. Their permeabilities range from 1800 to 3000. Core loss data for 25 0 C. and 100 0 C. is shown for the F5 series at 16 and 25 KHz., F44 and F45 up to 100 KHz. and F47 to 400 KHz. See Table 6A12. 194 MAGNETIC COMPONENTS FOR POWER ELECTRONICS MMG-Neosid Common-Mode Choke materials- MMG has 4 materials with permeabilities of 5000 and above. They are the F9C, FlO and F39 whose permeabilities are 5000, 6000, and 10,000. MMG-Neosid EM] Suppressor Materiab--MMG-Neosid list 4 materials for EMI suppression, F19, F14, F16, F25, F28 and F29, the latter three being Perminvar ferrites for higher frequencies. Their permeabilities are 1000, 220, 125, 50,30 and 12 respectively. 6.11-KASCHKE POWER FERRITE MATERIALS Kaschke has two materials for use as power transformers' K2004 and K2006. The K2004 has a higher saturation and lower losses. The losses are given at 16 KHz. The 2004 material has a minimum loss temperature of 80 0 C while that of 2006 at near 100\u00b0 C. See Tables 6A28-29 and Figure 6A9. Kaschke Common-Mode Choke materials- Kaschke has one material K6000 with a permeability of 6000 that may be used for common-mode chokes 6.12- VOGT POWER FERRITE MATERIALS Vogt has three power ferrite materials, Fi323,Fi324 and Fi325. All three have saturations in the 5000 Gauss range with the 325 material slightly higher than the other two it also has the lowest losses at the higher frequen cies. The other two are meant for the 100-300 KHz range with the 324 mate rial having a higher minimum loss temperature than the 323 (80-100 0 C. vs 60 0 C. See Table 6A31. Vogt Common-Mode Choke materiab--Vogt has three materials suitable for common-mode chokes. They are Fi410, Fi360 and Fi 350 with permeabilities of 10,000, 6000 and 5,000. Their properties are listed in Table 6A31. 6.13-SAMWHA POWER FERRITE MATERIALS Samwha has three power ferrite materials, PL-5, PL7 and PL9. The saturations for all three are about the same at 5000 Gausses. The core loss at 100 KHz and 100 0 C is lowest for the PL9 then the PL 7 and then the PL5. The minimum loss temperature for the PL9 is about 80 0 C while those for the other two are about 95 0 C. Samwha also lists three other materials for flyback COMMERCIAL POWER MAGNETIC COMPONENTS 195 transformer operation, SMI9B, SM 19C and SMI9D. All the magnetic pa rameters are identical to the other three power materials except that the core loss is quoted at 32 KHz. See Table 6A39. Samwha EMI Suppressor Materials-Samwha lists 4 NiZn materials for EMI suppression, SN20, T314, SN065 and SN201. They range down in perme ability from 2000 to 500. 6.14- STEWARD POWER FERRITE MATERIALS Steward does not specifically list a power transformer material but does recommend their 21(presumably a NiZn Material) material for tempera ture-stable high frequency inductor and some very high frequency choke ma terials. They list several EMI suppression materials including their 25 and 38 materials. Their materials are listed in Table Steward Common-Mode Choke materials-Steward recommends their 1700 perm 38 material for broadband common-mode choke applications. They do however have some high perm materials for the lower frequencies. The are; 35 and 36 (5000 perm), 37 and 42 (7500 perm) and 40 (10,000 perm). All of these are listed in their toroid catalog. (see Tables 6A20-1.) Steward EMI Suppressor Materials- Steward lists 3 EMI suppresion materi als, 25, 28 and 29. Their permeabilities range from 125 to 850. They are nickel ferrites with high resistivities. Steward makes a very long line of EMI cores and filters. Their material specs are given in Table 6A22 . 6.15-FERRITE INTERNATIONAL POWER FERRITES Ferrite International has 4 materials for power ferrite applications, TSF 5099 TSF7099, TSF7070 and TSF8040. The first three have saturations of 5000 Gausses with TSF8040 at 5100 for integrated magnetics. TSF5099 has the lowest core loss at 25 and 100 KHz. and 100 0 C. TSF 5099 and 7099 have core has minimum temperatures at about 100 0 C, TSF7070 at 80 0 C and 8040 at 60 0 C. They also list a \"Boost\" material for DC bias operation in gapped inductors. Their material properties are shown in Table 6A37 . Ferrite International Common-Mode Choke materials-Ferrite International has two high perm materials for common-mode choke usage. They are TSF5000(5000 perm and TSFOIOK (10,000 perm). See Table 6A37. 196 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 6.16-CERAMIC MAGNETICS POWER FERRITE MATERIALS Ceramic Magnetics has 4 power ferrite materials MN80, MN67, MN60LL and MN8CX. The first three have data at 125 0 C. MN80 shows core loss data at 3000 Gausses and 100 KHZ. with a minimum core loss tem perature of 75 0 C. Under the same frequency at 1000 Gausses, the minimum core loss temperature is 125 0 C. MN60LL has the lowest core losses at 200- 300 KHz. MN67 has the highest saturation at 5200 Gausses. MN8CX has the highest operating frequency at .5-2.0 MHz. See Table 6A38. Ceramic Magnetics Common-Mode Choke materials-Ceramic Magnetics lists 4 materials wth permeabilities above 5000. They are MNIOO (10,000 perm ,MC25 (9500 perm) and MN60 and MN60LL (6000 perm) 6.17-TOMITA POWER FERRITE MATERIALS Tomita lists two power ferrite materials, 5G and 15 G. Data is given at 16 KHz. and 25 0 C and 100 0 C. also at .1 and .2 T up to 100 KHz. Core shapes include RM, X, U, E, EP ETD, PM and toroids. See Table 6A30. Tomita Common-Mode Choke materials-Tomita has 5 materials whose permeabilities are between 5,000 and 10,000. They are 2E2, 2E2B, @#I, 2GI, 2G3 and 2Fl. 6.18-ISKRA POWER FERRITE MATERIALS Iskra lists core loss data for three materials although others are shown with high saturations but no loss data. The materials with core loss data are; 2E6 2F6 and 2F8 at 100, 200 and 300 KHz. respectively. Core shapes listed for these materials are; EE, EI, EP, RM, EER, ETD, EC and PP.See Table 6A33. Iskra Common-Mode Choke materials-Iskra lists 2 materials with perme abilities above 5000. They are 22G (6,000 perm and 12G (10,000 perm) 6.19- nOMEN POWER FERRITE MATERIALS Domen lists two materials for High power applications, 2500HMC 1 and 2500HMC2. The losses are given at 16 KHz. 2000 Gausses at 25 0 C and 100 0 C. See Table 6A32 COMMERCIAL POWER MAGNETIC COMPONENTS 197 Domen Common-Mode Choke materials-Domen has 3 materials with high permeability, 6000HM and 6000HMI at 6000 perm and 10000HM at 10,000 perm. 6.20- HITACHI POWER FERRITE MATERIALS There are 4 power ferrite materials in the Hitachi catalog, SB5S, SB3L, SB7C, and SB9C. SB5S has a higher permeability (3000) than the oth ers but higher losses at 100 KHz. and 2000 Gausses. SB7C and SB9C have low losses at higher frequencies with a core loss maximum at 100 0 C. SB3L has a high saturation and is particularly useful with imposed DC bias. These materials are available in EI, EE, EER, and PQ shapes.See Table 6A35. Hitachi Common-Mode Choke materials-Hitachi lists several materials for common-mode chokes. They are GPll, GP9,GP7 GP5 and GQ5C with per meabilities from 5,000 to 10,000 for use at lower frequencies. Hitachi EMf Suppressor Materials-Hitachi lists 4 NiZn materials (DL) for use in EMI suppression up to 10 MHZ.(See Table 6A36) At 100 MHz. mate rials QM, KP, DV and SH are recommended but no data given. Shapes avail able are beads or filters. 6.21- COSMO POWER FERRITE MATERIALS Cosmo has four power ferrites listed in their catalog. They are CF138, CF 129, CF 196, and CF 1 0 1. The power losses are given at 16 KHz and 25 KHz at a 2000 Gauss level.The saturation ofCF129 is 5100 Gausses and the other range from4800 to 5000 Gausses. An unusual parameter they list is the temperature of the secondary permeability maximum, which should corre spond to the minimum core loss temperature. The materials are available in EFD, EPC,EE, EI, ETD, EER, EC and uu. shapes. Cosmo Common-Mode Choke materials- Cosmo has two materials CF 195 and CF197 with permeabilities of 5000 and 7500. See Table 6A40. 6.22- ACME POWER FERRITE MATERIALS Acme lists 3 power ferrite materials, P2, P4 and P5. The saturation of P2 is 4500 Gausses and the other two are at 4800 Gausses. P2 is meant for 100 KHz operation, P4 at 300 KHz. and P5 at 500 KHz. Acme lists an un usual property namely the amplitude permeabilities at 25 KHz. and 2000 Gausses at 25 0 C. and 100 0 C. See Table 6A43 Acme Common-Mode Choke materials- Acme lists several high permeability materials that can be used for common-mode chokes. Acme EMf Suppressor Materials-Acme-Malaysia lists a number ofNiZn materials for EMI suppression in Table 42. They are H2, H3 H4, H5, DIe and D28.Their permeabilities range from 50 to 870. They are available in several shapes including cable cores. 198 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 6.23- HINODAY POWER FERRITE MATERIALS Hinoday was the former Morris Electronics Co. an old Indian ferrite company. Hinoday has 3 ferrite power materials MSB-58, MSB-7C and MSP5F. The saturation of the fIrst is 4800 Gausses while the other 2 are at 5000 Gausses. The MSB-7C has core loss listed at 100 KHz. and 2000 Gausses while the fIrst is easured at 16 KHz. and 2000 Gausses at 40 0 C. The last one is also a 16KHz. material with the higher flux density. See Table 6A44 Hinoday Common-Mode Choke materials-Hinoday has 2 materials MGQ5C and MGP-9 with permeabilities of 5300 and 7000 for common-mode chokes. The properties are given in Table 6A44 . 6.24- ISU POWER FERRITE MATERIALS Isu has 6 power ferrite materials, PM, PM2, PM2A, PM5 PM7 and PM9. The fIrst 3 are for lower frequencies from 16-25 KHz. and 85 0 C. while the other three are mainly for 100 KHz. and 100 0 C. operation. The saturations of the fIrst three are also slightly lower than the last three. See Ta ble 6A41 Isu Common-Mode Choke IIUlterials- Isu does not list any materials for common-mode chokes 6.25- MIANY ANG POWER FERRITE MATERIALS Mianyang has 3 power ferrite materials, R2KD, R2KH and R2KBP 1. The fIrst has a saturation of 4800 Gausses and the second 5100 Gausses. The fIrst material is meant for 16KHz operation, the second for 16,32 and64 KHz. while the third is a 25 KHz. material. See table 6A45. Mianyang Common-Mode Choke IIUlterials-No common-mode materials listed. 6.26- HEBEl POWER FERRITE MATERIALS Hebei has one power ferrite material for operation at 25 KHz and 2000 Gausses. The saturation is high at 5100 Gausses. See Table 6A46 Appendix 6.1 Listing of Catalog Data for Ferrite Core Suppliers Tables Appendix List No. 1. 6Al 2. 6A2 3. 6A3 4. 6A4 S. 6AS Vendor TDK \" \" \" Magnetics Figures Appendix List No. COMMERCIAL POWER MAGNETIC COMPONENTS 199 6. 6A6 7. 6A7 8. 6A8 9. 6A9 10. 6AI0 11. 6A11 12.6A12 13.6A13 14.6A14 15.6A15 16.6A16 17. 6A17 18.6A18 19.6A19 20.6A20 21.6A2l 22.6A22 23.6A23 24.6A24 25. 6A25 26.6A26 27. 6A27 28.6A28 29.6A29 30.6A30 31.6A31 32.6A32 33.6A33 34.6A34 35.6A35 36.6A36 37.6A37 38.6A38 39.6A39 4O.6A40 41.6A41 42.6A42 43.6A43 44.6A44 45.6A45 466A46 \" \" Fair-Rite \" Tokin \" MMG-Neosid Philips \" \" \" Epcos \" \" Steward \" \" Ferronics FDK \" AVX \" Kaschke \" Tomita Vogt Domen Vogt Iskra Hitachi \" TSC CMI Samwha Cosmo Isu Acme \" Hinoday Mianyang Hebei 6Al,6A2 6A3 6A4 6A5 6A6 6A7 6A8 6A9 200 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Table 6A.I-Properties ofTDK Power Transformer and Choke Ma terials PC46 I'CI6 PCo4 ~1 \"\"''''1 ''''''''_!r - . . . \"' 2501Io25\"J. 3Z00025'\" 24OOo2ft _r_ 57OI25'Cl 36CQ5'CI ~l [100kHz. 2CIOtnTl \"'\" ow\",., 2SIlI75'C1 250[46'CI 4Ot(8O'C1 41IO[100'C! 88O(IOO'C! 300(1OO'C) s-....,., ....gnootc .... III .. T !Z\"CI &30 830 \"0 do~ IIOO\"C) - \"0 -~\"',.\",,~ Br OIT [ZSC) 120 115 1 10 ['OO'C) 110 10 10 c-_ He AIm [26\"C) 12 11 13 IlIaoNmI I'OO'C) \u2022 10 0 ... c.....~ Te 'C _?,.ZJIJ it 230 ;' 215 Table6A3-Properties ofTDK Common-Mode Choke Materials _!lIIC PfIEVEIO'1OII~ CHOKI! -- HSI2 HS72 IISl0 ...... ,.-,\", .. -- 1SOQo2S\", ,~ f!!!OOn*I. . -~ --- ~x 'it\" 10 30 30 t- t'_I tl_> --- ---donoi1y' \u2022 ..T 410 4.0 -(Mon ..... \" ' -\"'d!r!Iy '\" OIl 70 10 .20 c-two_ ... MIl a 8 , c..._ ... T. 'C .,30 .'30 .'20 - ..... ~ ~ ~ 1 D.2 D..2 ~ do .\"... ....... 0- . .... 0- ...... 0> ........ ge .... \u2022 lM _..- .... 6tlMlned~ IDn:IiIW (lICn!t III \"-\" ......... ~~ Ihawn.. Tc Q - - 01\" (.IO- YC) (\"C)I\"I'I~ _ (D140 >125 >120 4300 4300 4200 430 430 420 WOO 800 800 100 SO 80 0.1 0.04 0.04 8 3 3 <3 <3 <2.5 1 .15 .1 4 .S 4.S 4.9 Table 6A.8 -Fair-Rite Power and Common-Mode Choke Materials - ..... - 'T7 70 n \" \" ..... - ... II1II B~laa-.... t300 ...., ..... I 'DODO .... 00n00y ...... B .... ..... \"\"\" \"\"'\" 4000 mr ..., ... ..,. 300 .... ._- - H ,. :V.S 'D 'D \u2022 \"'\" IlOO lOCO ... ... , .. -.. .... o-ty - B. \" .. , ... 'ODD , ... , ... In' \". ,'\" 'DO ' .. '20 c-..... - H. .. ..., ,. ,. 'D ...... lUi ,. US 13 \u2022 -'-- , .. \u2022\u2022 &\\0, ... .. 7 ,S 'S . - , , 1 . , ..... .-f--T~ea.ttonCII vc \u2022 ,.2 \u2022 .0 \u2022 ~ F'WTftMIb(Iyt\u00bb7D\"C) - CwteT~ -C >; >2OD \"\"'\" ,\"'\" \"40 ., .. - Don \u2022 '0' \"0' '0' . ,.. .. Powwu.~ - P 2SIHI \u00b7 2OIXIO\u00b71C1J!C 20D ..:11,5 - '40 - ,0QIttz - ,ClOD Q - 1DIJI'C - .,.., - - - ......... ..- - f-- '-- -- L <3 <2.0 a, .\" .s - \u2022 <30 - <30 ... - \"-- p . , I ... . , -I - s - - - - - s.. .. s-9tIDr.-orw 11li111 '., 1t ,S 20 21 -- COMMERCIAL POWER MAGNETIC COMPONENTS 203 Table 6A.9 -Fair-Rite EMI Suppression Materials \"'-tY UnA -,- ., .. OJ II' T1 71 n -~ II, I 125 500 .... 000 2000 2300 25110 oe.togaw -Conoly - ZI60 3000 ~750 3000 4100 !>OOO 4000 \",T 8 235 300 :us 390 '60 500 -- ..... St/ongIIl - 10 '0 .0 10 10 37 .\u2022 .0 Nm \" 800 800 \\100 800 \\100 \"\"\"\" 800 - --~ - ,2QO 1100 I2QO :1400 tI\"\" ..... '000 \",T 8. I~ 110 \u2022 20 3010 \" . .\"\" 100 ~- - '-II .3e .JU .... .22 . .. ,e Mo i( '28 21! 2' <0 17' Ie \" 5 U.F_ '0- \"\"III!. 32 16 1~ 50 '.5 4.5 7 -~ ,... U 1,0 ' .0 .1 : , I , I .1 T_~o/ vc 10 6 1.2 .B ...... ~ (20-1O'C) .s - - Quior_ 'C T. .asa \"eo ,130 I >200 >200 I >200 \"eo I Roo..ovooy gem P ' 0' '0' '0' 2'0' 10' 2'0' .0' --_u. Donoity -- p 2SUU \u2022 2IXD G \u2022 1CJ01C - - - - 200 <115 - ~OOIcHz\u00b7,DOD G\u00b7 ,OO'C - - - - - c,lIO - ---F_ .. ~ MHz [l <100 - c'O - <3 <2.5 <2.' ~ E .2QO 30-\"'\" 3O-2QO - <30 - <30 .t.r.. : - - - - < \u2022 ... - I - - - <,15 - - - I---800 ... _\",,_ \u2022 0 12 .. 11 la\" 17 11& \" 15 -- Table 6A.I0- Tokio Power Ferrite Materials _c_ Ull\" 8\", - Uta -ApjIIIM....-. .... MH:I <0.3 ,Q.3 O.S-\" .O -,...,--, p , - - , 5IIIIt2D'Io - ~-....---. 23\"1: 520 5'0 530 500 limo \",T '-\"\"- 111111M111 ,oo\u00b7c 4.0 400 - -z:rc '00 '00 2110 120 --.-..., om. l00\"C mT 6& 1511 .211 aD 23\"C .a.o 14.3 43.6 11.0 --lolly Hemo Mn V &.5 l00'C 6.0 5..0 -\"'--(1-.) _11/1 , '0\" <5 ce 4 <20 C .... ___ 1. \"C 220 220 240 '80 2:S'C 560 8Oi) ~ r---, __ T Po. IID\"C r--3SO 450 500 100'C 2!50 \"0 .:10 eo.._ 8O\"C Wi~ -__ 1 P\", r--- 8O'C 500 8O'C 3110 t.HII_T P\", r--- 80'(; Jell 0..17 d II9'm' ..... ,0' 4Ax1G' \u2022\u2022 111<10' ...... ,0' 204 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Table 6All-Properties ofoew Tokio BH3 vs those ofBHl llam BH-3 BHl InilioJpermieabiil)' I'i 18OOf2O'l1, 25OOt2()% ---.. npt:\"'1MIy Bmo; mT 2:!\"C 530 520 Hxrc 420 410 Elf..,.\". retantilly 8r mT 2:!\"C 120 100 100'C 70 55 EIIectve N\\Ka1Ion coen:MI IOroI He Aim 23'C 17 13 l00'C 13 5 Core lou Pcv kW/rrf 25'C 580 SSO 6O'C 400 350 100'C 380 250 120'C 420 300 C .... poInI Te 'C l00'C 280 220 __ I.t 25\u00b0c .t 15\u00b0c Co C) type .\"\"'kat ..... (3000A/_) ( M) .r_ 3C15 1800 .. 500 . 20 0 > 2 0 0 3 3 - . 4. 8 4. 8 6H 40 6H 41 6H 42 24 00 25 00 34 00 S 30 53 0 53 0 f - - ~ 43 0 43 0 _ . 11 0 11 0 11 0 10 10 1 0 1 -_ _ < 3 < 3 < 3 90 75 6 0 75 60 5 0 eo 5 0 40 5 0 40 45 _. 4 0 <4 5 55 6 5 0 55 0 45 0 55 0 45 0 S5 0 45 0 35 0 30 0 35 0 SO D 32 5 30 0 32 5 37 5 - - - - ---= -- . - - - - - - - - - - - - .-- -_ . 8 - _. - - B B > 2 0 0 > 2 0 0 > 2 0 0 2 2 2 4 .9 4. 9 4. 9 7H l0 15 00 48 0 38 0 -- \u00b7,S O - .-- 30 ' . _ < 5 - - - - - - - - - - 10 0 BO 10 0 40 0 40 0 50 0 ~ - 8 - > 20 0 5 4 .8 7H 20 10 00 48 0 ~ -- 13 0 .. 2 5 - < 4 _._ = ..... - - - - -, - - - - - 50 40 50 20 0 20 0 25 0 8 > 20 0 5 4 .8 N ~ ~ ~ ~ .., .... ~ ~ ~ 2 ~ ~ 00 ~ ~ ~ ~ ~ ~ t ~ q ~ ~ 00 COMMERCIAL POWER MAGNETIC COMPONENTS 215 ~ P O W E R A P P U C A T IO N S = N =\" B1 I B 2 1 83 \u00b7 \u00b7\u00b71 BS . If f I F1 I F2 , 'F 4 - - U ni ts T .l :O nd _ _ S I ~ ' E C 1 ~ =\" tD S ym bo ls =\" P W 1. 1 PW lb PW 3b PW 1b P W 'Z M fP W 2b PW 2b PW 3b PN oi D fW 5 b ~ ~ III 25 'C 25 00 ,* 2 5% 19 00 t ZS 'J( ; 19 00 t 25 5( . 18 00 , *2 5% : 20 Q 0: ~ 2 5% llO O t 25 % 19 00 * 25 % !1 0 0 't 2 5% ~O O 2S 'C 45 0 4a o. -4 70 \"i ll 47 0 '~ S' o 42 0, 31 10 =\" 8 a l' l-! A Im 10 0\" 0 3' 40 36 0 JB O :.3 80 38 0 34 0 32 0 31 0 ~ I ~ ~ (n om in al m T 16 00 ZS ''C '' 41 10 49 0 ~ . :\" ~ O SO O ~ 8 0 45 0 42 0 C> ve llH !s l Ai m JO O 'C \" '\u00b7 37 0 38 0 41 )0 40 0 , 40 0 a7 0 35 0 33 0 .., ~ ., .. 2S 'C ', .. 12 H i \u00b7 '1 6' 16 16 1I i 15 15 ..... tD H < A Im 1 ~ ' C :: 10 :' t'O ' .. III 10 :' :\"1 0: '0 ,1 0 10 ~ ., ~ T, \"C ,> 2 00 > 2 !1 O ,. : :: > i! 50 :: ,: > 'l 50 ' > 2 SC l > 2 30 : > 2 0 0 > 2 Q O ~ 16 ~ H ~ \u2022 1 00 'C 0 = :,: ~ 10 0 .. ~ .... 20 0m T , . 8 0 , tD 25 k 'H r \u2022 1 '0 0 '; :1- '< ; 15 Q: = za O m l < le O .. , .. ~ - 32 k H r \u2022 10 0\" C C\" IJ ZO O m l . < ,2 ~ . <2 O Q .. >< l~ 9 c oH O ~ I ~ > 60 k H l \u2022 l0 0\" C < ZO O m T . ~ 3- 40 < 3 50 - < 3 30 < :2 BO ' .., P ll lP m W /1 iIT I1 1Q O lH t -'1 00 'C rJ ) >< ~ I l0 0 m T ,, < 1 50 0 ~ 10 0 kH z ~ '1 00 'C c:r ZO O m T < 7 00 < 6 (1 0 .. .. 58 0 ~ C> 30 0 k lb \u2022 'l O O 'C ' ~ e .. 5Q m T : :< 1 20 < 1 00 ~ 51 10 'k H l c , 0 0' c, : ~ C> ... = . ' SO 'm T ' .. < 2 ]0 < T ao ~ , t, 4H ~ ,\u00b7 . l 0 0 'C , ~ . 5O :m T \" < 6 00 1. 5 M H 1- l0 0 'C :: ~ \"S O: m T ' .. . , . < 1 21 )0 t\"\" ' .P . T nx -m -, .. \"1 ' 6 .. 6 . . 6 , 6 , 6 6 6 ~ ~ D el lS it} ' gl s: m J .. ... /1 . 4.8 4. 8 U U 4. 8 4. 6 U ' .., V ak Je s m ea su re d on 0 l1 i X 0 12 >1 14 r e1 \u00abe nc e to rO id . ~ 0 -V al J< !s m el lS ur ed on 0 2 1 .1 )( 0 1 3 .8 .1 1 r ef er en ce t o 'o id . ~ ..... ~ rJ ) COMMERCIAL POWER MAGNETIC COMPONENTS 217 218 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2000\u00b125% -3 ~ ;- ~ I -3 e ~ = ~ ~ ~ a:: = ;- ::3 . = ~ IV ll lt 8 n il 15 t; f. ~ 16 K H z 1 0 K H z\u00b7 \u00b7 2D \u00b7C -6 ~~ ~ 10 (D ~~ ~~ ' (A Im ) (\" C ) _. . (O -m ) - (k g !m 3 ) 2H l 15 00 0 0. 95 X 1 0 -5 0 .1 1 X IO -' tc 35 0 2 .3 10 5 0. 06 5 .0 X 1 03 - - ~ - - - - - - - - ~ - - - - - - ~ 2E 2 10 00 0 1 .5 x 1 0 -5 0. 1 X 1 0- ';- C 37 0 4 .0 12 0 0. 02 4 4 .9 x 1 03 3 2E 2B Ili DO O 0 .3 4 x 1 0 -5 0. 28 x 10 -6 /,C 39 0 8 .0 12 0 0. 04 7 4. 9X 1 03 ~ - - - - - - - + - - - - - - - - ~ ' - - - - - - - - + - - - - - - - ~ - - - - - - - - - + ' - - - - - - - - 4 - - - - - - - - - ~ - - - - - - - 4 - - - - - ~ - - - + - - - - - - - - - - 2E l 70 00 1. 8X 1 0 -5 -0 .8 X I0 G tc 41 5 8 .0 15 0 0. 01 2 4 .9 )( 1 03 3 2G l 70 00 0 .5 4 )( 1 0 -5 0. 41 )( 1 0, -s /'e 41 0 6 .0 13 5 0. 02 4 .8 x 1 0J 2G 3 SO OO O .J sx IO -s a. Z 8x IO \u00b76 /\u00b7e 43 0 S .1 14 5 0 .2 4 .9 )( 1 0 3 \" - 2 F ' 53 00 0 .2 )( 1 0 -5 L O X IO -s /'C 37 0 1 .2 12 0 0 .1 3 4 .8 X I0 3 4 - - - - - - - 1 lO S e 40 00 0. 1 x 10 -~ 0. 2> <. l o\u00b7 '/\" C 41 0 8 .0 14 0 0. 1 4 .9 x 1 0J ZE . 40 00 0 .1 5 )( 1 0 -5 -O .5 X IO -' /\" C 45 0 11 .9 18 0 0. 1 4 .8 )( 1 0 3 2F 6 33 00 0 .0 7 )( 1 0 -5 2. 65 X 1 0 6/ ,C 47 0 11 .9 > 20 0 2. 1 4 .8 X 1 03 5 ~ --- - 20 3 30 00 0 .3 X 1 0 -5 -0 .4 x 1 0- '/' C 45 0 11 .9 16 0 0. 9 4 .9 x 1 03 - - ~ ~ - - - - - - ~ - - - - - - - 4 ZE e 30 00 0 .1 )( 1 0 -5 -0 .5 x lo 6 / 'c 49 0 11 .9 > 20 0 0. 23 4 .9 X 1 0 3 4 -- ., - ZE 7 24 00 0 .1 5 )( 1 0 -5 1. 25 X 1 0- it C 49 0 11 .9 19 0 3 4 .8 x 1 03 ._ -- -- + -- -- -_ ... -. ~ 2F 8 22 00 0. 1 x 1 0 -5 6 .3 x lo \u00b7S te 49 0 9 .5 > 20 0 8 4 .8 X 1 03 5 ~ - - - - - - ' - + - - - - - - - - 4 - - - - - - - - - ~ - - - - - - - 4 - - - - - - ' - - - + - - - - - - - .. -_. .- .- -- - 2 E IC 20 00 O .I S )( 1 0 -5 1. 5) ( IO \u00b7'/ 'C 51 0 14 .3 > 23 0 0. 37 4 .8 x 1 03 2C 3 20 00 0 .6 )( 1 0 -5 3. 0) ( IO \u00b7& /\"C 37 0 15 .9 11 0 1. 3 4 .9 )( 1 03 2H 8 80 0 O(~ ~O~ ~~) s~ .4 X ~ O-'/ 'C ._ ~~O !. 22 .0 > 20 0' \" 2. ~. - 4 .8 )( 1 0 3 1 n o ~ ~ ~ ~ ~ ~ ~ ~ ~ .., .... n n ~ ~ ~ rJ j N .... \\C 220 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Spec. Unit Mn-Zn Cerna Ni-Zn lerritI:. 2500HMCl 25OOHMC2 250BHC 300BHC IJi - 4500(+ 20\u00b0(,) 4500 (+ 20 0q 250 300 4100 (+120 0c) 4100 (+120 0c) fe mHz 0.4 - 8 8 mW 10.5 (+25 0q 8.5 (+25 0c) 30 <30 Psp cm~ 8.7 (+100 0q 6.0 {+100 0q (3) (3) tgt, / . 10-6 30 <30 - - (3) (3) Il.J.Il (MHz) R mT 290 330 - 320 Rm mT 450 - - 130 Br mT 100 - - 80 He Aim 16 - - - Te \u00b0c >200 >200 >250 >250 COMMERCIAL POWER MAGNETIC COMPONENTS 221 - - - - - - - - - . M~; E~I ALS I I -- ... . ~ . S Y M B O L U N IT TE M P C H A R A C T E R I S T I . ~ , .. .. . AC I N IT IA L P E R M E A B IU TY I ,n ac --- 23 '(; --.. - -.. - \u00a5 _ \u2022 \u2022 \u2022 _ _ \u2022 SA TU R AT IO N F LU X D E N S IT Y ! 23 'C B m s m T f_ .\u2022 _-- - ; 10 0' C _ ._ -_ .- .- . -. -. .. .. .. . . .. . \" 23 'C R ES ID U AL F l.U X D EN SI TY B rm s m T 10 0' C . _._ - 23 'C C O ER C IV E FO R C E H an s A im -- lO O t: .- - -. .. .. .. . \" ... _- _._ -_ .... 23 'C -- -_ .. \" CO RE L O SS 60 'C (f \"' 2 5 kH z B m = 20 0m T ) Pc kW /m ' 10 0' \\; 12 0' \\; -_ ... ._- -- 23 'C C O R E LO SS 60 '\\; (f = 1 00 kH z B m \", 20 0m T ) Pc kW /m ' 1 0 0 't 12 0' C -_ .. ..... . _- -\u2022. .. - -\u2022 .. - ---.. . . - .. R EL AT IV E LO SS F AC TO R ta n8 /l li ac X 1 0. 1 2 3 't -- - C U R IE T EM PE R AT U R E Te '\\; - SP EC IF IC R E S IS TI V IT Y p Q -m 2 3 't D E N S iT Y ds kg /m ' 23 'C L - - - ~ - - -- - - - - -T S B -5 S S B -3 L S B -7 C . - - . ~ ... - ~ ~ 2 5 % \u00b1 2 5 % \u00b1 2 S % 3, 00 0 1, 60 0 2, 40 0 -. -. . r - 48 0 51 0 50 0 -_ ... .. 34 0 42 0 38 0 . -- \u2022.. . ~ ._ .. 18 0 18 0 15 0 .- .. -- 10 0 70 .. 12 15 13 --- .\" .. -- - 8 7 -- .... .. - .. -- 14 0 20 0 14 0 - _. . __ .. _ -- 14 5 15 0 10 0 .... .... . _. 17 5 12 0 80 - 13 0 90 -_ ._ \",- _ .. 1, 10 0 1, 10 0 78 0 I, IS O 82 0 56 0 --- -. 1, 50 0 75 0 50 0 - 85 0 57 0 .1 ., \u2022\u2022 2 .5 3 .5 2 .0 > 1 9 0 > 2 6 0 > 2 0 0 0 .4 1. 5 5 .0 4 .8 5 x 1 0' 4 .8 x 1 0' 4. S x 1 0' ~ - - - ~ - - - - L - - - - - S B -9 C l. 25 ~ 2, 60 0 49 0 36 0 14 0 .... _ .- 60 . _ -- -- -- 12 6 14 5 90 \" . . - - . - - - 70 80 68 0 45 0 40 0 48 0 .2 5 .0 > 2 0 0 5 .0 4 .S x lO S -- . , f1 0 kH z ~ ;: ~ .. it So .. r a: = ;' :::1 . = ;r w w w ~ ~ ~ r=; n I ~ rI J ~ ~ := ~ ~ I rIJ .\" oumTlRSlXS ~ ~~~~~Ll-UNI~ --! _~L_-_2 _+-D_L_-J-i-DL- -4C-+_DL- -SC-+-_DL_-_6C-j'-D_L-_7C--D_L_-SC---j ! 2.200 I .SlIO 250 l50 650. 1.200 3<0 mT 280 260 ' 10 .- . - ----------4-----~----~---_T----_+ 310 ! ' 00 380. -- ---r---t---. _. B ... SATURATION nux IlfNSITY (B800 ) 20 15 23 20 18 I~'~' ~\"; '~~' -\" . COERCIVE FORCE Hem. I )t Ier' RELATIVE LOSS FACTOR lInAlJ'lOC I .' IOOkHz ' mT liD ~60 I ~O 27 24 ---------~---+---+--~------+---~ AI .. 16 10. 12 13 12 12 - -I-.---+---~---+---. -- \u2022 RELATIVE TEMP. FACTOR au' 22 14 16 I ; 224 MAGNETIC COMPONENTS FOR POWER ELECTRONICS SYHIOLI UNIT' TDT V!>II v..\" VN) PMI rMl PM) P:wtj CONDrT\\Ol'I1 iii 2l,0,\u00a3 900~ J:JOi\u00a5..:2O'9!i. .... ...,.\". nIO,Y.:lOW. 2OOOjV.,JO% 1900~ ZlOO IY~ 8 2l,0;t l30 2lO 210 'SO I '\" '70 I ~ ''Il10 I SIO \"' \" .. .1 loo,t :tlO 190 , .. 3\u00ab1 1 \"0 ,so I 400 ''' 1''0 390 I \u2022 H tv.- .600 .600 .200 400 I .600 ..., I 1600 ... 1 1600 400 \" Ii< tv.- 2l'~ \u2022\u2022 40 ,. '1 ,. I. Il 100.' 12 2l \" I. ,0 10 T. .t \u00a3%130 .rn1)(J \"\"1<1 \"'- -\"WO \".lSO W0.2)l '\" \"lit. 2lot 1.1 2., 2., PC \".,WI 2OOaIn. ,t ,.. I ,40\" 9\\\" I 200\" ISO\" 1 l~ no 1 1311 7S I lIS tD, 1240 210 I ~ 'KIIZ 16 I J2 16 1 12 ]2 1 1W 2l 1 '\" ICI I 2) 2l 1 1<1 1<1 1 1{ .. Iv... so \"\"\"10 \u00a3%10 3 , 6 o...c,. ;u.l .. 7 .. .. , ... ..\u2022 U .. c ... c ... \"\"'\"' Co\"\" E.U E.U E.U E.U v .... v .... MONYTQR .c- ..,.., -c- -c.... ...... t:... <;on. y~ TEST SYMBOLs UNITS CONDJTI()NS PlICI PMl PMll PI>e P\"\" PM9 WiJ 25IE ~y~ 2000iY~ l4OOl'I..2Mt. 2lOOtI.2O% 2AOO.%ln% JOOOjY~ II 25.~ .SO , ,,, .70 1 SOO '10 I '\" _ 1 '10 460 I 410 \"' 1 \"\"\" \",T .. 100,~ 3\u00ab1 1370 310 1 400 340 1 370 190 I 410 )110 I 400 400 I .20 A Ma 400 11600 400 11 600 400 11600 400 11 600 400 11600 400 11600 lljE 11 16 12 II 11 11 H< ,.., 100,t I. ,0 9 T< ,t L%11IO waso l'Io2SO ly.zJD .('/0210 \u00a3\\U(IO I< MIi1 21'\" I .\u2022 2.0 I.' lOOaoTlI'\" no I 310 11 1 II! 130 1 llO 3111 300 PL .. WI..,} lOOooT lOO;~ .101500 4<0 310 {kHz 2' 1 10 16 1 2' D l so so 1100 100 100 II to ... 6 n-ky s/ ....... .4!- 76 ...... ..... ........ 4W-207 2!i().11' F SupernollOr' s.w.z ...... . . 70 .-- 2 ..... .oD4--CUi ~1 19 ~ S S~IT\".ndur , .... 1 \u2022\u2022 2..2 .90 up , .. 30 '''''' .. ...... 10 31..1-45 7 ... ,\"\" \u2022 ~rphOt.\"\"A 1,5..,& 1 5.-U .110 l.p \"\" .. ~ .... ,04-.1 32-7.8 ........ E . _ ,--- ...... . ..... .... ooa-oz ....... . 0,\u00b7025 7'i-. -~ ... _. G _0 , 4..,5.., &..IJ '4.500 ' M <60 eo.w __ 35 ....... . 1011HL 1T - 232 MAGNETIC COMPONENTS FOR POWER ELECTRONICS SISSnYOOlnl-I-NOIcnaNI Figure 6Al0 - Core Loss Curve vs Frequency for 2 mil Silectron SiFe- Arnold 234 MAGNETIC COMPONENTS FOR POWER ELECfRONICS en 'W CI) CI) ::I ~ ~ o = ::.: I CD I Z o ~ ::I o Z WATTS PER POUND 236 MAGNETIC COMPONENTS FOR POWER ELECTRONICS I lOOO~-----+~~~4--4--- 500 t----___+_ - 200 ,... e u '- 100 3 S I - U) 50 U) 0 ~ ~ 20 0: a u 10 1 2 3 5 B(kG} Figure 6Al6- Core Loss for Toshiba Amorpbous Alloy COMMERCIAL POWER MAGNETIC COMPONENTS 237 238 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Nanoperm\u00ae is a registered trademark of Magnetec GmbH COMMERCIAL POWER MAGNETIC COMPONENTS 239 COMMERCIAL POWER MAGNETIC COMPONENTS 241 ,'6 -~ V '\\ ~ ~ ~ \\ f..--\"\", ~ 6~ I-~ ~ ~\\\\ ~ ~ ~ f--- --.~ ~:\\\\ = +8 J +. '& ~ -8 -'2 -16 100 1000 10000 M: Flu\" .,..,..., ( .... , .... FNquency \u2022 1 khz Figure 6A25- Permeability vs Flux Density Hi-Flux Arnold- Permeabilities from top Curve to bottom are 200, 160,147, 125,60,26 and 14 COMMERCIAL POWER MAGNETIC COMPONENTS 243 244 MAGNETIC COMPONENTS FOR POWER ELECTRONICS COMMERCIAL POWER MAGNETIC COMPONENTS 245 246 MAGNETIC COMPONENTS FOR POWER ELECTRONICS COMMERCIAL POWER MAGNETIC COMPONENTS 247 248 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 310 f-I-I..- e-300 1110 100 10 1 PERCENT PERMEA8lUTY VS A. C. flUX DENSITY 7 20 ao 48 110 100 h W ~ II \" / / / :;;; C;;; V - ~ 1/ - l..I---- 200 aoo 400 IlOO 1_ _ aooo _ l1OOO 10._ A. C. FLUX DlNSITY {G.-j Figure 6AJ3- Penneability vs ac flux density for several different penneability iron powder cores. Curve nwnbers are the penneabilities. From Pyroferric 100 90 -~ 80 --., u 70 c as I 60 .E 'ii 50 c m 40 .;: 0 - 30 c 8 ... 20 at a. 10 0 ~ 1 ~ I\" l\\ '~ r\" \" , ~ \"- t----.Io.. '\" ~ ~ ......... ~ 100 MHz ~ r---. -........ ~ so MHz ......... ......... ~ 100.... - I 25 MHz_ I I o 1 2 3 4 5 6 7 8 9 10 11 1213.1415 H = .41t NIII. (Oersted) Figure 6AJ4-Percent reduction in permeability with DC bias for several different permeability iron powder cores. Curve nwnbers are the penns. From Pyroferric COMMERCIAL POWER MAGNETIC COMPONENTS 249 250 MAGNETIC COMPONENTS FOR POWER ELECTRONICS This chapter has listed the properties of a great number of materials and cores from the major power magnetic component vendors. The final chapter will be present a compilation of many of the design aids that are available to the engineer who is making the choice of the optimum power magnetic component. Chapter 7 DESIGN AIDS IN MAGNETIC COMPONENT CHOICE FOR POWER ELECTRONICS INTRODUCTION In the early days of power electronics, the design engineer had few design aids in magnetic component choice. As a result, the choice was made by using whatever component happened to be on the shelf and after numerous hit-and miss tries, he finally found the most suitable choice. At that time, both power semiconductor and high frequency power materials were primitive with very little choice of materials or shapes. However, today with the explosion of information through media like the Internet, CD ROM, CAD-CAM, and computers in general, there is a great deal of help that makes the proper choice faster and with greater assurance of success. This chapter will review the various design aids available. In Appendix 7.1, articles of interest on Power electronics are listed. In Appendix 2, the pertinent IEC and ASTM standards on magnetic components and Materials are listed. 7.1- Books on Power Electronics The following is a compilation of some of the power electronics books listed by EJBloom Associates; Books on Power Magnetics 1. Transformer and Inductor Design(2nd Edition)- C. McLyman 2. Magnetic Core Selection for Transformers and Inductors (Second Edition)- C. McLyman 3. Applications ofMagnetism-J.K. Watson 4. Handbook of Transformer Applications- W. Flanagan 5. Designing Magnetic Components for High frequency DC-DC Converters- C. Mc Lyman 6. Handbook of Modem Ferromagnetic Materials- A. Goldman Books on Power Electronic Circuits 1. Modem DC-DC Switchmode Power Converter Circuits- Severns and Bloom 2. Switching Power Supply Design(2nd Edition) A. Pressman 252 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 3. High Frequency Resonant and Soft Switching Converters-VPEC Staff 4. Power Supply Cookbook(Second Edition) M.Brown 5. Fundsamentals of Power Electronics(2nd Edition)- R. Erickson and D. Maximovic 6. Power-Switching Converters-S.Ang 7. Elements of Power Electronics-P.Krein 8. 1995 VPEC Seminar Proceedings 9. 1996 VPEC Seminar Proceedings 10. 1997 VPEC Seminar Proceedings 11. 1998 VPEC Seminar Proceedings 12. 1995 VPEC Seminar Proceedings 13. 1999 VPEC Seminar Proceedings 14. Introduction to Modern Power Electronics-A. Trzynadlowski 15.2000 VPEC Seminar Proceedings w/CDROM 16. Advanced Soft-Switching Techniques, Device and Circuit Application-VPEC/CPES Staff PSMA Industry Standards and Publications 1. The Power Technology Roundup Report (Year 2000)-PSMA 2. Handbook of Standardized Technology for the Power Sources Industry (2nd Edition)-PSMA 3. Low Voltage Study-Workshop Report L. Pechi-PSMA Circuit Design 1. Switch Mode aPower Conversion-K.Sum 2. SPICE-A Guide to Circuit Simulation & Analysis using Pspice(3rd Edition)-w?IBM Program Disk-P. Tuinenga 3. Modeling, Analysis & Design ofPWM Converters-VPEC Staff 4. Pspice Simulation of Power Electronics-R. Ramshaw 5. SMPS Simulation with SPICE 3 (wlDiskette)-S.Sandler 6. Circuit Simulation of Switching Regulators Using SPICE (wlDiskette)-V. Bello 7. Switch-Mode Power Supply SPICE Cookbook (Includes CDROM)-C.P . Basso 7.2-Power Electronics Magazines The following magazine are concerned with power electronics; 1. PCIM Power Electronics Intertec Publishing Co. 9800 Metalf Ave. Overland Park KS 66212 DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 253 2. Switching Power Magazine Ridley Engineering Co. Ltd. 1575 Old Alabama Road Suite 207-147 Roswell, GA 30076 3. Magnews UK Magnetics Society Berkshire Business Centre Post Office lane Wantage, Oxon, OXI2H, UK 4. IEEE Transactions on Magnetics IEEE 445 Hoes Lane P.O. Box 1331 Piscataway, NJ 08855-1331 5. EDN Cahners Publishing Co. Cambridge, MA 6. Power Pulse Darnell Group 1159 B. Pomoma Road Corona, CA 92882-6926 7. Power Quality 7.3-Power Electronics Organizations There are a number of government organizations, societies and private groups involved in power electronic. The are; 1. IEEE Power Electronics Society IEEE Power Electronics Society Robert Meyers, Admin. 799 N. Beverly Glen Los Angeles CA 90077 2. Power Electronics & Electronics Machinery Research Center Oak Ridge National Laboratory U.S. Dept. of Energy P.O. Box 2009 Oak Ridge TN 37831-2009 3. IEEE 445 Hoes Lane P.O. Box 1331 Piscataway, NJ 08855-1331 3. Power Sources Manufacturers Association P.O. Box 418 254 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Mendham, NJ 07945-0418 4. Electric Power Institute 5. National Science Foundation 6. PCIM 7.4 Power Electronic Web Sites There are many Web sites related to power electronics. We will try to list all we now; 1. pesc.org 2. orln.gov/etdJpeemcIPEEMCHome.htm 3. smpstech.com 4. psma.com 5. efore.ft! 6. jobsearch.monster.com 7. greshampower.com 8. tycoelectronics.com 9. spangpower.com 10. ardem.com (R.D. Middlebrook) 11. pels.org 12. home.aol.comlDrVGB (V. Bello) 13. venableind.com 14. darnell.com 15. cpes. vt.edu 16. kgmagnetics.com 7.5 Power Electronic Conferences The Power Electronics Society Sponsors or co-sponsors several conferences. They are 1. Power Electronics Specialist Conference 2. Applied Power Electronics Conference 3. International Telecommnnications Energy Conferenc There are other Conferences related to the Magnetics community; 1. Intermag Conference 2. Magnetism and Magnetic Materials Conference(MMM) 3. International Conference on Ferrites 4. Soft Magnetic Materials Conference 5. Intertech Conferences on Magnetic Materials DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 255 7.6-Power Electronics at Universities and Research Labs Listed below are the universities and research labs that are doing major project in power electronics; 1. Colorado Power Electronics Center (CoPEC) 2. Caltech Power Electronics Group 3. School of Electrical Engineering, University of Belgrade,Yugoslavia 4. UC Berkley 5. UC Irvine Power Electronics Laboratory 6. Virginia Power Electronics Laboratory(VPEC) 7. University ofWisconsin-Madison(WEMPEC) 8. Georgia Tech Electric Power Research 9. North Carolina State Electric Power Research Center 10. Surrey University Electrostatic Systems and Power Electronics Research Group 11. Texas A&M University 12. Northeastern University 13. University of Central Florida 14. JPL Power Electronics Group 15. University of Waterloo 7.7- Web Tutorials Listed below are some of the Internet tutorial sites; 1. Switching Power Supply Design-Jerrold Foutz at smpstech.com 2. Interactive Power Electronics OnlineText- ee.uts.edu.aul~venkatJ 3. SPICE-A Brief Overview-seas.upenn.edul~jan.spice.overview.htm 4. Power Factor; Dissipating the Myths- Microconsultants.comltips/pwrfact Ipfartil 7.8 Power Electronics Software There are many power electronics software programs. Listed below are the ones listed on the ejbloom associates website 1. Power Witts\u2122 Forward Converter Simulation 2. Pspice Electronic Simulation-N.Mohan 3. Computer Aided DesignforIndictors and Transformers-KG Magnetics 4. Magnetic Core Data for Converters-KG Magnetics 5. Flyback Converter Magnetic Design 6. Specialty I-Magnetic Design-De-DC Converters-KGMagnetics 7. Computer-Aided Inductor and Transformer Design-KG Magnetics 8. Specialy II-Common-Mode Chokes-KG Magnetics 256 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 9. Titan Systems-KG Magnetics 7.9-Power Electronic Short Courses EJBloom Associates runs frequent courses on Power Electronics. For information log on to ejbloom.com or e-mail toejbloom@compuserve.com. The address is; EJ Bloom Associates 115 Duran Drive San Rafael, CA 94903 7.10- Component Vendors CDROM or Diskettes Many suppliers offer product information and design on CDROM disks or IBM diskettes. Below is a list of some that are available 1. FDK 2. Ferroxcube 3. Tokin 4. MetglasR (Honeywell) 5. Epcos 6. Magnetics 7. Kaschke 7.11-INTERNET WEB SITES Just about all the manufacturers of ferrites have Web sites on the Internet. In most cases, the core data can be down loaded and printed by the user. Where large catalogs are involved, the use of the Acrobat reader is needed but the vendor can often download this as well. Some of the vendors that maintain Web sites are; 1. Magnetics 2. Philips 3. Siemens 4. Fair-Rite Products 5. Steward 6. MMG North America 7. Micrometals 7.12-Magnetic Component Stan'\" In Appendix 7.2 below are the appropriate lEe and ASTM Standards for Magnetic Components and Magnetic Materials DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 257 Appendix 7.1 Recent Power Electronic Articles on Specific Power Electronic Subjects Planar Magnetics 1. Designing Planar Magnetics, J. Martinos, PCIM, August 2000, 102 2. Planar Magnetics, Philips Components, PClOI2, 2/2/94 3. Planar Transformers Dispense with Bulkiness, D. Maliniak, Electronic Design, Feb. 1993,34 4. Design Techniques for Planar Windings with Low Resistance, HX. Huang, D.T. Ngo and G. Bloom, IEEE Appl. Power Elect. Conf. (1995) 5. Planar Magnetics Lower Profile Improve Converter Efficiency, A. Estrov and I. Scott PCIM, May 1989, 16 6. Planar Magnetics Simplifies SMPS Design and Production, E. Brown, PCIM, July 1992, 46 7. Design of a HF Planar Power Transformer in Multilayer Technology, D. van der Linde C.A.N.Boon and J. B. Klaasens, IEEE Trans. Ind. Electr., 38, (1991) 137 8. Effects of Air Gaps on Winding Loss in HF Planar Magnetics, K.D.T. Ngo and M.H. Kuo, PESC '88 Record april 1988 9. A Comparative Study ofHF, Low Profile Planar Transformwer Technologies, A.W. Lofti, N. Dai, G. Skutt, W. Tabisz and F.C. Lee, Va. Power Electr. Center EPE, 1993 10. Planar High Density Design for Automotive and Telecommunications Applications, High Frequency Magnetic Materials Workshop '99,1999 Santa Clara, CA Organized by Gorham-Intertech, Portland Maine, 10. Planar Ferrites, M. A. Swihart, PC 1M, July 1999, 12 11. Planar Transformers Dissipate Up to 150 kW with Copper Trace Windings, G.T. Tarzwell, PCIM, March 2000,58 Integrated Magnetics 1. Issues in Flat Integrated Magnetics Design, E. Santi and S. Cuk, 1996 Power Electronics Spec. Conf .Proc. Vol. 2. Integrated PC Board Transformers Improve PWM Converter Performance, B. E. Mohandes, PCIM, July 1994, 8 3. Integrated Magnetics Design with Flat Low Profile Cores, S. Cuk, F. 4. Stavaovic and E. Santi, Power Elecronics Group,Cal. Inst. Of Technology Surface Mount Design 1. Manufacturing Advances Increase Availability of Surface Mount Magnetics, B. Tscosik and W. Dangler PC 1M, July 1994, 60 2. Surface Mount Transformers, Surface Mount Technology, Feb 1993,27 3. Isolated Innovation Marks Movement Towards Miniature Magnetics, R.A. Quinnell, EDN, July 1994, 59 Magnetic Core Materials 1. Core Materials, D.J.Nicol, PCIM, July 1999,58 258 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2. Power Supply Magnetics- Part II-Selecting a Core Material, D.E. Pauly, PC 1M, Feb. 1996,36 3. Data Sheets Provide Clues for Optimizing Selection ofSMPS Ferrite Core Material, L.M. Bosley, PC 1M, July 1993, 13 4. High Frequency Magnetic Materials and Markets, L.M. Bosley and T. Holmes, High Frequency Magnetic Materials, '99, Santa Clara CA. Organized by Gorham-Intertech, Portland MN. 5. Soft Ferrites,Potential-Further Development, R. Dreyer and L. Michalowsky, ibid 6. High Frequency Applications of Amorphous Metal, R. Hasagawa, ibid 7. Ferrite \"Boost\" Material Improves Inductor Characteristics under DC Bias Conditions, G. Orenchak, PCIM, Nov. 1999, 48 8. Common-Mode Inductors for EMI Filters Require Careful Attention to Core Material Selection, R. West, PCIM, July 1995, 52 9. Inductor Core Material Operates Efficiently at High Frequencies, W.A. Martin, PCIM, July 1992, 10 Design 1. Core Selection and Winding Design for HF Magnetics, R. Severns, , High Frequency Magnetic Materials, '99, Santa Clara CA. Organized by Gorham Intertech, Portland MN. 2. Designing Flyback Transformers Part I.-Design Basics, R. Ruble and R. Clarke, PCIM, Jan. 1994,43 3. Designing Flyback Transformers Part 11-48 v. Dual Outpt DC-DC Converter., R. Ruble and R. Clarke, PCIM, April 1994, 23 4. CAD Software and Experience Cut High Power Transformer Design Time and Cost, PCIM, April 1992,50 5. Advances in Magnetic Modeling Using Finite Element Analysis, M. Christini, ,High Frequency Magnetic Materials, '99, Santa Clara CA. Organized by Gorham Intertech, Portland MN. 6. Redesigned Input Filter Limits DC-DC Converter Inrush Current, B. Bell, PCIM, March 2000, 66 7. DC-DC Converter Power Density Design Issues, W. Leitner, PCIM, Sept. 1990,22 8. Power Ferrite Loss Formulas for Transformer Design, S. Mulder, PCIM, July 1995, 22 9. System Integration ofa DC-DC Converter Requires a Look at All Angles, S. Davis, PCIM, Oct. 2000,88 10. Power Factor Basics, M. Amato, PCIM, Oct. 1995, 10 11. Expert SystemIFuzzy Logic Select Core Geometry for HF Power Transformers, Part I and II, R. K. Dhawan, P. Davis and R. Naik, PCIM, April and May 1995, 44 and 34 12. Understand Data Book Parameters When Selecting DC-DC Converter Inductors, L. Crane, PCIM, Oct. 2000, 54 DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 259 13. Keep Core Geometry In Mind When Designing Transformers, c.R. Wild, PC 1M, July 2000, 32 14. DC-Bias Behavior Calculation for Uniform and Non-Uniform Cross Section Ferrite Cores\" D. Lange and S. Ahne, PCIM, March 2000, 12 15. Transformer Bobbin and Core Selection Involves Interdisciplinary Design and Cost Issues, J. Casmero and R. Barden, PC 1M, Oct. 2000, 20 Applications 1. Power Supply Basics-Voltage Regulators, R.J. Shah, PCIM, April 1996, 20 2. Optimizing Flyback Techologies for Portable ACIDC Adapter/Charger Applications-Part I:Adapter/Charger Requirements, L.Huber and M.M. Jovanovic, PCIM,August 1996, 68 3. Low-Cost Battery Charger Transformer Design Require Performance and Safety Considerations, R.M. Haas, PC 1M, June 1994, 46 4. EMI Design Factors for Medical-Grade Switching Power Supplies, R. Hood and J. Belna, PCIM, Oct. 1992, 32 5. New Magnetic Circuit Design Yields High orce, Long Stroke Linear Actuators, B. Bartosh, PCIM, Oct. 1991,38 6. Telcom Power, D.L. Cooper, PCIM, April 1999,38 7. Automotive Power, J.M. Miller, P.R. Nicastri and S. Zarei, PCIM, Feb. 1999,44 8. Low-Cost UPS Guards Against Data Loss, S. Davis, PCIM, July 1992, 32 9. Mag Amps, J. Goodin, PCIM, July 1998,30 10. Low Profile Inductors, Semiconductors and Capacitors Make PCMCIACard DC-DC Converters Possible, B. Tschosik,PCIM, June 1996,9 Flexible Circuits 1. Magnetics Component, M. San Roman and D. Longden,PCIM, July, 1999, 67 2. I-MHz Resonant Converter Power Transformer Is Small, Efficient, Econ omical,A. Estrov, PC 1M, Aug. 1986, 14 3. Converters Pull for Flat Magnetism, Y. B. Salih, Electr. Eng. Times, Aug. 1992,52 4. Building Magnetics with Flexible Circuits, V. Gregory, Powertechnics Mag. (1989), 16 EM! Applications 1. Selecting EMI Suppression Ferrites Requires Attention to Complex Permeability C.U. Parker, PCIM, Feb. 2000, 62 2. Transients vs Electronic Circuits, Part IV, Ferrites for EMI Suppression, PC 1M, July 1996, 76 3. Power Analysis for IEC 1000-3-2/3- Q&A. T. Mahr, PCIM, Feb. 2000,82 260 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Appendix 7.2- IEC and ASTM Standards 133 (1985) Dimensions of pot-cores made of magnetic oxides and associated parts. (Third Edition). 205 (1966) Calculation of the effective parameters of magnetic piece parts. Amendment No.1 (1976). Amendment No.2 (1981). 205A (1968) First supplement. 2058 (1974) Second supplement. 220 (1966) Dimensions of tubes, pins, and rods of ferromagnetic oxides. 221 (1966) Dimensions of screw cores made of ferromagnetic OXides. Amendment No.2 (1976). 221 A (1972) First supplement. 223 (1966) Dimensions of aerial rods and slabs of ferromagnetic oxides. 223A (1972) First supplement. 2238 (1977) Second supplement." ] }, { "image_filename": "designv10_13_0002138_robot.1989.100048-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002138_robot.1989.100048-Figure1-1.png", "caption": "Figure 1 Coordinate Systems of RM501 Xo'wt", "texts": [ " The robot has five degrees of freedom and its maximum repeatability is specified as f0.5 mm. The coordinate measuring machine(CMM) is a computer controlled machine equipped with an MP-30/35 processor and Hp 9000 series 300 computer with a 9153 disk drive. The accuracy of this CMM is about 0.006 mm. Therefore, the measurement device is adequately accurate for this study. For simplicity, joints 4 and 5 of the robot are locked(fixed) in this experiment. Its coordinate systems along with kinematic parameters are shown in Figure 1 and their corresponding nominal values are given in the third column of Table 1. Since it is difficult to precisely locate the probe tip of the CMM to the center of the end-effector, as shown in Figure 2, four measurements are taken on the plane A and the other four on the cylinder surface, then, the center point C of the endeffector is calculated. This procedure is repeatedly used to obtain well-spaced 102 center positions of the end-effector over the work volume of the robot. The resulting raw data are then used to identify parameter values of the robot kinematic model and to study the implications of the defined observability measure in robot calibration" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002975_tmag.2009.2022398-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002975_tmag.2009.2022398-Figure1-1.png", "caption": "Fig. 1. Field region in the plane at the rotor position , the angle that the interpolar center shifts from the slot center.", "texts": [ " The excitation of a surface-mounted PM with radial magnetization can be modeled by two sheet currents at the two sides of the PM. As the air-gap magnetic field is normally approaching to a constant at the pole centre, only the two sheet currents on both sides of an interpolar space between two adjacent poles need to be considered in the air-gap field computation. Using Gaussian integration, a sheet current is modeled by several line currents at Gaussian points. The field region considering such line current excitations with a single slot is shown in Fig. 1. 0018-9464/$26.00 \u00a9 2009 IEEE For surface-mounted PMs with parallel magnetization, the excitation can be modeled by four sheet currents, two at the two interpolar surfaces, and two at the outer and inner arc surfaces for each PM. The current density distribution for the outer and inner arc sheets can be determined according to increases in magnet height in the magnetization direction. These two sheet currents can also be modeled by several line currents at Gaussian points when using Gaussian integration", " For any other magnetization patterns, the general procedure to obtain equivalent excitation is 1) find the equivalent excitation by sheet currents and 2) replace each sheet current by several line currents at Gaussian points. In order to use conformal transformation, the permeability in the field region has to be uniform. Therefore, the PM relative permeability is assumed to be 1. When , an equivalent PM inner radius, derived on the basis of the same air-gap permeance, is employed (1) where and are the outer and original inner radii of the PM, respectively. The field region in the plane of Fig. 1 can be transformed to the region in the plane, as shown in Fig. 2, by the following transformation: (2) Two parameters to define the field region are (3) where is the slot opening width. The field region in the plane of Fig. 2 can be transformed to the upper half of the plane, as sown in Fig. 3. The SchwarzChristoffel transformation from Figs. 2 and 3 is (4) where (5) with (6) and in Fig. 3 (7) In the field region of the plane as shown in Fig. 3, if a line current of is located at , its complex magnetic potential is (8) where is the mirror point of in the lower half of the plane. The cogging torque is computed from the magnetic co-energy changes in the air gap and the slot as the rotor advances by an infinitesimally small angle. If the rotor position is defined as the angular movement of the interpolar center from the slot center, as shown in Fig. 1, then, the interpolar center at the rotor surface in the plane, as shown in Fig. 2, is depicted as (9) and its mapping point in the plane is , as shown in Fig. 3. If the interpolar leakage flux is neglected, the magnetic co-energy in the whole field region is (10) where (11) and and are the respective fluxes leaving and entering the rotor surface on both sides of the interpolar center in the plane, and is the magnetomotive force (MMF) of one pole of PM as follows: (12) where is the magnetic coercivity" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002645_j.automatica.2006.04.025-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002645_j.automatica.2006.04.025-Figure1-1.png", "caption": "Fig. 1. Schematic interpretation of Theorem 2.", "texts": [ " The equation det(Q(k, t1, t2) + I ) = 0 (5) admits a solution t\u22171 , t\u22172 > 0 when k = k\u2217, but such a solution does not exist for any k \u2208 [0, k\u2217). Geometrically, this implies that there exists x0 \u2208 R3 such that Q(k\u2217, t\u22171 , t\u22172 )x0 = \u2212x0, that is, x0 is an eigenvector of Q(k\u2217, t\u22171 , t\u22172 ) corresponding to the eigenvalue =\u22121. Defining x1 := exp(At\u22171)x0, we see that exp(Bk\u2217 t\u22172 )x1 = \u2212x0. In other words, taking x0 as an initial point, following the trajectory of x\u0307 = Ax for t\u22171 seconds, and then the trajectory of x\u0307 = Bk\u2217x for t\u22172 seconds, we reach \u2212x0 (see Fig. 1). By symmetry, this implies that for k = k\u2217 the system (2) admits a closed, periodic trajectory with four (two) switching points in every period (half period). The intuition underlying Theorem 2 can be explained as follows. Consider the \u201cmost unstable\u201d solution x\u2217(t) of (4). If k < k\u2217 then, by definition, all trajectories converge to the origin and, therefore, so does x\u2217. In particular, there cannot exist a solution t1, t2 > 0 for (5). For k > k\u2217, x\u2217 is unbounded. Between these two extremes, that is when k = k\u2217, there exists an initial point x0 such that x\u2217(t), with x\u2217(0)=x0, is a closed and periodic trajectory", " Assume that (1) the iteration steps t1 and t2 in the algorithm are sufficiently small; and (2) the initial interval is valid. Then, after N iterations the algorithm returns a valid interval of length l02\u2212N , where l0 is the length of the initial interval. Thus, we can estimate k\u2217 and, therefore, t\u22171 and t\u22172 with arbitrary accuracy. The algorithm can also be used to estimate the adjoint vector p(t) along the periodic trajectory. Indeed, once we have estimates of k\u2217, t\u22171 , and t\u22172 , we know that there exists a periodic trajectory, as depicted in Fig. 1, where x0 is the eigenvector of Q(k\u2217, t\u22171 , t\u22172 ) corresponding to the eigenvalue =\u22121. It follows that for x(0) = x0, the optimal control of (4) is u\u2217(t) = { 0 if t \u2208 [0, t\u22171 ), 1 if t \u2208 [t\u22171 , t\u22171 + t\u22172 ). (8) Substituting this in (6), we find that p(t\u22171 + t\u22172 ) = exp(\u2212BT k\u2217 t\u22172 ) exp(\u2212ATt\u22171 )p(0). However, the fact that x\u2217(t\u22171 + t\u22172 ) = \u2212x\u2217(0) implies that p(t\u22171 + t\u22172 ) = \u2212p(0). Hence, exp(\u2212BT k\u2217 t\u22172 ) exp(\u2212ATt\u22171 )p(0) = \u2212p(0), so p(0) is an eigenvector of exp(\u2212BT k\u2217 t\u22172 ) exp(\u2212ATt\u22171 ) corresponding to the eigenvalue = \u22121" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001715_7.489516-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001715_7.489516-Figure1-1.png", "caption": "Fig. 1. Orbital and satellite coordinate systems.", "texts": [ " In the closed-loop system, pitch dynamics evolve according to a fourth-order linear differential equation and feedback parameters are easily chosen to provide desirable pitch angle response characteristics. The controller is nonlinear and can be synthesized using a microprocessor. The organization of this work is as follows. Section III describes the mathematical model and the control problem. A nonlinear feedback control law is derived in Section IV, and simulation results are presented in Section V. Consider an unsymmetrical satellite with its center of mass S moving in a circular orbit about the Earth\u2019s center O (Fig. 1). The inertial frame XYZ has its Y axis pointing towards ascending node, and YZ defines the orbital plane. The unit vector e is along the Earth-Sun line. The rotating orbital frame xoyozo has its xo axis normal to the orbital plane, yo axis is along the local vertical and zo axis is tangential to the orbit pointing towards the velocity vector of the satellite. The coordinate system xbybzb is fixed to the satellite body, with yb and zb axes in the orbit plane and xb axis normal to the orbit plane" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001712_vss.1996.578618-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001712_vss.1996.578618-Figure1-1.png", "caption": "Fig. 1. Bicycle muck-semitrailer Model", "texts": [], "surrounding_texts": [ "In this section, a truck-semitrailer system shown in Fig- The nominal linearized truck-semitrailer model is given in the following state space form: X = A x + B 6 (29) where z is the state vector given by [VI r1 r2 V, : Lateral velocity of the tractor q : Yaw rate of the tractor r2 : Yaw rate of the semitrailer !P : Articulation angle S with : Steer angle on the front tires of the tractor and 2.6838 5.6393 -3.3453 -5.2011 -14.5045 12.2412 6.5102 10.2890 -11.3014 -53.7688 3.2160 5.0828 0 -1 1 0 A = [ r -110.8316 1 110.5998 = 1 1.00463 The control aim is to observe the articulation angle between the tractor and the semitrailer and the lateral velocity of the tractor using the measured yaw rates of the tractor and the semitrailer during a lane change manevueur with a constant longitudinal velocity of 15 mls. The discrete time observer parametres T and L have been chosen r o 1 0 0 1 0 0 1 T = l 0.2190 0.6789 0.9347 L 0.0470 0.6793 0.3835 0.8310 ] = [ 2.1064 0.6581 ] 2.2648 1.8354 with a sampling time of 0.1 whereas those of the continuous time sliding mode observer have been chosen 0 1 0 0.0346 0.5297 0.0077 0.0535 0.6771 0.3834 0.4175 P I = [ O 0 1 0.8585 -0.2205 1 -3.0632 0.5716 PZ = [ LI = 0.151~~2, LZ = 0.1512,~ with an equivalent filter time constant of 0.005 sec. The following figures show the behaviours of the observer states corresponding to unmeasurable states of the plant for both continuous and discrete time observers. The zoomed versions of the figures which include the lateral velocity of the tractor have been also attached to present the performances of the observers in terms of the chattering around the sliding manifold. V. CONCLUSIONS The sliding mode observer design for a discrete time system has been considered. Previous work for the continuous time sliding mode observer design has been reviewed and summarized. Simulation results demonstrate the effectiveness of the theoretical work on a practical implementation of the proposed observers for an Intelligent Vehicle Highway System project performed at CITR-OSU. The superiority of the discrete time observer over the continuous one in terms of the chattering reduction has been illustrated. REFERENCES [l] H.Hashimoto, V.I.Utkin, J.X.Xu, H.Suzuki and F.Harashima VSS Observer For Linear Time Varying System IECON'SO pp. 34-39, 1990. S.V.Drakunov, D.B.Izosimov, A.G.Luk'ayonov and V.I.Utkin The Block Contml Principle Automation and Remote Control, V.51, no.6 pp. 737-746, 1992. [2] - 197 - [31 141 - 198 - S.V.Drakunov V.Utkin Sliding-Mode Observers. Zbtorial Proceedings of the 34st IEEE Conference on Decision and Control (CDS), New Orleans, LA , December pp. 3376-3378, 1995. V.Utkin Sliding Modes and Their Application in Variable Structure Systems Moscow: Mir,1978. V.Utkin Variable Structure Systems with sliding modes IEEE Trans. Automat. Contr., vol. AC-22, pp. 212-222, 1977. . . [5]" ] }, { "image_filename": "designv10_13_0001558_0954407011525593-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001558_0954407011525593-Figure4-1.png", "caption": "Fig. 4 Driveline system for a lumped\u2013lumped model", "texts": [ " The equations of each block are T2(s)= kp s [\u00f62(s)\u00d5\u00f6 3(s)]+Cp [\u00f62(s)\u00d5\u00f6 3(s)] given by equations (1), (2), (3), (7), (8), (11), (17) and (21). Equations (22) to (31) are substituted for the appropriate distributed elements of Fig. 3. The lumped = Akp s +CpB (\u00f62 \u00d5\u00f6 3) (34) parameter values are given in Table 1 and are substituted in the lumped elements of Fig. 3. and as for the axle half-shaft as T 3(s)= k a s [\u00f64(s)\u00d5\u00f6 5(s)]+C a [\u00f64(s)\u00d5\u00f6 5(s)]2.2 Lumped\u2013lumped modelling technique In accordance with the notation shown in Fig. 4, the = Aka s +CaB (\u00f64 \u00d5\u00f6 5) (35)governing equations for the ywheel, clutch, gearbox and diVerential for the lumped model are given in equations (7), (8), (11) and (14) respectively. However, in Using the parameter values given in Table 1, the torsional stiVnesses of the rst and second driveshafts canthis model the driveshaft and axle half-shafts will also D13599 \u00a9 IMechE 2001Proc Instn Mech Engrs Vol 215 Part D at VIRGINIA COMMONWEALTH UNIV on June 7, 2014pid.sagepub.comDownloaded from be calculated as 3 SIMULATION AND ANALYSIS k1 = G1J1 l1 =28 438 N m/rad The main objective of this analysis was to study the torsional vibration of the driveline system and to investigate the shuZe ( low frequency) and clonk (high fre- k2 = G2J2 l2 =161715 N m/rad quency) phenomena" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure3-1.png", "caption": "Fig. 3 Kinematic sketch for the position and centrodes analyses: fixed F (O, X, Y) and moving f (X, x, y) frames", "texts": [ " In particular, the three boundary lines of the diagram of U versus W can be expressed in the following forms: U \u00bc W\u00fe 1 U \u00bc 1 W U \u00bc W 1 (2) which divide the plane of the diagram in four areas. Each of them corresponds to the type A, B or C of an offset slider-crank/rocker mechanism, while the grey area corresponds to the no closure condition. The singular configurations of the mechanism for the boundary lines of Eqs. (2) are sketched in Fig. 2 according to what reported in the diagram of Fig. 1. Moreover, the centered slider-crank mechanisms are obtained for W\u00bc 0, while U\u00bc 1 and W\u00bc 0 give the Scott-Russell mechanism for which l \u00bcr and e\u00bc 0. Referring to the kinematic sketch of Fig. 3, the position analysis of a slider-crank/rocker mechanism ABC is carried out by developing the following closure equation: r\u00fe l \u00bc m\u00fe e (3) Vectors r, l, m and e are given in the fixed frame F\u00f0O;X;Y\u00de by r \u00bc r cos d sin d\u00bd T l \u00bc l cos u sin u\u00bd T m \u00bc \u00f0r cos d\u00fe l cos u\u00de 0\u00bd T e \u00bc e 0 1\u00bd T (4) where r and l are the crank and coupler lengths, respectively. T indicates the transpose for each vector matrix, and the angles d and u give the orientation with respect to the fixed frame F\u00f0O;X;Y\u00de of vectors r and l, respectively", " 4, FEBRUARY 2012 Transactions of the ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Franz Reuleaux (1829-1905) related in his book [8] on how the relative motion between any two bodies in a plane can be described by the rolling of one body on the other. Thus, the rolling curves traced by the instantaneous center of rotation on both planes of the two bodies were called \u201ccentrodes.\u201d In particular, referring to Fig. 3, the fixed centrode p for the planar motion of the coupler link BC is the path traced by the instantaneous center of rotation I with respect to the fixed frame F\u00f0O;X;Y\u00de, during the motion of the slider-crank/rocker mechanism. Likewise, the moving centrode k is the path traced by I with respect to the moving frame f \u00f0X; x; y\u00de that is attached to the coupler link BC. The implicit algebraic equations of both fixed and moving centrodes are formulated in the following according to the approach, which was introduced by Walter Wunderlich (1910\u20131998) in his German book [10] by using complex algebra", " In fact, assigning n and m as n \u00bc l2x2 \u00fe 2 r 2l x 2 l3x 2 r 2x2 \u00fe l4 (32) and m \u00bc 2 r 2 x3 l r 2 l2 x2 r 2 x4 \u00fe l2 x4 2 l3x3 \u00fe l4x2 (33) Equation (31) can be solved by giving the following four solutions y1;2 \u00bc 6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 \u00fe 4 m r 2 p 2 r 2 s and (34) y3;4 \u00bc 6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 \u00fe 4 m r 2 p 2 r 2 s (35) Thus, Eqs. (32)\u2013(35) represent the explicit algebraic equations of the moving centrode k with respect to the moving frame f \u00f0X; x; y\u00de. These equations can be expressed with respect to the fixed frame F\u00f0O;X;Y\u00de through the position vector r i X M \u00bc x y i 1\u00bd T (36) for i\u00bc 1, 2, 3 and 4, as shown in Fig. 3 and by means of Eqs. (34) and (35). Finally, the moving centrode k can be expressed in F\u00f0O;X; Y\u00de by r i O M \u00bc TXO r i X M (37) where the transformation matrix TXO is given by Eq. (8). The proposed algorithm has been implemented in a MATLAB code and the graphical results of Figs. 6\u20138 have been obtained for U\u00bc 2 and 011003-4 / Vol. 4, FEBRUARY 2012 Transactions of the ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use W\u00bc 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003913_cm.21093-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003913_cm.21093-Figure1-1.png", "caption": "Fig. 1. (a) Schematic of a short ellipsoidal section, length q, of flagellum showing the normal and tangential forces. (b) Typical circular cross-section of flagellum. (c) Elliptical flagellum section with greater height than width: this shape models, very crudely, the presence of fins on the flagellum. Although not the exact geometry of a finned flagellum, the hydrodynamic forces may be computed exactly.", "texts": [ " Purcell [1977] gives a good, easily accessible, description of low Reynolds number propulsion. A flagellum propagates a travelling wave along its length to achieve propulsion. A propulsive effect is achieved because elements of the flagellum that are moving largely normal to their length create a greater thrust force than the resistive force on elements of the flagellum that are being dragged largely along their length. This extra force created by elements of the flagellum moving normal to the fluid also overcomes fluid drag on the sperm head. The normal force FN (see Fig. 1 for example) is the force created if a small element, length l is moved at velocity U in the fluid, with its axis normal to the direction of motion. Similarly the tangential force FT is the force created if a small element, length l is moved at velocity U in the fluid, with its axis parallel to the direction of motion. These forces are normally expressed in coefficient form with resistance coefficients CN \u00bc FN/Ul, i.e. the normal force coefficient is the normal force per unit length, divided by the velocity, and so has units of viscosity [Pa s]", ", by having fins) can generate a greater hydrodynamic resistance ratio than that of a circular section, we initially investigated the resistance coefficients generated by translating a short section of ellipsoidal cross-section, because translating ellipsoids in Stokes flow may be dealt with by exact hydrodynamic theory [Happel and Brenner, 1981 (p 223)]. An ellipsoidal flagellum, with greater height than width, is a crude representation of a finned flagellum. A short section of finned flagellum may be idealized to the shape of a needle-like ellipsoid, as shown in Fig. 1a with the semimajor axis q along the flagellum length, and the height of the fins equal to the height of the ellipsoid, and the width of the flagellum equal to its width. Computation of the tangential and normal hydrodynamic resistances of this ellipsoid indicates approximately if the finned flagella produce significantly different coefficients than a flagellum with circular, or \u2018\u2018normal,\u2019\u2019 CYTOSKELETON Hydrodynamic Analysis of Siberian Sturgeon Sperm 87 n cross-section. The advantage of using ellipsoids is that the fluid mechanics is exact, and RFT is relatively well understood by biologists" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001459_jsvi.1998.1988-Figure26-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001459_jsvi.1998.1988-Figure26-1.png", "caption": "Figure 26. Modeshape at 3526 Hz (major tooth critical frequency for stage 2; spur gears, type A). (a) Bending; (b) torsion.", "texts": [], "surrounding_texts": [ "T 7\nMajor tooth critical frequencies for spur (helical) gears (type A)\nFrequency (Hz) r1 (%) r2 (%)\n3310 (3272) 41 (42) 1 (10) 5009 (4831) 26 (17) 10 (10) 5443 (5492) 11 (15) 10 (2\u00b78) 1981 (1980) 6 (6) 10 (10) 3526 (3611) 1 (10) 67 (69)", "(a) 1.10E+02\n3.00E+01\n4.00E+01\n5.00E+01\n6.00E+01\n7.00E+01\n8.00E+01\n9.00E+01\n1.00E+02\n2.00E+01\n20 l\no g\n( a\nm p\nli tu\nd e)\n(b) 1.10E+02\n3.00E+01\n4.00E+01\n5.00E+01\n6.00E+01\n7.00E+01\n8.00E+01\n9.00E+01\n2.00E+01\n1.00E+03 5.00E+02 1.50E+03 2.00E+03 2.50E+03 3.00E+03 3.50E+03 4.00E+03 4.50E+03 0.00E+00 5.00E+03\nFrequency (Hz)\n20 l\no g\n( a\nm p\nli tu\nd e)\nf2\nf3\nf2\n3.f2 2.f2\n4.f2\nf2\nfm2+f2\n2.fm2\nfm1\n3.fm2 5.fm2\n4.fm2 6.fm2 3.fm1\nf1\nfm2\nfm2+f2\n2.fm\nfm1\n4.fm2\n5.fm2\n2.fm1\n6.fm2 7.fm2\n3.fm1\nfm2\u2013f2\nfm2\u2013f2 2.fm1\n1.00E+02\nAs an illustration of the potential of the method in gear dynamics, the original equations of motion in the physical space (14) and the reduced system (22) are integrated by the same time-step Newmark procedure. The practical applications correspond to the single stage unit defined in Figure 8 and Tables 1 and 2. Figure 9 shows, for different modal bases [F], the corresponding maximum relative deviations in terms of dynamic transmission errors under load (results from equation (14) being the reference) which, for 25 modes, is reduced to less than 2% over the 0\u20131600 rad/s speed range.\nFig. 28a & b." ] }, { "image_filename": "designv10_13_0002981_1.2937899-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002981_1.2937899-Figure2-1.png", "caption": "Fig. 2. Geometry of the ball-bat collision. The initial velocity of the ball and bat are vball and vbat, respectively, and the pitched ball has backspin of magnitude i. The bat-ball offset shown in the figure is denoted by D = rball+rbat sin , where rball and rbat are the radii of the ball and bat, respectively. For the collisions discussed in the text, the entire picture should be rotated counterclockwise by 8.6\u00b0, so that the initial angle of the ball is 8.6\u00b0 downward and the initial angle of the bat is 8.6\u00b0 upward.", "texts": [ " We will show that the trajectory is qualitatively different for a pop-up, because a ball-bat collision resulting in a pop-up will have considerable backspin, resulting in a significantly larger Magnus force than for a fly ball. Moreover, the direction of the force is primarily horizontal and is opposite on the upward and downward paths. These conditions will result in unusual trajectories, sometimes with cusps and loops. The collision model is identical to that used by Sawicki, Hubbard, and Stronge5 and by Cross and Nathan.6 The geometry of the collision is shown in Fig. 2. A standard base- ball rball=1.43 in. ,mass=5.1 oz approaches the bat with an initial speed vball=85 mph, initial backspin i=126 rad /s 1200 rpm , and a downward angle of 8.6\u00b0 not shown in the figure . The bat has an initial velocity vbat=55 mph at the point of impact and an initial upward angle of 8.6\u00b0, which is identical to the downward angle of the ball. The bat is a 34-in.-long, 32 oz wood bat, with radius rbat=1.26 in. at the impact point. If lines passing through the center of the ball and bat are drawn parallel to the initial velocity vectors, these lines are offset by the distance D" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002131_j.finel.2004.04.007-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002131_j.finel.2004.04.007-Figure4-1.png", "caption": "Fig. 4. Overlapping gear flanks in an arbitrary meshing position.", "texts": [ " This vector is n\u0302rinj = [ cos n cos sec tj sin wtj j cos n cos sec tj cos wtj \u2212 sin i sin n \u2212 j cos sin i cos n ] = [ cos ij sin wtj j cos ij cos wtj \u2212j sin ij ] , (36) where we have used expression (33). The surface of action passes through the instantaneous axis of rotation I that lies on the xrizri-plane. Substituting yrinj = 0 into (28) gives us xrinj = ri cos tj / cos( inj + inj \u2212 j tj ) = ri cos tj / cos wtj = rwi, (37) where rwi is the radius of the working pitch circle. Finally, we get from (32) and (37) a = rw1 + rw2. (38) Fig. 4 shows two (non-deformed) tooth flanks that overlap due to interference. Since, the transverse flank interference + is measured along the line of action, the relation between the two overlapping tooth flanks is rr1 nj ( 1nj , w1nj , 1j ) = Mr1r2rr2 lj ( 2lj , w2lj , 2j ) + [a 0 e]T + j j a\u0302r1 ,j . (39) By using (33) and the equations in (39) that relates yr1 nj to yr2 lj and zr1 nj to zr2 lj , we obtain 2( 1, e, j ) = j j /r2 cos tj + j (1 + z1/z2)(inv wtj \u2212 inv tj ) + 2(j \u2212 1)/2 \u2212 j (s1j (e) + s2j (0))/2r2 \u2212 ( 1 + 1(e))z1/z2, (40) where we also have used expressions (5)\u2013(8) and (19)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002570_rspa.2007.0006-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002570_rspa.2007.0006-Figure5-1.png", "caption": "Figure 5. Problem C: riding an accelerating elevator. Both the point mass and the elevator start at the same position (START) with zero vertical speeds. The elevator maintains a constant downward acceleration ae. The point mass can push or pull against the elevator using arbitrarily strong vertical telescoping legs. When the elevator reaches END, the vertical speed of the point mass should again be zero. The objective is to ensure this by doing the least amount of work with the vertical telescoping legs.", "texts": [ " ae ZK\u20acyp Z v2 l 0 : \u00f05:2\u00de Note further that the cost to be minimized (equation (3.2)) and the boundary conditions (equation (3.3)) also depend on only the vertical motion of the telescoping leg. Therefore, we can rewrite problem B with the parabolic track, just in terms of the vertical coordinates. (c ) Problem C: elevator problem The foot moving downwards with constant downward acceleration aeZv2/l0 is most conveniently represented as being attached to an elevator moving downwards with constant acceleration ae (figure 5). At time tZ0, both the person and the elevator are at the same position (without loss of generality). This initial state corresponds to mid-step, the apex of the parabolic or circular arc. The person can push or pull on the elevator with his vertical telescoping legs without affecting the elevator\u2019s motion. The person must have zero vertical velocity at time tZtstep/2. The objective is to meet this zero vertical velocity constraint by reacting against the elevator in a manner that incurs the least cost. Figure 5 shows the key variables in the elevator problem. Downward displacements and velocities are considered positive. ye is the position of the elevator, ym is the position of the mass m, and yrZyeKym is the relative position of the elevator with respect to the mass. The vertical motion of the point mass is governed by the equation m\u20acymZmgKF, where F is the compressive leg force. The differential equation for the relative position yr is m\u20acyr Zm\u20acyeKm\u20acym ZmaeKmgCF : \u00f05:3\u00de Proc. R. Soc. A (2007) At mid-step tZ0, the positions and the velocities of both the elevator and the mass are equal to zero: ye(0)Zym(0)Zyr(0)Z0 and _ye\u00f00\u00deZ _ym\u00f00\u00deZ _yr\u00f00\u00deZ0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003255_1.3151805-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003255_1.3151805-Figure3-1.png", "caption": "Fig. 3 Normal cross section of the circular-arc rack cutter g", "texts": [ " The work piece s indexed to one tooth and the generating cycle is repeated until ll the gear teeth and spaces are produced. Although the gear is generated by a face-mill cutter, however, it an also be considered that the gear is generated by a rack cutter. n this paper, the circular-arc curvilinear tooth gear pair is generted by two complemented rack cutters p and g. The normal ections of the rack cutters p and g are shown in Fig. 2. The nlarged normal section of the circular-arc rack cutter g and its orresponding design parameters are shown in Fig. 3. Coordinate ig. 2 Normal cross section of the proposed circular-arc rack utters Fig. 4 Relationship among coord 81003-2 / Vol. 131, AUGUST 2009 https://mechanicaldesign.asmedigitalcollection.asme.org on 01/08/2019 Terms o system Sr g Xr g ,Yr g ,Zr g is rigidly attached to the middle of transverse section of the imaginary rack cutter. Figure 4 illustrates the relations between rack cutter coordinate system Sc g Xc g ,Yc g ,Zc g and rack cutter normal cross section coordinate system Sr g . The surface equation of the imaginary rack cutter surface g and its unit normal vector can be expressed in coordinate system Sc g Xc g ,Yc g ,Zc g as follows: Rc g = xc g yc g zc g = \u2212 R g sin \u2212 sin g Rab 1 \u2212 cos g cos g \u2212 SG 2 + R g cos \u2212 cos g sin g Rab SG 2 \u2212 R g cos \u2212 cos g 1 where \u2212 sin\u22121 W 2Rab g sin\u22121 W 2Rab 2 and nc g = nXc g nYc g nZc g = sin g \u2212 cos g cos g sin g cos g 3 where the upper sign of symbol \u201c \u201d indicates the right-side of the rack cutter surface, g is a design parameter of the circular-arc rack cutter ranging from min g to max g , g indicates the instanta- \u201ei\u2026 \u201ei\u2026 inate systems Sc , Sr , and Sf Transactions of the ASME f Use: http://www", "org on 01/08/2019 Terms o Transactions of the ASME f Use: http://www.asme.org/about-asme/terms-of-use m m i 4 G m p m t a o K a t I b H = i m s n c s c 3 c e w t t s o o a c s a R t J Downloaded From: entioned algorithm, a computer program is developed to deterine the points, which the amount of surface-separation distance s the same as the thickness of the coating for contact pattern tests. Numerical Examples for Meshing Simulations of ear Drives Example 1. The relationships between the KE and radius R i Fig. 3 of the circular-arc cutter profile are investigated. Some ajor design parameters of the circular-arc curvilinear tooth gear air are shown in Table 1. This example investigates the gear pair eshing under different R i , and it is defined that R g =R p for wo complemented circular-arc rack cutters. The KE curves of the mating gear pair meshing under different ssembly conditions are shown in Fig. 7. It is found that this type f gear pair is very sensitive to the center distance variation, and E is decreased with the increase in R i when the center distance ssembly error C=0", " Table 2 illustrates the ontact ratios versus different major design parameters of the gear et. Contact ratio increases with the decrease of the pressure angle nd radius of the cutter\u2019s circular-arc profiles. However, the radius ab of the face-mill cutter i.e. radius of curvilinear tooth-trace akes no effect on the contact ratio. Example 3. A value of R is pre-designed in this example, and p g Table 2 Contact ratios und Design parameters: M =3 mm / tooth, A=1M, B=1M, T g =36 teeth, T p =18 tee Rab Figs. 1 and 4 mm R g Fig. 3 mm R p Fig. 3 mm 30 80 80 30 80 80 30 40 40 20 80 80 1b represents the rotation angle of the gear at the beginning at the end point of contact. R is defined as R= R \u2212R . The major design parameters of ournal of Mechanical Design https://mechanicaldesign.asmedigitalcollection.asme.org on 01/08/2019 Terms o the circular-arc curvilinear tooth gear set are the same as those shown in Table 1. KEs under different meshing conditions with different R are illustrated in Fig. 8, where R=0, 2, and 4 mm. There is no KE under ideal assembly conditions with R=0 mm because the gear pair is generated by two complemented rack cutters", " The major design parameters of the gear pair are the same as those listed in Table 1 except that R g =R p =40 mm with different values of curvilinear tooth-trace Rab. Figure 10 shows the contact ellipses that appeared on the gear tooth surfaces of the gear pair with Rab=20, 30, and 40 mm, respectively, under ideal assembly condition. In Fig. 10, symbol 1 = 1b indicates the rotation angle of the gear at the beginning point of contact while 1 = 1e represents the rotation angle of the gear at the end point of contact. 1b and 1e are obtained from TCA results and shown in Table 2. Meanwhile, the contact ratio of ifferent design parameters 1b deg 1e deg CR Fig. 3 deg 20 \u221213.54 5.45 1.90 25 \u221211.53 4.60 1.61 20 \u221215.03 4.99 2.00 20 \u221213.54 5.45 1.90 t of contact and 1e represents the rotation angle of the gear er d th poin the gear drive can be calculated by applying Eq. 18 . The contact AUGUST 2009, Vol. 131 / 081003-5 f Use: http://www.asme.org/about-asme/terms-of-use F u under different assembly conditions \u201eR =R =80 mm\u2026 0 Downloaded From: ig. 8 Kinematical errors of the gear pair with different R nder different assembly conditions \u201eR =30 mm\u2026 ab 81003-6 / Vol" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002787_robot.2008.4543695-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002787_robot.2008.4543695-Figure5-1.png", "caption": "Fig. 5. The swept volume of pivoting. It converges to the swept volume of the supporting edge along the straight line segment by reducing the rotation angles. Therefore, the original collision-free Reeds and Shepp path can be converted into a collision-free pivoting sequence.", "texts": [ " (1) In the regular sequence, elementary motions are repeated m times alternatively on the each edge, while \u03b8 > m\u03b1. Then the adjustment sequence is applied in a similar manner to the computation for the straight line path. We introduced the angle \u03b2 as half the maximum angle the robot may realize by a single pivoting. We should notice that this angle may be tuned for obstacle avoidance purpose. Indeed the first stage of the algorithm provides a collisionfree path that guarantees collision-freeness for the sliding supporting edge. Moving by pivoting along the planned path introduces some gap (see Fig. 5) with respect to the volume swept by the supporting edge when sliding along the path. More the rotation angle decreases, more the final swept volume converges to the initial one. This property accounts for the small-time controllability of the pivoting system we consider [1]. The 3D collision detection can be done by estimating the swept volume of the box attached to the supporting edge during the rotational motion. The inclination for pivoting can be taken into account by using a bounding volume including the inclining motion of the box" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003678_14763141.2012.674154-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003678_14763141.2012.674154-Figure2-1.png", "caption": "Figure 2. The test driver head, reflective markers, orthogonal clubhead coordinate system, and clubhead orientation angles.", "texts": [ " Prior to testing, temporary markers were attached to the club to define a clubface-aligned coordinate system. The club was then placed in the capture area and a trial was recorded. Using the method of Soderkvist and Wedin (1993) and Matlab software (MathWorks Inc., Natick, MA, USA), this information was used to establish a clubhead relevant orthogonal coordinate system with the origin embedded at the center face and with axes normal to the club face, parallel to the score lines, and perpendicular to the score lines (Figure 2). The raw 3D position data of the clubhead coordinate system origin were first differentiated to calculate clubhead speed. This was used to identify the time of ball impact, which occurred when there was a dramatic and sudden decrease in clubhead speed. The raw position data were then clipped at this time point, and filtered using a 60 Hz low-pass filter. As the last data point of these filtered signals was divergent, the last two data points were clipped off, and the remaining curves were extrapolated up to the time of ball impact", " This was verified by plotting every differentiated filtered curve over the corresponding differentiated raw trace and visually inspecting to ensure that the end points of the filtered curve lay centrally within the noise band of the raw trace. The analyzed variables of interest were clubhead speed, loft angle, face open angle, lie angle, in to out path angle, and attack angle, all at time of ball impact. The clubhead orientation angles were calculated relative to the laboratory coordinate system (Figure 2): loft angle (the angle between the face normal axis and the horizontal laboratory plane), face open angle (the angle between the face normal axis and the laboratory \u2018target\u2019 axis in the horizontal laboratory plane; positive indicating an open face), and lie angle (the angle between the clubhead axis parallel to the groove lines and the horizontal laboratory plane; positive indicating a \u2018toe up\u2019 orientation). Clubhead speed was defined as the magnitude of the velocity vector of the clubhead coordinate system origin" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002044_00207170500171329-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002044_00207170500171329-Figure3-1.png", "caption": "Figure 3. Finding a periodic solution via the LPRS approach.", "texts": [ " However, unlike in the DF analysis, we will be able to obtain exact values of the frequency of the oscillations and of the equivalent gain. Let us call the function J(!) defined above as well as its plot on the complex plane (with the frequency ! varied) the locus of a perturbed relay system (LPRS). Suppose, we have computed the LPRS of a given system. Then (like in the DF analysis) we are able to determine the frequency of the oscillations (as well as the amplitude) and the equivalent gain kn (figure 3). The point of intersection of the LPRS and of the straight line, which lies at the distance b/(4c) below (if b> 0) or above (if b< 0) the horizontal axis and parallel to it (line \u2018 b/4c\u2019) offers computing the frequency of the oscillations and the equivalent gain kn of the relay. According to (1), the frequency of the oscillations can be computed via solving the equation Im J\u00f0 \u00de \u00bc b 4c \u00f02\u00de (i.e. y(0)\u00bc b is the condition of the relay switch) and the gain kn can be computed as kn \u00bc 1 2ReJ\u00f0 \u00de : \u00f03\u00de Formula (2) furnishes a necessary condition of the periodic motion existence" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002134_j.jbiomech.2005.03.013-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002134_j.jbiomech.2005.03.013-Figure4-1.png", "caption": "Fig. 4. The comparison of the calculated and measured club-head path in the global frame {G}.", "texts": [ " Both the computed and measured velocities were resolved in negative x-direction of the laboratory frame, where the target was located. The computed club-head velocity time trace was in good agreement with the measured velocity time curve. The closeness between the two traces indicates the viability of this algorithm in the study. The comparison of the calculated club-head displacement time curve, in global frame, using position vector analysis with that of the video measured displacement time curve (Fig. 4) also indicated similarity in trend and magnitude. The obvious difference between the measured and calculated velocities and displacements occurred at about 0.1 s before impact. The possible reasons for the difference will be discussed in the following section. Time course of angular velocity of the different joints are presented in Fig. 5. At the impact (club\u2013ball contact), the wrist extension has the highest angular velocity of 11.8 rad s 1. The external rotation of the upper arm also had a notable angular velocity of 9", " This placement provides the measurement of the upper arm adduction/abduction, an action due to the contraction of the deltoid and suprasinatus muscles. At about 0.1 s before the impact, the outward rotation of the scapula was initiated to abduct the arm above the shoulder joint to execute the swing. This movement was not detected by the goniometer but the abduction was noted in the video analysis. Therefore, in Fig. 3, the two curves match initially but when the scapula rotation kicked in, it was not detected by the goniometer and hence the deviation in the two curves became apparent. This problem (illustrated in Fig. 4.) can be alleviated if the goniometer is attached to the lower side of the arm, from the medial side of the right upper arm to the breastbone, under the armpit. In this way, the goniometer reading will provide a measurement of the adduction/abduction that is generated by the deltoid and suprasinatus muscles as well as the scapula rotation. These results indicated somewhat fundamental limitations on usage of goniometers in capturing human motion even though they are considered as convenient tools, whose reliability largely depends on testers\u2019 skills to yield consistent results" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003568_s00502-013-0133-5-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003568_s00502-013-0133-5-Figure3-1.png", "caption": "Fig. 3. Inverted pendulum", "texts": [ " In order to control the position of humanoid robot we must know its dynamic properties, to know how much force needs to be exerted on it to move: too little force is associated with slow reaction of humanoid; too much force and the foot may crash into objects or oscillate around its desired position. A humanoid robot is a nonlinear, nonholonomic multivariable system because of the large number of DOF\u2019s. In this model the mass of robot is assumed to be lumped at the center of mass of the robot and the legs of the robot are assumed to be mass. Furthermore, for simplicity is assumed the height of the pendulum to be constant, this means that we have linear dynamic model. An inverted pendulum with a mass rod can is shown in Fig. 3. The ZMP equations for x\u2013y plane are as follows. xzmp = \u2211n i=1 mi (z\u0308i \u2212 gi ) \u00b7 xi \u2212 \u2211n i=1 mi (x\u0308i \u2212 gi ) \u00b7 zi\u2211n i=1 mi (z\u0308i \u2212 gi ) (2) yzmp = \u2211n i=1 mi (z\u0308i \u2212 gi ) \u00b7 yi \u2212 \u2211n i=1 mi (y\u0308i \u2212 gi ) \u00b7 zi\u2211n i=1 mi (z\u0308i \u2212 gi ) (3) Now, let the ZMP of coordinates of this pendulum to be P = [px , py , pz]T , the mass of the pendulum (mass of the foot Archie) to be mi Fig. 4. Using the ZMP equation (2) and (3) the dynamics equations of the inverted pendulum can be derived as follows; Px = m \u00b7 (c\u0308z + g) \u00b7 cx \u2212 m \u00b7 c\u0308x \u00b7 cz m \u00b7 (c\u0308z + g) (4) Py = m \u00b7 (c\u0308z + g) \u00b7 cy \u2212 m \u00b7 c\u0308y \u00b7 cz m \u00b7 (c\u0308z + g) (5) Thus, (4) and (5) converted into linear equations as follows; Px = cx \u2212 c\u0308x \u03c92 n (6) Py = cy \u2212 c\u0308y \u03c92 n (7) Hereafter, (6) and (7) are going to be referred as ZMP equations" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001351_j.1460-2687.1999.00018.x-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001351_j.1460-2687.1999.00018.x-Figure2-1.png", "caption": "Figure 2 Arrangement of test apparatus. Force plate measured forces in the X, Y and Z (transverse, front\u00b1back and vertical, respectively) directions during stick contact. Radar gun was positioned behind net to measure peak velocity (in front\u00b1back direction). Stick movement (front\u00b1back direction) during each shot was recorded using high-speed video (480 Hz). Peak de\u00afection (h) was determined by digitizing the position of re\u00afective marks placed at the top and bottom of the shaft.", "texts": [ " Data collection consisted of the simultaneous use of a force platform (AMTI OR6\u00b15), high speed video recording (EG & G Reticon; San Diego, CA) and a radar gun (Sports Radar Gun model SR 3300), linked to a data acquisition card (DAQ) and 486 PC. The force plate was used to record the initial reaction forces occurring between the stick and surface during the shot. The puck was positioned to the front edge of the force platform to ensure that the stick struck the platform during the preloading phase. (Fig. 2). Lubricating \u00afuid (WD-40s\u00e4 ) was applied to the force platform to reduce the coef\u00aecient of friction between the force platform and the stick blade (lstatic \u00bb 0.5). Forces were recorded at 1000 Hz for 2 s. Data were recorded through virtual instrument software on an AT MI0 16X (National Instrumentss\u00e4 ) DAQ controlled by Labviews\u00e4 (Version 3.1.1) on a 486 PC. Force\u00b1time pro\u00aeles were recorded in the X (transverse), Y (front\u00b1back) and Z (vertical) directions (Fig. 2). To obtain the kinematics of the stick, high speed video (480 Hz) was recorded during the shot. The camera was positioned 3.3 m lateral to the puck and 1.83 m vertically above the puck. The camera was orientated 20\u00b0 below horizontal and approxi- \u00d3 1999 Blackwell Science Ltd \u00b7 Sports Engineering (1999) 2, 3\u00b111 5 mately perpendicular to the stick's plane of motion determined from pretrials. Thirteen re\u00afective markers were placed on the shaft at 10-cm intervals. One marker was placed on the back of the left thumb (at the metacarpal\u00b1phalangeal joint) of the player's lower hand on the stick" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001662_s0094-114x(01)00082-9-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001662_s0094-114x(01)00082-9-Figure7-1.png", "caption": "Fig. 7. Three typical mounting types of beveloid gear pairs: (a) intersected axes; (b) crossed axes; (c) parallel axes.", "texts": [ " The orientation of the contact ellipse is determined by the angle c which can be represented with the following equations [5,6]: tan 2c \u00bc g2 sin 2r g1 g2 cos 2r ; \u00f034\u00de where g1 \u00bc j\u00f01\u00de I j\u00f01\u00de II ; \u00f035\u00de and g2 \u00bc j\u00f02\u00de I j\u00f02\u00de II : \u00f036\u00de Meanwhile, angle r is formed by the first principal directions of the gear and pinion tooth surfaces i \u00f02\u00de I and i \u00f01\u00de I , and it can be evaluated by r \u00bc cos 1 i \u00f01\u00de I i\u00f02\u00deI : \u00f037\u00de The half length of the major and minor axes of the contact ellipse, a and b, can be expressed in terms of the elastic approach D by [5,6] a \u00bc D A 1 2 ; \u00f038\u00de and b \u00bc D B 1 2 ; \u00f039\u00de where A \u00bc 1 4 j\u00f01\u00de R h j\u00f02\u00de R \u00f0g2 1 2g1g2 cos 2r \u00fe g2 2\u00de 1=2 i ; \u00f040\u00de B \u00bc 1 4 j\u00f01\u00de R h j\u00f02\u00de R \u00fe \u00f0g2 1 2g1g2 cos 2r \u00fe g2 2\u00de 1=2 i ; \u00f041\u00de j\u00f01\u00de R \u00bc j\u00f01\u00de I \u00fe j\u00f01\u00de II ; \u00f042\u00de and j\u00f02\u00de R \u00bc j\u00f02\u00de I \u00fe j\u00f02\u00de II : \u00f043\u00de Thus, the orientation and dimension of the contact ellipse can be determined by utilizing Eqs. (34)\u2013(39). Fig. 7 illustrates three typical types of gear mounting for beveloid gear pairs with intersected, crossed and parallel axes. Applying the developed computer simulation programs, the TCA results can be obtained and the contact ellipses can be plotted on the contact tooth surfaces. The elastic approach D for the contact ellipse simulation is chosen as 0.00635 mm, identical with the thickness of the coating paint used for contact pattern tests. Table 1 lists some major design parameters of the beveloid gear pair chosen for the following examples. In this example, the gear pair is composed of straight beveloid pinion and gear \u00f0bF \u00bc bG \u00bc 0 \u00de with cone angles d1 \u00bc d2 \u00bc 30 , mounted with an intersected angle of 60 , as Fig. 7(a) illustrates. Cases 1\u20133 simulate the meshing of the gear pair under the following assembly conditions: Case 1: Dch \u00bc Dcv \u00bc 0 and Dxg \u00bc Dyg \u00bc Dzg \u00bc 0 mm (ideal assembly condition). Case 2: Dch \u00bc Dcv \u00bc 0 and Dxg \u00bc Dyg \u00bc Dzg \u00bc 0:3 mm. Case 3: Dch \u00bc 0:5 , Dcv \u00bc 0:5 and Dxg \u00bc Dyg \u00bc Dzg \u00bc 0:3 mm. Case 1 is the ideal assembly condition. Case 2 indicates that the gear has a mounting position deviation but there is no axial misalignment. Case 3 indicates that the gear pair has both mounting position deviation and axial misalignments", " However, the contact ellipses of a beveloid gear pair with intersected axes are relatively small, especially with large cone angles. Therefore, tooth surface durability is generally low owing to its high contact stress. Considering the straight beveloid gear pair in this example, one curve \u00f0bF \u00bc bG \u00bc 0 \u00de in Fig. 9 shows how with the increase of cone angles d1 and d2, the ratio between the major and minor axes of the contact ellipse, a=b, decrease significantly. Notably, the ratio a=b approaches to infinity when the cone angles d1 and d2 tend to zero, which represents a spur gear pair in line contact. Fig. 7(b) illustrates a beveloid gear pair consisting of helical beveloid pinion and gear with crossed axes. The cone angles of the helical beveloid pinion and gear are d1 \u00bc d2 \u00bc 20 , and the helix angles on the pitch planes of the rack cutters for the pinion and gear are bF \u00bc bG \u00bc 15 (right handed). The crossed angle formed by axes Zf and Zg, as shown in Fig. 4, is calculated as 49.6284 by applying the algorithms proposed by Mitome [2]. This example investigates the meshing simulations of gear pairs under the following assembly conditions: Case 4: Dch \u00bc Dcv \u00bc 0 and Dxg \u00bc Dyg \u00bc Dzg \u00bc 0 mm (ideal assembly condition)", " Even under various assembly errors, the TEs remain zero and the loci of contact points also remain in the middle region of the tooth flank. Therefore, the helical beveloid gear pair with crossed axes is also insensitive to assembly errors. Another curve in Fig. 9 indicates the relationship between the cone angles and the ratio a=b of this helical beveloid gear pair with bF \u00bc bG \u00bc 15 . It is reasonable to find the ratio a=b approaches to a limited value when the cone angles tend to zero, which represents that a crossed axes helical gear pair is in point contact. Fig. 7(c) illustrates a straight beveloid gear pair mounted with the parallel axes. The pinion and gear are identical to those in Example 1 (cf. Section 5.1). However, the gear is now turned over to allow the heel of the gear to engage with the toe of the pinion. Thus, the axes of pinion and gear are now parallel. Cases 7\u20139 simulate the meshing of the gear pair under the following assembly conditions: Fig. 11 illustrates the bearing contacts of the gear pair on the pinion surface under three assembly conditions" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002347_tie.1986.351703-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002347_tie.1986.351703-Figure4-1.png", "caption": "Fig. 4. Orientation of stator current with rotor flux.", "texts": [ " In the present control scheme shown in Fig. 3, the second method has been adopted. The speed controller sets the torque reference, which, when divided by the magnitude of the flux 14, serves as the demanded value i 2. The flux controller sets the value of i From these two references, the demanded slip (24) is calculated. The required orientation of current is obtained from the integral of the sum of the demanded slip and the rotor speed: (26) The demanded position of the current vector p* thus obtained (Fig. 4), determines the position of the current vector and the magnitude of the current vector i* is obtained from (27): i*Vi *2 + i*2 (27) where Tl = (Lr - Lm)/Rr and Tr = Lr/Rr. From (16), it can be inferred that the flux dynamics depend on both the current components i4m 1 and i C. Orientation With Respect to Rotor Flux The rotor flux is defined by Pr=Lrir+Lmis=Lmimr (19) where imr-(1 +Ur)ir+is and ar = (Lr/Lm - 1). The three-phase reference currents are generated from p and iFfrom which the gating pulses for the current source inverter are obtained" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002131_j.finel.2004.04.007-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002131_j.finel.2004.04.007-Figure6-1.png", "caption": "Fig. 6. FE model of gear pair.", "texts": [ " The last methodology can be modified such that the local models are incorporated directly into the global model, thereby enabling feedback from the local models to the global model. This approach was used by Cavaciuti et al. [42] in an investigation of the contact of spiral bevel gears and by Brauer and Andersson [41], who investigated wear in spur gears with flank interference. The method is simple (it can be implemented relatively easily using commercial FE codes) and gives robust FE mesh with a high element shape quality and was thus also used in the study reported here. Fig. 6 shows the FE model of the gear pair. It was created using ANSYS 6.1 [43]. The complicated 3D gear geometry was determined by the work in [18], and in order to represent this properly 20-noded isoparametric brick elements (ANSYS: SOLID95) were used. The FE meshes of the local dense-meshed contact regions and the global coarse-meshed model do not match at the common interfaces (the node locations do not coincide) and therefore some kind of coupling method is needed to connect the meshes (see [44,45])" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure15-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure15-1.png", "caption": "Figure 15. The Bit Carousel", "texts": [ " The average power during the drilling process is less than 50 Watts and the Weight on Bit is 25 Newton, i.e. within the range of what the Arm can provide. Figure 14. MSR Core Drill in a Stand-off position. Bit Carousel The Bit Carousel consists of actuated rings of stowed Bits that can be retrieved by the drill. In the base scenario, the Bit Carousel has as many bits as needed for the core samples. However, additional bits can be added by increasing the diameter of the rings or adding additional rings. The Current Best Estimate (CBE) mass is 2.3 kg. The Bit Carousel is shown in Figure 15. The Bit Carousel is a single actuator system (to rotate the bit carousel) and has 2 actuated dust covers. To retrieve the bit, the Dust Cover is first opened, and then the drill docks to the outside of the Bit Carousel using one of the two sets of alignment spikes. This aligns the drill bit with the access port on the Bit Carousel. The Bit Carousel is rotated to the next available bit station, and the drill linear stage is then used to reach into the Bit Carousel and mate with a bit. After mating and locking onto the bit, the drill linear stage retracts, leaving a fresh bit attached to the drill" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003026_1.3212679-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003026_1.3212679-Figure11-1.png", "caption": "Fig. 11 A serially connected HR mechanism", "texts": [ " Depending on the torsion being 0 or not, a constant-parameter circular surface can be generated by a RR or HR mechanism. It is easy to obtain the following theorems. THEOREM 2. The necessary and sufficient condition for a circular surface to be a HR circular surface is (1) scalars , , , and are constants and (2) + 0. THEOREM 3. The necessary and sufficient condition for a circular surface to be a RR circular surface is (1) scalars , , , and are constants and (2) + =0. The parameters of a HR mechanism can be obtained through scalars , , , and . Figure 11 gives a serially connected HR mechanism with D-H parameters. Direct computation gives = e2 \u00b7 e3 = cot 1 = e1 \u00b7 M = \u2212 a1 + h cot 1 55 = e2 \u00b7 M = d2 = e3 \u00b7 M = a1 cot 1 + h where h is pitch of the H joint. From Eq. 55 it follows that h = + 1 + 2 , a1 = + 1 + 2 , 1 = acot , d2 = 56 Figure 12 is an example of HR circular surfaces. OCTOBER 2009, Vol. 131 / 101009-7 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use b g 7 l t p i i a f v d T t a d s t p v R 1 Downloaded Fr The parameters of a RR mechanism through , , , and can e obtained from Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure1.13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure1.13-1.png", "caption": "Figure 1.13-Minor hysteresis loop traversed when unipolar pulses are applied to a feed-through converter. The hatched area represents the portion of the hysteresis loop actually used. From Ferroxcube Application Note F602", "texts": [], "surrounding_texts": [ "In the design of transformers for inverters, the worst case scenario is used with regard to transient voltages that may increase the input voltage. Knowing the maximum and minimum voltages will help in the design process. Another Circuit Push-pull Feed forward Flyback Advantages Medium to high power Efficient core use Ripple and noise low Medium power Low cost Ripple and noise low Lowest cost Few components Disadvantages More components Core use inefficient Ripple and noise high Regulation poor Output power limited \u00ab100 Watts) operational problem that must be considered in the design of push-pull con verters is the possibility of D.C. imbalance in the two arms of the circuit. For this reason, full bridge converters are used for most high-power applications even though they have twice as many power semiconductor switches. The voltage stress is only on the DC Bus voltage, not twice the value. In addition, a DC blocking capacitor can be added to the full bridge where it cannot in a push-pull circuit. 1.6-THE HYSTERESIS LOOPS FOR POWER MATERIALS Since this book is involved with the application and choice of magnetic components in power electronics, it is important to relate the action and prop erties of the magnetic materials in the transformers and inductors in the cir cuits we have been studying. What produces the voltage is not the alternation but the rate of change of the flux. As the current and voltage wave-forms change during operation, the magnetic components go through the hysteresis loop characteristic of the magnetic material. In some cases only part of the hysteresis loop is traversed. The operation of a power transformer or choke can be designed to have a bipolar drive as in the push-pull type or unipolar (forward or flyback mode). In the bipolar case, the course of the induction or the excursion is in both directions so that the magnetization is reversed. The In the unipolar case, the induction is unidirectional and the magnetization is not reversed. In Figure 1.12b, for the forward converter, a slow-rise capacitor or ringing choke has been added to reset the core. In the case of the flyback converter, (Figure 1.12c), the offset ofthe ac induction loop is due to the DC usually present in flyback converter. In certain instances in power electronics, the limits of induction are from the remanent to a higher induction. The loop traversed is a minor loop in the first quadrant similar to the one shown in Fig ure 1.13. In this case, the B used in the induction equation is still Lffi/2 even though the magnetization is not reversed. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 13 Whereas the ~B and thus the corresponding voltage are smaller in a unipolar than in the bipolar drive, the construction and operation are much simpler and more economical. The hysteresis loop traversals for flyback, forward and push-pull converters are shown in Figures 1.14, 1.15, and 1.16 . In the use of ferrites as flyback transformers for television receivers, the voltage and cur rent waveforms are not sinusoidal but saw-tooth or flyback shape. This per mits the electron beam to sweep across the TV screen with its visual signal and when it comes to the end, it would rapidly return or fly back to the start ing horizontal sweep position to present the next lower line of information. In this case, the transformer operation is unipolar. The basis of the modem elec tronic switching power supply is the action of the transistor as a switch. Early transistors were not built to carry much power and thus, as was the case for early ferrite inductors and transformers, they were used mainly in telecommu nication applications at low power levels. The first power electronic compo nent was the inverter that is a device that takes a DC input and produces an ac output in a manner other than the usual rotary generator. A transformer may be incorporated in the device to give the required voltage. The device can be mechanical such as a vibrator or chopper or it can be of the solid state variety using a transistor. The word, oscillator, may sometimes be confused for an inverter but in the oscillator, the frequencies may be higher and the power levels lower. The second important item, a DC converter, takes the DC of one voltage and converts it to DC at another voltage. One might call it a DC trans former. The intermediate step in a converter is that of an inverter namely the conversion of DC to AC. Of course, the additional step is rectification to D.C. The input to a converter can sometimes be a low frequency (50-60 Hz.) which is rectified, inverted, transformed, and then again rectified. The advantage over a conventional transformer is that the transformation is much more effi cient at the higher frequency. 1. 7-SWITCHING POWER SUPPLIES The complete switching power supply may consist of several auxiliary sections in addition to the power transformer. If ac is the input, it must first go through a noise filter to keep out unwanted transients. It is then rectified be fore entering the power transformer where it is first inverted to a square wave of the higher frequency (or pulse repetition rate) and then transformed to the desired output voltage. The transistor is driven by an auxiliary timing trans former or driver. After passing through the power transformer, the secondary voltage is again rectified. It then passes through a voltage regulator to main tain the voltage limits in the required range. Often this is done in a feedback circuit which controls the on-off ratio of the switching transistor. This 14 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 15 B t Bmax B ~B ----~~~---...... L ~'4--_---L-B H technique is called \"pulse width modulation\" or PWM and is widely used. An example of such a circuit is shown in Figure 1.17. Switching power supplies have efficiencies on the order of 80-90% compared to those of linear power supplies that may range from 30-50%. The switching supplies are, therefore, lighter and smaller than their counterparts. A typical switching power supply is shown schematically in Figure 1.18 (Magnetics 1984). 1.8-FERRORESONANT CONVERTERS In a previous section, we have discussed the use of pulse width modula tion (PWM) as a means of regulating a high frequency power supply. This method using square wave produces high switching loss because of all the odd harmonics produced by the square wave. There are several other control mechanisms which we will discuss One is the use of a resonant or ferroreso nant converter. The other is the use of a magnetic amplifier. There are many instances of resonance as it relates to low level linear fer rite components. In such cases a series or parallel combination of an inductor and capacitor acted as an LC circuit for frequency control in low level filters. The term resonance (more properly, ferroresonance) here has more of a connotation of resistance to changes in the input voltage and current by stor ing energy in the resonant circuit. As a matter of fact the first uses of ferro resonance was in the construction of a constant-voltage 60 Hz. transformer by Sola. In power supplies, an important use of the ferroresonant transformer is as a regulator. The early 60Hz transformers have given rise to the high-frequency type, which as noted earlier, may be even more useful at the highest frequencies than the conventional switching transformer design. As a high-frequency power inductor, the ferroresonant transformer has a quite different function. For one thing, the magnetic circuit is non-linear and because of the high currents and fields, operation is close to saturation. Most often when used as a power inductor, it is necessary to insert an air gap or spacer to avoid saturation. Figure 1.19 shows a simple ferroresonant regulator that consists of a lin ear inductor, Lh a non-linear saturating inductor, L2 and a capacitor, C, in parallel with L2\u2022 The latter two components form the ferroresonant circuit that controls the input voltage. The input energy is stored in L, and the resonant circuit acts to pass a uniform voltage to the load. Although the linear trans former may be of the typical power ferrite found in transformers, the saturat ing transformer is quite different. In addition to the usual attributes of power ferrites, it should possess a rather square hysteresis loop. The squareness ratio, BIBs should be over 85%. The permeability over the linear portion ofthe loop APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 17 18 MAGNETIC COMPONENTS FOR POWER ELECTRONICS should be as high as possible with the saturation permeability quite low (Jl = 20-30) By combining the ferroresonant regulator with a high frequency inverter, a ferroresonant converter can be constructed as shown in Figure] .20 Then, with the addition of a rectifier in front, a switching power supply can be made. See Figure 1.21. McLyman(1969) has shown how a high frequency ferroresonant trans former, tuned to about 20 KHz. can be used to stabilize high frequency inverters. With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for en ergy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 19 To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10\u2022 There are applications in which a high-frequency inverters is needed with low harmonic distortion. In a resonant inverter, a square-wave is produced by the switch network. The square wave has many odd harmonics that produces distortion and high switching loss. When the square wave is fed into the reso nant tank circuit that is tuned to the fundamental frequency, a pure sine wave is produced that is then rectified and filtered. By changing the frequency closer or further from the resonant frequency, the voltage and current at the load can be controlled. A resonant inverter circuit with two switches is shown in Figure 1.22.With the addition of a rectifier and low pass filter network, a resonant converter circuit is formed. See Figure 1.23. 1.9-S0FT SWITCHING IN COMMON TOPOLOGIES The reduced switching loss is the chief advantage of a resonant converter brought about by either zero-current switching (ZCS) or zero-voltage switch ing (ZVS). These fall under the heading of soft switching that can also 20 MAGNETIC COMPONENTS FOR POWER ELECTRONICS be applied to other topologies. The switching using the resonant inverter is done at the zero crossing points of the sinusoidal current or voltage wave forms and thus reduce the semiconductor switching loss allowing operation at higher frequencies. In a buck converter, zero-current switching can be imple mented by insertion of a quasi-resonant switch cell in place of the PWM switch cell as shown in Figure 1.24 . It is also possible to insert a ZVS switch cell into a buck converter as shown in Figure 1.25. A Zero Voltage Switching Circuit using an active-clamp snubber network in a forward and flyback con verter is shown in Figure 1.2. SUMMARY This chapter has reviewed the various circuits that are commonly used in power electronics. The hysteresis loop traversals of the magnetic components were correlated with the three topologies for unipolar and bipolar cases. The magnetic functions of the magnetic components involved in the operation a switching power supply will be discussed in Chapter 2. APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 21 22 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPLICATIONS-TOPOLOGIES FOR POWER ELECTRONICS 23 References Severns, R. P. and Bloom, G. E.,(1984) Modern DC-to-DC Switchmode Con verter Circuits, EJ Bloom Associates, San Rafael, CA Bracke, L.P.M.,(1983) Electronic Components and Applications, Vo1.5, #3 June 1983,p171 Bracke L.P.M.(1982) and Geerlings, F.C., High Frequency Power Trans former and Choke Design, Part I, NY Philips Gloeilampenfabrieken, Eindhoven, Netherlands Erickson, R.W. and Maximovic, D., (2001)Fundamentals of Power Electron ics, Second Edition Kluwer Academic Publishers, Boston, Dordrecht Magnetics (2000) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Martin, W.A.(1987), Proceedings, Power Electronics Conference (1987) Chapter 2 MAIN CONSIDERATIONS FOR MAGNETIC COMPONENT CHOICE INTRODUCTION After having reviewed the applications and topologies for the various power electronic circuits in Chapter 1, we can now proceed to investigate the main considerations that are made in choosing the appropriate magnetic com ponent. In this chapter, these considerations are related to the function of the component in the circuit. They include a general review of material properties and the core shapes and sizes. The final size will be determined by the design considerations and the input and output variables. Lastly, the question of cost will come into play depending on the market that the component and the fm ished product is aimed. 2.1-CONSIDERA TIONS BASED ON COMPONENT FUNCTION At the end of Chapter 1, we listed the various magnetic functions that are used in a switching power supply. They are; 1. Power Transformer 2. Power Inductor or Choke 3. In-line or Differential-Mode Choke 4. Common-mode Choke 5. EMI Suppression Core 6. Pulse Transformer for Transistor Firing 7. Magnetic Amplifier Core 8. Power Factor Correction Core In choosing the best magnetic component for these functions, we use a proc ess similar to that employed for low-level components except that the neces sary parameters are somewhat different. The choice will be determined by: 1. The type of converter circuit used. 2. Frequency of the circuit. 26 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 3. Power requirements. 4. The regulation needed (percentage variation of output voltage permitted) 5. Cost of the component. 6. Efficiency required. 7. Input and output voltages The components for each of these functions will be considered separately as their requirements are somewhat different. The cores selected to meet these requirements will be discussed with regard to; 1. Core material 2. Core configuration which includes associated hardware (bobbins, clamps, surface-mount connections etc.) 3. Size of the core 4. Winding Parameters- (number of turns, wire size) This chapter will review these requirements in general for the various func tions and in much more detail in the following chapters. 2.2-MAGNETIC COMPONENT CHOICES Having limited the choice of material somewhat to only power and power-related applications, there are still a large variety of components that can be used. These include; 1. Soft ferrite cores 2. Powdered metal toroids (and some E-cores) 3. Magnetic metal strip cores (Tape cores, laminations, cut-cores) 4. Amorphous metal strip wound tape-cores 5. Nanocrystalline material strip-wound tape cores F or the last two materials, there are several variations of material available but the core shape (a toroidal tape-wound core) is set by the physical attributes of the material (brittleness). These properties also may limit the size of the core particularly with respect to the inside diameter. The choice for the various components for each function will be discussed separately. 2.3-COMPONENTS FOR POWER TRANSFORMERS In power transformer functions, a large induction swing may be trav ersed calling for a core with highest effective permeability derived from the best core material and shape. A high saturation material with low losses under CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 27 the operating conditions is desirable. While a toroid gives the highest effec tive permeability for a specific material, it is costly to wind. An ungapped ferrite E-core or other power shape is preferable for noncritical applications. For lower frequency power applications (line or mains frequency) laminated strip of iron or SiFe is commonly used. For somewhat higher frequency power applications, tape cores of thin strip SiFe, high permeability NiFe (80 Per malloy) high saturation NiFe (50 Permalloy) or CoFe (Supermendur) can be used. For high frequency operation, the workhorse of the power electronics components is the ferrite core that is available in many materials, shapes and sizes. Recently, some inroads have been made with the new amorphous and nanocrystalline materials. Power transformers have one requirement in common, that is that the material saturation be as high as possible consistent with other factors such as core loss. As we shall see later, at very low frequencies, the materials are satu ration-driven as eddy current losses are moderately low. These materials such as iron, low-carbon steel and heavy gage silicon iron will not be discussed in this book since they do not enter into the field of power electronics. At high frequencies, the materials are core-loss-driven so that materials such as fer rites are generally used. For medium high frequencies, materials such as thin gage silicon iron, amorphous materials and the new nanocrystalline materials are available. We normally make this choice on the basis of frequency of op eration. Vendors usually provide guidelines as to what materials are suitable for the various frequency ranges. The core losses are often given as a function of frequency. Although vendors generally list power materials separately, the user often has a choice of several available materials varying according to losses, frequency and sometimes, cost. Since power ferrites operate at the highest possible induction, we find, as we would expect, that they have the highest saturation of the ferrites consistent with maintenance of acceptable losses at the operating frequency. For frequencies up to about 1 MHz., Mn-Zn ferrites are the most widely used materials. Above this frequency, NiZn fer rites may be chosen because of their higher resistivities. Since ferrite cores make up the largest proportion of high frequency power transformers, the considerations for their choice will be discussed first. 2.4- FERRITE POWER TRANSFORMERS Having mentioned that ferrite cores are the major components for power electronics we will discuss them first. Switching power supplies and ferrite expansion went hand in hand. To explain why ferrites were made to order for these applications, we must understand the implications of going to higher frequency operation. Ferrites have low saturation compared with most common metallic magnetic materials (such as iron) and also have much lower 28 MAGNETIC COMPONENTS FOR POWER ELECTRONICS permeabilities than materials such as 80% NiFe. The low saturation of ferrites comes about from the fact that the large oxygen ions in the spinel lattice con tribute no moment and so dilute the magnetic metal ions. This situation is compared to a metal such as iron where there is no such dilution. In addition, because of the anti ferromagnetic interaction, not all the magnetic ions con tribute to the net moment in ferrites but only those with uncompensated spins. The first use of ferrite material in a power application was to provide the time-dependent magnetic deflection of the electron beam in a television receiver. The two ferrite components used were the deflection yoke and the flyback transformer. This application remains the largest in tons of soft ferrite used. Another early use of power ferrites was in matching line to load in ultra sonic generators and radio transmitters. Ferrites were not considered for line power inputs because at the lower frequencies (50-60 HZ.),they wereeco nomically unattractive (lower Bsat and higher cost than electrical steels). How ever, today's ferrites are employed as noise filters in power lines on the input to all types of electronic equipment. The potential for using ferrites at high frequencies was always there but the auxiliary circuit components (mostly semiconductors) were not yet developed. In addition, earlier there was no great market or stimulus for high frequency power supplies. One envisaged use was in high frequency fluorescent lighting at about 3000 Hz. This idea was suggested in the early 1950's but the need for setting up line power at these frequencies was never fulfilled. (See Haver 1976) In the 1970's, the rapid growth of ferrites for use at high power levels oc curred shortly after the similar growth of power semiconductors that could switch at very high frequencies. This design specifically required moderate cost magnetic components with low losses at higher frequencies and elevated power levels. Thus the age of the switched mode power supply (SMPS) was born. Coincidentally, the rapid growth of computers and microprocessors has required small, efficient power supplies that could be constructed with power ferrite components. The computer and allied markets are certainly providing much of the present day impetus for today's power ferrite development. The matching of SMPS component needs with ferrite properties is explained in the following two sections. 2.4.1- Frequency-Voltage Considerations A changing electric current in a winding provides a corresponding change in a magnetizing field which sets up a resultant varying magnetic in duction in a magnetic material. This changing flux will induce a voltage in another (secondary) winding. The general case of a voltage produced by a changing (not necessarily alternating) magnetic flux is given by Faraday's equation namely; CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 29 E = -N dcjl/dt = -N d(BA)/ dt [2.1] For a sine wave, the induced voltage is given by: E = 4.4BNAfxlO-8 [2.2] where:cjl = Magnetic flux, maxwells E = induced voltage, volts B = maximum induction, Gausses N = number of turns in winding A = cross section of magnetic material, cm2 f = frequency in Hz. For a square wave, the coefficient is 4.0 instead of 4.44. If we, for the present, minimize the effects of complicating problems such as core losses and temperature rise (which we will discuss later), we can use this important induction equation to examine the use of the variables in the most preliminary design. To obtain a given voltage with the most efficient arrangement, the tradeoffs can be as follows; 1. Increasing B by using a material with high induction such as 50% Co-Fe. This material is used in aircraft and space application where space and weight are important. However, there is a material limitation on how high the B can go. Ferrites may have saturation of 4-5,000 gausses. The highest RT saturation of about 23,000 gausses is found in 50% Co-Fe, so that there is a possible 4:1 or 5:1 advantage here for metals. See Table 2.1. 2. N can be increased which leads to higher wire resistance losses. Also, there is a maximum number of turns that can be wound around a core with a window or bobbin area. Using small wire size allows more turns, but the increased resistance (due to the increased length to cross sectional area) limits the useable current through the wire. 3. A can be increased. In addition to higher core losses, the larger cross-section requires a longer length of wire per tum leading to higher copper losses and a larger and heavier device. The larger cross section in a poor thermal conductor such as a ferrite also creates the problem of how to remove the heat produced in a large core. If the heat isn't removed, the temperature rise lowers the saturation induction, Bs of the ferrite. Under these conditions, if the induction-swing, ~B, is large enough, the core may actually saturate and the current in the winding can become very large possibly causing catastrophic failure. This can damage the core, the winding and other components. 4. f can be increased. Here the effect can be quite dramatic depending on the frequency dependence of core losses. For instance, in going from a 60-Hz power supply to 100KHz supply, the factor is 1666. This coupled 30 MAGNETIC COMPONENTS FOR POWER ELECTRONICS with a 4: 1 reduction in going from high B metals to low B ferrite still leaves 400+:1 advantage. This permits a great reduction in the size & weight of the transformer, which reduces wire and core losses. In a high frequency power supply, increasing the frequency can exacerbate the thermal runaway problem if the exponent of frequency dependence is higher than that for flux density. We will deal with this subject with later in this chapter. NiFe (50% Ni, 50% Fe) NiFe (79% Ni, 4% Mo, Balance Fe) NiFe Powder (81% Ni, 2% Mo, Balance Fe) Fe Powder Ferrites Amorphous Metal Alloy(Iron-Based) Amorphous Metal Alloy (Co-based) Nanocrystalline Materials (Iron-based) 2.4.2-Frequency-Loss Considerations 15,000 7,500 8,000 8,900 4,000-5,000 15,000 7,000 12,000-16,000 We have shown that by increasing the frequency of a transformer, we can produce the desired voltage requirement at a greatly increased efficiency. However, we have neglected one consideration, that is, the increased losses that occur when we increase the frequency of operation. The additional losses incurred in the frequency increase are mainly eddy current losses caused by the internal circular current loops that are formed under ac excitation. The eddy current losses of a material can be represented by the equation: Pe = KBm2Fd2/ P [2.3] where: P e = Eddy Current losses, watts K = a constant depending on the shape of the component Bm = max induction, Gausses f= frequency, Hz d = thickness-narrowest dimension perpendicular to flux, cm p = resistivity, ohm-cm Again there is a trade-off for lower P e. B can be lowered which means larger A to get the same voltage. Frequency, f, can be lowered which again means CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 31 larger components. The thickness, d, can be made smaller, such as in thin metallic tapes, wire or powder. There are physical limitations to this variable, and also the high cost of rolling metal to very thin gauges. The other measure we can take is to increase the resistivity. (See Table 2.2.) A comparison will demonstrate the advantage of ferrites. The resistiv ity for metals such as Permalloy or Si-Fe is about 50 x 10-6 ohm-cm. The re sistivity of even the lowest resistivity ferrite is about 100 ohm-cm. The dif ference then is about 2 million to 1. Since the effect of the frequency on the losses is a square dependence and that of resistance only a linear one, the net effect on frequency is about 1400 to 1. Thus, losses to the 60 Hz operation, for the same size core, extend to 84,000 Hz, close to the 100 KHz we postu lated for the voltage calculation. Granted this calculation is simplified, having omitted wire losses and loss differences due to B variations, but the order of magnitude is probably reasonable. In actual cases, 60 Hz power supplies op erate at efficiencies of about 50%, whereas the ferrite high frequency switch ing power supplies operate at 80-90%. Table 2.2 Resistivities of Ferrites and Metallic Magnetic Materials Material Zn Ferrite Cu Ferrite Fe Ferrite Mn Ferrite NiZn Ferrite Mg Ferrite Co Ferrite MnZn Ferrite Yttrium Iron Garnet Iron Silicon Iron Nickel Iron Resistivitity, n -cm 102 105 4 X 10-3 104 106 107 107 102_103 1010_1012 9.6 X 10-6 50 X 10-6 45x10-6 We must include another consideration in the comparison. We have men tioned the poor thermal conductivity of ferrite and ceramics in general. Aside from the difficulty of firing very dense, large, ceramic parts without produc ing cracks, there is also the previously mentioned problem of heat transfer. Because of this limitation, ferrite switching power supplies have not been made larger than about 10 KW. This is in comparison to the over 100 KW supplies that are made of metallic materials. However, since the large mar kets in power supplies are for home computers or microprocessors, and since these are well within the operational size of ferrites, there is no real size problem here. A comparison of magnetic properties of ferrites with other 2.4.3-Choosing the Best Ferrite Power Transformer Material A material slated for a power application must meet certain special requirements. Although ferrites in general have low saturations, we must, at least, provide the highest available variety consistent with loss considerations. This is mostly a matter of chemistry. Along with this consideration is the need for a high Curie point. This generally means maintaining a high saturation at CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 33 some temperature above ambient which approaches actual operational tem perature. In addition to the saturation requirement, the material must possess low core losses at the operating frequency and temperature. The transformer losses, which include both the core loss and the winding loss, will heat the ferrite causing a reduction in the saturation to a value lower than that at room temperature. If this fact is not taken into account, the core may saturate at the higher temperature with disastrous results. A runaway heating situation could develop leading to catastrophic failure. Many ferrite suppliers have redes igned their materials such that the core losses will actually minimize at higher operating temperatures preventing further heating of the cores. The negative temperature coefficient of core loss at temperatures approaching the operating temperature helps compensate for the positive temperature coefficient of the winding losses in the same region. Roess(l982) has shown that the minimum in the core loss versus temperature occurs at about the position of the secon dary permeability maximum. Thus, if the chemistry of the ferrite can be de signed to have the secondary permeability maximum at the temperature of device operation of the transformer as described above, the core losses will also be lowest at that temperature. However, we must consider that this is only a local minimum. Having the minimum at 75-1 OO\u00b0C.is a tremendous aid to the designer in avoiding thermal runaway, but still requires careful design work as the core loss increases above this minimum and the capacity for thermal runaway is still very real. Some smaller portable devices such as lab top computers operate intermittently at low ambient temperatures so materials with core loss minimum temperatures near room temperature may be used. 2.4.4-Power Ferrite Core Shapes Power ferrites come in a variety of shapes. Although pot-cores were the ferrite shapes of choice in telecommunication ferrites, several required or preferred features for this application are not as critical in power usage. These include: 1. Shielding 2. Adjustability In addition, pot cores are more costly and power ferrites must compete with other alternative materials. Therefore, shapes such as E cores, U cores, and PQ cores are more applicable to power application. Other shapes including solid center post pot cores can be used. The following chapter describes the types of shapes available. The shape of the core has a bearing on the ampli tude permeability since the inductance is given by; L = .41tJ.lN2/IA [2.4] 34 MAGNETIC COMPONENTS FOR POWER ELECTRONICS where: I = length of the winding, cm. A = Cross sectional area, cm2 L = Amplitude Permeability Therefore, the longer the section on which the winding is placed and the shorter the height of the winding, the higher the inductance. 2.4.S-Component Processing after Assembly After the ferrite component is wound, there are additional process steps that may affect the choice of component. These include; 1. Encapsulation 2. Soldering 3. Clamping 4. Winding 5. Gluing 6. Coating Encapsulation, coating, gluing and clamping all put stresses on the core that may affect the magnetic properties. Some materials are more sensi tive to stresses than others even though the properties are superior. Winding also stresses the core. Toroidal winding is costlier than bobbin winding. In modern printed circuit design, wave soldering is often used to attach compo nents and leads to the board. Proper component choice will minimize the ef fect of the soldering temperature. 2.4.6-High Frequency Applications Special attention must be paid if the frequencies of power supplies extend past 100 KHz and even to the 1 MHz region. First, the size of the core may be reduced significantly. Second, the core material must be modified to lower the core losses at these frequencies. The maximum flux density or B level used which, at lower frequencies, may have extended to 2000-2500 gausses may have to be reduced to something on the order of 500-600 gausses to attain the lower losses. The increase in frequency with smaller size and better efficiency may more than offset the lower saturation used. We will dis cuss designs at these higher frequencies at a later point in this chapter. Ven dors design instructions are based on allowing the flux density to drop to lower values at higher frequencies in order to keep the core loss constant at 100 mW/cm3. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 35 2oS-METAL STRIP POWER TRANSFORMERS In our discussion in Section 2.4.1, we found that a great advantage of some of the metal strip magnetic components was their high saturation, (Si Fe, Ni-Fe, and Co-Fe). However, as we examined the core losses in Section 2.4.2, we also found that due to their low resistivity, the usefulness of these materials was diminished. Reducing the thickness or gage of these materials allowed them to operate at somewhat higher frequencies. For the 80% Ni-Fe, with a lower saturation, the very high permeability also reduced high frequency losses especially in thinner gages. The Ni-Fe alloys had an addi tional advantage of being able to be reduced to an extremely thin gage (0.0005\") Provided that the frequency is not too high, this material can be used in the form of tape cores, laminations an also cut cores. The advantages and disadvantages of Si-Fe and Co-Fe are given in Table 2.5. The compara ble listings for Ni-Fe are given in Table 2.6. One general advantage of the metallic strip cores is that they can handle higher power levels than the ferrite cores. Aside from their higher saturations, their higher thermal conductivities allow them to dissipate heat more efficiently. 206o-AMORPHOUS METAL STRIP CORES A newer line of metal strip materials other than those described in the previous section are the amorphous metal alloys. The iron-based alloys have the high saturation for use as power transformers. Their resistivities are higher 36 MAGNETIC COMPONENTS FOR POWER ELECTRONICS than the crystalline magnetic alloys and they can be annealed for either low frequency or higher frequency operation. However, they are magnetostrictive and are only used at lower frequencies. The Co-based materials have almost zero magnetostriction which gives them a high permeability and lower losses. The advantages and disadvantages of the amorphous materials are given in Table 2.7. In Figure 3.34 are shown the real and imaginary values of the com plex permeability. Roess gives one advantage of ferrites over the amorphous materials in that they can only be produced in toroidal tape-wound cores. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 37 2.7. -NANOCRYSTALLINE-BASED POWER TRANSFORMERS The newest of the soft magnetic strip power materials are the nano crystalline. These materials were developed as an extension of the amorphous metal materials and are made by a similar process except that the material is annealed to produce a very fine grain size on the order of 10 nanometers. The iron based material has high saturation and permeability. The latter is due to almost zero magnetostriction similar to the Co-based amorphous alloys 2.8-COST CONSIDERATION FOR MAGNETIC COMPONENTS Aside from the technical performance of the magnetic component, some consideration must be given to the comparative cost of the component. The final cost is determined by several factors; 1. Cost of raw materials 2. Cost of core fabrication 3. Cost of winding Some of the advantages of a ferrite core are the low raw material and fabrication costs. Thin gage metals (SiFe, amorphous and nanocrystalline) have relatively high fabrication costs. For winding costs, toroids are the most 38 MAGNETIC COMPONENTS FOR POWER ELECTRONICS expensive, then pot cores and finally, E-cores. Figure 2.1 gives the trans former cost utility in maxwells per dollar as a function of frequency. The pre dominance of ferrites especially at higher frequencies is evident. 2.9-COMPETITIVE HIGH FREQUENCY POWER MATERIALS Roess( 1987) has recently emphasized that a great virtue of ferrite power material is their adaptability, and even at higher power frequencies. He compares the losses of several competing power materials for the higher fre quency operation. Trafoperm is a NiFe strip material. Vitrovac is an amor phous metal strip material and Siferrit is of course, a ferrite. The results are given in Figure 2.2 . Up to 100 KHz., the amorphous metal materials have lower losses than the ferrite especially the thinner gage type which remains lowest even at the higher frequencies. Roess points out that despite this disad vantage, a ferrite core is still the magnetic component of choice because of its much lower cost and its adaptability to be produced in many different shapes. The strip, on the other hand, has limitations on the shapes in which it can formed as shown in Figure 2.3. The new nanocrystalline materials were de veloped after this study. A new fine-grained rapidly solidified nanocrystalline (not amorphous) strip material was introduced by Hitachi Ltd. It has much higher saturation (13,500 Gausses), higher permeability (16,000 at 100 KHz.) than ferrites and very low losses at 100KHz. Although these properties compare favorably to ferrites, it remains to be seen if the price and performance will allow it to compete with ferrites. In addition, the nanocrystalline cores have the same lack of fabrication versatility as other strip-wound cores 2.10-DESIGN CONSIDERATIONS IN COMPONENT CHOICE Aside from the items previously mentioned in choosing a mag netic component for power electronics, there are additional considerations based on the other design requirements. These include; 1. Space, Volume and Weight Restrictions 2. Ambient Temperature-Heat removal 3. Environmental-Corrosion, Radiation, Vibration and Shock 4. Reliability-Lifetime 5. Regulation- Voltage variation 6. Safety considerations CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 39 2.11- FERRITES VS METALLIC MAGNETIC MATERIALS There have been many comparisons of ferrites with other magnetic materials for power applications. The author (Goldman 1984) listed other metallic materials that were used for SMPS's. Goldman (1995) compared metal strip, powder cores and ferrites for various applications including power. Bosley (1994) presented a rather extensive study of the different mate rials for transformers and inductors versus frequency where the maximum flux was limited by saturation or core losses. The useable flux density under these limitations is given in Figure 2.4. For frequencies above 100 KHz., the MnZn and NiZn ferrites had the highest values. The performance factor in 40 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Tesla-hertz vs frequency is shown in a figure in next chapter. Here again, above 100 KHz., the two ferrites were the highest. The economic trade-off for these materials is given in Figure 2.1 which charts the maxwells of flux per dollar as a function of frequency for the competing materials. Bosley (1994) also listed the advantages and disadvantages of the competing materials for SMPS transformers. Table 2.5 show these for SiFe and Permendur, Table 2.6 for the NiFe alloys, Table 2.7 for the amorphous alloys and Table 2.4 for fer rites. Snelling C 1996) presents a plot of the power loss density of power fer rite, Co-Fe amorphous metal strip and the Vitrovac 6030 nanocrystalline ma terial vs frequency in figure in next chapter. The relative advantages in core loss depend on the frequency and flux density. The previous comparisons did not include the nanocrystalline materials that gained recognition shortly after the Bosley article even though Y oshizawa (1988) reported on them earlier. The frequency dependence of the permeability and loss factor of a nanocrys talline material was compared (Herzer 1997)along with those for a Co-based amorphous material and a MnZn ferrite. The permeability is higher and the loss factor is lowest for the nanocrystalline material. In addition the saturation induction was measured for the same materials (Herzer 1997). The nano crystalline material has the advantage there. It remains to be seen whether the pricing of the nanocrystalline can be low enough to compete with the rela tively inexpensive ferrite materials. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 41 2.12-0UTPUT POWER INDUCTORS Power Inductors differ from the low-level inductors that we have dealt with in telecommunication applications. They are not used in LC circuits for frequency control. In power inductors, use is made of their ability to store large amounts of power in their magnetic field. As such, they can limit the amount of ac voltage and current. When this is done in the presence of a high D.C. current, the inductor, usually in combination with a capacitor, serves as a smoothing choke to remove the ac ripple in a D.C. supply. This is often done in the output circuit ofthe supply after rectification. Since there are large D.C. and smaller superimposed a.c. currents, they usually need gaps to prevent saturation. In addition to the increase in current and possible catastrophic fail ure at saturation, the incremental permeability drops close to zero and there fore, the required inductance specification is not met. With the gap, the mag netization curve is skewed to avoid saturation (See Figure 4.11). With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for energy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10 , In some power inductor applications, as in the common mode choke, the magnetic core must sense the small difference between 2 magnetic cur rents and a high permeability toroid or ungapped shape must be employed. In some other of these inductor functions, the full power of the circuit passes through the magnetic component and some feature must be added to keep the core from saturating. The same is true for some energy-storage functions where a high DC current is present. In these two cases, either a core with a discreet gap (ferrite E core) or a distributed gap toroid (iron powder core) is warranted. 2.12.I-Ferrite vs Metallic Powder Inductors Earlier in this chapter, we compared ferrite power transformer materi als with their counterparts in metallic materials. For ferrite power inductors, the materials are mostly the same as the transformer materials. However in the case for metallic materials, the materials for power inductors are different than those used for power transformers. Whereas gapped ferrite cores are used for many power inductor applications, in the case of the metallic cores, the gap is a distributed one as found in powder cores. Bosley (1994) who did the analysis on SMPS transformer materials compared the materials for SMPS inductors in the same paper. The materials evaluated were; 42 MAGNETIC COMPONENTS FOR POWER ELECTRONICS I.NiFe Powder Cores- Molypermalloy and Hi_Flux Cores 2.Sendust Powder Cores- Kool-Mu and MSS cores 3.Amorphous Choke Cores 4.Powdered Iron Cores 5.Gapped Ferrite Cores 6, Metal Strip Cut Cores Some of these materials were used for low level telecommunications applica tions. For power applications at high power levels, the materials may be somewhat different. Bosley (1994) listed the advantages and disadvantages of the above mentioned materials for power inductor applications. Table 2.8 lists these for NiFe powder cores, Table 2.9 for Sendust (FeAISi) powder cores. Table 2.10 for amorphous metal choke cores, Table 2.11 for powdered iron cores, Table 2.12 for gapped ferrite cores and Table 2.13 for cut cores. Since power inductor often must operate under high D.C. bias conditions, the effec tive permeability for these materials are given. The DC bias curves for several of these materials are shown in Figure 2.5. Again, the nanocrystalline materi als were not considered. Bosley also listed the core losses of the various in ductor materials compared to ferrites in Table 2.14. Although the ferrites are lower in losses than the others listed. Bosley notes that, with a medium to large gap, there may be increased losses due to fringing flux This may in crease ac copper losses near the gap. Nanocrystalline materials were not con sidered here as well. CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 43 44 MAGNETIC COMPONENTS FOR POWER ELECTRONICS CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 45 Pauly (1996) reviewed the selection of a high-frequency core material for power line filters. He compared various powder core materials and gapped ferrites with respect to volume, sound level and cost. All cores were 1.84 inch toroids except the gapped ferrite which wa a gapped EC70/70G . The induc tors were 4.0 mHo Ripple current was a 40 KHz. triangular Wave with peak to-peak level of 33% of rated current. Output power was theoretical. Table 2.15 summarizes the results. The losses of the MPP, MSS (Sendust) and Hi Flux cores were much lower than that of the powdered iron but the cost was dramatically lower. Best performance was found in the MPP cores. Table 2.16 is the author's opinion in the ranking of the cores as to the suitability of the various cores for a given application. In general smaller cores may be oper ated at higher frequencies and flux levels. 46 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2.13- POWER FACTOR CORRECTION CORES In some new ac input lines for switching power supplies, a \"front end\" boost pre-regulator is used to obtain an essentially Unity Power Factor or UPF. The circuit for this function is shown in Figure 2.6. An external logic circuit serves to control the duty cycle of the main switch, Q 1 to raise the in put voltage, Vi to the output voltage, Vo. Higher peak ac flux densities are present than in conventional output chokes so core losses are quite important here. If the wrong core or material is used, core losses will increase and the possibility of thermal failure may occur. As in the case of the output choke, the materials used are the various types of powder cores (iron, molyperm, high flux NiFe, Sendust) or a gapped ferrite. However, special considerations of the losses must be taken into account with iron powder cores so that larger cores and lower loss materials must be used. A_C. IIIVT + Cl \u2022 D.C. CIlITM Fgure 2.6- A front-end boost preregulator for Power Factor Correction (PFC), (From B. Car sten, Application Note, Micrometals (2001) 2.14 -MAGNETIC AMPLIFIER CORES In cases of multiple outputs in switching power supplies, their may be an imbalance in the output voltages. In cases where the regulation must be controlled very precisely, one solution is the use of a magnetic amplifier CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 47 regulator circuit. The circuit for a forward converter with a 5V and 12V. ou put is given in Figure 2.7 . The 5V output uses PWM feedback circuitry to regulate. The 12 V output uses the magnetic amplifier or saturable-core reac tor to regulate. The materials used for the mag amp must have high square ness or B/Bs ratios, low coercive force for small reset current and low core loss for small temperature rise. Components for this function are Square-loop NiFe tape cores, Co-based amorphous metal cores and square loop ferrite toroids. We have considered the use of square loop ferrites previously in conjunction with the ferroresonant transformer design. The advantages and disadvantages of the square permalloy are shown in Table 1.17.Those of the cobalt-based amorphous metal material are given in Table 1.18 and the corresponding ones for the square-loop ferrite are given in Table 1.19. 48 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2.tS-PULSE TRANSFORMERS There are instances when the transistor switch supplying the square wave is triggered or fired by an external source or pulse generator. Ferrite cores, especially small toroids, are widely used in pulse transformers. This application requires transmission of a square wave with little distortion. The shape of a typical square wave voltage pulse is shown in Figure 2.8. During the time that the voltage pulse is on, the current is ramping up as is the flux CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 49 density. In the case of a square wave, the ~B is given in terms of the applied voltage, E, and the pulse width, T. For a specific core area and number of turns, the equation is; B = ET xI0-8/NAe [2.5] From the value of ~B , the corresponding value of H, the magnetizing field can be determined from the vendor's curves on the material properties. From this value of H, and the Ie of the trial core, the excitation current can be deter mined from; H =.4 nNIp//e [2.6] IfE, T, N are given and a AB is assumed, the effective dimensions of the core can then be given as; IJAe = O.4nN\\ m x1081ET~H [2.7] The cores corresponding to various values of IJAe are listed by the vendor. The pulse permeability is given by; ~p = ETlIp [2.8] The pulse transformers used in digital data processing circuits will usually have ~B's on the order of 100 Gausses and are always little toroids inserted in small TO-5 cans for use on PC boards. Higher power pulse transformers may use pot cores or E cores that may be gapped to prevent saturation. All of the frequency related problems encountered in wide-band transformers are pres ent in the pulse transformer, but here, it is evidenced by pulse attenuation (droop). As in the previous case, the permeability should be as high as possi ble, but when high pulse repetition rates or fast rise times are used, perme ability concerns may be compromised for lower losses. Permeabilities of about 5-7000 are frequently used for small ferrite toroids. 2.16-COMPONENTS FOR EMI SUPPRESSION Before our discussion of the actual components used for EMI sup pression, it is useful to look at the circuitry involved along with the currents both intentional and unintentional. The latter, of course are the EM! interfer ence or noise currents. Basically, there are two types of EMI currents, namely the common-mode and the differential currents. These are contained in a pair of wires leading to and from the load. The first of these is the differential cur- 50 MAGNETIC COMPONENTS FOR POWER ELECTRONICS rents whose current flow is the same as in ordinary intended or designed cir cuitry as shown in Figure 2.9. The differential EMI currents then flow in the same direction as the intended currents. If a current probe is placed around the pair of conductors, no current flow will be detected for either the intentional or unintentional (EMI) currents. In the case of the common-mode EMI cur rents, they flow in the same direction in both conductors. Now, while the dif ferential intended currents will cancel, the non-intentional (EMI) currents will not and there will be a current indicated with a probe. Another way of de scribing the two types of current flow is shown in Figure 2.9 that shows the voltages producing the currents. In the differential case, the voltage is be tween the high voltage line and the neutral line while in the common-mode case, it is the voltage between both the high voltage and neutral lines to ground. The components for EMI suppression extend from very small beads to rather large cable clamp cores. Some and even slug-type cores toroids are used in the coil type of suppressor 2.16.1-Materials For EMI Suppression Until recently, the materials available for EMI suppression applica tions essentially were of two types. The most widely were and still are soft ferrites and the other less widely used one would be powder cores. Recently, amorphous and nanocrystalline cores have been used for the same purpose. Although sometimes the principal operational frequency of the circuit may be quite low (line or mains frequency, 50-60 Hertz), it is not primarily that fre quency which is designed for in EMI suppression. It is rather the interference or disturbance frequency that mostly determines the choice of material used although the effect of the lower frequency (DC) must be dealt with in the de sign of the EMI filter. This interference frequency frequency can be high fre quency ac or square or other digital waveform in the high Kilohertz or Mega hertz region. The secondary consideration would be the operational frequency in that the material must pass the lower frequency with sufficient inductance. This means that, at low frequencies, the material must behave as a fairly good inductor but at high frequencies, it must be quite lossy. The frequencies in volved in this application preclude any of the conventional metallic strip ma terials. Other possible new materials which will be listed later are the High Flux NiFe powder cores and the Sendust (Fe-AI-Si) powder cores. 2.16.2-Amorphous-Nanocrystalline Materials- EMI Suppression One of the earliest uses of the amorphous material was for a choke coil that Toshiba called the \"Spike-killer\". Presumably, only the cores are sold. The Fe-based amorphous materials used are under license from Allied's CONSIDERATIONS IN MAGNETIC COMPONENT CHOICE 51 l Metglas\u00ae Division (now Honeywell) . Vacuumschmelze does market a Cobased amorphous materials for EMI suppression applications. It is designated Vitrovac 6025 and is essentially a zero magnetostriction material. As an out growth of the amorphous materials, the iron-based nanocrystalline materials are the newest ones available and they have been used for EMI suppression. Their high permeabilities and low magnetostrictions made it very useful as a" ] }, { "image_filename": "designv10_13_0001896_bf00975058-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001896_bf00975058-Figure2-1.png", "caption": "Figure 2 Laser processing apparatus.", "texts": [ " In laser surface alloying, alloying elements, to be introudced into the melted layer, were in the form of thin foils with a thickness of 0.127 mm placed on the surface of the specimen. A GTE Sylvania Model 975 CO2 gas transport laser, which provides a nominal output power of 5 kW continuous infrared radiation at a wavelength of 10.6 I~m, was used. The beam diameter at the laser exit aperture is 45.7 mm and can be focused down to 0.5 mm through a focusing lens. The laser processing apparatus is shown in Fig. 2. The specimen is mounted on a rotating table, swept through the beam focused on the specimen surface. Approximately 2 c m 2 laser-melted or alloyed surfaces were obtained with an overlap of 50%. Following the laser processing, specimens were cut parallel to the laser beam raster direction. With suitable polishing and etching, melt depth and width as well as gross microstructural characterization were made through optical microscopy. A Vickers microhardness test was used to determine the hardness increments in laser surface melted and alloyed samples" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002590_0020-7403(80)90009-0-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002590_0020-7403(80)90009-0-Figure4-1.png", "caption": "FIG. 4. Equil ibrium shapes for the same F = - 10.0120706, M0 = 2\u00a2r. The left shape is unstable.", "texts": [ " 3 shows the force as a funct ion of dis tance a for various initial curvature M0. These curves are ext remely nonlinear in general. Infinite force is needed to straighten (a = 1) an initially curved spring except for the initially straight spring which requires a negative force (F<_ F , = - 2 . 4 6 7 4 0 1 ) to buckle it. Of interest are the force-dis tance curves for M0 > 1.6115\u00a2r where there exist local minimums. On these curves a given force cor responds theoretically to two equilibrium states. Only the state with the positive slope is stable dynamically. Fig. 4 shows the two different s tates for the same F = - 10.01257 and M0 = 2\u00a2r. Fig. 5 shows the m a x i m u m momen t M which occurs at x = 0. M increases to M0 as a increases to 1. M0 = 0 cor responds to the initially straight spring. As a ~ 0 the spring is bent, but not into a semicircle. Note that the upper two curves (M0 = 1.75~-, 2\u00a2r) exhibit the same discontinuity (tend to infinitely) for small a as the force-dis tance curve. The asympto tes are a* = 0.18427 for M0 = 2~r and a* =0.076707 for M0 = 1-75~r" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003862_1350650112441747-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003862_1350650112441747-Figure2-1.png", "caption": "Figure 2. Contact deformation of the jth roller.", "texts": [ " Thereinto, the line OCj 0 was also the normal of the contact point between the roller and the outer raceway. However, in the coordinate system on the inner ring, the roller position angle that was the included angle between the x0-axis and the line O0Cj 0 was changed to j 0. Similarly, the line O0Cj 0 was also the normal of the contact point between the roller and the inner raceway. Among the angles j and j 0, there was a D-value that equaled the included angle between OCj 0 and O0Cj 0. A magnified sketch of a deformed roller is given in Figure 2 to introduce the shift of roller center. The notation oj in Figure 2 was the roller deformation due to the contact force Qoj between the roller and the outer raceway. However, the roller deformation due to the contact force Qij between the roller and the inner raceway did not affect the shift of the roller center. Thus, the center of the roller displaced from Cj to Cj 0 by oj. It was explicit that Qij and Qoj were not collinear and there was an included angle among them. Thus, their relationship can be expressed as equation (2). However, forces on the roller cannot be in equilibrium in the strict sense" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002131_j.finel.2004.04.007-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002131_j.finel.2004.04.007-Figure1-1.png", "caption": "Fig. 1. Conceptual model of backlash control with conical involute gears.", "texts": [ " This approach yields a dense FE mesh in the contact regions and a coarse mesh in the rest of the teeth. 2004 Elsevier B.V. All rights reserved. Keywords: Conical involute gear; Anti-backlash; Finite element; Global\u2013local; Transmission error Backlash between meshing gear teeth can cause impacts, reduce system stability and generate noise and undesired vibrations in mechatronic products such as industrial robots. Conical involute gears can eliminate or reduce backlash between gear teeth and are frequently used in anti-backlash gear transmissions (see Fig. 1). The conical involute gear, which is also known as the beveloid gear, was introduced by Merrit [1] and is an involute gear with tapered tooth thickness, a tapered root and, in most cases, a tapered outer diameter. Mitome, [2,3], conducted both analytical and experimental investigations of the effect of mounting errors and backlash on the motion and the transmission error between two conical involute gears with intersecting axes. Liu and Tsay [4] used tooth contact analysis to examine the transmission error of \u2217 Tel" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003293_978-90-481-9262-5_33-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003293_978-90-481-9262-5_33-Figure1-1.png", "caption": "Fig. 1 22-CDPR: (a) general model; (b) equilibrium configurations for the case a2 = (10, 0,\u22122), b1 = (\u22120.5, 0,\u22120.5), b2 = (3, 0, 0), and \u03c11 = \u03c12 = 7.", "texts": [ " platform posture coordinates or cable lengths) are given. The problem of equilibrium stability is formulated as a constrained optimization problem, and a purely algebraic method, which rules out the need of differentiation, is provided. The geometrico-static study of a general 33-CDPR is outlined as an application example. Let a mobile platform be connected to a fixed base by n cables, with 2 \u2264 n \u2264 5. Ai and Bi are, respectively, the anchor points of the ith cable on the frame and the platform, and si = Bi \u2212 Ai (Fig. 1(a)). The set C of theoretical geometrical constraints imposed on the platform comprises the relations |si | = \u221a si \u00b7 si = \u03c1i, i = 1 . . . n, (1) where \u03c1i is the length of the ith-cable, which is assumed, for apparent practical reasons, strictly positive (so that, as a consequence, Bi \u2261 Ai). Since only n geometrical constraints are enforced, the platform preserves 6 \u2212 n degrees of freedom, with its posture being determined by equilibrium laws. If Q$e, with Q > 0, is an arbitrary external wrench acting on the platform (including inertia forces, in the case of dynamic conditions) and (\u03c4i/\u03c1i) $i is the force exerted by the ith cable ($e and $i/\u03c1i are assumed to be unit screws), then n \u2211 i=1 \u03c4i \u03c1i $i + Q$e = 0, (2) with \u03c4i \u2265 0, i = 1 ", " if the rank loss is \u2018concentrated\u2019 among the set of screws associated with the cable lines. In this case, the rank of the block1 M1...6,1...n is at most equal to n \u2212 1 and Eq. (2) may be satisfied only if rank(M) \u2264 n \u2212 1. Cases like the one described here, however, are sufficiently unlikely to occur not to be, in practice, of particular concern. Nonetheless, a check of the rank of M1...6,1...n is advisable before attempting to solve for cable tensions. Throughout the text, the following notation is adopted (Fig. 1(a)). Oxyz is a Cartesian coordinate frame fixed to the base, with i, j and k being unit vectors along the coordinate axes. Gx \u2032y \u2032z\u2032 is a Cartesian frame attached to the platform. e is a unit vector directed as $e, x = G \u2212 O , ai = Ai \u2212 O , ri = Bi \u2212 G, si = Bi \u2212 Ai = x + ri \u2212 ai , ui = (Ai \u2212 Bi)/\u03c1i = \u2212si/\u03c1i and rij = ri \u2212 rj , with i, j = 1 . . . n, i = j . Without loss of generality, O is chosen to coincide with A1 (so that a1 = 0) and k = e. If bi is the projection of Bi \u2212 G on Gx \u2032y \u2032z\u2032, is the array grouping the variables parameterizing the platform orientation with respect to the fixed frame and R( ) is the corresponding rotation matrix, then ri = R ( ) bi ", " If g is the frontier of this region, the equilibrium is stable any time the potential energy U associated with the external force Q$e, namely \u2212Qe \u00b7x, is at a minimum on g. Loosely speaking, the platform is at rest in all points G\u0304 of g in which the variety tangent to g is perpendicular to e, with the equilibrium being stable if and only if a neighborhood WG\u0304 of G\u0304 exists such that (P \u2212 G\u0304) \u00b7 e < 0, for all P \u2208 (g \u2229 WG\u0304). In such a condition, when the platform displaces under the effect of a perturbation, the original configuration is restored if the perturbation ceases. Figure 1(b) helps to depict this concept. The figure shows the locus g of the positions that G may assume for an exemplifying 22-CDPR, under the constraints (1) and with m = n = 2. If the platform is thought of as the coupler of a four-bar linkage whose grounded links are the cables (with assigned lengths), g is the coupler curve of G, namely a bicursal sextic. The stationary configurations of G are the points of g in which the tangent line is perpendicular to e, with U being at a minimum in G\u03042 and G\u03044", " sT m (rm \u00d7 sm)T \u23a4 \u23a5 \u23a6 [ \u03b4x \u03b4 ] = 0, (18) where the ith row of Jp coincides with $i , expressed in axis coordinates and assuming G as the moment pole. Jp is the pseudo-Jacobian of the constraint equations. If Np is any 6 \u00d7 (6 \u2212 m) matrix whose columns generate the null space of Jp, the reduced Hessian of C is the following (6 \u2212 m) \u00d7 (6 \u2212 m) matrix: Hr = NT p HpNp. (19) A sufficient condition for the equilibrium to be stable consists in Hr being positive definite. If the method described above is applied to the example portrayed in Fig. 1(b), results that agree with those expected are obtained. The equilibrium configurations 315 M. Carricato and J.-P. Merlet are the real solutions of the DGP of the robot,3 i.e. G\u03041 = (1.94,\u22126.43), G\u03042 = (5.98,\u22122.89), G\u03043 = (6.31,\u22120.42) and G\u03044 = (4.18, 6.07). Since the problem is planar, Hp and Jp are, respectively, 3 \u00d7 3 and 2 \u00d7 3 matrices, so that the reduced Hessian is a scalar. Hr is positive in G\u03042 and G\u03044 and negative in G\u03041 and G\u03043, namely Hr |G\u03041 = \u221229589, Hr |G\u03042 = 18709, Hr |G\u03043 = \u221222875, Hr |G\u03044 = 61650" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure2-1.png", "caption": "Fig. 2. Complete tooth surface.", "texts": [ " In (4) the vector f \u00bc \u00f0n; h; /\u00de containing the triplet of coordinates n; h; / has been defined. The envelope surface Cg is then obtained as the solution of sg \u00bc pg\u00f0f\u00de; fm\u00f0f\u00de \u00bc 0: \u00f05\u00de In Section 5, we will employ a surface intersection procedure and, since we seek for a closed shape intersection curve, we need to define the complete tooth surface including the lateral surfaces. These surfaces are portions of the blank cones and are bounded by the intersection between the tooth active flanks and the blank surface. Fig. 2 shows the complete tooth surface2 C which is subdivided into five patches. The patches Ct; Cf and Cb are the topland, the front cone and the back cone surface respectively. The two flank surfaces are identified by Cv and Cx for the concave and convex side. We define a unique tooth parametrization and we map C onto a plane as shown in Fig. 3. We have divided Cf and Cb into three parts each for convenience, in order to obtain a 3 3 patch grid. We remark that the complete tooth surface has C0 continuity over the intersection curves between the active flanks and the lateral surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002047_robot.1993.291873-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002047_robot.1993.291873-Figure2-1.png", "caption": "Figure 2: The two link manipulator at the end points of the specified path.", "texts": [ " Iterate on Ssb \u20ac [ S h , s] from the backward trajectory and integrate backward 's,in until the trajectory is tangent to the minimum acceleration curve at some point S t b . Set s = S t b and repeat Step 2. 0 Step 3: Integrate the intermediate trajectory Iterate on scf E [so,s,] from the forward trajectory and integrate forward 8,in until the trajectory crosses the backward trajectory at some point S c b , and Scb satisfies the continuity condition. 5 Example The following example demonstrates the algorithm for a two link planar manipulator moving along the 2: Kt=5N-m/A I R=lOQ I L=2H I V,,,=lOV path shown in Figure 2. The parameters of the manipulator are given in Table l. The motor parameters given in Table 2 were selected to exaggerate the effect of motor dynamics. In particular, the motor inductance is an order of magnitude higher than the actual values for some high torque Direct Drive motors [3]. This extends the electrical time constant with respect to the total motion time, making the effects of motor dynamics more noticeable for motions along reasonably long paths. The resulting optimal trajectory is shown in Figure 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002062_6.2003-5520-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002062_6.2003-5520-Figure1-1.png", "caption": "Figure 1: The Quad-Rotor UAV", "texts": [ " The nonlinear simulation results proving the robustness and the satisfactory of the combined MBPC/H\u221e controller architecture are presented in Section 7 followed by conclusions in Section 8. The UAV used in the project is a commercial four-rotor helicopter, Draganflyer III, currently with a 3 min flying time but extensible to 1 hour by adequate sizing of the power source and actuators. Quad-rotor helicopters using the variant rotor speeds to change the lift forces are dynamically unstable and therefore a control law is permanently required to ensure their stability. Motions of the quad-rotor helicopter can be briefly described in Figure 1. The vertical motions along z-axis in the body-fixed frame can be obtained by changing the speeds of all the four rotors simultaneously. The forward motions along x-axis in the body-fixed frame can be achieved by changing the speeds of rotor 1 and 3 reversely and retaining the speeds of rotor 2 and 4. The lateral motions along y-axis in the bodyfixed frame can be reached by changing the speeds of rotor 2 and 4 reversely and retaining the speeds of rotor 1 and 3. The yaw motions are related to the difference between the moments created by the rotors" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003182_pssb.2220640137-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003182_pssb.2220640137-Figure2-1.png", "caption": "Fig. 2. Equi-displacement contour plot of up in units of b for a prismatic dislocation loop lying in the (111) plane of copper", "texts": [ " 1 and 2 show equi-displacement contour plots of the displacement components uz and u,, respectively, in units of the magnitude of the Burgers vector for a pure edge prismatic dislocation loop of vacancy type lying in the (1 11) plane of copper. The loop is located in the plane x = 0 and the plane of drawing is the (110) plane. Compared to similar plots for an isotropic crystal, the contour lines for a given displacement extend considerably further from the loop. Consequently, the magnitude of the displacement a t any given point is greater in copper than that predicted in the isotropic crystal. An interesting feature shown in Fig. 2 is that in a region outside the loop near the loop plane the displacement component u, has reversed its direction relative to the rest of the crystal. That is, the region has expanded somewhat while the rest of the crystal has collapsed Displacement Field of a Dislocation Loop in Anisotropic Cubic Crystals 321 Pig. 1. Equi-displacement contour plot of uz in units of b for a prismatic dislocation loop lying in the (1 11) plane of copper to form the vacancy type loop. The displacement component uy vanishes in the (110) plane of the drawing because of crystal symmetry" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003491_20120905-3-hr-2030.00031-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003491_20120905-3-hr-2030.00031-Figure3-1.png", "caption": "Fig. 3. Comparison between the direction of rotation of the propellers in a standard quadrotor model Fig. 3(a) and in the modified version Fig. 3(b).", "texts": [ " 1, where a scheme of the proposed quadrotor is reported. As it can be seen, an actuated rotational (pivot) joint ri is installed on each arm of the vehicle, thus allowing to rotate the corresponding propeller by the angle \u03b1i. In this manner, the force Pi generated by the propeller may be directed along any direction in a plane orthogonal to the corresponding arm (the plane \u03c0i in Fig. 2). Another difference with respect to a standard quadrotor is the rotating direction of the thrusters. In fact, as shown in Fig. 3(a), in a standard quadrotor the couple of propellers {1, 3} rotates clockwise, while propellers {2, 4} rotate counter-clockwise. This configuration ensures that, in hovering maneuvers, it is always possible to rotate the quadrotor about its z-axis by slowing down opposite propellers, but preserving the balance of the counteracting torques. In our case, as depicted in Fig. 3(b), we consider as rotating in the same direction the thrusters positioned at the opposite side of the quadrotor, e.g {1, 4} rotate clockwise and {2, 3} rotate counterclockwise. This choice is motivated by the goal of increasing the maneuverability of the quadrotor with respect to classic models. In particular, considering the case that a rotation along the z-axis is required, the non compensated counteracting torques generated by the motors can be easily compensated by properly rotating the pivot motors" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003330_1.3197142-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003330_1.3197142-Figure10-1.png", "caption": "Fig. 10 Geometry of sandwich", "texts": [ " A nonzero solution for w\u0302 and \u0302 for zero p\u0302 and t\u0302 requires solving the eigenvalue problem, setting the determinant of the stiffness matrix to zero. The condition for buckling becomes GAs 2EI \u2212 P GAs + 2EI = 0 17 Accounting for Eq. 2 , it can be rewritten as PPb + PPs \u2212 PbPs = 0 18 which is similar to Eq. 3 in the derivation by Timoshenko and Gere. Solution Eq. 5 again applies, here alternatively written as 1 Pcr = 1 Pb + 1 Ps 19 As could be expected, the classic result of Engesser is obtained. 4.3 Sandwich Column. Figure 10 shows the composition of a sandwich column and its position with respect to the x- and z-axis. We do not restrict the derivation to thin-faced sandwiches and start from a general thick-faced sandwich, which may be nonsymmetric. The face material is fully linear-elastic with modulus of elasticity E. The two layers are numbered 1 and 2, which numbers will be used as subscripts to quantities related to the face cross sections. The thicknesses are t1 and t2, the areas are A1 and A2, and the second-order moments are I1 and I2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001393_1350650011541783-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001393_1350650011541783-Figure8-1.png", "caption": "Fig. 8 Measurement of the frictional torque of the bearing", "texts": [ " The motor provides rotating power through the coupling and rotating spindle to drive the test bearing. By means of the nozzle shown in Fig. 7, the oil\u2013air stream will enter the lubrication point of the test bearing at a high speed. The positions and number of nozzles can be changed for the tests. A loading mechanism consisting of a regulating screw, disc springs and a load cell is used to impose a preload on the test bearing. The preload can be adjusted by rotating the regulating screw. The magnitude of the preload is measured using the load cell. Figure 8 illustrates the measuring mechanism for the frictional torque in this test rig. As the test bearing runs, the load cell receives a frictional force from the test bearing. The product of the frictional force and the distance between the centre of the outer bearing seat and the measuring point of load cell is the frictional torque. A data acquisition system is established to receive and store measurement data including the temperature, preload and frictional torque. Table 3 shows the specifications of the ball-bearing used in the tests" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002340_bfb0042512-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002340_bfb0042512-Figure2-1.png", "caption": "Figure 2: The Impact Event", "texts": [ "1: it preserves the disparity in degrees of freedom between them but abstracts away most of the dynamical complications introduced by spin, collision, and friction. Section 2.2.2 presents a greatly simplified account of the manner in which collisions between the robot and environment affect their behavior. Locate a frame of reference, 5%, at the center of the robot shaft, with x-axis perpendicular to the plane, and z-axis defined by the projection of a vertical ray pointed directly into the earth's gravitational field onto the plane, as depicted in Figure 2. Define r so that it measures the angle of the right hand portion of the robot's bar (with the hitting surface - - the billiard cushion - - facing up) away fi'om the x-axis on the juggling plane. The configuration space of the entire problem is the cross product, C ~ 13 \u00d7 T~, of the body and the robot configurations. We will represent the location of the falling body on the plane B = ]R 2 with the coordinates (bl,b~) denoting, respectively, the position of its centroid relative to the \"horizontal\" (y) and \"vertical\" (z) axes of the reference frame, 9%", " Thus, denoting the \"body angle\" by, 0(bl,b~) =~ ata,~(bdb,), (3) it is clear that Z is the graph of 0 in C. That is to say, 2\" is simply the image of the map = 0 ) ' or, alternatively, the zero level set of the map ~(b, r) --\" r - O(b). [3 An impact configuration, (r, b) E 2\", implicitly defines the robot's \"virtual gripper\" - - the point of contact on the billiard cushion - - and it is useful to define a new \"virtual gripper frame,\" ~-1 whose origin is in the body's center, b, whose x-axis is parallel to that of ~0, but whose y-axis is aligned with the robot bar, all depicted in Figure 2. The new frame has a representation with respect to the \"base frame\" given (in two dimensional homogeneous coordinates) by \u00b0~'1 = 1 ; R = sinr cosr \" 43 We now develop a simplified model of the dynamics of repeated puck-robot impacts based upon the following assumptions. First, we assume here that all interactions between ball and robot during impact can be modeled as an instantaneous evenS: 5. posteriori velocities are related to b. priori velocities via a simple \"coefficient of restitution,\" a E (0, 1) [17]", " More formally, within the puck-robot phase space, X ~ T C = W x V , consider the set of all possible velocities at each impact configuration, T'C U (5) (b,,,)ez The first assumption amounts to the hypothesis of a \"collision map,\" c : TzC ~ TzC which takes an 5. priori phase at contact, x E TzC, into a new phase, z ' =- c(x) E TzC, in the same contact configuration - - in coordinates, (b', r ') = (b, r). The second assumption may be expressed in coordinates as the hypothesis that \u00f7' = \u00f7. It is left to describe a map b' = Consider, first, the simplified case shown in Figure 2. The k posteriori velocity of the body after impact, b' is related to the 5. priori velocity of the body b, and that of the robot's gripper, ~: as b' =- - a b + (1 + a)\u00f7. (6) In the full model the velocity of the revolute robot's virtual gripper is u2 ~ I[bl[ \u2022 \u00f7 and will be considered in the subsequent section a robot control input. Let us now further assume that the puck's velocity componcnt parallel to the robot bar is unchanged by the impact. Then the h. posteriori velocity of the two degree of freedom body after impact, b', is related to the ~ priori velocity of the body, b, and that of the robot's virtual gripper, in the ", " Probably the simplest systematic behavior of this environment imaginable (after the rest position), is a periodic vertical motion of the puck in its plane. Specifically, we want to be able to specify an arbitrary \"apex\" point, and from aa'bitrary initial puck conditions, force the puck to attain a periodic trajectory which impacts at zero position and passes through that apex point. This corresponds exactly to the choice of an appropriate fixed point, w*, of (11). To see this, consider first the one degree of freedom environment, B = IR as depicted in Figure 2. Selecting w* = (b*, b*) as the desired constant set point indicates that we wan.t the impact to occur at tl~e poditlon b\" and with the velocity just before impact given by b*. If w* is truly a fixed point of the closed loop dynamics, then the velocity just after impact must be -b*, and this \"escape velocity\" leads to a free flight puck trajectory whose apex occurs at the height b~p~ = b* + ~ , assuming the simple ballistic model of free flight with no friction (2). Thus, a constant w* \"encodes\" a periodic puck trajectory which passes forever through a specified apex point, b~p,~", " First, we \"reflect\" the desired periodic puck trajectory in W into a \"distorted mirror image\" in 12: the \"distortion\" is so designed that the \"cross product\" trajectory of the puck and robot reflection in X = ]4' \u00d7 12 intersects the impact set, TIC, with characteristic tangent vectors, (6, \u00f7), whose image under the collision map, e (8), is \"favorable\" to the task at hand. Second, we borrow from Raibert [14, 3] the idea of modifying the robot's trajectory by \"servoing\" on the discrepancy between the (constant) total mechanical energy of the puck in its desired steady state, and the currently measured value. To better convey the nature of the new algorithm, we will first discuss the one degree of freedom case (Figure 2). Let the puck drop fi'om the desired steady state height corresponding to a steady state value of w* = (0, 6*) E 7\" __. W. Suppose the robot tracks 5 4 exactly the \"distorted mirror\" trajectory of the puck, r = -a;10b, where tqo is a constant. Contact between the two can occur only when (r,b) = (0, 0). Therefore, in this case, the contact configurations are limited to a single configuration point s = ((0,0), (b , - tqob)) E TzC C_ X . Now solving the equation c(s) = -b\" for ~,0, yields a choice of that constant, l - i x ~1o= i + a ' which ensures a return of the puck to the original height" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002736_j.jmatprotec.2008.03.065-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002736_j.jmatprotec.2008.03.065-Figure6-1.png", "caption": "Fig. 6 \u2013 The form grinding wheel is subjected to a parabolic motion in the vertical plane with respect to the generated gear, so that the teeth are crowning modified.", "texts": [ " Crowning modification Although the tooth faces of the input and output gears have been established, a further crowning modification is still required to transform the meshing from line contact to point contact. For tooth surfaces that are theoretically tangent along a line, any small assembly error will lead to contact at the edge of the tooth face. Edge contact causes a serious concentration of stress and a significant decrease in the lifetime of the gear drive. The crowning modification can be applied on either (1) or (2). Here, (2) is selected and the crowning strategy is illustrated as shown in Fig. 6, where a form grinding wheel is driven by a parabolic motion with respect to the generated gear. The surface of revolution of the form grinding wheel is denoted by (3) and is the same as the section profile of (2) in the middle transverse plane. As shown in Fig. 7, the section profile of (2) in the middle transverse plane is a curve denoted by (2) and represented by r\u2217 2 = {x2( 1), y2( 1), 0, 1}T (27) A coordinate system S3 (x3, y3, z3) is applied to connect rigidly to (3) and x3 is the axis of revolution" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003849_taes.2013.120135-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003849_taes.2013.120135-Figure6-1.png", "caption": "Fig. 6. Forces and motion of aircraft on experimental platform.", "texts": [ " Four accelerometers are used to measure pitch and roll accelerations, respectively. The estimate results are compared with the measurement outputs of an IMU (XsensMTI AHRS). We consider Fig. 5 where the quadrotor aircraft mounted on an experimental platform is presented. It is important to say that in this particular case the quadrotor aircraft is in an out ground effect condition. The effects of the compressed air take-off and landing are then neglected. The theoretical scheme of the experimental platform is described in Fig. 6. 616 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 50, NO. 1 JANUARY 2014 From accelerations (a1, a2, a3, a4) by four accelerometers, we can obtain \u03b8\u0308 and \u03c6\u0308 (see Fig. 6). In fact, a\u03b8 = \u03b8\u0308 = a1 \u2212 a3 la , a\u03c6 = \u03c6\u0308 = a2 \u2212 a4 la (63) where la is the distance from the accelerometer to the center of gravity. We know that angular rates and angles can be expressed as, respectively, \u03b8\u0307 = \u222b t 0 a\u03b8 (\u03c4 )d\u03c4, \u03c6\u0307 = \u222b t 0 a\u03c6(\u03c4 )d\u03c4 (64) WANG & SHIRINZADEH: NONLINEAR MULTIPLE INTEGRATOR AND APPLICATION TO AIRCRAFT NAVIGATION 617 618 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 50, NO. 1 JANUARY 2014 and \u03b8 = \u222b t 0 \u222b s 0 a\u03b8 (s)dsd\u03c4, \u03c6 = \u222b t 0 \u222b s 0 a\u03c6(s)dsd\u03c4. (65) In the experiment, (\u03c6(0), \u03b8(0)) and ( d\u03c6 dt (0), d\u03b8 dt (0)) can be known" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002572_adsc.200600257-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002572_adsc.200600257-Figure6-1.png", "caption": "Figure 6. Electroenzymatic production of 2,3-dihydroxybiphenyl. Hydroxybiphenyl monooxygenase (HbpA) is used for the conversion of 2-hydroxybiphenyl to 2,3-dihydroxybiphenyl in a divided batch cell. NADH is regenerated at a carbon felt electrode using the electrochemical mediator [Cp*Rh ACHTUNGTRENNUNG(bpy) ACHTUNGTRENNUNG(H2O)]2+. The co-substrate dioxygen (O2) is supplied by sparging with air.", "texts": [ " All other evaluated dehydrogenase-based processes did not fulfill the defined minimal requirements for efficiency, either because of insufficient productivities[34,35] or because of too low final product concentrations[36] or both.[37\u201339] The reaction with the highest STY employing an oxygenase coupled to cathodic cofactor regeneration was developed by Hollmann et al.[40] 2-Hydroxybiphenyl-3-monooxygenase (HbpA) was employed to catalyze the reaction from 2-hydroxybiphenyl to 2,3- dihydroxybiphenyl (Figure 6). The cofactor NADH was regenerated electrochemically in a divided cell at a carbon felt working electrode using [Cp*RhACHTUNGTRENNUNG(bpy)ACHTUNGTRENNUNG(H2O)]2+ as electrochemical mediator. Molecular oxygen, necessary for the enzymatic reaction, was supplied by sparging with air. The productivity had a maximum of 0.2 gL 1h 1 and was sufficiently high to meet the minimal process requirements. However, the process could not be continued for more than 2 h due to inactivation of the enzyme and thus the final product concentration reached only 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.10-1.png", "caption": "Fig. 6.10 A moat bridge and a folding bridge. a A moat bridge (\u58d5\u6a4b) (Mao 2001). b Structural sketch. c A folding bridge (\u647a\u758a\u6a4b) (Mao 2001). d Structural sketch of folding device", "texts": [ " The device has the same function as Chao Che, but without the pulley and the rope. It only has a roller device, and its Ban Wu is set on a standing rod (as the frame). Thus, the scouts need to climb up to the Ban Wu on their own. Figure 6.9b shows the structural sketch. In the Shang Dynasty (1600\u20131100 BC), entrenchments had been used outside the city walls for defense. Soldiers needed to pass over the entrenchments in order to attack the city. Hao Qiao (\u58d5\u6a4b, a moat bridge) is a device to assist soldiers to cross the entrenchments as shown in Fig. 6.10a (Mao 2001). It is a mechanism with two members and one joint, including a bridge body as the frame (member 1, KF) and wheels on the frame as the roller members (member 2, KO). The wheel is connected to the frame with a revolute joint JRz. Figure 6.10b shows the structural sketch. Moreover, sometimes another link (member 3, KL) is added to the original moat bridge to increase the distance for reaching the other side of the entrenchment. The link can be folded to save space, as a folding bridge shown in Fig. 6.10c (Mao 2001). The folding device is also a mechanism with two members and one joint, including a frame (member 1, KF) and a folding link (member 3, KL). The folding link is connected to the frame with a revolute joint JRz. Figure 6.10d shows the structural sketch for the folding device. Yang Feng Che (\u63da\u98a8\u8eca, a winnowing device), also known as Feng Shan Che (\u98a8\u6247\u8eca), has similar structures as Feng Che Shan (\u98a8\u8eca\u6247) in Sect. 6.3, but they are used for different purposes. The device for war is to rotate the vanes to produce strong winds for the purpose of lighting fires and assist in attacking, or to bring dust up as shown in Figs. 6.11a and b (Mao 2001). It is a mechanism with two members and one joint, including a stand as the frame (member 1, KF) and a crank with vanes (member 2, KW) that is connected to the frame with a revolute joint JRx" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002861_robot.2008.4543833-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002861_robot.2008.4543833-Figure5-1.png", "caption": "Fig. 5. High-level control with collision avoidance. The yellow path shows the trajectory generated by the collision avoidance algorithm in order to avoid the obstacle (the green box) while moving towards the tray.", "texts": [ " That is, for any configuration (rotation and translation) of the crane, the cameras are always directed towards the crane. The top right view pane shows the crane from the side, while the bottom right view pane shows the crane from above. This allows the operator to always have a detailed view over the crane and the environment near the crane. Virtual environments are suited for the introduction of operator assisting features. As one example of this, visualization of the crane workspace has been implemented. This can be seen in Figure 5. The user can specify the target position of the crane-tip in a number of different ways. One way is to use the mouse to click on the top right camera view. This will result in a position in the vertical plane. The second method is to use an ordinary joystick to move a pointer in the virtual environment. A 2-axis joystick is used and two buttons are used to simulate a third axis for full 3D motion. When the user presses a button, the current position of the pointer is sent to the control system" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001698_robot.2002.1014695-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001698_robot.2002.1014695-Figure2-1.png", "caption": "Figure 2, Working principle of the FMP swimming microrobot", "texts": [ " The fins were 10 K ~ ~ T I long, 3 mm wide and The thickness of FMP was varied fiom 1 mm thick. The mixing-ratio of the FMP fins was 3:l . The total size of the: microrobot was 20 mm long, 14 mm wide and 5 mm thick. to be required values by modifying the mixing-ratio and spin-rate. Mixing-ratio -m- 1:3 +1:2 -'I- 2: 1 -A- 111 C - 3 1 9 1 2 I I . I * I ' I . I . I ' 0 10 20 30 40 50 Magnetic Field (mT) Figure 1. Actuation forces of FMP beams 3. Working Principle A pair of FMP fins was designed as the micro actuators of a swimming microrobot (Figure 2 and 3). The robot body was a boat-shaped plastic I When magnetic field was applied, both FMP tins were polarized and tended to range along the magnetic lines. If the m,agnetic field disappeared, vessel that could float on water. The FMP fins the actuators tended to resume their original shapes because of the spring forces. Therefore, the fins were bended towards the opposite direction. The actuators vibrated when an altemating magnetic field was applied. The amplitude was \" k e d when the frequency of magnetic field was equal to the resonant frequency of the fins" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003509_s10846-012-9717-2-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003509_s10846-012-9717-2-Figure2-1.png", "caption": "Fig. 2 The autopilot board", "texts": [ " Aircraft control is achieved with trailing edge elevon (symmetric deflection for elevator \u03b4e and antisymmetric for aileron \u03b4a). This aircraft has enough specific excess power to climb with non-marginal rates at altitude. A numerically derived database comprehensive of all aerodynamic derivatives is employed to build the linear and nonlinear aircraft models. The MH850 aircraft is able to perform autonomous flight thanks to the on board installation of an autopilot. As commercial boards do not allow the modification of control laws already implemented, a custom-made autopilot has been designed and produced (see Fig. 2). PID control method was initially considered for its simplicity and ease of tuning, its first application concerned the control of a quadrotor UAV [16]. Main characteristics comprehend an open architecture, the possibility to be reprogrammed in flight and real time telemetry. Sensors include GPS, barometric sensor, differential pressure sensor and three-axis gyros and accelerometers. The CPU is the AtMega 1280 model with 128Kb flash memory and 8Kb of RAM. The choice of the L1 adaptive controller for the aircraft control is motivated by the high level of uncertainty which generally characterizes UAVs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002177_bit.260300902-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002177_bit.260300902-Figure3-1.png", "caption": "Figure 3. Details of the enzyme electrode and its measurement cell: (A) 0, probe body, (B) jacket, (D) electrolyte, (C) selective gas film, (C') active-selective membrane, (K) thermostated cell, (N) cell body, and (R) cell screw for fixing the probe inside the cell.", "texts": [ " Peripherals were added to the computer, including a disk controller, a parallel-type interface card for the printer, and converter multiplexer card to connect the PO, meter to the computer. The flow system (Fig. 2) was connected to the microcomputer. It is composed of a measurement cell containing GRAPHICAL SCREEN COMPUTER 48 K / // ( m o o INSTRUMENTATION BLOCK Figure i. Schematic diagram of the analyzer. CCC 0006-3592/87/091001-05$04.00 M I I I A I I I I I I I I I t ' , I ' I , ' I ( , l ' , I ' , \\ I I 1 , ; 1 ; : ( 1 , \" I -_' P I - 4 .---- - I 1 1 WASTE (B) rinsing buffer, and (A) air the enzyme sensor (Fig. 3) which is connected to a pump through electromagnetic valves controlling the access to the measurement cell for the different medium. , ' I I L ._._. ... > - I . . . . . . . . . . . . . . . . METHODS Reagents Gelatin from bone had a hardness characteristic of 250 blooms and was purchased from Rousselot Chemical Co. (Paris, France). A 25% aqueous glutaraldehyde solution was used (Merck Co., Darmstadt, W. Germany). The polypropylene film acting as a selective gas membrane was 6 pm thick (Bollore Co" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001403_0021-9673(96)84622-x-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001403_0021-9673(96)84622-x-Figure6-1.png", "caption": "Fig. 6. Drawing of a typical planar external filtration module: 1, sample inlet: 2, sample outlet; 3, spiral groove; 4, filtrate collection; 5, filtrate outlet. The membrane is clamped between the two blocks. From Ref. [25].", "texts": [ " The A-SEP filtration device (Applikon, Schiedam, Netherlands) was utilized for determining acetate and phosphate during an Escherichia coli culture [24] and the filter/acquisition module (FAM), marketed by Waters (Millipore), for monitoring of the production of ethanol by Saccharomyces cerevisiae in a complex and viscous growth medium, spent sulphite liquor (SSL) [25,26]. Both with a 0.22-/zm and a 0.45 /zm-membrane, recoveries of essentially 100% were found for several small carbohydrates in SSL, whereas recoveries of about 50% were found for amino acids from SSL. The reason for this surprising behaviour remains unclear. The FAM module is depicted in Fig. 6 as a typical example of an external filtration device. In all these applications, concentration polarization and membrane fouling were kept at an acceptable level and no negative effect on the sampling performance has been reported when bacterial or yeast cultures were filtered. On the other hand, handling of samples containing filamentous fungi generally is impossible with these modules because the inhomogeneous broth components easily clog the flow channels [15,21,27]. Internal filtration and dialysis units do not have these problems to such an extent and, therefore, seem to be preferable in this context, although one external ultrafiltration module has been described to work satisfactorily with filamentous fungi cultures [27]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002368_j.snb.2004.11.028-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002368_j.snb.2004.11.028-Figure4-1.png", "caption": "Fig. 4. Signal response of the bienzyme biosensor to 0.3 mM of ammonium at various pH (n= 3) (sensor: 0.21 U l\u22121 GXD and 0.22 U l\u22121 GlDH in 1 l of matrix per membrane. Buffer: 100 mM K-PBS pH 7.5, 0.5 mM 2- oxoglutarate and 0.6 mM NADH). The relative response (%) was calculated by normalizing the signal to the maximum signal.", "texts": [ " In membranes I and II, the loading of GXD was varied and immobilized with fixed maximum loading of GlDH (0.22 U l\u22121). The sensitivity increased (\u223c3 times) with doub s l a s M G m w t w t H s s G w l T s r m N o a T b b loading of 2-oxoglutarate is shown in Fig. 3. The response increased with increasing loading of 2-oxoglutarate and became saturated at a loading of 0.5 mM. For the optimization of buffer pH, the bienzyme system was studied in K-PBS with pH values ranging from 5 to 10. The signal was obtained by measuring 300 M of ammonium in the measuring cell. The biosensor response is shown in Fig. 4, in which the maximum response was observed at pH 8. However, buffer pH 7.5 was applied in order to prevent the formation free gaseous NH3 from occurring in alkaline condition, and to keep close to the optimum pH of the individual enzyme (pH 7.5 for GXD and pH 8 for GlDH) [20,23,24]. At buffer pH 7.5, the signal response was similar (>95%) to maximum signal achieved at buffer pH 8. Therefore, the optimized working buffer was standardized as K-PBS buffer (100 mM, pH 7.5) containing 0.5 mM 2-oxoglutarate and 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001948_robot.2001.932980-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001948_robot.2001.932980-Figure1-1.png", "caption": "Fig. 1: SubProbRT (a) non-perp. (b) perpendicular", "texts": [], "surrounding_texts": [ "1 Introduction It is difficult to find a generic inverse kinematics solver for reconfigurable robots because such robots may assume different configurations [I], [2 ] , [3]. Numerical inverse kinematics [4], [5] is viable, but its robustness and completeness are the major drawbacks. To obtain closed-form solutions is still desirable as the convergence and Completeness of the solution can be guaranteed [6], [7], [8], [9]. The objective of this work is to automate the generation of closed-form kinematic solutions of reconfigurable robots regardless of their geometry and DOFs. When the robot is re-configured, the corresponding inverse kinematics can be generated automatically in the robot controller. The approach we used here is based on the Product-of-Exponentials (POE) formulation of robot kinematics [lo]. The POE forward kinematics of an n-DOF serial-typed robot has the form:\nA\nwhere & E se(3) is a joint twist of the instantaneous motion ( 3 x 3 skew-symmetric matrix); g s t ( 0 ) and g, t (O) E SE(3) are the initial and the final poses of the endeffector. 5% also can be written as tL = (w8,/%) E !R6, called a twist coordinate [Ill, bearing the uniform line geometry of the joint axes for both revolute and prismatic joints. Each term, etiez E SE(3) , represents a rigid motion. Though g,,(0) may be expressed as a 4 x 4 homogeneous matrix, the form of (1) is qignifi-\ncantly different from the standard Denavit-Hartenberg (D-H) kinematics equation. Using the POE equation (1) to model a reconfigurable robot is better than using the D-H parameters because it is a constructive approach to establish kinematics of the robot according to its module arrangement [la]. Also, the POE formulation is robust in dealing with kinematic singularities occurred in the robot calibration process [13], [14]. In deriving the inverse kinematics of (I), it is often required to solve a POE equation of the following form:\n- A A\n(2) eCl0leE202 . . . &n@n = T\nwhere T = gs,(0)g,'(O) E SE(3) is known and n 1 6 non-redundant). To obtain the closed-form solution of i 2) is difficult because of its matrix exponential form. Based on the line geometry of joint twists, Paden and Kahan [Ill proposed to use a set of canonical equations formed by the POE, termed subproblems, to solve ( 2 ) . The subproblems are defined to solve the Oi 's in following types of equations (POE operated on a point):\nm - n eta*ip = q m 1 3 (3) i=l\nwhere p , q E 8' are two given points. Through a proper reduction process, the POE equation ( 2 ) can be simplified to the form of ( 3 ) . As there are a t most 3 matrix exponentials involved, Eq. (3) can be solved geometrically. Because this is a geometric method, all possible closed-form solutions can be obtained. The work here is an attempt to systematically stud and extend the scopes of the subproblems defined in [Ilc and to use them to solve the POE inverse kinematics equation of (2). Unlike [ll], here we make a clear distinction between POE reduction and the subproblems. Three techniques for the reduction of POE equations are introduced. With these techniques, the POE equation ( 2 ) can be properly reduced to the subproblem-form of (3). There are 11 subproblems identified in this work in total. Solutions of some subproblems are highlighted for their geometric meanings. Due to the reduction, exponential terms in Eq.(3) also reflect part of the original robot structure, thus the subproblems can be re-used for inverse kinematics of modular robots with identical sub-structures. Solving inverse kinematics of the reconfigurable robots becomes a process of identifying the kinematic structure of the robot and selecting the appropriate subproblems for solutions. There is no need to re-derive the solution of a specific robot configuration after every reconfiguration effort. The complete inverse kinematics solver using this approach is introduced. The number of solvable robot configurations are estimated. An example is provided to demonstrate its effectiveness.\n0-7803-6475-9/01/$10.000 2001 I EEE 2395", "2 Reduction of POE Equations Since Eq.(2) represents a series of rigid motions caused by the joints, it is possible to simplify a POE equation by using properties of the rigid motions. The following methods are the basic techniques we found to be useful. Technique 1 Position Presewation\nLet T = e@ E SE(3) be a purl: rotary mot ion , where [ = , (w ,v ) E 3?6 is a revolute twist. Let p E !R3 be a poznt o n the axis of rotation. According t o the rzgid mot ion , p will n o t be affected by this rotation, i.e.,\nh\ne s 8 p = T p + p = T p (4) T h e e f fec t of the jo in t variable of a P O E equation ca.n be eliminated if the equation is operated o n a point along i t s corresponding rotary jo in t axis. Technique 2 Orientation Pr.eservation\nLet T = e te E SE(3) be a pure translation, where [ = (0,v) E !R6 i s a translational twist. Le t p E !R3 be a point. T h e displacement of p ctcused by the translation i s parallel t o the direction of travel, v, i .e.,\nh\nh\ne E s p = T p + ( T p - p ) x v = 0 (5) During the rigid body translation, the orientation of the body is preserved. T h e effect of the translational jo in t variable of a P O E equation can be eliminated. Technique 3 Distance Preservation\nLet T = ets E SE(3) be a pure rotary mot ion , where < = (w, v) E 8' is a revolute twist. Let p and q E g3 be two points, and q o n the axis o,F rotation. T h e distance between p , q remains unchangec! after the rotation, i.e.,\n* T h e rotary j o i n t variable of a POE equation can be also eliminated through the distance preservation property. Using the Position preservatio:n on a properly chosen point, more than one joint variable in a POE equation can be eliminated at the same time, e.g., the intersecting point of several joint axes (on the right hand side of the POE equation). The other two xchniques can eliminate only one joint variable a t a time.\n3 Introduction to Sub'problems 3.1 Classification As indicated in Eq.(3), the sutlproblems are defined to solve the equations formed by the POEs. Because p and q are in 3D space, the number of joint twists can be at most 3 in order to have a solution. Based on the types and sequence of joint twists, we have identified 11 subproblems (Table 1). The naming of the subproblems is based on the sequence of the revolute joints, denoted by R, and the translational joints, denoted by T. The total number of joint twists is defined to be the order of the subproblem. There are two lSt tsrder subproblems, three 2nd order subproblems, and six 3rd order subproblems. Some subproblems of the same order are equivalent because they can be converted into the same joint twist\nh\nIle% - 411 = llTP - 411 IIP - 411 = IlTp - 911 (6)\narrangement through matrix operations. For example, SubProbRRT is to solve Eq.(7) with given p , g :\n(7) where G , & are revolute tyists,and-& is a translational twist. Left-multiplying (eE1'1et282et3Q3)-1 to Eq.(7):\nA A A\n4 (8) = e - ~ 3 e 3 e- t202 e -cl o1 Changing the signs of the joint twist does not affect its basic property. Therefore, Eq.(8) has the form of the subproblem SubProbTRR. The solution of SubProbTRR can be obtained by using the substitutions: p tt q, 0 3 +t\nt3 on the solutio: of_SubP_obRRT once it is obtained. The operation,(et181et2Q2et383)-1. is called a symmetr ic mappzng [15]. Among the 11 subproblems, there are three types of equvalent subproblems (Table 2 ) .\n01, 0 2 * 02, 01 * 0 3 , -b * 61, -& * t 2 , and -51 *\n3.2 Solutions of some subproblems The solutions of some subproblems are highlighted to show their geometric meanings. The work of Gao[l5] provides complete solutions of all the 11 subproblems. Subproblem 1 SubProbR(<, p , q ) [Rotate about a single axis] - Find a n angle 8 such that ec8p = q, where the input parameters: [ = ( w , v ) is a revolute twist and points p , q E !R3. Solution: Refer to [ll], Subproblem 1. 0 Subproblem 2 SubProbRT-TR(t1, &, p , q ) [Rotate and translate about two axes] - D u e to equivalence, the solution of SubProbRT i s provided. SubProbRT([1, [a, p , q ) ~ Find a n angle 81 and a displacement 82 such that ei181ei202p = q , where the input parameters: [I = (w1 ,VI) is a reerolute twist , \u20ac 2 = (0, va) i s a translational twist, and points p , q E 8'. Solution: and & non-perpendicular - Geometrically the POE operation of SubProbRT on p is to translate p first along & by 0 2 and then rotate about & by", "O1 until it reaches q (Figla) . To obtain 81 and 01, 7 one needs to find the intersection point p1 of a line passing through p and a circle passing through q . The straight line is parallel to $2 and the circle is centered around $1. The value of 82 can be found first. Let $a be a line parallel to & and passing through p (Fig.2) . The common normal between tL and $.; is denoted as OC. Points o and c are located along $1 and $; respectively. Let nproJect be a plane passing through OC and perpendicular to '1111. The vertical projection p d and q d of points p and q along wl-direction could be found by:\n(9) T pd - p = w1w1 (P - 0) qd - 4 = wlw?(q - 0)\nLet a be the angle between $; and the plane nproJect. then a = 7r/2 - cos-I(I tu1 . 112 I). Assume that $.; is the image of axis $; after rotating about [I by 81 and passing through poi@, q . The common normal between $1 and $.; becomes oc' . The distance 11 from c to p and the distance 12 fiorn c' to q are:\nThe net translat,ion becomes 8 2 = 12 - Z1. Since 8 2 is obtained] now let p1 = e tzszp; the original subproblem becomes: etl ' lpl = q. By applying SubProbR, the solution of O1 can be obtained. If 51 intersects with 5 2 ' : the plane nproject will pass through the intersecting point. Let o be the intersecting point, the derivation of 81 and 8 2 follows the saine procedure. If $1 and $a are parallel, the plane nprojecf can he arbitrarily located. Let o be an arbitrary point on (1 and nproject pass through 0, the rest of the derivation will be the same with ck = 7r/2. $1 and $2 perpendicular - When $1 and ( 2 are perpendicular, a solution exists if and only if p and q are on the same plane perpendicular to (Fig.lb), i.e., h\nand parallel to $2. The common normal between t1 and E.; is OC (Fig.3). Let T =I1 c - o 1 1 and the distance from c to p be 11 = ( p - o) . v2. Assume that 6: is the image of after rotating about 51 by 81 and passing through q . The common normal between $1 and $; becomes oc1. The distance from c1 to q is: 12 = f 1 1 q - o [ I 2 -r2. The net translation_becomes B2 = l 2 i l l . Since 0 2 is obtained, let pl = &'Zp and the rest of the derivation is identical to the Non-perpendicular case. The number of the solutions for B2 depends on th,e value of r and 1 1 q - o 1 1 ranging from zero to two. If C2 and $1 intersect a t point o, l1 = ( p - 0) . v2 and 12 = f I ( q - o 1 1 . The net translation is = la - 11. Once 8 2 is obtained, 81 can be obtained in a similar manner. 0 Subproblem 3 SubProbRRT-TRR($l, $2 , $3, p , q ) [Rotate, rotate and translate about three axes] - D u e t o equivalence, the solution of SubProbRRT is provided. SubProbRRT(t1, E 2 , $3, p , q ) ~ Find angles 81, 82\nwhere the input: = (wl,v1) and ( 2 = ( ~ 2 , 2 1 2 ) are revolute twists, $3 = (0, w3) is a translational twist. Solution: Due to space limit, refer to [15] for detail.\n4 POE Inverse Kinematics Solver 4.1 Solvability of POE equation\nThe existence of a geometric solution for a POE equation depends on whether it can be decomposed or solved by the subproblems directly. The POE equations of all non-redundant robot configurations can be solved by: 1 ) using subproblems directly, 2) using reduction techniques and the subproblems, or 3) using subproblems and other decomposition methods. As the maximum order of subproblems is 3, all robots with DOFs of 3 or less with revolute and prismatic joints can be solved by the subproblems directly. For robots with 4 DOFs or more, the intersection of the joint axes determines whether the POE equation can be decomposed or not. If it is, reduction techniques and subproblems are applied together (Approach 2 ) . Otherwise, another decomposition method will be studied (Approach 3). Here we look into the solutions of robot configurations under approaches 2 and 3. Aprch. 2 - Intersecting revolute joints (IRJ) Two or three intersecting revolute joints can form a\nand a displacement 83 such that e~1B1eiz'Ze43'3 P = 9,\nwrist. The intersecting ioint of joint axes forms the wrist center. The location of the wrist center does not necessarily to be at the end of the robot arm. Proper adjoint m a p p i n g s [ l l ] can put the intersected joints to the right side of the POE equation. Applying the Posit ion preservation technique on the wrist center, the POE equation can be reduced. After the reduction, the variables associated with the wrist are all annihilated. The reduced POE equation can be solved by the subproblems if its order is 3 or less. The wrist itself with two or three revolute joints can be solved through subproblems SubProbRR or SubProbRRR respectively. Aprch. 3 - Non-intersecting rev. joints (NRJ)\n( p - q ) . w1 = 0. Let $a be a line passing through p When a non-redundant robot has no intersecting revo-" ] }, { "image_filename": "designv10_13_0002932_j.robot.2009.12.002-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002932_j.robot.2009.12.002-Figure9-1.png", "caption": "Fig. 9. Obstacle avoidance criterion is obtained by using a ball-covering object modeling scheme. The links and objects are covered with balls of known radii.", "texts": [ " In this section, we demonstrate a simplified obstacle avoidance scheme using the inverse-forward scheme explained in Section 2 and the ball-covering object modeling method used earlier by Mao et al. [13]. Since the KSOM-SC architecture provides multiple joint angle solutions for a given target point, a suitable initial value of joint angle vector can be obtained by using a criterion that avoids the obstacle. The criterion used for resolving redundancy is based on the ball-covering modeling method. In this method, spheres of different radii are used to cover different shapes of links and objects as shown in Fig. 9. The centers and radii of these spheres are fixed a priori. In this figure, di represents the Euclidean distance between the center of the obstacle Co and the center of each link Ci, i = 1, 2, 3, 4. Ri is the radius of the sphere covering the link i and Ro is the radius of the sphere covering the obstacle.While the location of the obstacle is fixed during the robot motion, the location of link centers (Ci, i = 1, 2, 3, 4) is a function of the manipulator joint angle vector \u03b8. If we define a scalar function as g(\u03b8) = 4\u2211 i=1 (Ri + Ro \u2212 di); {Ri, Ro, di} > 0 (7) then the obstacle avoidance criterion is given by g(\u03b8) < 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001441_2.5490-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001441_2.5490-Figure1-1.png", "caption": "Fig. 1 Schematic of compressor disks used for analysis and testing. Material: titanium (Ti-6Al-4V) alloy.", "texts": [ " In addition to the conventionalstress contours for the component, contourplots are provided for probability of survival (or failure) and life. Turbine Disks Specimens and Procedure Mahorter et al.22 studied two different groups of aircraft gasturbine-engine compressor disks designated disks A and B. The disks were manufactured from a titanium (Ti-6Al-4V) alloy. The material parameters for this alloy, taken from various published sources, are given in Table 1. Schematic drawings of these disks are shown in Fig. 1. Five unfailed disks of each type were randomly selected from those removed from engines at overhaul. The disk operating times are summarized in Table 2. These failure data are the only such data reported and available in the open literature. Table 1 Turbine disk material parameters [Material, titanium (Ti-6Al-4V) alloy] Parameter Property Elastic modulus GPa (ksi) 11:0 .16 \u00a3 103/ Poisson\u2019s ratio 0.33 Weibull slope 2 Density, kg/m3 (lb/in.3 ) 4429 (0.16) Stress-life exponent 9.2 \u00bf45 fatigue limit, MPa (ksi) 2585 (37", " ai aa .o rg | D O I: 1 0. 25 14 /2 .5 49 0 Table 3 Normalized predicted L10 lives of gas-turbine-engine compressor disks as function load [Material, titanium (Ti-6Al-4V) alloy; reference stress, \u00bf45, 509.2 MPa (73.846 ksi); reference volume, Vref , 2:264709 \u00a3 10\u00a1 10 m3 (1:3820105 \u00a3 10 \u00a1 5 in.3); reference life, L10, 1 cycle (normalized); disk speed, 11,200 rpm; stress-life exponent, 9.2; Weibull slope, 2; \u00bf45, fatigue limit, 258.6 MPa (37.5 ksi).] Predicted normalized L10 life, cycles Disks A (Fig. 1a) Disks B (Fig. 1b) Unloaded Loaded Unloaded Loaded Segment angle, deg Parameter 60 30 No fatigue limit Segment life 2630.9 0.14618 75.118 0.15307 Disk life 1074.1 0.05968 21.7049 0.04419 Time at load, % 82 18 85 15 Combined load-cycle disk life 0.33147 0.29123 Fatigue limit Segment life 8171.2 0.14673 7692.5 0.15324 Disk life 3335.8 0.05990 2220.6 0.04424 Time at load, % 82 18 85 15 Combined load-cycle disk life 0.33275 0.29490 the loaded (engine) conditions. Under these conditions the lives of disks A would be expected to be 35% longer than those of disks B" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003800_s40430-014-0133-3-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003800_s40430-014-0133-3-Figure1-1.png", "caption": "Fig. 1 Dynamic model of a planetary transmission gear [7]", "texts": [ " This involves a disturbance in the dynamic force generated in the gearmesh, when the faulty tooth of the planet meshes with the ring and/or sun. If the fault comprises only one tooth flank, this can mesh with the sun or ring depending on the direction of rotation, because the driving flanks are different in each rotation case. Differently if both flanks are faulty, the effect of the fault will be when it meshes with the sun and ring gear, i.e., every half rotation of the planet gear. This failure will be described below and simulated in both dynamic and phenomenological models. 2.1 Dynamic model The dynamic model is shown in Fig. 1. The nomenclature and degrees of freedom (DOF\u2019s) used, together with the equations of motion shown in Eq. (1), are given in [7] and adopted here. Each component of the planetary transmission: sun, ring, planet gears and carrier has three DOF\u2019s (two translations, xj, yj and one rotation xj) in a non-inertial reference system. To facilitate the formulation of the equations, the translational DOF\u2019s planet gears are defined in radial and tangential coordinates, gi and ni, respectively. Bearings are modeled by linear springs and dampers; the gearmesh is modeled by linear springs and dampers acting on the line of action" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.16-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.16-1.png", "caption": "Fig. 4.16 A foot-operated paddle blade machine, aOriginal illustration (Wang 1968), b Structural sketch, c Chain", "texts": [ " A longer device was approximately two zhang; a shorter device was half the size. Inside the device was a chain of boards that were operated to push water upwards. One person\u2019s effort in a day could irrigate approximately five mu (\u755d, ancient Chinese area of acre) of land. A cow\u2019s effort irrigated double the area.\u201d\u300e\u5176\u6e56\u6c60\u4e0d\u6d41\u6c34,\u6216\u4ee5\u725b\u529b\u8f49\u76e4,\u6216\u805a\u6578\u4eba \u8e0f\u8f49\u3002\u8eca\u8eab\u9577\u8005\u4e8c\u4e08,\u77ed\u8005\u534a\u4e4b,\u5176\u5167\u7528\u9f8d\u9aa8\u62f4\u4e32\u677f,\u95dc\u6c34\u9006\u6d41\u800c\u4e0a\u3002\u5927\u62b5\u4e00\u4eba \u7adf\u65e5\u4e4b\u529b,\u704c\u7530\u4e94\u755d,\u800c\u725b\u5247\u500d\u4e4b\u3002\u300f Based on the way they were operated, the manually-driven paddle blade machines were classified as either hand-operated or foot-operated. Figure 4.16a shows a foot-operated paddle blade machine (Wang 1968). It consists of the frame (member 1, KF), an upper sprocket with a long shaft and pegs (member 2, KK1), a lower sprocket (member 3, KK2), and a chain (member 4, KC). Figures 4.16b and c show the corresponding structural sketch and chain, respectively. 82 4 Ancient Chinese Machinery The water device Jing Che (\u4e95\u8eca, a device used to draw water from water wells) was used to draw water from water wells. It was also called a wooden dipper water machine" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure4-1.png", "caption": "Fig. 4 Analysis in the Gauss plane to determine the fixed centrode of offset slider-crank/rocker mechanisms", "texts": [ " 3, the fixed centrode p for the planar motion of the coupler link BC is the path traced by the instantaneous center of rotation I with respect to the fixed frame F\u00f0O;X;Y\u00de, during the motion of the slider-crank/rocker mechanism. Likewise, the moving centrode k is the path traced by I with respect to the moving frame f \u00f0X; x; y\u00de that is attached to the coupler link BC. The implicit algebraic equations of both fixed and moving centrodes are formulated in the following according to the approach, which was introduced by Walter Wunderlich (1910\u20131998) in his German book [10] by using complex algebra. Thus, referring to Fig. 4 and supposing to consider the complex plane of Gauss as coincident with the fixed plane of F\u00f0O;X; Y\u00de, the position complex vectors ZI, ZB and ZC for the points I, B and C can be expressed as ZI \u00bc X \u00fe i Y (9) ZB \u00bc r ZI ZIk k and (10) ZC \u00bc ReZI i e; (11) where i \u00bc ffiffiffiffiffiffiffi 1 p is the imaginary number, ZIk k and ReZI are the module and the real part of the complex vector ZI. The module of the difference between the complex vectors ZC and ZB can be expressed as ZC ZBk k \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ZC ZB\u00f0 \u00de ZC ZB\u00f0 \u00de q \u00bc l (12) Therefore, substituting Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002490_3.20089-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002490_3.20089-Figure2-1.png", "caption": "Fig. 2 Effect of rotor dynamics, CH47 at hover.", "texts": [ "1, rad/sec) D S61 (fi = 21.3, rad/sec) CONING REGRESSING Q 1.5 1.0 -1.5 -1.0 -.5 0 Fig. 1 Tip-path-plane modes for S-61 and GH47B at hover. translational velocities, which have little effect on the roll oscillation problem, were neglected. Using this model for the CH47, the root-locus diagram for increasing values of roll-rate and roll-attitude feedback gains was determined using the stability and control matrices shown in Table 2. The results also are shown in Table 2, and they are plotted in Fig. 2. The effect of increasing the roll-rate feedback gain is to increase the frequency quickly and to reduce the damping of the migrating mode, while increases in the rollattitude gain act to rapidly destabilize the closed-loop system without much effect on frequency. The roll-rate gain for neutral stability is slightly larger than 3 deg/deg/s. These results are similar to those obtained in Ref. 6 for the singlerotor S-61 helicopter. The open-loop roll-rate to lateral-cyclic transfer function was also calculated for the CH47 (Table 1), and the same migration of the regressing-flapping mode to the right-half plane zero was found to prevail", " 3 by first-order time constants, and the nominal 25-ms computer frame time, were represented by a combined transport delay of 75 ms. A firstorder Fade' approximation was used in the analysis to model the transport time delays. Figure 4 shows the influence on the CH47 roll-axis dynamics when the 5-Hz filter and the 75-ms actuator plus digital transport delay are included in the analysis. The results indicate that the roll-rate gain limit is greatly reduced (by a factor of 6) compared to modeling of rotor dynamics alone (Fig. 2) and that the frequency of the roll oscillation is also greatly reduced. The influence of various filter break frequencies is shown in Fig. 5, where the root loci of the roll-oscillation eigenvalues are plotted for filters with break frequencies of 10, 5, and 3.3 Hz. Even for the highest bandpass filter, the reduction in achievable roll-rate feedback gain compared to the case of rotor dynamics alone is dramatic. Of course, the 10-Hz filter would be impractical to implement by itself in the CH47 since there would be insufficient attenuation of the 11-Hz rotor system noise in the command signals to the actuators" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002930_j.mechmachtheory.2009.02.003-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002930_j.mechmachtheory.2009.02.003-Figure1-1.png", "caption": "Fig. 1. Geometry of the straight-edged cutting blade.", "texts": [ " In addition, tooth working surface, contact lines and boundary of the contact lines of the ZN-type hourglass worm wheel are also investigated and compared with those of the ZA-type. It is found that the contact zone of the ZN-type hourglass worm gear set is increased more than twice of that of the ZA-type with an increase of its lead angle to 30 . The increase of pressure angle and normal module of the hourglass worm gear set also results in the increase of its tooth working surface. The proposed analysis procedures and the developed computer aided simulation programs are most helpful to the design and contact analysis of hourglass worm gear sets. Fig. 1 shows the normal section of the straight-edged cutting blade. It is noted that the ZN-type hourglass worm is generated by a straight-edged cutting blade with upper and lower fillets. The straight-edged cutting blade, which generates the working tooth surfaces, can be expressed in the blade coordinate system Sc(Xc,Yc,Zc) by Rc \u00bc xc yc zc 2 64 3 75 \u00bc \u00f0u1 sina R0 cos a\u00de u1 cos a\u00fe R0 sin a 0 2 64 3 75; \u00f01\u00de where u1 \u00bc jM0M1j is a surface parameter of the straight-edged cutting blade and its effective range is umin 6 u1 6 umax", " Herein, u is the design parameter that determines the coordinates of any point on this cutter fillet, and q represents the design parameter of fillet radius. The upper \u2018\u2018\u00b1\u201d signs of Eqs. (2) and (3) indicate the left-side fillet while the lower signs represent the right-side fillet. Fig. 2 shows the schematic generation mechanism for a ZN-type hourglass worm. In Fig. 2, coordinate system Sb(Xb,Yb,Zb) represents the blade coordinate system and coordinate system Sc(Xc,Yc,Zc) is attached to the straight-edged cutting blade (as shown in Fig. 1) while Sa(Xa,Ya,Za) is the hourglass worm coordinate system, and axes Zb and Za are rotational axes of the cutting blade and the generated hourglass worm, respectively. In the cutting process of an hourglass worm, the normal section of the straight-edged cutting blade should form a lead angle k with respect to the worm rotational axis Za. Therefore, the blade performs a rotational velocity xb about axis Zb while the worm blank rotates about axis Za with a rotational velocity x1. According to Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure10.17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure10.17-1.png", "caption": "Fig. 10.17 Atlas of feasible designs of Zhuge repeating crossbow with fixed magazine", "texts": [], "surrounding_texts": [ "Ancient Chinese crossbows used cams and flexible members to shoot bolts for attacking targets, by the elasticity of bows and bowstrings. It was one of the most representative weapons in ancient China. This chapter discusses the original crossbow, Chu State repeating crossbow, and Zhuge repeating crossbow in the ancient books described in Chap. 2, as listed in Table 10.1. All of them belong to Type III mechanisms with uncertain numbers and types of members and joints. The original crossbow had been used from the earliest time and in the widest areas. Chu State repeating crossbow is the earliest repeating crossbow, even though it is not seen in any of ancient literature. Zhuge repeating crossbow had been one of the standard weapons in the army until the Qing Dynasty (AD 1,644\u20131,971). There are a total of two original illustrations, four simulation illustrations, three imitation illustrations, three prototypes, and two real objects described in this chapter. Through the reconstruction design methodology for ancient mechanisms with uncertain structures, the atlas of the feasible designs is obtained and a variety of crossbows are reconstructed. 10.5 Zhuge Repeating Crossbow 241" ] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure9.14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure9.14-1.png", "caption": "Fig. 9.14 A cottonseed removing device (\u8d95\u68c9\u8eca) a Original illustration (Pan 1998), b Structural sketch of hand-operated turning shaft mechanism, c Structural sketch of foot-operated rope transmission mechanism, d Real object (photoed in China Agricultural Museum in Beijing)", "texts": [ " This is a mechanism with four members and three joints, including a wooden stand as the frame (member 1, KF), a pulley (member 2, KU), a rope (member 3, KT), and a cloth bag (member 4, KB). The pulley is connected to the frame with a revolute joint JRz. The rope is connected to the pulley and the cloth bag with a wrapping joint JW and a thread joint JT, respectively. Figure 9.13b shows the structural sketch. 9.4.3 GanMian Che (\u8d95\u68c9\u8eca, A Cottonseed Removing Device) Gan Mian Che (\u8d95\u68c9\u8eca, a cottonseed removing device) in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b, as shown in Fig. 9.14a (Pan 1998), has the same function asMu Mian Jiao Che (\u6728\u68c9\u652a\u8eca, a cottonseed removing device) described in Sect. 6.6. It belongs to the step of fiber processing. Mu Mian Jiao Che (\u6728\u68c9\u652a\u8eca) requires two persons to operate by hand, while Gan Mian Che (\u8d95\u68c9\u8eca) can be operated by only one person\u2019s hands and foot. The operator pedals the treadle to make the rope turn one shaft, while the operator\u2019s hand turns another shaft in the opposite direction. The other hand can place the cotton into the device and gin out the cores and seeds", " However, it is necessary to add an extra flywheel (not shown in the illustration) to utilize inertia force, making the shaft turn continuously. The device can be divided into two parts including the hand-operated turning shaft mechanism and the foot-operated rope transmission mechanism. The handoperated turning shaft mechanism has two members and one joint, including the frame (member 1, KF) and a turning shaft as the moving link (member 2, KL). The turning shaft is connected to the frame with a revolute joint JRz. Figure 9.14b shows the structural sketch. The foot-operated rope transmission mechanism has four members and four joints, including a wooden stand as the frame (member 1, KF), a treadle (member 2, KTr), a rope (member 3, KT), and another turning shaft (member 4, KL1). The treadle is connected to the frame with a revolute joint JRz. The rope is connected to the treadle and the turning shaft with thread joints JT. The turning shaft is connected to the frame with a revolute joint JRz. Figures 9.14c\u2013d show the structural sketch and a real object, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002196_j.cma.2004.07.031-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002196_j.cma.2004.07.031-Figure9-1.png", "caption": "Fig. 9. surface", "texts": [ "0 We have considered in the numerical example a = 10 a very small correction of installment angle d2 of the gear for the purpose of representation of the line of intersection. Intersection of gear and pinion tooth surfaces has been obtained at point M \u00f00\u00de 1 . This additional angle is Dd2 = 0.0089 rad. The surface parameters of pinion and gear for such a common point are u2 \u00bc 1:714695 mm; h2 \u00bc 0:039974 rad; w2 \u00bc 0:000380 rad; u1 \u00bc 2:046011 mm; h1 \u00bc 0:113550 rad; w1 \u00bc 0:003252 rad: \u00f042\u00de Parameters (42) correspond to point M(0) of the line of intersection of surfaces R1 and R2. The exaggerated line of intersection on gear tooth surface (shown in Fig. 9(b)) passes through point M(0). Point M \u00f00\u00de 1 on pinion tooth surface coincides with point M(0). Point M is the exact point of tangency. Point M \u00f00\u00de 2 is the middle point of the cell determined in the plane of surface parameters of the gear and is also represented in Fig. 9(b)). Point M \u00f00\u00de 2 does not coincide with point M(0), as point M \u00f00\u00de 1 does, since the intersection of surfaces R1 and R2 has been forced to be obtained at point M \u00f00\u00de 1 and not at point M \u00f00\u00de 2 . Such an intersection of R1 and R2 has required a very small correction of installment angle d2 in the gear. The TCA computer program developed by the authors has allowed to obtain the path of contact (Fig. 10(a)), and the predesigned function of transmission errors (Fig. 10(b)). It follows from the analysis of the TCA output, that the machine-tool settings applied for gear generation provide a favorable direction of the path of contact (in longitudinal direction) and a predesigned parabolic function of transmission errors" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003878_j.robot.2013.08.005-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003878_j.robot.2013.08.005-Figure2-1.png", "caption": "Fig. 2. This figure shows the numbering convention used to identify parts of different type. The assembly drawing shows the locations of each part in the constructor.", "texts": [ " With the exception of the motor modules, each component must have at least one connector of each type. A \u2018\u2018male connector\u2019\u2019 is used to refer to a set of two conical pins and a screw, and a \u2018\u2018female connector\u2019\u2019 is two conical holes and a nut. The male connectors are used as a standard handle so that components may be easily handled by the common end effector. The presence of a female connector allows a module to be added to an assembly. The motors lack female connectors because they are slid into place onto track components. The simplest structural component (Part Type 1 in Fig. 2) consists of a plate with two male connectors and two female connectors. Having two of each connector style allows the basic component to form long chains and rigid columns. A simple constructor made of these components was demonstrated in [29]. These short structural parts did not produce structures that were rigid over long distances, so a larger structural piece (Part Type 2) was designed. The unit distance between centers for the pins and holes is chosen as an integral number of pitch lengths of the rack used for sliding motion", " However, these two lines, combined with the common power/ground bus, could also be used to drive a standard stepper motor. The DC brush motor with encoder was chosen over a stepper motor for development purposes due to greater versatility, lower Fig. 17. Photographs of motor components. Clockwise from upper left: horizontal motor (Part Type 9); right vertical motor (Part Type 15); left and right vertical tracks (Part Types 10 and 12); horizontal track (Part Type 7). Fig. 18. Key features of the vertical motor and track components. These are Part Types 15 and 12, respectively, as seen in Fig. 2. cost, smaller size, and somewhat greater efficiency. A topic of future work is to reduce motor module complexity by replacing the DC motor system with a simple standard stepper motor. In keeping with the theme of easy-to-fabricate components, a castable encoder wheel with 16 windows is used for position feedback. This provides a resolution of about 1.2 encoder counts per linear millimeter traveled. There are hundreds of electrical contact interfaces between the control and the motors themselves, as well as several sliding contact interfaces", " The x, y, and z axes are outfitted with computer-controlled stepper motors, while the remaining degrees of freedom are actuated manually [29]. A base component is fixed to the X\u2013Y table, and a test component rests on top of it. The standard grasper Fig. 21. Photograph of long and short grasper styles. Transitions to and from a short grasper to a cascaded two-grasper stack can be seen in Supplemental Videos 3 and 4. Fig. 22. The hub component contains the microcontroller for one robot and a rotary table to orient parts. This component is Part Type 14 as seen in Fig. 2. Operation of the rotary table can be seen in Supplemental Video 1. mechanism is fixed to the Z stage. Measurements were taken on the first portion of the assembly process \u2014 aligning the grasper and tightening the screw in order to connect the grasper to the part. It is possible to use the same setup to measure success rates for the second assembly step (tightening the captured nut to connect two components together) but this is a topic for future work. The screw connector within the grasper is spring-loaded, and designed to be compressed when the grasper is placed on a part" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001656_ac00033a016-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001656_ac00033a016-Figure5-1.png", "caption": "Figure 5. Effect of pH on the relative sensor response.", "texts": [ " The concentrations of NAD+ and alanine used in all subsequent experiments were 4 and 10 mM, respectively. ANALYTICAL CHEMISTRY, VOL. 64, NO. 9, MAY 1, 1992 1053 0.8 0.6 h d d Y Q) I E! 2 0.4 Q) E h Po rA 2 0.2 0.0 Flgure 3. I I I 1 I 1 2 3 4 5 6 Concentration of NAD (mM) + Effect of NAD' concentratlon on the sensor response. I 2 4 6 8 10 12 Concentration of Alanine [mM) Flgure 4. Effect of alanine concentration on the sensor response. The effect of pH has been determined by comparing the relative sensor response to 5 pM glutamate over the pH range from 6.5 to 8.5. Figure 5 shows the pH profile obtained from this experiment. \"he maximum sensor response was obtained over the pH range from 7.4 to 7.8. Only 75% of the maximum response is obtained at pH 8.5, and only 37% of the maximum is present at pH 6.5. The optimum response over the physiological pH range is a major advantage for this glutamate biosensor compared to the glutamate biosensor based on glutamate decarboxylase which cannot be used when the pH is greater than 5.5.6 All subsequent measurements were performed at pH 7" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001662_s0094-114x(01)00082-9-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001662_s0094-114x(01)00082-9-Figure5-1.png", "caption": "Fig. 5. Assembly errors of the beveloid gear.", "texts": [ " Thus, the meshing model regresses to the case which can simulate the meshing of beveloid gears with intersected axes. Furthermore, when the intersected angle becomes zero, the axes of the two imaginary cones become parallel, and the meshing model regresses again to the case which can simulate the meshing of beveloid gears with parallel axes. To investigate the meshing of beveloid gear pair with assembly errors, auxiliary coordinate systems Se\u00f0Xe; Ye;Ze\u00de, Sh\u00f0Xh; Yh; Zh\u00de and Sv\u00f0Xv; Yv; Zv\u00de have been set up to simulate the assembly errors of the gear R2 as depicted in Fig. 5. Coordinate system Se is set up and keeps its orientation with respect to coordinate system Sg. However, the origin Oe of coordinate system Se has an offset deviation from the origin Og of coordinate system Sg. The offset OgOe \u00bc Dd \u00bc \u00f0Dxg;Dyg;Dzg\u00de indicates the mounting position deviation of the gear R2. Moreover, coordinate system Sh simulates the gear R2 having a horizontal misaligned angle Dch with respect to coordinate system Se, while coordinate system Sv simulates the gear R2 having a vertical misaligned angle Dcv with respect to coordinate system Sh" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003151_j.triboint.2009.11.004-Figure13-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003151_j.triboint.2009.11.004-Figure13-1.png", "caption": "Fig. 13. Diagram of hertz contact area.", "texts": [ " Therefore, in a high surfacepressure environment, such as that which is found under EHL, lubrication oil is introduced into the contact area at the average speed of the two sliding surfaces. In other words, the lubrication oil must be introduced to the whole contact area initially when the amplitude ratio is greater than 2.0. Ikeuchi et al. [2] had already determined that the length of minimum sliding distance for non-contact conditions was twice the length of initial contact width. However, this condition applies only to a line contact. Fig. 13 illustrates the point contact area of a ball specimen. Compared to the contact length D of line segment a\u2013a0 near the center of the contact area, contact length D0 of line segment b\u2013b0, which is the perimeter of line segment a\u2013a0, is shorter. Therefore, for example, even though the amplitude ratio at line segment a\u2013a0 is less than 2.0, the amplitude ratio of line segment b\u2013b0 likely becomes greater than 2.0. Fig. 14 shows the oil film profile of line segments a\u2013a0 and b\u2013b0 when amplitude ratio was 1", " This figure indicates that even though the oil film does not form at line segment a\u2013a0, an oil film forms sufficiently at line segment b\u2013b0. In a point contact, the oil film can be formed even if the amplitude ratio is less than 2.0 because the oil film can appear at line segment b\u2013b0 and support the load. The critical amplitude ratio at which an oil film begins to form was roughly estimated by calculating the average contact length of DA because the contact length differs depending on the position like the differences of line segments a\u2013a0 and b\u2013b0 as shown in Fig. 13. In other words, a point contact was regarded as a line contact. Contact length 2y (Fig. 15) at each x-coordinate can be indicated as follows: 2y\u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 2 x2 s Accordingly, the average contact length of DA is indicated as follows: DA \u00bc 2 D Z D=2 0 2y dx\u00bc 4 D Z D=2 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D 2 2 x2 s dx\u00bc pD 4 Here, the oil film begins to form when the amplitude ratio is greater than 2.0 under a line contact" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure3.24-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure3.24-1.png", "caption": "Fig. 3.24 An ancient Chinese mill (Wang 1968)", "texts": [ " Therefore, NL = 4, CsT = 3, NJT = 2, CsS = 3, and NJS = 1. Based on Eq. (3.2), the number of degrees of freedom, Fs, of this mechanism is: \u00bc 6\u00f0 \u00de 4 1\u00f0 \u00de 2\u00f0 \u00de 3\u00f0 \u00de \u00fe 1\u00f0 \u00de 3\u00f0 \u00de\u00bd \u00bc 18 9 \u00bc 9 The function of the device is to move the shield to resist rocks through the operation of the connecting link. It is still workable although the number of degrees of freedom is more than the independent input. Example 3.5 Calculate the number of degrees of freedom for the ancient Chinese mill for removing rice hulls shown in Fig. 3.24 (Wang 1968). Since the threads are designed for the purpose of providing an efficient input through human power and are symmetrical, this device can be analyzed as a spatial mechanism with four members (the frame KF, member 1; the thread KT, member 2; the horizontal bar with the connecting link KL1, member 3; and the crank with the mill stone KL2, member 4). There are four joints consisting of two thread joints (JT; joint a and joint b) and two revolute joints (JRy; joint c and joint d). Therefore, NL = 4, CsT = 3, NJT = 2, CsRy = 5, and NJRy = 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001953_87.572127-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001953_87.572127-Figure8-1.png", "caption": "Fig. 8. Single plane CLOS guidance.", "texts": [ " CLOS guidance is classified as a three point guidance law since its behavior is determined by the position of the missile with respect to the target and the target tracker. A guidance computer is utilized at the ground-based station and produces the acceleration commands which are sent via radio link to the autopilot. The basic objective of CLOS guidance is to drive the missile onto the LOS, joining the launch point to the target, and to keep it there for the rest of the engagement, as shown in Fig. 8. A typical CLOS guidance scenario was used to generate the required reference trajectory for the hybrid neural adaptive autopilot to track. Note that the reference yaw acceleration will always be zero. The guidance scenario represented a missile tracking a stationary target with a range of 3 km, horizontal displacement 353.5 m, and a vertical displacement of 353.5 m. At launch it was assumed that there is zero missile dispersion. The CLOS guidance loop of the missile is illustrated in Fig. 1, with the guidance shapers and roll compensation as designed by Roddy [21] for a missile operating at a constant speed of 500 m/s" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003039_j.cirp.2010.03.077-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003039_j.cirp.2010.03.077-Figure1-1.png", "caption": "Fig. 1. The meshed domain: the probes elements are the white lines.", "texts": [ " This problem is faced by solving the Fourier equation with the Finite Difference Method (FDM) into the meshed workpiece obtained with CUBIT 12.0. The meshed domain is then imported into the Laser Hardening Simulator (LHS) environment developed by the authors for the thermal and microstructure calculation. In LHS the laser parameters such as shape, dimension, power, velocity and trajectories of the beam can be set together. LHS stores the output in terms of temperature, structures and hardness in the investigation points by setting the probe elements into the domain as presented in Fig. 1. The physical properties have also to be assumed to be temperature dependant and the thermal history of the material after the laser interaction is then used for the microstructure transformations. The second step deals with the microstructures transformation temperature evaluation. Laser heat treatment, in fact, is always characterized by high heating rates typically ranging between 104 and 105 8C/s and, according to this, the eutectoid temperature and the ferrite to austenite transformation temperature are higher if compared to the ones concerning conventional heat cycle in oven as they mostly depend on the heat cycle gradient occurring into the workpiece" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002929_s0025654409020034-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002929_s0025654409020034-Figure1-1.png", "caption": "Fig. 1.", "texts": [ "OI: 10.3103/S0025654409020034 1. STATEMENT OF THE PROBLEM Consider a system consisting of two pivotally connected physical pendulums 1 and 2 (Fig. 1) rotating about horizontal axes in the gravity field. By O1, O2 and C1, C2 we denote the pendulum suspension points and centers of mass, respectively. We assume that O1, O2, and C1 lie on a straight line (see Fig. 1). We also assume that point O1 (the system suspension point) performs harmonic vibrations along the vertical about a given point O\u2217 according to the law O\u2217O1 = a sin \u03a9t. Let m1 and m2 be the pendulum masses, and let \u03c11 and \u03c12 be their radii of inertia with respect to the rotation axes. By l, b1, and b2 we denote the distances O1O2, O1C1, and O2C2, respectively. We assume that l and b2 are nonnegative; b1 is defined to be positive if C1 and O2 lie on one side of O1 (just as in Fig. 1) and negative if C1 and O2 lie on different sides of O1. The angles of deviation of segments O1O2 and O2C2 from their lower vertical positions are denoted by \u03d51 and \u03d52. *E-mail: kholostova_o@mail.ru 184 The kinetic and potential energies of the system are determined by the expressions (we omit the terms independent of \u03d5j and \u03d5\u0307j , j = 1, 2) T = 1 2 (m1\u03c1 2 1 + m2l 2)\u03d5\u03072 1 + 1 2 m2\u03c1 2 2\u03d5\u0307 2 2 + m2lb2\u03d5\u03071\u03d5\u03072 cos(\u03d51 \u2212 \u03d52) \u2212 [(m1b1 + m2l)\u03d5\u03071 sin \u03d51 + m2b2\u03d5\u03072 sin\u03d52]a\u03a9 cos \u03a9t, \u03a0 = \u2212(m1b1 + m2l)g cos \u03d51 \u2212 m2b2g cos \u03d52", " We nondimensionalize the momenta p\u0302\u03d51 and p\u0302\u03d52 by the canonical transformation \u03d5\u0302j , p\u0302\u03d5j\u2192 \u03d5\u0303j , p\u0303\u03d5j (j = 1, 2) defined by the formulas \u03d5\u0302j = \u03d5\u0303j and p\u0302\u03d5j = m1l 2\u03a9p\u0303\u03d5j . We also introduce the dimensionless time \u03c4 = \u03a9t and the dimensionless parameters \u03bc = m2 m1 , \u03b2 = b2 l , \u03b3 = b1 l + \u03bc, ij = \u03c1j l (j = 1, 2). Here \u03bc \u2265 0, ij > 0, \u03b2 \u2265 0, and the parameter \u03b3 can have either sign. The case \u03b2 = 0 means that pendulum 2 is suspended at the center of mass (i.e., O2 \u2261 C2). The parameter \u03b3 is zero if the suspension point O1 of pendulum 1 is at the center of mass O\u2032 (see Fig. 1) of the system consisting of point masses m1 and m2 under the assumption that they are concentrated at points C1 and O2. The parameter \u03b3 is negative if point O1 lies in the interior of segment O\u2032O2 and positive if O1 lies outside this segment. We note that if \u03b2 = 0 or \u03b3 = 0, then the potential energy of the original system depends on a single coordinate (\u03d51 or \u03d52, respectively). In the dimensionless variables, the Hamiltonian of the system acquires the form H\u0303 = \u03bci22p\u0303 2 \u03d51 \u2212 2\u03bc\u03b2 cos(\u03d5\u03031 \u2212 \u03d5\u03032)p\u0303\u03d51 p\u0303\u03d52 + (i21 + \u03bc)p\u03032 \u03d52 2\u03bcf(\u03d5\u03031, \u03d5\u03032) \u2212 (\u03b52\u03c92 + \u03b5 sin \u03c4)g(\u03d5\u03031, \u03d5\u03032), (1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure10.2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure10.2-1.png", "caption": "Fig. 10.2 Chu State repeating crossbow (Jing 2009) a Real object b Kinematic sketch", "texts": [ " After the Han Dynasty, the structures of the original crossbow and trigger mechanism have not changed except that the size became larger to increase the shooting range. With the enhancement of accuracy, the next development in the crossbows was to increase the shooting efficiency. Therefore, the repeating crossbow was invented, one that can complete all four shooting processes at once by operating the input link. According to the archaeological discoveries, the earliest object of the repeating crossbow was excavated in Jiangling County of Hubei Province (\u6e56 \u5317\u7701\u6c5f\u9675\u7e23) in China and can be dated back to 400 BC as shown in Fig. 10.2a. Since the excavated site belonged to the Chu State (\u695a\u570b) of the Warring Period, the device was named as Chu State repeating crossbow (Zhong 2008; Jing 2009). It consists of the frame (member 1, KF), a bow (member 2, KCB), a bowstring (member 3, KT), an input link (member 4, KI), a percussion link (member 5, KPL), and a connecting link (member 6, KL) as shown in Fig. 10.2b. The magazine is fixed on top of the frame and contains 20 bolts. Each bolt is placed in the two bolt channels in sequence. The percussion link and the connecting link are cleverly attached on the input link in order to pull the bowstring. When pushing the input link forward, the connecting link hooks the bowstring and then pulls the input link backward. When the percussion link touches the switch point on the frame, the bowstring is released to shoot two bolts at one time. By gravity, the bolts on the 10", " For the case shown in Fig. 10.9b2, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.9c2. 3. For the case shown in Fig. 10.9b3, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.9c3. Therefore, three specialized chains with identified frame, bow, bowstring, input link, percussion link, and connecting link are available as shown in Figs. 10.9c1\u2013c3. Step 4. The rectangular coordinate system is defined as shown in Fig. 10.2b. The shooting processes of Chu State repeating crossbow is to transform the reciprocating motion of the input link to pull and release the bowstring to shoot the bolts. The uncertain joints may have multiple types to achieve the equivalent function. 1. Considering uncertain joint J1, it has one possible type: the input link rotates about the z-axiswith respect to the percussion link, denoted as JRz. 2. Considering uncertain joints J2, J3 and J4, each one has two possible types. When any one is a cam joint, denoted as JA, the others rotate about the z-axis, denoted as JRz" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003517_s00170-012-4481-9-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003517_s00170-012-4481-9-Figure4-1.png", "caption": "Fig. 4 T- and V-shaped CAD material models", "texts": [ " They can be geometrically and materially complex and are thus difficult or impossible to fabricate using conventional processes. They have multiple, thin members that are preferably made from lightweight materials with high specific strength and stiffness. Such structures are readily applicable to the aerospace and automotive industries where there is continuous emphasis on higher strength and lower-weight structures for improved fuel efficiency and performance. Material-specific CAD models were used to fabricate the dual-material structures. In Fig. 4, the T-shaped CAD model was designed for material A (Ti6Al4V), while the V-shaped CAD model was designed for material B (Ti6Al4V/10 wt.% TiC). Bringing the two models together forms scarf joints at locations \u201cA\u201d and butt joint at location \u201cB\u201d. Attempts to fabricate the structures using these models with scarf and butt joints were unsuccessful as cracks developed visibly after the eighth layer of material deposition. Residual stresses resulting from uneven thermal expansion of the two materials at the transition joint may have caused the crack initiation and propagation" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001649_00207540310001595873-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001649_00207540310001595873-Figure6-1.png", "caption": "Figure 6. 3D test part model.", "texts": [ " After the best-matched setting scheme is found from the database, the data are selected from the database, and a user interface is displayed to feed back the \u2018optimal\u2019 answer. The detailed algorithm of the whole process is given in figure 5. As figure 5 shows, to make the system select the correct process parameter settings, the user first needs to qualify his or her requirements on the four resulting properties. After that, the system will scan the database; find the most suitable parameter settings and feed back to the user. The whole process can be iterated until the user is satisfied with the results. Two parts (parts 1 and 2 shown in figure 6) under different property requirements were built to evaluate the system. A higher priority was given to the process time and dimensional accuracy for the first part. The second part, however, was given a priority on the other two resulting properties. After the user inputs the weights correctly, the system feeds back the relative process parameter settings and gives the expected result values. The user-interface displays for the requirement settings and corresponding result outputs of the two cases are shown in figures 7 and 8, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003341_icma.2010.5589079-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003341_icma.2010.5589079-Figure3-1.png", "caption": "Fig. 3. Coordinate system of the wheelchair robot.", "texts": [ " In this step, the robot stops moving and the back flippers rotate clockwise to make the tracked mechanisms transform to concave geometry with the assistant of the front flippers until the back planetary wheels support on the upper floor, as shown in Fig 2(e)-(f). Then the second step of phase 4 starts, the robot keeps on climbing and the back and front flippers rotate anticlockwise until the robot loads on the upper floor completely, as shown in Fig 2(g)-(h). A. Coordinate System of the Wheelchair Robot For configuration analysis of stair-climbing, the coordinate system is established in the lateral symmetry plane of the robot mechanism as shown in Fig. 3. In Fig. 3, the world frame oW-xWyWzW is established at the base point of the first stair, frame oR-xRyRzR whose coordinate axes are parallel correspondingly to those of frame oW-xWyWzW is established at the front road wheels to represent the movement of the front road wheels, frame oA-xAyAzA is fixed with the supporting frame to represent the obliquity of the chair, frame oB-xByBzB and oC-xCyCzC are fixed with the back and front flippers separately to represent the rotation of the flippers and the planetary wheels" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002901_0278364909348762-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002901_0278364909348762-Figure1-1.png", "caption": "Fig. 1. Sketches of the hybrid robot illustrating (a) a wheel assembly and (b) its use for rolling.", "texts": [ " Each joint has two arms and two Jk joints in opposite directions. The knee rotates around the Jh to make the robot travel while standing using the leg pivoted at the joint Jk. This robot has same specifications of arm design in length, radius, and width, as well as the leg design in both sides, and moves with synchronism in its front and back. However, the left driving joints disconnect from the right so that arms and legs take different postures freely on each side. Normally, only four of eight legs contact the ground at a certain moment (see Figure 1(a)). A suspension mechanism is not necessary since our robot frame is not so rigid to stand at three contacts on the ground, in general. In critical cases, more than five legs touch the ground. The robot has two actuators M1 and M2 to control the left and right arms. Arms at the front and back are combined mechanically so that they can behave similarly with synchronism. Two actuators M3 and M4 are installed for two leg pairs in the left and right, respectively. Similar to the arm mechanism, two leg pairs located at the front and back are combined mechanically so that they move with synchronism. Accordingly, the robot is composed of four DOFs in total one arm set and one leg set for each side. In addition, we introduced wheels to the legged robot to make it a hybrid robot (Okada et al. 2006) so that it moves not only as an L-type but also as a W-type (see Figure 1(b)). The introduction of legs to a wheeled robot might also lead it to be hybrid, of course. In either introduction, two legs are fixed at the knee axes with an offset that is necessary to prevent the legs from touching together in W-type. Note that the actuators remain, even when we attach the wheel (see Figure 2). Then no additional motors are needed. The arm behaves as a link of a serial manipulator in L-type and as a spoke of a wheel in W-type. Schematic models including parameters and constants are shown in Figure 3" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure3.23-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure3.23-1.png", "caption": "Fig. 3.23 Trigger mechanism of an ancient Chinese crossbow (Mao 2001)", "texts": [ " This is a planar mechanism with three members (members 1, 2, 3) and three joints consisting of two revolute joints (a and c) and one gear joint (b). Therefore, NL = 3, CpRy = 2, NJRy = 1, CpRx = 2, NJRx = 1, CpG = 1, and NJG = 1. Based on Eq. (3.1), the number of degrees of freedom, Fp, of this mechanism is: Fp \u00bc 3 NL 1\u00f0 \u00de NJRyCpRy \u00fe NJRxCpRx \u00fe NJGCpG \u00bc 3\u00f0 \u00de 3 1\u00f0 \u00de 1\u00f0 \u00de 2\u00f0 \u00de \u00fe 1\u00f0 \u00de 2\u00f0 \u00de \u00fe 1\u00f0 \u00de 1\u00f0 \u00de\u00bd \u00bc 6 5 \u00bc 1 Therefore, the motion of this mechanism is constrained. Example 3.3 Calculate the number of degrees of freedom for the trigger mechanism in an ancient Chinese crossbow shown in Fig. 3.23 (Mao 2001). It is used to hook the tense bowstring for stable shooting. The shooter presses the input link (member 2) to drive the percussion link (member 3) to release the bowstring. The frame (member 1) is not shown in the figure. This is a planar mechanism with four members (frame, member 1; input link KI, member 2; percussion link KPL, member 3; and connecting link KL, member 4) and five joints consisting of three revolute joints (JRz; a, b, and e) and two cam joints 3.7 Constrained Motion 55 (JA; c and d)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002380_an9840900453-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002380_an9840900453-Figure1-1.png", "caption": "Fig. 1. Effect of NH4+ concentration on the GDH - HRP system", "texts": [], "surrounding_texts": [ "The reaction sequence was as follows: Triglyceride + 3H20 glycerol + 3 fatty acids (7) Glycerol + N A D + z dihydroxyacetone + NADH + H+ (8) NH4+ NADH + H+ + B025 NAD+ + H 2 0 (9) The particular ions (NH4+, Mn2+ and Ca2+) associated with each reaction have been found to be the principal activators for the enzymes. 17 Other potentially influential compounds will be discussed later. Glycerol Determination Reactions (8) and (9) were performed simultaneously in the determination of glycerol. Simplex optimisation18 was employed in determining optimum reagent concentrations in the two-step glycerol measurement system. The results are summarised in Table 1. Glycerol dehydrogenase has been reported to exhibit optimum activity at pH 8-10 and at lo-3-10-1 M NH4+, as well as being inhibited by Na+ and solutions of high ionic ~trength.19~20 In this work the following optimum reagent concentrations were found for reaction (8) [when combined with reaction (9)]: NH4+ = 0.12 M; and GDH = 0.65 U per run (Table 1). High ionic strength and Na+ concentration were avoided by diluting the serum samples. The variables of GDH activity and NH4+ concentration were also optimised individually and independently (Figs. 1 and 2). Differences from the simplex optimisation method were probably due to intervariable dependencies. An optimum pH of 8.0 for the two-step system (Fig. 3) was the same as that previously reported for reaction (9).*4 At pH values above 8.0, Mn2+ tends to precipitate, causing irreproducible reaction rates for reaction (9).14 Of the two buffers tested, Tris resulted in signals 40% larger than those using glycine buffer. The indicator (trigger) reaction (9) was that developed by Cheng and Christian.14 Considerable variation in the reaction rate and reproducibility has been found with respect to substrates, reaction conditions and possible mechanisms. 1421 It was necessary that reaction conditions be slightly alkaline for adequate reproducibility. 14 Similar variation in reagent dependence was seen in this study, with the exception of the lack of an absolute requirement for Mn2+ (although the reaction was accelerated in the presence of Mn2+). In coupling the peroxidase reaction to the GDH reaction, optimum Pu bl is he d on 0 1 Ja nu ar y 19 84 . D ow nl oa de d by U ni ve rs ity o f Fi nd la y on 2 7/ 10 /2 01 4 20 :4 1: 59 . ANALYST, APRIL 1984, VOL. 109 455 v) *-' 'c 250 3 > 2! 5 200 tu X m 2 150 9 0 - N -0 I 100 1 0 7 8 PH Fig. 3. Effect of pH on the GDH - HRP system 300 v) S 3 c .- L2\" 200 -f! E .- X c F! - 100 -0 I 0 I I I -5 -4 -3 -2 Log([glyceroll/~) Fig. 4. Semilogarithmic plot of the calibration graph for the determination of glycerol in standard aqueous samples reagent concentrations for the second reaction were Mn2+ = 0.24 mM and HRP = 30 U per run (Table 1). These concentrations were higher than previously employed. l4,22 It was observed that the GDH reaction (8) proceeded much more slowly than reaction (9), which adversely affected the analysis time and the sensitivity. This problem was approached by firstly increasing the NAD concentration (0.01 M NAD or 5.5 mg per run, from simplex optimisation), secondly, maintaining the reaction at 33 \"C and thirdly, incubating for 5 min. In incubating, however, feedback inhibition by both NADH (competitively) and dihydroxyacetone (uncompetitively) takes place,20 which resulted in a non-linear calibration graph (approximately a logarithmic response over wide concentration ranges, as shown in Fig. 4) and reduced sensitivity compared with that of the NADH - oxygen reaction14 (detection limit 5 x 10-5 M glycerol for aqueous standards and 1 X 10-4 M glycerol for serum samples) (Fig. 5). A within-run precision of 3% was obtained. This could be reduced further by combining reagents in a single stock solution, thus decreasing the number of required pipette measurements. Note in Fig. 5 that the response for glycerol is reduced in serum, necessitating calibration using serum controls. Triglyceride Determination Lipase catalyses the hydrolysis of triglycerides to glycerol and fatty acids. The hydrolysis of triglycerides [reaction (7)] was performed either in series with (internal hydrolysis) or separate from (external hydrolysis) the glycerol reaction. Complete hydrolysis is slow and not substrate specific.19J) The optimum pH and effect of several activators such as Ca2+, Na+, bile salts and emulsifiers are reported to vary significantly with different isoenzymes.23-25 With the external hydrolysis scheme, optimum activity for the hog pancreas isoenzyme was seen at pH 7.5 (Fig. 6). Ca2+ and bile salt activation of the lipase was obtained using 0.05 M Ca2+ externally or 0.005 M Ca2+ internally and 0.05% mlV sodium taurocholate (bile salt). Na+ and gum arabic (emulsifier) were found to have no significant effect on hydrolysis. a-Chymotrypsin, a non-specific esterase known to increase the rate of hydrolysis,6 was observed to have no effect in these studies. Of the two standard substrates used, olive oil was found to be more reactive and more convenient than solid tristearin. Olive oil was determinable down to 25 mg dl-1 (0.3 mM) (Fig. 7) with a relative standard deviation of 8%. Analysis by internal hydrolysis was faster and more sensitive than by external hydrolysis, by a factor of two in both Pu bl is he d on 0 1 Ja nu ar y 19 84 . D ow nl oa de d by U ni ve rs ity o f Fi nd la y on 2 7/ 10 /2 01 4 20 :4 1: 59 . 456 80 Lo C - .- 2 60 I -E! Y .- X 40 +.I 9 9 - N U I - 20 I I 1 I I 0 100 200 300 400 500 Triglyceride/mg per 100 ml Fig. 7. Calibration graph for the determination of triglycerides in standard aqueous samples (by the external hydrolysis procedure) instances. Sequential samples could be analysed more rapidly following external hydrolysis? however. Calibration must be carried out concurrently with sample analyses. The presence of lipase influenced the behaviour of reaction (9), at times giving a significant blank or slightly inhibiting HRP, and at other times substantially activating the catalysis. It was necessary to recharge the electrode and change the membrane on a weekly basis. It appears as though the presence of oils and suspensions has adverse surface effects on the PTFE membrane." ] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure8-1.png", "caption": "Fig. 8. Motion graph of three consecutive tooth pairs.", "texts": [ " This guess procedure was deeply tested for different transmission layouts and proved to be successful. In the view of contact pattern estimation we need to find the rigid rotation of the two mating members about their rotation axis over a complete mesh cycle. The solution of (16) yields u2\u00f0u1\u00de over the complete mesh cycle, and the transmission error Du2\u00f0u1\u00de is defined as Du2\u00f0u1\u00de \u00bc u2\u00f0u1\u00de u1 N1 N2 ; \u00f025\u00de where N1 and N2 are the pinion and gear number of teeth, respectively. The graphical representation of (25) is known as motion graph. A typical motion graph is shown in Fig. 8. However, different tooth flank geometries can produce more complex motion graphs as the ones presented in [18]. For a given tooth pair the two extremum values u1s and u1e, as in Fig. 8, correspond to the extremum points of the path of contact. For a given value u1 of the pinion rotation angle, the corresponding rigid rotation of the gear u2 is determined by the tooth pair that produces the greatest transmission error value: u2\u00f0u1\u00de \u00bc u1 N1 N2 \u00femax k Du2 u1 \u00fe k 2p N1 \u00f026\u00de with k 2 Zju1i 6 u1 \u00fe k 2p N1 6 u1o : The path of contact over the pinion and gear tooth surface is given by the union of the tangency points over a complete mesh cycle. The values u1\u00f0u1\u00de; v1\u00f0u1\u00de; u2\u00f0u1\u00de, v2\u00f0u1\u00de are mapped on eCf 1 and eCf 2 to obtain the path of contact on the two mating member surfaces, as depicted in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002335_1.2406088-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002335_1.2406088-Figure4-1.png", "caption": "Fig. 4 Hybrid model\u2014schematic representat one tooth pair model is represented\u2026", "texts": [ " The kinetic nergy associated with the teeth is considered as being part of the ear body contributions, i.e., the high frequency modes related to ooth eigenfrequencies are neglected and the tooth or foundation ig. 5 Gear geometry \u202010\u2021 \u201etooth number on pinion/on gear is 0/50, module is 4 mm, pressure angle of 20 deg, torque on inion of 294 N m\u2026 ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash mass matrices are nil. Considering a model similar to the one shown in Fig. 4, the assembly of all the individual mass and stiffness matrices leads to a differential system of the form 0 0 0 Mxq d\u0308 x\u0308 q\u0308 + Kdd t Kdxq t Kdxq t Kxq d x q = Fdd Fxq 10 where d represents the instantaneous number of dof which is also the number of discrete slices of the foundations on pinion and gear teeth; x is the degree of freedom dof vector of the pinion and the pinion shaft two node shaft elements+lumped parameter elements for bearings ; q are the modal dof of the substructure gear, output shaft, and bearings ; and Mxq is the global matrix made of the pinion/pinion shaft submatrix Mx and that of the substructure Mred " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002980_978-3-642-01153-5-Figure1.8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002980_978-3-642-01153-5-Figure1.8-1.png", "caption": "Figure 1.8.1 Size of each part of magnetic pole of salient pole synchronous machine Figure1.8.2 Size of damping bar hole of salient pole synchronous machine", "texts": [ " The problem has been discussed in a lot of literatures[8], here we only list the result. (1) Leakage self inductance of excitation winding of salient pole synchronous machine is 0 2 22 fd f f fd w L P l a (1.8.1) where f is the specific leakage permeance of excitation winding; l is rotor iron length; and 2 4.00 0.25 1.75 0.20 1.27 0.50 1.15 0.44 t P f P P m mP P m d a c c h ba c c l in which 2 14 2 2 ( 2 2 ) 2 P t P t P P m m m P bd h D dc b P c b h h P The size of each part of the magnetic pole of the salient pole synchronous machine is shown in Fig. 1.8.1, here 1D is the inter diameter of the stator iron; is air-gap length; Ph and Pb are the height and width of the pole shoes respectively; mh and mb are the height and width of the pole body, respectively. (2) Leakage self inductance of damping winding of the salient pole synchronous machine is 0 ( )c c c tL l AC Machine Systems 38 where cl is rotor pole length; c is the specific slot leakage permeance; t is the specific tooth top leakage permeance; and 1 / 0.30 0.64 1 / s c s c s c s b d h b d b (for circular bar) 2 21 1 2 2ln arctan 2 s t s s s b b b b The size of each part is referred to in Fig. 1.8.2. (3) Leakage inductance of each segment of the end ring of the salient pole synchronous machine is 02 2 ln 0.25 2 e e e ltL r where 2t is length of each segment of the end ring; el is the interval between the end ring and rotor end surface; er is the equivalent radius of the cross-section of the end ring. In analyzing the inductance of each stator loop produced by the air-gap magnetic field, the harmonic magnetic field is considered already, so the effect of stator differential leakage reactance is included in this inductance" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002327_cdc.2006.377687-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002327_cdc.2006.377687-Figure2-1.png", "caption": "Fig. 2. Formation control of vessels.", "texts": [ " Therefore, the forward velocity (satisfying |u| < Umax) becomes dominant, see (6). Assumption (5) means that if the angular rate r converges to zero, the sway velocity v is damped out due to hydrodynamic drag and also converges to zero. B. Control Objective In this paper we deal with cross-track control for formations of underactuated surface vessels. We will design decentralized control laws for n vessels such that, after transients, the vessels form a desired formation and move along a desired straight-line path with a given velocity profile, as illustrated in Fig. 2. The desired formation is characterized by a formation reference point Pref (t) and a set of vectors r j 1,... ,n giving the desired relative positions of the vessels with respect to the point Pref(t). The desired path of the formation is given by a straight line L. The desired velocity profile is given by a differentiable function ud(t). The control objective is to guarantee that asymptotically, i.e. in the limit for t -> +oo, a) the vessels constitute the desired formation, i.e. r I (t) -rpl = ... = rn(t) -rP. = Pref(t), FrlP3.2 45th IEEE CDC, San Diego, USA, Dec. 13-15, 2006 where rj, j 1,... n, are the position vectors of the vessels; b) Pref (t) follows the desired path L with the desired velocity profile ud(t), i.e. Pref(t) C L and kIref(t) = Ud(t), and the orientation of the vessels are aligned with the desired straight line paths. By choosing an inertial coordinate system with the x-axis aligned with the desired straight-line path, i.e. L = {(x, y): x C R, y = O} (see Fig. 2), the control objective can be formalized as follows t ( i(t ) / ud(s)ds) =c-D j (7) (8) 1, ... n, (9) where c is a constant of integration and [xj, yj]T and [Dxj, Dyj]T are the coordinates of the vessel position vectors rj and relative position vectors rpj, respectively, in the chosen inertial coordinate system. The above stated control problem will be solved in two steps. First, for each vessel we design independent crosstrack controllers guaranteeing that the cross-track control goal (7) is achieved, the orientation of each vessel satisfies (8), and that the remaining dynamics in the x direction track the speed reference command u,j (j corresponds to the jth vessel)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003314_j.ymssp.2010.11.013-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003314_j.ymssp.2010.11.013-Figure3-1.png", "caption": "Fig. 3. Golden section search.", "texts": [ " We also ignore the stop band ripples Rs as type1 Chebyshev filters do not exhibit stop band ripples. The values for Fp1, Fp2 are calculated from the following equations: Fp1 \u00bc Fc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe 1 4Q2 r 1 2Q Fp2 \u00bc Fc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe 1 4Q2 s \u00fe 1 2Q ! : \u00f01\u00de An accelerated one dimensional search is performed in coarse tuning step (Fig. 1). The method we use here is golden section search, which deals with a unimodal objective by rapidly narrowing an interval guaranteed to contain optimum [8]. Fig. 3 illustrates the idea of golden section search, where four carefully spaced points are iteratively considered. Leftmost x\u00f0lo\u00deis always a lower bound on the optimalx , and x\u00f0hi\u00de is an upper bound. The function optimum lies between the interval \u00bdx\u00f0lo\u00de,x\u00f0hi\u00de . Points x\u00f01\u00de and x\u00f02\u00de are the intermediate points. Each iteration determines whether the objective is better at x(1) or x(2), if x(1) proves better, the move direction for the next iteration is left and x\u00f02\u00de becomes x\u00f0hi\u00de and if x\u00f02\u00de proves better, the more direction for the next iteration is right and x\u00f01\u00de becomes x\u00f0lo\u00de", " It then determines the search direction (right or left) and fits a quadratic function with either \u00f0x\u00f0lo\u00de, x\u00f01\u00de, x\u00f02\u00de\u00de or \u00f0x\u00f01\u00de, x\u00f02\u00de, x\u00f0hi\u00de\u00de or it calculates the quadratic fit x\u00f0qu\u00de from Eq. (3) and again applies criteria similar to golden section search to discard one point and so on. The combination of parabolic interpolation and golden section search can speed up the optimal search process by 35\u201340% as compared with golden section search only [9]. Fig. 4 shows the process visually. Algorithm1. Golden section search\u2014Refer to Fig. 3 Step 1: Initialization Lower bound) x(lo) on f(x) Upper bound) x(hi) on f(x) Stopping tolerance) e40 Step 2: Computation Evaluate f(x) on all four points x\u00f0lo\u00de ,x\u00f0hi\u00de ,x\u00f01\u00de ,x\u00f02\u00de x\u00f01\u00de\u2019x\u00f0hi\u00de a\u00f0x\u00f0hi\u00de x\u00f0lo\u00de\u00de x\u00f02\u00de\u2019x\u00f0lo\u00de \u00fea\u00f0x\u00f0hi\u00de x\u00f0lo\u00de\u00de a\u20190:618 t\u20190 Step 3: Stopping if \u00f0x\u00f0hi\u00de x\u00f0lo\u00de\u00derethen stop and x \u2019 1 2 \u00f0x \u00f0lo\u00de \u00fex\u00f0hi\u00de\u00de )approx. optimal solution Step 4: Direction if f \u00f0x\u00f01\u00de\u00deo f \u00f0x\u00f02\u00de\u00de then left search x\u00f0hi\u00de\u2019x\u00f02\u00de x\u00f02\u00de\u2019x\u00f01\u00de x\u00f01\u00de\u2019x\u00f0hi\u00de a\u00f0x\u00f0hi\u00de x\u00f0lo\u00de\u00de t\u2019t\u00fe1 go to Step3 Step 4: Direction if f \u00f0x\u00f01\u00de\u00de4 f \u00f0x\u00f02\u00de\u00de then right search x\u00f0lo\u00de\u2019x\u00f01\u00de x\u00f01\u00de\u2019x\u00f02\u00de x\u00f02\u00de\u2019x\u00f0lo\u00de a\u00f0x\u00f0hi\u00de x\u00f0lo\u00de\u00de t\u2019t\u00fe1 go to Step3 The parameters found by golden section search are passed to direct search method for fine tuning" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003500_j.scient.2011.08.005-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003500_j.scient.2011.08.005-Figure1-1.png", "caption": "Figure 1: Half-toroidal CVT with 2 rollers.", "texts": [ " Moreover, it makes driving easier, passengers more comfortable, and increases the fatigue life of engine [2]. Measurements \u2217 Corresponding author. E-mail address:m_saadat@sharif.edu (M.S. Foumani). 1026-3098\u00a9 2011 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved. Peer review under responsibility of Sharif University of Technology. doi:10.1016/j.scient.2011.08.005 show fuel consumption reduction of up to 10% for CVTs [3]. To avoid surface contact, elastohydrodynamic oil film with high contact pressure endurance is used [4]. Figure 1 shows a schematic half-toroidal CVT. As the rollers rotate around AB and CD axes, transmission ratio changes continuously [5]. There are two types of toroidal CVT: halftoroidal and full-toroidal. Many researchers tried to introduce a model to calculate traction coefficient between disks and roller. Jacod et al. [6] defined a numerical model for prediction of traction coefficient in isothermal elliptical contact area for a wide range of operating conditions. Newall and Lee [7] presented a model to derive the EHL oil viscosity as a function of temperature, pressure and oil properties" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.17-1.png", "caption": "Fig. 4.17 A device used to draw water from water wells (\u4e95\u8eca), a Original illustration (Liu 1962), b Structural sketch, c Chain", "texts": [ " 82 4 Ancient Chinese Machinery The water device Jing Che (\u4e95\u8eca, a device used to draw water from water wells) was used to draw water from water wells. It was also called a wooden dipper water machine. The machine used wooden dippers instead of paddle blades. A series of wooden dippers were connected by a chain, and the chain was connected to a vertical wheel installed at the mouth of the water well. When the vertical wheel rotated, the wooden dippers were continuously raised to scoop the water, achieving a conveying function. Its main difference from the paddle wheel machine is that it did not have a sprocket at the lower portion. Figure 4.17a shows a design structure 4.6 Chain Drives 83 of Jing Che (Liu 1962). Since it was not possible to use wooden paddles to scoop water from a vertical well, a series of wooden dippers were used instead. The dippers were connected to the large wheel on the mouth of the water well. At one end of the wheel shaft was a vertical gear (member 3, KG2), that was connected to a horizontal gear (member 2, KG1). An animal was used to rotate the horizontal gear, that in turn drove the vertical gear. The vertical gear caused the large wheel connected to the chain of dippers (member 4, KC) to move, too" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003709_j.compfluid.2013.04.025-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003709_j.compfluid.2013.04.025-Figure3-1.png", "caption": "Fig. 3. Sketch of the computational domain D1 and presentation of the boundary", "texts": [ " As a consequence when a plane of symmetry and/or rotationally periodic solutions is present the numerical approach may greatly be simplified. These physical aspects are present with spur gears rotating in a region far from walls. The purpose of the next section is then to take advantage of simplifications studied in this section to estimate WPL generated by spur gears. conditions imposed at external surfaces. Based on the simplified approach which has been previously highlighted the computational domain (D1) comprises one halfwidth single tooth and the associated fraction of blank and the plane of symmetry (Fig. 3). The radial dimension of the domain is taken 15 times the tooth height while the axial dimension beyond the gear side is set to one-half the real tooth width. The vertical surface which is near the rotational axis (opening 1 in Fig. 3) is located at a radial distance equal to 10% of root radius. These values seem sufficient since increasing the size of the domain leads to insignificant variation of WPL estimation (i.e. less than 1%). The same boundary conditions as the ones used for the disk are employed here and RRF approach is still used. The numerical predictions are compared with experimental results from test rigs described by Diab et al. [6] and Changenet and Velex [2] in order to validate the use of the simplified configuration" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002640_bit.260250203-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002640_bit.260250203-Figure8-1.png", "caption": "Fig. 8. Effect of amount of enzyme spread on electrode surface.", "texts": [ " These basic species are able to decrease the intramembrane pH if the buffer capacity is not high enough. Hence, a concentration of 0.2M was chosen in the remaining experiments. The effect of temperature on the enzyme electrode is shown in Figure 7 . Increasing the temperature from 20 to 30\u00b0C affected the electrode response to a large extent. A further increase to 37\u00b0C caused a large decrease in the response and the response did not recover fully upon a return to 23\u00b0C. All experiments were thus run at 23\u00b0C (room temperature) to avoid any denaturation of the enzyme. Figure 8 shows how the amount of enzyme spread on the surface of the electrode affects the response. The widest range of linearity (down to 1 g/L) was obtained with 6 IU/membrane. With excess of enzyme, the electrode response in this range was not significantly affected by the amount of lysine decarboxylase used. Electrodes were tested containing the same density of enzyme on membranes of varying thickness (Fig. 9). The largest response was obtained with thinner immobilized enzyme layer (5.5 pm thickness)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001459_jsvi.1998.1988-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001459_jsvi.1998.1988-Figure4-1.png", "caption": "Figure 4. Eccentricities on pinion and gear.", "texts": [ " Upon neglecting second order terms and gyroscopic effects, the inertial kinetic energy of stage s is expressed as To s = 1 2[mps [u\u03072 ps +(v\u0307ps +Sps )2 + (w\u0307ps +Cps )2]+ Ips [f 2 ps +c 2 ps ]+ Iops [Vps + u ps ]2 +mgs [u\u03072 gs +(v\u0307gs +Sgs )2 + (w\u0307gs +Cgs )2]+ Igs [f 2 gs +c 2 gs ]+ Iogs [Vgs + u gs ]2], (11) with Sp,gs =\u2212ep,gsVp,gs sin (Vp,gst\u2212 lp,gs ), Cp,gs = ep,gsVp,gs cos (Vp,gst\u2212 lp,gs ). lps , lgs define the angular position of the eccentricity of the pinion and gear of stage s, respectively, mps , mgs are the masses, Ips , Igs and Iops , Iogs are respectively the transverse and polar moments of inertia of the pinion and the gear of stage s, and eps , egs are the eccentricities on the pinion and gear of stage s (see Figure 4). Lagrange\u2019s equations lead to the following elementary mass matrix and excitation vector: [Ms ]=diag (mps , mps , mps , Ips , Ips , Iops , mgs , mgs , mgs , Igs , Igs , Iogs ), (12) Hs (t)= T(0, \u2212mpsC ps , \u2212mpsS ps , 0, 0, IopsV ps , 0, mgsC gs , \u2212mgsS gs , 0, 0, IogsV gs ). (13) A complete drive can be decomposed into a set of pinion-gear elements, shaft elements (including axial, flexural and torsional displacements) and lumped parameter elements in order to simulate the contributions of bearings, couplings, load machines [16] ", " A 12 angle between the centre lines of stages 1 and 2 Cint , Cout input, output torque ca modal damping coefficient associated with the ath modeshape es (M*) maximum normal gap in the base plane of stage s f1, f2, f3 rotational frequency of shaft 1 (input), shaft 2 (intermediate), shaft 3 (output) fm mesh frequency fm1 mesh frequency stage 1 fm2 mesh frequency stage 2 fa (t) defined in equation (23) Ix spectrum imaginary part amplitudes Ips , Igs pinion, gear transverse moment of inertia Iops , Iigs pinion, gear polar moment of inertia Jk polar moment of inertia of the kth shaft line ksi stiffness of the ith cell in the base plane of stage s (Figure 2) kms , Dks (t) average and time-varying component of stage s mesh stiffness ka average modal stiffness associated with the ath modeshape mps , mgs mass of stage s pinion, gear ma modal mass associated with the ath modeshape M* a point of contact in rigid-body conditions Ncs (t), Ns (t) actual and nominal time-varying number of contacting cells in the base plane of stage s Nstage number of stages p1s (Mi ) distance from a potential point of contact Mi to pinion (Figure 2) p2s (Mi ) distance from a potential point of contact Mi to gear (Figure 2) qs degree-of-freedom vector of the pinion-gear pair of stage s Rbps , Rbgs base radii of stage s pinion, gear Rx spectrum real part amplitudes SF(TE) shape factor of transmission error TEi (v) ith frequency content of transmission error Tms mesh period of stage s T1 mid-point of the tangent between base plane and pinion base cylinder (Figure 2) T2 mid-point of the tangent between base plane and gear base cylinder (Figure 2) ups , vps , wps pinion translational degrees of freedom (stage s) ugs , vgs , wgs gear translational degrees of freedom (stage s) Vs (Mi ), Vms structure vector in Mi , average structure vector of stage s aps apparent pressure angle (stage s) bs , bbs helix angle, base helix angle (stage s) d vector of the unknowns in the pseudo-modal basis des (Mi ) normal gap at Mi , potential point of contact in the base plane of stage s fps , Cps , ups pinion rotational degrees of freedom (stage s) fgs , Cgs , ugs gear rotational degrees of freedom (stage s) lps , lgs angular position of the pinion, gear eccentricity (Figure 4) hs (Mi ) co-ordinate of a potential point of contact Mi along the line of contact (equation (7) and Figure 2) r1, r2 percentages of modal strain energy on mesh 1 and 2, respectively Ds (Mi ), Dso (Mi ) deflection at Mi , quasi-static deflection at Mi , (stage s) Vint , Vout input, output rigid-body angular velocity Vps , Vgs pinion, gear rigid-body angular velocity (stage s) A . vector A completed by zeros to the total system size TA transpose of A (matrix or vector)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001516_60.986436-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001516_60.986436-Figure2-1.png", "caption": "Fig. 2. SMIG under perfect phase balance. (a) Phasor diagram. (b) Phasor diagram showing angular relationship between currents.", "texts": [ " 1 with the Smith connection for the motoring mode [11] reveals that phases B and C have been interchanged, a condition necessary for proper phase balancing as will be explained in Section III. In this paper, the motor convention has been adopted for the direction of currents. The Smith connection is essentially an asymmetrical winding connection. But, with an appropriate choice of the terminal capacitances, it is possible for the induction generator to operate with balanced phase currents and phase voltages. As shown in Fig. 1, the B-phase current is the sum of the capacitor currents and . Consider the phasor diagram in Fig. 2(a), drawn for the special case for perfect phase balance. The current leads (or ) by rad and hence lags by rad. The voltage (which is equal to ), is equal to . The capacitor current leads by rad and hence it lags by rad. For generator impedance angles between rad and rad, the phase current can be synthesized with the required magnitude and phase angle to give phase balance, by using suitable values of and . Under perfect phase balance conditions, the phase currents of the induction generator must sum to zero", " When is less than rad, is positive but and TABLE I SUSCEPTANCES TO GIVE PHASE BALANCE IN THREE-PHASE INDUCTION GENERATOR are negative, hence one capacitance and two inductances are required for perfect phase balance. It is interesting to note that, when rad, and are both equal to zero, hence the capacitances and are not required. Under this condition, the Smith connection is identical to the Steinmetz connection for a star-connected induction generator. When rad, however, is equal to zero and only capacitances and need to be used for achieving perfect phase balance. Referring to the phasor diagram of the SMIG shown in Fig. 2(b), the following angular relationships may be deduced: From the current phasor triangles, it can be shown that the line current and the generator phase current are related by (21) The angle between and in Fig. 2(b) is given by (22) If the input power factor angle is defined to be positive when the line current lags the supply voltage , then (23) Equations (22) and (23) indicate that the input power factor angle of the SMIG under perfect phase balance is a function of the generator impedance angle only. Fig. 3 shows the variation of the line power factor angle with the positive-sequence impedance angle . It is observed that the line power factor angle is 180 (i.e., line power factor is equal to unity) when is equal to 130" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002049_robot.2002.1013650-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002049_robot.2002.1013650-Figure5-1.png", "caption": "Fig. 5. Constrained variables in the control algorithm", "texts": [ " Using the Lagrange formulation, the dynamic model of the robot can be written as [23]: M(d0 + N(q , 414 + G(q) = r (1) This equation provides with the joint torques vector l? as a function of the joint positions vector (fig.1) q = (q1,q2,q3,q4,q5,q6)T and joint velocity vector q , with M , N and G respectively the inertia matrix, the Coriolis matrix and the gravity vector. B. Impact During collision, the contact of one foot with the ground consists in unilateral constraint without sliding [22]. The foot is kept in the horizontal position. The impact is considered as occurring at the ankle. The condition of the geometric closure is given by: where (fig.5) ( ~ a u p p . ankle , ~supp. ank le ) are the Cartesian coordinates of the ankle of the support leg, (xfly. yyfly. ankle) , the Cartesian coordinates of the ankle of the swing leg, and L, the step length. By derivating 4: Let's C(q) be the Jacobian of #(a): (3) where Cn(q) is the normal component and Ct(q) the tangential component. When the end point of the kinematic chain enters in contact with the ground, velocity vector suddenly changes [14], [15], [19]. Using the conservation of linear and angular impulse and momentum for the entire chain, one can write the impulsive dynamic model: M(4)(4+ - 0-1 = C ( d T A (5) q- and q+ are respectively the velocity of the joints before and after impact", " According to these intuitive but physical considerations, a set of equality and inequality constraints listed below has been established: Robot internal constraints: Actuator torque limitations: 4 6 x 2 = 12 Constraints Joint posit ion limitations: qmin L q I q m a x (13) + 6 x 2 = 12 constraints Locomotor rhythm: It will guarantee the \"gravity compensation\" and the forward propulsion. - Erected Body Posture: the biped should maintain an erected posture during locomotion. This condition is guaranteed by a constraint on the pelvis height upelvia (fig.5): Ypelvia 2 hppelvis,i, (14) .+ 1 constraint - Overall Progression: the overall progression is de- fined as the speed of the ankle of the flying foot VXfly. ankle in the positive x-direction: 4 2 constraints 0 Equilibrium of the moving body: In this study, with the manipulator based model described in section 11, the locomotion we can consider is limited to static walking. The static stability is guaranteed by maintaining the projection of the center of mass X C ~ M within the soil of the support foot: xsupp", " As the pelvis x-position and the projection of the center of mass are located closely to in the BIP case, this constraint will also contribute to the static stability. Adaptation to environment: The swing limb has to be lifted off the ground at the beginning of a step and landed back at the end of the step. During the step, the flying foot has to stay clear off the surface to avoid contact. To satisfy this condition, the flying foot is maintained in the horizontal position: \u201cflu. foot = 0 (19) -+ 1 constraint Limits for the y-coordinates of the ankle of the swing 1% Yfly. ankle are given by (fig.5): fm(Xf1y. ankle) 5 Yfly. ankle 5 fiM(Xf1y. ankle) (20) -+ 2 constraints where fm and f~ are chosen as polynomial functions depending of the desired minimum tip clearance h, and the minimum step length XM - xm (fig.4). This way of specifying the constrained environment makes the algorithm easily adaptable to an obstacle-filled environment by changing on line the physical constraints over the prediction horizon (fig.2). Finally for a 6 dof biped robot, the optimization problem is subjected to 36 constraints" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure10.10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure10.10-1.png", "caption": "Fig. 10.10 Atlas of feasible designs of Chu State repeating crossbow", "texts": [], "surrounding_texts": [ "According to the study of excavated objects and historical literature, the original crossbow consists of the frame (member 1, KF), a bow (member 2, KCB), a bowstring (member 3, KT), an input link (member 4, KI), a percussion link (member 5, KPL), and a connecting link (member 6, KL). It also contains one bamboo joint (JBB), two thread joints (JT), two cam joints (JA), and three revolute joints (JRz). Therefore, the original crossbow can be considered as a cam mechanism with six members and eight joints. Since the crossbows and trigger mechanisms have been used extensively in many areas in ancient China, the structure of the original crossbow also varied in the different dynasties or areas. Furthermore, from the viewpoint of modern mechanisms, if the connecting link is omitted, the trigger mechanism still can hook the bowstring to save energy by utilizing the delicate geometrical shape of the frame, the input link, and the percussion link. The bowstring is hooked by the percussion link, and the input is driven to release 224 10 Crossbows the bowstring to shoot the bolt. It is a Type III mechanism with uncertain numbers and types of members and joints. Therefore, according to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction designs of the original crossbow with five or six members and eight joints is presented as follows: Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a cam mechanism with five members (members 1\u20135) or six members (members 1\u20136) with eight joints. 2. The frame (KF) is a multiple link. 3. The bow (KCB) is a binary link and connected to the frame (KF) with a bamboo joint (JBB). 4. The bowstring (KT) is a binary link and connected to the bow (KCB) with a thread joint (JT). 5. The input link (KI) is connected to the frame (KF) with a revolute joint (JRz), but not to the bowstring (KT). 6. The percussion link (KPL) is connected to the frame (KF) and the input link (KI) with uncertain joints. 7. The connecting link (KL) is connected to the input link (KI) and the percussion link (KPL) with uncertain joints. Step 2. Since the device is a mechanism with five or six members with eight joints, the corresponding 15 generalized kinematic chains are shown in Fig. 10.5. Step 3. There must be a pair of binary links as the bow and the bowstring that must be connected to the multiple link as the frame. Therefore, only those four generalized kinematic chains shown in Figs. 10.5b2, d3, d4, and d6 are qualified for the process of specialization. The feasible specialized chains are identified as follows: Frame, bow, and bowstring (KF, KCB, and KT). There must be a multiple link as the frame (KF) and a pair of binary links as the bow (KCB) and bowstring (KT). The bow must be connected to the frame and the bowstring with a bamboo joint (JBB) and a thread joint (JT), respectively. Therefore, the frame, the bow, and the bowstring are identified as follows: 1. For a generalized kinematic chain shown in Fig. 10.5b2, the assign- ment of the frame, the bow, and the bowstring generates one result as shown in Fig. 10.6a1. 2. For a generalized kinematic chain shown in Fig. 10.5d3, the assign- ment of the frame, the bow, and the bowstring generates two results as shown in Figs. 10.6a2 and a3. 3. For a generalized kinematic chain shown in Fig. 10.5d4, the assign- ment of the frame, the bow, and the bowstring generates one result as shown in Fig. 10.6a4. 10.3 Original Crossbow 225 4. For a generalized kinematic chain shown in Fig. 10.5d6, the assign- ment of the frame, the bow, and the bowstring generates one result as shown in Fig. 10.6a5. Therefore, five specialized chains with identified frame, bow, and bowstring are available as shown in Figs. 10.6a1\u2013a5. Input link (KI) Since the input link (KI) must be connected to the frame (KF) with a revolute joint (JRz) and not connected to the bowstring (KT), the input link is identified as follows: 1. For the case shown in Fig. 10.6a1, the assignment of the input link generates one result as shown in Fig. 10.6b1. 2. For the case shown in Fig. 10.6a2, the assignment of the input link generates one result as shown in Fig. 10.6b2. 226 10 Crossbows 3. For the case shown in Fig. 10.6a3, the assignment of the input link generates two results as shown in Figs. 10.6b3 and b4. 4. For the case shown in Fig. 10.6a4, the assignment of the input link generates one result as shown in Fig. 10.6b5. 5. For the case shown in Fig. 10.6a5, the assignment of the input link generates one result as shown in Fig. 10.6b6. 10.3 Original Crossbow 227 Therefore, six specialized chains with identified frame, bow, bow- string, and input link are available in Figs. 10.6b1\u2013b6 Percussion link and connecting link (KPL and KL) The percussion link (KPL) is connected to the frame (KF) and the input link (KI) with uncertain joints, and the remaining link should be the connecting link (KL) that is connected to the input link (KI) and the percussion link (KPL) with uncertain joints. Therefore, the percussion link and the connecting link are identified as follows: 1. For the case shown in Fig. 10.6b1, the assignment of the percussion link generates one result as shown in Fig. 10.6c1. 2. For the case shown in Fig. 10.6b2, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.6c2. 3. For the case shown in Fig. 10.6b3, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.6c3. 4. For the case shown in Fig. 10.6b4, since there is no the connecting link that is connected to the input link and the percussion link, Fig. 10.6b4 is not qualified for the process of specialization. 5. For the case shown in Fig. 10.6b5, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.6c4. 6. For the case shown in Fig. 10.6b6, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.6c5. Therefore, five specialized chains with identified frame, bow, bowstring, input link, percussion link, and connecting link are available as shown in Figs.10.6c1\u2013c5. However, the connecting link (KL) in Fig.10.6c2 and the percussion link (KPL) in Fig.10.6c4 are redundant during the shooting process. This means that the concepts in Figs.10.6c2 and c4 degenerate into five members, and these two specialized chains are not feasible. Step 4: The coordinate system is defined as shown Fig. 10.1a. The function of the trigger mechanism is to pull the input link to release the bowstring through the transmission of the percussion link and the connecting link. The uncertain joints may have multiple types to achieve the equivalent function. 1. Considering uncertain joints J1 and J2, each one has two possible types and they cannot be the same type simultaneously. When any one joint rotates about the z-axis, denoted as JRz, the other one is a cam joint, denoted as JA. 2. Considering uncertain joint J3, it has two possible types. If J3 is a revolute joint, denoted as JRz, J4 must be a cam joint, denoted as JA. 228 10 Crossbows In addition, J5 and J6 have two possible types and they cannot be the same type, simultaneously. When any one rotates about the z-axis, denoted as JRz, the other one is a cam joint, denoted as JA. 3. If J3 is a cam joint, denoted as JA, J4, J5 and J6 have two possible types. When any one is a cam joint, denoted as JA, the others rotate about the z-axis, denoted as JRz. By assigning the possible types of uncertain joints J1 (JRz and JA), J2 (JRz and JA), J3 (JRz and JA), J4 (JRz and JA), J5 (JRz and JA), and J6 (JRz and JA) to the specialized chains shown in Figs. 10.6c1, c3 and c5, 12 specialized chains with particular joints as shown in Figs. 10.6d1\u2013d12 are obtained. Step 5: Considering the motions and functions of the mechanism, each spe- cialized chain with particular joints is particularized to obtain the atlas of feasible designs that meet the ancient technical standards. Figures 10.7a\u2013l show the corresponding 3D solid models of the feasible designs of trigger mechanism. Figures 10.8a and b show an imitation illustration and a prototype of the original crossbow, respectively. 10.3 Original Crossbow 229 10.4 Chu State Repeating Crossbow Based on the excavated objects, Chu State repeating crossbow consists of the frame (member 1, KF), a bow (member 2, KCB), a bowstring (member 3, KT), an input link (member 4, KI), a percussion link (member 5, KPL), and a connecting link (member 6, KL). It also contains one bamboo joint (JBB), two thread joints (JT), two cam joints (JA), and three revolute joints (JRz). Therefore, Chu State repeating crossbow can be considered a cam mechanism with six members and eight joints. The function of the connecting link is to hold the bowstring. When the input link pulls the bowstring to its limited position, the percussion link touches the switch point and then releases the bowstring. However, Zhuge repeating crossbow replaces the connecting link by the magazine (the percussion link) that can hold the bowstring directly. Such a design may have existed in the design of Chu State repeating crossbow as well. Therefore, the number of members of Chu State repeating crossbow may be five or six. It is a Type III mechanism with uncertain numbers and types of members and joints. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction designs of Chu State repeating crossbow with five or six members and eight joints is presented as follows: 230 10 Crossbows Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a cam mechanism with five members (members 1\u20135) or six members (members 1\u20136) with eight joints. 2. The frame (KF) is a ternary link. 3. The bow (KCB) is a binary link and connected to the frame (KF) with a bamboo joint (JBB). 4. The bowstring (KT) is a binary link and connected to the bow (KCB) with a thread joint (JT). 5. The input link (KI) is connected to the frame (KF) with a prismatic joint (JPx), but not to the bowstring (KT). 6. The percussion link (KPL) is connected to the frame (KF) with a cam joint (JA). Step 2. Since the device is a mechanism with five or six members with eight joints, the corresponding generalized kinematic chains are shown in Fig. 10.5. Step 3. There must be a pair of binary links as the bow and the bowstring that must be connected to the ternary link as the frame. Therefore, only those three generalized kinematic chains shown in Figs. 10.5b2, d3, and d6 are qualified for the process of specialization. The feasible specialized chains are identified as follows: Frame, bow, and bowstring (KF, KCB, and KT) There must be a ternary link as the frame (KF) and a pair of binary links as the bow (KCB) and bowstring (KT). The bow must be connected to the frame and the bowstring with a bamboo joint (JBB) and a thread joint (JT), respectively. Therefore, the frame, the bow and the bowstring are identified as follows: 1. For a generalized kinematic chain shown in Fig. 10.5b2, the assign- ment of the frame, the bow, and the bowstring generates one result as shown in Fig. 10.9a1. 2. For a generalized kinematic chain shown in Fig. 10.5d3, the assign- ment of the frame, the bow, and the bowstring generates one result as shown in Fig. 10.9a2. 3. For a generalized kinematic chain shown in Fig. 10.5d6, the assign- ment of the frame, the bow, and the bowstring generates one result as shown in Fig. 10.9a3. Therefore, three specialized chains with identified frame, bow, and bowstring are available as shown in Figs. 10.9a1\u2013a3. Input link (KI) Since the input link (KI) must be connected to the frame (KF) with a prismatic joint (JPx) and not connected to the bowstring (KT), the input link is identified as follows: 10.4 Chu State Repeating Crossbow 231 232 10 Crossbows 1. For the case shown in Fig. 10.9a1, the assignment of the input link generates one result as shown in Fig. 10.9b1. 2. For the case shown in Fig. 10.9a2, the assignment of the input link generates one result as shown in Fig. 10.9b2. 3. For the case shown in Fig. 10.9a3, the assignment of the input link generates one result as shown in Figs. 10.9b3. Therefore, three specialized chains with identified frame, bow, bowstring, and input link are available in Figs. 10.9b1\u2013b3. Percussion link and connecting link (KPL and KL) The percussion link (KPL) is connected to the frame (KF) with a cam joint (JA), and the remaining link should be the connecting link (KL). Therefore, the percussion link and the connecting link are identified as follows: 1. For the case shown in Fig. 10.9b1, the assignment of the percussion link generates one result as shown in Fig. 10.9c1. 2. For the case shown in Fig. 10.9b2, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.9c2. 3. For the case shown in Fig. 10.9b3, the assignment of the percussion link and the connecting link generates one result as shown in Fig. 10.9c3. Therefore, three specialized chains with identified frame, bow, bowstring, input link, percussion link, and connecting link are available as shown in Figs. 10.9c1\u2013c3. Step 4. The rectangular coordinate system is defined as shown in Fig. 10.2b. The shooting processes of Chu State repeating crossbow is to transform the reciprocating motion of the input link to pull and release the bowstring to shoot the bolts. The uncertain joints may have multiple types to achieve the equivalent function. 1. Considering uncertain joint J1, it has one possible type: the input link rotates about the z-axiswith respect to the percussion link, denoted as JRz. 2. Considering uncertain joints J2, J3 and J4, each one has two possible types. When any one is a cam joint, denoted as JA, the others rotate about the z-axis, denoted as JRz. By assigning the possible types of uncertain joints J1 (JRz), J2 (JRz and JA), J3 (JRz and JA), and J4 (JRz and JA) to the specialized chains shown in Figs. 10.9c1\u2013c3, seven specialized chains with particular joints as shown in Figs. 10.9d1\u2013d7 are obtained. Step 5. Considering the motions and functions of the mechanism, each spe- cialized chain with particular joints is particularized to obtain the atlas of feasible designs that meet the ancient technical standards. Figures 10.10a\u2013g show the corresponding 3D solid models of the feasible designs. Figures 10.11a\u2013b show an imitation illustration and a prototype of Chu State repeating crossbow, respectively. 10.4 Chu State Repeating Crossbow 233 234 10 Crossbows 10.5 Zhuge Repeating Crossbow For Zhuge repeating crossbow, the existing literature does not specify whether its magazine is movable or not. Therefore, it has two different types according to the magazine is movable or fixed on the frame. Both of them are Type III mechanisms with uncertain numbers and types of members and joints and are presented as follows:" ] }, { "image_filename": "designv10_13_0003841_061407-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003841_061407-Figure2-1.png", "caption": "Figure 2. Schematic of a dipole system and detail of an individual vortex dipole. For clarity, the two point vortices and the line joining them is drawn. The dipole orientation \u03b1n with respect to the x-axis is perpendicular to the line joining the two vortices.", "texts": [ " It is quite remarkable that for a range of initial conditions, a pair of dipoles synchronizes its motion passively, via hydrodynamic-coupling only. We construct phase diagrams mapping the space of initial conditions to the respective behavior. We conclude by commenting on the integrability property of these systems. Consider N pairs of point vortices of equal and opposite strengths \u0393\u00b1 separated by a distance \u2113 in an inviscid, unbounded, two-dimensional fluid. Each vortex pair is called a dipole. The interactions of N dipoles are depicted in figure 2. According to the detailed schematic of a single dipole, the \u2018left\u2019 ( \u0393+ ) vortex and \u2018right\u2019 ( \u0393\u2212 ) vortex of the dipole are located in the complex z-plane (where = +z x yi and = \u2212i 1 ) at = + \u2113 = \u2212 \u2113\u03b1 \u03b1 z z z z i e 2 , i e 2 , (1)n n n n,l i ,r in n respectively. Here, = +( )z z z 2n n n,l ,r denotes the center of the vortex dipole and \u03b1n represents the \u2018orientation\u2019 of the vortex dipole with \u2113 = \u2212\u03b1e z zi n n i ,l ,r n , =n N1 ,..., . It is well known that the kinematic solution to the incompressibility condition in inviscid fluid amounts to determining a complex potential, \u03d5 \u03c8= +F z( ) i , that is analytic in the domain (except at singular points) and decaying at infinity" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003654_j.optlaseng.2011.05.016-Figure14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003654_j.optlaseng.2011.05.016-Figure14-1.png", "caption": "Fig. 14. Steam turbine blade fabricated by DLF.", "texts": [ " But the temperature gradient can be controlled by the intermittent liquid argon cooling method, and the direction of heat dissipation is nearly perpendicular to substrate, by which heat exchange dominates the process of heat dissipation. On the other hand, because of the heat accumulating result of the substrate and deposited layers, heat dissipation slows down so that heat conduction and heat convection cannot be neglected. Hence, the microstructures are mainly columnar crystals while there are a few mixed crystals at their top of specimens. Fig. 14 shows the fabricated steam turbine blade at the above technology parameters, whose surface roughness is about Ra of 10.08\u201326.51 mm by shot sanding. So DLF will be a novel technology for fabricating complex parts with columnar crystals in the aerospace field using liquid argon cooling system. In the future work, the effect of liquid argon cooling mode on the microstructures and mechanical performances of steam turbine blade will be investigated in detail. (1) The laser specific energy, scanning speed and powder feeding rate are the main factors influencing the characteristic parameters of elementary units in DLF" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001538_s0302-4598(97)00042-1-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001538_s0302-4598(97)00042-1-Figure4-1.png", "caption": "Fig. 4. Cyclic voltammograms of NADH in 0.1 M KCI and 0.05 M phosphate buffer (pH 7.0). (a) At the dopamine-SAM modified electrode at 20 mV s - i with (1) 0 mM NADH, (2) 2.0 mM NADH. (b) At the dopamine-SAM modified electrode with 2.0 mM NADH at a series of scan rate: (2) 20 mV s - ~, (3) 40 mV s - i, (4) 60 mV s - i (5) 80 mV s I, (6) 100 mV s -I . (c) at a bare gold electrode. Scan rate: 50 mV s I.", "texts": [ "5 m V / p H unit over a pH range from 4 to 8, in accord with a two-electron, two-proton electrochemical reaction. It is also found that as the value of pH was over 10, the modified electrode became not so stable. This may be due to the fact that the quinone form of the dopamine-SAM was susceptible to nucleophilic attack by hydroxide [12]. 3.2. Electrocatalysis o f NADH oxidation at the dopamineSAM modified electrode Cyclic voltammograms for the dopamine-SAM modified el,~ctrode with and without NADH are shown in Fig. 4(a). Drastic enhancement in oxidation current at ca. + 230 mV vs. SCE shows that the modified electrode could catalyze the oxidation of NADH effectively. Compared with the direct oxidation of NADH at a bare gold electrode (Fig. 4(c)), the modified electrode was capable of oxidizing NADH at potentials that were 400 mV less positive. This should be ascribed to the o-quinoidal moiety possessed by the dopamine-SAM, which is an oxidizer of NADH and the redox couple of Q / Q H 2 can cycle reversibly. The EC reaction process can be expressed as follows: R - Ph - ( - O H ) 2 ~ R - Ph - ( = 0 ) 2 + 2 e - + 2 H + (4) R - Ph - ( = 0)2 + NADH + H \u00f7 =-) R - P h - ( - O H ) 2 + NAD + (5) where R indicates the other group in dopamine-SAM, Ph-(= 0) 2 is a quinone, and Ph-(-OH) 2 is the reduced, dihydro form. Generally, reaction (5) is irreversible. In the case of small value of u, the peak current ip of CVs is proportional to v I/2 [23]: ip = 0.496nFACDI/2( Fv/RT) i/2 (6) where A is the geometrical area of the gold electrode, C and D are the concentration and diffusion coefficient of the bulk species respectively. It is found from Fig. 4(b) that for 2.0 mM NADH, D = (2.4 +_ 0.2) \u00d7 i0-6 cm 2 s- i in 0.1 M KCI plus 0.05 M phosphate buffer (pH 7.0). This value is in good agreement with the result obtained by Moiroux and Elving [24]. The differential pulse voltammetric response of the dopamine-SAM modified electrode to NADH has been examined. Fig. 5(a) depicts the differential pulse voltammograms (DPVs) of a series of concentrations of NADH. The peak intensity increases with the increasing concentration of NADH. These results show that the electrode responds in a reproducible manner to NADH concentration (not more than 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003824_tmag.2012.2237390-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003824_tmag.2012.2237390-Figure1-1.png", "caption": "Fig. 1. Components of the rotor.", "texts": [ " However some problems such as the sensing method [8], low torque, large size and narrow rotation range remain. To solve these problems, the employment of an outer rotor structure is one of the solutions. In this paper, we propose a new 2-degree-of-freedom outer rotor spherical actuator and its open loop control method. We also compute its static torque characteristics and dynamic characteristics by employing 3-D finite element method and finally verify it from experimental results of a prototype. The proposed outer rotor spherical actuator consists of a stator and a rotor. In the rotor, as shown in Fig. 1, four rows of identically polarized, small spherical shell-shaped permanent magnets are placed around the Z-axis. The rows are arranged so that along the Z-axis, the N and S poles alternatively appear every 22.5 degrees. Components of the stator are shown in Fig. 2. The stator has 24 electromagnetic poles (EM poles) with 310 turn concentrated windings, which are arrayed around the Z-axis at even intervals. Fig. 3 shows the assembled structure. Generally, outer rotor motors can produce a higher torque than that of inner rotor motors of the same size" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002867_icma.2009.5246352-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002867_icma.2009.5246352-Figure2-1.png", "caption": "Fig. 2. Proposed gravity compensation system for 1 link system", "texts": [ " The device introduced in Sect ion 2 can not generate the enough moment to cancel out the whole gravitational moment of the patients. Thus, in Section 4, we introduce the new gravity compensation mechanism which can amplify the generated gravity compensation moment arbitrarily by changing the gear ratio of the gear in the system . The effectiveness of the system is shown in Section 6 through some experiments using the prototype. In this section, we construct a new gravity compensa tion system . At first, to simplify the argument, the gravity compensation system for the inverted pendulum illustrated in Fig.2 is established. When this pendulum is inclined at 0, the gravitational moment mgt sin 0 is exerted around the root joint. Therefore, to cancel out the gravitational moment, the system must generate the counter moment -mgt sin 0 around the joint by synthesizing the restoring forces generated by the springs . In the proposed mechanism illustrated in Fig .2, the gear attached to the joint shaft is connected to the pulley I in the gear ratio of I :2. Thus, when the joint rotates by 0 [rad], the pulley I rotates by -0/2 [rad] ", " Thus, totally, the gravitational moments (3) (5) K _ mgL2 2 - h2 ' K _ mgLl 1 - h2 ' g(q) = [ gl] [mg (\u00a31 sin8l :- \u00a32 sin(8l + 82)) ] , g2 mg\u00a32 sm(8 l + 82 ) (4) are successfully compensated by the system composed of the gravity compensation mechanism for the I link system and that for the 2 link system, if the spring constants K, and K 2 are set to respectively. Fig. 6. Gravity compensation by the proposed device To verify the effectiveness of the proposed mechanism, we construct an actual equipment as shown in Fig.4 and Fig.5. In these devices, the timing belt and an additional gear are used instead of the crossing wire in Fig.2 and Fig.3 to make the assembling task simple and make the performance precisely. The length of the link body, mass properties and spring constants of the equipment are listed in Table!. the gravitational moment and maintain the balance at any given posture . IV. VERIFICATION OF THE EFFECTIVENESS AS A LOWER LIMB REHABILITATION SYSTEM In the previous section, it is confirmed that the system can compensate the gravitational moment successfully. However, it is still unclear whether it can work effectively in the rehabilitation therapy to reduce the loads exerting on the joints of patients " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure4.11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure4.11-1.png", "caption": "Figure 4.11-Shearing of a hysteresis loop by the application of an air gap in the magnetic cir cuit.", "texts": [ " current, the inductor, usually in combination with a capacitor, serves as a smoothing choke to remove the ac ripple in a D.C. supply. This is often done in the output circuit ofthe supply after rectification. Since there are large D.C. and smaller superimposed a.c. currents, they usually need gaps to prevent saturation. In addition to the increase in current and possible catastrophic fail ure at saturation, the incremental permeability drops close to zero and there fore, the required inductance specification is not met. With the gap, the mag netization curve is skewed to avoid saturation (See Figure 4.11). With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for energy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10 , In some power inductor applications, as in the common mode choke, the magnetic core must sense the small difference between 2 magnetic cur rents and a high permeability toroid or ungapped shape must be employed", " These often occur when there is a threat of saturation that would allow the current in the coil to build up and overheat the core catastrophically. The gap can either be ground into the cen ter post or a non-magnetic spacer can be inserted in the space between the mating surfaces. The gapped core is extremely important in design of filter inductors or choke coils. We shall discuss this application later in this chapter. The basis of the gapped core is the shearing of the hysteresis loop shown in Figure 4.11a and 4.11b where 4.11a represents the ungapped and 4.l1b the 117 CORE SHAPES FOR POWER ELECTRONICS gapped core. The effective permeability, J.le, of a gapped core can be ex pressed in terms of the material or ungapped permeability, J..l, and the relative lengths of the gap, Ig, and magnetic path length, 1m : [4.5] With a very small or zero ratio of gap length to magnetic path length, the ef fective permeability is essentially the material permeability. However, when the permeability is high(lO,OOO), even a small gap may reduce the perme ability considerably. For a power material with a permeability of 2,000 and a gap factor of .001, the effective permeability will drop to 1/3 of its ungapped value. When each point of the magnetization curve is examined this way, the result is the sheared curve shown in Figure 4.11. Ito(1992) reported on the design of an ideal core that can decrease the eddy current loss in a coil by the use of the fringing flux in an air gap. The design includes a tapering of the core at the air gap. The reduction in temperature rise will depend on the oper ating frequency, the gap length and the wire diameter. 4.3.1-Prepolarized Cores Another variation of the gapped core is one that is prepolarized with a permanent magnet. If the transformer operates in the unipolar mode and the polarity of the magnet is opposite to the direction of the initial ac drive, the starting point for this induction change will not be the remanent induction as is usually the case but a point much lower down on the hysteresis loop and in MAGNETIC COMPONENTS FOR POWER ELECTRONICS 118 the opposite quadrant" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003528_045008-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003528_045008-Figure1-1.png", "caption": "Figure 1. Full SBFA assembly. Three chambers are bonded together to form the SBFA. Three polyethylene tubes are attached to each of the three chambers. A polyester string lies in the center of the structure and is oriented parallel to the three chambers.", "texts": [ " Section 3 presents the fabrication methodology of the SBFA. Section 4 illustrates the experimental set-up used to gather data presented in this paper. Section 5 summarizes the performance of the SBFA. Section 6 presents an open-loop control strategy for the SBFA. Conclusions are drawn at the end of the paper. The SBFA consists of three parallel chambers that can be pressurized individually. Each of the three chambers of the SBFA consists of a BFA [13\u201315] with 120\u25e6 isosceles triangle cross section. Figure 1 illustrates the structure of the SBFA where the three obtuse angles of each of the BFAs join together to cover the full 360\u25e6. It should be noted that the chambers in the SBFA are numbered from 1 to 3 in figure 1. Similarly to the FMAs presented in [5\u20138], the SBFA bends due to the anisotropic elongation between the three chambers. If one or two chambers are pressurized to elongate, the SBFA bends away from the elongated chambers as illustrated in figure 2. Due to the presence of an inextensible polyester string along the center of the SBFA, simultaneously pressurizing the three chambers would not allow the SBFA to elongate. The winding channel walls in each SBFA chamber limits expansion along the radial direction of the SBFA", " The winding channel structure was hermetically sealed with a thin sheet of silicone elastomer smeared with uncured TC-5005. Polyethylene tubing was inserted into the structure to allow for access to the channel. Uncured TC-5005 was used to secure the polyethylene tubing and ensure a leak-free connection. This process enabled fabricating a single SBFA chamber. Three SBFA chambers, each with its independent tubing, were fabricated following the procedure presented above and subsequently joined together with a polyester string placed in the center and bonded with TC-5005. The finished SBFA assembly is illustrated in figure 1. The manufactured SBFA prototypes had length equal to 78.4 mm and an equilateral triangular cross section, whose side was equal to 9.6 mm. The total mass of the prototype was 3.85 g. The channels within the SBFA had widths of 0.5 mm. The channel wall was 0.5 mm thick. In order to characterize the quasi-static performance of the SBFA, an experiment was set up to obtain the position of the SBFA at different input pressures. The root of the SBFA (see figure 4) was secured to a plastic (polymethyl methacrylate, PMMA) post with Dow Corning R\u00a9 732 RTV sealant and secured onto a lab stand" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001851_20.312742-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001851_20.312742-Figure4-1.png", "caption": "Fig 4 The field distribution at no load condition", "texts": [ " To overcome this difficulty, we have used the bi-conjugate gradient as solver [5]. PARAMETER COMFWTA-IION We propose to compute the L-equivalent circuit parameters (fig. 2.) using the load and the no-load conditions simulations. The parameters are determined through a stator phase in two steps. First, in the load condition simulation (fig. 3.), the reluctivity of each element and the stator phase voltage are calculated from the results of non-linear solution, in the second step the simulation of no-load condition (fig. 4.) is performed using the reluctivities calculated in the previous step. The phase voltage is obtained from Faraday's law: - V = jw2pN1, < A > (6) with p the number of pole pairs, N the number of series turns per phase, 1, the effective core length and the average value of A over a phase. The stator inductance is easily derived from the second simulation since there is no current induced in rotor bars. - V L, =- jwf, Once Ls is known, we can deduce the magnetising current I,,,. Then, the rotor resistance R2 and the total leakage inductance 12 are obtained from the results of the first simulation as follows : - (9) TI is the imposed stator current and is the rotor impedance" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002948_j.molcatb.2008.08.014-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002948_j.molcatb.2008.08.014-Figure1-1.png", "caption": "Fig. 1. Schematic illustration of: (a) the anodic alumina membrane used in this work; (b) the assembly of silica-surfactant nanochannels (channel diameter = 8 nm) formed inside the columnar alumina pore (pore diameter = 200 nm). Typical SEM images: (c) cros alumina pore after treatment with the precursor solution. Typical TEM image of column pore. The columnar structures were obtained as a white precipitate by complete etching o", "texts": [ " However, for the artificial iomembrane to act effectively, the direction of mesoporous sil- ca channels prepared in the pores of a porous alumina membrane btained by anodic oxidation should be the same as the alumina olumnar pore direction, i.e., perpendicular to the face of the base \u2217 Corresponding author. Fax: +81 22 237 7027. E-mail address: t-itoh@ni.aist.go.jp (T. Itoh). p o t i 5 i t p 381-1177/$ \u2013 see front matter \u00a9 2008 Elsevier B.V. All rights reserved. oi:10.1016/j.molcatb.2008.08.014 2, whereas the native lost its activity after 40 cycles. \u00a9 2008 Elsevier B.V. All rights reserved. lumina membrane (Fig. 1a and b) [10,15]. As can be seen from he SEM images (Fig. 1c and d) and TEM image (Fig. 1e) of the urface of the silica\u2013alumina composite membrane slightly etched ith a 10% phosphoric acid solution, each mesoporous silica tube in ts alumina pore is perpendicular to the alumina membrane face, aving a diameter of about 200 nm, corresponding to that of the lumina columnar pore. The nanochannels of the silica tube run redominantly parallel to the wall of the columnar alumina pore Fig. 1e). When single component helium was fed into the memranes, the helium permeances for the base and composite were pproximately 8000 and 500 nmol m\u22122 s\u22121 p\u22121, respectively, indiating that the pores of the base membrane narrowed because of he mesoporous silica preparation there. For binary mixtures of elium and water at 40 \u25e6C, the membranes showed the helium ermeances depicted in Fig. 2 as a function of the partial pressure f water, i.e., the permeance of the base membrane was constant o approximately 8000 nmol m\u22122 s\u22121 p\u22121 for the mixtures containng water vapor, but that of the composite membrane decreased to " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003375_s0025654411040042-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003375_s0025654411040042-Figure1-1.png", "caption": "Fig. 1.", "texts": [ "3), we obtain the following assertion. Theorem. If the condition \u2016yk\u2016 \u2264 \u03b5 is satisfied and the matrix \u03c4Ak and the remainder term (\u03c42/2)y(2) in the series expansion of yk+1 are bounded by \u2016E + A\u03c4\u2016k \u2264 \u03b2 < 1 and (\u03c42/2)\u2016y(2)\u2016 \u2264 (1 \u2212 \u03b2)\u03b5, then the inequality \u2016yk+1\u2016 \u2264 \u03b5 is satisfied. Indeed, \u2016yk+1\u2016 \u2264 \u2016(E + \u03c4Ak)\u2016\u2016yk\u2016 + \u03c42 2 \u2016y(2)\u2016 \u2264 \u03b2\u03b5 + (1 \u2212 \u03b2)\u03b5 = \u03b5. 7. EXAMPLE Consider a plane manipulator with two degrees of freedom consisting of a weightless crank OA rotating about the axis Ox3 and a sliding block B fixed on the crank (Fig. 1). The position of B is determined by polar coordinates q1 = r, q2 = \u03b8. The point P moves along the axis Ox1 according to the law x1 = x(t), and the light ray issuing from the point P is directed to the mirror fixed on the surface of the sliding block B. It is required to determine the value of F of the reaction F of the constraint r \u2212 R = 0, R = const, and the expression of the moment M applied to the crank under which the light ray reflected from the mirror gets into a fixed point C(c, 0) on the axis Ox1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002356_bf02451562-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002356_bf02451562-Figure6-1.png", "caption": "Fig. 6. - This diagram supplies a visual explanation of the significance of the ,,orthocline constraints, eq. (7). For orthoclines every point about the circumference of the apertural growth ring, hence the vector b, always lies in the (e2,r which, due to orthogonality of Frenet coordinates, is perpendicular to tl. And the dot product of two perpendicular vectors is zero.", "texts": [ " It is a well-known property of Frenet coordinates that (6) i , =xe2 , @e = - \u2022 1 6 2 ~e3, e8 = '~ee, where torsion ~ and curvature \u2022 are the two fundamental constants of differential geometry. Of course dots in (6) again denote ~/~r See (s). Corollary 2. The geometrical significance of our orthocline requirement is summarized by the following equation: (7) (r(O, r - Y(r 9 i~(r = 0, for all 0 e [0, 2=] and any specified value of r In other words, the vector b = r - Y lies in the plane of the generat ing curve and is always perpendicular to the principal direction of growth Y (see fig. 6). To check (7) we need only subst i tute (5) into it. Eve ry th ing simplifies because is parallel to r and the Frene t vectors are orthogonal: 3\"1. Generalized surface equations. - F r o m the earl ier pape r (4) we know tha t seashells grow along any of a whole range of clockspring t ra jec tor ies sat isfying the second-order real-space differential equation (8) ~Y(~) = o , where (9) ~ = + t ) - ~ 2 - t } ~ , [ 00] = 1 a 0 and t) = 0 )~ 0 , 0 0 a 0 0 for specified real constants a, )~ and ~. But the differential opera to r (9) can be factorized as follows: (10) and the component [ 3 / 3 r ~] Y = 0 ensures the existence of the equiangular ((first-order, t ra jec tor ies Y(r = exp [~r Y(0) a l ready discussed in eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001662_s0094-114x(01)00082-9-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001662_s0094-114x(01)00082-9-Figure4-1.png", "caption": "Fig. 4. Schematic relationship for the meshing of pinion, gear and the pitch plane of the imaginary engaging rack.", "texts": [ " (7) is the general form of the equation of meshing which can be obtained by applying the concept that the normal vector to any point on the generated tooth surface passes through the instantaneous axis of gear rotation I\u2013 I [5,6]. Substituting Eqs. (2) and (5) into Eqs. (6) and (7) yields the mathematical models of beveloid pinion R1 (i \u00bc 1 and j \u00bc F ) and gear R2 (i \u00bc 2 and j \u00bc G) expressed in coordinate systems S1\u00f0X1; Y1;Z1\u00de and S2\u00f0X2; Y2;Z2\u00de, respectively. The surface unit normal of the generated beveloid gear tooth surfaces can also be obtained by nix \u00bc n\u00f0j\u00dexc cos /i n\u00f0j\u00deyc sin /i; niy \u00bc n\u00f0j\u00dexc sin /i \u00fe n\u00f0j\u00deyc cos /i; niz \u00bc n\u00f0j\u00dezc : \u00f08\u00de Adopting the engagement model proposed by Mitome [2], Fig. 4 illustrates the schematic meshing model of the beveloid gear pair, including the pinion R1, the gear R2, and the pitch plane of the imaginary engaging rack. Beveloid pinion and gear can be considered two imaginary cones with cone angles d1 and d2, lying on opposite sides of the pitch plane of the imaginary engaging rack, while Sf \u00f0Xf ; Yf ;Zf \u00de and Sg \u00f0Xg; Yg; Zg\u00de are the reference coordinate systems for the pinion coordinate system S1\u00f0X1; Y1; Z1\u00de and gear coordinate system S2\u00f0X2; Y2; Z2\u00de, respectively", " Notably, the ratio a=b approaches to infinity when the cone angles d1 and d2 tend to zero, which represents a spur gear pair in line contact. Fig. 7(b) illustrates a beveloid gear pair consisting of helical beveloid pinion and gear with crossed axes. The cone angles of the helical beveloid pinion and gear are d1 \u00bc d2 \u00bc 20 , and the helix angles on the pitch planes of the rack cutters for the pinion and gear are bF \u00bc bG \u00bc 15 (right handed). The crossed angle formed by axes Zf and Zg, as shown in Fig. 4, is calculated as 49.6284 by applying the algorithms proposed by Mitome [2]. This example investigates the meshing simulations of gear pairs under the following assembly conditions: Case 4: Dch \u00bc Dcv \u00bc 0 and Dxg \u00bc Dyg \u00bc Dzg \u00bc 0 mm (ideal assembly condition). Case 5: Dch \u00bc Dcv \u00bc 0 and Dxg \u00bc Dyg \u00bc Dzg \u00bc 0:3 mm. Case 6: Dch \u00bc 0:5 ;Dcv \u00bc 0:5 and Dxg \u00bc Dyg \u00bc Dzg \u00bc 0:3 mm. Table 3 summarizes the TCA results and TEs of the gear pair, and Fig. 10 illustrates the loci of contact points and their corresponding contact ellipses on the pinion surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002719_iros.2007.4399390-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002719_iros.2007.4399390-Figure3-1.png", "caption": "Fig. 3. Planar model", "texts": [ " In this equations s is arc length, which is the length of the curve measured from the end to a point we focus on. dc(s) ds = e1(s) de1(s) ds = \u03ba(s)e2(s) de2(s) ds = \u2212\u03ba(s)e1(s) (1) Where e1(s) is defined as a unit vector facing to tangential direction of the curve and e2(s) is defined as a unit vector facing to bending direction. As a model of a snake-like robot, we consider e1(s) expresses the longitudinal direction of robot and e2(s) expresses the side direction of it. Most of snake-like robots can be expressed as a series of links and the shape is defined with joint angles \u03b81, \u03b82, \u00b7 \u00b7 \u00b7 as shown in Fig. 3(b). Let us call this model a discrete model. A discrete model can approximate a continuous model if the number of joints is enough and the joint angles are decided properly. Here we assume the length between joints l is even. As a way of approximation of a continuous model, an iterative calculation is proposed in [7][8], in which joint angles are calculated iteratively as each joint\u2019s coordinate is fitted to a continuous model. But cost of calculation in such method is relatively high. So we have proposed an approximation method in which joint angles are calculated directly from curvature of a continuous model without iterative calculation[6][9]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure11.14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure11.14-1.png", "caption": "Fig. 11.14 Belt drive spinning devices. a Human or animal-operated Da Fang Che (\u5927\u7d21\u8eca) (Wang 1991) b Shui Zhuan Da fang Che (\u6c34\u8f49\u5927\u7d21\u8eca) (Wang 1991)", "texts": [ "2 Pi Dai Chuan Dong Fang Che (\u76ae\u5e36\u50b3\u52d5\u7d21\u8eca, Belt Drive Spinning Devices) In the Song and Yuan dynasties (AD 960\u20131368), the most advanced spinning device is Da Fang Che (\u5927\u7d21\u8eca, a large spinning device). This device was first used for twisting hemp threads, and then used for silk processing. The book Nong Shu\u300a\u8fb2\u66f8\u300b(Wang 1991) has records about Da Fang Che (\u5927\u7d21\u8eca) and Shui Zhuan Da Fang Che (\u6c34\u8f49\u5927\u7d21\u8eca, a water-driven spinning device). Both devices have the same basic structures and are a kind of application of the belt drive, as shown in Fig. 11.14. Since there are many uncertain portions in the illustration, it is difficult to identify the actual numbers of its members as well as the combinations and transmission process among the members. Therefore, the belt drive spinning device is a Type III mechanism with uncertain numbers and types of members and joints. Figure 11.15a shows an existing reconstruction concept for the belt drive spinning device that helps to clarify the structure of this device (Zhang et al. 2004). The belt drive spinning device consists of the frame, two pulleys, a belt, several spindles, a yarn circle with a wooden wheel, and yarns" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure19-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure19-1.png", "caption": "Fig. 19 Paths of significant coupler points (U 5 1.55 and W 5 0.5) for r 5 200 mm, l 5 310 mm, e 5 100 mm and d 5 30 deg", "texts": [ " 14(c), the inflection circle degenerates into the line at infinity and the asymptote across the point C, while the cubic of stationary curvature degenerates in the same lines, along with the line through the point B and orthogonal to both asymptotes. Finally, the coupler curves of the instantaneous center of rotation I, point P1 of the moving centrode, points P2 and P3 of the cubic of stationary curvature, point P4 of the inflection circle and point P5 that coincides with the inflection pole, are shown in Fig. 19. Thus, these coupler points can be considered as significant points of the moving plane that is attached to the coupler link BC, because they belong to these specific geometric loci. In particular, at the assigned mechanism configuration (d\u00bc 30 deg) of Fig. 19, points I and P1, P2 and P3, P4 and P5, show a cusp, an inflection point and a stationary curvature of their paths, respectively. The evolutes ep and ek of the fixed and moving centrodes p and k, along with the cubic of stationary curvature and the inflection circle, are depicted in Figs. 20(a) and 20(b) for d\u00bc 30 deg and d\u00bc 0 deg, respectively. The osculating circles of both fixed and moving centrodes are also shown in Fig. 20 for each mechanism configuration, which allow to recognize the Cardan position of Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002560_j.triboint.2006.11.002-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002560_j.triboint.2006.11.002-Figure1-1.png", "caption": "Fig. 1. MTM, (a) MTM pot and test specimens (ball and disc), (b) sketch of test specimens.", "texts": [ " This amount will be estimated using traction coefficient measurements. The first part of this paper deals with the experimental study of the influence of the lubricant amount on the traction coefficient in the contact. The second part is devoted to the use of this study to determine the film thickness in the contact. Finally, the influence of the amount of lubricant on the fatigue life is analysed. This section studies the influence of the amount of lubricant on the traction coefficient in the contact, using a Mini Traction Machine (MTM). The MTM (see Fig. 1a) is a computer-controlled traction measurement system, supplied by PCS Instruments. In this test rig, a 20mm diameter steel ball is loaded against a flat steel disc with a known roughness. The geometry and the load allow Hertzian pressures up to 1.2GPa. The rolling speed ranges from 0 to 5m/s, with a slide-to-roll ratio from 0% to 200%. The ball axis of rotation intersects the centre of the top surface of the disc in order to minimise spin effects (see Fig. 1b). Ball and disc are enclosed in a controlled temperature chamber and the temperature can be imposed from ambient to 150 1C. Usually, the disc is submerged in lubricant and the machine automatically runs through a range of speeds or slide-to-roll ratios in order to plot Stribeck or traction curves (see samples, Fig. 2). The aim of this work is to study the influence of the lubricant amount on the traction coefficient. The MTM was used to measure the friction coefficient versus time for a range of operating conditions and lubricant volumes (see Table 1)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003363_1350650111419567-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003363_1350650111419567-Figure1-1.png", "caption": "Fig. 1 Schematic representation of the contact with spinning kinematics between a spherical-end solid of radius of curvature R2 (solid 2) and a plane specimen (solid 1)", "texts": [ " A numerical non-Newtonian TEHD model is described and results in terms of pressure, film thickness, heat fluxes, temperature, friction, and power losses are presented, leading to a new insight of spinning contacts. In the following, the stationary thermal nonNewtonian numerical model for point contacts under fully flooded lubrication condition is presented. Smooth contacting surfaces are assumed. Spin is a general term used to describe the selfrotation of a body, inducing both longitudinal and transverse velocity components when considering a Cartesian coordinate system, as in Fig. 1. Spin may be also a consequence of skewing or tilting rolling elements in bearings. The mean entrainment velocity is defined as Um,j,0 \u00bc U1,j,0 \u00feU2,j,0 2 \u00f01\u00de and the often-used longitudinal slide-to-rolling ratio SRRx,0 \u00bc U2,x,0 U1,x,0 Um,x,0 \u00f02\u00de with Ui,j,0 the constant velocity of solid i in the direction j. The subscript (0) denotes the centre of the contact (x \u00bc y \u00bc 0). Indeed, these two parameters alone fail to describe the spinning contact kinematics which cannot be represented anymore by a scalar value calculated in the contact centre since the lubricant entrapped between the two spinning surfaces is sheared in different directions and with different intensities within the contact area. Spin contributes to local rolling and sliding motions distributed around the contact centre which is taken as the spin pole in this study (Fig. 2) and by the following kinematical formula Ui,x\u00f0x, y\u00de \u00bc Ui,x,0 iy Ui,y\u00f0x, y\u00de \u00bc Ui,y,0 \u00fe ix \u00f03\u00de where Ui,j\u00f0x, y\u00de is the velocity in the direction j at a point Ai\u00f0x, y\u00de (Fig. 1) located on the surface of solid i and i the angular velocity of solid i along z. Proc. IMechE Vol. 226 Part J: J. Engineering Tribology at CARLETON UNIV on June 18, 2015pij.sagepub.comDownloaded from Inspired from the works of Najji et al. [16], Yang and Wen [17], and Habchi [18], a generalized Reynolds equation is used in order to take into account variations of density and viscosity with temperature and shear stress across the film thickness r h3 12 rp @ \u00f0 xh\u00de @x @ \u00f0 y h\u00de @y \u00bc 0 \u00f04\u00de where , , and p denote the density, viscosity, and pressure, respectively", " These integral terms find their origin in the integration of the simplified Navier\u2013Stokes equations [16] and may be written as follows \u00bc e 0 e 0e 00e \u00f05\u00de j \u00bc \u00f0U2,j U1,j\u00de 0 eR h 0 1 dz \u00fe eU1,j \u00f06\u00de where e \u00bc \u00f0h 0 dz 0e \u00bc \u00f0h 0 \u00f0z 0 1 dz0 dz 00e \u00bc \u00f0h 0 \u00f0z 0 z0 dz0 dz 1 e \u00bc \u00f0h 0 1 dz 1 0e \u00bc \u00f0h 0 z dz \u00f07\u00de where e and e are, respectively, the equivalent viscosity and density across the film thickness. The film thickness equation takes into account the curvature of the solid 2 and the elastic deformations using the equivalent body theory [19] h \u00bc h0 \u00fe 1 2R2 x2 \u00fe y2 \u00few\u00f0x, y\u00de \u00f08\u00de where h0 is the lubricant gap in the contact centre when no deformation occurs and w\u00f0x, y\u00de the z-deformation of the equivalent body computed with the finite element method (Fig. 1). As for boundary condition, the pressure is set to ambient pressure on the boundaries of the contact area located at 4:5a and 3a (a being the Hertzian radius) from the centre of the contact in the x- and y-directions, respectively. The size of the computational domain is thus large enough so that the pressure can reach smoothly the ambient pressure at the chosen boundaries (i.e. the derivatives of p with respect to x and y are equal to zero in these regions). Load balance equation ensures that the applied load (W ) is carried by the fluid pressure (p)\u00f0 \u00f0 @ c p\u00f0x, y\u00dedx dy \u00bcW \u00f09\u00de where @ c is the contact area" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001662_s0094-114x(01)00082-9-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001662_s0094-114x(01)00082-9-Figure1-1.png", "caption": "Fig. 1. The normal section of rack cutter.", "texts": [ " In this work, the rack cutter is used to simulate the generating process of beveloid gears. The beveloid gear pair for the meshing simulation comprises a pinion and a gear. Assume that the cutter surface RF generates the pinion tooth surface R1, and the cutter surface RG generates the gear tooth surface R2. Notably, subscripts i \u00bc 1 and 2, and j \u00bc F and G represent the surfaces of pinion R1 and gear R2 and their corresponding cutters RF and RG, respectively, in the following derivation. According to Fig. 1, the normal section of the rack cutter consists mainly of two straight edges. The straight edge M \u00f0j\u00de 0 M \u00f0j\u00de 2 can be represented in coordinate system S\u00f0j\u00den \u00f0X \u00f0j\u00de n ; Y \u00f0j\u00de n ; Z\u00f0j\u00de n \u00de by x\u00f0j\u00den \u00bc \u2018j cos a\u00f0j\u00de n aj; y\u00f0j\u00den \u00bc \u2018j sin a\u00f0j\u00de n aj tan a\u00f0j\u00de n bj; z\u00f0j\u00den \u00bc 0; \u00f01\u00de where design parameter \u2018j \u00bc jM \u00f0j\u00de 0 M \u00f0j\u00de 1 ! j represents the distance measured from the initial point M \u00f0j\u00de 0 , moving along the straight line M \u00f0j\u00de 0 M \u00f0j\u00de 2 , to point M \u00f0j\u00de 1 ; a\u00f0j\u00de n denotes the normal pressure angle, and symbols Pn and pn represent the gear diametral pitch and circular pitch, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001608_robot.1995.525529-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001608_robot.1995.525529-Figure1-1.png", "caption": "Figure 1. Constraint conditions for co-planar points", "texts": [ " Similar to (3), we have: &+I x Zi = [AOi BOi CoilT + [Ali Bli CliITAp = o (5 ) where AOi = bOi~Oi+l - bOi+lcOi; BOi = coiaoi+1 - cOi*lUOi; COi = UOibOi+l - uOi+lbOi; A l i = (bOicli+l + ~Oi+ lb l i ) - (bOi+lcli + cOibli+l); Bli = (COioUli.,l+ UOi+lCli ) - (COi+lUli + uOicli+l); Cli = (UOibli,l + bOi+lUli) - (UOi+lbli + bOiUli+l). AX = [A01 BO1 CO1 ... AO, BO, CO,lT, Denoting H =: [AIl B11 Cll ... AIm B1, CImIT; and We have a linear system: Although the exact locations of touch points are unknown, they are constrained to lie on a plane. The consistency condition of a plane leads to the construction of the identification model (Figure 1). The difference vector between two consecutive touch points is: APi = Pi - Pi.1 = [AxiO Ay? Az?]T + [AJi\" AJiy AJ:lTAp (2) where Ax? = xiO - ~ i . 1 ' ; Ayio = yio - yi-1'; Az? = zi0 - zi-1' ; In (6) , the coeffcicient matrix H and AX can be calculated based on the difference of nominal positions predicted by controller, and the difference of special Jacob for each pair of consecutive touch points(on1y joint readings are required for the computations). The only unknown remaining is the kinematic error to be identified" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001409_12.388828-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001409_12.388828-Figure3-1.png", "caption": "Figure 3: Example oflnitial Gearbox State for Planet Gear Data Collection.", "texts": [ " First, consider again a single accelerometer. Define the accelerometer as j= 1 , and let it be aligned with the annulus gear tooth = Pi,a = 1. Recall that the transfer function between an accelerometer and the planet gear h(t) is defined such that the first peak of the function occurs at time t = 0. Letting this peak be associated with the point that planet gear tooth Po, = 1 is meshing with annulus tooth Pi,a = 1, h1(t) = h1 (t). This condition defines the state of the gearbox at n= 0 for accelerometer 1. Figure 3 shows an example of this state. Next, consider a second accelerometer aligned with annulus tooth P2,a, numbered sequentially from annulus tooth 1 in the direction of carrier rotation. Define the spacing between two accelerometers j and 1, in terms of the number of annulus teeth, as Si_l Pj,aPi,a Hence, the spacing between accelerometers 1 and 2 is given by S2_l = P2,a \u2014Pi,a = P2,a \u2014 1 (9) (10) Recall that at time t = 0, the planet gear under consideration is passing accelerometer 1 and gear tooth P0, = 1 is meshing 255 Downloaded From: http://proceedings" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003510_j.ymssp.2013.06.002-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003510_j.ymssp.2013.06.002-Figure1-1.png", "caption": "Fig. 1. Schematic representation of BRB model.", "texts": [ " Section 2 presents the BRB model, and the analytical correlation between grip parameters and strain. Section 3 shows numerical simulations in which the grip is identified for different rolling conditions and for different combinations of the kinematic and dynamic friction coefficients, discussing the algorithm robustness in the presence of injected noise in the data. Finally Section 4 presents some perspectives of the work and draws some conclusions. 2. Tire modelling for grip identification: the BRB (Brush-Rod-Beam) model The present model of the elastic wheel, see Fig. 1, consists of the coupling of two systems, an inner rigid body B (the rim) wrapped by an outer elastic body E (the tire), the interface between the two characterized by kinematic congruence conditions implying the elastic displacement is zero at the boundary B\u2013E. Further congruence conditions involve indeed the road-E interface. More specifically, the elastic structure E of the wheel consists of a set of elastic brushes attached to a cylindrically shaped (in unloaded conditions) elastic belt, modelled as a rod-beam element, attached to the rim B through an elastic foundation, that would reproduce distributed elastic effects related to the air gap and the sidewall", " In fact, the elastic phenomena at the contact wheel-road interface are accounted by the brush set, while the elastic phenomena observed in the inner part of the tire, namely those monitored by the strain measurement, are described by a rod-beam elastic element, coupled to the brush set. In fact, the modelling of the elastic deformation inside the tread is a necessary step to develop a well funded identification process of the grip, based on some direct strain measurements acquired by the sensor S, as represented in Fig. 1. In other words, the present model introduces the needed correlation between the accessible measurement made inside the tire, and the interface phenomenon that would be monitored, that indeed takes place outside the tire at the contact with the road. The model so developed, named BRB (Brush-Rod-Beam), forms the basis for the grip identification procedure described in the next section. As illustrated in Fig. 1, three reference systems are introduced: the road-coordinate system R(O, x, y, z) of unit vectors i, j, k, the wheel coordinate systemW(C, x\u2032, y\u2032, z\u2032), with origin in the wheel centre C, integral with the B-part of the wheel, and the reference system G(\u039b, \u03be, \u03b7, \u03b6) following the flat tire\u2013road contact region \u0393. The origin \u039b is the projection of C on the x axis, and the \u03be, \u03b7 and \u03b6 axes are parallel to x, y and z, respectively, and with the same orientation. VC is the velocity of the centre C of the wheel and \u03a9 is its angular velocity", " Switching to an Eulerian representation of the velocity field, needs the use of the inverse of (2): x\u2032 P\u00f0t\u00de \u00bc \u00bdR\u00f0t\u00de\u00f0I\u00fe U\u00f0s\u2032; t\u00de\u00de \u22121xCP\u00f0t\u00de \u00f04\u00de Please cite this article as: A. Carcaterra, N. Roveri, Tire grip identification based on strain information: Theory and simulations, Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2013.06.002i Through this map, we are interested to represent the velocity of the points of the wheel on the tire\u2013road contact region, namely of those passing through the same location T on the footprint (see Fig. 1), identified by the time-independent vector xCT in R. In this representation, x\u2032 P\u00f0t\u00de and s\u2032(t) become time-dependent, while xCP \u00bc xCT is now constant and Eq. (4) becomes: x\u2032 P\u00f0t\u00de \u00bc \u00bdR\u00f0t\u00de\u00f0I\u00fe U\u00f0s\u2032; t\u00de\u00de \u22121xCT \u00f05\u00de that substituted into (3) produces: VT \u00bcVC \u00fe\u03a9xCT \u00fe _RU\u00bdR\u00f0I\u00fe U\u00de \u22121xCT \u00fe R \u2202U \u2202s\u2032 Ds\u2032 Dt \u00fe \u2202U \u2202t \u00bdR\u00f0I\u00fe U\u00de \u22121xCT that is the most general representation of the Eulerian velocity field for the rolling wheel on its peripheral surface. Note this mapping, involving elastic displacements through U, does not exactly preserve lengths", " Finally, it is interesting to calculate the abscissa ~\u03be n opt which maximizes Fx: dFx d~\u03be n \u00bc 0 \u00f016\u00de that can be solved numerically in terms of ~\u03be n opt . The explicit forms of Eqs. (15) and (16) are not displayed here due to their large number of terms, however they can be easily obtained employing the Symbolic Math Toolbox in MatlabTM. The core of the present paper, relies on the extraction of information contained into the strain measurement \u03b5exp\u00f0s\u2032\u00de \u00bc \u03b5exp\u00bd\u03be\u2212\u00f0r\u2212\u03b4\u00det provided by the sensor S (see Fig. 1). On the basis of the theory illustrated in the previous part of this section, the general form of the strain along the tread is determined by the formula: \u03b5tr\u00f0\u03be\u00de \u00bc dutr d\u03be \u2212htr d2wtr d\u03be2 Note that the second term would represent the strain related to flexural radial tire displacement. However, considering that the previous simplified approach produced ~wtr \u00bc 1 2 \u03be 2 \u00fe ~\u03b4, a poor parabolic approximation for ~wtr is used. This means d2wtr d\u03be2 would be constant. To easily improve the quality of our solutions, especially for experimental data comparison, still preserving the closed form expressions, we can use Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002231_robot.2003.1242095-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002231_robot.2003.1242095-Figure1-1.png", "caption": "Fig. 1: Orthoglide kinemafic archifecfure.", "texts": [], "surrounding_texts": [ "1 Introduction\nThe inverse dynamic model is important for high performance control algorithms, and the forward dynamic model is required for their simulation. For, these two applications the numerical values of thy dynamic parameters (inertial and friction) must he known. The determination of the base inertial parameters, which represent the only identifiable parameters [Z], is treated in this paper by a numerical method [3]. This method is based on the QR decomposition of the observation matrix of the dynamic identification model of the robot. The experimental identification of the dynamic parameters is based on the use of a dynamic model linear in the parameters. This model permits to use the least squares solution to solve the estimation problem [4].\n2 Kinematic modeling of the Orthoglide\nThe Orthoglide has three PWaR identical legs (where P, R and Pa stand for Prismatic, Revolute and Parallelogram joint, respectively). Each leg is composed of six passive revolute joints and 1 active prismatic joint, (fig. I). We define frame Fo fned with the base and frame FP fixed with the mobile platform (fig. 2). Their origins are A, and P respectively. Their axes (xo, yo, a) and (xp, yp,, zp) are parallel. The base frames of the legs are defined by the frames FA,, Fm and FA, (fig. 2 ) , whose origins are A,, Q and A3 respectively. The zAi axes are\nThis work has been supported by the project MAX of the p r o p ROBEA of the department S n C ofthe French CNRS.\nalong the prismatic joint axes. The Khalil and Kleinfinger notations [ 5 ] , are used to describe the geometry of the system (fig. 3).\nThe following notations are used: L (3x1) vector of the motorized joint variables:\nL = h , qn 4131T; \"V, (3x1) vector of the linear velocity of the origin of the\nThe derivative of L and 'Vo with respect to the time are\ndenoted L and 'Vu respectively.\nplatform\n0-7803-7736-2/03/$17.00 2003 IEEE 3272", "The following kinematic models are presented in [6]: i) The inverse kinematic model of the robot:\nWhere 'J; is the inverse Jacobian mabix of the Orthoglide, which is always regular in the working space. ii) The inverse kinematic model of a leg i:\nL=oJJI'oVp (1)\nq, = 'J;\"VP (2)\n4, =[ill, il,, &IT (3)\nWhere J;' is the inverse Jacobian matrix of the leg i The velocities of the other joints of each leg can be obtained in terms of q, (see appendix). iii) The second order inverse kinematic model of the leg:\niij = OJJ;' ( O V V - O J 1 q j ) (4)\n3 Inverse dynamic model\nThe inverse dynamic model gives the motorized forces, rrobot, in terms of the desired trajectoly of the mobile platform oPp,ov,,ov~. The dynamic model is computed in two steps. First we calculate, :the reaction forces of the platform on the legs at point P, which is denoted by fj, then the Newton-Euler equation of the platform is applied to obtain the motor forces [6].\nThe general form of the inverse dynamic model of a leg i, is written as (see appendix):\nWhere: HI is the inverse dynamic model of leg i, when its terminal point is kee.\nTi =H,(q,,4,,iii)+'JT Of, ~ ( 5 )\nri is composed of the independent torqueslforces of the joints of the leg i, where Tli and Ta are zero:\nr, =[r,, r2i rljIT =[r,; o 0IT (6)\n(7) Using equation ( 5 ) the forces fi can he written as: Off, = -H , ( %Ai,q,)+'JiT ri\nH, ( q , , q , , & ) = ' J ~ H, (qj,4,,iif) (8)\nWhere:\nHe is the inverse dynamic model with respect to the position Cartesian space at point P (fig.3) [7][8]. We show that [6]:\nOff, = -H, (q~,q~,q,)+'J~,:,,,r, (9)\nWhere J:,:,i, represents the i' column of the inverse\ntranspose Jacobian matrix of the robot. The Newton-Euler equation of the platform is written as (no rotation):\nWith: 'g\nOFp = 'Vi: M, -M, 'g\n'g=[O g o ] T , g=9.~1m.s-'\n(10)\nAcceleration of gravity, referred to kame Fo:\nM, Mass of the platform; OF, Total external forces on the platform. given by: From equations (9) and (lo), the dynamic model is\n1 rmbOt =' '~,+C[~,(q,,q~,ii~ )I] (11) Jp i iil\nDifferent methods can he used to calculate Hj(qj,qi,qj)[9][10][1 I]. To reduce the computational cnst, the customized Newton-Enler method, which is linear in the dynamic parameters is used [12].\n4 Dynamic identification model\nThe dynamic model of each leg i can he represented as a linear function of the inertial and Wction parameters of the leg K,. Thus the equation (1 1) can be written as:\nrnsat = D,,,,, K,bd (12) K,,,, is the vector of the standard dynamic parameters\nof the Orthoglide:\nLo, =[MP K : KT KT]T\nD,,,,, = [D' D, D, D,]\nK, =[Ma,j FS,~ Fv,, x:]'\n(13)\n(14) K, is the vector of the standard dynamic parameters of\nthe leg i, such that:\n(15)\nxi = [ x T ' '_ x f ] r (16) Where:" ] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure17-1.png", "caption": "Fig. 17 Fixed and moving centrodes along with the cubic of stationary of curvature and the inflection circle (U 5 0.67 and W 5 0.33) for r 5 450 mm, l 5 300 mm, e 5 150 mm and d 5 35 deg", "texts": [ " In particular, for d\u00bc 30 deg, Fig. 15 shows a mechanism of Type C, while Fig. 16 shows a Scott-Russell mechanism, which performs a typical Cardan motion, since the diameter of the circular moving centrode is equal to the radius of the circular fixed centrode. The cubic of stationary curvature degenerates in a /-curve, which circle coincides with both inflection circle and moving centrodes for any mechanism configuration by avoiding the singular configuration, where point C coincides with point A. Figure 17 refers to a mechanism configuration for d\u00bc 35 deg and shows the case for l\u00bc r\u00fe e (U\u00bc 0.67 and W\u00bc 0.33), which corresponds to a point that lies on the boundary line that distinguishes the mechanisms of type B and C on the diagram of Fig. 1. Moreover, the case of an offset slider-crank mechanism of type A has been considered in Fig. 18 for a crank angle d\u00bc 90 deg, where the fixed centrode shows two parallel asymptotes and the moving centrodes shows four branches. Likewise to the example of Fig. 14(c), the inflection circle degenerates into the line at infinity and the asymptote across the point C, while the cubic of stationary curvature degenerates in the same lines, along with the line through the point B and orthogonal to both asymptotes" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003411_iros.2011.6094663-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003411_iros.2011.6094663-Figure12-1.png", "caption": "Fig. 12. Representative solutions for the object circle in row 1 of Table I.", "texts": [ ", the angle between planes of section 1 and section 2) and \u03c63 into the following four types: (1) \u03c62 is negative and \u03c63 is positive. (2) \u03c62 is positive and \u03c63 is negative. (3) \u03c62 and \u03c63 are both positive. (4) \u03c62 and \u03c63 are both negative. Table I shows the descriptions of three object circles, two of them are of Grasping Model 1, in terms of circles for section 3 (see Fig. 11), and the other one is of Grasping Model 2, in terms of a circle that both section 3 and section 2 share. For the object circle specified in row 1 of Table I, four valid solutions are obtained by Algorithm 1 as illustrated in Fig. 12, where solutions 1 and 2 belong to the type (1), and solutions 3 and 4 belong to the type (2), and corresponding configurations are shown in Table II. Note that solutions 1 and 2 belong to the same neighborhood where \u03c61 changes continuously from 0.4 to 0.6 when \u03ba1 = 0.0228. Note also that solutions 2 and 3 are of different types but share the same pair of \u03ba1 and \u03c61 values. This is one example to show that there can be multiple solutions for the same \u03ba1 and \u03c61, which belong to separate (continuous) neighborhoods (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002594_j.jmatprotec.2007.05.052-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002594_j.jmatprotec.2007.05.052-Figure2-1.png", "caption": "Fig. 2 \u2013 Laser cladding setup for the two laser beam process.", "texts": [ " For the cw and the w laser cladding process a single laser beam was applied. he setup can be seen in Fig. 1. For the spatial modulation of the power density on the surace of the base material a second laser beam similar to the rst laser beam was added to the process. The second laser as generated by another laser source but the focusing lenses nd the diameter of the laser spot on the surface were simlar in comparison to the firs laser beam. The setup for the aser cladding experiments with an adaptation of the spatial ntensity is given in Fig. 2 ig. 1 \u2013 Laser cladding setup for pw and cw radiation xperiments. In order to have a simple mathematical description for the exploitation of the laser power an energetic efficiency was defined. The energetic efficiency energetic is given by the ratio of the energy necessary to melt the additional mass onto the specimen to the energy supplied by the laser beam, Eq. (1): energetic = h m P (1) The energy needed to melt the cladding material onto the specimen is given by the product of the mass m and the specific enthalpy term h" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003821_j.jsv.2013.02.035-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003821_j.jsv.2013.02.035-Figure1-1.png", "caption": "Fig. 1. Cam-follower system in the general state where a non-linear contact stiffness model, k\u03bb(\u03c8i(t)), is employed.", "texts": [ " However, the dynamics of the sliding contact are sometimes studied using simple translating systems [20\u201326]. Rolling contacts have been investigated by Remington using a lumped system model [27] and experiments [28]. Gray and Johnson [29] have analyzed the rolling contact problem using a simple vibration model All rights reserved. that included the contact mechanics concept. This paper will examine only the rotational sliding contact and utilize some of the contact mechanics principles employed in other mechanical system [30,31]. Fig. 1 shows a single degree-of-freedom (SDOF) cam-follower system in the general position, when the cam and follower are not in contact. The fixed orthogonal coordinate system \u00f0e\u0302x,e\u0302y\u00de describes the horizontal and vertical directions, with its origin at E. The circular cam of radius, rc, is considered; it rotates about the fixed pivot E, which is at a distance, e, from the geometric center of the cam (Gc). The angular movement of the cam is given by \u0398(t), the angle made by GcE ! with the horizontal line in the counter-clockwise direction; it is also the motion input to the system", " The objectives of this article are as follows: (a) Develop a contact mechanics model for the cam-follower system with rotational sliding contact; (b) Examine the applicability of different viscous and impact damping models and the coefficient of restitution concept by comparing the predictions with the experimental results reported by Alzate et al. [8]; (c) Study the effects of contact and friction non-linearities in the sliding contact regime; and (d) Analyze the effect of kinematic nonlinearity of the system by comparing it with a linearized model. Since all the non-linearities are inter-related with each other, the dynamic system is very complex even with a single degree-of-freedom formulation. In Fig. 1, QOc ! is represented by \u03c8 i\u00f0t\u00dei\u0302\u00fe\u03c8 j\u00f0t\u00dej\u0302 in the moving coordinate system, and \u03c8i(t) and \u03c8j(t) are used to calculate the contact force and the moment imparted by the cam on the follower, respectively. A non-negative value of \u03c8i(t) indicates that the cam and follower are not in contact. When \u03c8i(t) is negative, the system is in the sliding contact regime with the magnitude of \u03c8i(t) representing the deflection of the contact spring. At any instant, \u03c8i(t) and \u03c8j(t) can be calculated for a given \u03b1(t) and \u0398(t) from the system geometry as shown below. From Fig. 1 the vectors are calculated as follows: POb !\u00bc PE !\u00feEGc !\u00feGcOb ! , (1) POb !\u00bc \u03c7\u00f0t\u00decos\u00f0\u03b1\u00f0t\u00de\u00de\u00fe wb 2 sin\u00f0\u03b1\u00f0t\u00de\u00de h i e\u0302x\u00fe \u2212\u03c7\u00f0t\u00desin\u00f0\u03b1\u00f0t\u00de\u00de\u00fe wb 2 cos\u00f0\u03b1\u00f0t\u00de\u00de h i e\u0302y, (2) EGc !\u00bc\u2212ecos\u00f0\u0398\u00f0t\u00de\u00dee\u0302x\u2212esin\u00f0\u0398\u00f0t\u00de\u00dee\u0302y, (3) GcOb !\u00bc \u2212\u00f0rc\u00fe\u03c8 i\u00f0t\u00de\u00desin\u00f0\u03b1\u00f0t\u00de\u00dee\u0302x\u2212\u00f0rc\u00fe\u03c8 i\u00f0t\u00de\u00decos\u00f0\u03b1\u00f0t\u00de\u00dee\u0302y: (4) Here, \u03c7(t)\u00bc\u03c70\u2212\u03c8j(t), where \u03c7(t) and \u03c70 are the components of jPOb !j and jPO0 b ! j, respectively, alongbj. The constant vector PE ! is evaluated based on the 0-state as follows, where \u03b10 is the angle of the follower at the 0-state: PE !\u00bc \u03c70cos \u03b10 \u00fe rc\u00fe wb 2 sin \u03b10 \u00feecos \u03980 h i e\u0302x \u00fe \u2212\u03c70sin \u03b10 \u00fe rc\u00fe wb 2 cos \u03b10 \u00feesin \u03980 h i e\u0302y: (5) Using Eqs", " 3 shows these as a function of the vr(t) between the cam and follower; here, vr(t) is given by vr\u00f0t\u00de \u00bc _\u03c8 j\u00f0t\u00de\u2212\u00f0rc\u00feesin\u00f0\u03b1\u00f0t\u00de\u00fe\u0398\u00f0t\u00de\u00de\u00de\u00f0\u03b1_\u00f0t\u00de\u00fe _\u0398\u00f0t\u00de\u00de. Model I (with a maximum value of \u03bcm) is given by \u03bcI\u00f0t\u00de \u00bc \u03bcmsgn\u00f0vr\u00f0t\u00de\u00de and has a sharp discontinuity at vr(t)\u00bc0, which is smoothened by model II using a regularizing factor (s) for the hyperbolic tangent function as: \u03bcII\u00f0t\u00de \u00bc \u03bcmtanh\u00f0svr\u00f0t\u00de\u00de. The proposed contact mechanics model is used to represent the physics of the cam-follower experimental system as reported by Alzate et al. [8]. In the prior experiment [8], the follower (along with its spring) is above the cam, unlike in Fig. 1 where the follower (and its spring) is placed below the cam. The follower is pivoted at its center of gravity, and the magnitude of Fs(t) is assumed to be the same in tension or compression. Consequentially, the proposed contact mechanics model is representative of the cam-follower experiment [8], and hence calculations can be compared with the reported measurements. The results are viewed in terms of the residual response (\u03b1r(t)) for a given constant rotational speed of the cam (\u03a9c), where the measurements are available at 110, 135, 143, 148, 150, 155, and 159 rev/min. Mathematically, \u03b1r(t) is given by \u03b1r(t)\u00bc\u03b1(t)\u2212\u03b1i(t), where \u03b1i(t) is the response assuming the follower to be in contact with the cam, and \u03b1i(t) is calculated from the kinematics of Fig. 1 as follows: \u03b1i\u00f0t\u00de \u00bc cos\u22121 0B@\u00bd\u00f0jPGc !j4x \u00fejPGc !j2x jPGc !j2y\u2212jPGc !j2x \u00f0rc\u00fe0:5wb\u00de2\u00de 0:5\u00fejPGc !jy\u00f0rc\u00fe0:5wb\u00de jPGc !j2x\u00fejPGc !j2y 1CA: (29) Here, jPGc !jx and jPGc !jy, the magnitudes jPGc !j along x and y directions, respectively, are functions of \u0398(t). At any \u03a9c, \u03b1r(t) is predicted using the contact mechanics model with the parameter values given in [8], and the input is \u0398(t)\u00bc\u03980\u00fe\u03a9ctwith the static equilibrium point as the initial condition. The contact stiffness is evaluated using the Hertzian theory [32] for a steel cam and follower (with Yc\u00bc200 GPa, Yb\u00bc200 GPa, \u03bdc\u00bc0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003951_hsi.2011.5937373-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003951_hsi.2011.5937373-Figure2-1.png", "caption": "Fig. 2. The dynamical diagram of the Triglide parallel robot", "texts": [ " p zp yp xp q q q J v v v 3 2 1 , (1) where Jp is the robot Jacobian analytically established. The inverse geometrical modeling of the considered Triglide parallel robot permits to obtain the liaison between independent joint variables {q1, q2, q3} and the moving platform coordinates {xp, yp, zp}: T 245978-1-4244-9640-2/11/$26.00 \u00a92011 IEEE III. DYNAMICAL MODELING OF TRIGLIDE PARALLEL ROBOT The dynamic modeling has been done in the following prerequisites: a) The elements are rigid bodies; b) The gravity vector is oriented in negative sense of the z axis (Figure 2); c) No external load on the moving platform; d) The inertial matrix J3=J6=J8 and J2=J5=J7; e) The mobile platform (the element no. 4) contains four parts (sub-elements): 41, 42, 43 and 44. Considering rigid elements with distributed masses, the dynamic model can be analytically developed using the Lagrange multipliers method: j jjj i k i i Q q L q L dt d q \u2227 = \u2212 \u2202 \u2202\u2212\u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b \u2202 \u2202= \u2202 \u0393\u2202 \u03bb\u2211 1 , (5) where: i\u03bb - Lagrange multipliers; jq - Displacements from the actuators; jQ \u2227 - Generalized external forces; L - Parallel robot Lagrangean: \u2211\u2211 == += n i i n i i PKL 11 , (6) where: Ki \u2013 the kinetic energy of the link i; Pi \u2013 the potential energy of the link i. The Lagrange multipliers ( i\u03bb ) are identified introducing the following set of geometric equations: a)B,B(dist =21 , where a is the side of 321 BBB\u0394 ; a)B,B(dist =32 ; a)B,B(dist =31 ; Coordinate after Z of point B1 and B2 need to be the same; Coordinate after Z of point B2 and B3 need to be the same; Cosine director between L si K (Figure 2) is equal with 1. Finally, the analytical expression of the driver forces Fq1, Fq2 and Fq3 (see Figure 2) are obtained using Maple software. Even the obtained analytical dynamic model is complex; this method used can be usefully applied to solve the dynamical model of any 3 DOF parallel robots and can be extended to 4 and more DOF parallel robots. IV. THE CAD MODEL OF THE TRIGLIDE PARALLEL ROBOT AND SIMULATION RESULTS The CAD model of the Triglide parallel robot is obtained using ADAMS software and the simple elements of type cylinders (see Figure 3). The mass and inertial parameters of CAD model obtained (see Table 1) were used also for simulation the analytical model obtained using Maple software" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure17-1.png", "caption": "Fig. 17. Pinion contact pattern estimation for the second example: nominal condition estimation).", "texts": [], "surrounding_texts": [ "The estimated contact pattern strongly depends on the chosen values of c2 in (27). For this reason a calibration step is required to obtain a realistic contact pattern shape. We calculate the contact pattern in the zr-plane using HFM [9] and we consider it as the target contact pattern we want to obtain. We search for the optimal values c 2 that minimize the non-overlapping area between the target and the estimated contact pattern. With reference to Fig. 13, the non-overlapping area An\u00f0c2\u00de is defined as follows: An\u00f0c2\u00de \u00bc Ac\u00f0c2\u00de \u00fe At 2Ai\u00f0c2\u00de Ac\u00f0c2\u00de \u00fe At ; \u00f029\u00de where At is the target area, Ac\u00f0c2\u00de is the current estimated area, Ai\u00f0c2\u00de is the area of the intersection between At and Ac\u00f0c2\u00de. The optimal values c 2 are the result of the following minimization problem: c 2 \u00bc argmin c2 \u00f0An\u00f0c2\u00de\u00de: \u00f030\u00de We remark that the marking compound identification needs only one run of HFM and, after this tuning step, the values of c2 can be used for further contact pattern estimates. In the next section, we present two different examples to show the capabilities of the proposed approach." ] }, { "image_filename": "designv10_13_0003453_j.ymssp.2012.12.001-Figure12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003453_j.ymssp.2012.12.001-Figure12-1.png", "caption": "Fig. 12. Helical mode shapes (Modal deformation strongly magnified to show the deformation directions).", "texts": [ " Backlash only has an influence when teeth lose contact, which is unusual for normal gears under constant load. However, in the wind turbine application backlash becomes important during greatly varying load and torque reversals. The different gear stages in a full gearbox system rotate at different speeds, which results in different gear meshing frequencies and corresponding multiples. This work focuses on the first 10 meshing orders of the different meshing stages. For the investigated gearbox the corresponding frequency ranges of excitation are shown in Fig. 7. From this Fig. and Fig. 12 it is clear that the Low Speed Stage Orders only have the potential to excite in the frequency range of influence of the gearbox housing structural flexibility and not in the range of influence of the shaft and planet carrier structural flexibility. Medium Speed Stage Orders on the other hand have the potential to excite in the frequency range of influence of all structural flexibilities except for the ISS. High Speed Stage Orders have the potential to excite in the frequency range of influence of all structural components", " These modes are similar to the modes typically found ig. 11. Planetary mode shapes: (a) Axial translation mode (b) No modal deformation (reference) (c) Rotation Mode of ISS about one of its radial axes. in helical gear systems. For the investigated gearbox, eigenfrequencies can be categorized into low speed helical stage modes and high speed helical stage modes, according to the helical stage in which they are manifested. Mode shapes involving the ISS are assigned to both categories. Two of these modes are visualized in Fig. 12(a) and (c). The Global modes are manifested in both the planetary gear stages and the helical gear stages of the gearbox. Mainly rotational components are important in these modes. It can be concluded, that apart from global modes, modal behavior is concentrated in the respective subcomponents, resulting in separated planetary and helical mode shapes. Therefore investigation of the excitation propagation is important as possible decoupling between planetary and helical stages can occur as is the case for a significant part of the modal behavior" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003957_iros.2011.6094783-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003957_iros.2011.6094783-Figure8-1.png", "caption": "Fig. 8 Phases of descending stairs.", "texts": [ " 7(b) if it is necessary so that the user can overcome the next step. This additional motion modification force vector is generated in order to prevent the user\u2019s foot from entering the virtual wall area of next step. The robot repeats these perception-assists so that the user can ascend stairs safely. D. Stairs-descending assist In general, the case that an elderly person descends stairs has high possibility of falling down compared with the case that an elderly person ascends stairs. Next, the stairs-descending assist is discussed. Figure 8 shows the phases when a person descends stairs. At first, a person moves own swing leg to the next step as shown in Fig. 8(a). In this phase, the COG of the person remains in the supporting leg. In the next phase as shown in Fig. 8(b), the person starts to put own foot down to the next step. The COG of the person moves forward gradually toward the swing leg during this phase. Finally, the person puts own swing leg on the next step and moves another leg to the next step as shown in Fig. 8(c). In the last phase, the shifting of the weight of the person has already finished and there is the COG of the person in the next step. It is expected that the stairs-descending assist help a user to realize the natural motion when the user descends stairs. However, in the phase of Fig. 8(b), the person moves own foot to the next step during falling down. Therefore, the robot cannot judge whether the user falls down or moves to the next step. In addition, the COG of the user moves from the supporting leg to the swing leg in the phase of Fig. 8(b). Many users will fall down forward if they lose own balance in this phase. When a user loses own balance at this phase, there are two methods to recover the user\u2019s balance. One is that the user puts own swing leg on the next step as fast as possible and struggles to stay on the swing leg. The other is that the user struggles to stay on the supporting leg and the COG of the user returns back in the supporting leg. If the robot assists these two methods, the load of the ankle joint motor becomes large", " EXPERIMENTS Fig. 11 Experimental result of ankle position of z axis when the subject ascended the stairs. Fig. 12 Experimental result of ankle position of x axis when the subject descended the stairs. In order to verify the effectiveness of the proposed method, the experiments were carried out. In the experiments, a young male subject ascended/descended the stairs shown in Fig. 5. The experimental result when the subject ascended the stairs is shown in Figs. 10 and 11. The direction of each axis is shown in Fig. 8. In Figs. 10 and 11, the black and red line show the positions of ankle joint of left and right leg, respectively. In addition, in Fig. 10, the blue line shows the ZMP. The lengths between green lines show the width and height of the stairs respectively. In this experiment, first, the subject moves right leg to the next step while the range (b) as shown in Figs. 10 and 11. After that, the subject moves left leg to the next step while the range (c). In the range (b) the subject did not lift up own right leg until the height of the stairs purposely in order to verify the effectiveness of the perception-assist" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001554_s0094-114x(98)00070-6-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001554_s0094-114x(98)00070-6-Figure4-1.png", "caption": "Fig. 4. A rotation about B1B3.", "texts": [ " Its rotating passing through center P is normal to the moving plane. This axis can be denoted by a screw with zero pitch, such as o1$1 0; 0; \u00ff1; 0; 0; 0 25 where o1 can be obtained by dividing the corresponding radius (1 m) into V1 o1=1 1/s. Three normal components,V 1 n, V 3 n and V 5 n along the z-axis are jVn 1j 0; jVn 3j 0; jVn 5j jV5j cos 308 2 cos 308 m=s: 26 As we also know, the tip points of all the velocities of points along a line in a rigid body are in a straight line. The normal velocity chart of the mobile is shown in Fig. 4. This velocity chart indicates that there is another rotational motion. Its rotational axis is the intersectional line B1B3 between two planes, one is moving plate B1B3B5 and another is the plane determined by three velocities' tips, B1, B3 and b. This rotational axis B1B3 is $2 \u00ff0:866025; 0:5; 0; 0; 0; 0:5 and its angular velocity o2 is o2 Vn 5=R V5 cos 308=1:5 1:154701 1=s: Thus the second rotational component of the moving plate is o2$2 \u00ff1; 0:577351; 0; 0; 0; 0:577351 : 27 The resultant in\u00aenitesimal motion of the upper plate is the sum of two components" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.18-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.18-1.png", "caption": "Fig. 4.18 Sky ladder (\u5929\u68af), a Original illustration (Su 1969), b Structural sketch, c Chain", "texts": [ " For example, the mercury-operated clock constructed by Zhang Si-xun (\u5f35 \u601d\u8a13) in AD 987 employed a chain drive to transmit power. Another example happened in the case of the astronomical tower constructed by Su Song (\u8607\u980c) and Han Gong-lien (\u97d3\u516c\u5ec9) in the Northern Song Dynasty (AD 960\u20131,127), since the vertical main shaft was too long, it was replaced by a ring chain for transmission to serve as the power source for driving the astronomical device. This device was called Tian Ti (sky ladder). It was a typical chain drive with metallic chains for transmitting motion and force. Figure 4.18a shows the sky ladder in the book Xin Yi Xiang Fa Yao\u300a\u65b0\u5100\u8c61\u6cd5 \u8981\u300b(Su 1969). In the device, the rotation of the driving axle was transmitted to the upper horizontal axle through two small chain rings. This caused three gears to move the celestial movement hoop and the sun-moon-star panel of the machine. The original text records: \u201cThe one zhang nine chi five cun long \u2018sky ladder\u2019 was a chain 4.6 Chain Drives 85 of connected metal braces. The chain was connected to the upper and lower hubs. Every turn of the chain caused the celestial movement hoop tomove a distance that in turn caused the sun-moon-star panel tomove, too" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003637_j.ast.2012.07.003-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003637_j.ast.2012.07.003-Figure2-1.png", "caption": "Fig. 2. Schematic geometry of terminal landing.", "texts": [ " In Section 2, the translational and rotational coupled dynamic model of a lunar module is formulated. Then, an integrated translational and rotational control law is proposed for the coupled system in Section 3. Next, numerical simulation results applying the proposed control law to a lunar module are presented in Section 4. At last, Section 5 draws the conclusions. 2. Problem formulation 2.1. Orbital dynamics To form the basis of the translational modeling, an inertial coordinate frame O \u2013XY Z is formulated with origin O attached to the center of moon. As shown in Fig. 2, the X O Y plane coincides with the moon equatorial plane, and the X-axis points from the origin to the line of zero degree longitude; while the Z -axis points to the arctic pole of the moon. During the terminal landing phase, suppose that the module aims at position P with longitude \u03b10 and latitude \u03b20, which is the pre-selected site on the moon surface. Then, a target coordinate frame P \u2013xyz with origin attached to the terminal point P is further defined with the x-axis pointing outer space along the direction OP; the z-axis is in the POZ plane and is perpendicular to OP; while the y-axis can be defined by the right-handed rule. v, F are the velocity of the lunar module and the force of propulsion unit, respectively. ROM , ROP , r represent vectors from O to M , from O to P , and from P to M , respectively. The body frame of the lunar module M\u2013xb yb zb referred to in Fig. 2 will be defined later. Moreover, to facilitate the modeling, assume that the gravity field of the moon is homogeneous and ignore the moon rotation. Notice r = ROM \u2212 ROP (1) and according to Ref. [21], the motions of the module satisfy R\u0308OM = \u2212 \u03bc \u2016ROP + r\u20163 ROM + F m (2) where \u03bc denotes the moon\u2019s gravitational parameter; m represents the mass of the module. In the target frame, let F = [Fx, F y, F z]T \u2208 R 3, r = [rx, ry, rz]T \u2208R 3, and v = [vx, v y, vz]T \u2208 R 3; thus one has\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 r\u0307x = vx, r\u0307 y = v y, r\u0307z = vz v\u0307x = \u2212 \u03bc \u2016ROP + r\u20163 (rx + ROP) + Fx m v\u0307 y = \u2212 \u03bc \u2016ROP + r\u20163 ry + F y m v\u0307z = \u2212 \u03bc \u2016ROP + r\u20163 rz + F z m (3) where ROP = \u2016ROP\u2016 is the radius of the moon. 2.2. Attitude dynamics This part takes the attitude dynamics of the module into account. As Fig. 2 depicts, the body frame M\u2013xb yb zb of the lunar module is defined with origin in the center of mass and unit vectors coincide with their principal axes of inertia. It should be noted that the propulsion unit is fixed to the module. Without loss of generality, consider that the Mxb axis is along the geometric vertical axis of the module and the single main thruster is aligned with the Mxb axis. Notice that the P x axis is perpendicular to the lunar surface; thus the anticipated landing attitude is considered herein to coincide with target frame P \u2013xyz", " Instead, the linear command filter (55)\u2013(56) is not only easy to realize, but also capable of overcoming the above defect. Remark 3. According to Theorem 2, since system states converge zero equilibrium, the control input uc 1 will approach to a constant \u03bc R2 OP due to Eq. (61), which will prevent the singular problem in computing p0 and q0 owing to Eqs. (23) and (28). 4. Numerical simulation and discussions This section provides a numerical simulation of a terminal descent mission to show the effectiveness of the proposed integrated translational and rotational landing strategy. As Fig. 2 shows, the initial position, velocity, attitude and angular velocity of the lunar module in the target frame P \u2013xyz are given as follows. r(0) = [ 1000 2000 1500 ]T m v(0) = [ \u221210 \u221215 \u221220 ]T m/s \u0398(0) = [ 45\u25e6 \u221245\u25e6 \u221245\u25e6 ]T , \u03c9(0) = [ 0 0 0 ]T rad/s The inertia matrix of the module is I = diag{100,80,80} kg m2 and the mass is m = 100 kg; other parameters are \u03bc = 4902.75 km3/s2, ROP = 1738 km. As mentioned above, it is noticeable that high order of coupled dynamics (10) makes it hard to derive the analytic computations of the standard backstepping-based integrated control law (18), (34), (41) and (48), due to the extreme complexity of high-order derivations of the virtual controls" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003824_tmag.2012.2237390-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003824_tmag.2012.2237390-Figure5-1.png", "caption": "Fig. 5. Definition of the posture.", "texts": [ " In this study, we developed a control method to generate the current pattern in accordance with the rotor\u2019s reference position. A similar idea was also developed in [12]. Current patterns are decided by using the block diagram shown in Fig. 4.When a desired signal is given as the trajectory, this system produces current patterns for all coils to track the given trajectory. The block diagram is explained in the following sections. 0018-9464/$31.00 \u00a9 2012 IEEE A. Definition of Posture The posture of the rotor is expressed using parameters and as shown in Fig. 5. Parameters and define the rotation axis and rotation angle, respectively. The world, axis, and rotor coordinate systems are defined as XYZ, and , respectively. When a desired trajectory is given, the system calculates the current pattern for all coils as follows: (1) where the subscript expresses the th pole, and are the current and amplitude, respectively, and is the mechanical angle between the th EM pole and plane as shown in Fig. 6. In (1), unknown parameters and are derived from the following: (2) (3) where and are the unit vector of the axis and position vector observed in the rotor coordinate, respectively", " Figs. 9 and 10 show the results for the dynamic characteristics analysis. For in Case 1, the computed rotation angle does not agree with the desired rotation angle between 20 and 30 degrees, and between 30 and 20 degrees due to the cogging torque which becomes prominent at said angle ranges, as shown in Fig. 9. As for , there was a sharp dip at 500 ms and 1000 ms. This is due to the transformation of the raw data into and when the rotor comes back to the initial posture . In this posture, as shown Fig. 5, the parameter has more than one value. This problem should be solvedwhen the actuator is controlled using a closed loop controller. For in Case 2, the rotor rotates with the desired trajectory. As for , the analysis result shows an oscillation of 6 Hz. This is thought to be due to the shape of the stator. As shown in Fig. 2, the stator poles are arrayed as a hexagon. When the rotor moves in a circular motion, the transmission torque when the permanent magnets are in line with the vertex of the hexagon is not the same as when they are not in line with the vertex" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001487_mssp.2001.1413-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001487_mssp.2001.1413-Figure1-1.png", "caption": "Figure 1. Gear model (degrees of freedom are represented on gear only).", "texts": [ "ectively extracted from acceleration signals by virtue of the power cepstrum properties. Finally, some applications to simulated and experimental signals illustrate the bene\"ts of the methodology. In order to qualitatively analyse the in#uence of tooth spalls on gear dynamic response, a simpli\"ed version of the model of Velex and Maatar [17] is used and extended to account for localised tooth faults. A pinion and a gear of a pair are modelled as two rigid cylinders connected by a set of lumped sti!nesses which accounts for contact, tooth and gear body de#ections (Fig. 1). The elemental sti!nesses are associated with all potential points of contact on the base plane as well as elemental normal deviations de(g, t) in order to simulate actual tooth #ank geometries. According to rigid body kinematics, the corresponding lines of contact are translated at constant speed and all relevant parameters are recalculated at each time step of the meshing process. Quasi-analytical indications on the response structure can be obtained if the following simpli\"cations are introduced: (a) except for localised tooth defects, the pinion and the gear are geometrically perfect; (b) the mesh sti" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure1-1.png", "caption": "Fig. 1.Geometryof generating rackcutter: (a) 3Dschematic viewof the rack cutter; (b)geometryof rackcutter inprofiledirection; and (c) geometryof rackcutter in longitudinal direction.", "texts": [ " The advantages of the new geometry are: (i) total controllability of gear tooth profiles for favorable tooth contact patterns; (ii) avoidance of edge contactswhen errors of alignment occur; (iii) favorable function of transmission errors that allows to absorb the lineal functions of transmission errors caused by errors of alignments; (iv) favorable load and unload cycles of the gear tooth surfaces; and (v) increase of the gear endurance and the service life of the gear drive. A numerical example of design will illustrate the advantages of the proposed geometry. 2. Generation of ideal geometry of the to-be-shaved helical gear The concept of generation of a helical gear by an imaginary rack cutter of modified geometry as shown in Fig. 1(a) is applied for determination of the ideal geometry of a modified helical gear. By considering one of the members of a helical gear drive with such a geometry, the above-mentioned advantages will be achieved. 2.1. Geometry of the generating rack-cutter Fig. 1(a) shows a 3D schematic view of the generating rack cutter. Fig. 1(b) and (c) shows the geometry of the rack cutter in profile and longitudinal directions, respectively. Coordinate systems Saand Sb (see Fig. 1(b)) are rigidly connected to the rack cutter surfaces \u03a31 and \u03a32 that generate the driving and coast side of the helical gear, respectively. Coordinate system Sc is rigidly connected to the rack cutter and locatedon the rack cutter pitchplane as shown in Fig. 1 (b). Coordinate systems Sg and Sh (see Fig. 1(c)) are auxiliary coordinate systems to take into account the longitudinal crowning of the rack cutter. Rack-cutter generating surfaces consist of nine zones as shown in Fig. 1(a) wherein: (i) Zone 5 is a non-modified surface (planar) corresponding to the standard geometry of a rack cutter. No modifications are provided in this zone. (ii) Zones 1, 3, 7, and 9 are areas of crowning in profile and longitudinal directions. (iii) Zones 2 and 8 are areas of crowning in profile direction. (iv) Zones 4 and 6 are areas of crowning in longitudinal direction. Profile of rack cutter is represented in coordinate systems Sg and Sh (see Fig. 1) for left and right sides as r\u00f0i\u00deg;h\u00f0u\u00de = a\u00f0i\u00depf \u00f0u\u2212u0\u00de2 u 0 1 2 666664 3 777775; \u00f0i = 1;2\u00de: \u00f01\u00de Here, u is the surface parameter in profile direction, apf (i) is the parabola coefficient for profile crowning, and u0 denotes the point of tangency of the parabolic profile with the corresponding yg or yh axes. The upper and lower signs of apf (i) correspond to representation of profile geometry in coordinate systems Sg and Sh for the left and right side, respectively. The following conditions are established in order to divide the rack cutter generating surfaces in three areas in profile direction: \u2022 If uNu0top , then apf=apftop and u0=u0top (area A of zones 1, 2, and 3) \u2022 If u\u2264u0top and u\u2265u0bottom , then apf=0 and u0=0 (area B of zones 4, 5, and 6) \u2022 If ubu0bottom , then apf=apfbottom and u0=u0bottom (area C of zones 7, 8, and 9)", " 9(d) represents the function of transmission errors for referred configurations of case of designA1. A piecewise almost linear function of transmission errors (see Fig. 9(d)), responsible of the noise and vibration of the gear drive is obtained when errors of alignment are present. Case of design A2 represent the application of partial crowning in longitudinal and profile direction by considering the theoretical generation by a rack cutter with generating surface divided in nine zones as shown in Fig. 1(a). The results of tooth contact analysis of the mentioned design of amodified helical gear drivewith partial crowning when (a) no errors of alignment occur, (b) errors \u0394H2=\u0394V2=0.01\u00b0 occur, and (c) errors \u0394H2=\u0394V2=0.025\u00b0 occur are shown through Fig. 10(a), (b) and (c), respectively. Themain advantages of application of partial crowning for modification of the geometry of a helical gear drive are obtained from the combination of the advantages of lineal and localized contacts.We can summarize the advantages as follows: (i) the bearing contact is localized when errors of alignment occur, and (ii) the smaller errors of alignment occur, the larger contact pattern is obtained, and lower contact stresses are expected. A very favorable function of transmission errors of low level is obtained for referred configurations of case of design A2 (see Fig. 10(d)). Case of design A3 represent the application of total parabolic crowning in longitudinal and profile direction. Total crowning means that the whole surface is crowned so that zones 2, 4, 5, 6 and 8 in Fig. 1 do not exist. The results of tooth contact analysis of mentioned case of design of a modified helical gear drive for same configurations than for the previous case of design are shown in Fig. 11. When total parabolic crowning is applied in longitudinal and profile directions, the bearing contact is localized and the gear drive is not sensitive to the appearance of errors of alignment. A parabolic function of transmission errors is obtained for all three cases of design. Based on the results of TCA, designs A2 and A3 with partial and total crowning, respectively, fulfill the requirements of gear drives of low noise and vibration levels, high endurance, and increased service life" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002747_med.2007.4433880-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002747_med.2007.4433880-Figure2-1.png", "caption": "Figure 2. A three degree of freedom robot.", "texts": [ " Thus, a path through N points for a robot with n joints will consist of (N-1)\u00d7 n unique spline functions. Once the spline functions have been defined for all robot joints, the parametric variable Tk+1 must assume some initial time value (e.g. by using (11) and assuming that robot joint speeds have unity values), and then it must be scaled iteratively until maximum velocities and accelerations of all robot joints drop within the imposed physical constraints. III. SIMULATION RESULTS Let us apply the proposed smooth trajectory planning method to a 3 DOF planar robot (Fig. 2). The lengths of robot segments are d1 = 1.1, d2 = 0.9. Twelve waypoints form a triangle (1,0), (0,1) and (1,1). Velocity and acceleration vectors at both ends of the trajectory are set to v1 T = [-0.1, 0.4, 0], a1 T = [1, 3, 0]. Being convenient, maximal velocities and accelerations of all joints are set to 2 rad/s and 10 rad/s2, respectively. For the sake of comparison, two trajectories were planned using the original \u201c434\u201d and the modified \u201c445\u201d interpolation algorithms. As mentioned before, the first and the last segment of \u201cTrajectory 434\u201d have the sets of fourth-order polynomials, while intermediate segments have the sets of third-order polynomials" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002560_j.triboint.2006.11.002-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002560_j.triboint.2006.11.002-Figure9-1.png", "caption": "Fig. 9. Twin disc fatigue machine.", "texts": [], "surrounding_texts": [ "The lubrication system was modified to vary the lubricant flow rate. Fatigue life tests were carried out for different flow-rates and for a given set of operating conditions (see Table 3). The tests were conducted with artificially dented surfaces. The 250 mm dents were made using a Rockwell indentor (see Fig. 11a.). Dented surfaces were used in order to decrease the fatigue life (see Coulon et al. [18,19]). Previous work has shown a standard deviation of the dented fatigue life of 10%. In addition, most contacts in industrial applications are working under contaminated conditions and thus with dented surfaces. The damage develops on the dented disc around the dents or on the smooth disc. The aim is to generate cracks and spalls (see Fig. 11b) and to avoid scuffing. Tests were run using two different lubricants with similar base oil viscosities (oil A: 7mPa. s@80 1C; oil B: 6.3mPa. s@80 1C). These are commercial lubricants with a semi-synthetic base oil and different additive packages. The first oil is used for marine transmissions and the second one is for passenger car gearboxes. The absolute fatigue lives obtained are different, but the trends are similar (see Fig. 12). It can be seen that for a relative lubricant flowrate of 50%, the fatigue life is significantly shortened (almost divided by two). This shows that the rolling contact fatigue life depends strongly on the amount of lubricant. These results can be compared with studies done by Dawson [16], using the lambda ratio as the driving parameter. In a first approximation, the comparison is done, assuming that the lambda ratio is proportional to the lubricant flow-rate. Similar tendencies are obtained." ] }, { "image_filename": "designv10_13_0001428_0094-114x(94)00048-p-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001428_0094-114x(94)00048-p-Figure1-1.png", "caption": "Fig. 1. Physical model: helical gear pair model showing plane-of-action, tooth normal vector ~/ and vibratory motions.", "texts": [ " Further, no misalignments or mass unbalances are considered\u2022 Loss of tooth contact due to gear backlash phenomenon and any other nonlinear effects are also ignored\u2022 Gear bodies are assumed to be rigid except for the elastic compliance of meshing gear teeth. Only time-invariant gear mesh stiffness, damping and inertial properties are considered\u2022 Inertial effects of shafting and bearings are neglected; although energy equivalent bearing stiffness and damping matrices are assumed in order to account for elastic deformations and dissipative effects associated with these elements\u2022 An external helical involute gear pair ij is shown in Fig. 1. Each gear i is represented by a base cylinder of radius a i and width 2b i. The origins O ~ of two non-rotating reference frames (X ~, Y~, Z') and (X j, YJ, Z j) are located on the respective gear bodies i and j as shown such that the orientation of either frame remains parallel to the inertial frame\u2022 Intended rotation of each gear is about its Z ~ axis and the Y~ axes are chosen to lie in the theoretical plane-of-action. Any out-of-plane motions in the X-direction are neglected. Accordingly, the displacement of each gear i from its ideal angular motion f~it is described by the generalized coordinate vector x~(t) = {yi(t) zi(t) Oi(t) O~,(t) 0~z(t)}T; these vibratory motions are labeled in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003829_aim.2014.6878099-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003829_aim.2014.6878099-Figure1-1.png", "caption": "Fig. 1. Simple free body diagram of 2-DOF helicopter [11]", "texts": [ " This study is organized as follows; In section II, the mathematical description of the 2-DOF helicopter system is given. In section III, type-1 fuzzy neural network with parameterized conjunctors is discussed. In section IV, the simulation results are given. In section V, the obtained results 978-1-4799-5736-1/14/$31.00 \u00a92014 IEEE 322 are analyzed and the future work in this area is discussed. Neuro-fuzzy system with parameterized conjunctors and a conventional control approach, PID are deployed on the 2-DOF helicopter shown in Fig. 1. It is a highly nonlinear multi-input-multi-output (MIMO) system with strong crosscouplings between the pitch and the yaw axes due to the thrust torques acting on the axes. Helicopter is mounted on a fixed base and its pitch and yaw (the front and the back) propellers are driven by two DC motors. The front propeller controls the vertical motion of the helicopter about the pitch axis. This angle is defined as positive when the front propeller causes a motion in the upward direction. When the propeller motors are not excited, i.e. when the helicopter is at rest, the pitch angle is about \u221240.5o and its motion is restricted between \u221240.5o and 40.5o. The propeller at the back controls the horizontal motion about the yaw axis. The helicopter is able to rotate 360o in the yaw axis. The yaw angle is defined as positive in the clockwise direction. The thrust forces Fp and Fy shown in Fig. 1 are generated at the distances rp and ry from the pitch and the yaw axes, respectively [11]. The voltages applied to the front and the back propeller motors are the inputs of the system and the pitch (\u03b8) and the yaw (\u03c8) angles in radians are the outputs. The aim is to design a controller to track the desired trajectories in the pitch and the yaw axes. The dynamic nonlinear equations of the system obtained by using Lagrangian mechanics are given for the pitch and the yaw axes as follows, respectively [11]: (Jeq,p +mhelil 2 cm)\u03b8\u0308 =KppVm,p+ KpyVm,y \u2212mheliglcmcos\u03b8\u2212 Bp\u03b8\u0307 \u2212mhelil 2 cmsin\u03b8cos\u03b8\u03c8\u0307 2 (Jeq,y +mhelil 2 cmcos 2\u03b8)\u03c8\u0308 =KypVm,p+ KyyVm,y \u2212By\u03c8\u0307+ 2mhelil 2 cmsin\u03b8cos\u03b8\u03c8\u0307\u03b8\u0307 (1) The descriptions of the variables in Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003752_001872086300500106-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003752_001872086300500106-Figure3-1.png", "caption": "Fig. 3. Acceleration diagrams.", "texts": [ " A, = SE = Ok * [(SE,) i+(SEy)j]+ +& *{&*[(SE,)i+(SEy)j]) A, = SE = -[O(J'Ey)+(e)2(SE,)]i+ These in turn are added vectorially to the elbow acceleration components : + [WE*) -(@2(sEy)lJ7 A,, = +A,,+A,,, (19) A, = Auy+Acey (20) which lead to inertial forces of the forearm-hand combination. Sf,, = -(Wc/981.0)Ac, (21) Sfcy = -(Wc/981.0)Ac,, (22) From the free body diagram (Fig. 4) it is evident that Rex = -ffccx (23) Bey = -qcy+ Pc (24) and approach simplifies programming. The graphical representation of the acceleration analysis is found in Fig. 3. To continue the force analysis, the values from equations (1 1) and (12) are used to determine the components of inertial force at the center of gravity of the upper arm. Sfux = -(W,/981) A-,,(Sc.g.,/SE) (13) Sfuy = -(W,/981)Auy(S~.g.,/SE) (14) A similar procedure is followed with the forearm-hand. Components of the distance from the elbow axis to the center of gravity of the forearm-hand combination are expressed as EG,, = (EG,) sin(bi (15) EG, = - (EG,.) cos #i (16) Values from equations (15), (16), (3) and (4) are substituted in equations (17) and (18) to give the components of acceleration of the fore- Figure 5 is a graphical representation of the summation of forces" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002023_rob.4620080106-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002023_rob.4620080106-Figure6-1.png", "caption": "Figure 6. Derivation of the optimal weighting factors (a) Initial arm-configuration and work-space (b) Optimal weighting factor CY for the DSTO method (c) Optimal weighting factor p for the DNTO method.", "texts": [ " APPENDIX A Let us consider the following least-squares problem Minimize under the restrictions (1). According to Albert,9 the solution is given as b = J'(X - Jb) + [H(I - J+J)]+[7,in - (C + g) - HJ+(X - J b ) ] . (A2) This formulation is identical with Hollerbach and Suh's solution. If we consider how the minimization of expression (14) instead of (Al) under the same restrictions (l), we obtain exactly the solution (12). APPENDIX B One example of the iterations for experimental derivation of the weighting factors for some end-point trajectories is shown in Figure 6. Figure 6(a) shows the arm initial configuration and one example of work space trajectories. The optimal calculated weighting factors a and p in relation to the direction and length of the end-point trajectory are shown in Figure 6(b) and Figure 6(c). Figure 7 shows the maximum squared-torques of joint in the case of DSTO and DNTO methods based on the derived optimal weighting factors, the pseudoinverse method, and the squared-torques minimizing (null-space) method. The results shows that the proposed DSTO and DNTO methods can result in a more stable joint motion than the conventional pseudoinverse and null-space methods in almost all motions. 90 Journal of Robotic Systems-1991 Ma, Hirose, and Nenchev: Improving Local Torque Optimization Techniques 91 References 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003143_j.bios.2009.09.018-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003143_j.bios.2009.09.018-Figure1-1.png", "caption": "Fig. 1. (a) Schematic overview of a NanoPhysiometer to measure glucose consumption from single cardiac myocytes in sub-nanoliter volumes: (A) microfluidic channels n seven v Ag/Ag m e com a in film", "texts": [ " The master was fabricated by spinning a 20 m thick layer of photoresist (SU-8 2025) on a silicon wafer and by exposing it to UV light through a metal mask. The master was placed in a Petri dish, which was filled to a height of approximately 1 cm with PDMS polymer and cured in an oven for 4 h at 70 \u25e6C. After curing, the elastomer was mechanically separated from the master and cut into discrete devices. The PDMS microfluidic device was manually aligned relative to the glucose sensitive electrodes with a stereomicroscope. The PDMS device was sealed to the glass substrate by auto-adhesion, and stabilized with a mechanical clamp (Fig. 1d). For cell manipulation we controlled the syringes connected to the output and control port by hand. For precise flow control we incorporated miniature mechanical screw valves into the microfluidic devices (Ges et al., 2008). Our design allowed us to place two valves within a footprint of 6 mm \u00d7 8 mm in close proximity to the 0.36 nL sensing volume (Fig. 1a). Mice were anesthetized by intraperitoneal injection of Avertin solution (5 mg Avertin per 10 g body weight, T48402, Sigma\u2013Aldrich) containing heparin (3 mg/10 mL, H9399, Sigma\u2013Aldrich). The heart was rapidly excised and placed into ice-cold Ca2+-free and glucose-free Hepes-buffered Tyrode\u2019s solution (TS). The TS contained (in mM): NaCl 140, KCl 4.5, MgCl2 0.5, NaH2PO4 0.4, NaHCO3 10, Hepes 10. The pH of all solutions was adjusted to 7.4 using NaOH. The aorta was cannulated and the heart was perfused with TS at room temperature for 10 min to stop contractions", " During this investigation, we conducted about 100 calibrations with each electrode without a significant decrease in sensitivity. The tested sensors were fabricated on one substrate under identical conditions. No appreciable loss in sensor sensitivity was observed for periods of about 3 months. To measure the metabolic activity of SCM in a confined extracellular space of comparable size we integrated the glucose sensor array into a microfluidic device (NanoPhysiometer). The layout and an image of a NanoPhysiometer to measure glucose consumption from SCM in sub-nanoliter volumes are shown in Fig. 1. The device consists of a PDMS microchannel network auto-adhered to a glass substrate with a microfabricated array of platinum electrodes functionalized with GOx. A clamp was used to provide the mechanical stability. The glass substrate typically had 7 Pt electrodes. Four of the electrodes were functionalized as glucose sensors. Three electrodes remained bare and were used as counter electrodes. The glucose sensitive electrode (labeled (3)) was aligned with the cell trap volume in the microfluidic devices and the input port (Fig. 1a and b) with the bare Pt thin film used as counter electrode (labeled (4)). The external reference electrode (2) was placed in the input port. During the measurement of glucose consumption the mechanical microvalves (1) were closed to eliminate the influence of residual fluid flow on the signal. In order to validate the performance of the glucose electrodes (100 m \u00d7 500 m) in a microfluidic environment, we filled the microfluidic channel (width \u223c40 m) with Tyrode\u2019s solution with a glucose concentration of 2 mM", " Furthermore, the data allowed us to compute the smallest etectable change in glucose concentration to be 1.69 mM at a NR of 3 and a bandwidth of 10 Hz. The SNR could be significantly mproved by reducing the bandwidth. .3. Glucose consumption measurements from single cardiac cells n sub-nL volume In order to measure the glucose consumption from single cardiac yocytes, we designed a microfluidic device (NanoPhysiometer), hich allows us to trap SCM above our miniature thin film glucose lectrodes in a volume of 360 pL. A layout of the configuration and he assembled device are shown in Fig. 1. A concentrated cell susension (6\u20138 L) was added to the input reservoir using a syringe ith a plastic needle. The input port is connected to the 360 pL cell rap volume through the cell input channel (Fig. 5A). By applying a ig. 4. Calibration of the glucose sensor (100 m \u00d7 500 m) in the microfluidic hannel (width \u223c40 m) with Tyrode\u2019s solution of different glucose concentrations 2 and 4 mM; 2 and 8 mM). The flow rate during calibration was 2 nL/min. rent cell culture media ((1) DMEM; (2) RPMI-1640; (3) Tyrode\u2019s solution (pH 7.4); ation of long time stability of the sensitivity of the glucose sensor for regions I and pressure gradient to the output and control ports, the cardiac cells move from the reservoir along the input channel toward the cell trap volume. After trapping a SCM, we closed the mechanical valves to block the output and control channels (Fig. 1a) to suppress residual flow. The results of our measurements to quantify the glucose consumption from a SCM in the sub-nanoliter (0.36 nL) volume in Tyrode\u2019s solution are shown in Fig. 5A and B. In the measurements shown in Fig. 5A, we used spin coated glucose sensitive electrodes (GOx \u223c 0.4 m, Nafion \u223c 0.4 m on Pt electrodes) with dimensions of 40 m \u00d7 100 m. Data from the initial setting of the amplifiers and the time required to trap cell in the sensing volume are not shown. In Fig. 5A three regimes can be identified" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure3.9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure3.9-1.png", "caption": "Fig. 3.9 Types of (link) chains and mechanisms", "texts": [ " The structural sketches of the roller device and the shield device are shown in Figs. 3.8a\u2212b, respectively. 48 3 Mechanisms and Machines When several links are connected together by joints, they are said to form a link chain or just a chain in short. An (NL, NJ) chain refers to a chain with NL links and NJ joints. A walk of a chain is an alternating sequence of links and joints beginning and ending with links, in which each joint is connected to the two links immediately preceding and following it. For example, for the (5, 4) chain shown in Fig. 3.9a, link 1\u2014joint b\u2014link 4\u2014joint d\u2014link 3\u2014joint d\u2014link 4 is a walk. A path of a chain is a walk in which all the links are distinct. For example, for the (5, 4) chain shown in Fig. 3.9a, link 1\u2014joint b\u2014link 4\u2014joint d\u2014link 3 is a path. If any two links of a chain can be joined by a path, the chain is said to be connected; otherwise the chain is disconnected. Figure 3.9a shows a (5, 4) disconnected chain with a separated link (link 5), and Fig. 3.9b shows a (5, 5) connected chain with a singular link (link 5). If every link in the chain is connected to at least two other links, the chain forms one or several closed loops and is called a closed chain. A connected chain that is not closed is an open chain. A bridge-link in a chain is a link whose removal results in a disconnected chain. Figure 3.9c shows a (6, 7) closed chain with a bridge-link (link 4). The connected chain shown in Fig. 3.9b is also an open chain. A kinematic chain generally refers to a movable chain that is connected, closed, without any bridge-link, and with revolute joints only. If one of the links in a kinematic chain is fixed as the frame (KF), it is a mechanism. Figure 3.9d shows a (6, 7) kinematic chain, and Fig. 3.9e shows its corresponding mechanism obtained by frame link 1 in the chain. A rigid chain refers to an immovable chain that is connected, closed, and without any bridge-link. If all joints have one degree of freedom in Fig. 3.9f, it is a (5, 6) rigid chain. A generalized kinematic chain consists of generalized links connected by generalized joints, i.e., the types of links and joints are not specified. For example, if the types of links and joints of the (6, 7) kinematic chain shown in Fig. 3.9d are not specified, it becomes a (6, 7) generalized kinematic chain. A generalized joint is a general type of joint, and it could be revolute, prismatic, spherical, helical, or other types of joints (Yan 1998, 2007). A joint with two connected members is called a simple generalized joint. A joint with more than two connected members is called a multiple generalized joint. Graphically, a generalized joint with NL incident members is symbolized by NL-1 small concentric circles. Figures 3.10a\u2013b show a generalized joint with two and three incident members, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002681_j.automatica.2007.10.019-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002681_j.automatica.2007.10.019-Figure1-1.png", "caption": "Fig. 1. Membership functions along the x1, x2 premise variables of the T\u2013S fuzzy model.", "texts": [ "8 m/s2, and shorthand notations c1 = cos(q1), s2 = sin(q2), c2 = cos(q2), and c12 = cos(q1 + q2). The parameter values used in our simulations are: m1 = m2 = 0.32, `1 = `2 = 0.3, Iz1 = Iz2 = 97.63 \u00d7 10\u22124. The system states are taken as x1 = q1, x2 = q2, x3 = q\u03071, and x4 = q\u03072. The motion dynamics (41) are modelled by fuzzy rules with nonlinear consequents of the form (2). To minimize model and design complexity only the states x1 and x3 are considered in the antecedent part. Each premise variable is partitioned using three fuzzy sets (Fig. 1), leading to a fuzzy model with r = 9 rules. We assume that no a priori knowledge is available, i.e. f (k)i (x) = G(k) i (x) \u2261 0, i = 1, . . . , 9. The objective is to design a stable control law for \u03c41(t) and \u03c42(t), such that q1 and q2 are forced to follow consistently a desired trajectory: xr,1(t) = 2\u03c0/9 + \u03c0/9 cos(\u03c0 t), xr,2(t) = \u2212\u03c0/9 cos(\u03c0 t). To accomplish our goal, the terms A(u)i (e, x), B(u)i (e, x) and C(e) are approximated via LWNNs. We develop common vectors Sa,i (e, x) \u2208 RQa,i and Sb,i (e, x) \u2208 RQb,i for all rules, i = 1, " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure8.6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure8.6-1.png", "caption": "Fig. 8.6 A cow-driven paddle blade machine (\u725b\u8f49\u7ffb\u8eca), a Original illustration (Pan 1998) b Structural sketch c Imitation of original illustration", "texts": [ " The horizontal gear is connected to the frame with a revolute joint, denoted as JRy. The vertical gear is connected to the frame with a revolute joint, denoted as JRx. The meshing activity between the gears can be considered as a gear joint JG. Figure 8.5b shows the structural sketch. 175 8.2.2 Niu Zhuan Fan Che (\u725b\u8f49\u7ffb\u8eca, A Cow-Driven Paddle Blade Machine) Niu Zhuan Fan Che (\u725b\u8f49\u7ffb\u8eca, a cow-driven paddle blade machine) consists of two parts including a gear train and a chain transmission mechanism as shown in Fig. 8.6a (Pan 1998). It has the same function as Fan Che (\u7ffb\u8eca, a paddle blade machine). Animals rotate the large horizontal gear, and the motion is transmitted from the gear train to the upper sprocket on the long shaft, the chain, and the lower sprocket. One half of the lower sprocket is located under the water, the scratch board on the sprocket carries water up to the path board, and the blades on the chain push the water up to the shore through the water-receiving slot installed on the chain. 176 8 Gear and Cam Mechanisms (member 1, KF), a large horizontal gear with a vertical shaft (member 2, KG1), a small vertical gear with a long shaft and the upper sprocket (member 3, KG2), a chain (member 4, KC), and the lower sprocket (member 5, KK)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003475_1.4005467-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003475_1.4005467-Figure8-1.png", "caption": "Fig. 8 ZYZ Euler angles", "texts": [], "surrounding_texts": [ "This paper presents a novel concept of Euler-angle-joints by introducing the DH parameterization of the well-known Euler angles used to describe three-dimensional spatial rotation. Eulerangle-joints are nothing but orthogonally intersecting revolute joints whose axes are defined using the well-known DH parameters. They are so connected by imaginary links of zero lengths and masses that they represent a particular set of Euler angles. Hence, the proposed concept not only establishes a correlation between the DH parameters and the Euler angles but also facilitates the systematic use of the intersecting revolute joints to describe the Euler angle rotations even though the configurations of links are defined using the DH parameters. Such correlations were never reported in the literature and, thus, they form an important contribution of this paper. While developing the EAJs, evolution of the DH parameters for different rotation sequences of Euler angles have been investigated. They are summarized in Table 9. The concept of EAJs lends its utility in the unified representation of one-, two-, and three-DOF joints, i.e., revolute, universal, and spherical, respectively. Such unification makes an algorithm development for kinematic and dynamic analysis much simpler, which was not possible with the original definition of the Euler angles." ] }, { "image_filename": "designv10_13_0001536_s0167-6911(00)00105-5-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001536_s0167-6911(00)00105-5-Figure4-1.png", "caption": "Fig. 4. Puck=mallet impact.", "texts": [ " In the previous section, we computed the set of achievable puck velocities allowing arbitrary impulsive forces applied at an arbitrary point on the puck. In this section, we discuss the case where the impulsive forces to the puck are produced by impacts with a mallet. E>ectively we take as control input the velocity of the mallet. The question of impact controllability then comes down to determining a mapping between mallet velocities and the resulting impulses at impact. We utilize the Routh two-dimensional impact model to determine these impulses in terms of the object velocities [10]. Consider the impact event shown in Fig. 4. We make the simplifying assumption that the inertia of the mallet is much larger than that of the puck so that the mallet velocities are not changed by the impact. We also assume that the rotational velocity of the mallet is zero. 1 In this section, we describe the application of the Routh method [10] to this problem following the work of Partridge [7,8]. The Routh method separates the normal impulse, Pn, into two parts, a compression impulse, and a restitution impulse. The compression impulse, Pc, is measured from the time the two objects collide to the time their relative velocity is zero" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure8-1.png", "caption": "Fig. 8. Applied coordinate systems for TCA.", "texts": [ " Undercutting is avoided by considering the approach proposed by F.L. Litvin and represented in detail in [10]. Undercutting can be avoided by choosing an appropriate number of teeth. Larger pressure angles are in favor of avoidance of undercutting. Pointing is avoided by increasing the number of teeth of the shaver and the proper control of the helix angle, the pressure angle and the crossing angle. Fig. 7. Face width of the to-be-shaved gear and the shaver: (a) 3D 5. Computerized simulation of meshing and contact 5.1. Applied coordinate systems Fig. 8 represents the applied coordinate systems for tooth contact analysis (TCA) of a helical gear drive comprising a pinion of new geometry obtained by plunge shaving and a conventional helical gear. The following errors of alignment are considered: (i) axial displacement of the pinion, \u0394A1, (ii) axial displacement of the gear, \u0394A2, (iii) gear horizontal positioning shaft error, \u0394H2, and (iv) gear vertical positioning shaft error, \u0394V2. Coordinate systems S1 and S2 are movable coordinate systems rigidly connected to the modified shaved helical pinion and a conventional helical gear, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002087_20.3398-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002087_20.3398-Figure2-1.png", "caption": "Fig. 2. Demagnetization characteristic of rare-earth magnet.", "texts": [], "surrounding_texts": [ "From\u2019 the laws Of e1ectromagnetics9 we know that the flux density B in a material medium may be written as\nimental data validates the method described. It is further indicated how this method can be extended to more complex problems.\nI. INTRODUCTION RMANENT-MAGNET disk (or axial-airgap) mo- p\u201d tors find numerous applications. In the past, such motors were fabricated with armature windings embedded in slotted structures made of iron. However, with the advent of rare-earth magnets, to avoid cogging due to slots, permanent-magnet disk motors are constructed with \u201caircore\u201d armature windings. Consequently, the effective airgap of the motor is very large. The effect of armature reaction on the airgap flux-density distribution is negligible. With this assumption, in the following we present an analytical method for determining the magnetic field distribution as a function of the three coordinates, in a disk motor. The method is based on the concept of magnetic charges and the method of images.\nTo determine accurately the flux-density distribution produced by the permanent magnet poles in a disk machine, we must consider the large airgap as well as the finite length along the radius since the ratio between pole pitch and length of airgap is significant. This ratio varies with radius in a disk machine. In other words, we must consider the field problem as a three-dimensional problem. As is generally known, it is extremely difficult to obtain an analytical solution of a three-dimensional field problem. However, using the concept of magnetic charge and the method of images, an analytical solution is obtained in a much less complex fashion. The method is validated by comparing test results with analytical results. For ready reference we briefly review the concept of magnetic charge and the magnetic field model.\nManuscript received March 31, 1987; revised October 13, 1987. This work was supported in part by the National Science Foundation under Grant\nThe authors are with the Department of Electrical Engineering, Univer-\nIEEE Log Number 8719173.\nECS-83 14238.\nsity of Kentucky, Lexington, KY 40506.\nE = p o ( H + n) (1)\nwhere po is the permeability of free space, is the magnetic field intensity, and a is the magnetic polarization or magnetization vector. Since a magnetostatic field E, in the absence of currents, may be derived from the gradient of a scalar potential 9,, that is,\nE = -v!Pm, (2 )\nv * B = o , (3)\n(4 )\nand since -\n(1)-(3) may be combined to yield\nv2qm = v - 2. Now comparing (4) with Poisson\u2019s equation for an elec-\ntrostatic scalar potential V\n( 5 ) P v2v= -- \u20ac \u2019\nwe may write - _ V . M = - p m ( 6 )\nv29, = -pm (7)\nand\nwhere pm is defined as the magnetic volume charge density. We emphasize that the magnetic charge is simply a concept and does not necessarily exist physically. To characterize completely the magnetic charge model for a magnetized body, we further let, in addition to (6) ,\n- V x M = 0 . ( 8 )\nWithout (8), (6) does not have a unique solution for 2 since V (M + v x E ) = v n. In fact, two models exist for a magnetized body. One is governed by (6) and (8), and the other by V X 2 = Jm and V -\nBecause of the similarity between (5) and (7), certain magnetostatic problems may be solved, via the concept of magnetic charge, by using known solutions to electrostatic problems. For complete analogy we replace E by\n= 0.\n0018-9464/88/0500-2038$01 .OO O 1988 IEEE", "NASAR AND XIONG: FIELD OF A PERMANENT MAGNET MACHINE 2039\n- H, P I E O by p m , V by 'Pm, and p by a. On the basis of this analogy we may write\n( 9 ) P m dv am ds ='[I,,,+ 41r SST-I\nwhere T. is the position vector from the source point to the field point; am is the surface density of magnetic charge, which is similar to polarization of dielectrics,\n- a m = M . i i (11)\nwhere ii is the unit normal vector to the surface. For a permanent magnet, may be described by\n72 = Po + XH\nB = p 0 ( p r H + Mo)\np, = 1 + x.\n(12) where x is the magnetic susceptibility. From (12) we rewrite (1) as\nwhere ( 1 3 )\n(14) For an idealized permanent magnet x = 0 ( p , = 1 ) in\n(14); thus\na = IC?,. (15)\nThus a is a constant and is independent of E. From (15) and (6) , pm = -v - a = 0 in an idealized magnet in which only magnetic surface charge density am exists on the surface such that\nConsidering pi = 00 and a zero potential difference ( A 'Pm = 0) between any two points in the back iron, and taking the potential at infinity to be the reference potential 'Pm = 0, the boundary conditions are\n' P m ( z = O = 0\n+ m ( z = L m + g = 0. (22)\nAs in an electrostatic field, the effect of boundaries on fields may be replaced by images. The boundary conditions and location of images here are similar to the problem of a point charge between two parallel conducting planes [5 ] .\nThe charge density on the surface of pole k is (Fig. 5 )\n(23) k 0mo.r - ( -1 ) a,.", "2040 IEEE TRANSACTIONS ON MAGNETICS, VOL. 24, NO. 3. MAY 1988\nm2 = r2 + rg - 2rorcos (e, - 8) ( 2 8 )\n0, & a = -\nR(Q) = -Q *,(e). ( 3 3 ) The z component of flux density is the most important one since only its distribution has a direct effect on the magnitude and the waveform of the EMF induced in the armature winding and on the torque of the machine. Besides, only the z component of the flux density exists on the surface of both pieces of back iron. Therefore, we focus on the z components of H and E. Thus\n0 2 . k p - 1 4?r 81.t k = O H z ( Q ) s ( - l ) k\nWhen Q is outside of the magnet,\nWhen Q is within the magnet,\nAccording to the field symmetry and periodicity, point Q is considered only in the following region:\n(0 I eo I e , / 2 ) (0 I z0 I L,,, + g )\nwhere R, , is the inner radius of the winding and R2w is the outer radius of the winding. Usually, R1, = Rl and Rzw = R2; these are the inner and outer radii of the back iron, respectively.\nIV. ANALYTICAL SOLUTION The drawback of (26) and (34) is that the integration can only be computed by a numerical method. To obtain an analytical solution, we must simplify these integrands." ] }, { "image_filename": "designv10_13_0001897_ip-epa:20030365-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001897_ip-epa:20030365-Figure1-1.png", "caption": "Fig. 1 Studied types of rigid rotor motions as in [9] Dg\u00bcwhirling radius of rotor a Cylindrical whirling motion b symmetrical conical whirling motion c combination of the two whirling motions", "texts": [ " The cylindrical whirling motion of the rotor means that the rotor remains aligned with the stator but the geometrical centreline of the rotor travels around the geometrical centreline of the stator in a circular orbit with a certain frequency known as a whirling frequency, and with a certain radius, known as the whirling radius. Symmetric conical whirling motion means that the whirling radii at each end of the rotor are equal but in opposite directions and the whirling frequency remains constant. These modes of rotor motions and a combination of them are illustrated in Fig. 1. To simplify the task, the present work focuses on the first harmonic force component, i.e. the force at the whirling frequency. Also, for simplicity, only the rigid rotor motions are considered, i.e. the bending of the rotor is neglected. Conventionally the electromagnetic forces acting between the rotor and stator have been studied analytically [1\u20134]. Most of these studies focused on two special cases of the whirling motion, i.e. static and dynamic eccentricity. Fr.uchtenicht et al. [5] derived equations for the forces in inductionmachines in general whirling motion", " The explanation for this behaviour may be the interbar currents. The test motor has an aluminium cast cage rotor. The resistance between the bars through the rotor sheet stack is not infinite, and equalising currents can flow in the end parts of the rotor cage through the rotor stack from bar to bar. This may explain the damping effects seen in Fig. 8. So far we have studied the basic modes of the rigid rotor motions. The next step is to calculate the forces caused by the combined cylindrical and conical motions of the rigid rotor. Fig. 1c presents the combined eccentric motion in which one end of the rotor is concentric and the other one is performing whirling motion with 40mm whirling radius. This motion presents a combination of the cylindrical whirling motion with radius 20mm and the symmetric conical whirling motion with whirling radius 20mm, for which the forces and moments are shown in Sections 3.1 and 3.2. The motor is running again at no load and supplied by a voltage of 230V. Fig. 9 shows the calculated forces for each slice as a function of whirling frequency" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001747_135065002760364804-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001747_135065002760364804-Figure7-1.png", "caption": "Fig. 7 Axial and radial \u00afow of air around a rotating pair of spur gears (adapted from references [26], [29] and [30]). The predominantly radial \u00afow across the gear sides is accompanied by rapid axial \u00afow near the mesh", "texts": [], "surrounding_texts": [ "A further important reason for the decline or failure of EHL is starvation, i.e. the restriction of the lubricant supply to \u00afowrates below the minimum required. Starvation was \u00aerst studied systematically in the 1960s [31\u00b133] and is widely recognized as an important modifying parameter in rolling bearings [34] where lubricant is swept from the track by each rolling element, leaving a restricted supply for its successors [31]. In gears, where the mesh may be supplied with oil from a dedicated jet, or indeed which may be partly immersed, this mechanism is rarely a problem except for the following exceptional cases. Firstly, at high peripheral speeds it may not be possible for oil droplets from the jet to penetrate to the lower part of the tooth gap. For a radially directed jet, this may occur when the time required for the oil to reach the lowest point of engagement, 2m=voil, is comparable with the time taken for the tooth gap to traverse the jet position, \u2026p=2\u2020m=vp; therefore voil, the jet velocity, needs to exceed about \u20264=p\u2020vp to avoid starvation. In practice, this limit is easily overcome by suitable jet orientation and posit ioning but there will still be a maximum pitch-line speed for satisfactory penetration. However, the \u00afow of air around the meshing gears (windage) is not only a source of losses in itself [20] but also can adversely in\u00afuence jet penetration and lead to starvation. In spur gears this \u00afow is predominantly radial around the gear sides but axial near the mesh (F ig. 7) but in helical and especially bevel gears [35] the \u00afow may be quite complex and usually requires development with prototype installations to achieve satisfactory results over a range of operating conditions. Secondly, in dip-lubricated gearboxes, probably the commonest source of starvation is variation in the attitude, or inclination, of the transmission, an extreme example being the propeller 908 transmission in airships which may be required to pivot through more than a complete rotation. Maintaining adequate oil immersion to the gears, which themselves may act as throwers to supply bearings or other components, is then very J03301 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part J: J Engineering Tribology at UQ Library on August 15, 2015pij.sagepub.comDownloaded from dif\u00aecult and recourse may be necessary to a circulating oil system with multiple scavenge pumps. A third source of possible starvation is the start-up of transmissions under cold conditions, particularly after a cold soak. Both aircraft and automotive manufacturers, for example, carry out rigorous cold-chamber and coldweather operation tests and appreciable changes are often necessary during development. Finally, the possibility of complete oil loss should not be overlooked. Seal failures combined either with neglectful maintenance or with failure of level-sensing equipment are an occasional cause of transmission failures. Under such circumstances, it need hardly be said that the Dowson\u00b1Higginson equation is less than adequate! As a result of worldwide airworthiness requirements, which require satisfactory operation for at least 30 min after losing oil pressure, the technology for `oil-loss tolerance\u2019 has reached a sophisticated level in aircraft. It includes increased bearing clearances, heat-resistant materials, friction-reducing coatings, oil-reta ining pockets and complete emergency lubrication systems. A particularly interest ing approach for helicopter main gearboxes is that of Maret [36] who reported the use of scoops to recycle vestigial lubricant in the gear environment. The same worker reported preliminary work on internal injection of coolant (polyglycol\u00b1water solutions) for emergency cooling in the manner of a \u00aere extinguisher. A common \u00aending in this \u00aeeld is the relative ease with which attention to relatively minor design details can greatly mitigate temperature rises and prolong survival." ] }, { "image_filename": "designv10_13_0003071_tmag.2008.2001660-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003071_tmag.2008.2001660-Figure10-1.png", "caption": "Fig. 10. Manufactured SRM: the assembled motor (upper left), the stator (upper right), the proposed rotor (bottom left), the conventional rotor (bottom right).", "texts": [ " The load torque regression curves are derived as follows: (4) (5) The simulation is performed at speed of 35 000 RPM, where the motor has a large windage loss. The current simulation results are shown in Fig. 8. From the results of this simulation, the motor with the proposed rotor shape consumes less current at the same speed. The process of the dynamic characteristics analysis using the inductance matrix is shown in Fig. 9. To verify the windage loss reduction effect of the proposed rotor, the authors manufactured the rotor and compared it with a conventional rotor. The manufactured rotors and assembled SRM are shown in Fig. 10. Fig. 11 is the measuring system. The specifications of the motor are given in Table I. The measured current values of the conventional rotor motor and the proposed rotor motor are shown in Fig. 12. It is clear that the simulated values of Fig. 8 match well with the measured current values. Also, the measured current value of the proposed TABLE I SPECIFICATION OF MANUFACTURED MOTOR Fig. 12. Measured current curves at 35 000 RPM. rotor SRM is less than the conventional rotor SRM because the proposed motor has reduced windage loss due to the cylindrical rotor shape" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.17-1.png", "caption": "Fig. 7.17 A horizontalwheel water-driven wind box revised by Liu (Liu 1962)", "texts": [ " The crank drives the connecting link and the left bar of the horizontal shaft. The right bar pushes the long rod to generate the oscillating motion of the wooden fan for blasting wind into the box (Liu 1962). There are many illogical or unclear parts in the illustration of the device, such as the rope (member 3) on the wooden cylinder (member 4) is too thick, the crank (member 4) is located in the wrong position, the connecting link (member 5) has unclear joints on both ends, and the long rod (member 7) passes over the left bar (member 6). Figure 7.17 shows the result of the reconstruction design by Liu Xianzhou (\u5289\u4ed9\u6d32, AD 1890\u20131975) (Liu 1962). Although some of the unclear structure 156 7 Linkage Mechanisms have been solved, such as, making the diameter of the rope thinner, adjusting the position of the crank, solving the problem of the long rod passing over the left bar, and assigning the two revolute joints on both ends of the connecting link. However, for the connecting link, how the two assigned revolute joints can transform the rotating motion of the crank into the oscillating motion of the left bar is still unclear. According to the classifying method described in Chap. 5, the device is a Type II mechanism with uncertain types of joints. The rectangular coordinate system is defined as shown in Fig. 7.17. The x-axis is defined as the direction of the axle of the horizontal shaft, the y-axis is defined as the direction of the diameter of the horizontal shaft, and the z-axis is based on the right-hand rule. The device can be divided into three parts: a rope and pulley mechanism, a spatial crank and rocker mechanism, and a planar double rocker mechanism (Hsiao et al. 2010). Each of them is explained below: 1. The rope and pulley mechanism includes the frame (member 1, KF), a vertical shaft with the upper and lower wheels (member 2, KU1), a rope (member 3, KT), and a wooden cylinder with a crank (member 4, KU2)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001643_1.1452197-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001643_1.1452197-Figure2-1.png", "caption": "FIG. 2. Configuration of the microrobot.", "texts": [ " Therefore, we propose an earthworm-type microrobot that employs a magnetic fluid in order to resolve these disadvantageous problematic points. In this configuration, a cell equivalent to a segment of the earthworm is composed of a natural rubber tube ~thickness: 0.5 mm! in which a water-based magnetic fluid ~W-35! is sealed up, and the cells are connected with rod-like elastic bodies of natural rubber. The total number of cells in this robot of our trial production was eight. Moreover, a shifting magnetic field is assumed to be an electromagnet, but a permanent magnet is used in this experiment. Figure 2 shows the configuration of the microrobot. Figure 3 shows a diagrammed outline of an experimental device. First, the microrobot from our trial production was inserted into an acrylic tube ~inner diameter: 12 mm; outer diameter: 14 mm!. A pair of permanent magnets ~Nd\u2013Fe, h25315 mm! provided on the right and left sides toward the advancing direction was made to travel at 40 mm/s. The clearance between the magnets was set at 16 mm. The displacement of the microrobot was photographed with a video camera and the image was analyzed" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001348_s0167-6105(97)00299-7-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001348_s0167-6105(97)00299-7-Figure3-1.png", "caption": "Fig. 3. Seam turned about the x axis.", "texts": [ " The resultant force acting on it can be resolved into three mutually perpendicular forces, namely the drag force D, the lift force \u00b8 and the side force S, acting in the directions x, y, z, respectively. Whether or not all three component forces are present at any particular time depends upon the seam angle and any spin which may be imparted to the ball. For a given air velocity, the angle of the seam plane from the vertical xy plane is defined in Fig. 2. Here, the seam plane is turned about the y axis through angle c y measured in the horizontal xz plane. In Fig. 3, the seam plane is turned about the x axis from the vertical xy plane through angle c x measured in the vertical yz plane. Turning the seam about the z axis does not change the orientation of the seam as far as the oncoming air flow is concerned. The side force generated in the z direction is responsible for the \u201cswing\u201d of the ball. For c y positive as shown in Fig. 2, the bowler would bowl an \u201cinswinger\u201d which moves in towards the batsman, while for c y negative, he would bowl an \u201coutswinger\u201d which moves away from the batsman" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003784_s12613-013-0781-9-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003784_s12613-013-0781-9-Figure8-1.png", "caption": "Fig. 8. Schematic illustration on the formation of soft zones along the grain boundary \u03b1.", "texts": [ " Moreover, the fatigue crack initiation region is characterized by stairs, ridges, and plateaux. Fig. 7 displays the SEM image of the subsurface of a fractured specimen. The main crack tends to propagate smoothly along the grain boundary \u03b1. It is widely known that grain boundaries have a blocking effect on the slipping of dislocations, thereby improving the resistance of deformation. However, for the present alloy, the continuous grain boundary \u03b1 precipitated preferentially during the heat treatment process. As shown in Fig. 8, \u03b1 stabilizing elements from the adjacent zone diffused into these \u03b1 phase, and the \u03b2 matrix was subsequently stabilized, which prevented the formation of \u03b1 lamellar. It is known that \u03b1 phase with hcp cubic structure was harder than \u03b2 phase with bcc cubic structure in titanium alloys. Thus, a softer \u03b1 precipitated-free zone was formed along the grain boundary \u03b1, which will deform preferentially under loading. Moreover, the effective slip length within the soft zone is directly related with the length of grain boundary \u03b1 phase [18]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001606_940870-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001606_940870-Figure10-1.png", "caption": "Figure 10 Relationship between rear wheels side slip angle and side force", "texts": [ " In comparison with the criteria condition in which = 0\u00b0, the range of yaw-moment controllable by controlling the rear wheel steering angle is large both in the increasing and decreasing direction in ranges with small p values. It decreases in the increasing direction as p increases, especially during deceleration. The dotted lines represent the characteristics of the vehicle during non-acceleration and non-deceleration. The figures indicate that, while the increase in yaw-moment during acceleration can be cariceled by steering the rear wheels in the opposite phase, the decrease in yaw-moment during deceleration cannot be cornpensated when P is 4\" or more. This is explained by Figure 10. If we use point A in the figure to represent the sum of side forces applied on the rear wheels when the vehicle makes a turn, the controllable range is as wide as represented by a' on the decrease side, but is oniy as wide as represented by a\" on the increase side. This was converted to yaw-moment (Figure 11). With rear wheel steering angle control, the controllabie range of stabilizing yaw-moment on the increase side decreases as P increases. steering angle control 3.2 Effect and effective ranges of each control met hod" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001729_978-4-431-68275-2-Figure24-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001729_978-4-431-68275-2-Figure24-1.png", "caption": "Fig. 24 A 3-way intersection", "texts": [], "surrounding_texts": [ "A system entrance is used to introduce robots into the system. And robots may withdraw from the system via a system exit. System entrances and exits are in fact passage segments incident to intersections or terminals." ] }, { "image_filename": "designv10_13_0002081_s0303-2647(03)00118-7-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002081_s0303-2647(03)00118-7-Figure1-1.png", "caption": "Fig. 1. A dynamical system model of human biped walking. The model includes seven rigid-link, and kinematics of all joint angles are constrained by a given function, \u03b6\u0304(t) (constraint trajectory). The constraint trajectory is usually a periodic function \u03b6\u0304std(t). The ground reaction forces are modeled by viscoelastic element and pseudo-Coulomb friction. The states of HAT-segment (\u03b8, x, y) and their derivatives, i.e. \u03be = (\u03b8, x, y, \u03b8\u0307, x\u0307, y\u0307), are the dynamical variables of the model. The constraint trajectory \u03b6\u0304(t) could be regarded as a forcing term to the six-dimensional dynamical system (Eq. (1)).", "texts": [ " It is shown that appropriate amounts of the phase reset can prevent the model from falling, even for the perturbation that induces falling in the case without the phase reset, suggesting that those phase resets can improve the dynamic stability of the gait. Moreover, the appropriate phase resets predicted by the model are compared with the experimentally observed phase resets during human stumbling reaction (Kobayashi et al., 2000) to show they share similar characteristics. We constructed a simplified dynamical system model of the human musculoskeletal system interacting with the ground (Fig. 1). The model was derived from the equations of motions of the rigid seven-link model in saggital plane. The kinematics of all joints during walking was constrained by a given periodic joint-angles-profile. The ground reaction forces in vertical and horizontal directions were modeled by viscoelastic element and pseudo-Coulomb friction, respectively. The detailed methodology of this modeling can be found in van den Bogert et al. (1989) and Yamasaki et al. (2003). The model can basically be described by the form of six-dimensional non-autonomous forced system, where the dynamical variables are \u03b8, the angle of HAT-segment (Head\u2013Arms\u2013Trunk) from the horizontal axis, (x, y), the position of HAT-segment in the Cartesian coordinate fixed somewhere on the ground, and their derivatives, i" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002258_0470033983.ch9-Figure9.4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002258_0470033983.ch9-Figure9.4-1.png", "caption": "Figure 9.4 CAD model of the custom-designed bone plate, showing the front and the backside", "texts": [ " Geomagic Studio from Raindrop Geomagic, United States, was used to convert the STL file into a NURBS model suitable for import into a CAD program. The CAD model of the distal femur was used as the basis for the custom-designed bone plate. The surgeon examined the CT scans and the 3D model in order to determine the optimal locations and angles for the screw holes. The engineering collaborators then designed a bone plate based on the recommendations of the surgeon. The bone plate was designed to conform to the shape of the bone without interfering with the surrounding soft tissue, ligaments and tendons. Figure 9.4 shows a CAD rendering of the custom bone plate, and Figure 9.5 shows an SLA model of the bone plate attached to SLA bone models following a mock surgery by the surgeon. In a second project, a custom bone plate was designed to fixate the proximal tibia after a closing wedge osteotomy. In this case, both a custom bone plate and a custom drill and cutting guide were designed. A closing wedge osteotomy on the tibia is commonly used to correct the tibial plateau slope to prevent femoral-tibial dislocations" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001727_28.287514-Figure20-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001727_28.287514-Figure20-1.png", "caption": "Fig. 20. Variable reluctance motor with two full pitch windings.", "texts": [ " Having higher torque ripple is clearly the main disadvantage of the new motor and more research needs to be done to develop a control to reduce the torque ripple itself or its effect on the speed. VII. FUTURE RESEARCH The authors believe that research on this type of motor drives described in this paper is just beginning. For example, as an extension of the concept proposed in this paper the authors have proposed another motor which have two full pitch windings and two short pitch windings, as shown in Fig. 20. The operating principles are similar to those of the motor shown in Fig. 2. The advantage of the second motor over the ACVFZM described in this paper is that the slot utilization is increased. The authors are conducting research on the motor shown Fig. 20 and the results will also be presented in a future paper. In addition to the research mentioned above, the authors are engaged in research in the following areas: 1) Additional converter topologies, including soft switching 2) Torque ripple control. 3) Elimination of the position sensor. converters. VIII. CONCLUSION Two of the perplexing problems conceming VRMs, namely current commutation and energy circulation, are the target problems of this paper. The cause of these two problems has been identified and a new concept for solving the problems is proposed in this paper" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003782_1.4863809-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003782_1.4863809-Figure10-1.png", "caption": "FIG. 10. Specifications of the improved prototype magnetic gear.", "texts": [ " The transverse axis is 0 mm when the inner and outer gaps are the same length of 1 mm. On the other hand, it is 1 mm when the inner gap length is 0 mm and it is 1 mm when the outer gap length is 0 mm, respectively. The sum of both gap lengths is constant at 2 mm. It is obvious that the closer the pole-pieces get to the outer rotor, the larger the torque. In fact, however, it is limited due to the machining accuracy. Based on the above investigation, an improved magnetic gear is prototyped as shown in Fig. 10. The axial length of the pole-pieces changes from 16 mm to 10 mm, and the radial position moves \u00fe0.5 mm to the outer rotor. Figure 11 demonstrates torque behavior when the inner rotor is rotated at the constant speed of 300 r/min. It is understood that the measured maximum torque is 13.6 N m, which is improved by 45% from the initial magnetic gear. Figure 12 shows the comparison of efficiency of the initial and improved magnetic gears. It reveals that the [This article is copyrighted as indicated in the article" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002017_bit.260380113-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002017_bit.260380113-Figure1-1.png", "caption": "Figure 1. Schematic diagram of the enzyme sensor system: (1) air; (2) buffer tank; (3) injection port; (4) oxygen electrode; (5) recorder; (6) peristaltic pump; (7) thermostatically controlled bath; (A) (a) oxygen electrode, (b) platinum cathode, (c) rubber ring, (d) enzyme and cellulose triacetate membranes, (e) Teflon membrane, and (f) dialysis or nylon membrane.", "texts": [ " The apparatus used for the simultaneous determinations of sucrose and glucose, lactose and glucose, or starch and glucose were the same as those reported for hypo~anthine, '~ ino~ine, '~ and IMP '' except for the enzyme electrode. The oxygen electrode employed in this study was a Clark-type electrode consisting of a platinum cathode, a lead anode, alkaline electrolyte (KOH), and an oxygen-permeable Tef Ion membrane. The enzyme membranes and three sheets of triacetate cellulose membranes containing l,~-diamino-4-amino-methyloctane were placed on the Teflon membrane of oxygen elec- 100 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 38, JUNE trode and covered with dialysis membrane except for the starch sensor, as shown in Figure 1. The enzyme membrane of the starch sensor was covered with nylon net (150-mesh) instead of dialysis membrane, because starch molecules cannot pass through a dialysis membrane. Unless otherwise stated, the temperature was controlled at 30\u00b0C during the enzyme reaction. Assay Procedures A 0.05M phosphate buffer solution at pH 7.0, 7.3, or 6.1, which was saturated with oxygen by bubbling air through the solution, was transferred continuously to the sucrose, lactose, or starch sensor, respectively, by a peristaltic pump" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002089_2.5107-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002089_2.5107-Figure2-1.png", "caption": "Fig. 2 Swashplate geometry.", "texts": [ " The total main rotor blade pitch as a function of blade azimuthal position (speci ed by rotation angle \u00c3 ) is given by45 \u00b5tot.\u00c3/ D \u00b5mr \u00a1 A1 cos \u00c3 \u00a1 B1 sin \u00c3 (4) Equations (1\u20133) can be written in matrix form as ub D Bs2bus (5) where ub D [\u00b5mr; B1; A1]T ; us D [zs ; \u00b5s; \u00c1s ] T Bs2b D 2 4 l\u00a11 mr 0 0 0 \u00a11 0 0 0 1 3 5 The relationship between the main rotor actuator positions and the swashplateparameters can also be derived.The actuatorgeometry that will be used to provideinteraxis coupling is de ned in Fig. 2 The variables\u00b4 and \u00b0 are free design parameters,where \u00b0 is the angle between the x axis and actuatorC . The x axis correspondsto the aircraft\u2019s x-axis body axis.The relationshipbetween the swashplate and the actuators for this geometry is40;41 2 4 zs tan\u00b5s tan \u00c1s 3 5 D Ba2s 2 4 zA zB zC 3 5 (6) where Ba2s D A1 A2 A3; A1 D 2 4 1 0 0 0 cos \u00b0 sin \u00b0 0 \u00a1sin \u00b0 cos \u00b0 3 5 A2 D 2 6666664 1 2[1 C cos.\u00b4=2/] 0 0 0 1 [2R.1 C cos.\u00b4=2/] 0 0 0 1 [2R sin.\u00b4=2/] 3 7777775 A3 D 2 4 1 1 2 cos.\u00b4=2/ 1 1 \u00a12 1 \u00a11 0 3 5 This is a generalization from earlier work that placed actuator C on the x axis, hence parameter \u00b0 was zero" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002853_s11012-006-9037-3-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002853_s11012-006-9037-3-Figure1-1.png", "caption": "Fig. 1 Side view of the 6-3 SPM", "texts": [ " Parallel mechanisms are employed in flight simulators, driving simulators, amusement parks, oil platforms, robot arms, CNC work benches, surface polishing, trimming, shaping, and assembling, mounting antennas and medicine. 6-3 Stewert platform mechanism (SPM), the most famous parallel mechanism, is composed of a fixed hexagonal base platform and a moving triangular top platform, linked by six rigid legs attached to the base at six points by universal joints and to the top at three points by spherical joints (Fig. 1). This architecture lets the top platform of the SPM have six degrees of freedom (dof) of motion with respect to the fixed base. The forward kinematics (FK) problem of the SPM solves for the position of the center of gravity of the top platform and the orientation of the top platform with respect to the base platform when the lengths of the legs are known, while the inverse kinematics (IK) problem solves for the leg lengths that will give a certain position and orientation of the top platform when that particular position and orientation are given" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002029_095440605x31463-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002029_095440605x31463-Figure1-1.png", "caption": "Fig. 1 Ball-sting arrangement used for the non-", "texts": [ " The velocity variation along the entire test section was+0.25 per cent, across the entire test section was +0.3 per cent, and the turbulence intensity in the test section was 0.3 per cent. Owing to the limiting size of the working section, a scale plastic model of a football was created using rapid prototyping (66 mm in diameter when compared with 218 mm for a full size football). The model had a generic seam pattern, commonly used by many football manufacturers, which consisted of 20 hexagonal and 12 pentagonal patches (Fig. 1). After the rapid protyping process the ball model was sanded and polished to create a smooth surface, as would be found for a real ball. This resulted in a test section blockage of only about 4 per cent (based on cross-sectional area) which is negligible for a 30 per cent open area slotted working section [12], and therefore blockage corrections were not applied. The effect of velocity on the drag of a nonspinning ball was first measured by mounting the ball on an \u2018L\u2019-shaped sting that was attached to a spinning tests, using scale model of a football", " (Reproduced from Biomedical Engineering Principles in Sports, Chapter 13, Fig. 13.18 with kind permission of Springer Science and Business Media) Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C15604 # IMechE 2005 at VIRGINIA COMMONWEALTH UNIV on March 16, 2015pic.sagepub.comDownloaded from three-component balance manufactured by TEM Engineering Limited. The force balance had a resolution of 0.018 N and was capable of measuring up to 10 N. A shroud was mounted in front of the sting in an attempt to reduce the drag force due to the sting itself (Fig. 1). The air speed in the working section of the wind tunnel was varied from 20 m/s (the minimum consistent speed achievable) up to 70 m/s and back down again. The drag and lift forces experienced by the ball-sting arrangement were measured using the force balance at regular intervals and three runs of tests were carried out, with the ball model mounted in three different orientations (the ball being rotated 908 about the sting between each run of tests). When this testing was complete, the drag acting solely on the sting, the \u2018tare\u2019 drag, was measured" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002130_019-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002130_019-Figure1-1.png", "caption": "Figure 1. Determining the elastic film shape.", "texts": [ " Therefore, the contact width, transverse to the flow direction, should be made finite, particularly considering that due to the abrupt changes in the vicinity of roller extremities large pressure spikes are generated as shown in [3, 34], inhibiting the flow of lubricant into these regions, yielding the absolute minimum film thickness (as shown later). The analysis with finite equivalent roller length is termed finite line contact. Since an equivalent system is used where the roller is considered to be in contact with an elastic half-space, only the deformation of the elastic surface is considered. 2.2.1. The elastic film shape. Assuming the undeformed profile of the roller to be parabolic, the lubricant film thickness at any location within the contact domain can be expressed as (see figure 1) h(x,y) = h0 + hgp(x,y) + \u03b4e(x,y). (4) By the principle of superposition, the total elastic deflection at node (k, l) can be formulated as [35] \u03b4e(k,l) = 2 \u03c0E\u2032 nx\u2211 j=1 ny\u2211 i=1 pi,jDm,n, (5) where m = |k \u2212 i + 1| and n = |l \u2212 j + 1| and the influence coefficient matrix, Dm,n, is given in appendix A. As the roller is edge blended, in order to reduce the edge stress concentrations, the alteration in its axial undeformed profile must be taken into account when evaluating hgp(x,y). Using parabolic lateral and axially blended undeformed profiles of the roller (see figure 2), and non-dimensionalizing groups in (2), the elastic film shape becomes h\u0304(x\u0304,y\u0304) = h\u03040 + [ (x\u0304i,j \u2212 g\u0304\u2032)2 2 + (y\u0304i,j \u2212 (z\u0304\u2032 \u2212 y\u0304d)) 2 2Rd ( a2R b2 )] +\u03b4\u0304e(x\u0304,y\u0304)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002596_physreve.73.051503-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002596_physreve.73.051503-Figure1-1.png", "caption": "FIG. 1. Picture of a magnetic filament.", "texts": [ " It is shown that the mean magnetic energy of the filament in dependence on its length has a minimum, the position of which depends on the frequency of the ac field. The streaming velocity induced by the oscillating tips of the magnetic filaments is estimated in Sec. V. II. MODEL Let us consider a spontaneously magnetized filament with the magnetization per unit length M. The shape of the filament with a curvature elasticity constant C is described by its tangent angle with a respect to the x axis along which an ac magnetic field H cos t is applied Fig. 1 . Normal and \u00a92006 The American Physical Society-1 tangential components of the stress F in the filament are given by 4,6 Fn = C 1 R ,l + MH cos t sin , 1 Ft = \u2212 C 2R2 + . 2 Here R is the radius of the curvature of the center line of the filament connected with the tangent t and the normal n according to the Frenet equation dt dl =\u2212 1 Rn . characterizes the tension in the filament and is determined from the condition of inextensibility. Partial derivative is denoted by subscript,\u00bc. The motion of the filament is considered in the Rouse approximation when the hydrodynamic interaction between its different parts is neglected and the velocity of its material point v is v = 1 K , where =4 / ln L /a +c is the viscosity of a liquid, c is the constant of order 1 , l is the contour length along the filament, K = dF dl , 2L is the length of the filament, and a is the radius of its cross section", " 6\u20138 we show the growth factors for a limited range of the magnetoelastic number due to the limited validity of the linear stability analysis. C. Time averaging In the case when the frequency of an ac field is enough large the behavior of the even mode in the nonlinear regime -4 can be considered on the basis of the time-averaging procedure. In this case we can consider the small deviations of the shape of the filament from the straight configuration characterized by its orientation angle t with the direction of an ac field Fig. 1 . Representing as + \u0303 and linearizing with the respect to \u0303 the tilde further is omitted we obtain the following equation: ,t + ,t = \u2212 ,llll + Cm cos t cos ,ll at boundary conditions ,l l=\u22121,1 = 0, ,ll l=\u22121,1 = Cmcos t sin + Cm cos t cos l=\u22121,1. The tangent angle perturbation can be decomposed into a fast oscillating part 0 and a slowly varying part w, where 0 is a solution of the problem considered in 7 : 0,t = \u2212 0,llll, 13 0,ll l=\u22121,1 = Cm cos t sin , 14 0,l l=\u22121,1 = 0. 15 The solution of the problem 13 \u2013 15 can be put in the form 7 051503 0 = \u2212 8 Cm sin 1,l l cos t \u2212 2,l l sin t , 16 where 1,2 l are known functions" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002915_j.1751-1097.1978.tb06961.x-FigureI-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002915_j.1751-1097.1978.tb06961.x-FigureI-1.png", "caption": "Figure I . Rates of epinephrine photooxidation and total amount of adrenchrome formed (a) in the absence and (b) in the presence of added catalase. Reaction mixture in 50 mM potassium phosphate, pH 7.8. Total volume: 2.5 ml. Initial [epinephrine] = 0.4 mM; Initial [02] = 0.25 mM; catalase, 0.7 units. A6,, (Chl) = 0.2. Intensity of actinic light: 0.85 Jm-'s-'. T = 25\u00b0C. Initial rates of adrenochrome formation with or without added catalase = 1.52 x 10-6Ms-'. Ratios of O2 consumed to adrenchrome formed: curve (a) = 2.08; curve (b) = 1.09.", "texts": [ " COHEN of adrenochrome when catalase is added? What is the explanation for the doubling in the yield A. W. FRENKEL The over-all reaction for the photooxidation of epinephrine (RH,; EP) to adrenochrome (R; ADR) at pH 7.8 can be written (in agreement with the data presented by Dr. J. D. Spikes at this meeting): and in the presence of low concentrations of catalase : In the presence of catalase, therefore, a given amount of O2 can oxidize twice as much RH, to R as in the absence of catalase. As indicated in the results section (Fig. I), the initial rates of photooxidation of RH4 are not affected by low conc. of catalase. Under these conditions, catalase only dismutes the H2Q2 formed in reaction (Ib), and it does not otherwise appear to affect the mechanism of the sensitized photooxidation of RH, to R." ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003500_j.scient.2011.08.005-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003500_j.scient.2011.08.005-Figure3-1.png", "caption": "Figure 3: Free body diagram of a half-toroidal CVT including one roller and two disks [10].", "texts": [ " (1) and (2), where \u03c91 and \u03c93 are rotational velocities of input and output disk, respectively, and \u03c92 is rotational velocity of the roller as follows: Spin = r1\u03c91 \u2212 r2\u03c92 r1\u03c91 , (1) Spout = r2\u03c92 \u2212 r3\u03c93 r2\u03c92 , (2) where r1 and r3 are functions of \u03b3 as shown in Eqs. (3) and (4): r1 = r0(1 + k \u2212 cos(\u03b8 + \u03b3 )), (3) r3 = r0(1 + k \u2212 cos(\u03b8 \u2212 \u03b3 )). (4) When there is no slippage between disk and roller, velocity ratio is SrID = r1 r3 , and actual velocity ratio could be obtained by: Sr = \u03c93 \u03c91 = (1 \u2212 Spin)(1 \u2212 Spout) r1 r3 = (1 \u2212 Sp) 1 + k \u2212 cos(\u03b8 + \u03b3 ) 1 + k \u2212 cos(\u03b8 \u2212 \u03b3 ) , (5) while speed efficiency could be obtained by [10]: \u03b7speed = Sr SrID = 1 \u2212 Sp. (6) Figure 3 shows the free body diagram of a half-toroidal CVT. Kinetic analysis of this system is expressed by [10]: FTin = \u00b5inFN , (7) FTout = \u00b5outFN , (8) where FN is the normal force at contact point, FTin and FTout are traction forces that exert input torque to roller and output disk, respectively. Spin moment between disks and roller MSin and MSout are expressed by: MSin = \u03c7inFN r1, (9) MSout = \u03c7outFN r3. (10) Input traction coefficient tin and output traction coefficient tout are expressed by: tin = Tin mnFN r1 , (11) tout = Tout mnFN r3 , (12) tin = \u00b5in + \u03c7in sin(\u03b8 + \u03b3 ), (13) tout = \u00b5out \u2212 \u03c7out sin(\u03b8 \u2212 \u03b3 ), (14) where Tin, Tout, n andm are input torque, output torque, number of rollers and number of disks, respectively, and \u03c7in and \u03c7out are both spin momentum coefficients and \u00b5in and \u00b5out are traction coefficients (effective friction coefficients between FT and FN )" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002608_tpas.1983.317993-Figure5-1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002608_tpas.1983.317993-Figure5-1-1.png", "caption": "Figure 5-1. Flux Plots for 0.1 Hertz; D-axis Current. Skin Depths: Figure 5-4. Flux Plot for 2.5 Hertz; Q-axis Current. Real ComRotor - 2.95 in.; Wedges - 16.7 in. ponent. Skin Depths: Rotor - 0.59 in.; Wedges - 3.34 in.", "texts": [ "g sinw t (5-2) Thus the real part of the vector potential gives the flux distribution at the time when the exciting current is at crest, while the imaginary part gives the flux distribution at the time when the exciting current is zero. The imaginary flux is, thus, produced by rotor body currents only, which lag the exciting current in time. Solutions to the diffusion equation, in general, do not yield spacestationary flux distributions, but rather, the flux in the conducting medium is an exponentially damped traveling wave. The traveling wave nature of the solution can be inferred from the relative shapes of the real and imaginary flux plots of Figure 5-1. Furthermore, in a conducting medium (in the absence of externally applied voltages), J=-o,aaA (5-3) from which, JAt) w a[Aia coswt+ Area; sinoa (5-4) Thus, the current densities in the rotor may be inferred from the flux plots to some degree. It should be remembered that the flux plots may contain both positive and negative potentials, which are not identified in the present format. Figure 5-2 shows the real component of the flux for d-axis currents applied at a frequency of 2.5 hertz; Figure 5-3 shows a similar plot for field currents applied; and Figure 5-4 shows the plot for q-axis currents applied" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003420_02640411003792711-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003420_02640411003792711-Figure2-1.png", "caption": "Figure 2. The putting robot allowed for the stroke path, face angle, lie angle, and backswing length to be set independently.", "texts": [ " Impact spot is defined as the distance from the centre of the putter face to the ball contact point, along the heel\u2013 toe axis of the putter. All four variables are measured at impact. The origin of the reference frame is a theoretical position located at the centre of the putter face when the centre of the putter face is flush with the ball and both face angle and impact spot are zero. TOMI1. The TOMI1 system consists of a batterycharged clip, comprising four light-emitting diodes (LEDs), which attaches directly to the putter shaft (Figure 2). A nearby camera receives information from the LEDs about their coordinates in 3D space and relays it to a computer. With the use of a laser, the TOMI1 system is calibrated by placing the putter head flush with the ball in the address position with the putter face square to, and centred on, the target line. The system captures the coordinates of the LEDs in the calibrated position. The real-time stroke variables reported by TOMI1 are based on a sampling rate of 30 Hz, which limits the ability to capture the moment of impact (MacKay, 2008)", " However, the raw 3D coordinate data from each LED are stored in a data file immediately after each stroke with the top line of each stroke data file containing the LEDs\u2019 coordinates in the calibrated position. This permits researchers to process the raw data using their own methods, such as those described later in this article. Putting robot and environment. A proprietary golf robot was designed and built, in a university machine shop, with the help of a machinist with 25 years of experience. The robot design allowed for the stroke path, face angle, lie angle, and backswing length to be set independently (Figure 2). The constrained pendular motion of the robot ensured that the address position of the putter was identical to the impact position. Lasers positioned on the putter face and robot stand indicated the face angle and stroke path of the putter, respectively. The putting robot, when used in conjunction with the procedures described later, generated identical putting strokes with known stroke paths and face angles at impact. All putts were executed with a Nike Unitized Retro Putter, 0.89 m (35 inches) in length, on a synthetic putting surface that was 7 m long and 5 m wide", "178 below or 0.218 above the laboratory measurement (Figure 3). Relative to face angle, the TOMI1 method showed more discrepancy in Validity and reliability of the TOMI1 system 895 measuring stroke path as the TOMI1 measurement may be \u20131.188 below or 1.128 above the laboratory measurement (Figure 4). The larger discrepancy in measuring stroke path may be related to our particular data-processing techniques in combination with the accuracy with which the TOMI1 clip can be placed on the putter shaft (Figure 2). The TOMI1 camera only \u2018\u2018sees\u2019\u2019 the four LEDs on the TOMI1 clip and not the putter head, while the laser\u2013grid system has no relationship to the clip. The data analysis program assumed that a line drawn between the two LEDs that protrude from the sides of the putter shaft was parallel to the target line (Figure 2). Assuming a vertical putter shaft (for simplicity), if the clip was rotated about the longitudinal axis of the putter by\u00fe 18, the theoretical target line created by the analysis program would be misaligned with the true target line (as indicated by the laser\u2013grid system) by 18. Given this scenario, if the putter head was swung with only velocity in the true target line direction at impact, the analysis program would erroneously report a stroke path of \u201318. A misaligned clip will not affect face angle" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001459_jsvi.1998.1988-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001459_jsvi.1998.1988-Figure1-1.png", "caption": "Figure 1. Degree-of-freedom definition (positive rotation of pinion).", "texts": [ " For generality, the following conventions are established: (a) the degrees of freedom attributed to the pinion and the gear of stage 1 are defined with respect to the frame (R1) such that (Op1, s1) is along the centre line of stage 1 (Op1, Og1); (b) the degree-of-freedom vector attributed to the pinion of stage s is defined in the same frame of reference as the degree-of-freedom vector of the gear of stage s\u22121; (c) the degree-of-freedom vector of the gear of stage s is defined in the frame linked to the pinion-gear centre line of stage s. Upon isolating a given pinion-gear pair, the most general situation, can be represented as shown in Figure 1. The deformable part of the pinion-gear system is assimilated to a Winckler type foundation formed by a series of lumped stiffnesses ksi distributed along the potential lines of contact on the theoretical base planes [19, 22] (see Figure 2). Such a \u2018\u2018thin-slice\u2019\u2019 approach does not include any convective effect and can hardly give the exact tooth load distribution especially near the flank edges. However, comparisons with experimental data on narrow-faced gears [22, 32, 33] indicate that the predicted transmission errors are correct while tooth load distributions remain acceptable for moderate defect amplitudes" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003044_j.matdes.2010.02.052-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003044_j.matdes.2010.02.052-Figure1-1.png", "caption": "Fig. 1. Schematic diagram showing the laser powder micro-deposition process.", "texts": [ " The substrate used was commercially pure Ti with dimensions of 100 12 6 mm. The 100 12 mm surface was sandblasted and cleaned with ethanol before deposition. During the thin wall build-up process, the laser microcladding head was moved up a preset distance after the deposition of each layer. Elemental powders of pure Ti and Cr were fed by the two hoppers simultaneously and the powders mixed before entering the melt pool for depositing a homogeneous Ti\u2013Cr alloy, as ights reserved. schematically shown in Fig. 1. The powder particle size ranges are between 75\u2013100 lm and 45\u201390 lm for Ti and Cr, respectively. The length of the walls was 20 mm. After deposition, the deposited walls were cross sectioned and prepared for metallographic observation. The samples were etched with Kroll\u2019s reagent (2 ml hydrofluoric acid, 10 ml nitric acid, 88 ml water) for 10 s. Microstructure observation was carried out on the cross-section perpendicular to the laser scanning direction with a scanning electron microscope (S-2400, Hitachi, Japan)", " The processing parameters used were laser power 150 W, scanning speed 8 mm/s. The total feed rate was 15 rpm for powder Ti and Cr, with Cr changed as 0.0, 3.0 to 8.5 rpm and Ti changed as 15.0, 12.0 to 6.5 rpm with a step change of 0.5 rpm. Ten layers of the material were deposited for each composition and the total number of layers in the composition gradient wall was 130. The height of the wall was about 2 mm with an individual layer height of about 15 lm. Fig. 3 shows the microstructure along the build-up direction (y\u2013 z plane in Fig. 1) of a composition gradient wall. The white arrows indicate the build-up direction. The wall is fully dense and the microstructure varies regularly with the composition along the wall height. There are no clear interfaces between layers. A heat-affected zone (HAZ) is observed in the substrate. At the wall bottom, the deposited material is pure Ti, with little metallographic contrast. As the Cr content increases, elongated grains form with the grain growth direction opposite to the heat conduction direction" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002095_elan.200303030-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002095_elan.200303030-Figure5-1.png", "caption": "Fig. 5. Cycilc voltamograms of a CGA modified carbon composite electrode at 10 mV s 1 in 0.1 M phosphate buffer solution (pH 7). a) in the absence, b) in the presence of 0.1 mM hydrazine; c) and d) as (a) and (b) for a bare carbon composite electrode.", "texts": [ " Since the method of the electrode preparation is simple and fast (less than 1 min), the current decay is not a serious limitation for this modified electrode. In order to study the reproducibility of the electrode preparation, the CCE was polished then immersed for 5 s in 1 mM chlorogenic acid. For eight successive polishings (not shown) the relative standard deviation of 2% was observed from measurement of anodic peak currents. The effect of pHon theCGA-CCEsignalwas investigated by recording cyclic voltammograms using 0.1 M buffer solution at various pH values from 3 \u2013 11 (Fig. 4). As can be seen in the inset of Figure 5, the formal potential of the surface redox couple was pH dependent, with a slope of 58 mV/pH unit in a wide range, which is very close to the anticipatedNernstian valueof 59 mVfor a twoelectron -two proton process. There was also a change in the surface coverage with increasing the pH of solution. As can be seen there was a decrease in coverage as pH values increased. A fraction of chlorogenic acid in its reduced formmay be in its deprotonated form, which would be expected to be more soluble due to its higher charge. Electrocatalytic oxidation of hydrazine at low potentials is very useful for practical applications since there is less risk for interfering electrochemical reactions to take place. In this way, there is great interest in finding mediators or ways to immobilize them on electrode surfaces resulting in even higher reaction rate. The electrocatalytic oxidation of hydrazine at modified chlorogenic acid carbon ceramic electrode is shown in Figure 5, where cyclic voltammograms at 10 mV s 1 of the modified electrode in 0.1 M posphate buffer (pH 7) in absence and presence of 1 mM hydrazine are comparatively presented. It can be seen upon the addition of hydrazine that there is a dramatic increase of the anodic peak current and the cathodic peak current disappears completely (Fig. 5b), which indicates a strong catalytic Electroanalysis 2004, 16, No. 23 D 2004 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim effect. The anodic peak potential for the oxidation of hydrazine at CGA modified CCE was about 200 mV, while at the bare electrode the hydrazine was not oxidized until 700 mV. Thus, a decrease in overpotential and enhancement of peak current for hydrazine oxidation is achieved with the modified electrode. Figure 6 shows the dependence of the voltammetric response of modified electrode on the hydrazine concentration with the addition of hydrazine (0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003761_cdc.2014.7040348-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003761_cdc.2014.7040348-Figure1-1.png", "caption": "Fig. 1. The Quad Tiltrotor experimental platform: The MAV equipped with imaging, inertial and altitude sensing systems: (a) The MAV in helicopter mode with the tilting angle \u03b3 = 0; (b) The MAV in airplane mode with the tilting angle \u03b3 = 90.", "texts": [ " While the convertible aircraft is a very promising concept, it also comes with significant challenges. Indeed it is necessary to design controllers which will work over the complete flight envelope of the vehicle: from low-speed vertical flight through high-speed forward flight. The main challenge is to deal with the large variation in the vehicle dynamics between these two different flight regimes. In this first part of our research, we focus on hover position control of the convertible tiltrotor MAV, see Fig. 1. This vehicle combines the high-speed cruise capabilities of a conventional airplane with the hovering capabilities of a helicopter by tilting its four rotors. Dynamics involved with the tilting mechanism are investigated. This tilting mechanism provides an additional input to the system, which Research supported in part by the Mexican National Council for Science and Technology (CONACYT) under grants 314448 and 314456. G. Flores is with the UMR CNRS 7253 Heudiasyc Laboratory, UTC, France (e-mail: gfloresc@hds", " The main contribution of this paper is to develop a Lyapunov-based control strategy suitable for handling the hover dynamics of the convertible aircraft in the 6-DOF (degrees of freedom). The key idea is that the dynamics of the aircraft lend themselves well to individual control strategies for hover, transition and and forward flight from a continuous point of view avoiding switching between both dynamics involved. In this first part of the work, we present an analysis of the convertible aircraft\u2019s mathematical model in which the control inputs for hover and airplane mode (see Fig. 1) are different, and then both dynamics can be controlled individually. The control inputs in the hover mode are given by the thrust and torques provided by the rotors, while the control inputs in airplane mode are the forward thrust and the torques generated by the controlling surfaces. Some simulations results are given, which demonstrate the effectiveness of the controller. Further, some experimental results are presented tested on the Quad Tiltrotor experimental platform. The remainder of this paper is organized as follows", " J \u2208 <3 is the inertia matrix; m is the mass of the body; and gezI is the gravitational force, where ezI = (0, 0, 1) is a unit vector. SO(3) denotes the special orthogonal group of <3\u00d73. Further, we define as S(v) the operator from <3 \u2192 SO(3) such that \u2200v \u2208 <3, S(v) = 0 \u2212v3 v2 v3 0 \u2212v1 \u2212v2 v1 0 where vi denotes the i-th component of vector v. S(v) is the group of antisymmetric matrices of <3\u00d73. Therefore, S(v)\u2126 = v \u00d7 \u2126. We use four additional coordinate frames: Ai = (Aix, Aiy, Aiz), for i = 1, ..., 4 which are associated with the four rotors (see Fig. 1). Thus, the orientation of each rotor w.r.t the body frame can be defined by the rotation matrix R\u03b3 = cos \u03b3 0 sin \u03b3 0 1 0 \u2212 sin \u03b3 0 cos \u03b3 (2) The force F generated by the rotorcraft expressed in the body frame is given by F = TT sin \u03b3 0 TT cos \u03b3 (3) where TT = \u22114 i=1 Ti and the thrust Ti can be modeled as Ti = Cl\u03c9 2 i , where Cl is the lift coefficient and \u03c9i is the velocity of the i-th rotor. Since in hover mode an angle greater than 20 degrees causes an increase in the lift force enough to achieve a transition from hover to fixed-wing mode [14], we take into consideration the following assumption: a) The tilting angle \u03b3 is imposed to be \u03b3 \u2264 20", " frame I, whose origin is located at the MAV\u2019s initial position. It can be observed that the vehicle performs the tracking mission inside a rectangular area of 4m \u00d7 6m. It is worth mentioning that the forward displacement (relative to the body fixed frame) is obtained by integrating the optical flow. Fig. 5 shows the input controllers given by torque \u03c4\u0303 , thrust T and tilting angle \u03b3. It is important to note that the MAV takes off around t = 15 seconds, and the thrust never achieves zero after that time. Fig. 1 shows an image of the MAV in the experimental area during the real-time tests. In addition, a video showing the Quad Tiltrotor experimental platform performing some experiments can be observed at https://sites. google.com/site/gerardoflorescolunga/ research/convertible-mav. The experimental platform shown in Fig. 1 has been used to evaluate the performance of the proposed controller. Such experimental platform has been developed at laboratory; it is based on the fuselage of a commercial airplane and a Hform quad-rotor. The H-form structure is built from balsa wood and carbon fiber. The tilt mechanism is controlled by two individual servomotors which can tilt the rotors from 0 up to 90 degrees. The flight control unit (FCU) is based on the PX4 Autopilot system. The PX4 Autopilot system consists of two boards: the PX4FMU and the PX4IO" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003528_045008-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003528_045008-Figure3-1.png", "caption": "Figure 3. SolidWorks drawings of both mold and mold cover for one SBFA chamber.", "texts": [ " The winding channel walls in each SBFA chamber limits expansion along the radial direction of the SBFA. Prototypes were fabricated to demonstrate the feasibility and assess the performance of the proposed SBFA. Due to the complexity of the design, the molding technique proposed in [13] was not suitable to fabricate the SBFA. Each chamber was molded separately by using molds consisting of two parts, which were manufactured through an InVision 3D printer. Drawings of the negative mold and mold cover are shown in figure 3. To create the body of one chamber, a liquid polymer was filled into the mold. The TC-5005 room temperature curing silicone elastomer (BJB Enterprise) was chosen as the substrate because it exhibits a high tear resistance, elongation and tensile strength [16]. TC-5005 consists of two parts, A and B. In this work, 10 parts of A and 1 part of B were mixed for 2 min. The mixture was then placed into an ultrasonic cleaner for 3 min to ensure a homogeneous mixture. Before filling the mold, a releasing agent consisting of a mixture of mineral oil and white petroleum jelly was applied onto the mold and mold cover" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002511_robot.1987.1088010-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002511_robot.1987.1088010-Figure4-1.png", "caption": "Figure 4: Gravitational Effects on Links 2 and 3,", "texts": [ " T h i s would certainly need t o be compensated f o r if t h i s robot were t o be accurately modeled for varying loads. Under the assumption of no loading, the other l i n k s and j o i n t s displayed negligible deformations. Thus, only the deformation of the j o i n t 1 bearing was modeled. As j o i n t s two and three are rotated, their mass centers extend i n front o f the robot causing t h @ bearing t o tilt about an axis parallel t o the j o i n t two axis as shown above. Consider the situation depicted i n Figure 4. It is easy t o see that the gravitational torque about 52 is given by: T L l R F i n ( B 2 ) t L2M3sin(B2) + L3N3sin(82+83) ( l o ) ASSUming the deflection of the bearing can be fnodeled as a linear spring, then 13, the amount of angular structural deformation can be expressed i n the form: (K1LlMztK2L2H3)sin(82) + K3L3M3sin(82+03) (11) The functional form that was used t o model the angular alef ormation was: I3 f(B2.83) = Klsin(B2) t Kpsin(B2 + 03) (12) where 62 i s expressed i n radians. The parameter, Kt was on the order of 3 " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002649_cdc.2005.1582798-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002649_cdc.2005.1582798-Figure2-1.png", "caption": "Fig. 2. Notation", "texts": [ " The system is propelled by two crossed rotors with fixed angle of attack on the propeller\u2019s blades. Thus, the system is controlled by changing the angular velocities of the rotors which, according to the action-reaction principle, involves the generation of a resultant torque on the body of the double rotor system, that makes it rotate in the opposite direction of the rotor. In this way, there are two kinds of forces applied to the system: \u2022 velocity dependent forces \u2022 acceleration dependent forces or inertial forces Fig. 2 shows the notation used for the system modelling. The equations of motion can be obtained by solving the Lagrange dynamic equation. The solution may be expressed 0-7803-9568-9/05/$20.00 \u00a92005 IEEE 4065 in a matrix formulation as follows: ( M11 M12 M21 M22 ) \u00b7 ( \u03b8\u0308 \u03be\u0308 ) =( K11 K12 K21 K22 ) \u00b7 ( \u03b1\u0308 \u03b3\u0308 ) + ( C11 C12 C21 C22 ) \u00b7 ( \u03b8\u03072 \u03be\u03072 ) +( A1 A2 ) \u03be\u0307\u03b8\u0307+ ( \u03b6\u03b8 \u03b6\u03be ) + ( V11 V12 V21 V22 ) \u00b7 ( \u03b8\u0307 \u03be\u0307 ) + ( Cte1 Cte2 ) + ( d11 d12 d13 d21 d22 d23 ) \u00b7 \u239b \u239d \u03b1\u0307\u03b8\u0307 \u03b3\u0307\u03b8\u0307 \u03b3\u0307\u03be\u0307 \u239e \u23a0 Where \u2022 \u03b8: Yaw angle. Rotation around the vertical axis, Z0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002768_j.cnsns.2007.07.004-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002768_j.cnsns.2007.07.004-Figure2-1.png", "caption": "Fig. 2. Schematic of underwater vehicle.", "texts": [ " Controller u2 is presented especially for the double integrator in [18], while u3 is called a 2-order sliding mode controller as the states x1 = 0 and x2 = 0 can be viewed as sliding surfaces [16]. Finally, u4 is a special form of u2 which is also proposed in [18] to especially stabilize the rotational double integrator to avoid the winding phenomenon. For instance, if x1 2 S1, the controller u4 is useful and finds use in this paper. The readers can refer to [14,16] for the robustness analysis of these controllers. The system we consider is an underwater rigid body moving in a horizontal plane (neutrally buoyant) as shown in Fig. 2. The configuration space is Q , R2 S1 and is parameterized by the coordinates (x,y,h) represented in inertial frame. The triple (x,y,h) represents the position of the center-of-mass and orientation of the body in the inertial frame. The corresponding linear and angular velocities in the body-frame are denoted by \u00f0vx; vy ;xz\u00de. The kinematic equations of the system, that is the relation between the body velocities and the inertial velocities are given by _x \u00bc vx cos h vy sin h _y \u00bc vx sin h\u00fe vy cos h _h \u00bc xz \u00f01\u00de and the dynamic equations [5] derived using Newtonian formulation are given by m11 _vx m22vyxz \u00fe d11vx \u00bc F x m22 _vy \u00fe m11vxxz \u00fe d22vy \u00bc F y m33 _xz \u00fe \u00f0m22 m11\u00devxvy \u00fe d33xz \u00bc sz \u00f02\u00de where mii; dii; i \u00bc 1; 2; 3, are positive constants that represent the elements of the inertia matrix including added masses and the elements of the damping matrix respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001570_tt.3020050303-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001570_tt.3020050303-Figure1-1.png", "caption": "Figure 1 Rolling-sliding contact. The three different positions illustrate how the surfaces move in relation to each other", "texts": [ " (25) assuming heat conduction into the material is only perpendicular, i.e., in only one dimension: Eq. (25) can be solved with a simple finite difference method. The algorithm is as follows: (26) T ( z , t + h t ) = - . [ T ( x + A ~ , t ) + T ( x - A x , t ) ] 1 2 if where Ax is the distance of a step into the material for one h,, which is the time step, and: Tribotest journal 5-3, Mnrch 1999. (5) 232 lSSN 1354-4063 $8.00 + $8.00 Wear simulation of spur gears 233 for a point P on wheel 1, notations according to Figure 1. The heat input is calculated as: where is the mean pressure for a point, and vmean is the mean velocity for the whole contact. At t = 0, the temperature in and transverse to the x direction is uniform and no cooling effects are accounted for. The division of heat is calculated according to Archard and Rowntree.' They assume that all heat enters both bodies, and calculate their respective temperatures, Tmaxl and Tmax2. The interface temperature, T, is then calculated as: For the specific set of gears simulated in this paper, the temperature variation through the mesh will be according to Figure 2 in which the maximum temperature for each time step is plotted", " (5) 233 I S S N 1354-4063 $8.00 + $8.00 234 Flodin and Andersson The maximum surface temperature rise for a pure sliding contact assuming a square uniform heat source can, according to Tian and Kennedy,\" be calculated as: where a is the contact length, Pe is the Peclet number, K, is the thermal conductivity of the gear material, and is the heat partitioning factor. The Peclet number can be interpreted as the ratio of speed of the surface to the rate of thermal diffusion into the solid. For the pinion in Figure 1, the speed of a point P on the surface is equal to: The Peclet number for the same point is then calculated for a rolling-sliding contact as: Williams'' has also proposed a model for contact temperatures assuming an infinitely long heat source of width Zu and valid at high Peclet numbers. The position in the contact zone and the frictional energy determine the temperature according to Eq. (34), where a 2 x 2 -a and K is the thermal diffusivity: for a rolling-sliding contact on the pinion, notations according to Figure 1. In Eqs. (25), (31), and (34), the contact radius of an asperity has an influence. The shape and the radius of the asperities on a surface can be considered as stochastic and difficult to predict, which also holds true for the contact pressure between asperities. Tribotest journal 5-3, March 1999. (5) 234 lSSN 1354-4063 $8.00 + $8.00 Wear simulation of spur gears 235 ~~ Finure 3 (a) Maximum temperature, one-dimensional heat transfer, as a function of body velocity. - (b) Maximum temperature, Tian and Kennedy's approach, as a function of body velocity" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002777_s10846-008-9284-8-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002777_s10846-008-9284-8-Figure8-1.png", "caption": "Fig. 8 Helicopter avionics", "texts": [ " This is a 50-size helicopter designed for competition aerobatics, able to make difficult maneuvers and move precisely in the 3D environment. One major characteristic of this helicopter is that it has electric power system so there is no need for fuel gas. Therefore, it does not produce any exhaust gasses during its operation, and makes it ideal for indoor testing. The technical specifications of the T-REX 600 helicopter are listed in Table 2. To fulfill our research needs, the T-REX 600 has been heavily customized. In what follows we describe the equipment and the avionics we have put on board. Figure 8 presents the position of the major installations on the helicopter. This unit is the most essential part of the avionics, since it computes the orientation of the vehicle on its body-frame system. The commercial product MTi from Xsens Motion Technologies has been used. The MTi is a miniature, gyro-enhanced Attitude and Heading Reference System (AHRS). Its internal low-power signal processor provides drift-free 3D orientation, calibrated acceleration, rate of turn and earthmagnetic field data. The unit consists of 3D gyroscopes, accelerometers and magnetometers and also outputs the three Euler angles (roll, pitch and yaw)", " Manual flight is controlled remotely by a human operator, while autonomous flight is supervised by a Central Processing Unit (CPU). Switching between manual and autonomous flight is an important operation because it allows the human tester to regain manual control at any time instant during experimentation, which is very useful in case of failure or insufficient control. The way digital switching works is quite simple (Fig. 7). A digital switch with two inputs and one output is placed onboard the helicopter (Fig. 8). Each input consists of control signals (lateral cyclic, longitudinal cyclic, throttle) coming from the human operator (pilot) or the control unit. Pilot input involves an extra switch signal dedicated to the selection between manual and autonomous flight. It is quite easy for the operator to change manually between these two modes by sending a signal through the transmitter. Digital switch monitors this signal and forwards the appropriate control actions (manual or autopilot) to the helicopter actuators. RC servos are the actuators used to control the motion of the helicopter. In manual operation, the onboard receiver forwards the transmitter commands to servos by sending appropriate PWM (Pulse Width Modulation) signals. In order to send such signals from the control station to the servos, a servo driver is needed. For that reason a PIC microcontroller (Fig. 8) is used, which translates control signals from the ground station to RC PWM servo signals and drives the servos. Further, the PIC reads the input from the localization system (x\u2013y position, altitude) and sends it to the control station. A wireless communication system has been established between the control station and the PIC microcontroller. Having two receiver/transmitter units (one on the helicopter and one on the ground station) and by using the Bluetooth protocol, we obtain two-way communication between the serial port of the PIC and the serial port of the control station. Through this communication, control signals are transmitted to the helicopter from the control unit, while input from the localization sensors is transmitted to the control unit. In Fig. 8, the transmitter/receiver unit attached to the helicopter is presented. All electric helicopters have high power consumption. During hovering, the electric motor of the helicopter used needs about 50 A current of 24 V. Normally in these helicopters, LiPo (Lithium Polymer) batteries are used that have high capacity and the ability to sustain such currents. With this consumption and with a high capacity LiPo battery, the helicopter can perform hovering for only about 15 min. To overcome this limitation, the test bed is provided with constant power supply of 24 V that gives continuous current to the helicopter (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002743_j.automatica.2006.10.013-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002743_j.automatica.2006.10.013-Figure1-1.png", "caption": "Fig. 1. Notation.", "texts": [ " Experimental results are shown in Section 5 and, finally, the major conclusions to be drawn are given in Section 6. The twin-rotor system used in this paper consists of two free joints thrusted by two rotors placed in perpendicular planes (Mullhaupt et al., 1997). This device is a multivariable, nonlinear and strongly coupled system, with degrees of freedom on the pitch and yaw angles (denoted by and , respectively), as well as on the angular positions of the main and tail rotor (denoted by and , respectively). Fig. 1 schematically shows the notation used throughout the paper. The two crossed rotors have fixed angle of attack blades. Thus, the system is controlled by changing the angular velocities of the rotors. According to the action-reaction principle, this involves the generation of a resultant torque on the body of the double rotor system, that makes it rotate in the opposite direction to the rotor. This way, two kind of forces are applied to the system, which are velocity dependent forces and acceleration dependent forces or inertial forces" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002661_978-1-4615-9882-4_4-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002661_978-1-4615-9882-4_4-Figure1-1.png", "caption": "Figure 1 SCARA robot configuration", "texts": [ " It should be noted that with the increasing interest and popularity of AC drive motors (also referred to as brushless DC motors), high impedance current-mode switching-power amplifiers and low reduction ratio or direct joint drives, the potential velocity range of manipulator joints is high. Thus the assumption of constant peak torque is not unrealistic. A further idealization initially made is to eliminate friction and gravity effects. For the well-known SCARA (Selective Compliance Assembly Robot Arm) class of manipulators (Figure 1) gravity acts only on the Z motion and as such can be treated independently. For high-performance manipulators, having acceleration capability in excess of Ig (peak accelerations of 4-10gs are realizable today), gravity effects on performance are relatively diminished. J oint related friction comes from several sources. For ball or roller-bearing mounted revolute joints, joint friction is generally small. Most of the friction comes from electromagnetic hysteresis drag, cogging torques, brush drag and bearing seal and grease friction in the drive motor and gear train (if used)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003498_0022-2569(71)90044-9-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003498_0022-2569(71)90044-9-Figure4-1.png", "caption": "Figure 4. Transmission ratio and angular acceleration in the four-bar linkage.", "texts": [ " The particularly distinguishing mark of such a four-bar linkage with the most favorable transmission quality is that the minimum value/Zm~. = 40 \u00b0 appears several times, once as/Zmt.~ between links e and f as an exterior angle in the initial position BoB~'C~Co of the linkage, and a second time as an interior angle/J-mtnr in the position BoBr'CTCo when the link b' in BoB; lines up with the fixed baseline BoCo = d'. Somewhere between these two positions of the mechanism, the optimal value /z = 90 \u00b0 Basic construction for determination of angular acceleration In the configuration of Fig. 4 the construction for the angular acceleration as of link f will be discussed, assuming that link b' instantaneously has an acceleration ab, = 0[6]. Pole Q is located as the point of intersection of the fixed baseline BoCo = d' with the connecting rod B'C = e, and pole P as the point of intersection of the cranks BoB' = b' and CoC =f . Next one draws a line through B0 parallel to the collineation axis PQ = k to intersect e in point S. The line perpendicular to e through S meets the perpendicular to d' through Bo at the terminus T of the vector ms", " 3 through 20-05 \u00b0 in the direction of the required motion, namely clockwise, one obtains from the dimensions of the four-bar linkage a rotation angle of Ctto. = 8.4 \u00b0 for the lever. For the transmission ratio of the composite mechanism one finds, according to equation (5), f o rx = 0-2: 17\" t3 = ~- x sin 36 \u00b0 = 0.923 (21 ) / and from equation (12): io.., = M~. v = 1\" 166 X 0-923 = 1\"076. (22) In the second component mechanism, namely in the four-bar linkage, one must first J.M. Vol. 6 No. 4 - F determine the transmission ratio i , . According to Fig. 4, it is true in general that: il t = q_.~a qb\" (23) As is well known, the transmission ratio of the distance of the pole QBo = q~ from the driving-link pivot and the distance QCo = qb of the pole from the output-link pivot. The transmission ratio is positive if the pole referred to lies outside the pivot points B0 and Co; it is negative ifQ lies between these pivot points. For the mechanism position given by x = 0.2 one gets 612=+2\"23 (24) and from this /02 i/~ = .---- = 0\"483. (25) 1112 Generally, d qb= l - - i (26) Therefore in mechanism I for position x --- 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003404_iros.2011.6095001-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003404_iros.2011.6095001-Figure8-1.png", "caption": "Fig. 8. We are currently working toward validating our simulation results on purpose-built machines of our own design and construction.", "texts": [ " In stance, we use PD torque control of the hip actuator to approximate an ideal hinge, such that the force-controlled model behaves like a SLIP model in stance with a pointmass body. The hip motor must track the motion of the leg in stance to maintain zero deflection of the hip spring; this task is equivalent to maintaining constant force against a moving load, a task which has been approached analytically in previous works [15]. Although optimal performance for a force control task would require very low motor inertia and spring stiffness, we use realistic values from the design of a legged robot we are currently constructing, shown in Fig. 8(a). The limitations imposed by these realistic passive dynamics are represented in our results. The leg actuator attenuates ground disturbances by controlling the force in the leg spring. The leg spring stiffness is tuned to the natural frequency of our desired spring-mass hopper, so energy will be stored in the spring during the first part of stance, and then recovered as the body mass accelerates towards liftoff. In the ideal scenario, the leg motor does no work, the hip motor is only responsible for moving its own inertia and does no work on the environment, and all of the model\u2019s behavior is expressed by the passive dynamics of the system as it bounces forward", " We compare, in simulation, three models: a passive springmass model with constant leg angle at touchdown, a springmass model that adjusts its leg angle in flight according to the EGB method, and our force-controlled model that combines the EGB method with force control. The three models are subjected to changes in ground height and ground stiffness. To better demonstrate the feasibility of disturbance rejection on our model in simulation, we choose somewhat arbitrary, but realistic values for a moderately-sized robot using a commercially available motor, such as our ATRIAS monopod, shown in Fig. 8(a). The unactuated spring-mass models are not subjected to any of the physical limitations that we impose on our forcecontrolled model. They are able to instantaneously set their leg angle, their hip behaves like an ideal hinge during stance, and they do not have motors that can hit their torque limit, accumulate angular momentum, or be backdriven. We expect ground disturbances to result in permanent shifts in hopping phase and height for the standard springmass models, if not a loss of stability and falls", " On a physical system with sensory, computing, and physical limitations, this dependency is unavoidable, and while such limitations could easily be lifted from our simulation, we chose to include them to better illustrate the feasibility of taking our force control approach on a physical system. The long-term goal of this work is to build a model and bio-inspired biped capable of robust walking and running gaits. Previously we showed how force control could be used to add disturbance rejection to a vertically hopping force-controlled spring-mass model [4]. We have now shown how this idea can be extended to the vertical plane in simulation on a model with similar limitations to a physical system we are building, shown in Fig. 8(a). We are now working to demonstrate our concept of adding force control to the spring-mass model on physical systems, including a single degree of freedom benchtop actuator, a two degree of freedom monopod, and eventually on a tether-free biped. Our biped will maintain as much of the energy economy of the equivalent passive system as possible by making excellent use of its passive dynamics, while limiting the need for sensory feedback and active control. With these real-world devices, we hope to approach the performance of animal walking and running" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001938_s0308-8146(02)00395-3-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001938_s0308-8146(02)00395-3-Figure2-1.png", "caption": "Fig. 2. Detector constructed for amperometric detection of H2O2 at constant potential of +0.6V. Ew\u2014platinum work electrode; Ea\u2014platinum auxiliary electrode; Er\u2014reference electrode Ag/AgCl (3 M KCl); P\u2014platinum electrodes; Cf\u2014confluence; Ce\u2014electric contact.", "texts": [ " A multiposition selection valve VICI (Valco Instruments Co. Inc.) with 8 inlets and one central outlet was used as injection system. The manifold was built from PTFE tubing (0.8 mm i.d.) with Gilson connectors. The confluence (Carlos Torres, Portugal) used was made of Perspex. A Metrohm 641 VA-Detector potentiostat, at a constant potential of +0.6 V, was used, with 3 electrodes: a 3 1.5 mm Pt working electrode, an Ag/AgCl (3 M KCl) reference electrode and an auxiliary electrode similar to the working electrode (Fig. 2). A Kipp and Zonen recorder attained the detector signal and signal evaluation was made by peak-height measurement. The data acquisition and system control was accomplished with a microcomputer, the software being developed in QuickBASIC. The communication between the microcomputer and the burette was achieved by standard serial interface using the RS232C protocol, whereas digital TTL signals, using an Advantech model PCL818 interface card were used for the connection with the valve. A fermenter with a 5-l glass compartment was used at a constant temperature of 8 C, obtained with a Haake EK20 refrigerator" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002692_cm.970010306-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002692_cm.970010306-Figure5-1.png", "caption": "Fig. 5. Change in @tip (see Materials and Methods) with Ca2+ concentration in the presence of 0.2 mM MgATPZ- and 1 mM Mg\". Spermatozoa were immobilized by adding 5 pM vanadate. @tip was measured on the dark field micrographs taken within 5 min of quiescence. Results from 3 experiments were averaged. More than 20 spermatozoa were measured in each condition.", "texts": [ " Dark field micrographs showing enlarged individual spermatozoa, immobilized by 5 pM vanadate in the presence of 0.2 mM MgATPZ- and 1 mM Mg\". (a) and (b) in the presence of the presence of lO-'M Ca2+. Spermatozoa were broken with vortex mixer for 10 sec before demembranation in (b) and (c). Scale bar, 10 pm. M Ca2+. (c) In A quantitative measure of this effect of Ca2+ concentration on intact flagella is given by measuring $tip, the total bend angle between the head axis and the distal end of the flagellum. As shown in Figure 5 , $tip increases gradually with Ca2+ concentration. This increase in $tip represents in part an increase in the number of flagella showing the characteristic hook-shaped configuration of quiescent flagella, illustrated in Figure 4a, but there are also flagella with intermediate values of &i,, at the intermediate Ca2+ concentrations. 356 Okuno and Brokaw The effect of Ca2+ on $tip is reversible. In a separate experiment, the average $tip for a sample of 20 spermatozoa was examined at trated CaCl, solution to produce a Ca2+ concentration of 1 0-3 M, and again after addition of concentrated EGTA solution to reduce the Ca2+ concentration to approximately The average $tip was initially 1", " Although in these experiments it is difficult t o separate the effects of a change in the ratio of Mg2+ and ATP4- concentrations from the effects of the changes in Ca2+ and CaATP2concentrations, the results suggest that the effect of Ca2+ on the curvature of the swimming path is a direct effect of Ca2+, rather than an effect of CaATP2-concentration. The measurements of @tip provide only weak support for this conclusion. The large increase in @tip in Figure 7b between lOW8and M Ca2+ is consistent with the measurements of curvature of the swimming path, but the further increase in Ca2+ to M at constant CaATP2concentration did not produce the further increase in @tip which might have been expected from the experiment in Figure 5 , where both Ca2+ and CaATP2-were increased. reactivating a flagellum in the presence of high Ca2+ and supplying vanadate by diffusion from the edge of the coverslip. The spermatozoon shown in Figure 8 was reactivated with 0.2 mM MgATP2-at 0.1 mM Ca2+ and 1 mM Mg2+. When the vanadate concentration at the location of the flagellum observed attained an effective value, the beat frequency began to decrease, followed by decrease of the amplitude of the bending wave accompanied by elongation of the distal paralyzed region" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002145_iros.2000.895302-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002145_iros.2000.895302-Figure8-1.png", "caption": "Fig. 8 M-Drive installed into the joint unit", "texts": [ " 7 (a), let T , and T, ( TI c T,) are the string's tension, ,U is the friction coefficient between the string and the pulley, and 8 is the winding angle of strings. The condition in which the slip occurs is the following. T, >TI exp( PO 1 So the maximum value of T,can be decided by TI which is set beforehand and by far smaller tension than T,. T, is the driving force of the pulley, and the torque that generates the tension over the maximum value of T, is not transmitted by slipping[3]. - 2244 - It is constructed as shown in Fig.7 @) and Fig.8. The wire drawn out from its winding pulley is hooked around the other pulley that is rotation free. This pulley is pulled by the spring for applying the tension on the wire. And the compressive force of coil spring, which is accumulated by turning the worm gear, has been applied on pulley by the link in this tensioner unit. 3 3 Float differential torque sensor It is useful to obtain torque information, which works in each axis in order to realize the advanced and three-dimensional motion control" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003824_tmag.2012.2237390-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003824_tmag.2012.2237390-Figure6-1.png", "caption": "Fig. 6. Mechanical angle between the th EM pole and plane.", "texts": [ " Definition of Posture The posture of the rotor is expressed using parameters and as shown in Fig. 5. Parameters and define the rotation axis and rotation angle, respectively. The world, axis, and rotor coordinate systems are defined as XYZ, and , respectively. When a desired trajectory is given, the system calculates the current pattern for all coils as follows: (1) where the subscript expresses the th pole, and are the current and amplitude, respectively, and is the mechanical angle between the th EM pole and plane as shown in Fig. 6. In (1), unknown parameters and are derived from the following: (2) (3) where and are the unit vector of the axis and position vector observed in the rotor coordinate, respectively. To calculate those two parameters, the position vector should be known and it is calculated by using the following equation: (4) (5) (6) where is the position vector of the th vector observed in the world coordinate, and are the transformation matrixes from the world coordinate (XYZ) to the axis coordinate and from the axis coordinate to the rotor coordinate , respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002111_s11044-005-4196-x-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002111_s11044-005-4196-x-Figure3-1.png", "caption": "Figure 3. Kinematic scheme of an independent limb.", "texts": [ " (11) Then, after a few computations, the coordinates of the universal joints, attached to the translational platform, expressed in the reference frame XY Z , result in U1 = (UX , a\u2032 1, UZ ), U2 = (UX , a\u2032 1 \u2212 a1, UZ ), U3 = (UX + a4 cos(\u03c0/2 \u2212 \u03b2), a4 sin(\u03c0/2 \u2212 \u03b2), UZ ). (12) where UX = 2a4(cos(\u03c0/2 \u2212 \u03b2)S3X + sin(\u03c0/2 \u2212 \u03b2)S3Y )) + q2 3 \u2212 a2 4 \u2212 S2 3X \u2212 S2 3Y \u2212 q2 12 2(a4 cos(\u03c0/2 \u2212 \u03b2) \u2212 S3X ) , and UZ = \u221a q2 12 \u2212 U 2 X . The inverse velocity analysis is stated as follows. Given the velocity state of the translational platform, with respect to the fixed platform, compute the joint rate velocities associated to the kinematic pairs of the independent limbs. To this end, each independent limb is modelled as a UPS-type serial manipulator, see Figure 3. According with expression (6) the velocity state of the translational platform, with respect to the fixed platform, can be written through any of the three independent limbs as follows 0\u03c91i 0$1i + 1\u03c92i 1$2i + 2\u03c93i 2$3i + q\u0307i 3$4i + 4\u03c95i 4$5i + 5\u03c96i 5$6i = 0V6 i = 1, 2, 3. (13) Therefore, the computation of the joint rate velocities of each independent limb results in 0\u03c91i 1\u03c92i 2\u03c93i q\u0307i 4\u03c95i 5\u03c96i = J\u22121 i 0V6 i = 1, 2, 3. (14) where, Ji is the i th Jacobian matrix, a subspace generated by the set of screws representing the kinematic pairs of the i-th independent limb, given by Ji = [0$1i 1$2i 2$3i 3$4i 4$5i 5$6i ]" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001773_bm0496662-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001773_bm0496662-Figure5-1.png", "caption": "Figure 5. Schematic of LbL self-assembly of glucose sensitivematerials on (a) thin films and (b) spherical substrates.", "texts": [ " Dissociation of glucose from apo-GOx has also been observed in preliminary experiments, though this requires approximately twice as long to reach steady state as the forward reaction. This issue will be more thoroughly addressed in future studies. As the glucose sensitivity of the apo-GOx/dextran complexes was successfully demonstrated, future work with these smart assemblies will be focused on developing nanoengineered microdevices. These sensing devices can potentially be fabricated using LbL26 self-assembly after crosslinking apo-GOx. The schematic of a proposed assembly process on thin film and spherical substrates is shown in Figure 5. On the basis of our previous findings, the ultrathin films layered on the substrates are expected to retain their binding capabilities;3 thus, apo-GOx/dextran thin films will dissociate in the presence of glucose. This paper demonstrates a highly specific, sensitive, and reversible fluorescent biosensor for monitoring glucose. The sensor design is based on energy transfer between two fluorophores and on the competition between glucose and dextran for the binding sites on apo-GOx. This sensor showed a very sensitive response with the addition of glucose in the interested physiological range (0-70 mM)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001843_1.2826131-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001843_1.2826131-Figure4-1.png", "caption": "Fig. 4 Standardized raci<-cutter profiles", "texts": [ " The imaginary process of generation of conjugate tooth surfaces is based on the application of two rack-cutters that are provided by two mismatched cylindrical surfaces 2, and 2\u0302 . as shown in Fig. 3(a). The rack-cutter surfaces 2, and 2^ are rigidly connected to each other in the process of imaginary generation, and they are in tangency along two parallel straight lines, a ~ a and b - b. These lines and the parallel axes of the gears form angle /3(), that is equal to the helix angle on the pinion (gear) pitch cylinder. The normal sec tions of the rack-cutters have been standardized in China [9], Fig. 4(a), and in the former USSR, Fig. 4(b) [8]. Rack-cutter surface 2^ generates the pinion tooth surface 2^, and rackcutter surface 2, generates the gear tooth surface 2\u201e. It is obvious that due to the mismatch of the surfaces of the two rack-cutters that generate the pinion and the gear, the tooth surfaces of the pinion and the gear will be in point contact at every instant. Each rack-cutter has two generating surfaces, above and below plane II, Fig. 3. Therefore, the 256/Vol. 117, JUNE 1995 Transactions of the ASME Downloaded From: http://mechanicaldesign", " 7(c); AA ,\u0302 and AA ,\u0302 are the errors of the lead angles of the pinion and the gear, respectively. Influence of Change of Center Distance. The change of center distance of N.-W. gears and modified involute helical gears does not cause transmission errors but only the shift of the bearing contact (the path of contact). The shift can be evaluated as the change of the pressure angle determined as follows: {i) In the case of N.-W. gears we have [10, 16] sin a : ^E -y\u201e,+ y\u201e. (13) where y^,. (r = c, t) is the coordinate of the circle center corresponding to circular arc p,. (r ~ c, t), Fig. 4; a* is the pressure angle in the normal section; a* = a\u201e, where a\u201e is the nominal value of the pressure angle, if A\u00a3, the change of the center distance, is equal to zero. The difference {a* - a\u201e) indicates the shift of the path of contact (the bearing contact) on the tooth surface. ((() The influence of the center distance change, in the case of modified involute helical gears, is represented by the equation sin a. 2AE sin a, + cos a, (14) where a* and a, represent the transverse pressure angles for the center distances ( \u00a3 -)- A\u00a3) and E, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure7-1.png", "caption": "Fig. 7. Teeth reference configuration for Step 2 of the TCA initial guesses search.", "texts": [ " Therefore, the corresponding values um 1 and um 2 are found as the solution of the following minimization problem \u00bdum 1 ;u m 2 \u00bc argmin u1 ;u2 \u00f0ksm f 1\u00f0u1\u00de sm f 2\u00f0u2\u00dek\u00de: \u00f020\u00de The values um 1 and um 2 represent a rough approximation of the pinion and gear rotations at a tangency condition. However, it could not be sufficient to assure the convergence of the numerical solution of (16) [5]. For this reason a refinement procedure is required. Consider the two mating members rotated of their respective angles um 1 and um 2 as in Fig. 7. We assume that the two tooth surfaces do not intersect, otherwise we can always give an additional rotation, e.g. to the pinion, in order to comply with this assumption. In any case, the central idea is that for that particular rotation of the gear um 2 , there exists a unique value of u1 such that proper tangency can be found, and this is attained at the minimum rotation for which contact occurs. The detailed procedure follows. Given um 1 , for each couple \u00f0u1;v1\u00de on the pinion tooth surface we seek the solution of the following non-linear system: sf 2\u00f0u2;v2;um 2 \u00de \u00bc R\u00f0sf 1\u00f0u1;v1;um 1 \u00de; e1;b\u00de \u00f021\u00de for the three variables u2;v2;b" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002046_robot.1997.606793-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002046_robot.1997.606793-Figure4-1.png", "caption": "Figure 4: Virtual robot", "texts": [ "3 From trajectory to motion : the control law The feedback is based on the odometer of the robot and the absolute encoder given the direction cp of the trailer w.r.t. the robot. The control law we have chosen to track a trajectory is very simple. When the robot goes forward, the trailer is not taken into account and we stabilize the robot according to the control law described in [ll]. When the robot goes backward, we define a virtual robot which is symmetrical to the real robot with respect to the wheel axle of the trailer (Figure 4). The configuration of the virtual robot with respect to the real one is given by : 5, = 2, - 2ccosot & = yT - 22sin et { & . = e t - c p + T If (ij,&) are the linear and angular velocities of the virtual robot, we get : 5 = -U,& = Fsin(cp) - w. We apply the same control law as above to the virtual robot (&, @, , 8,). Therefore, at the current level of the experimentation, our control law is very simple. It is sufficient to reach the experimental objectives presented below. 5 Results Figures 5, 6 and 7 show three real experiments conducted on the site of LAAS" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001949_iros.2003.1248797-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001949_iros.2003.1248797-Figure5-1.png", "caption": "Figure 5: The coordinate systems used in the frontal plane for (a) single support phase, and (b) double support phase. The origin is set to the position of the ZMP in single support phase, and to the center in double support phase.", "texts": [ " By setting x, = 1, in Equation 2 and xg = -1d in Equation 3, we obtain the following condition: (4) Therefore, if the constant values c,, Cd , I , , l d are chosen in a manner that satisfies Equation 4, the acceleration becomes continuous. As shown in Figure 4, the motions of the COG during the single support phase and the double support phase are symmetric. The angular momentum generated in the initial half of the phase is compensated by that in the latter half. Therefore, it is not necessary to tune parameters to avoid divergence of the angular momentum. 2.2 Application of AMPM for motion in the frontal plane The coordinate systems used here are shown in figure 5. These systems are the same as those defined in Kajita et a1 131. The distance between the feet when they are both on the ground is 2s + 2p. The COG travels 20 during the double support phase. After switching to single support phase, i t travels along until it stops and returns back the same path. The analytical models of the single support phase and the double support phase can be explained by AMPM. The way they are modeled is explained in the following. The relationship between ZMP, COG and ground force during the single support phase is y , : ( i , + g ) = G y g : H . ( 5 ) where G is a constant value that can be set by the user (Figure 5(b)). Using the terminal condition, the motion of the COG can be finally written as: t t yg = s cosh - - ueZ sinh - TLS TI8 where uez is the velocity when the single support phase starts, and 4, = ,,\". Since the duration of the single support phase T is determined by the motion in the sagittal plane (T = t z - t o ) , uez can be calculated by setting t = T, yg = s into Equation 6. As a result, U,, can be calculated as --s + s cosh The y-component of the ground force can be written as t Fu = $ (yo cosh - - ueT sinh - I s 9, F, = -mg As the trajectories of the ground force, COG, and ZMP are known, the rotational moment around the anterior axis can be calculated as: T , = ygFz - HF," ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.16-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.16-1.png", "caption": "Fig. 7.16 A horizontalwheel water-driven wind box (Wang 1991)", "texts": [ " Feng Xiang is a planar mechanism with two members and one joint, including a box as the frame (member 1, KF) and a pushing rod outside the box with the piston inside. The pushing rod is connected to the piston as an assembly (member 2, KP). 7.3 Grain Processing Devices 155 The piston is connected to the frame with a prismatic joint JPx. It is a Type I mechanism with a clear structure. Figure 7.15b shows the structural sketch. 7.4.2 Shui Pai (\u6c34\u6392, A Water-Driven Wind Box) Nong Shu\u300a\u8fb2\u66f8\u300b(Wang 1991) shows another device for blast metallurgy in ancient China namely Wo Lun Shi Shui Pai (\u81e5\u8f2a\u5f0f\u6c34\u6392, a horizontal-wheel water-driven wind box) as shown in Fig. 7.16. The function of the device is to transmit water power through its linkage mechanism for wind blasting. The structure and the transmission process are explained as follows: A vertical shaft contains the upper and lower horizontal wheels. One half of the lower wheel is installed under the water, and both wheels are fixed to the shaft. The upper wheel is encircled by a rope. The rope also passes around the wooden cylinder with a crank. The connected link is attached to the crank and the left bar. The horizontal shaft is connected to the left and right bars as an assembly" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002240_j.precisioneng.2002.12.001-Figure17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002240_j.precisioneng.2002.12.001-Figure17-1.png", "caption": "Fig. 17. Contact arc and n\u0302(\u03b8ri), l\u0302(\u03b8ri) coordinates for a cross-section at \u03b8 = \u03b8ri.", "texts": [ " To ensure that contact is not lost between the ball and groove, we monitor a \u201cconstant contact\u201d constraint, \u03b4 \u21c0 n (\u03b8ri) \u2264 0, along the arc of contact. If this is violated, the ball and groove have separated over some portion of the contact and our analysis may predict tensile contact forces. Clearly this invalidates the model. A.5. Step 5: reaction force on an arc contact We define a unit vector, s\u0302(\u03b8ri) = n\u0302(\u03b8ri)\u00d7 l\u0302(\u03b8ri), that is tangent to the contact arc and changes orientation with \u03b8ri. This unit vector points into the page in the cross-section within Fig. 17. In Eq. (A.5) we calculate the resultant force on the arc contact via a line integral along the arc of contact. \u21c0 Fj = \u222b sfinal sinitial [fn(\u03b8ri)n\u0302(\u03b8ri)+ fl(\u03b8ri)l\u0302(\u03b8ri)+ fs(\u03b8ri)s\u0302(\u03b8ri)] ds \u2248 \u222b \u03b8jr final \u03b8jr initial [fn(\u03b8r)n\u0302(\u03b8ri)]Rc d\u03b8ri (A.5) The limits of the integral are defined by the ends of the arc contact as illustrated in Fig. 5B. The subscripts n, l, and s differentiate between unit contact forces in the subscripted directions. It is good design practice to minimize friction (\u00b5static < 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure11.1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure11.1-1.png", "caption": "Fig. 11.1 A foot-operated silk-reeling mechanism (Wang 1969)", "texts": [ " Since these complex textile devices consist of several mechanisms, it is difficult to classify them based on the types of mechanical members. This chapter systematically reconstructs all feasible designs of the complex textile devices that meet the ancient technological standards. The functions and components of the textile devices are explained. The mechanism structures of the textile devices are analyzed. The design constraints for the reconstruction designs are concluded and examples are provided for explaining. Sao Che (\u7e45\u8eca, a foot-operated silk-reeling mechanism), also called Zao Che (\u7e70 \u8eca), is used to extract and coil silk. Figure 11.1 shows the original illustration of Sao Che (Wang 1969). It consists of a cocoon cooking pot, several guide eyes, Gu (\u9f13, a pulley with an eccentric lug), one or two guide links, a belt, Ren Zhou (\u8ee0\u8ef8, a reel with a crank), a treadle, and one or two connecting links. Silk is extracted from cocoons in the cooking pot and passes through the guide eyes and the rack in the cooking pot. By the motion of the guide link(s), silk is coiled around the reel. There is a vertical pulley that has an eccentric lug on the top", " Each of them is presented as follows: Treadle Crank Mechanism The treadle crank mechanism includes the frame (member 1, KF), a treadle (member 2, KTr), a reel with a crank (member 3, KCR), and one or two connecting links (member 4, KL1, and member 5, KL2). Since there are many uncertain portions in the illustration, it is difficult to clarify how the oscillating motion of the treadle transfers to the rotation of the reel. Thus, this sub-mechanism is a Type III mechanism with uncertain numbers and types of members and joints. A rectangular coordinate system is defined as shown in Fig. 11.1. The z-axis is determined by the direction of the shaft of the reel, and the x and y axes are defined as the horizontal and vertical directions of the frame, respectively. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction design of the treadle crank mechanism is presented as follows: Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a planar mechanism with four members (members 1\u20134) or five members (members 1\u20135)", "3c3, the assignment of connecting link 1, con- necting link 2, and uncertain joints J2, J3, J4, generates one result as shown Fig. 11.3d3. 11.1 Shao Che (\u7e45\u8eca, A Foot-Operated Silk-Reeling Mechanism) 247 4. For the case shown in Fig. 11.3c4, the assignment of connecting link 1, con- necting link 2, and uncertain joints J5, J6, J7, generates one result as shown Fig. 11.3d4. Therefore, four specialized chains with identified frame, treadle, reel, con- necting link 1, and connecting link 2 are available as shown in Figs. 11.3d1\u2013d4. Step 4. The coordinate system is defined as shown in Fig. 11.1. The function of the treadle crank mechanism is to generate the rotation of the crank from the oscillating motion of the treadle. The uncertain joints may have multiple types to achieve the equivalent function. Since the device is planar, the uncertain joints must be planar joints. 1. Considering uncertain joints J1, J2, and J5, each joint has one possible type: connecting link 1 rotates about the z-axis with respect to connecting link 2, denoted as JRz. 2. Considering uncertain joints J3 and J4, each joint has two possible types and they can not be the same type simultaneously", " Guide Silk Mechanism The guild silk mechanism consists of the frame (member 1, KF), a reel with a crank (member 3, KCR), a belt (member 6, KT), a cylinder with an eccentric lug (member 7, KWC), and one or two guide links (member 8 KGL1, and member 9 KGL2). Since there are many uncertain portions in the illustration, it is difficult to clarify how the guide links guide the silk string to form even layers. Thus, this submechanism is a Type III mechanism with uncertain numbers and types of members and joints. A coordinate system is defined as shown in Fig. 11.1. According to the reconstruction design methodology for ancient mechanisms with uncertain structures, the reconstruction design of the guide silk mechanism is presented as follows: 248 11 Complex Textile Devices Step 1. Study the historical archives and analyze the structural characteristics as follows: 1. It is a planar mechanism with five members (members 1, 3, and 6\u20138) or six members (members 1, 3, 6\u20139). 2. The reel with a crank (KCR) is a binary link and connected to the frame (KF) with a revolute joint (JRz)", "6c2, the assignment of guide link 1, guide link 2, and uncertain joints J10, J11, and J12 generates one result as shown in Fig. 11.6d2. 3. For the case shown in Fig. 11.6c3, the assignment of guide link 1, guide link 2, and uncertain joints J13, J14, J15, and J16 generates one result as shown in Fig. 11.6d3. 252 11 Complex Textile Devices Therefore, three specialized chains with identified frame, reel, belt, cylinder, guide link 1, and guide link 2 are available as shown in Figs. 11.6d1\u2013d3. Step 4. The coordinate system is defined as shown in Fig. 11.1. The function of the guide silk mechanism is to transfer the rotation of the cylinder to the reciprocating motion of the guide link and make the silk broad bands on the reel. The uncertain joints may have multiple types to achieve the equivalent function. Since the device is planar, the uncertain joints must be planar joints. 1. Considering uncertain joints J8 and J9, each joint has two possible types and they can not be the same type simultaneously. When any one rotates about the y-axis, denoted as JRy, the other one not only rotates about the y-axis but also translates along the z-axis, denoted as JPzRy 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002327_cdc.2006.377687-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002327_cdc.2006.377687-Figure3-1.png", "caption": "Fig. 3. Illustration of the LOS angle ~bLOS.", "texts": [ " (10) The right-hand side of system (10) contains no control inputs. To regulate the cross-track error to zero, we will control the surge speed u and the yaw angle 4 in such a way that the cross-track error converges to zero. This will be done with the help of LOS guidance. We choose a LOS guidance law where we pick a point that lies a distance A > 0 ahead of the vehicle, along the desired path. The angle describing the orientation of the line of sight is referred to as the LOS angle. With reference to Fig. 3, the LOS angle is given by the following expression: In the next subsections we will propose two controllers. The first controller regulates the surge speed u to asymptotically track some commanded speed signal u,(t). The second controller makes the yaw angle b asymptotically track the LOS angle OLOS. We will then show that this makes the cross-track error ey and the yaw angle y exponentially converge to zero. B. Surge Control The vessel considered in this work is underactuated. It can be actuated only in surge and yaw" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003174_2052546.1975.11908735-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003174_2052546.1975.11908735-Figure1-1.png", "caption": "Fig. 1. Idealized arm and arm plus atlatl arcs of motion.", "texts": [ " Browne (1940:211-212) correctly describes the motion involved and the fact that the arm and atlatl are extended to the \"height above the head equal to the length of the arm and the atlatl \". The following discussion is intended to de scribe the function of the atlatl as a logical consequence of the application and operation of a few basic laws of physics-especially that of Newton's second law for rotation. Eleven assumptions and/or observations will be made to facilitate the analysis of an ideal situation involving the use and function of the atlatl. Assumptions (see Figure 1 for graphic repre sentation) 1. Both the arm and the arm plus atlatl basically will be considered to inscribe an arc when in motion. 2. The center, or pivot point (P) of the arc in both cases is at the shoulder. 3. The human arm is considered both with and without the atlatl as being essentially straight. No account is made for the multi- pie angular and acceleration changes be tween the shoulder, upper arm, elbow, forearm and wrist which actually take place. The mathematics involved in these angular, acceleration and momentum changes are extremely complex and would not serve to better demonstrate or explicate the phe nomenon being discussed" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.12-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.12-1.png", "caption": "Fig. 7.12 A mill (\u7931). a Original illustration (Wang 1968), b Structural sketch", "texts": [ " Considering the functions of roller devices, joint J\u03b2 not only may rotate but also translate, and its characteristics are 7.3 Grain Processing Devices 151 similar to the combination of a rolling joint and a prismatic joint, that can be denoted as JPxO . Meanwhile, joint J\u03b1 has two possible types including a revolute joint JRz as shown in Fig. 7.11f1 and a cylindrical joint JPzRz as shown in Fig. 7.11f2. Figure 7.11g shows a real object of the water-driven roller. 7.3.5 Long ( \u7931, A Mill) Long (\u7931, a mill) is a mill for removing grain husk and has the similar structure as Mo (\u78e8, a grinder) as shown in Fig. 7.12a (Wang 1968). It consists of the frame, a mill disc with a crank, a horizontal rod, and two ropes hung on the horizontal rod. The operator pushes the horizontal rod by hands to rotate the mill disc on the base, achieving the purpose of grinding grains (Zhang et al. 2004). Long is a spatial mechanism with four members and four joints, including the frame (member 1, KF), a rope (member 2, KT), a horizontal rod (member 3, KL1), and a mill disc with a crank (member 4, KL2). The rope is connected to the frame and the horizontal rod with thread joints JT. The mill disc with a crank is connected to the frame and the horizontal rod with revolute joints JRy. It is a Type I mechanism with a clear structure. Figure 7.12b shows the structural sketch. 152 7 Linkage Mechanisms 7.3.6 Mian Luo (\u9eab\u7f85, A Flour Bolter) Mian Luo (\u9eab\u7f85, a flour bolter) is a powder-sieving device as shown in Fig. 7.13a (Ortai et al. 1965). Its function is to separate fine powders from other rough parts. The members include a box (frame), a treadle with a swing rod, a connecting link with a flour-sieving screen, and the rope. The flour-sieving screen is made from bamboo or wood. The bottom of the screen is covered by a mesh with tiny holes, and the connecting link is fixed on the screen and extends out the box" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure11-1.png", "caption": "Figure 11. Robotic Arm places the Drill against a rock", "texts": [ " The system components of the proposed architecture are shown in Figure 9 and include: 1. Drill 2. Sample Cache 3. Bit Carousel 4. 5 DOF Robotic Arm 5. Rock Abrasion and Brushing Tool (RABBit) The core acquisition and caching sequence takes only 4 steps as follow: 1. Drill docks with the Bit Carousel and acquires a new Bit (Figure 10). 2. Robotic Arm preloads the Drill against a target rock. The Drill commences its core acquisition operation: it drills to a target depth, breaks off and captures the core, and retracts the bit from the hole (Figure 11). 3. Robotic Arm positions the core bit in front of the camera (PanCam, HazCam etc.) and verifies the presence of the core inside the bit (Figure 12). 4. The Drill docks with the Cache. The bit with the core inside is initially inserted into the sleeve within the Cache and then screws in, creating a Hermetic seal (Figure 13). Robotic Arm Stowed Robotic Arm Unstowed \u2013 Ready Position Figure 12. PanCam images bottom of Bit to confirm collection of core. Insert Bit with sample into Sample Cache Align Sample Acquisition Tool with Cache and extend Z-Axis while rotating Auger Sample Encapsulated R o c k C o re Figure 13" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001735_robot.1995.525421-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001735_robot.1995.525421-Figure4-1.png", "caption": "Figure 4: Model for a Free-Flying, Two-Arm Space Robot", "texts": [ " 4 Experiments The Extended Operational Space Formulation has been implemented and validated experimentally at the Stanford University Aerospace Robotics Laboratory. The laboratory has three prototype free-flying space robots which float in two-dimensions on a frictionless air bearing over a granite surface plate. The robot shown in Figure 3 has thrusters and a momentum wheel for locomotion, two DC motor-driven manipulators with pneumatic griplpers, force sensing, real-time vision, on-board computation and power, and wireless communications. Figure 4 depicts the modeling for the free-flying space robot: a nine degree-of-freedom system that operates in a plane. A mobile-based robot can be modeled simply as a fixed-base robot in which the first two joints are prismatic and without joint limits, and the third joint is revolute. - 1059 4.1 Open-Chain Control To apply the open-chain formulation of Section 3 to the space robot, let x = [xT X T ] ~ and J(q) = [JF(q) J?(q ) lT , where Jl(q) and J2(q) are the basic Jacobians from the origin of the inertial frame to each end-effector. J(q) is easily constructed from the Jacobians corresponding to the base and each arm: As shown in Figure 4, J L and J R are the Jacobians for each manipulator extending from the base, as if they were fixed-based manipulators. Z is the rotation matrix that represents the rotation of the base relative to the inertial frame. J B L and J B R are the Jacobians from the origin of the inertial frame to each shpulder, where each branching manipulator begins. VL and ?R are cross product operators that account for the effect of the rotation and translation of the base on the velocities a t each end-effector. Control of the robot is achieved by Equation (9)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001719_6.1997-3765-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001719_6.1997-3765-Figure1-1.png", "caption": "Fig. 1. Missile Coordinate Systems", "texts": [ " When compared with linear methods, nonlinear control design methods require higher amount of initial analysis effort. However, once the analysis completed, the results are applicable over a wide range of missile configurations. 2. Missile Model The missile model forms the basis for autopilot development. A six degree of freedom rigid missile model is employed in the present research. The missile state variables are defined using a body coordinate system and an earth-fixed coordinate system shown in Figure 1. The origin of the body axis system is assumed to be at the missile center of mass. The XB axis of the body axis system points in the direction of the missile nose, the YB axis points in the starboard direction, and the ZB axis completes the right-handed triad. The missile position and attitude are defined with respect to an earth-fixed inertia! frame. The origin of the earth-fixed coordinate system is located at the missile launch point, with the X axis pointing towards the initial location of the target, and the Z axis pointing along the local gravity vector" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002980_978-3-642-01153-5-Figure2.8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002980_978-3-642-01153-5-Figure2.8-1.png", "caption": "Figure 2.8.1 Pulsating torque after 3-phase sudden short circuit", "texts": [ " It is not difficult to know that the relative speeds between those fields are zero, s and 2 s and the fundamental and second harmonic pulsating torque components can be produced. The interaction between stator and rotor fields whose relative speed is zero will produce an average torque, but the average torque is equal to zero because the stator and rotor resistances have been neglected and their field-axes coincide with each other. AC Machine Systems 156 The electromagnetic torque after 3-phase sudden short circuit is shown in Fig. 2.8.1. (2) Average torque after 3-phase sudden short circuit After 3-phases of a synchronous machine are suddenly short-circuited, in stator winding there are the fundamental, second harmonic and aperiodic currents and in rotor winding there are the fundamental and aperiodic currents, which is the synthetic result when the aperiodic currents circulate through the stator and rotor windings simultaneously. Because the fields produced by the two groups of currents have different speeds, the average torque components corresponding to them can be studied separately" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003718_s12008-012-0163-y-Figure15-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003718_s12008-012-0163-y-Figure15-1.png", "caption": "Fig. 15 Simulation of the contact", "texts": [ " For each meshing position of the master flank and for each node of the master flank mesh, the respective point existing on the slave flank is generated. Subsequently, the angle around the slave part axis between the two points is computed. The pair of points with the smallest angle is considered as the Fig. 14 Generation of the slave surface point Tooth mO ts t\u03c6 Tool mr Master sR sO tO s\u03c6 s\u03b3 s m Slave \u03b3 sr Slave Master sO mO sy sx c\u03b4 sr sr\u03b8 m\u03b8 c\u03b4 my sx sy sp mx mp mO sO Master Slave Fig. 16 Simulation of the meshing approximated contact point. This approach is illustrated for a spur gear in Fig. 15. The smallest angle value computed for each meshing position of the master part is compared with its value one pitch earlier. If the first is smaller than the second, the contact point exists in the meshing zone. Else, the contact point is out of the contact pattern and it does not exist. All the contact points of the contact pattern are selected in this way. This approach is illustrated for a spur gear in Fig. 16. The method can be quite easily coded in a computer program. 3.2 Results The algorithm remains stable whatever the tooth flank topographies, whatever the relative position of the parts, whatever the discretizations of the master flank surface and the meshing motion" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002185_j.talanta.2004.08.010-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002185_j.talanta.2004.08.010-Figure3-1.png", "caption": "Fig. 3. Cyclic voltammograms of CGA modified carbon composite electrode in 0.1 M phosphate buffer solution (pH 6) at scan rate 20 mV s\u22121 in the absence (a) and 1 mM NADH solution (b). (c and d as a and b) for bare electrode at the same condition.", "texts": [ " 2 shows the atomic force microscopy (AFM) images of bare carbon composite electrode and carbon composite electrode modified with chlorogenic acid. As it can be seen, a thin film of chlorogenic acid has been adsorbed on electrode surface. acid CCE for oxidation NADH oaking the carbon ceramic electrode in 1 mM chlorogenic cid solution for different times at 20 mV s\u22121 in the blank Due to high electrochemical reversibility and stability of carbon ceramic electrodes modified with thin film of chlorogenic acid, they are widely used in electrochemistry as elec- tron transfer mediator to shuttle electrons between NADH and substrate electrodes. Fig. 3 shows the cyclic voltammograms of the bare and modified CCE in the presence and absence of NADH. As shown in Fig. 3c and d, no response is observed at the surface of bare CCE in the presence and absence of NADH in potential range 0.15\u20130.45 V. The CGA modified CCE in the blank solution (0.1 M phosphate buffer solution pH 6), exhibits a well-defined cyclic voltammogram at 0.27 V versus reference electrode (Fig. 3a). Upon the addition of 1 mM NADH, there is a dramatic enhancement of the anodic peak current at less positive potentials (before oxidation potential of chlorogenic acid) and the cathodic peak current disappears, indicating a strong electrocatalytic effect of chlorogenic acid for NADH oxidation (Fig. 3b). The electrocatalytic oxidation of NADH at low potentials is also very useful for practical applications since there is less risk for interfering electrochemical reactions to take place. As we reported previously [42], the electrochemical properties of CGA-modified CCE are strongly pH-dependent in buffered solutions. To optimise the electrocatalytic response of the modified CCE to NADH oxidation, we investigated the effect of pH on the catalytic oxidation. The cyclic voltammograms of modified CGA\u2013CCE in 1 mM NADH solution at different pH values (pH 3\u20138) are presented in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002570_rspa.2007.0006-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002570_rspa.2007.0006-Figure1-1.png", "caption": "Figure 1. Idealized motions for walking and running. (a) In inverted pendulum walking, the body vaults in circular arcs on a straight leg. One leg is on the ground at a time. At the change from one circular arc to the next the trailing leg pushes off and then the leading leg heelstrikes the ground. (b) In impulsive running, the body travels from one parabolic arc to the next with a bounce in between. Adapted from Srinivasan (2006) and Srinivasan & Ruina (2006).", "texts": [ " Then we use elementary geometric arguments on the resulting phase plane to show optimality of the two gaits: walking at low speeds and running at high speeds. Keywords: locomotion; energy; optimality; walking; running; optimal control *A Rec Acc When people travel by foot from point A to point B, and are not rushed, they walk. When they are in a hurry, they run. Classically, human walking has been idealized as a gait in which the hip (or the body centre of mass) travels in a series of inverted pendulum circular arcs about the foot on the ground as shown in figure 1a (e.g. Alexander 1976). In one energy-consistent version of this idealization, only one foot is on the ground at a time, and the transition from one circular arc to the next is accomplished by the trailing leg pushing off just before the heel of the leading leg strikes the ground (Kuo 2001; Kuo et al. 2005; Ruina et al. 2005; Srinivasan & Ruina 2006). Analogously, as shown in figure 1b, running is simply idealized as a series of parabolic freeflights of the body, interrupted by brief bounces. In idealized running, the work absorbed in the downward part of a bounce is regenerated on the way back up (Rashevsky 1948; Ruina et al. 2005; Srinivasan & Ruina 2006). Proc. R. Soc. A (2007) 463, 2429\u20132446 doi:10.1098/rspa.2007.0006 Published online 10 July 2007 uthor for correspondence (msriniva@princeton.edu). eived 28 May 2007 epted 16 June 2007 2429 This journal is q 2007 The Royal Society Among the essentially infinite variety of motions that our two legs are capable of, why do we choose to walk and run in ways that are somewhat close to these two idealizations", " (d ) Limit of infinite force-bounds As in Srinivasan & Ruina (2006) and as alluded to in \u00a72a, we formally wish to determine the limit of the sequence of optimal solutions as the force-bounds in the elevator problem increase without bound (Fmax/N and Fmin/KN) for every combination of speed v and step-length dstep. To show the similarity of problem A to problem B (\u00a74) in the limit of small step-lengths, we assumed that the leg forces were bounded. However, in the following discussion, we find it convenient to allow infinite leg forces, in particular, impulses that change the vertical speed instantaneously. (a ) Walking and running in the elevator problem We now describe how the two idealized gaits, inverted pendulum walking and impulsive running, described earlier in \u00a71 and illustrated in figure 1, can be most naturally described in the context of the elevator problem. Inverted pendulum walking can be most naturally described as riding the elevator till tZtstep/2 and then pushing off impulsively against the elevator at exactly tZtstep/2 so that the vertical velocity of the person is reset to zero. Impulsive running, on the other hand, is jumping impulsively off the elevator at tZ0 giving the point mass an initial vertical velocity that ensures that the vertical speed at tZtstep/2 equals zero" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003181_10402004.2010.492925-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003181_10402004.2010.492925-Figure5-1.png", "caption": "Fig. 5\u2014Sketch of a spherical roller bearing including a lubricant layer thickness distribution. It is assumed that the distributions on the rollers and the inner and outer raceways are equal.", "texts": [ " This behavior was observed in the experiments presented in van Zoelen, et al. (18). In these ball-and-disk experiments an oil droplet was placed on the surface of the rolling element and it was observed that after a running-in period the lubricant was distributed equally along the track. Due to this effect, in the long run the layer thickness distribution in a bearing will be uniform in the circumferential direction and equal for the raceways and the rollers. An example of such a distribution for a spherical roller bearing is shown in Fig. 5. h\u0303\u221e (y, t) is the layer thickness distribution. It is assumed that the equipartition of the layers takes place over the full width of the track, even though the Hertzian contact width may vary along the circumference of the bearing. Strictly, for a ball bearing this distribution only occurs when the rolling elements do not spin. The change of the layer thickness distribution h\u0303\u221e (y, t) in time can be described by the following differential equation (see van T ri bo lo gy T ra ns ac tio ns 2 01 0", " is diminished, the steel surfaces in the EHL contact may still be separated by the thickener-rich layer deposited on the running tracks. In this section the results for the lubricant layer thickness distribution across the track of the spherical roller bearing are discussed. It should be recalled that the lubricant layer thickness is assumed to be distributed evenly along the circumference of the bearing. The results shown in this section represent a cross section of this three-dimensional distribution shown in Fig. 5. In Fig. 8 the layer thickness distribution at different times t is shown for the case of a constant radial bearing load and three different rotational speeds. The values of the parameters used are as given in Table 2 for cases 1, 2, and 3. The initial layer is uniform with thickness 50 nm. After 7.5 min the layer no longer has a uniform thickness. The solution shows a furrow in the center and at both sides of this furrow a levee is formed. The distribution is symmetrical with respect to y = 0. At the boundaries of the solution domain the layer thickness tends to become very large, which means that liquid accumulates in these areas" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure5.18-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure5.18-1.png", "caption": "Figure 5.18-The Construction of a swinging-gap choke. From Martin, W.A. Powertechnics Magazine, Feb. (1986) p.19", "texts": [], "surrounding_texts": [ "Figure 3.34-Penneability versus frequency for various materials. Reprinted from Herzer, Handbook of Magnetic Materials Vol. 10, \u00a91997, pA55, with pennission from Elsevier Science. 3.4.2-Amorphous-Nanocrystalline Materials for EMI Suppression One of the earliest uses of the amorphous material described earlier was as a choke coil that Toshiba called the \"Spike-killer\". Presumably, only the cores are sold. The amorphous materials used are under license from Al lied's Metglas\u00ae Division. Vacuumschmelze does market a Co-based amor phous material for EMI suppression applications. It is designated Vitrovac 6025 and is essentially a zero magnetostriction material. The characteristics are shown in Table 3.3. As an outgrowth of the amorphous materials, the iron based nanocrystalline materials are the newest ones available and they have been used for EMI suppression. Their high permeabilities and low magne- MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 91 tostrictions made it very useful as a common-mode choke at relatively low frequencies. The earliest nanocrystalline soft magnetic alloy was made by Hitachi and names \"Finemet\". The properties of the Finemet nanocrystalline material are given in Table 3.4. The saturation is high but not in the Si-Fe class. The permeability is high but not in the 80 permalloy class. The magne tostriction is low and about the same as the Co-based amorphous material. The resistivity is the same as the amorphous alloys but many orders of mag nitude lower than ferrite. It is really the combination of most of the good at tributes that make it attractive. High permeability materials without the high resistivities are useful for the inductive or permeability portion of the imped ance and are limited to the lower frequencies. Vacuumschmelze has two nanocrystalline materials, Vitroperm 500F and 800F that they recommend for EMI suppression(common-mode chokes) along with their Co-based amorphous zero-magnetostriction material Vitrovac 6025. The permeability of the 800F is somewhat higher than the 500F. A comparison of the Co-based amorphous, the nanocrystalline material and a MnZn ferrite is given in Figure 9.35 The permeability is higher and the loss factor is lower for the metallic material than for the other materials. The in- The use of gapped ferrite cores as output chokes was discussed ear lier. in Section 3.1.10 . Another series of good material choices for the appli cation are the metal powder cores. Aside from output chokes, a recent and MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 93 related application is that of power factor correction (PFC) cores. For these applications, there are two main advantages of powder cores over ferrites. They are; 1. Their saturation flux densities are much higher ( as much as 2-3 times higher) 2. The gap is a distributed one while that of ferrite is discreet lead ing to high gap losses. A disadvantage of the powder core is the need for costly toroidal winding as they are mostly used as ring cores. Some metal powder E-cores are now available. Similar to the metal strip analog, the lowest loss, highest perme ability material of the powder cores are the 80% Ni variety which allows for operation at higher frequencies (especially in thin gage). The 50% Ni alloy has twice the saturation of the 2-81 Moly Permalloy (MPP) material but it has higher losses and is used for lower frequencies. The iron powder cores have the highest saturation and lowest cost but the highest losses. For EMI applications, while common-mode filters are mostly used in unbalanced circuits where the currents return to ground, the differential-mode filter is used primarily in balanced systems. Consequently, putting a ferrite toroid around both wires would not cause any flux change in the core and so not suppress the EM!. The solution in this case is to put suppressor cores on each of the wires. However, this means that the full ac (and D.C.) signals would pass through the suppressor core. While the common-mode ferrite core can be used in high current power filters, the differential-mode suppressor ferrite core is only used in low current power filters. With the differential mode or in-line filters, the core losses could be a problem (except for D.C.), the main problem would be core saturation. To prevent this, a core with low permeability is needed. Either a gapped ferrite core or a powder core can be used. 3.5.1-Iron Powder Cores The iron powder cores, unlike those listed for low level telecommuni cations applications are of the higher permeabilities (from 70-100 perm). They are usually of the hydrogen-reduced variety. Before discussing the mag netic properties of powder cores for EMI suppression, we must point out that, while permeability has been our criterion for EM! ferrite suppression ability, with powder cores, vendors do not specify impedance. Since the application of these cores involves high flux densities and often D.C. bias, the magnetic properties usually listed are; 94 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 1. Permeability versus Flux Density 2. Permeability versus DC Bias 3. Core Losses 4. Permeability versus Frequency 5. Permeability versus Temperature 6. D.C. Energy storage curves Another important property for an application as a D.C. choke is the variation of energy stored versus D.C. current. The energy storage criterion is given by Y2 U 2\u2022 For the iron powder cores, the high saturation of about 20,000 Gauss is suited for this application. Curves displaying the variation of permeability with flux density and DC bias for iron powder cores are shown in Figures 3.36 and 3.37. Permeability versus frequency is shown in Figure 3.38.Core loss and Energy storage curves are shown in Figures 3.39-3.40. MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 95 96 MAGNETIC COMPONENTS FOR POWER ELECTRONICS --- 710 100 ... - '10 .. 40 .. .. \u2022\u2022 t-- -, .... \" I-- ... A. C. iOIeIIly 810M0t I\"'U') I-- -65 MATERIAL , , , , A~ V' ,- -- / ~'\" -,- , -./ -..... , I. .... .. '10 zoo 100 100 1000 1iIOO'\" .- ,ocoo IOOCIO.... ICIIIIIIII 10100D 0\\., C. PlU'Q1' 8TOI'&OI \\'IlL\" ~I Figure 3.40- Energy storage curves for 85 penn iron powder cores. From Pyroferric MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 97 3.5.2-NiFe Powder Core Materials Nickel iron powder cores come in two varieties, the 2-81 MPP (Moly permalloy Powder) and the 50-50 Hi Flux Cores. The NiFe powder cores listed as High Flux cores are different from the MPP cores listed in the chap ter on low level applications of powder cores. These NiFe cores are 50% Nickel-50% Iron. The have about twice the saturation (l5,000)of the MPP cores and thus are much better for the present application. Cores of this mate rial are available in permeabilities of 200, 160, 147, 125, 60, 26 and 14. The variations of permeability with flux density and D.C. bias, frequency and temperature for different permeabilities of this material are shown given in Figures 3.41 and 3.42. Plots of permeability versus frequency and temperature are found in Figures 3.43 and 3.44.The core losses are given in Figure 3.45. As expected, the stability is inversely proportional to the permeability but the high frequency core losses are proportional to the frequency. Cost-wise the High Flux powder cores are more expensive than the iron powder cores, but somewhat less expensive than the MPP cores. 98 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 100 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 3.5.3- Sendust Powder Material The Sendust cores are marketed under the trade names of Kool-Mu and MSS materials. It is a new application of an old material having been de scribed by Matsumoto in 1936 and patented in 1940 (Matsumoto 1940). Sen dust is a ternary alloy containing about 6% aluminum and 9% silicon. Its at traction is that it is close to a zero anisotropy-zero magnetostriction material. Its brittleness and difficulty in producing it have limited its use in the past to recording head material due to its great hardness. When used in powder cores, its brittleness helps in the comminution process. The high saturation of this material (on the order of about 10,000 Gauss provides much more energy storage than MPP cores or gapped ferrites. The cores come in permeabilities of 60, 75, 90 and 125. Figures 3.46-3.49 show the permeability variations of different permeabilities of this material for flux density, D.C. bias, frequency and temperature. The core loss of the 125 perm material is given in Figure 3.50. The core losses are significantly lower than the iron powder cores. However, the Sendust cores are somewhat more expensive. Cores with O.D's from. 140 inches to 2.25 inches are available. MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 101 Permeability versus Frequency Curves, Kool MIJ 102 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Permeability versus Temperature Curves, Kool MIJ Core Loss Density Curves, Kool MIJ MAGNETIC MATERIAL CHOICE -POWER ELECTRONICS 103 References Buthker,C.(1986) and Harper, OJ., Transactions HFPC, 1986,186 Bozorth, R.M. (1951) Ferromagnetism, Van Nostrand New York Fair-Rite (1996) Fair-Rite Soft Ferrites, 13th Ed. Fair-Rite Products Corp. One Commercial Row, Wallkill, NY 12589 Goldman, A. (1985), Advances in Ceramics U, Proc 4th ICF, p.421 Goldman, A. (1995), J. Mat. Eng. And Performance 1,395 Herzer, G. (1997) Handbook of Magnetic Materials, Vol. 10, Elsevier Science B.V. Amsterdam, 418,444,454,455 Hitachi (1998) FINEMET FT-IKM-KN Series Core Page on Internet Product Guide Hilzinger, H.R. (1996)Soft Magnetic Materials '96, Feb.26-28, 1996, San Francisco, Gorham-Intertech Consulting, 411 U.S. Route One, Portland ME, 04105Magnetics (1987) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Honeywell (2000). Metglas@ Technical Bulletin, Metglas@ Products, 6 Eastman Rd. Parsippany NJ 07054 Magnetics (1995) Tape-Wound Cores Design Manual, TWC-400, Magnetics, Division of Spang and Co., Butler, PA 16001 Magnetics (1998) Powder Cores MPP Cores for Filter and Inductor Applica tions, Magnetics, Div. of Spang and Co. Butler, PA 16001 Magnetics (2000) Ferrite Core Catalog, FC601, Magnetic Div., Spang and Co, Butler, PA 16001 Makino, A. (1997),Hatanai, T., Naito, Y. Bitoh, T.,Inoue, A., and Masumoto, T., IEEE Trans. Mag. MAG33, 3793 Micrometals (1990) Micrometals Iron Powder Cores, EMI and Power Filters Micrometals, 1190 N. HawkCircle, Anaheim ,CA, 92807 MMPA (!996) Soft Ferrites, A User's Guide SFG-96 Parker, C. (1994) Presented at MMPA Soft Ferrite Users Conference, Feb. 24- 25, 1994, Rosemont ,IL Pyroferric(1984) Toroidal Cores for EMI and Power Filters, Pyroferric Inter national, 200 Madison St., Toledo, IL 62468 Roess, E.(1982), Transactions on Magnetics MAG 18,#6,Nov.1982 Smit,J.(1954) and Wijn,H.PJ. Advances in Electronics and Electron Physics, 2.,69 Snelling E.(1988) Soft Ferrites, Properties and Applications Butterworths, London Vacuumschmelze (1995) Vitrovac 500F-Vitroperm 6025, PK-004, Vac uumschmelze GMBH, Hanau, Germany Yoshizawa, Y (1988) Oguma, S. and Yamaguchi, K.,J. Appl. Phys.,64, 6044 Yoshizawa, Y (1989) and Yamaguchi, K., IEEE Trans. Mag. MAG25, 3324 Chapter 4 CORE SHAPES FOR POWER ELECTRONICS INTRODUCTION In the previous chapter, the inherent material properties of compo nents for power electronics were examined. In most cases these properties were measured on toroids because their magnetic cross-sectional area is con stant and they have an uninterrupted magnetic path. This makes for ease of interpretation of the measurements. However, while toroids are still used in some applications, designers of magnetic circuits (including those for power electronics) find it more practical to rely on many other shapes for technical and economic reasons. Because the shape of the component influences the performance of the device, modified component parameters including mate rial and shape considerations must be developed. This chapter will list the possibilities of core shapes used in power electronics. In addition, several new changes in the overall height to cross-section brought about by mounting on PC boards will be discussed. Since, very often the magnetic component is the largest on the board, the shape of the component takes on much more ill'por tance. 4.1-FERRITE CORE SHAPES Ferrite cores possess one advantage over other magnetic materials in that they come in a large variety of shapes. This feature is made possible by the part-forming process in which the ferrite powder is pressed in a die before sintering to final dimensions. The die can be complex as long as the pressed part can be ejected from the die. Some parts such as round-leg E-cores must be pressed with legs up which creates a need for a minor adjustment. A vari ety of ferrite shapes for power applications are shown in Figure 4.1 4.1.1 Pot Cores Pot cores are sometimes used ungapped in power applications with a solid center post since there is no need for the adjustor found in telecommuni cation applications. The shielding to protect a low-level telecommunication signal in LC circuits is not necessary. There may be some advantage to the shielding in that it does provide the lowest leakage inductance. Besides cost, MAGNETIC COMPONENTS FOR POWER ELECTRONICS 106 from the windings to escape. Since pot core dimensions all follow IEe stan dards, there is interchangeability between manufacturers. 4.1.2-Double Slab Cores In slab-sided solid center pot cores, a section of the core has been cut off on each side parallel to the axis of the center post. This opens the core considerably. These large spaces accommodate large wires and allow heat to be removed. In some respects, these cores resemble E-cores with rounded legs. See Figure 4.2 107 CORE SHAPES FOR POWER ELECTRONICS 4.1.3-RM Cores and PM Cores RM cores (See Figure 4.3) were originally developed for low power, telecommunications applications because of the improved packing density. They have since been made in larger sizes without the center hole. Their large wire slots are an advantage while still maintaining some shielding PM cores are large RM-shaped cores specifically for power applications. Zenger(1984) feels that the geometry and self-shielding of RM cores make them useful at high frequencies. Roess (1986) points out that the stray field from an E-42 core is 5 times higher than that of an RM core. With the trend towards in creased operating frequencies, he feels that there may be a backs wing to the RM cores in mains (line) applications. Since that time, the use of RM cores for power applications has grown significantly. Low-profile RM cores are available in the RM4, RM5, RM6, RM7, RM8, RmIO, RM12 and RM14 sizes . Surface mount bobbins are available in RM 4 Low Profile, RM5, RM6, and RM6LP. For power non-linear choke cores, Siemens offers special RM8 to MAGNETIC COMPONENTS FOR POWER ELECTRONICS 108 RM 14 cores with tapered center posts. PM (Pot-core Module) cores are used for transformers handling high powers, such as in pulse power transformers in radar transmitters, antenna matching networks, machine control systems, and energy-storage chokes in SMPS equipment. It offers a wide flux area with a minimum of turns, low leakage and stray capacitance. Because of the weight of these pot cores, they may not be suitable for mounting on PC boards. The numbering system of the RM cores is based on the grid system for holes on printed circuit boards. There are 10 grids to an inch (25.4mm) The RM number corresponds to the number of grids that a side of the square that contains the core. Thus an RM4 core would fit in an are of 4X4 grids (O.4X 0.4 inches) or about 10 x 10 mm. 4.1.4-E Cores These cores are the most common variety used in power transformer applications. As such they are used ungapped. There are some variations that we shall discuss here. Their usefulness is based on their simplicity. Initially, E- cores were made from metal laminations and the early ferrite E cores were made to the same dimensions and were called lamination sizes. However, as 109 CORE SHAPES FOR POWER ELECTRONICS the ferrite industry matured, E core designs especially useful for power ferrite applications were developed.( Figure 4.4). Many standard E-cores have bob bins that permit horizontal mounting. Some of the smaller sizes also are avail able in surface mount design with gull-wing terminals. 4.l.S-E-C Cores E-C cores are a modification of the simple E core. The center post is round similar to a pot core and since round center bobbins wind easier and are more compact than square center bobbins, this is an advantage. The length of a tum on the round bobbin is 11 percent shorter than the square bobbin that means lower winding losses. The legs of these cores have grooves to accom modate mounting bolts. (Figures 4.5 and 4.6) 4.1.6-ETD Cores ETD cores are similar to E-C cores. They have a constant cross sec tion for high output power per unit weight and simple snap-on clips for hold ing the two halves together. They also have a bobbins which provides for creepage for mains (line) isolation and have enough space for many terminals. Zenger( 1984) suggests that the constant cross section of the ETD is an im portant attribute for high frequency at\"~ high drive levels. (Figure 4.5) These cores are available only in the large s:z~;, and thus are not used with surface mount bobbins. 111 CORE SHAPES FOR POWER ELECTRONICS 4.1. 7-E-R Cores These cores combine high inductance and low overall height. They have a round center post and surface mount bobbins available with the smaller sizes. 4.1.8-EP Cores EP cores are a modification of a pot core but the overall shape is rec tangular. A large mating surface allows better grinding and lapping, preserv ing more of the material's permeability. The EP core is usually mounted on its side with the bobbin below it facilitating printed circuit mounting. The best advantage of this core is in high permeability material. Shielding is very good. Some sizes of E-P cores (EP7 and EP13) are available with surface-mount bobbins with gull-wing terminals. Figure 4.7 shows an assortment of EP cores with the mounting accessories. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 112 4.1.9-PQ Cores TDK says it stands for Power and Quality. These are one of the new est types of cores for power ferrites for switched mode power supplies. The lowest core losses in a transformer usually exist when the core losses equal the winding losses. The geometry in a PQ core is such as to best accomplish this requirement in a minimum volume. The clamp is also designed for a more efficient assembly. A more uniform cross sectional area is also achieved so that the flux density is uniform throughout the core so that the temperature will not vary much. See Figure 4.8. 4. 1. 10-Toroids Toroids are sometimes used as power shapes because they take full advantage of the material permeability. Since there is no gap, leakage is very low. The toroid's main disadvantage is the high cost of winding as compared to an E or pot core. (Figure 4.9). Engelman (1989) constructed a multi-toroid power transformer that provides digital control. 40 toroids were used. 113 CORE SHAPES FOR POWER ELECTRONICS Bates (1992) reported on a new SMP core technology combining new high frequency ferrite power materials as toroids in a matrix transformer that can deliver 2000 watts at 5V D.C. It has the advantage of being low profile, has low leakage inductance excellent winding isolation and higher thermal dissi pation due to increased surface area. 4.1.11-EFD Cores Probably the newest design in miniature power shapes is the EFD cores which stands for E- core with flat design. (See Figure 4.10) The center leg was flattened for the extra low profile needed for PC board mounting. Simple clips are available. As expected surface mount bobbins are available. Mulder (1990) has written an extensive application note on Design of Low Profile High Frequency Transformers. He finds an empirical relation between effective volume and the thermal resistance of a magnetic device with which a MAGNETIC COMPONENTS FOR POWER ELECTRONICS 114 CAD program can be constructed to develop the optimum range of EFD cores for the frequency band 100KHz to 1 MHz. 4.2-EFFECTIVE CORE PROPERTIES-POWER CORE SHAPES In Chapter 3, the inherent properties of the various power magnetic materials were listed. In most every case, the measurements reported were made on toroids or ungapped shapes. We know that most power shapes are gapped. Even the so-called \"ungapped\" cores have a gap in the mating sur faces. For gapped cores, the dimensions and magnetic properties must be modified to the effective parameters The toroid was described as a closed magnetic circuit with uniform cross section. Even in a toroid, however, the magnetic path length varies from the circumference formed by the ID and to that formed by the OD. The mean length is often taken as the circumference of the average diameter [ Ie = n( do + dj)/2]. Where there is a large variation between the OD and ID, the average 115 CORE SHAPES FOR POWER ELECTRONICS Figure 4.10- EFD Cores for Power Applications value is invalid and a more complex method involving integration of all the paths is necessary. The situation on other shaped components is usually not as simple. First, the circuit may have an air gap (intentional or that formed by mating surfaces). The permeability of the magnetic circuit will be; Jl e == JlJ{1+ JlJllm } [4.1] where; Jle == Effective permeability of gapped structure J.1o = permeability of the un gapped structure Ig == length of gap 1m = length of magnetic path It is very important for us to appreciate the impact of this relationship espe cially in high permeability materials. For example, let us take the case of an EP core of 10,000 permeability material with no intentional gap. A separation of only 1 micron(or .00004 inches} will reduce the effective permeability to about 6700. The effective permeability, Jle is actually the permeability of an equivalent ungapped structure having the same inductance and same dimensions. If there is a varying cross section of the component (such as a pot-core), then special methods are available for determining the effective length, Ie, the ef fective cross section, Ae, and effective volume, Ve, of these shapes by com bining the contributions of each varying section. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 116 4.2.1-Measurement of Effective Permeability The effective permeability can be measured by several different methods. Impedance Bridges which separate the inductive and resistive com ponents of an impedance are generally used for ferrites. The effective perme ability is given by; /-le = LJJ.41tN2Ae [4.2] 4.2.2-Inductance Factor, AL One characterization of the inductance of a component is the induc tance factor AL. It is defined as the inductance of the core in henries per tum or millihenries per 1000 turns. This factor for a specified core can be used to calculate the inductance for any other number of turns, but we must remember that since L varies as N2, so does AL. LN = ALN2/(l oooi for L in millihenries [4.3] LN = ALN2 for L in henries [4.4] The standard AL values for pot cores are chosen from the International Stan dards Organization R5 series of preferred numbers. In this system, the anti logs of .2, .4 .6 .8, 1.0 and their multiples of 10 are selected numbers. Thus common AL'S are 16, 25, 40, 63, 100,160,250, 400 and so on. Some compa nies include AL'S from the RIO series which include antilogs of .1, .5 and .9 and have AL'S of 125,315 and 800. 4.3-GAPPED CORES In low power transformer or inductor applications, gapped cores were used to control the inductance and to raise the Q of the core. Although many ferrite power cores are used in the \"ungapped\" state, either as an E core or pot core without any intentional gap, in some situations, the intentional gap can be quite useful even in power applications. These often occur when there is a threat of saturation that would allow the current in the coil to build up and overheat the core catastrophically. The gap can either be ground into the cen ter post or a non-magnetic spacer can be inserted in the space between the mating surfaces. The gapped core is extremely important in design of filter inductors or choke coils. We shall discuss this application later in this chapter. The basis of the gapped core is the shearing of the hysteresis loop shown in Figure 4.11a and 4.11b where 4.11a represents the ungapped and 4.l1b the 117 CORE SHAPES FOR POWER ELECTRONICS gapped core. The effective permeability, J.le, of a gapped core can be ex pressed in terms of the material or ungapped permeability, J..l, and the relative lengths of the gap, Ig, and magnetic path length, 1m : [4.5] With a very small or zero ratio of gap length to magnetic path length, the ef fective permeability is essentially the material permeability. However, when the permeability is high(lO,OOO), even a small gap may reduce the perme ability considerably. For a power material with a permeability of 2,000 and a gap factor of .001, the effective permeability will drop to 1/3 of its ungapped value. When each point of the magnetization curve is examined this way, the result is the sheared curve shown in Figure 4.11. Ito(1992) reported on the design of an ideal core that can decrease the eddy current loss in a coil by the use of the fringing flux in an air gap. The design includes a tapering of the core at the air gap. The reduction in temperature rise will depend on the oper ating frequency, the gap length and the wire diameter. 4.3.1-Prepolarized Cores Another variation of the gapped core is one that is prepolarized with a permanent magnet. If the transformer operates in the unipolar mode and the polarity of the magnet is opposite to the direction of the initial ac drive, the starting point for this induction change will not be the remanent induction as is usually the case but a point much lower down on the hysteresis loop and in MAGNETIC COMPONENTS FOR POWER ELECTRONICS 118 the opposite quadrant. The flux excursion will be much greater, possibly two or more times higher than the simple unipolar case. Magnetic biasing is old but the extension to this application has been described by Martin (1978) . To avoid eddy current losses, the magnet used may be a ferrite magnet often of the anisotropic variety. Shiraki (1978) reported a reverse-biased core for this purpose. Using a high-energy rare-earth cobalt magnet for the bias, he re duced the volume of the core 56% and the copper wire by a corresponding amount. Shiraki points out that the reverse-biased core has higher inductance near the normal saturation than the unbiased core. With this device, he more than doubled the volt-amp rating of the transformer. Nakamura (1982) re ported a 70% increase in the figure of merit namely the U 2. Thus, size and weight was reduced. The losses were not significantly higher under these conditions. Sibille (1982) also reported on several different geometries to im plement the prepolarized core. Prepolarized cores are especially useful in flyback and inductor appli cations with high DC components. Huth (1986) has described a clever way of biasing a core using orthogonal winding techniques. (See Figure 4.12 ). 119 CORE SHAPES FOR POWER ELECTRONICS 4.4-LOW-PROFILE FERRITE POWER CORES F or low power ferrite applications, the past 5-10 years have seen the introduction of low profile cores in several configurations. One reason for this change is explained in the section in which the permeability is maximizes by having the winding length large and the cross section small. This condition can be accomplished in a low profile or low height core. The other reason (also mentioned in Chapter 1) is the growing use of PC (printed circuit) boards on which to mount the magnetic cores. This method of attaching cores is even more important in the power ferrite area than in the low power tele communications area since PC technology is increasingly placing the power supply for a circuit on the same PC board as the other circuit components. The space between the boards is one half inch so the power ferrite core must be designed to fit in that space with the bobbin and mounting hardware. The availability of low profile cores has been discussed under the sections dealing with the various core shapes. A low-profile EFD core is shown in Figure 4.13. 4.S-SURF ACE-MOUNT DESIGN IN POWER FERRITES The use of surface mount design has been used for low power ferrite applications. The motivation was the development of PC board technology surface-mount design (SMD. As with the low profile cores, the application has been widespread mostly in the power ferrite application. The use of low profile ferrite cores can be complemented to a large degree by surface-mount technology. The two terminal mounting types used for power ferrites are the gullwing and the J-type terminals shown in Figure 4.14. The gull wing form is used when thin wire up to .18 mm in diameter is used. The J-type design is used in wire sizes greater than .8 mm. Surface mount design lends itself to high speed automatic component placement on the PC board. A surface mount bobbin with gullwing terminals is shown in Figure 4.15. The place ment on the PC board is also shown. 4.6-PLANAR TECHNOLOGY Continuing with the low-profile design tendency particularly with PC board mounting has led to a completely new generation of cores called planar cores. Huth(l986) reported on this earlier and now, most ferrite companies offer planar cores in several varieties. Some of the arrangements are shown in Figure 4.16. Either the E-E or E-I configuration is used. The I core is actu ally a plate completing the magnetic circuit. In many cases the windings are fabricated using printed circuit tracks or copper stampings separated by insu lating sheets or constructed from multilayer circuit boards.(See Figure 4.17 ) MAGNETIC COMPONENTS FOR POWER ELECTRONICS 120 121 CORE SHAPES FOR POWER ELECTRONICS In some cases, the windings are on the PC boards with the two sections of the core sandwiching the board. Philips (1998) claims the advantages of this ap proach as; 1. Low profile construction 2. Low leakage inductance and inter-winding capacitance. 3. Excellent repeatability of parasitic properties. 4. Ease of construction and assembly 5. Cost effective 6. Greater reliability 7. Excellent thermal characteristics-easy to heat sink. Yamaguchi(1992) performed a numerical analysis of power losses and in ductance of planar inductors. A rectangular conductor was sandwiched with magnetic substrates. He suggested that the air gap between two magnetic sub strates is an important factor governing the trade off between inductance and iron losses. Sasad (1992) examined the characteristics of planar indutors using NiZn ferrite substrates. A planar coil of meander type is embedded in one of the NiZn ferrite substrates and covered with another with a specified air gap. A buck converter ofthe 10 Watt class was constructed using the inductors with an efficiency as high as 85 percent and a switching frequency of 2 MHz.Varshney (1997) has described a monolithic module integrating all of the magnetic components of a 100 Watt I MHz. forward converter using a plasma-spray process for deposition of the ferrite which serves as the core. Mohandes (1994) used integrated PC boards and planar technology to im prove high frequency PWM (Pulse Width Modulated Converter) performance. Estrov (1986) has described a 1 MHz resonant converter power transformer using a new spiral winding with flat cores that solved eddy current losses, leakage inductance and other problems. He also used planar magnetics and low-profile cores to cut the height and improve converter efficiency from 20 KHz. to 1 MHz. Brown (1992) replaced the traditional copper wire with a winding from the PC board or stamped copper sheet and using a low-profile ferrite core improved the performance and manufacturability of HF power supplies. Huang (1995) described design techniques for planar windings with low resistance. Three representative pattern types were explored; circular, rectangular and spiral. Gregory (1989) has described the use of flexible cir cuits to work with new planar magnetic structures. He claims that printed cir cuit inductors reduce losses and increase packing density making them an ex cellent choice for high-frequency magnetics. Figure 4.18 shows a collection of low-profile and planar cores. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 122 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 124 4.7-INTEGRATED MAGNETICS Bloom (1994) has shown the application of planar-type \"integrated\" magnet ics wherein the transformer and inductor element can be combined on the same core with separate wing. An example of this technique is shown in Fig ure 4.19. The use of folded windings on printed circuit boards with flexible fold lines is shown in Figure 4.20. 125 CORE SHAPES FOR POWER ELECTRONICS 4.8- CORE SHAPES FOR METAL STRIP MATERIALS Metal strip materials as discussed here for power electronics applica tions include; 1. Thin gage Si-Fe alloys (0.001-0.004 inches) 2. NiFe Alloys (Permalloys) 3. CoFe Alloys (Supermendur) 4. Amorphous Alloys 5. Nanocrystalline Alloys The shapes of the into which these alloys are formed are; 1. Tape-Wound Cores 2. Tape-Wound Cut Cores 3. Stacked Laminations For the power electronic applications, stacked laminations are rarely used since the metal thicknesses of laminations are normally greater than those compatible with high frequency operation. In addition, with the amorphous and nanocrystalline materials, their hardnesses make it economically unat tractive to punch because of die wear. For lower frequencies and higher power, cut cores can be used successfully because of the lower winding costs of cut cores compared to tape-wound cores. That leaves the bulk of the usage of metal strip components for power electronics to tape wound cores. Unlike ferrites whose inherent magnetic properties for a single material are the same regardless of shape or size, core properties of a specific strip wound core are dependent on strip thickness. This condition arises from the lowering of high frequency Eddy Current losses as the strip thickness is decreased. In addition, the so-called \"stacking factor\" or ratio of volume of metal to volume of wound core must be accounted for in flux density consideration. 4.9 CORE SHAPES OF METAL POWDER COMPONENTS Metal powder core components of a specific base chemistry are clas sified according to permeability. The permeability of a particular material is determined by the physical properties including particle size, amount of insu lation and pressed density. There are two main shapes of metal powder core components. They are; I. Toroids 2. E-Cores MAGNETIC COMPONENTS FOR POWER ELECTRONICS 126 Although, traditionally, toroids have been the shape of choice since the low permeabilities of powder cores are additionally lowered by a gap. However, in recent years, there has been growing usage of the E-core design. Here again, the motivation has been the elimination of costly toroidal wind ing. SUMMARY This chapter has listed the shapes that are commonly used in compo nents for power electronics. The next chapter will discuss the techniques that are used to determine the optimum size of the component. As such the mater rial and component parameters will be integrated into the circuit requirements. References Bloom, 0.(1989) Powertechnics April 1989, 19 Estrov, A. (I 989) and Scott,!., PCIM, May 1989 Huth, J.F. III, (l986)Proc. Coil Winding Conf. Sept. 30-0ct. 2, 1986 Magnetics (1987) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Martin, W.A.(l978), Electronic Design, April 12,1978, 94 Nakamura, A.(l982) and Ohta, J.,Proc. Powercon 9,C5, 1 Shiraki, S.F.(1978), Electronic Design, ~ 86 Sibille,R. (1981), IEEE Trans. Magnetics, Mag.22 #5,Nov. 1981,3274 Sibille, R.( 1982), and Beuzelin, P., Power Conversion International, 1982, 46 Chapter 5 CORE SIZES-DESIGN CONSIDERATIONS IN POWER ELECTRONICS INTRODUCTION The last few chapters, the choices of components for power electron ics were considered based on the circuit topology, component function, mate rial and shape. This chapter will be concerned with the selection of the size of the core. First consideration will center on satisfying the electrical input re quirements with regard to input and output voltages and currents, followed by efficiencies, regulation, temperature-rise and safety requirements. The first section will concentrate on output transformers and output inductors, followed by common-mode chokes, EMI suppression cores and magnetic amplifier components. The appendices will deal with design examples for the various functions. S.l-DETERMINING SIZE OF THE TRANSFORMER CORE Years ago, transformers were designed by using cut-and-try methods involving many modifications and final optimization. Such techniques are time-consuming and ineffective procedure and although some use of them remains, many design aids have been established to assist the designer in at least a close fit to the required circuit with only some minor adjustment needed. Several schemes of sizing the core and completing the circuit design are presented in this chapter. The first approach is the use of the core area window area product that has been adopted by many manufacturers of power magnetic components. These vendors correlate the area products with certain core sizes and materials. Variations of the product area have been used by the manufacturers or authors in books. The next approach involves the use of other power specifications offered by the vendors. These may include the core losses for the cores (either per cc or gm), the core surface areas and the ther mal resistances. In many cases when not all the input and output conditions are specified, some reasonable assumptions will be made in the initial desig nation of the core size. Since no universal scheme for sizing the core has yet emerged, the variety of different methods will be discussed. 128 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 5.l.l-Initial Considerations in Designing a Power Transformer Core In the design of a core for a power transformer used in SMPS con verters, we must take into account the input current requirements to provide the ac field to drive the core to the proper B level. This will be determined by the following equation; H= .4nNIII [5.1] In strict operational terms, the NI of the primary winding will provide the flux variation to induce the necessary secondary voltage. This voltage is related to the operating conditions by the following equation; E = 4.44 BNAfx 10-8 [5.2] for sine wave with the coefficient changing to 4 for square wave. Although part of the dimensions (cross sectional area) of the magnetic core is related directly to the flux requirements imposed by the second equation, all the windings in a power core are contained inside the core. This includes the pri mary turns, Np, determined by the magnetizing current equation and the sec ondary turns, Ns, given by the induction equation. These windings are con tained either inside the window of the toroid or a U or E core or are on a bob bin surrounding the center post in a pot core. Consequently, the size of the window or bobbin winding space does directly affect the overall size of the core. Therefore, it is these two requirements that are related in the design de termining the shape and size of the core. In other words, the flux equation contains the cross sectional area of the core. The NI requirements must be met by a certain number of turns each having a certain capacity to carry a current I. Achieving a higher current may allow only a few turns with a larger cross sectional area per tum as opposed to a design carrying a larger number of turns with a smaller cross sectional area per tum. It is the product of the NI which is a measure of the total copper cross sectional area and which will determine the window area. Therefore, there are two areas that will at first determine the size of the core. One criterion used for years by design engineers is the product of these areas that is called the Area Product, Ap, (Magnetics 1987) described by; Ap = WaAc (cm4) [5.3] Where; Ap = Area Product Wa = Area of the window (cm2) Ac = Area of the window (cm2) Of course, the Ac is the area transverse to the flux and the Wa is the area transverse to the current flow. The area of the window is not completely us able because of the space between the wires and also the insulation thickness. Therefore, we introduce a copper-filling factor, K, which is the fraction of the CORE SIZES- DESIGN IN POWER ELECTRONICS 129 window containing the copper. The total cross sectional area of the copper is given by; Acu =NAw where; Aeu = area of copper (cm2) [5.4] Aw = Cross sectional area of the copper wire, cm2\u2022 Therefore, the copper filling factor, K, is; [5.5] N=KWjAw [5.6] If we multiply by Ae, we get; [5.7] Now, from Equation 2.2 for a square wave; [5.8] Setting the two equations equal and rearranging; WaAe = EAw x 108/4BfK [5.9] The area of the wire is related to its current- carrying capacity by one of sev eral analogous factors. Traditionally, electrical engineers have spoken of wire sizes in circular mils instead of cm2 (possibly because the number is quite small in cm2). A circular mil is the cross-sectional area of a wire whose di ameter is 1 mil or .001 inches. The area is then .7854 square mils or 5.0671 x 10-5 cm2 \u2022 Therefore, to convert from a Aw or possibly a Wa in cm2 to circular mils, divide the circular mils by this last number. If, as is a common practice, the current carrying capacity of the wire is given in terms of C in circular mils/ampere, the relevant equations are; C=AwfI Circular mils/ampere [5.10] Then; Aw=IC [5.11 ] The input power, Pi is Pi=EI [5.12] If we further define the efficiency; [5.13] Where; Po = Output power 130 MAGNETIC COMPONENTS FOR POWER ELECTRONICS We can then relate the output power, Po to the Area Product, Ap; VlaAc = PoCxl08/4BetK [S.14] If some assumptions are made about C (800-1000 circular mils/amp), e at about 80-90%, and K (about .2-.3) we can simpify the equation. Note that the K value is only the copper-filling factor only for the primary that normally occupies about SO% of the winding space. The rest is occupied by the secon dary winding. Based on these assumptions, we arrive at an equation relating Po to operating conditions with a single constant, k1; [S.1S] If the B level is set at 2000 Gausses, families of curves relating the output power, Po to the Area Product, WaAc, can be generated as shown in Figure S.I. The various cores having the corresponding WaAc values are also shown. The Po calculated from this equation is compared to the measured values in Table 18.2. The agreement is quite good. The WaAc ranges can also be corre lated to the temperature rise of the core in operation. The table below from Magnetics Catalog(2000) gives an approximation of the temperature rise that can be expected. CORE SIZES- DESIGN IN POWER ELECTRONICS 131 S.1.2-0ther Area Product Relationships McLyman (1982) points out a similar relationship between the area product, Ap, to the power handling capability as well as to several other important pa rameters used in transformer design. For current carrying capacity, a new constant, Kj is introduced making his equation; Ap = (Pt x 104/KrBmfKuKjY where: Kr = wave form coefficient = 4.00 for square wave [5.16] = 4.44 for sine wave Ku = window utilization factor as previous K Kj = current density coefficient related to copper losses x = exponent related to geometry (for pot cores, x = 1.2) Bm = Maximum induction in Teslas (Note the change from Gausses. (1 Tesla = 104 Gausses) 132 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 5.1.3-Voltage Regulation in Transformers McLyman(1982) has also developed a new criterion and design method for transformers and inductors where the so called \"regulation\" is an important consideration. Smith (198S) describes regulation as \"the variation in voltage from no load to full load expressed as a percentage\". Thus, regulation of S% means that S% of the input voltage is dropped across the series resis tances and reactances and the balance is transmitted to the load. McLyman (1982) combines the power handling ability and the regu lation by relating them to two constants, one a function of geometry and the other related to magnetic and electrical operating conditions. The equation is: [S.17] where Pt == apparent power a == regulation in percentage Kg == geometry coefficient Ke == electrical coeffecient The apparent power, Ph is the sum of the input power, Pi, and the output power, Po; [S.18] With a given efficiency, TJ , and in the typical D.C.-D.C Converter, the equa tion becomes; Pt == Po {..j2iq +..fi} [S.19] The geometry constant, Kg is given as; Kg == WaAc2K/ML T where ML T == Mean length per turn [S.20] Rather than using circular mils for the wire size, Aw and window area, Wa. these units are each given in cm2\u2022 The constant Ke or the electrical constant is given by; Ke == 0.14S K/fBm2xI0-4 [S.21] (B is in Teslas or Wb/m2) The current density, J, in Alcm2 is given by; [S.22] CORE SIZES- DESIGN IN POWER ELECTRONICS 133 McLyman gives an example of the Kg approach in the design of a transformer for a single-ended forward converter. It is shown in Appendix 2. This ap proach may appear long and and requires data which may not be in the manu facturers catalog. Fortunately, McClyman has supplied a compilation of the needed data in his books( 1982,1988) . Grossner (1983) has also called attention to the dependence of Po on the area product. He uses the same approach as previously discussed with several geometrical coefficients to approximate the output power, Po. Grossner is more concerned with the temperature rise in the calculation that is expressed as; where; resistance [5.23] C2 = a constant involving core and winding fractions and wire h = Coefficient of heat transfer e = Temperature rise ~ = Geometrical constant involving surface area, magnetic path length and wire length per turn Thus, Grossner concludes that the power level is more responsive to increases in frequency and flux density than to an increase in the temperature rise. In practice, f is defined by the circuit and B is limited by the core material. With Band f fixed, keeping a small size and a high power level are aided by oper ating at the highest possible temperature rise. Because circuits may be de signed to optimize different requirements, Grossner develops the parameters, gl - gs, which in some combination will lead to optimization of power, induc tance, and optimum power. Smith (1985) uses the area product as a design criteria, but reduces it to Normalized core dimensions so that any size core can be calculated. Another author using the WaAc approach is Pressman (1977). Here the tables of the supplier are used to approximate the core for the power level required. DeMaw (1981) approximates the temperature rise in a core as; Trise = SOP/Po [5.24] Where Po is not the output power as previously used but the power dissipation level within a specified core that will cause a 50\u00b0C temperature rise. Pt is the total power dissipated in an inductor including core loss and winding loss. The core loss data can be obtained from the manufacturing catalog while the winding losses can be estimated by formulae. 134 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Watson ( 1986) also uses the Area product and McLyman's Kg method but derives equations based on two kinds of current density, rms and instanta neous. This distinction is important for flyback transformers. Although the WaAc approach is merely a starting point in the design, many other factors may have to be considered in finalizing the design. With ferrites in power supplies some of these factors are as follows; I. Max temperature of the core \u00ab100\u00b0C.) 2. DC imbalance 3. Magnitude and linearity of magnetizing current 4. Magnitude of transient current 5. Under transient loading, need to limit Bm to avoid saturation 5.1.4-0ther Transformer Design Techniques Snelling( 1988) has divided the design of power transformers into several dif ferent categories. They are: I. Winding loss limited 2. Saturation limited 3. Regulation limited 4. Core loss limited 5. High frequency limited Items numbered 2-5 are discussed previously. Snelling has added the other two. He discusses them each separately, stating that, in general, they come into playas the frequency of operation increases. 5.1.4.1-Winding-Loss-limited Design This is almost the same situation we have been discussing using the WaAc approach or the wire current density approach. As in the previous cases, there is also some limit on the B level. However, here the only real source of dissipation is the winding loss and, depending on the size of the transformer, the treatment is only applicable to a frequency of about 5-10 KHz. The equa tion for the input power, Pi , Snelling(l988)gives as; Pi 2 = PwfB/lmk) [5.25] Where; m = Fractional increase in the resistivity of the copper over that at and; CORE SIZES- DESIGN IN POWER ELECTRONICS lw= mean length ofa tum of the winding F w = Winding factor ofthe copper 5.1.4.2-Regulation-Limited Design 135 In this category, the regulation can be a constraint on the winding loss listed above. Again, the winding loss is really the only source of dissipation, that is, the core loss, Pc is much smaller than P w at these frequencies. The voltage regulation, ,is given as [5.26] Then; Pi = (fB/almkl )xlOO [5.27] Since the core loss is negligible, we can ignore it and the output power is given by; Po = Pi-Pw = Pi[l- al100] = fBe2(a- .01a 2)/mkl xl00 [5.28] [5.29] B/ is limited by the saturation flux density of the material. The other pa rameters are given so that k\\ can be calculated. Snelling (1988 ) presents a table of the values of k\\ in his book for many power core sizes in so that the choice can be made. Most ferrite transformers are not regulation limited. 5.1.4.3-Saturation-Limited-Design As the flux density increases, the hysteresis curve will flatten out as saturation is approached. When this happens, the incremental permeability drops sharply. In this case, the impedance (or inductive reactance) becomes quite small and the current, therefore, increases. See Figure 5.2. The manu facturer will often give limit values for the maximum flux density that the designer should not exceed. Since the saturation drops at higher temperatures, the saturation value at the operating temperature should be examined in this regard. For operation at 100\u00b0C., the value of 3200 gausses would be a real maximum. The constant k\\ is still a valid constant for saturation-limited designs. Since the efficiencies at these lower frequencies are close to 100 percent, the output power, Po, can be considered the same as the input power, Pi- There fore; 136 MAGNETIC COMPONENTS FOR POWER ELECTRONICS [5.30] If the flux, <1>2, is used instead of B/, the factor k2 is used where k2 = k1A/. If core loss is included in the saturation limited case, the equation for the square wave drive becomes; Po={Pt-Pc)ll2k3FwI/2f Watts [5-31] where; Pt =Total Losses = P w + Pc [5-32] Pt is also listed in Snelling's (1988 )Table 9.3. At low frequencies, the core loss is less than half the total loss and so may be set to 0 especially because of the square root dependence. [5.33] Again, Snelling lists the values of k2 and k3 in Table 9.3 of his book (1988). In addition the value of Pt which is the sum of all the losse (winding and core) is also given in the same table. The permitted temperature rise in this table is 40\u00b0C. If the proposed temperature rise is different, the new value of Be or can be recalculated from the thermal resistance, ~. At low frequencies, where core loss is a small fraction of the total loss, the output power is proportional to f. If the operating variables such as fre quency, temperature rise and copper factor are assumed, the power handling values for a given core can be given. Most manufacturers provide such infor mation. The values of Po are similar to the ones derived earlier from the area product technique. 5.1.4.4 -Core-Loss-Limited Design Traditionally, design of a transformer is optimized by making the winding losses equal to the core losses. It has generally been taken as a de vice. Other calculations place the division as; [5.34] When n=2, the two losses are indeed equal. However at higher frequencies, the value of n is between 2 and 3. For core loss limited designs assuming the output power, Po, is equal to the input power, Pi, the equation for the core loss, Po, for a square wave is; CORE SIZES- DESIGN IN POWER ELECTRONICS 137 Po = [P.I(1 +2/n)] 112 x k3Fwl/2f ~p-p [5.35] where K3 is defined as before. With PI and k3 given in the table, the output power can be given in the case of a core-loss limited design. To check the flux density, the manufactur ers' graphs showing core loss as a function of frequency and flux density can be consulted. When PI is known, the core loss can be estimated from the pre vious equation or just set to 112 PI' From this core loss and the operating fre quency, the B value can be read off the graph. If there is a varying cross sec tional area of the core, the equation is modified as such for square wave; P (1+2/n)II2]/2fBF 112 = P A 1m I ]112 X A . = Ir owl wi w mm ~ [5.36] The values for ~ are also tabulated in Snellings Table 9.3. Based on the input design specifications, ~ and B can be calculated from the minimum area and a core can be chosen. For the division of losses, a value of 2.5 is typical. For a fully-wound transformer, Fw can be set at .5. With these assumptions, ~ can be written as; and ~ = O.845PoIfB for sine wave ~ = O.949PoIfB for square wave [5.37] [5.38] 138 MAGNETIC COMPONENTS FOR POWER ELECTRONICS The manufacturers' data is certainly a good way to check the core loss as sumptions. These design methods are useful in initially picking a core and modifications must be made if one or more condition is not met. S.1.S-Power Ferrite Design from Vendors' Catalogs The vendors of ferrite cores have proposed several different design schemes. The one used in the Magnetics Catalog( 1987) has been discussed. Design methods described by other ferrite vendors are: 5. 1.5. I-Philips-(Yageo) In the case of Philips catalog, the throughput power, Po, information is supplied in the form of graphs of the Po and output voltage, Vo for each type of converter. Such a graph is shown in Figure 5.3. In addition, the perform ance factor (f x BmroJ is graphed as a function of frequency for their power ferrite materials. A graph of this type is given in Figure 3.11. 5.1.5.2-Epcos (Siemens) Epcos lists the output powers for each power shape in several power materials and for each converter type. The output powers are given at a typi cal frequency and a cut-off frequency for each material. A portion of this table is given in Table 5.3. The material-specific values on which the table values are based were taken from the maximum temperature rise for each material given in Table 5.4 and the thermal resistance for each size and shape of core that is listed in Table 5.5. The total core losses are related to these factors by ; PV,tot == i1TlRtb [5.39] The values of output power are obtained from the following formula; Where PF = Performance factor P v == Specific Core Loss CORE SIZES- DESIGN IN POWER ELECTRONICS ~ T = Temperature Rise oK Rth = Thermal Resistance fcu = Winding Factor PCu = Wire Resistance. AN = Winding Cross-Sectional Area Ae = Core Cross-Sectional Area IN Winding length Ie = Effective Magnetic path length 139 The assumption is made that the temperature rise and the losses in the core are evenly distributed. The application area for flyback transformers were re stricted to 150 KHz .. The overtemperature, ~ T is the sum of the temperature rises resulting from the core and winding losses. The maximum flux densities were <200mT for flyback converters and <400mT for push-pull converters. 140 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Table S.3-Power handling capabilities of various shape cores & materials Power capacities Push-pull Single-ended Ryback converter converter converter C= 1 ' ) C=0,71 ' ) C =0,62 ' ) Core shapes Mate- Version ftyp fcuIDII P'rons P'rans P'rans P'rons Ptrans Ptrans rial (LP=Low (~) (fculDff) (ftypl (fcutoll) (ftyp) (fClJIOff) profile) kHz kHz W W W W W W EFD2511319 N59 Nonna! 750 1500 311 417 221 296 193 258 N49 500 1000 196 263 139 187 122 163 N67 100 300 175 280 124 199 109 173 N87 100 500 242 482 172 342 150 299 EFD3OI1519 N59 Nonna! 750 1500 401 343 285 244 249 213 N49 500 1000 253 544 180 386 157 337 N67 100 300 226 365 160 259 140 227 N87 100 500 312 630 221 447 193 390 U cores Ul511116 N27 Normal 25 150 31 81 22 58 20 50 .... U17/1217 N27 Normal 25 150 37 97 26 69 23 60 U2011617 N27 Normal 25 150 74 161 52 114 46 100 U25120113 N27 Normal i 25 150 198 432 141 306 123 268 UU93I15213O N27 Normal 25 150 2527 5508 1794 3910 1567 3415 1) NI.IT1III1eaI data are staIad in IICCOIIIanc8 with the publication \"Ellact althe ~ ~ on the ohape and dirnenaiOnS allnInsform- 8IBandchokes in_power supplies\", G. RoeepeI, Siemens AG M~ J. 01 Ms!11. and Magn. _189(1978) 1~ From Siemens (1998) Table S.4- Maximum Temperature Rise and Typical and Cut-off fre quencies for various ferrite power materials aTmax ftyp 'cutoff K kHz kHz N59 30 750 1500 N49 20 500 1000 N62 40 25 150 N27 30 25 100 N67 40 100 300 N87 50 100 500 N72 40 25 150 N41 30 25 100 CORE SIZES- DESIGN IN POWER ELECTRONICS 141 Thomson(1988) presents charts of average wattage for the various size and shape power cores listed according to inverter type. The frequencies are 25KHz(2000 Gausses), 100 KHz(1000 and 1200 Gausses). 5.1.5.4-TDK TDK lists the calculated output power under the specifications of each type of power core. These power levels are given at 50 and 100 KHz for their standard power materials. These power levels are given for the forward converter mode. TDK also gives the power losses for each power core. The conditions are 25 KHz(2000 Gausses) and 100 KHz(200&- Gausses). In an older catalog, the temperature rise was also plotted against the power loss for each core. See Figure 5.4. 142 MAGNETIC COMPONENTS FOR POWER ELECTRONICS I . .1. ~-'----'----i ,G' Note N11tTrvt ~ fMoptWfl 'o\\I1Ie/'Io lI\u00bb.J'Oh'IO GunMf q: 2OGI- _ffd of the transistor switch, using a feedback system from the output. The result is a regulated DC output, expressed as: [5.57] The off time of the transistor switch is related to the voltages by !off = (l-Eou/Eirunax)/f [5.58] For Einmin: fmin = (l-Eou/Einmin)/toff [5.59] If we assume the ripple current, i, through the indictor to be equal to 21 Omin, the inductance is; L = Eout!ortl Lli [5.60] The ferrite core to supply this inductance can be obtained by again calculating the U 2 product and using the charts such as the one shown in Figure 5.16. CORE SIZES- DESIGN IN POWER ELECTRONICS 153 From the intersection of the LI2 with one of the core lines, the appropriate AL can be read. In this case it is convenient to refer to the standard gapped cores available under each core's description. The number of turns can be calculated from; The wire size is chosen from the wire tables using a current density of 500 circular mils/amp. An example of this method from the Magnetics Catalog is shown in Appendix D. An approach given by Jongsma (1982a) and contained in the Philips Catalog is shown in Figure 5.16. The LI2 is plotted against the spacer thick ness or center leg gap-width for a series of different core shapes and sizes. When a core supplying the required Lf is chosen, reference is made to the data for the individual core chosen. 154 MAGNETIC COMPONENTS FOR POWER ELECTRONICS The specific graph of LJ2 versus spacer thickness for that core is given for various choke designs (depending on the IaJlo ratio). A graph of this type is shown in Figure 5.17. On the same graph, the curve of LJ2 versus AL for that particular core is given. For the particular LJ2 chosen, the intersection with the line for the converter is found. The working point must be below this line. A vertical can be dropped to the spacer thickness axis and from the tolerance on the spacer thickness, !>min and !>max can be chosen on the axis. These lines can be extended to the AL curve for the converter type. The two intersections when read across to AL (to right hand scale) will give the limits of AL. To avoid saturation Nmax is given by; [5.62] CORE SIZES- DESIGN IN POWER ELECTRONICS 155 To achieve Lmin, the Nmin is given by; [5.63] An integral number of turns is chosen. The winding procedure can be com pleted as outlined under transformers or if special considerations are needed, the design by Jongsma is recommended. 5.7.2-McLyman Treatment ofInductor Design Following a treatment similar to the one used for transformers, McLy man(1982) employs the Kg constant. The applicable expression is: a = (Energy)2/KgK., [5.64] j.!H A2 156 MAGNETIC COMPONENTS FOR POWER ELECTRONICS where a and Kg have been defined under the transformer calculation. The energy in an inductor is given by Energy = 112 U 2 [5.65] The Ke constant is varied somewhat from the transformer equation. It is rep resented by: [5.66] The area product approach can also be used for inductors: The fraction, Ku, of the available winding space that will be occupied by the copper is given by [5.68] where S) = conductor area/ wire area S2 = wound area/usable window area S3 = usable window area/window area S4 = usable window area/ usable window area + insulation The design of an inductor using McLyman's approach is given in Appendix 5. 5.7.3\"-Flyback Converter Design Previously, we stated that the design of a tlyback converter is similar to that of a power choke or inductor because in both cases, the energy is stored in the inductor during the current rise period and released when the current is turned off. If the converter is a simple non-isolating type (no trans former coupling as shown in Figure 18-6), the design (Jongsma 1982) is treated as a power inductor where; Lmin = 9 Omin vimaxf and: [5.69] 1m = Idcmax +21ac [5.70] = (Pel omax Vimin) + ( omax V imin/2tL) [5.71] With the calculated values of Imax and Lmin. the design can then be completed using the power inductor methods. If however, there is transformer coupling as shown in Figure 1.9, the turns ratio must be controlled to avoid damage to the semiconductor switches. Jongsma gives the limiting equations in this case as; CORE SIZES- DESIGN IN POWER ELECTRONICS 157 Ferrite DC Bias Core Selector Charts ,-I_ --1100 \",.~ _eo.. ..... ,- -. . ..... \" .. ,- C-4121J ........ Do4Mn -_. l - ~. L_ ~ -l! - - \u00a7 700 ... ~ 100 !. 100 i -JU .. 200 ,. '00 .en ....... .. ., .. .. . , .... , \u2022 \u2022 \u2022 I \u2022 l' .. ... . \u2022\u2022 LP (m4I11/OUIM) PQCoNe ... 1200 1100 poc.. - (I'Q 2IW2III ... -(l'Q1IIK) ~ (I'Q JIIIO) .. - - (I'Q UIIII) e-(l'QMIM) E ~ (I'Q t114II) a 100 \u00a7 700 A ... ... % 100 !. 100 -I \u2022 -... .. -'. 100 .I, . ...... . .. . ..J \u2022\u2022 .... ' \u2022 \u2022 , \u2022\u2022 t \u2022 \u2022 ..... , . UI (mllll/OUIM) Figure 5.15- A Graph showing the AL needed in a particular core to furnish a specific Le. From Magnetics Catalog (1989) 158 MAGNETIC COMPONENTS FOR POWER ELECTRONICS CORE SIZES- DESIGN IN POWER ELECTRONICS For VimaxNimin <2 r = 3/7 {VimaxNo+VF+VI0} [5-72] Where, VF = Voltage drop across the output choke and VR = Voltage drop across the rectifier 159 We see then that not only the characteristics of the magnetic devices must be considered but also the voltage drop and current distribution in many of the auxiliary circuit elements. Because of this, when completing the design of these and other magnetic components, the reader is advised to consult the many books, vendors' literature and various periodicals that deal with this subject. 160 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 5.S-SWINGING CHOKE We have spoken of the use of the air gap and the prepolarized cores as techniques in the design of power inductors. Another such design variation that is used to improve the regulation and efficiencies of choke is called the swinging choke or divided gap choke. This is described by Keroes( 1969), Martin(l982) and by Snelling(l988). The action is non-linear as shown in Figure 5.l8. The use of the stepped gap (Figure 5.l9) allows for a wide swing of D.C. currents or magnetic fields. At low D.C. levels, the ripple current is a large part of the total current so a high inductance is needed and is provided by the small gap. However as the D.C. level increases, the ferrite at the small gap will saturate and the large gap will take over, protecting the circuit and main core from saturation and overheating. Thus, a dual action is accom plished. CORE SIZES- DESIGN IN POWER ELECTRONICS 161 5.9-MAGNETIC AMPLIFIER-MULTI-OUTPUT DESIGN In a multi-output power converter, it is often important to control one or more of the outputs independently. One method of doing this is by using a core having a square-loop material as a magnetic amplifier. As pointed out by Snelling (1976), this delays the leading edge ofthe secondary circuit 'on' pulse by an amount depending on the re-set condition. The re-set condition determines the amount of volt-seconds needed to drive the core to saturation. When saturation occurs, the inductance falls to a low value and the energy transfer can commence. Appendix 5.1 Design Example ofMcLyman Kg Approach The following section is abstracted from Magnetic Core Selection for Trans formers and Inductors by Colonel Wm. T. McLyman, Marcel Dekker, New York, 1982 Single-Ended Forward Converter Design The following parameters are given: Input voltage (Vin) = 140 V min Output voltage(VoutF 10 V Output current (10) = 5.0 A 162 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Frequency(f) = 20 KHz Switching efficiency= 90% Regulation = 1.0% Ferrite toroid matl.= 5000Jl (Magnetics) The design steps used can be summarized as follows 1. Calculate output power which is equal to (Vout + V(diode drop\u00bbX (10) = (10 + 1)5 = 55 Watts 2. Calculate the apparent power using Equation 5.19 Pt = Po{..j2iq +.fi} = 55 {1.411.9 +1.41} = 164 10 % is added to the apparent power for the demagnetizing winding; P.(l.l) = 180 Watts 3. Calculate the electrical conditions assuming Bm =.2T and square wave (KF4.0) using Equation 5.20 K., = 3712 , 4. Calculate Kg = P.l2K.\" using Equation 5.21 Kg = 180/2(3712) =.0242 Kg is then recalculated for additional insulation because of the high voltage between primary & secondary windings. Kg= .03025 5. Select a toroid from McLyman's table (Table 11.5) with the comparable Kg and record the data regarding the toroid. Magnetics 52507, Kg = .0352 6. Calculate primary turns, Np, using Equation 2.2 using coefficient 4 for square wave in place of 4.44 for sine and using Teslas for the units for Bm (1 T =104 Gausses). Np = Vp x 104/ KrfBmAc = 140 x 104/4 x.2 x 2 x 104 x .393 = 222 Np = Nm (Demagnetizing winding) 7. Calculate primary current, Ip using a duty cycle, D, of .5 and a switching efficiency,,,, of .9. Ip = Po/DVp\" = 55/(.5 x 140 x .9) = .873 A. 1m = Ip x.l = .0873 A. 8. Calculate current density, J, from Equation 5.22. Use Ku (Window Utiliza tion Factor) =.4 J= 380 9. Calculate bare wire size Aw(B). For forward converter, Ip and 1m must be multiplied by .707 Aw(B) = Ip(.707)/J =(.873 x .707)/380 = .00162 CORE SIZES- DESIGN IN POWER ELECTRONICS 163 Aw(B) = Im(.707)/J =(.0873 x .707)/380 = .000162 10. Select wire size from table AWG #25 has bare area of.00162 J,lfiIcm = 1062 11. Calculate primary winding resistance, Rp Rp = (MLT)(N) x J,lfiIcm. = 3.3 x 1062 x223 x 10-6 = .7810 12. Calculate primary copper loss. Pp P p = (Ip x .707 i R, = (.873 x .707) x .781 = .297 Watts 13. Calculate secondary turns, Ns Vs =( Vo + Vd)ID = (10 + 1)/.9 = 22 Ns=Np VJVP = (223X22)/140 = 35 Turns 14. Calculate bare wire size, AW<:B) for secondary Aw(B) = 10(\u00b7707)/J = (5)(.707)1380 = .00930 cm2 15. Select wire size from table A WG Wire with area of .00823 cm2 J,lfiIcm = 209.5 16. Select secondary winding resistance Rs = (MLT)(NXJ,lfiIcm) = (3.3)(35X209) x 10-6 = .02420 17. Calculate secondary copper loss, P s Ps = (10 x .707i Rs = (5 x .707)2 .0242 = .302 Watts 18. Calculate transformer regulation a. = P cu x 100/(Po +P cu) where P cu = sum of primary and secondary copper losses = (.297 + .302) = .599 Watts = (.599 x 100)/ (55 + .599) = 1.08 % 19. Calculate core loss, P e from core loss curves and core weight. 164 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Pfe = (Milliwatts/gm) Wfe X 10-3 = (20)(12.1) X 10-3 = .242 Watts 20. Calculate Total Losses PI: = Peu + Pfe = (.599) + (.242) = .841 Watts 21. Calculate efficiency for transformer e=(Po xl00)/(Po +PI: ) = [(55) X 100]/(55 + .599) = 98.9% 22. Calculate WattslUnit Area from surface area of core. 'P = PI: 1 At = (.841 )/33.4 = .025 Watts/cm2 A value of.03 Watts/cm2 normally gives a 25\u00b0C. rise. APPENDIX 5.2 The following section is abstracted from the Magnetics Catalog FC405, pub lished by Magnetic, Division of Spang and Co., Butler PA 16001, 1987 Magnetics Inductor Design Method using Hanna Curves Example - The following example illustrates the use of a Hanna curve to find the core for a particular power inductor. Let L = .1 mH and IDe = 10 amperes. Find the core, the air gap and number of turns required. I. Calculate U 2 Le = (.1 x 10-3) x (10i = lOx 10-3 2. Refer to Hanna Curve in Figure 5.16. Assume (Ui/V = (from center of vertical scale). 5 X 10-4 3. Core Selection- Choose a core geometry, for example an E core, and se lect a size with the volume nearest to 20 cm3\u2022 Use P45021-EC. CORE SIZES- DESIGN IN POWER ELECTRONICS 165 Volume = 21.6 cm3,le=9.58cm,Wa=.351 x 106 circ.mils 4. Recalculate Le/V = 10 xlO-3/21.4 = 4.6 x 10-4 5. Determine Hand l.jle from the Hanna curve (P material),using recalcu lated value of LeN. H=18 and l.j/e = .006 6. Calculate N H =.4 NIII, N = HV.4 1= 13.7Turns-Use N=14 7. Calculate Wa needed. For loe = 10 amperes, use A W G # II wire. Wa = 9 X 103 cir. mils per turn Wa needed = Aw x NIK where Wa = core or bobbin window area Aw = cross sectional area of the wire N = number of turns K=winding (or space utilization) factor (K varies with the designer and operating conditions of the inductor. Typically, this factor is 0.4). Wa needed = (9 x 103) x (14/0.4) = 315 x 103 circ. mils 8. Compare Wa values Wa needed = 315 x 103 circ. mils Wa available in 45021-EC = 351 x 103 circ. mils At this point, the designer can use the core selected or repeat this process to select a smaller (or larger) core. 9. Gap calculation. If the P-45021-EC core is chosen, the air gap is calcu lated as follows. l.jle = .006, Ie = 9.58 cm. 19 = .006 x 9.58 = .057 cm.(.023 in.) APPENDIX 5.3 Magnetics Inductor Design for SwitclBng. Regulators The following is abstracted from Magnetics Catalog FC405, published by Magnetics, Division of Spang & Co.,Butler, PA 16001, 1987 Only two parameters ofthe design application must be known: (a) Inductance required with DC bias (b) DC current 166 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 1. Compute the product of U 2 where: L = inductance required with DC bias (millihenries) I = maximum DC output current = lomax + i 2. Locate the U 2 value on the Ferrite Core Selector charts such as the one shown in Figures 5.16. Follow the U 2 coordinate to the intersection with the first core size curve. Read the maximum nominal inductance, AL, on the Y axis. This represents the smallest core size and maximum AL at which satu ration will be avoided. 3. Any core size line that intersects the U 2 coordinate represents a workable core for the inductor if the core's AL value is less than the maximum value obtained on the chart. If possible, it is advisable to use the standard gapped cores because of their availability. These are indicated by dotted lines on the charts and can be found in the catalog. 4. Required inductance L, core size, and core nominal inductance (Ad are known. Calculate the number of turns using N ~ 10' ~ L AL where L is in millihenries. 5. Choose the wire size from the wire tables using 500 circular mils per amp. Example - Choose a core for a switching regulator with the following re quirements: Eo = 5 Volts eo =.5 Volts lomax = 6 amp lomin = 1 amp Einmin= 25 Volts Einmax= 35 Volts f=20KHz. 1. Calculate the off-time and minimum switching, fmin, of switch using equations 5.58 and 5.59. toff = (1-Eou/Einmax)/f toff = (1-5/35)/(20,000) = 4.3 x lO-5 sec. fmin = (1-Eou/Einmin)toff the transistor CORE SIZES- DESIGN IN POWER ELECTRONICS fmin = (1-5/25)/(4.3 x 10-5) = 18,700 Hz. 2. Let the maximum ripple current, i, through the inductor be Lli = 2Iomin Lli = 2(1) = 2 Amps 3. Calculate L using Equation 5.60. L = (Eout x !off)/ Lli L = 5(4.3 x 10-5)/2 = .107 millihenries 167 4. Calculate the value of the capacitance, C and maximum equivalent series resistance, ESR max C = il8fmin Lleo C = 2/8(18700)(.5) = 26.7 J.I. farads ESRmax = Lleo / Lli ESRmax = .5/2 = .25 ohms 5. The product ofLf = (.107) (8i = 6.9 millijoules. 6. Due to the many shapes available in ferrites, there can be several choices for the selection. Any core size that the U 2 coordinate intersects can be used if the maximum AL is not exceeded. Following the U 2 coordinate, the choices are: (a) 45224 EC 52 core, AL315 (b) 45015 E core, AL250 (c) 44229 solid center post core, AL315 (d) 43622 pot core, AL400 (e) 43230 PQ core, AL250 7. Given the AL, the number of turns the required inductance can be found for each core using Equation 5.61. AL Turns 250 21 315 19 400 17 8. Use #14 wire. 168 MAGNETIC COMPONENTS FOR POWER ELECTRONICS APPENDIX 5.4 MCL YMAN DESIGN -SWITCHING INDUCTOR - \"K<; APPROACH This section is abstracted from Magnetic Core Selection for Transformers and Inductors by Colonel Wm. T. McLyman, Marcel Dekker, New York, 1982 Design of a Buck Switching Inductor Given; Input Voltage, Vi = 28 +1- 6 V. Output Voltage, Vo = 20 V. Output Current Range, 10 = 5 - 0.5 A Frequency, f, = 20 KHz. Switching Efficiency, = 98% Regulation = 1.0% Ferrite Pot Core Step 1. Calculate time period, t, of operation t = lIf= 1I20x 103 = 50 X 10-6 s. Step 2. Calculate Minimum duty cycle Dmin = VoIVin(max) = 20/34(0.98) = .60 Step 3 Calculate maximum duty cycle Dmax = VoIVin(min) = 20/22(0.98) = .927 Step 4. Calculate Load Resistance at Minimum Load Current Ro = Vo/IO(min) = 20/0.5 = 40 Step 5. Calculate Minimum Required Inductance F or a Buck Converter Lmin = ~min)t(l-D)min)/2 =(40)(50xl0-6)(I-0.6)/2 = 400 x 10-6 H. Step 6. Calculate ~I in the Inductor M = tVin(maxP(min(l-D(min\u00bb1L = (50 xl 0-6)(34)(0.6)(1-0.6)/400 x 10-6 = 1.0 = 210(min) A. Step 7. Calculate Lel2 1= 100max) + ~1/2 = (5.0) + 1.0/2 = 5.5 A. U 2/2 = (400 x 10-6) (5.5f/2 = .00605 W-s. Step 8. Calculate Ke using Equation 5.66. Po = Yolo = (20)(5) =100 W. CORE SIZES- DESIGN IN POWER ELECTRONICS Assume Bm = .35 T (3500 Gausses) K.: = 0.145 PoB2 xl0-4 = 0.000178 Step 9. Calculate ~ ~ =(Energy)21K.: using Equation 5.64 = (0.00605i/(0.000 1781) = 0.213 169 Step 10. Select a comparable core geometry Kg from listing of pot cores (McLyman, 1982 ). Record all pertinent dimensional data. Pot core = B6561I, 36x22(Siemens) For this pot core, Kg = 0.221 G(window height) =1.46cm. Wtfe(weight ferrite) = 26 gm. MLT = 7.3 cm.,Ac = 2.01 cm2, Wa = 1.00 cm2 At(Surface area) = 45.24 cm2 Step II. Calculate current density (Correlation with Kg is derived in book (McLyman 1982) J = 2(Energy) x 104/BmKuAp Use K = 0.4 (window utilization factor) J= 2(0.00605) x 10R4F/(0.35)(0.4X2.01) = 430Alcm2 Step 12. Calculate bare wire size Aw(8) Aw(8) = loIJ =5/430 = .0116 Step 13. Select a wire size from the wire table. If area is not within 10%,take smaller size. Record wire data. AWG #17 with 0.01039 cm2 )lO/cm = 166 Aw = 0.0117 cm2 (with insulation) Step 14. Calculate the effective window area, Wa(eft) Wa(eft) = WaS3 For single section bobbin on pot core, S3 = 0.75 Wa(eft) = (1.00) (0.75) = 0.75 Step 15. Calculate number of turns N = Wa(eft) S2/Aw Typical value of S2 = 0.6 N = (0.75XO.6)/(0.0117) = 38 turns Step 16. Calculate gap required for inductance 19 = 0.4 N2 Ac xl 0-8/ L = (1.26)(38i(2.01) x 10-8/412 xlO-Q =0.089 cm. For fishpaper spacer, thickness is given in mils. 170 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 19 = 0.089 cm x 393.7 mils/cm = 35 mils Paper comes in 10 and 7 mils .One of each across entire pot core mating sur face doubles gap.(a gap each for skirt and centerpost) Therefore the total gap is 17 mils or 0.034x2.34 = 0.0864cm. Step 17-18. Recalculate new turns correcting for fringing flux (not shown here) N=34 Step 19. Calculate Winding Resistance R = (MLT)(N) 0 /cm x 10-6 = (7.3)(34XI66) X 10-6 = 0.0410 Step 20. Calculate Copper Loss, P cu Peo = eR = (5.5i(o.041) = 1.24 W. Step 21. Calculate Regulation, . a = P cu xlO0/(Po +P cu) =(1.24)(100)/(100+ 1.24) = 1.22% Step 22. Calculate total a.c. + d.c. flux density Bm = O.41tN(Ide +~I12) x 10-4/lg = (1.26)(34)(5.5) x 10-4/0.0864 =0.273T(2730G.) Step 23. Calculate a.c. flux density Bmae= 0.41tN(M/2) x 10-4/lg = (1.26X34)(O.5) x 104 /0.0864 = 0.0248 T Step 24. Calculate Core Loss Pfe. Use core loss curves for 0.0248 T. or 248 Gausses. Use the ferrite weight given before. Pfe = (mW/grnXWtfe) x 10-3 = (O.06X57)x 10-3 = 0.0034 W. Step 25. Calculate total loss Pt = Pcu + Pfe = (1.24) + (0.0034) = 1.2434 W. Step 26. Calculate the efficiency e = (Po)(100)/(Po + Pt)= (100)(100)/(100+1.2434) =98.8% Step 27 Calculate the Watts/unit area \\II = P /At = (1.2434)/45.24 = 0.0275 W/cm2 CORE SIZES- DESIGN IN POWER ELECTRONICS 171 The value of .03 W/cm2 corresponds to a temperature rise of25\u00b0C. APPENDIX 5.5 Design of Output Inductor using Metglas Amorphous Choke Cores The following is the design procedure suggested by Honeywell (pre viously Allied-Signal) for the design of a high frequency output inductor us ing Metglas amorphous choke cores. 1. Determine the Choke Ripple Current, AI- For continuous operation, the minimum DC current Iomin, must be equal to or greater than 112 the choke ripple current, ~I lomin =1>~1/2 ~I =/< 2 Iomin When the minimum DC current is not given, assume that ~I is 10- 20% oflomax. ~I = o. 2 lomax 2. Determine the critical inductance, Lmin Where and Dmin = Eo /(Eo-Epk) toffinax= 1- Dmin T = ton + toff= 1If ton = DT and toff= T-DT For average volt-seconds across inductor to equal zero, DT Epk = Eo (T-DT) Solving for D; 3. Determine the required energy; I pk = lomax + (~I12) 172 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 4. Determine the area product WaAc; WaAc= {2W /(BmaxKJ)} x 104 (cm4) Choose a core from the the Metglas Core Table 5. Calculate the number of turns and wire size N = {Lmin (nH)/ Ad 0.5 Aw=KWA/N 6. Calculate the ripple current, BM 7. Calculate the DC flux density, Boc Boc = 0.4 nNIoc x 104/lm Check for the maximum flux density, Bmax Bmax = Boc + Bt.l2 Teslas Check for percent permeability vs DC Bias(From ~ vs DC Graph) H = 0.4 nNIoc/lm Oersteds 8 . Losses and Temperature Rise p c( W) = P c( W /Kg) x wt.(Kg) Calculate copper loss R = (MLT) x (Rw) x (N) Calculate Total Loss CORE SIZES- DESIGN IN POWER ELECTRONICS Estimate Temperature Rise SA = {1t(OD)wouniI2} + {1t(OD)wound x (htcore +ODwound + ODcore) Appendix 5.6 Push-Pull Output Inductor Design Using a LPT E2000Q Core Nanocrystalline Core by Coremaster International Article ANl14 by Colonel Wm T. McLyman +0-_---...... , J Figure S.20-Push-Pull Converter with Single Output 1. Frequency 2. Output Voltage 3. Output current, max 4. Output current, min 5. Delta current 6. Input Voltage, maximum 7. Input Voltage, minimum 8. Regulation 9. Output Power IO.Operating Flux Density II.Window Utilization 12.Diode Voltage Drop f = 100 KHz. Vo = 5 V. lomax = 10 A IOmin = 2 A ~I =4A Vsimax = 9V Vsimin = 6V a = 1.0% Po = 50 W. BM =0.8T Ku = 0.4 Vd = 1 V Step No.1. Calculate the period, T T= lIf T = 11100,000 = 10. 10-6 L1. L...-+_--o+ 1 C2 .. J 173 174 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Step No. 2.Calculate the minimum duty ratio, Dmio Dmio = 5/9 = 0.555 Step No.3. Calculate the required inductance, L L = T. (Yo - Vd). (1- Dmio) L = 10. 10-6.6. (1-0.555) = 6,675 use 7 [~H] Step No.4. Calculate the peak current, Ipk Ipk = lomax +!J.. 112 Ipk= 10 + 4/2 = 12 A Step No.5. Calculate the energy-handling capability in watt-seconds, [w.s] Energy = L.I pk 2 /2 Energy = 7. 10-6.122 = 0.000504 [w.s] Step No.6. Calculate the electrical condition, Ke Ke = 0.145. Po. BM2. 10-4 Ke = 0.145.50.0.8 2.10-4 = 0.000464 Step No.7. Calculate the core geometry, Kg Kg = Ener~/ Ke. (l Kg = 0.0005042/0.000464.1.0 = 0.000547 [cm2 Step No.8. Select from the LPT data sheet a E2000Q core comparable in core geometry, Kg Core number Manufacturer Magnetic path length, MPL Core weight, W tfe Copper weight, Weu Mean length per tum (ML T) Iron area, Ac Window Area, Wa Area Product, A p GC70111 CMI 4.1 cm 4.3 g. 5.6 g. 2.7cm. 0.14 cm2 0.581 0.08132 cm4 CORE SIZES- DESIGN IN POWER ELECTRONICS 175 Core geometry, Kg Surface Area, At Permeability MilliHenries per 1000 turns Step No. 9.Calculate the rms current I =~12 + (81/2)2 nns max 0.00168 cm5 16.3 cm2 Il = 300 mH= 129 Step No.1 O.Calculate the current density, J,using a window utilization,Ku= 0.4 J = (2. Energy. 104)/ Ap. Bm .Ku J = (2 x 0.000504 x 104)/(0.08132 x 0.8 xO.4) =387 [A/cm2) Step No.ll Calculate the required permeability, L\\1l ~Il = (0.8 x 3.14 x 0.581 x.387 x 0.4) = 290 use 300 Step No.1 2. Calculate the number of turns N = 1000 ~ L(new) / ~(XX) N = 1000.JO.007 1 129 = 7.37 use 7 turns Step No. 13 Calculate the peak flux density, Bm Bm = (O.41tNIpk Ill: .1 04)IMPL Bm = (0.4 x3.14x 7 x 12x 300. 104)/4.06 = 0.779 [T] Step No.14. Calculate the required bare wire area, Aw(B). Aw(B) = Inn/J Aw(B)= 10.2/387 = 0.0264 [cm2] 176 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Step No.15. Select the wire size with the required area from the Wire Table. If the area is not within 10% of the required area, then go to the next smaller size. AWG= 13 Aw(B) = 0.0263[cm2] JJfl/cm = 65.5 Step No. 16. Check the ~I current density using the skin effect e. s = 6.621.fl .JI00,000 s = 6.621 .Jl 00,000 = 0.0209 [cm] Calculate the diameter of a #13 AWG D = ~4Aw(B/ Jr D= .J4xO.0263 13.14 = 0.183 [cm] Subtract 2 times the skin depth from the diameter and calculate the new area. Dn = D-2e Dn= 0.183 -2x 0.0209 = 0.141 [cm] A = nD 2/4 n n An = 3.14 xO.1412/4 = 0.0156 [cm2] Take the difference between Aw(B) and An. This will be the area for the M CUT rent. A~I = Aw(Br An A~I= 0.0263- 0.0156 = 0.0107 [cm2] Check the current density to see if it is close to the designcurrent density, J. J=~I1 AM J = 4/0.0107 = 374 [Alcm2] ~I current density = 374 DC current density = 387 Step No.17 .Calcuate the winding resistance, R R = MLT xN x (J.lnlcm) xlO\u00b76 Rv = 2.7 x 7 x 65.6 xl 0-<> = 0.00124 [Q] CORE SIZES- DESIGN IN POWER ELECTRONICS 177 Step No. 18. Calculate the copper loss, P cu P cu = Inns 2 R Pcu = 10.22 X 0.00124 = 0.124 = 0.129 [W] Step No. 19. Calculate the magnetizing force in Oersteds, H H = O.4n NIpklMPL H = 0.4 x 3.14 x 7x 12/4.06 = 25.98 [Oe] Step No. 20. Calculate the ac flux density in T, Bac Bac = (O.4nN x M12)x f..lr xl04IMPL Bac = O.4n x 7x 2 x 300 x 104/4.06 = 0.13 [T] Step No. 21 Calculate the regulation, a, for this design New regulation= Kg(requiredyKg(used)= 0.00547/0.00168 = 0.326 Step No. 22. Calculate the WattslKilogram, WIK WIK = 8.64 x 10-7 f 1.834 X Ba/\u00b71l2 WIK= 8.64 x 10-7 x 100,0001.834 X 0.132.JJ2 = 17.0[W] Step No. 23. Calculate the core loss, Pre Pre = (mW/g) Wre xlO-3 Pre = 17 x 4.3 xlO-3 = 0.0738 [W] Step No. 24. Calculate the total loss, P~ P~ = Pcu + Pre P~ = 0.129 0.0731 0.202 [W] Step No. 25. Calculate the watt density, \\}I \\}I = P~ 1 At \\}I = 0.202/16.3 = 0.0124 [W/cm2] Step No. 26. Calculate the temperature rise, Tr 178 MAGNETIC COMPONENTS FOR POWER ELECTRONICS T = 450 x qIl.826 r Tr = 450 X 0.0124\u00b0.826 = 1.98 [OC.] Step No. 27. Calculate the window utilization factor, Ku Ku = N SN Aw(B) Ku =7x Ix 0.0263/0.581=0.317 References Bracke, L.P.M.,(1983) Electronic Components and Applications, Vo1.5, #3 June 1983,p171 Bracke L.P.M.(1982) and Geerlings, F.C., High Frequency Power Trans former and Choke Design, Part I, NV Philips Gloeilampenfabrieken, Eindhoven, Netherlands Buthker,C.(1986) and Harper, D.l, Transactions HFPC, 1986,186 Carsten, B.(1986), PCIM,Nov.1986,34 De Maw,M.F .(1981 ),Ferromagnetic core Design and Applications Handbook, Prentice Hall, Englewood Cliffs, NJ, 1981 Grossner, N.R.(1983), Transformers for Electronic Circuits, McGraw-Hill Book Co., New York Hanna,C.R.,J.Am.(1927) I.E. E., 46,128, Hess, J.(1985) and Zenger, M., Advances in Ceramics, Vo1.l6 501 Hiramatsu, R.(1983) and Mullett, C.E.,Proc. Powercon 10,F2, I Hnatek,E.R.(l981), Design of Solid State Power Supplies, Van Nostrand Reinhold,New York IEC (19 ) Document 435,International Electrotechnical Commission Jongsma, J.(1982),High Frequency Ferrite Power Transformer and Choke Design, Part 3, Pilips Gloeilampenfabrieken, Eindhoven Netherlands Jongsma, J.(1982a) and Bracke, L.P.M. ibid Part 4 Magnetics (2000) Ferrite Core Catalog, Magnetic Div.,Spang and Co, Butler, PA 16001 Magnetics (1984) Bulletin on Materials for SMPS Martin,H.,(1984), Proc. Powercon II, BI, 1 Martin, W.A.( 1978), Electronic Design, April 12,1978, 94 Martin, W .A.( 1986), Powertechnics Magazine,F eb.1986,p.19 Martin, W.A.(l982), Proc. Powercon 9 Martin,. W.A.( 1987), Proceedings,Power Electronics Conference (1987) McLyman, Col. W.T.(1969) JPL, Cal Inst. Tech. Report 2688-2 McLyman, CoI.W.T.,(1982), Transformer and Inductor Design Handbook, Marcel Dekker, New York CORE SIZES- DESIGN IN POWER ELECTRONICS McLyman, Col.W.T.(1982), Magnetic Core Selection for Transformers and Inductors, Marcel Dekker, New York McLyman, Col. W.T. (1990) KG Magnetics Magnetic Component Design Software Program 179 Pressman, A.(1977) Switching and Linear Power Supply Converter Design, Hayden Book Co., Rochelle Park, N.J. Philip Catalog,(1986) Book C5, Philips Components and Materials Div., 5600Md, Eindhoven, Netherlands Roddam, T.( 1963), Transistor Inverters and Converters, Iliffe, London and Van Nostrand Reinhold, New York Siemens (1986-7) Ferrites Data Book, Siemens AG, Bereich Bauelemente, Balanstrasse 73, 8000 Munich 80 Germany Smith, S.(1983), Magnetic Components, Van Nostrand Reinhold, New York Smith, S. (1983a) Power Conversion International, May 1983, 22 Snelling E.(1988) Soft Ferrites, Properties and Applications Butterworths, London Snelling, E(1989) presented at ICF5 Stijntjes,T.G.W.(1985), and Roelofsma, J.J., Advances in Ceramics, Vol 16, 493 Stijntjes, T.G.W.(1989) Presented at ICF5, Paper CI-0l TDK (1988) Catalog BLE-OOIF, June 1988, TDK, 13-1 Nihonbashi, Chuo-ku, Tokyo, lO3, Japan Thomson (1988) Soft Ferrites Catalog, Thomson LCC, Courbeville, Cedex, France VDE ( ) Document 0806 Watson, J.K.(1980) Applications of Magnetism, John Wiley and Sons, New York Watson, J.K.(1986) IEEE Trans Magnetics Wood, P.(1981) Switching Power Converters, Van Nostrand Reinhold, New York Zenger,M. (1984), Proceedings, Powercon 11(1984) APPENDIX 5.6 RECENT ARTICLES ON DESIGN OF FERRITES FOR POWER APPLICATIONS Baasch, T.L., Electronic Products, Oct. 1971,25 Bledsoe, C., Electronic Business, June 1,1984, 128 Bloom,E., IEEE Transactions on Magnetics,(1986), 141 Bosley, L.M. (1994) Magnetics Brochure. Brown, B.(1992) PCIM, July 1992) 46 Brown, J.F., Powetechnics. Dec. 1986, 17 Carlisle, B.H.(1985) Machine Design,Sept. 12, 53 180 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Cattermole,P.(1988) and Cohn,Z .. Proc. HFPC,1986, III Chen, D.Y., Solid State Power Conversion, Nov/Dec., 1978,50 Ciarcia, S.A,Byte,Nov.1981, 36 Cuk,S., Power Conversion International, 1981, 22 Dull,W., Kusko, A& Knutrud,T., EDN, Mar.5, 1975, 47 Engelman, R.( 1989)PCIM, ~ #7...J..1 Estrov, A(1989) PCIM, May, 1989 16 Estrov, A(1986) PCIM, August 1986, 14 Finger, C. W. (1986) Power Conversion International, 1986 Fluke,J.C.,Proc. Power Electronics Show, 1986, 128 Gatres B.( 1992) PCIM, il, #7 July 1992, 28 Harada, H. and Sakamoto, K., IEEE Translation Journal of Magnetics in Ja- pan, #7, Oct.1985 Hew, E., Power Conversion International, Jul.! Aug. 1982, 14 Hill, P.C., Proc. Powercon 2, 1975,243 Hiramatsu, R. (1983),and Mullett, C.E.,Proc. Powercon,lO, F2,1 Kamada, . (1985), and Suzuki, K., Advances in Ceramics,Vol. 16,507 Kepco (1986) Kepco Currents, Vol 1.#2 Kitagawa, T. and Mitsui, T.,IEEE Translation Journal of Magnetics in Japan, Sept, 1985 Konopinski, T. and Szuba, S. Electronic Design, 12,June 7, 1979,86 Margolin, B., Electronic Products, Mar.28, 1983, 53 Martin, H. (1984) Proc. Powercon, 11, B 1, I Martin, W.A Proc. Powercon 9, 1982, Middlebrook, R.D., Power Conversion International, Sept. 1983,20 Mochizuki, T. (1985) Sasaki, I. And Torii, M.,Advances in Ceramics, Vol. 16,487 Mohandes B.E.(1994) PCIM, July 1994, 8 Mullett, C.E.,Proc. Power Electronics Show, 1986,36 Sano, T. (1988), Morita, A and Matsukawa, A Proc. PCIM,July 1988, 19 Schlotterbeck, M.(1981 ),and Zenger,M., Proc. PCIM, 1981 ,37 Shiraki, S.F.(1980) Proc. Powercon,7,J4, I Smith, S., Power Conversion International, May 1983, 22 Stratford, J.M., EDN, Oct. 13,1983, 140 Sum, K.K.,Power Electronics,1986, 153 Triner, J.E.,Power Conversion International, Jan. 1981,69 Turnbull, J., Electronic Products, May, 15, 1972, 53 Ying X. and Zhi,Z.,IEEE Transactions on Magnetics,Feb.1985,148 Zenger,M.( 1984) Proc. Powercon, 11 (1984 Chapter 6 COMMERCIALL Y -A V AILABLE COMPONENTS FOR POWER ELECTRONICS INTRODUCTION In the previous two chapters, the component material and shape prop erties of components for power electronic systems were reviewed. This chap ter will list these components that are available commercially. 6.1- TDK FERRITE POWER ELECTRONIC COMPONENTS TDK offers a wide variety of materials and component shapes for power electronic applications. The materials will be considered first followed by the cores that are offered in the various materials. The specifications listed for each core as it applies to design will be reviewed. The catalog pages for material and representative listings of core properties are found in the Appen dix at the end ofthe chapter. 6.1.1-TDK Power Ferrite Materials TDK has 6 ferrite materials that can be used for power supply transformers and chokes. They are; 1.-PC40- an standard low frequency material in various E-type cores, (ETD, EC, EI, EE, EF, EP, and RM) 2.-PC44- a lower loss improved material in LP, PQ, EPC (low pro file) cores. 3.-PC50- a higher frequency material in PQ,EPC,EP, and RM cores Tables of magnetic properties are found in Table 6Al. These three materials have a minimum core loss temperature of about 1000 C. for continuous serv ice. Recently, TDK has also introduced 2 other materials that have a mini mum core loss temperature of 40-80 0 C. for small portable power supplies that operate intermittently and one that has a higher permeability. Another lower temperature material has a moderately high permeability. 4. PC45-has a minimum core loss temperature between 40-50 0 C. 5. PC46-has a minimum core loss temperature between 60-80 0 C. 182 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 6. DNSO-has a core loss minimum at SO\u00b0 C. and has a higher perme ability than the others. It is available in EPC, ER (high power), EEM cores and also in a special EER core whose design gives 13- 20% reduced loss. The properties of the above three materials are found in Table 6A2. Figure 6.1 shows the core loss vs T for several TDK power materials. For large high power reactor and transformer cores, TDK has, in ad dition to the previously cited PC40, another material PC22 with a slightly higher saturation value. The high power cores are available in T (Toroids), VV, EC, EIC, PQ, E, EI, PT and SP cores. In addition to the material specifications, TDK lists some design data for each core such as the effective parameters (Ae, Ie, and Ve). For ungapped cores, they list the calculated output power in Watts for 100 KHz.and SOO KHz. (PCSO). For gapped cores for chokes, the list the AL at 1 KHz.,O.S rnA and 100 T (1,000 Gausses).PQ cores have an NI limit for gapped cores and AL vs gap. Listed is also the temperature rise versus total loss an also core loss at 100 0 Cat 100 KHz. and 200 mT (2,000 Gausses). TDK Common-Mode Choke materials-TDK has three materials for common mode choke applications. They are HSS2,HSn and HS 10. Their permeabil ities are respectively SSOO, 7S00 and 10,000. They are available in T(Toroids), FT, FTR, ET and UU cores. Except for the V-V, they are all con tinuous-path (no mating surface) cores. Provided are the AL values and the effective parameters. Toroids are also available in the HSC2 high permeability material. TDK also offers Common-mode filters equivalent circuit model for Spice. See Table 6A3. TDK EM] Suppressor Materials-TDK lists 6 materials for EMI suppressor cores. They are HF30, HF40, HFSO, HFSS, HF60 and HF70. Their properties are given in Table 6A4 . From their resistivities, all except HF 60 are NiZn materials, while HS 60 is a MnZn material. These materials are available in multi-hole substrates, chip suppressors, beads, wire-wound-beads, cable clamps, and toroids. TDK also makes their own EMI filters. 6.2- PHILIPS (YAGEO) POWER FERRITE COMPONENTS Philips has 12 ferrite materials for power applications. Eleven ofthem are MnZn ferrites and one N iZn ferrite. The properties of these materials are listed in Table on page . The first 3 materials are used for line output trans formers for TV deflection yokes. The remaining 9 materials are arranged es sentially in order of their frequency of operation. 3CSI has a minimum core loss minimum at SO 0 C. 3C94 is an industrial use material. For 400 KHz. operation, 3C94 is a low loss high Bm material and 3C9 a very low loss mate rial. The 3F materials are for higher frequencies, 3F3 for 700 KHz, 3F35 for 1 MHz. and 3F4 for 3 MHz. A graph of the performance factor(PF) defined 184 MAGNETIC COMPONENTS FOR POWER ELECTRONICS earlier in Section 3.14 is given in Figure 6A6 for a 500 mW/cm3 limit for for 5 representative material grades. For selecting a core according to power out put, Table 6.1 lists the core sizes capable of handling the power ranges at 100 KHz. Table 6.1-Power Handling Capacities of Ferrite Cores-Philips Power throughput for different core types (at 100 kHz switching frequency) POWER RANGE CORE TYPE (W) <5 RM4; P11n; R14; EF12.6; Ul0 5 to 10 RM5; Pl418 10 to 20 RU6; E20; Pl8111; R23; U15; EF015 20 to 50 RM8; P22113; U20; RM10; ETD29; E25; R26110; EFD20 50 to 100 ETD29~ ETD34; EC35; EC41; RM12; P30/19; R2612O; EFD25 100 to 200 ETD34; ETD39; ETD44; EC41; EC52; RM14; P36I22; E30; R56; U25; U30; E42; EFD30 200 to 500 ET044; ETD49; E55; EC52; E42; P42129; U37 <500 E65;EC70;U93;U100 The individual core sheets list the AL ,J.le and Bsat at H = 250 Aim and T = 100 0 C. as well as the core loss at 25, 100 and 400 KHz. Gappe core data lists the AL ,J.le and the air gap. In addition , for RM cores, the core loss is given at IMHz. and 3 MHz. and planar E-cores at 30 and 10 mT respectively. Philips Common-Mode Choke materials-Philips offers 5 high perm materials that can be used for common-mode choke applications at lower frequencies. They are 3E25, 3e27, 3E26, 3E5 and 3E6 which range in permeabilities re- COMMERCIAL POWER MAGNETIC COMPONENTS 185 spectively from 6000, 6,000, 7,000, 10,000 and 12000.They are mostly avail able in beads, toroids and other common mode shapes. For higher frequencies SMD common-mode chokes are available in the NiZn material, 4S2. Philips EMf Suppressor Materials-Philips lists a variety of EMI suppression materials. They are listed in Table 6AIS . The 3E series are MnZn common mode choke materials. 3S 1 is also a rather high perm material that can not withstand a high DC bias and instead the lower perm 4S2 should be used. Two new materials,3S3 and 3S4 are MnZn with high resistivity. All of the remaining materials (4 series)are NiZn materials with high resistivities and lower perms. An impedance versus frequency plot for 3S4 is shown in Figure 6AS. 6.3- EPCOS POWER FERRITE COMPONENTS Epcos (formerly Siemens-Matsushita) has 10 different power materi als. For 100 KHz., there are N27,NS3 and N41; for 200 KHz. there are N62,N67\"N72, and N82; for SOO KHz. there is N87; for 300 Khz. to I MHz. and resonance converters, there are N49 and NS9. See Tables 6A17-19 anf Figure 6A6Just released at this book's publication is a new material N97 which listed best in class at 2S-400 KHz. The loss at 100 0 C. is 20% lower than that ofN87. It also claims a better DC bias property than N87. They also list a new material, N92 with which they claim it is possible to increase the rated current of output chokes by 10% against N87.At the same time, the losses at 1000 C. are comparable to N87. They also claim that their N49 mate rial has been improved to meet the needs of rising performance requiements of DC to DC converters. The aim was to reduce losses while increasing satu ration. At SOO KHz. the losses have been reduced by 30%. and saturation has been increased by 10%. The material data and The material data and core loss curves for all three materials are given in Tables 6.2-6.4 and Figures 6.2, 6.3, 6.S, 6.7 and 6.8 . In addition DC bias curves are given for N92 and N97 in Figures 6.4 and 6.6 . A table of transformer power capabilities at several frequencies is given for each core. Epcos lists performance factor, PF for 100 0 C. and 300 kW/m3 and a rather little cited property, the standardized hysteresis constant as a function of temperature. There is a very wide variety of core shapes. The RM cores are particularly featured in sizes from RM4 to RM 14. They are also available in low profile in this range. Other cores include EP, standard pot cores, E-cores including ELP and EFD. Some cores including the RM's are available with surface -mount accessories. Individual sheets for cores include AL ,/J.e and core loss at 100 KHz. and SOO KHz. and 100 0 C. at 200 mT and SO mT. respectively. Gapped core 186 MAGNETIC COMPONENTS FOR POWER ELECTRONICS data show the AL ,J.le and the air gap. Low profile and planar cores are avail able in a several sizes. Epcos Common-Mode Choke moterials-Epcos does not specifically list common-mode choke materials but they have 5 materials that have perme abilities of 6000 and higher (up to 15,000). They are T35,T37,T38 T42 and T46. The last one is only available in small ring cores. 'JDO ., -\"'7 ~~~ ____ ~ _____________________________________ - _- ~\"~'1~ I: ~ ~ ~------------~~~-~--------~----~--- COMMERCIAL POWER MAGNETIC COMPONENTS 187 Figure 6. 4- \u2022 Reversible Permeability of N97 compared with N87 COMMERCIAL POWER MAGNETIC COMPONENTS 189 6.4-MAGNETICS POWER FERRITE COMPONENTS Magnetics has 4 different power materials. One material, F, has a minimum core loss temperature at about 25 0 C and is meant for low frequen cies. K and P materials have core loss minimum temperatures at about 60 0 C at 100 and 500 KHz. R has the lowest core loss at 100 0 C for 100KHz and 500 KHz. K material has the lowest core loss at 700 KHz. See Table 6A5 The various materials are available in all the popular core shapes. In cluded in the power ferrite design information is a table of core cross section window area products for all the power cores. Graphs showing the same area product plotted against the output power allowing the core selection to be made for the various core shapes and sizes. Another table gives the power handling capabilities for different frequencies and core shapes for a forward converter. Output power is also plotted against temperature rise for different frequencies. The individual core size sheets list the core-window product area and the AL for ungapped cores . Using the common core-loss equation; Where PL = the core loss in mW/cm3 COMMERCIAL POWER MAGNETIC COMPONENTS 191 Magnetics Common-Mode Choke materials- Magnetics has 3 high penn~ ability materials for common mode choke operation. They are J, W and H materials whose permeabilities are 5,000, 10,000 and 15000 respectively. The latter is available only in toroids. The others can be had in most other core shapes. See Table 6A7 6.5 TOKIN POWER FERRITE COMPONENTS Tokin's power ferrite line is listed in Table 6A1O .Four materials are listed spanning the range from 100KHz. to 1 MHz. The core loss minimum temperature for the BHI and BH2 are in the range 90-100 0 C while that of BH40, the higher frequency materia~ is between 70-80 0 C. Properties of new material with somewhat higher saturation, BH3 is listed in Table 6Al1 com pared with BHI. Plots of core loss versus frequency and flux density at three temperatures are presented. 192 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Tokin Common-Mode Choke materials- Tokin has one material, BH5000 which has a higher permeability(5000) for lower frequency common-mode choke application. 6.6- FAIR-RITE POWER FERRITE COMPONENTS Fair-Rite Products has two materials for use as power trans formers, 77 material for 25 Khz. operation and 78 with a saturation of 5000 Gausses for 100 KHz. operation. The 75 material can be used at 25Khz. at 100 0 C. Power materials are available in EP, PQ, U, E and ETD cores. See Table 6A8 Fair-Rite Common-Mode Choke materiais- Fair-Rite lists one material 75 for their common-mode choke aplications. It has a permeability of 5000.Another material, 76 has a 10000 permeability and is recommended for frequencies up to 500 Khz. Fair-Rite EMI Suppressor Materials -Fair-Rite lists 5 materials for EMI suppression, 43, 44, 61,73 and 77. The 73 and 77 materials are MnZn for lower frequencies( <30 MHz.) while the other 3 are NiZn for higher frequencies (30-250 MHz.). The 61 material is the most stable with temperature. See Table 6A9. 6.7-FERRONICS POWER FERRITE COMPONENTS Ferronics Common-Mode Choke materials-Ferronics has 2 MnZn ferrite materials, B (5000) and T(lO,OOO) perm which can be used for common mode chokes at lower frequencies. See Table 6A23 Ferronics EMI Suppressor Materials- Ferronics has 3 NiZn materials that are used for EMI suppression, J, K, and P. The permeabilities are 850, 125 and 40 respectively. The latter two are perminvar materials that list the cau tion that the permeabilities and loss factors may be irreversibly increased if excited with a high magnetizing force. This factor should be considered when applying high DC or ac currents. J perm is recommended for frequencies from 5-500 MHz, K for above 20 Mhz. and P for above 80MHz. The materials are offered in toroids, multi-hole wide band cores and beads. The material prop erties are given in Table 6A23 . COMMERCIAL POWER MAGNETIC COMPONENTS 193 6.8-FDK POWER FERRITE COMPONENTS FDK lists 7 different power ferrite materials as shown in Table 6A25. The 6H series are high flux density materials for 25-100 KHz. operation. The higher the number after the 6H, the lower the losses. The minimum loss tem peratures vary from 40 0 C - 100 0 C. The 7H series are lower flux density materials for higher frequencies. The newest material 7H20 has half of the core loss of7H1O at I Mhz. and 100 0 C. The individual core data include the effective parameter, the window and core cross-sectional areas and the AL'S. See Fig 6A7-8 FDK Common-Mode Choke materials- FDK recommends two high perme ability materials, 2H07 and 2H1O with permeabilities of 7,000 and 10,000 respectively for common mode usage. 2H lOis recommended for frequencies lower than 500 KHz. FDK EMf Suppressor Materials-FDK lists 4 EMI suppressor materials, K32, L51, K 14, and K26. They are NiZn materials ranging in permeability from 700 to 40 over a range of increasing frequencies. Their properties are listed in Table 6A24. 6.9-A VX POWER FERRITE COMPONENTS The A VX ferrite product line is that of the former Thomson company. Their power ferrite component line is made from 8 materials listed in Table 6A26. The PWI materials are for the lower frequencies up to 32 KHz. proba bly for line output TV transformers. The PW2 materials operate at 100 KHz. The PW3 and PW4 materials run up to 500KHz. and the PW5 to 1.5 MHz. See Table 6A26. A JIX Common-Mode Choke materials-There are 3 high perm A VX materials that can serve as common mode chokes. They are A2, A3 and A4 with per meabilities of 10,000, 7500 and 6000 respectively. Their properties are given in Table 6A27 . 6.10-MMG-NEOSID POWER FERRITE MATERIALS MMG has six materials for power transformers and chokes, F47, F45, F44, F5, F5A and F5C. Their permeabilities range from 1800 to 3000. Core loss data for 25 0 C. and 100 0 C. is shown for the F5 series at 16 and 25 KHz., F44 and F45 up to 100 KHz. and F47 to 400 KHz. See Table 6A12. 194 MAGNETIC COMPONENTS FOR POWER ELECTRONICS MMG-Neosid Common-Mode Choke materials- MMG has 4 materials with permeabilities of 5000 and above. They are the F9C, FlO and F39 whose permeabilities are 5000, 6000, and 10,000. MMG-Neosid EM] Suppressor Materiab--MMG-Neosid list 4 materials for EMI suppression, F19, F14, F16, F25, F28 and F29, the latter three being Perminvar ferrites for higher frequencies. Their permeabilities are 1000, 220, 125, 50,30 and 12 respectively. 6.11-KASCHKE POWER FERRITE MATERIALS Kaschke has two materials for use as power transformers' K2004 and K2006. The K2004 has a higher saturation and lower losses. The losses are given at 16 KHz. The 2004 material has a minimum loss temperature of 80 0 C while that of 2006 at near 100\u00b0 C. See Tables 6A28-29 and Figure 6A9. Kaschke Common-Mode Choke materials- Kaschke has one material K6000 with a permeability of 6000 that may be used for common-mode chokes 6.12- VOGT POWER FERRITE MATERIALS Vogt has three power ferrite materials, Fi323,Fi324 and Fi325. All three have saturations in the 5000 Gauss range with the 325 material slightly higher than the other two it also has the lowest losses at the higher frequen cies. The other two are meant for the 100-300 KHz range with the 324 mate rial having a higher minimum loss temperature than the 323 (80-100 0 C. vs 60 0 C. See Table 6A31. Vogt Common-Mode Choke materiab--Vogt has three materials suitable for common-mode chokes. They are Fi410, Fi360 and Fi 350 with permeabilities of 10,000, 6000 and 5,000. Their properties are listed in Table 6A31. 6.13-SAMWHA POWER FERRITE MATERIALS Samwha has three power ferrite materials, PL-5, PL7 and PL9. The saturations for all three are about the same at 5000 Gausses. The core loss at 100 KHz and 100 0 C is lowest for the PL9 then the PL 7 and then the PL5. The minimum loss temperature for the PL9 is about 80 0 C while those for the other two are about 95 0 C. Samwha also lists three other materials for flyback COMMERCIAL POWER MAGNETIC COMPONENTS 195 transformer operation, SMI9B, SM 19C and SMI9D. All the magnetic pa rameters are identical to the other three power materials except that the core loss is quoted at 32 KHz. See Table 6A39. Samwha EMI Suppressor Materials-Samwha lists 4 NiZn materials for EMI suppression, SN20, T314, SN065 and SN201. They range down in perme ability from 2000 to 500. 6.14- STEWARD POWER FERRITE MATERIALS Steward does not specifically list a power transformer material but does recommend their 21(presumably a NiZn Material) material for tempera ture-stable high frequency inductor and some very high frequency choke ma terials. They list several EMI suppression materials including their 25 and 38 materials. Their materials are listed in Table Steward Common-Mode Choke materials-Steward recommends their 1700 perm 38 material for broadband common-mode choke applications. They do however have some high perm materials for the lower frequencies. The are; 35 and 36 (5000 perm), 37 and 42 (7500 perm) and 40 (10,000 perm). All of these are listed in their toroid catalog. (see Tables 6A20-1.) Steward EMI Suppressor Materials- Steward lists 3 EMI suppresion materi als, 25, 28 and 29. Their permeabilities range from 125 to 850. They are nickel ferrites with high resistivities. Steward makes a very long line of EMI cores and filters. Their material specs are given in Table 6A22 . 6.15-FERRITE INTERNATIONAL POWER FERRITES Ferrite International has 4 materials for power ferrite applications, TSF 5099 TSF7099, TSF7070 and TSF8040. The first three have saturations of 5000 Gausses with TSF8040 at 5100 for integrated magnetics. TSF5099 has the lowest core loss at 25 and 100 KHz. and 100 0 C. TSF 5099 and 7099 have core has minimum temperatures at about 100 0 C, TSF7070 at 80 0 C and 8040 at 60 0 C. They also list a \"Boost\" material for DC bias operation in gapped inductors. Their material properties are shown in Table 6A37 . Ferrite International Common-Mode Choke materials-Ferrite International has two high perm materials for common-mode choke usage. They are TSF5000(5000 perm and TSFOIOK (10,000 perm). See Table 6A37. 196 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 6.16-CERAMIC MAGNETICS POWER FERRITE MATERIALS Ceramic Magnetics has 4 power ferrite materials MN80, MN67, MN60LL and MN8CX. The first three have data at 125 0 C. MN80 shows core loss data at 3000 Gausses and 100 KHZ. with a minimum core loss tem perature of 75 0 C. Under the same frequency at 1000 Gausses, the minimum core loss temperature is 125 0 C. MN60LL has the lowest core losses at 200- 300 KHz. MN67 has the highest saturation at 5200 Gausses. MN8CX has the highest operating frequency at .5-2.0 MHz. See Table 6A38. Ceramic Magnetics Common-Mode Choke materials-Ceramic Magnetics lists 4 materials wth permeabilities above 5000. They are MNIOO (10,000 perm ,MC25 (9500 perm) and MN60 and MN60LL (6000 perm) 6.17-TOMITA POWER FERRITE MATERIALS Tomita lists two power ferrite materials, 5G and 15 G. Data is given at 16 KHz. and 25 0 C and 100 0 C. also at .1 and .2 T up to 100 KHz. Core shapes include RM, X, U, E, EP ETD, PM and toroids. See Table 6A30. Tomita Common-Mode Choke materials-Tomita has 5 materials whose permeabilities are between 5,000 and 10,000. They are 2E2, 2E2B, @#I, 2GI, 2G3 and 2Fl. 6.18-ISKRA POWER FERRITE MATERIALS Iskra lists core loss data for three materials although others are shown with high saturations but no loss data. The materials with core loss data are; 2E6 2F6 and 2F8 at 100, 200 and 300 KHz. respectively. Core shapes listed for these materials are; EE, EI, EP, RM, EER, ETD, EC and PP.See Table 6A33. Iskra Common-Mode Choke materials-Iskra lists 2 materials with perme abilities above 5000. They are 22G (6,000 perm and 12G (10,000 perm) 6.19- nOMEN POWER FERRITE MATERIALS Domen lists two materials for High power applications, 2500HMC 1 and 2500HMC2. The losses are given at 16 KHz. 2000 Gausses at 25 0 C and 100 0 C. See Table 6A32 COMMERCIAL POWER MAGNETIC COMPONENTS 197 Domen Common-Mode Choke materials-Domen has 3 materials with high permeability, 6000HM and 6000HMI at 6000 perm and 10000HM at 10,000 perm. 6.20- HITACHI POWER FERRITE MATERIALS There are 4 power ferrite materials in the Hitachi catalog, SB5S, SB3L, SB7C, and SB9C. SB5S has a higher permeability (3000) than the oth ers but higher losses at 100 KHz. and 2000 Gausses. SB7C and SB9C have low losses at higher frequencies with a core loss maximum at 100 0 C. SB3L has a high saturation and is particularly useful with imposed DC bias. These materials are available in EI, EE, EER, and PQ shapes.See Table 6A35. Hitachi Common-Mode Choke materials-Hitachi lists several materials for common-mode chokes. They are GPll, GP9,GP7 GP5 and GQ5C with per meabilities from 5,000 to 10,000 for use at lower frequencies. Hitachi EMf Suppressor Materials-Hitachi lists 4 NiZn materials (DL) for use in EMI suppression up to 10 MHZ.(See Table 6A36) At 100 MHz. mate rials QM, KP, DV and SH are recommended but no data given. Shapes avail able are beads or filters. 6.21- COSMO POWER FERRITE MATERIALS Cosmo has four power ferrites listed in their catalog. They are CF138, CF 129, CF 196, and CF 1 0 1. The power losses are given at 16 KHz and 25 KHz at a 2000 Gauss level.The saturation ofCF129 is 5100 Gausses and the other range from4800 to 5000 Gausses. An unusual parameter they list is the temperature of the secondary permeability maximum, which should corre spond to the minimum core loss temperature. The materials are available in EFD, EPC,EE, EI, ETD, EER, EC and uu. shapes. Cosmo Common-Mode Choke materials- Cosmo has two materials CF 195 and CF197 with permeabilities of 5000 and 7500. See Table 6A40. 6.22- ACME POWER FERRITE MATERIALS Acme lists 3 power ferrite materials, P2, P4 and P5. The saturation of P2 is 4500 Gausses and the other two are at 4800 Gausses. P2 is meant for 100 KHz operation, P4 at 300 KHz. and P5 at 500 KHz. Acme lists an un usual property namely the amplitude permeabilities at 25 KHz. and 2000 Gausses at 25 0 C. and 100 0 C. See Table 6A43 Acme Common-Mode Choke materials- Acme lists several high permeability materials that can be used for common-mode chokes. Acme EMf Suppressor Materials-Acme-Malaysia lists a number ofNiZn materials for EMI suppression in Table 42. They are H2, H3 H4, H5, DIe and D28.Their permeabilities range from 50 to 870. They are available in several shapes including cable cores. 198 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 6.23- HINODAY POWER FERRITE MATERIALS Hinoday was the former Morris Electronics Co. an old Indian ferrite company. Hinoday has 3 ferrite power materials MSB-58, MSB-7C and MSP5F. The saturation of the fIrst is 4800 Gausses while the other 2 are at 5000 Gausses. The MSB-7C has core loss listed at 100 KHz. and 2000 Gausses while the fIrst is easured at 16 KHz. and 2000 Gausses at 40 0 C. The last one is also a 16KHz. material with the higher flux density. See Table 6A44 Hinoday Common-Mode Choke materials-Hinoday has 2 materials MGQ5C and MGP-9 with permeabilities of 5300 and 7000 for common-mode chokes. The properties are given in Table 6A44 . 6.24- ISU POWER FERRITE MATERIALS Isu has 6 power ferrite materials, PM, PM2, PM2A, PM5 PM7 and PM9. The fIrst 3 are for lower frequencies from 16-25 KHz. and 85 0 C. while the other three are mainly for 100 KHz. and 100 0 C. operation. The saturations of the fIrst three are also slightly lower than the last three. See Ta ble 6A41 Isu Common-Mode Choke IIUlterials- Isu does not list any materials for common-mode chokes 6.25- MIANY ANG POWER FERRITE MATERIALS Mianyang has 3 power ferrite materials, R2KD, R2KH and R2KBP 1. The fIrst has a saturation of 4800 Gausses and the second 5100 Gausses. The fIrst material is meant for 16KHz operation, the second for 16,32 and64 KHz. while the third is a 25 KHz. material. See table 6A45. Mianyang Common-Mode Choke IIUlterials-No common-mode materials listed. 6.26- HEBEl POWER FERRITE MATERIALS Hebei has one power ferrite material for operation at 25 KHz and 2000 Gausses. The saturation is high at 5100 Gausses. See Table 6A46 Appendix 6.1 Listing of Catalog Data for Ferrite Core Suppliers Tables Appendix List No. 1. 6Al 2. 6A2 3. 6A3 4. 6A4 S. 6AS Vendor TDK \" \" \" Magnetics Figures Appendix List No. COMMERCIAL POWER MAGNETIC COMPONENTS 199 6. 6A6 7. 6A7 8. 6A8 9. 6A9 10. 6AI0 11. 6A11 12.6A12 13.6A13 14.6A14 15.6A15 16.6A16 17. 6A17 18.6A18 19.6A19 20.6A20 21.6A2l 22.6A22 23.6A23 24.6A24 25. 6A25 26.6A26 27. 6A27 28.6A28 29.6A29 30.6A30 31.6A31 32.6A32 33.6A33 34.6A34 35.6A35 36.6A36 37.6A37 38.6A38 39.6A39 4O.6A40 41.6A41 42.6A42 43.6A43 44.6A44 45.6A45 466A46 \" \" Fair-Rite \" Tokin \" MMG-Neosid Philips \" \" \" Epcos \" \" Steward \" \" Ferronics FDK \" AVX \" Kaschke \" Tomita Vogt Domen Vogt Iskra Hitachi \" TSC CMI Samwha Cosmo Isu Acme \" Hinoday Mianyang Hebei 6Al,6A2 6A3 6A4 6A5 6A6 6A7 6A8 6A9 200 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Table 6A.I-Properties ofTDK Power Transformer and Choke Ma terials PC46 I'CI6 PCo4 ~1 \"\"''''1 ''''''''_!r - . . . \"' 2501Io25\"J. 3Z00025'\" 24OOo2ft _r_ 57OI25'Cl 36CQ5'CI ~l [100kHz. 2CIOtnTl \"'\" ow\",., 2SIlI75'C1 250[46'CI 4Ot(8O'C1 41IO[100'C! 88O(IOO'C! 300(1OO'C) s-....,., ....gnootc .... III .. T !Z\"CI &30 830 \"0 do~ IIOO\"C) - \"0 -~\"',.\",,~ Br OIT [ZSC) 120 115 1 10 ['OO'C) 110 10 10 c-_ He AIm [26\"C) 12 11 13 IlIaoNmI I'OO'C) \u2022 10 0 ... c.....~ Te 'C _?,.ZJIJ it 230 ;' 215 Table6A3-Properties ofTDK Common-Mode Choke Materials _!lIIC PfIEVEIO'1OII~ CHOKI! -- HSI2 HS72 IISl0 ...... ,.-,\", .. -- 1SOQo2S\", ,~ f!!!OOn*I. . -~ --- ~x 'it\" 10 30 30 t- t'_I tl_> --- ---donoi1y' \u2022 ..T 410 4.0 -(Mon ..... \" ' -\"'d!r!Iy '\" OIl 70 10 .20 c-two_ ... MIl a 8 , c..._ ... T. 'C .,30 .'30 .'20 - ..... ~ ~ ~ 1 D.2 D..2 ~ do .\"... ....... 0- . .... 0- ...... 0> ........ ge .... \u2022 lM _..- .... 6tlMlned~ IDn:IiIW (lICn!t III \"-\" ......... ~~ Ihawn.. Tc Q - - 01\" (.IO- YC) (\"C)I\"I'I~ _ (D140 >125 >120 4300 4300 4200 430 430 420 WOO 800 800 100 SO 80 0.1 0.04 0.04 8 3 3 <3 <3 <2.5 1 .15 .1 4 .S 4.S 4.9 Table 6A.8 -Fair-Rite Power and Common-Mode Choke Materials - ..... - 'T7 70 n \" \" ..... - ... II1II B~laa-.... t300 ...., ..... I 'DODO .... 00n00y ...... B .... ..... \"\"\" \"\"'\" 4000 mr ..., ... ..,. 300 .... ._- - H ,. :V.S 'D 'D \u2022 \"'\" IlOO lOCO ... ... , .. -.. .... o-ty - B. \" .. , ... 'ODD , ... , ... In' \". ,'\" 'DO ' .. '20 c-..... - H. .. ..., ,. ,. 'D ...... lUi ,. US 13 \u2022 -'-- , .. \u2022\u2022 &\\0, ... .. 7 ,S 'S . - , , 1 . , ..... .-f--T~ea.ttonCII vc \u2022 ,.2 \u2022 .0 \u2022 ~ F'WTftMIb(Iyt\u00bb7D\"C) - CwteT~ -C >; >2OD \"\"'\" ,\"'\" \"40 ., .. - Don \u2022 '0' \"0' '0' . ,.. .. Powwu.~ - P 2SIHI \u00b7 2OIXIO\u00b71C1J!C 20D ..:11,5 - '40 - ,0QIttz - ,ClOD Q - 1DIJI'C - .,.., - - - ......... ..- - f-- '-- -- L <3 <2.0 a, .\" .s - \u2022 <30 - <30 ... - \"-- p . , I ... . , -I - s - - - - - s.. .. s-9tIDr.-orw 11li111 '., 1t ,S 20 21 -- COMMERCIAL POWER MAGNETIC COMPONENTS 203 Table 6A.9 -Fair-Rite EMI Suppression Materials \"'-tY UnA -,- ., .. OJ II' T1 71 n -~ II, I 125 500 .... 000 2000 2300 25110 oe.togaw -Conoly - ZI60 3000 ~750 3000 4100 !>OOO 4000 \",T 8 235 300 :us 390 '60 500 -- ..... St/ongIIl - 10 '0 .0 10 10 37 .\u2022 .0 Nm \" 800 800 \\100 800 \\100 \"\"\"\" 800 - --~ - ,2QO 1100 I2QO :1400 tI\"\" ..... '000 \",T 8. I~ 110 \u2022 20 3010 \" . .\"\" 100 ~- - '-II .3e .JU .... .22 . .. ,e Mo i( '28 21! 2' <0 17' Ie \" 5 U.F_ '0- \"\"III!. 32 16 1~ 50 '.5 4.5 7 -~ ,... U 1,0 ' .0 .1 : , I , I .1 T_~o/ vc 10 6 1.2 .B ...... ~ (20-1O'C) .s - - Quior_ 'C T. .asa \"eo ,130 I >200 >200 I >200 \"eo I Roo..ovooy gem P ' 0' '0' '0' 2'0' 10' 2'0' .0' --_u. Donoity -- p 2SUU \u2022 2IXD G \u2022 1CJ01C - - - - 200 <115 - ~OOIcHz\u00b7,DOD G\u00b7 ,OO'C - - - - - c,lIO - ---F_ .. ~ MHz [l <100 - c'O - <3 <2.5 <2.' ~ E .2QO 30-\"'\" 3O-2QO - <30 - <30 .t.r.. : - - - - < \u2022 ... - I - - - <,15 - - - I---800 ... _\",,_ \u2022 0 12 .. 11 la\" 17 11& \" 15 -- Table 6A.I0- Tokio Power Ferrite Materials _c_ Ull\" 8\", - Uta -ApjIIIM....-. .... MH:I <0.3 ,Q.3 O.S-\" .O -,...,--, p , - - , 5IIIIt2D'Io - ~-....---. 23\"1: 520 5'0 530 500 limo \",T '-\"\"- 111111M111 ,oo\u00b7c 4.0 400 - -z:rc '00 '00 2110 120 --.-..., om. l00\"C mT 6& 1511 .211 aD 23\"C .a.o 14.3 43.6 11.0 --lolly Hemo Mn V &.5 l00'C 6.0 5..0 -\"'--(1-.) _11/1 , '0\" <5 ce 4 <20 C .... ___ 1. \"C 220 220 240 '80 2:S'C 560 8Oi) ~ r---, __ T Po. IID\"C r--3SO 450 500 100'C 2!50 \"0 .:10 eo.._ 8O\"C Wi~ -__ 1 P\", r--- 8O'C 500 8O'C 3110 t.HII_T P\", r--- 80'(; Jell 0..17 d II9'm' ..... ,0' 4Ax1G' \u2022\u2022 111<10' ...... ,0' 204 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Table 6All-Properties ofoew Tokio BH3 vs those ofBHl llam BH-3 BHl InilioJpermieabiil)' I'i 18OOf2O'l1, 25OOt2()% ---.. npt:\"'1MIy Bmo; mT 2:!\"C 530 520 Hxrc 420 410 Elf..,.\". retantilly 8r mT 2:!\"C 120 100 100'C 70 55 EIIectve N\\Ka1Ion coen:MI IOroI He Aim 23'C 17 13 l00'C 13 5 Core lou Pcv kW/rrf 25'C 580 SSO 6O'C 400 350 100'C 380 250 120'C 420 300 C .... poInI Te 'C l00'C 280 220 __ I.t 25\u00b0c .t 15\u00b0c Co C) type .\"\"'kat ..... (3000A/_) ( M) .r_ 3C15 1800 .. 500 . 20 0 > 2 0 0 3 3 - . 4. 8 4. 8 6H 40 6H 41 6H 42 24 00 25 00 34 00 S 30 53 0 53 0 f - - ~ 43 0 43 0 _ . 11 0 11 0 11 0 10 10 1 0 1 -_ _ < 3 < 3 < 3 90 75 6 0 75 60 5 0 eo 5 0 40 5 0 40 45 _. 4 0 <4 5 55 6 5 0 55 0 45 0 55 0 45 0 S5 0 45 0 35 0 30 0 35 0 SO D 32 5 30 0 32 5 37 5 - - - - ---= -- . - - - - - - - - - - - - .-- -_ . 8 - _. - - B B > 2 0 0 > 2 0 0 > 2 0 0 2 2 2 4 .9 4. 9 4. 9 7H l0 15 00 48 0 38 0 -- \u00b7,S O - .-- 30 ' . _ < 5 - - - - - - - - - - 10 0 BO 10 0 40 0 40 0 50 0 ~ - 8 - > 20 0 5 4 .8 7H 20 10 00 48 0 ~ -- 13 0 .. 2 5 - < 4 _._ = ..... - - - - -, - - - - - 50 40 50 20 0 20 0 25 0 8 > 20 0 5 4 .8 N ~ ~ ~ ~ .., .... ~ ~ ~ 2 ~ ~ 00 ~ ~ ~ ~ ~ ~ t ~ q ~ ~ 00 COMMERCIAL POWER MAGNETIC COMPONENTS 215 ~ P O W E R A P P U C A T IO N S = N =\" B1 I B 2 1 83 \u00b7 \u00b7\u00b71 BS . If f I F1 I F2 , 'F 4 - - U ni ts T .l :O nd _ _ S I ~ ' E C 1 ~ =\" tD S ym bo ls =\" P W 1. 1 PW lb PW 3b PW 1b P W 'Z M fP W 2b PW 2b PW 3b PN oi D fW 5 b ~ ~ III 25 'C 25 00 ,* 2 5% 19 00 t ZS 'J( ; 19 00 t 25 5( . 18 00 , *2 5% : 20 Q 0: ~ 2 5% llO O t 25 % 19 00 * 25 % !1 0 0 't 2 5% ~O O 2S 'C 45 0 4a o. -4 70 \"i ll 47 0 '~ S' o 42 0, 31 10 =\" 8 a l' l-! A Im 10 0\" 0 3' 40 36 0 JB O :.3 80 38 0 34 0 32 0 31 0 ~ I ~ ~ (n om in al m T 16 00 ZS ''C '' 41 10 49 0 ~ . :\" ~ O SO O ~ 8 0 45 0 42 0 C> ve llH !s l Ai m JO O 'C \" '\u00b7 37 0 38 0 41 )0 40 0 , 40 0 a7 0 35 0 33 0 .., ~ ., .. 2S 'C ', .. 12 H i \u00b7 '1 6' 16 16 1I i 15 15 ..... tD H < A Im 1 ~ ' C :: 10 :' t'O ' .. III 10 :' :\"1 0: '0 ,1 0 10 ~ ., ~ T, \"C ,> 2 00 > 2 !1 O ,. : :: > i! 50 :: ,: > 'l 50 ' > 2 SC l > 2 30 : > 2 0 0 > 2 Q O ~ 16 ~ H ~ \u2022 1 00 'C 0 = :,: ~ 10 0 .. ~ .... 20 0m T , . 8 0 , tD 25 k 'H r \u2022 1 '0 0 '; :1- '< ; 15 Q: = za O m l < le O .. , .. ~ - 32 k H r \u2022 10 0\" C C\" IJ ZO O m l . < ,2 ~ . <2 O Q .. >< l~ 9 c oH O ~ I ~ > 60 k H l \u2022 l0 0\" C < ZO O m T . ~ 3- 40 < 3 50 - < 3 30 < :2 BO ' .., P ll lP m W /1 iIT I1 1Q O lH t -'1 00 'C rJ ) >< ~ I l0 0 m T ,, < 1 50 0 ~ 10 0 kH z ~ '1 00 'C c:r ZO O m T < 7 00 < 6 (1 0 .. .. 58 0 ~ C> 30 0 k lb \u2022 'l O O 'C ' ~ e .. 5Q m T : :< 1 20 < 1 00 ~ 51 10 'k H l c , 0 0' c, : ~ C> ... = . ' SO 'm T ' .. < 2 ]0 < T ao ~ , t, 4H ~ ,\u00b7 . l 0 0 'C , ~ . 5O :m T \" < 6 00 1. 5 M H 1- l0 0 'C :: ~ \"S O: m T ' .. . , . < 1 21 )0 t\"\" ' .P . T nx -m -, .. \"1 ' 6 .. 6 . . 6 , 6 , 6 6 6 ~ ~ D el lS it} ' gl s: m J .. ... /1 . 4.8 4. 8 U U 4. 8 4. 6 U ' .., V ak Je s m ea su re d on 0 l1 i X 0 12 >1 14 r e1 \u00abe nc e to rO id . ~ 0 -V al J< !s m el lS ur ed on 0 2 1 .1 )( 0 1 3 .8 .1 1 r ef er en ce t o 'o id . ~ ..... ~ rJ ) COMMERCIAL POWER MAGNETIC COMPONENTS 217 218 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2000\u00b125% -3 ~ ;- ~ I -3 e ~ = ~ ~ ~ a:: = ;- ::3 . = ~ IV ll lt 8 n il 15 t; f. ~ 16 K H z 1 0 K H z\u00b7 \u00b7 2D \u00b7C -6 ~~ ~ 10 (D ~~ ~~ ' (A Im ) (\" C ) _. . (O -m ) - (k g !m 3 ) 2H l 15 00 0 0. 95 X 1 0 -5 0 .1 1 X IO -' tc 35 0 2 .3 10 5 0. 06 5 .0 X 1 03 - - ~ - - - - - - - - ~ - - - - - - ~ 2E 2 10 00 0 1 .5 x 1 0 -5 0. 1 X 1 0- ';- C 37 0 4 .0 12 0 0. 02 4 4 .9 x 1 03 3 2E 2B Ili DO O 0 .3 4 x 1 0 -5 0. 28 x 10 -6 /,C 39 0 8 .0 12 0 0. 04 7 4. 9X 1 03 ~ - - - - - - - + - - - - - - - - ~ ' - - - - - - - - + - - - - - - - ~ - - - - - - - - - + ' - - - - - - - - 4 - - - - - - - - - ~ - - - - - - - 4 - - - - - ~ - - - + - - - - - - - - - - 2E l 70 00 1. 8X 1 0 -5 -0 .8 X I0 G tc 41 5 8 .0 15 0 0. 01 2 4 .9 )( 1 03 3 2G l 70 00 0 .5 4 )( 1 0 -5 0. 41 )( 1 0, -s /'e 41 0 6 .0 13 5 0. 02 4 .8 x 1 0J 2G 3 SO OO O .J sx IO -s a. Z 8x IO \u00b76 /\u00b7e 43 0 S .1 14 5 0 .2 4 .9 )( 1 0 3 \" - 2 F ' 53 00 0 .2 )( 1 0 -5 L O X IO -s /'C 37 0 1 .2 12 0 0 .1 3 4 .8 X I0 3 4 - - - - - - - 1 lO S e 40 00 0. 1 x 10 -~ 0. 2> <. l o\u00b7 '/\" C 41 0 8 .0 14 0 0. 1 4 .9 x 1 0J ZE . 40 00 0 .1 5 )( 1 0 -5 -O .5 X IO -' /\" C 45 0 11 .9 18 0 0. 1 4 .8 )( 1 0 3 2F 6 33 00 0 .0 7 )( 1 0 -5 2. 65 X 1 0 6/ ,C 47 0 11 .9 > 20 0 2. 1 4 .8 X 1 03 5 ~ --- - 20 3 30 00 0 .3 X 1 0 -5 -0 .4 x 1 0- '/' C 45 0 11 .9 16 0 0. 9 4 .9 x 1 03 - - ~ ~ - - - - - - ~ - - - - - - - 4 ZE e 30 00 0 .1 )( 1 0 -5 -0 .5 x lo 6 / 'c 49 0 11 .9 > 20 0 0. 23 4 .9 X 1 0 3 4 -- ., - ZE 7 24 00 0 .1 5 )( 1 0 -5 1. 25 X 1 0- it C 49 0 11 .9 19 0 3 4 .8 x 1 03 ._ -- -- + -- -- -_ ... -. ~ 2F 8 22 00 0. 1 x 1 0 -5 6 .3 x lo \u00b7S te 49 0 9 .5 > 20 0 8 4 .8 X 1 03 5 ~ - - - - - - ' - + - - - - - - - - 4 - - - - - - - - - ~ - - - - - - - 4 - - - - - - ' - - - + - - - - - - - .. -_. .- .- -- - 2 E IC 20 00 O .I S )( 1 0 -5 1. 5) ( IO \u00b7'/ 'C 51 0 14 .3 > 23 0 0. 37 4 .8 x 1 03 2C 3 20 00 0 .6 )( 1 0 -5 3. 0) ( IO \u00b7& /\"C 37 0 15 .9 11 0 1. 3 4 .9 )( 1 03 2H 8 80 0 O(~ ~O~ ~~) s~ .4 X ~ O-'/ 'C ._ ~~O !. 22 .0 > 20 0' \" 2. ~. - 4 .8 )( 1 0 3 1 n o ~ ~ ~ ~ ~ ~ ~ ~ ~ .., .... n n ~ ~ ~ rJ j N .... \\C 220 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Spec. Unit Mn-Zn Cerna Ni-Zn lerritI:. 2500HMCl 25OOHMC2 250BHC 300BHC IJi - 4500(+ 20\u00b0(,) 4500 (+ 20 0q 250 300 4100 (+120 0c) 4100 (+120 0c) fe mHz 0.4 - 8 8 mW 10.5 (+25 0q 8.5 (+25 0c) 30 <30 Psp cm~ 8.7 (+100 0q 6.0 {+100 0q (3) (3) tgt, / . 10-6 30 <30 - - (3) (3) Il.J.Il (MHz) R mT 290 330 - 320 Rm mT 450 - - 130 Br mT 100 - - 80 He Aim 16 - - - Te \u00b0c >200 >200 >250 >250 COMMERCIAL POWER MAGNETIC COMPONENTS 221 - - - - - - - - - . M~; E~I ALS I I -- ... . ~ . S Y M B O L U N IT TE M P C H A R A C T E R I S T I . ~ , .. .. . AC I N IT IA L P E R M E A B IU TY I ,n ac --- 23 '(; --.. - -.. - \u00a5 _ \u2022 \u2022 \u2022 _ _ \u2022 SA TU R AT IO N F LU X D E N S IT Y ! 23 'C B m s m T f_ .\u2022 _-- - ; 10 0' C _ ._ -_ .- .- . -. -. .. .. .. . . .. . \" 23 'C R ES ID U AL F l.U X D EN SI TY B rm s m T 10 0' C . _._ - 23 'C C O ER C IV E FO R C E H an s A im -- lO O t: .- - -. .. .. .. . \" ... _- _._ -_ .... 23 'C -- -_ .. \" CO RE L O SS 60 'C (f \"' 2 5 kH z B m = 20 0m T ) Pc kW /m ' 10 0' \\; 12 0' \\; -_ ... ._- -- 23 'C C O R E LO SS 60 '\\; (f = 1 00 kH z B m \", 20 0m T ) Pc kW /m ' 1 0 0 't 12 0' C -_ .. ..... . _- -\u2022. .. - -\u2022 .. - ---.. . . - .. R EL AT IV E LO SS F AC TO R ta n8 /l li ac X 1 0. 1 2 3 't -- - C U R IE T EM PE R AT U R E Te '\\; - SP EC IF IC R E S IS TI V IT Y p Q -m 2 3 't D E N S iT Y ds kg /m ' 23 'C L - - - ~ - - -- - - - - -T S B -5 S S B -3 L S B -7 C . - - . ~ ... - ~ ~ 2 5 % \u00b1 2 5 % \u00b1 2 S % 3, 00 0 1, 60 0 2, 40 0 -. -. . r - 48 0 51 0 50 0 -_ ... .. 34 0 42 0 38 0 . -- \u2022.. . ~ ._ .. 18 0 18 0 15 0 .- .. -- 10 0 70 .. 12 15 13 --- .\" .. -- - 8 7 -- .... .. - .. -- 14 0 20 0 14 0 - _. . __ .. _ -- 14 5 15 0 10 0 .... .... . _. 17 5 12 0 80 - 13 0 90 -_ ._ \",- _ .. 1, 10 0 1, 10 0 78 0 I, IS O 82 0 56 0 --- -. 1, 50 0 75 0 50 0 - 85 0 57 0 .1 ., \u2022\u2022 2 .5 3 .5 2 .0 > 1 9 0 > 2 6 0 > 2 0 0 0 .4 1. 5 5 .0 4 .8 5 x 1 0' 4 .8 x 1 0' 4. S x 1 0' ~ - - - ~ - - - - L - - - - - S B -9 C l. 25 ~ 2, 60 0 49 0 36 0 14 0 .... _ .- 60 . _ -- -- -- 12 6 14 5 90 \" . . - - . - - - 70 80 68 0 45 0 40 0 48 0 .2 5 .0 > 2 0 0 5 .0 4 .S x lO S -- . , f1 0 kH z ~ ;: ~ .. it So .. r a: = ;' :::1 . = ;r w w w ~ ~ ~ r=; n I ~ rI J ~ ~ := ~ ~ I rIJ .\" oumTlRSlXS ~ ~~~~~Ll-UNI~ --! _~L_-_2 _+-D_L_-J-i-DL- -4C-+_DL- -SC-+-_DL_-_6C-j'-D_L-_7C--D_L_-SC---j ! 2.200 I .SlIO 250 l50 650. 1.200 3<0 mT 280 260 ' 10 .- . - ----------4-----~----~---_T----_+ 310 ! ' 00 380. -- ---r---t---. _. B ... SATURATION nux IlfNSITY (B800 ) 20 15 23 20 18 I~'~' ~\"; '~~' -\" . COERCIVE FORCE Hem. I )t Ier' RELATIVE LOSS FACTOR lInAlJ'lOC I .' IOOkHz ' mT liD ~60 I ~O 27 24 ---------~---+---+--~------+---~ AI .. 16 10. 12 13 12 12 - -I-.---+---~---+---. -- \u2022 RELATIVE TEMP. FACTOR au' 22 14 16 I ; 224 MAGNETIC COMPONENTS FOR POWER ELECTRONICS SYHIOLI UNIT' TDT V!>II v..\" VN) PMI rMl PM) P:wtj CONDrT\\Ol'I1 iii 2l,0,\u00a3 900~ J:JOi\u00a5..:2O'9!i. .... ...,.\". nIO,Y.:lOW. 2OOOjV.,JO% 1900~ ZlOO IY~ 8 2l,0;t l30 2lO 210 'SO I '\" '70 I ~ ''Il10 I SIO \"' \" .. .1 loo,t :tlO 190 , .. 3\u00ab1 1 \"0 ,so I 400 ''' 1''0 390 I \u2022 H tv.- .600 .600 .200 400 I .600 ..., I 1600 ... 1 1600 400 \" Ii< tv.- 2l'~ \u2022\u2022 40 ,. '1 ,. I. Il 100.' 12 2l \" I. ,0 10 T. .t \u00a3%130 .rn1)(J \"\"1<1 \"'- -\"WO \".lSO W0.2)l '\" \"lit. 2lot 1.1 2., 2., PC \".,WI 2OOaIn. ,t ,.. I ,40\" 9\\\" I 200\" ISO\" 1 l~ no 1 1311 7S I lIS tD, 1240 210 I ~ 'KIIZ 16 I J2 16 1 12 ]2 1 1W 2l 1 '\" ICI I 2) 2l 1 1<1 1<1 1 1{ .. Iv... so \"\"\"10 \u00a3%10 3 , 6 o...c,. ;u.l .. 7 .. .. , ... ..\u2022 U .. c ... c ... \"\"'\"' Co\"\" E.U E.U E.U E.U v .... v .... MONYTQR .c- ..,.., -c- -c.... ...... t:... <;on. y~ TEST SYMBOLs UNITS CONDJTI()NS PlICI PMl PMll PI>e P\"\" PM9 WiJ 25IE ~y~ 2000iY~ l4OOl'I..2Mt. 2lOOtI.2O% 2AOO.%ln% JOOOjY~ II 25.~ .SO , ,,, .70 1 SOO '10 I '\" _ 1 '10 460 I 410 \"' 1 \"\"\" \",T .. 100,~ 3\u00ab1 1370 310 1 400 340 1 370 190 I 410 )110 I 400 400 I .20 A Ma 400 11600 400 11 600 400 11600 400 11 600 400 11600 400 11600 lljE 11 16 12 II 11 11 H< ,.., 100,t I. ,0 9 T< ,t L%11IO waso l'Io2SO ly.zJD .('/0210 \u00a3\\U(IO I< MIi1 21'\" I .\u2022 2.0 I.' lOOaoTlI'\" no I 310 11 1 II! 130 1 llO 3111 300 PL .. WI..,} lOOooT lOO;~ .101500 4<0 310 {kHz 2' 1 10 16 1 2' D l so so 1100 100 100 II to ... 6 n-ky s/ ....... .4!- 76 ...... ..... ........ 4W-207 2!i().11' F SupernollOr' s.w.z ...... . . 70 .-- 2 ..... .oD4--CUi ~1 19 ~ S S~IT\".ndur , .... 1 \u2022\u2022 2..2 .90 up , .. 30 '''''' .. ...... 10 31..1-45 7 ... ,\"\" \u2022 ~rphOt.\"\"A 1,5..,& 1 5.-U .110 l.p \"\" .. ~ .... ,04-.1 32-7.8 ........ E . _ ,--- ...... . ..... .... ooa-oz ....... . 0,\u00b7025 7'i-. -~ ... _. G _0 , 4..,5.., &..IJ '4.500 ' M <60 eo.w __ 35 ....... . 1011HL 1T - 232 MAGNETIC COMPONENTS FOR POWER ELECTRONICS SISSnYOOlnl-I-NOIcnaNI Figure 6Al0 - Core Loss Curve vs Frequency for 2 mil Silectron SiFe- Arnold 234 MAGNETIC COMPONENTS FOR POWER ELECfRONICS en 'W CI) CI) ::I ~ ~ o = ::.: I CD I Z o ~ ::I o Z WATTS PER POUND 236 MAGNETIC COMPONENTS FOR POWER ELECTRONICS I lOOO~-----+~~~4--4--- 500 t----___+_ - 200 ,... e u '- 100 3 S I - U) 50 U) 0 ~ ~ 20 0: a u 10 1 2 3 5 B(kG} Figure 6Al6- Core Loss for Toshiba Amorpbous Alloy COMMERCIAL POWER MAGNETIC COMPONENTS 237 238 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Nanoperm\u00ae is a registered trademark of Magnetec GmbH COMMERCIAL POWER MAGNETIC COMPONENTS 239 COMMERCIAL POWER MAGNETIC COMPONENTS 241 ,'6 -~ V '\\ ~ ~ ~ \\ f..--\"\", ~ 6~ I-~ ~ ~\\\\ ~ ~ ~ f--- --.~ ~:\\\\ = +8 J +. '& ~ -8 -'2 -16 100 1000 10000 M: Flu\" .,..,..., ( .... , .... FNquency \u2022 1 khz Figure 6A25- Permeability vs Flux Density Hi-Flux Arnold- Permeabilities from top Curve to bottom are 200, 160,147, 125,60,26 and 14 COMMERCIAL POWER MAGNETIC COMPONENTS 243 244 MAGNETIC COMPONENTS FOR POWER ELECTRONICS COMMERCIAL POWER MAGNETIC COMPONENTS 245 246 MAGNETIC COMPONENTS FOR POWER ELECTRONICS COMMERCIAL POWER MAGNETIC COMPONENTS 247 248 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 310 f-I-I..- e-300 1110 100 10 1 PERCENT PERMEA8lUTY VS A. C. flUX DENSITY 7 20 ao 48 110 100 h W ~ II \" / / / :;;; C;;; V - ~ 1/ - l..I---- 200 aoo 400 IlOO 1_ _ aooo _ l1OOO 10._ A. C. FLUX DlNSITY {G.-j Figure 6AJ3- Penneability vs ac flux density for several different penneability iron powder cores. Curve nwnbers are the penneabilities. From Pyroferric 100 90 -~ 80 --., u 70 c as I 60 .E 'ii 50 c m 40 .;: 0 - 30 c 8 ... 20 at a. 10 0 ~ 1 ~ I\" l\\ '~ r\" \" , ~ \"- t----.Io.. '\" ~ ~ ......... ~ 100 MHz ~ r---. -........ ~ so MHz ......... ......... ~ 100.... - I 25 MHz_ I I o 1 2 3 4 5 6 7 8 9 10 11 1213.1415 H = .41t NIII. (Oersted) Figure 6AJ4-Percent reduction in permeability with DC bias for several different permeability iron powder cores. Curve nwnbers are the penns. From Pyroferric COMMERCIAL POWER MAGNETIC COMPONENTS 249 250 MAGNETIC COMPONENTS FOR POWER ELECTRONICS This chapter has listed the properties of a great number of materials and cores from the major power magnetic component vendors. The final chapter will be present a compilation of many of the design aids that are available to the engineer who is making the choice of the optimum power magnetic component. Chapter 7 DESIGN AIDS IN MAGNETIC COMPONENT CHOICE FOR POWER ELECTRONICS INTRODUCTION In the early days of power electronics, the design engineer had few design aids in magnetic component choice. As a result, the choice was made by using whatever component happened to be on the shelf and after numerous hit-and miss tries, he finally found the most suitable choice. At that time, both power semiconductor and high frequency power materials were primitive with very little choice of materials or shapes. However, today with the explosion of information through media like the Internet, CD ROM, CAD-CAM, and computers in general, there is a great deal of help that makes the proper choice faster and with greater assurance of success. This chapter will review the various design aids available. In Appendix 7.1, articles of interest on Power electronics are listed. In Appendix 2, the pertinent IEC and ASTM standards on magnetic components and Materials are listed. 7.1- Books on Power Electronics The following is a compilation of some of the power electronics books listed by EJBloom Associates; Books on Power Magnetics 1. Transformer and Inductor Design(2nd Edition)- C. McLyman 2. Magnetic Core Selection for Transformers and Inductors (Second Edition)- C. McLyman 3. Applications ofMagnetism-J.K. Watson 4. Handbook of Transformer Applications- W. Flanagan 5. Designing Magnetic Components for High frequency DC-DC Converters- C. Mc Lyman 6. Handbook of Modem Ferromagnetic Materials- A. Goldman Books on Power Electronic Circuits 1. Modem DC-DC Switchmode Power Converter Circuits- Severns and Bloom 2. Switching Power Supply Design(2nd Edition) A. Pressman 252 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 3. High Frequency Resonant and Soft Switching Converters-VPEC Staff 4. Power Supply Cookbook(Second Edition) M.Brown 5. Fundsamentals of Power Electronics(2nd Edition)- R. Erickson and D. Maximovic 6. Power-Switching Converters-S.Ang 7. Elements of Power Electronics-P.Krein 8. 1995 VPEC Seminar Proceedings 9. 1996 VPEC Seminar Proceedings 10. 1997 VPEC Seminar Proceedings 11. 1998 VPEC Seminar Proceedings 12. 1995 VPEC Seminar Proceedings 13. 1999 VPEC Seminar Proceedings 14. Introduction to Modern Power Electronics-A. Trzynadlowski 15.2000 VPEC Seminar Proceedings w/CDROM 16. Advanced Soft-Switching Techniques, Device and Circuit Application-VPEC/CPES Staff PSMA Industry Standards and Publications 1. The Power Technology Roundup Report (Year 2000)-PSMA 2. Handbook of Standardized Technology for the Power Sources Industry (2nd Edition)-PSMA 3. Low Voltage Study-Workshop Report L. Pechi-PSMA Circuit Design 1. Switch Mode aPower Conversion-K.Sum 2. SPICE-A Guide to Circuit Simulation & Analysis using Pspice(3rd Edition)-w?IBM Program Disk-P. Tuinenga 3. Modeling, Analysis & Design ofPWM Converters-VPEC Staff 4. Pspice Simulation of Power Electronics-R. Ramshaw 5. SMPS Simulation with SPICE 3 (wlDiskette)-S.Sandler 6. Circuit Simulation of Switching Regulators Using SPICE (wlDiskette)-V. Bello 7. Switch-Mode Power Supply SPICE Cookbook (Includes CDROM)-C.P . Basso 7.2-Power Electronics Magazines The following magazine are concerned with power electronics; 1. PCIM Power Electronics Intertec Publishing Co. 9800 Metalf Ave. Overland Park KS 66212 DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 253 2. Switching Power Magazine Ridley Engineering Co. Ltd. 1575 Old Alabama Road Suite 207-147 Roswell, GA 30076 3. Magnews UK Magnetics Society Berkshire Business Centre Post Office lane Wantage, Oxon, OXI2H, UK 4. IEEE Transactions on Magnetics IEEE 445 Hoes Lane P.O. Box 1331 Piscataway, NJ 08855-1331 5. EDN Cahners Publishing Co. Cambridge, MA 6. Power Pulse Darnell Group 1159 B. Pomoma Road Corona, CA 92882-6926 7. Power Quality 7.3-Power Electronics Organizations There are a number of government organizations, societies and private groups involved in power electronic. The are; 1. IEEE Power Electronics Society IEEE Power Electronics Society Robert Meyers, Admin. 799 N. Beverly Glen Los Angeles CA 90077 2. Power Electronics & Electronics Machinery Research Center Oak Ridge National Laboratory U.S. Dept. of Energy P.O. Box 2009 Oak Ridge TN 37831-2009 3. IEEE 445 Hoes Lane P.O. Box 1331 Piscataway, NJ 08855-1331 3. Power Sources Manufacturers Association P.O. Box 418 254 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Mendham, NJ 07945-0418 4. Electric Power Institute 5. National Science Foundation 6. PCIM 7.4 Power Electronic Web Sites There are many Web sites related to power electronics. We will try to list all we now; 1. pesc.org 2. orln.gov/etdJpeemcIPEEMCHome.htm 3. smpstech.com 4. psma.com 5. efore.ft! 6. jobsearch.monster.com 7. greshampower.com 8. tycoelectronics.com 9. spangpower.com 10. ardem.com (R.D. Middlebrook) 11. pels.org 12. home.aol.comlDrVGB (V. Bello) 13. venableind.com 14. darnell.com 15. cpes. vt.edu 16. kgmagnetics.com 7.5 Power Electronic Conferences The Power Electronics Society Sponsors or co-sponsors several conferences. They are 1. Power Electronics Specialist Conference 2. Applied Power Electronics Conference 3. International Telecommnnications Energy Conferenc There are other Conferences related to the Magnetics community; 1. Intermag Conference 2. Magnetism and Magnetic Materials Conference(MMM) 3. International Conference on Ferrites 4. Soft Magnetic Materials Conference 5. Intertech Conferences on Magnetic Materials DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 255 7.6-Power Electronics at Universities and Research Labs Listed below are the universities and research labs that are doing major project in power electronics; 1. Colorado Power Electronics Center (CoPEC) 2. Caltech Power Electronics Group 3. School of Electrical Engineering, University of Belgrade,Yugoslavia 4. UC Berkley 5. UC Irvine Power Electronics Laboratory 6. Virginia Power Electronics Laboratory(VPEC) 7. University ofWisconsin-Madison(WEMPEC) 8. Georgia Tech Electric Power Research 9. North Carolina State Electric Power Research Center 10. Surrey University Electrostatic Systems and Power Electronics Research Group 11. Texas A&M University 12. Northeastern University 13. University of Central Florida 14. JPL Power Electronics Group 15. University of Waterloo 7.7- Web Tutorials Listed below are some of the Internet tutorial sites; 1. Switching Power Supply Design-Jerrold Foutz at smpstech.com 2. Interactive Power Electronics OnlineText- ee.uts.edu.aul~venkatJ 3. SPICE-A Brief Overview-seas.upenn.edul~jan.spice.overview.htm 4. Power Factor; Dissipating the Myths- Microconsultants.comltips/pwrfact Ipfartil 7.8 Power Electronics Software There are many power electronics software programs. Listed below are the ones listed on the ejbloom associates website 1. Power Witts\u2122 Forward Converter Simulation 2. Pspice Electronic Simulation-N.Mohan 3. Computer Aided DesignforIndictors and Transformers-KG Magnetics 4. Magnetic Core Data for Converters-KG Magnetics 5. Flyback Converter Magnetic Design 6. Specialty I-Magnetic Design-De-DC Converters-KGMagnetics 7. Computer-Aided Inductor and Transformer Design-KG Magnetics 8. Specialy II-Common-Mode Chokes-KG Magnetics 256 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 9. Titan Systems-KG Magnetics 7.9-Power Electronic Short Courses EJBloom Associates runs frequent courses on Power Electronics. For information log on to ejbloom.com or e-mail toejbloom@compuserve.com. The address is; EJ Bloom Associates 115 Duran Drive San Rafael, CA 94903 7.10- Component Vendors CDROM or Diskettes Many suppliers offer product information and design on CDROM disks or IBM diskettes. Below is a list of some that are available 1. FDK 2. Ferroxcube 3. Tokin 4. MetglasR (Honeywell) 5. Epcos 6. Magnetics 7. Kaschke 7.11-INTERNET WEB SITES Just about all the manufacturers of ferrites have Web sites on the Internet. In most cases, the core data can be down loaded and printed by the user. Where large catalogs are involved, the use of the Acrobat reader is needed but the vendor can often download this as well. Some of the vendors that maintain Web sites are; 1. Magnetics 2. Philips 3. Siemens 4. Fair-Rite Products 5. Steward 6. MMG North America 7. Micrometals 7.12-Magnetic Component Stan'\" In Appendix 7.2 below are the appropriate lEe and ASTM Standards for Magnetic Components and Magnetic Materials DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 257 Appendix 7.1 Recent Power Electronic Articles on Specific Power Electronic Subjects Planar Magnetics 1. Designing Planar Magnetics, J. Martinos, PCIM, August 2000, 102 2. Planar Magnetics, Philips Components, PClOI2, 2/2/94 3. Planar Transformers Dispense with Bulkiness, D. Maliniak, Electronic Design, Feb. 1993,34 4. Design Techniques for Planar Windings with Low Resistance, HX. Huang, D.T. Ngo and G. Bloom, IEEE Appl. Power Elect. Conf. (1995) 5. Planar Magnetics Lower Profile Improve Converter Efficiency, A. Estrov and I. Scott PCIM, May 1989, 16 6. Planar Magnetics Simplifies SMPS Design and Production, E. Brown, PCIM, July 1992, 46 7. Design of a HF Planar Power Transformer in Multilayer Technology, D. van der Linde C.A.N.Boon and J. B. Klaasens, IEEE Trans. Ind. Electr., 38, (1991) 137 8. Effects of Air Gaps on Winding Loss in HF Planar Magnetics, K.D.T. Ngo and M.H. Kuo, PESC '88 Record april 1988 9. A Comparative Study ofHF, Low Profile Planar Transformwer Technologies, A.W. Lofti, N. Dai, G. Skutt, W. Tabisz and F.C. Lee, Va. Power Electr. Center EPE, 1993 10. Planar High Density Design for Automotive and Telecommunications Applications, High Frequency Magnetic Materials Workshop '99,1999 Santa Clara, CA Organized by Gorham-Intertech, Portland Maine, 10. Planar Ferrites, M. A. Swihart, PC 1M, July 1999, 12 11. Planar Transformers Dissipate Up to 150 kW with Copper Trace Windings, G.T. Tarzwell, PCIM, March 2000,58 Integrated Magnetics 1. Issues in Flat Integrated Magnetics Design, E. Santi and S. Cuk, 1996 Power Electronics Spec. Conf .Proc. Vol. 2. Integrated PC Board Transformers Improve PWM Converter Performance, B. E. Mohandes, PCIM, July 1994, 8 3. Integrated Magnetics Design with Flat Low Profile Cores, S. Cuk, F. 4. Stavaovic and E. Santi, Power Elecronics Group,Cal. Inst. Of Technology Surface Mount Design 1. Manufacturing Advances Increase Availability of Surface Mount Magnetics, B. Tscosik and W. Dangler PC 1M, July 1994, 60 2. Surface Mount Transformers, Surface Mount Technology, Feb 1993,27 3. Isolated Innovation Marks Movement Towards Miniature Magnetics, R.A. Quinnell, EDN, July 1994, 59 Magnetic Core Materials 1. Core Materials, D.J.Nicol, PCIM, July 1999,58 258 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 2. Power Supply Magnetics- Part II-Selecting a Core Material, D.E. Pauly, PC 1M, Feb. 1996,36 3. Data Sheets Provide Clues for Optimizing Selection ofSMPS Ferrite Core Material, L.M. Bosley, PC 1M, July 1993, 13 4. High Frequency Magnetic Materials and Markets, L.M. Bosley and T. Holmes, High Frequency Magnetic Materials, '99, Santa Clara CA. Organized by Gorham-Intertech, Portland MN. 5. Soft Ferrites,Potential-Further Development, R. Dreyer and L. Michalowsky, ibid 6. High Frequency Applications of Amorphous Metal, R. Hasagawa, ibid 7. Ferrite \"Boost\" Material Improves Inductor Characteristics under DC Bias Conditions, G. Orenchak, PCIM, Nov. 1999, 48 8. Common-Mode Inductors for EMI Filters Require Careful Attention to Core Material Selection, R. West, PCIM, July 1995, 52 9. Inductor Core Material Operates Efficiently at High Frequencies, W.A. Martin, PCIM, July 1992, 10 Design 1. Core Selection and Winding Design for HF Magnetics, R. Severns, , High Frequency Magnetic Materials, '99, Santa Clara CA. Organized by Gorham Intertech, Portland MN. 2. Designing Flyback Transformers Part I.-Design Basics, R. Ruble and R. Clarke, PCIM, Jan. 1994,43 3. Designing Flyback Transformers Part 11-48 v. Dual Outpt DC-DC Converter., R. Ruble and R. Clarke, PCIM, April 1994, 23 4. CAD Software and Experience Cut High Power Transformer Design Time and Cost, PCIM, April 1992,50 5. Advances in Magnetic Modeling Using Finite Element Analysis, M. Christini, ,High Frequency Magnetic Materials, '99, Santa Clara CA. Organized by Gorham Intertech, Portland MN. 6. Redesigned Input Filter Limits DC-DC Converter Inrush Current, B. Bell, PCIM, March 2000, 66 7. DC-DC Converter Power Density Design Issues, W. Leitner, PCIM, Sept. 1990,22 8. Power Ferrite Loss Formulas for Transformer Design, S. Mulder, PCIM, July 1995, 22 9. System Integration ofa DC-DC Converter Requires a Look at All Angles, S. Davis, PCIM, Oct. 2000,88 10. Power Factor Basics, M. Amato, PCIM, Oct. 1995, 10 11. Expert SystemIFuzzy Logic Select Core Geometry for HF Power Transformers, Part I and II, R. K. Dhawan, P. Davis and R. Naik, PCIM, April and May 1995, 44 and 34 12. Understand Data Book Parameters When Selecting DC-DC Converter Inductors, L. Crane, PCIM, Oct. 2000, 54 DESIGN AIDS FOR MAGNETIC COMPONENT CHOICE 259 13. Keep Core Geometry In Mind When Designing Transformers, c.R. Wild, PC 1M, July 2000, 32 14. DC-Bias Behavior Calculation for Uniform and Non-Uniform Cross Section Ferrite Cores\" D. Lange and S. Ahne, PCIM, March 2000, 12 15. Transformer Bobbin and Core Selection Involves Interdisciplinary Design and Cost Issues, J. Casmero and R. Barden, PC 1M, Oct. 2000, 20 Applications 1. Power Supply Basics-Voltage Regulators, R.J. Shah, PCIM, April 1996, 20 2. Optimizing Flyback Techologies for Portable ACIDC Adapter/Charger Applications-Part I:Adapter/Charger Requirements, L.Huber and M.M. Jovanovic, PCIM,August 1996, 68 3. Low-Cost Battery Charger Transformer Design Require Performance and Safety Considerations, R.M. Haas, PC 1M, June 1994, 46 4. EMI Design Factors for Medical-Grade Switching Power Supplies, R. Hood and J. Belna, PCIM, Oct. 1992, 32 5. New Magnetic Circuit Design Yields High orce, Long Stroke Linear Actuators, B. Bartosh, PCIM, Oct. 1991,38 6. Telcom Power, D.L. Cooper, PCIM, April 1999,38 7. Automotive Power, J.M. Miller, P.R. Nicastri and S. Zarei, PCIM, Feb. 1999,44 8. Low-Cost UPS Guards Against Data Loss, S. Davis, PCIM, July 1992, 32 9. Mag Amps, J. Goodin, PCIM, July 1998,30 10. Low Profile Inductors, Semiconductors and Capacitors Make PCMCIACard DC-DC Converters Possible, B. Tschosik,PCIM, June 1996,9 Flexible Circuits 1. Magnetics Component, M. San Roman and D. Longden,PCIM, July, 1999, 67 2. I-MHz Resonant Converter Power Transformer Is Small, Efficient, Econ omical,A. Estrov, PC 1M, Aug. 1986, 14 3. Converters Pull for Flat Magnetism, Y. B. Salih, Electr. Eng. Times, Aug. 1992,52 4. Building Magnetics with Flexible Circuits, V. Gregory, Powertechnics Mag. (1989), 16 EM! Applications 1. Selecting EMI Suppression Ferrites Requires Attention to Complex Permeability C.U. Parker, PCIM, Feb. 2000, 62 2. Transients vs Electronic Circuits, Part IV, Ferrites for EMI Suppression, PC 1M, July 1996, 76 3. Power Analysis for IEC 1000-3-2/3- Q&A. T. Mahr, PCIM, Feb. 2000,82 260 MAGNETIC COMPONENTS FOR POWER ELECTRONICS Appendix 7.2- IEC and ASTM Standards 133 (1985) Dimensions of pot-cores made of magnetic oxides and associated parts. (Third Edition). 205 (1966) Calculation of the effective parameters of magnetic piece parts. Amendment No.1 (1976). Amendment No.2 (1981). 205A (1968) First supplement. 2058 (1974) Second supplement. 220 (1966) Dimensions of tubes, pins, and rods of ferromagnetic oxides. 221 (1966) Dimensions of screw cores made of ferromagnetic OXides. Amendment No.2 (1976). 221 A (1972) First supplement. 223 (1966) Dimensions of aerial rods and slabs of ferromagnetic oxides. 223A (1972) First supplement. 2238 (1977) Second supplement." ] }, { "image_filename": "designv10_13_0002307_s00542-006-0303-z-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002307_s00542-006-0303-z-Figure1-1.png", "caption": "Fig. 1 Schematic illustration of 3D microstructure of a polyimide hinge", "texts": [ " Structures assembled using the thermal shrinkage of V-groove polyimide joints permit dynamic actuation after assembly by making use of the thermal expansion of the polyimide joints. However, the bending angle is limited to 5 per V-groove joint. In addition, the structural materials that can be used are limited by fabrication processes using crystalline anisotropic etching. The objective of this study is to develop a simple self-assembly method using the thermal shrinkage of polyimide. A schematic illustration of the 3D microstructure of a polyimide hinge is shown in Fig. 1. Two rigid plates are connected by an elastic hinge. A 3D structure can be assembled from this planar structure by bending the hinge. In this study, PIX-1400 (HD Micro System Corp.) was used as the hinge material. PIX-1400 has a low Young\u2019s modulus and a high elongation at room temperature, and its Young\u2019s modulus increases and thermal shrinkage occurs when it is heated at 500 C (Naka et al. 2004). These properties of polyimide enable the hinged plates to be rotated out of the wafer plane by using a simple heating process and their configuration can be maintained without the need to use any interlocking mechanisms" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002501_recl.19841030701-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002501_recl.19841030701-Figure5-1.png", "caption": "Fig. 5 . Adsorption modification: a ) chemisorption of a functionalized vinyl compound at a platinum electrode2' ; b ) ruthenium complexes immobilized via an adsorbed bridge molecule, at a pyrolytic graphite (C,) electrode3'.", "texts": [ " Several such techniques, for example sublimation, adsorption from dilute solutions or electrosorption, are frequently used. A clear distinction between adsorption modification and covalent modification is not always possible. Ordinary adsorption, accomplished via van der Waah or coulombic interactions with the surface, is well defined, as is covalent bonding. However, for adsorption of halogens or ethylene compounds27 at a platinum surface, the type of bonding is less defined (chemisorption). As an example, Lane and Hubbard\u2019* adsorbed functionalized olefins at platinum electrodes (Fig. 5a) and E d ~ t r O m ~ ~ used adsorbed allylamine as a bridge molecule for subsequent covalent bonding of ferrocenecarbaldehyde. Although a multilayer of 40-3OOOA thickness3\u2019 is no longer the result of simple adsorption, this type will also be included in this section. Numerous systems have been immobilized via adsorption modification. We mention here adsorption of See also refs. 1 and 3c-f,gj,k. Lenhard and R. W. Murray, Anal. Chem. 50, 576 (1978). R. W. Murray, ibid. 51, 745 (1979). H. S. White and R" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003503_1350650112445672-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003503_1350650112445672-Figure1-1.png", "caption": "Figure 1. Spur gear lumped-mass model.", "texts": [ " Lubrication performance is mainly evaluated from minimum film thickness as well as maximum pressure. The proposed line contact lubrication model is capable of dealing with the so-called \u2018asperity contacts\u2019 using the reduced Reynolds technique proposed by Hu and Zhu.10 The Ree\u2013Eyring non-Newtonian fluid behavior is considered by deriving the Reynolds\u2013Eyring equation.11 The dynamic transmission error (DTE) of the gear pair, used to calculate the dynamic force, could be computed as the response of a non-linear, mass\u2013spring oscillator,12 as shown in Figure 1. Taking the friction excitation and the clearance-type backlash into account, the semi-definite two-degree-of-freedom system could be represented by a single-degree-of-freedom system with the DTE x as the variable me \u20acx\u00fe c _x\u00fe k\u00f0t\u00de f \u00f0x\u00de \u00bc \u00f0T1 \u00fe Tf \u00de=rb1 \u00f02\u00de where me is the equivalent mass and is expressed as me \u00bc I1I2= I1r 2 b2 \u00fe I2r 2 b1 \u00f03\u00de where I1 and I2 are rotation inertia of the pinion and the wheel, respectively, and rb1 and rb2 the base radius of the pinion and the wheel, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001740_(sici)1097-4563(199811)15:11<599::aid-rob1>3.0.co;2-o-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001740_(sici)1097-4563(199811)15:11<599::aid-rob1>3.0.co;2-o-Figure2-1.png", "caption": "Figure 2. Frame assignment on mobile manipulator k.", "texts": [ " The combined model for the system of multiple mobile manipulators handling a common deformable object is constructed in section 4. In section 5, the dynamic constraints imposed on the system are presented and analyzed. Section 6 summarizes conclusions drawn from the present work. This section is devoted to modeling one mobile manipulator. Modeling the rest of the set of mobile manipulators follows the same lines. Let this mobile manipulator be denoted by k. Consider a 4fixed inertial frame, I as in Figure 2. Its x and y axes lie on the horizontal plane. On the mobile 4platform of mobile manipulator k, a frame v isk attached at its mass center. The xv axis is alignedk with the vehicle linear velocity and zv is parallel tok z I. At the mass center, the center principal inertial 4frame, v , is assigned, which can generally differcpi k 4from v . The mounting point of the attached ma-k nipulator is named mm and coincides with thek \u017dplatform point mm the distinction between the twok .points will be justified in the sequel ", " Thus, the system representation is simplified with the nonholonomic constraint equations taking the place of the missing dynamic equations. The velocities of the wheels are directly related to the nonholonomic constraints, and this fact will be used to derive expressions for them. 4 4The velocity in I of the frame\u2019s w origin canj be expressed as a function of the generalized speeds w j I I \u017d v w j .v su x qu y qu z =ell1 2 3 where ellw j is the position vector from the origin of 4frame v to the contact point between the wheel \u017d .and the ground Fig. 2 . The expression of this 4velocity in frame w is calculated asj w j w j w j w j \u017dv v w j .v su Rx qu Ry qu R z = ell1 I I 2 I I 3 v v The rotation matrices w j R and w j R can be expressedI v as w wj j\u017d . \u017d .cos f qu sin f qu 0 w j w wj jRs \u017d . \u017d .ysin f qu cos f qu 0I 0 0 1 w wj jcos f sin f 0 w j w wj jRs ysin f cos f 0v 0 0 1 Utilizing the above expressions, vw j can be rewritten w w wj j j\u017d . \u017d .v s u cos f qu qu sin f qu1 2 v vw w w w wj j j j jqu l sin f y l cos f x\u017d .3 x y w wj j\u017d . \u017d .q u cos f qu yu sin f qu2 1 v vw w w w wj j j j jqu l sin f q l cos f y\u017d " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002273_1077546304042047-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002273_1077546304042047-Figure8-1.png", "caption": "Figure 8. Schematic diagram of the leaf spring.", "texts": [ " The graphical techniques are too complex to be used for design optimization. In other models used in vehicle dynamic simulations, the leaf springs are represented by simple linear springs and the interleaf friction is neglected (Attia, 1996). Guo (1991) presented a general kinematic model for all varieties of leaf springs, including traditional laminated, asymmetrical, and tapered leaf springs, to calculate the longitudinal and winding deformations of axles during bouncing, braking, and traction. A model for a curved leaf of a spring is shown in Figure 8. Assuming the spring deformation is the result of an external load Q applied at the spring eye, the radius of curvature R(s) can be calculated using a static solution from (Guo, 1991) E J s R s Ql 1 s l (1) where s is the arc length, E is the modulus of elasticity, J(s) is the second moment of area, l is the effective length of half of the spring, and Q is the nominal vertical load. It is clear from Figure 8 that dx cos ds dy sin ds (2) at GEORGIAN COURT UNIV on December 11, 2014jvc.sagepub.comDownloaded from and, as d s ds R s , we have s 0 s 0 1 R s ds (3) where 0 s 0 . Substituting for R(s) from equation (1) in the preceding equation, we obtain s 0 Ql E s 0 1 s l J s ds (4) Using this result, x and y can be written as x l 0 cos s ds rsin l y l 0 sin s ds rsin l (5) where l is defined by equation (3), and r is the radius of the spring eye. Using Taylor expansion and neglecting the higher-order terms, the horizontal coordinate of the spring eye can be written as x l 1 2 3 y r l 0 2 y r l 0 2 0 2 r l 2 y r l 0 (6) This equation gives the longitudinal distance from the loading spring eye to the spring setting point for any value of y and 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002608_tpas.1983.317993-Figure5-3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002608_tpas.1983.317993-Figure5-3-1.png", "caption": "Figure 5-3. Flux Plot for 2.5 Hertz; Field Winding Current. Real Component. Skin Depths: Rotor-0.59 in.; Wedges3.34 in.", "texts": [ " The traveling wave nature of the solution can be inferred from the relative shapes of the real and imaginary flux plots of Figure 5-1. Furthermore, in a conducting medium (in the absence of externally applied voltages), J=-o,aaA (5-3) from which, JAt) w a[Aia coswt+ Area; sinoa (5-4) Thus, the current densities in the rotor may be inferred from the flux plots to some degree. It should be remembered that the flux plots may contain both positive and negative potentials, which are not identified in the present format. Figure 5-2 shows the real component of the flux for d-axis currents applied at a frequency of 2.5 hertz; Figure 5-3 shows a similar plot for field currents applied; and Figure 5-4 shows the plot for q-axis currents applied. Figures 5-5 and 5-6 show flux plots for a frequency of 100 hertz. In these figures, close-ups of the rotor region are shown for increased resolution in the flux distribution. The real part of the vector potential is shown. Figure 5-5 shows a plot for the normal condition of the rotor in which the aluminum slot wedges form a complete amortisseur circuit. The skin depth in the wedges is about 5" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure4.17-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure4.17-1.png", "caption": "Figure 4.17 Illustrations of Planar technology for mounting cores on PC boards From Philips (1998)", "texts": [ "6-PLANAR TECHNOLOGY Continuing with the low-profile design tendency particularly with PC board mounting has led to a completely new generation of cores called planar cores. Huth(l986) reported on this earlier and now, most ferrite companies offer planar cores in several varieties. Some of the arrangements are shown in Figure 4.16. Either the E-E or E-I configuration is used. The I core is actu ally a plate completing the magnetic circuit. In many cases the windings are fabricated using printed circuit tracks or copper stampings separated by insu lating sheets or constructed from multilayer circuit boards.(See Figure 4.17 ) MAGNETIC COMPONENTS FOR POWER ELECTRONICS 120 121 CORE SHAPES FOR POWER ELECTRONICS In some cases, the windings are on the PC boards with the two sections of the core sandwiching the board. Philips (1998) claims the advantages of this ap proach as; 1. Low profile construction 2. Low leakage inductance and inter-winding capacitance. 3. Excellent repeatability of parasitic properties. 4. Ease of construction and assembly 5. Cost effective 6. Greater reliability 7. Excellent thermal characteristics-easy to heat sink" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001766_1.1318351-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001766_1.1318351-Figure1-1.png", "caption": "Fig. 1 Graphical interpretation of SMC", "texts": [ " In this paper we use the unit of X(s) as fraction of the transmitter output, fraction TO; the unit of U(s) is fraction of the controller output, fraction CO. K, t0 , and t are the steady-state gain, deadtime, and time constant, respectively. The SMC is a kind of Variable Structure Control that can modify its structure. The design problem consists of selecting the parameters of each structure and defining the traveling logic. The first step in SMC is to define a surface S(t)50, along which the process can slide to its desired final value. Figure 1 depicts the SMC objective. The sliding surface divides the phase plane into regions where the switching function S(t) has different signs. The structure of the controller is intentionally altered as its state crosses the surface in accordance with a prescribed control law. There are many options to choose the Sliding Surface; the S(t) selected in this work, is the integral control presented by Slotine and Li @7#. This is an integral-differential equation acting on the tracking-error expression S~ t " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.4-1.png", "caption": "Fig. 4.4 Water wheel lever escapement mechanism in Su Song\u2019s clock tower, a Original illustration (Su 1969), b Structural sketch, c Chain", "texts": [ " This outstanding mechanical design included the water wheel power device, the two-level noria device, the two-level float device, the water wheel lever escapement mechanism, the programmable cam mechanism, and the time-telling device. The mechanisms and mechanical members used included links, gears, chains, ratchets, cams, hinges, and sliding bearings. Among the mechanisms, the escapement regulator was made up of the driving wheel, the left and right upper locks, the upper stopping device, the upper balancing lever, the upper weight, the connecting rod, and the upper stopping tongue, as shown in Fig. 4.4a. The driving wheel transformed the potential energy from the water level to drive the entire machine, and acted as the escape wheel as well. This invention already had the functions and capabilities of the escapement regulators of modern mechanical clocks. The book Xin Yi Xiang Fa Yao\u300a\u65b0\u5100\u8c61\u6cd5\u8981\u300bwritten by Su Song (\u8607\u980c, AD 1,020\u20131,101) in 1,088\u20131,096 (Su 1969), documented in detail the structure, components, and diagrams of the motion and structure of the water-powered clock tower. It clearly describes how the water wheel lever escapement worked in unison to perform the isochoric and intermittent timekeeping function" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002570_rspa.2007.0006-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002570_rspa.2007.0006-Figure3-1.png", "caption": "Figure 3. Problem A. (a) One step of a gait that is symmetric about the mid-step. (b) Assuming periodic steps that are symmetric about mid-step implies that the vertical component of the velocity is zero at mid-step and at the end of the step.", "texts": [ " The stance cost over a step (with duration Ktstep/2%t%tstep/2) is given by Cstance Z \u00f0tstep=2 Ktstep=2 b1\u00bdP CCb2\u00bdP K dt; \u00f02:2\u00de where [P]C registers positive leg power, equalling P when PR0 and equalling zero when P!0. [P]Kh[KP ]C registers negative leg power. Typically, muscles are assumed to have b1O0 (work costs) and b2O0 (absorbing mechanical work also has a metabolic cost) but here we only need that b1Cb2O0. (b ) Symmetry assumptions We assume periodic gaits with each step similar to the next. To simplify the analytic argument here, we assume that the trajectory of the centre of mass within a step is symmetric about the \u2018mid-step\u2019 (figure 3a). Mid-step (at tZ0) is 1 In running, \u2018step-length\u2019 includes the horizontal distance covered while one foot is in contact with the ground in addition to the distance travelled in flight. Proc. R. Soc. A (2007) when the body is directly above the foot-contact point. Hence, only half a step\u2014 from mid-step till the end of the step\u2014contains all of the information about the gait. Although this symmetry assumption limits the generality of the analytic demonstration, we note that all the numerical optima we previously found had this symmetry about mid-step (Srinivasan & Ruina 2006)", " (c ) Direct implications of the model assumptions The periodicity assumption, for level-ground locomotion, implies that there is no energy change from one mid-step to the next. The boundedness of the leg force FA(t) implies that the acceleration is always bounded and that the velocity of the body is continuous. Because the velocity vector along the gaittrajectory is continuous, the symmetry conditions above require that the vertical component of the velocity vanishes both at mid-step and at the end of the step (figure 3b). Because there are no passive dissipation mechanisms, the net work of the legs in one step is zero: \u00d0 P dtZ \u00d0 \u00f0\u00bdP CK\u00bdP K\u00de dtZ0; and the net positive work equals the netnegativework: \u00d0 \u00bdP C dtZ \u00d0 \u00bdP Kdt.Therefore, the cost inequation (2.2) isCstance Z\u00f0b1Cb2\u00de \u00d0 \u00bdP Cdt and is proportional to the total positive work. In other words, minimizing a weighted sum of the positive and negative work is equivalent to minimizing either the total positive work or the total negative work and does not depend on the values of b1 and b2 (as long as b1Cb2O0)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002901_0278364909348762-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002901_0278364909348762-Figure9-1.png", "caption": "Fig. 9. The importance of in avoiding sticking of two legs on the ground and bumping with unexpected obstacles.", "texts": [ " Then we estimate the total energy cost as E Th 2 cTk 2 (20) To make the value of E minimal it follows that E r 0 (21) Using (16)\u2013(18) yields the sixth-order equation of unknown parameter sin , expressed as E r r4 A2 2A 3 sin6 r 2Hr3 2A2 3A 5 sin5 r r2 6H2 A2 A 2 r2 l2 A2 2A 3 sin4 r 2Hr H2 2A2 A 3 r2 2A2 3A 4 l2 A2 A 3 sin3 r [H2 H2 A2 1 r2 6A2 6A 7 l2 A2 2 r2 r2 l2 A2 2A 1 l4] sin2 r 2Hr H2 2A2 A 1 r2 l2 A2 A 1 sin r H2 H2 A2 r2 l2 A2 0 (22) where A c2 1 (23) Solving (22) is not simple, but graphical tracing and exploration gave the angle r through sin r. With this, (18) gives the . However, in selecting a reasonable solution, such a check is necessary to make sure that the conjugate solution locates the other leg end at upper side on the ground. Otherwise, the solution is multiple root. Specifically, the case when two leg ends touch the ground at the same time should be avoided because the ground friction prevents the robot from sitting or standing. For instance, Figure 9(a) shows the robot configurations with two contacts, i.e. the primary and secondary leg contacts at the marks of normal and painted triangles, respectively. We call this case a stuck configuration. Evidently, the stuck configuration constrains vertical motion of the robot and degrades its mobility. To avoid the stuck configuration and to make one leg always free as a swing phase, we calculate for r so that one of the two legs faces upside without bumping with obstacles on the ground by estimating h R (24) where 0 1. Then the configurations in Figure 9(a) reconfigure into those in Figure 9(b). The details of the calculation of is given in Section 6.1. For balancing payload factors of the two driving motors, it is necessary to distribute power proportional to motor capacity. For this purpose, we calculate the control variables r and by supposing Th cTk. Unbalanced error (Eb), between driving power of Jh and Jk is evaluated by Eb Th 2 cTk 2 2 (25) As well as (21), Eb r 0 determines the value of that makes Eb minimal. However, it is difficult to solve the equation, since Th and Tk change their signs, in general" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002230_112515.112566-Figure7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002230_112515.112566-Figure7-1.png", "caption": "Figure 7: Sofa-bed mechanism (extended).", "texts": [ " The TLA program has also been empirically compared with the ADAMS mechanism simulator, which employs iterative numerical solution techniques [ADAMS, 1987]. The graph of Figure 6 shows the runtimes of ADAMS and TLA as a function of the number of bodies in a mechanism. The daehed line shows the time per iteration for ADAMS; typically, between 2 and 12 iterations are required to solve a GCSP, as indicated by the gray area. In contrast, the behavior of TLA is linear, and is substantially more efficient. TLA has simulated dozens of comDlex Dlanar and spatial mechanisms; the largest exam~le is \u2018a sofa-bed, shown in Figure 7. This me.haniam h- 16 rigid bodies (or links), 22 joints, and two driving inputs, and is described bv 115 algebraic constraints, 19 of which are redundant: The z&embly plan generated by TLA is stored as a program which is 655 lines of Lisp code. This Lisp program runs almost two orders of magnitude faster than iterative numerical techniques embodied in ADAMS, when used to solve the same set of constraints,5 Discussion Algebra has long been the lingua franca of science and engineering, but it can provide only a partial appreciation of the actual domain under study" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001662_s0094-114x(01)00082-9-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001662_s0094-114x(01)00082-9-Figure3-1.png", "caption": "Fig. 3. Coordinate relationship between the rack cutter and generated gear.", "texts": [ " To simulate the taper hobbing process, the pitch plane of the rack cutter is set to have an inclination angle di with respect to the plane axode coordinate system S\u00f0j\u00dec \u00f0X \u00f0j\u00de c ; Y \u00f0j\u00de c ; Z\u00f0j\u00de c \u00de, and the rack cutter surface can be represented in coordinate system S\u00f0j\u00dec as follows: x\u00f0j\u00dec \u00bc \u2018j cos a\u00f0j\u00de n aj cos di \u00fe \u2018j sin a\u00f0j\u00de n aj tan a\u00f0j\u00de n bj sin bj \u00fe uj cos bj sin di; y\u00f0j\u00dec \u00bc \u2018j sin a\u00f0j\u00de n aj tan a\u00f0j\u00de n bj cos bj \u00fe uj sin bj; z\u00f0j\u00dec \u00bc \u2018j cos a\u00f0j\u00de n aj sin di \u00fe \u2018j sin a\u00f0j\u00de n aj tan a\u00f0j\u00de n bj sin bj \u00fe uj cos bj cos di: \u00f02\u00de Owing to that the surface coordinates of rack cutter are \u2018j and uj, the unit normal to the rack cutter surface can be attained by n\u00f0j\u00dec \u00bc N \u00f0j\u00de c N \u00f0j\u00de c \u00f0j \u00bc F ;G\u00de; \u00f03\u00de where N \u00f0j\u00de c \u00bc oR\u00f0j\u00de c ouj oR\u00f0j\u00de c o\u2018j : \u00f04\u00de Herein, R\u00f0j\u00de c denotes the position vector of the rack cutter surface represented in plane axode coordinate system S\u00f0j\u00dec . Eqs. (2) and (3) result in the corresponding unit normals to the rack cutter surface as follows: n\u00f0j\u00dexc \u00bc sin di sin bj cos a\u00f0j\u00de n cos di sin a\u00f0j\u00de n ; n\u00f0j\u00deyc \u00bc cos bj cos a\u00f0j\u00de n ; n\u00f0j\u00dezc \u00bc cos di sin bj cos a\u00f0j\u00de n \u00fe sin di sin a\u00f0j\u00de n : \u00f05\u00de Fig. 3 illustrates a schematic generation mechanism and the coordinate relationship between the rack cutter and the generated gear. Herein, S\u00f0j\u00deb \u00f0X \u00f0j\u00de b ; Y \u00f0j\u00de b ; Z\u00f0j\u00de b \u00de is the fixed coordinate system, Si\u00f0Xi; Yi;Zi\u00de is the coordinate system attached to the generated pinion R1 \u00f0i \u00bc 1\u00de or gear R2 \u00f0i \u00bc 2\u00de, and S\u00f0j\u00dec is the plane axode coordinate system attached to the rack cutter. In the gear generation process, the gear blank rotates with angular velocity xi while the rack cutter translates with velocity V \u00bc xiri", " When \u00f0d\u2018F=dt\u00de \u00bc 0, the first principal direction i \u00f0F \u00de I and curvature j\u00f0F \u00de I are derived as follows: i \u00f0F \u00de I \u00bc V \u00f0F \u00de rI V \u00f0F \u00de rI \u00bc sin d1 cos bF sin bF cos d1 cos bF 2 4 3 5; and j\u00f0F \u00de I \u00bc 0: \u00f013\u00de 2. When \u00f0duF =dt\u00de \u00bc 0, the secondary principal direction i \u00f0F \u00de II and curvature j\u00f0F \u00de II are derived as follows: i \u00f0F \u00de II \u00bc V \u00f0F \u00de rII V \u00f0F \u00de rII \u00bc cos d1 cos a\u00f0F \u00de n sin d1 sin bF sin a\u00f0F \u00de n cos bF sin a\u00f0F \u00de n sin d1 cos a\u00f0F \u00de n cos d1 sin bF sin a\u00f0F \u00de n 2 4 3 5; and j\u00f0F \u00de II \u00bc 0: \u00f014\u00de Herein, unit vectors i \u00f0F \u00de I and i \u00f0F \u00de II are represented in the coordinate system S\u00f0F \u00deb \u00f0X \u00f0F \u00de b ; Y \u00f0F \u00de b ; Z\u00f0F \u00de b \u00de as shown in Fig. 3. Noted that the principal curvatures j\u00f0F \u00de I and j\u00f0F \u00de II are both zero since the gen- erating surface RF is a plane. The generated pinion tooth surface R1 and the cutter surface RF are in line contact and in continuous tangency at every instant during the generation process. Therefore, the principal directions and curvatures of the generated pinion tooth surface R1 can be determined by applying the following equations [5,6]: tan 2r\u00f0F 1\u00de \u00bc 2F \u00f01\u00de j\u00f0F \u00de I j\u00f0F \u00de II \u00fe G\u00f01\u00de ; \u00f015\u00de j\u00f01\u00de I \u00fe j\u00f01\u00de II \u00bc j\u00f0F \u00de I \u00fe j\u00f0F \u00de II \u00fe S\u00f01\u00de; \u00f016\u00de and j\u00f01\u00de I j\u00f01\u00de II \u00bc j\u00f0F \u00de I j\u00f0F \u00de II \u00fe G\u00f01\u00de cos 2r\u00f0F 1\u00de ; \u00f017\u00de where F \u00f01\u00de \u00bc a\u00f01\u00de31 a \u00f01\u00de 32 b\u00f01\u00de3 \u00fe V \u00f0F 1\u00de i\u00f0F \u00deI a\u00f01\u00de31 \u00fe V \u00f0F 1\u00de i\u00f0F \u00deII a\u00f01\u00de32 ; \u00f018\u00de G\u00f01\u00de \u00bc a\u00f01\u00de31 2 a\u00f01\u00de32 2 b\u00f01\u00de3 \u00fe V \u00f0F 1\u00de i\u00f0F \u00deI a\u00f01\u00de31 \u00fe V \u00f0F 1\u00de i\u00f0F \u00deII a\u00f01\u00de32 ; \u00f019\u00de S\u00f01\u00de \u00bc a\u00f01\u00de31 2 \u00fe a\u00f01\u00de32 2 b\u00f01\u00de3 \u00fe V \u00f0F 1\u00de i\u00f0F \u00deI a\u00f01\u00de31 \u00fe V \u00f0F 1\u00de i\u00f0F \u00deII a\u00f01\u00de32 ; \u00f020\u00de a\u00f01\u00de31 \u00bc n\u00f0F \u00dex\u00f0F 1\u00dei \u00f0F \u00de I h i j\u00f0F \u00de I V \u00f0F 1\u00de i\u00f0F \u00deI ; \u00f021\u00de a\u00f01\u00de32 \u00bc n\u00f0F \u00dex\u00f0F 1\u00dei \u00f0F \u00de II h i j\u00f0F \u00de II V \u00f0F 1\u00de i\u00f0F \u00deII ; \u00f022\u00de and b\u00f01\u00de3 \u00bc n\u00f0F \u00dex\u00f01\u00deV \u00f0F \u00de tr h i n\u00f0F \u00dex\u00f0F \u00deV \u00f01\u00de tr h i : \u00f023\u00de All the vectors in Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002787_robot.2008.4543695-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002787_robot.2008.4543695-Figure4-1.png", "caption": "Fig. 4. Transforming an arc of circle path into a pivoting sequence. The regular sequence is composed of symmetric rotations. The center of pivoting line segment arrives at the end point of the arc with the perpendicular orientation after adjustment sequence.", "texts": [ " Considering the constraint of the reachable area of robot arms, we introduce an angle \u03b2 such that the robot is able to perform an elementary pivoting motion of total angle 2\u03b2. After initializing the process by a pivoting of angle \u03b2, we then apply n times the elementary pivoting motion of angle 2\u03b2, n being defined as the greater integer verifying L > nl sin\u03b2. Then for the last part an adjustment pivoting motion is added to reach the final goal. The same principle applies to the arcs of a circle (see Fig. 4). Let R and \u03b8 denote the radius and the angle of the arc. We apply a regular sequence shown in Fig. 4 with a symmetrical motion such that the center of the line segment 1Notice that we do consider the cases where the robot would overcome small obstacles on the floor by pivoting the box above the obstacles. comes on the arc with perpendicular orientation, after two times \u03b2 rotation at the left corner and one \u22122\u03b3 rotation at the right corner. The angle \u03b1 and \u03b3 can be computed from l, R, and \u03b2 as: \u03b1 = arctan( l sin\u03b2 R\u2212 l 2 + l cos \u03b2 ), \u03b3 = \u03b2 \u2212 \u03b1. (1) In the regular sequence, elementary motions are repeated m times alternatively on the each edge, while \u03b8 > m\u03b1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002719_iros.2007.4399390-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002719_iros.2007.4399390-Figure5-1.png", "caption": "Fig. 5. Model", "texts": [ " A continuous model is probably useful for theoretical study, so this method can be effective. In this section we discuss about stabilization method of the head of undulating snake-like robot. As a model of robot we use a continuous model, that is, a planar curve. First we consider a robot consists of \u201chead\u201d, \u201cneck\u201d and \u201dbody\u201d, and we assume the \u201cbody\u201d makes undulating motion. So the boundary of \u201cneck\u201d and \u201cbody\u201d is shaken during undulation. Our purpose in this paper is to obtain a control method of the \u201cneck\u201d to cancel the undulation of that boundary, and stabilize the \u201chead\u201d. Fig. 5 shows a model of snake-like robot. x-axis indicates to a moving direction and y-axis indicates to the left of it. PN means the boundary between \u201cneck\u201d and \u201cbody\u201d, PH means that between \u201chead\u201d and \u201cneck\u201d. We define other symbols used here as following. s: Arc length t: Time sN : Value of s at PN (constant value) sH : Value of s at PH (constant value) lN : Neck length (lN = sH \u2212 sN ) \u03c8N (t): Angle between x-axis and a tangent at PN \u03c8H(t): Angle between x-axis and a tangent at PH yN (t): y coordinate of PN yH(t): y coordinate of PH \u03ba(s, t): Curvature at s = s, t = t Let us determine 2 goals in this section: one is to realize \u03c8\u0307H(t) = 0 to stabilize the direction of the head, and the other is to realize y\u0307H(t) = 0 and \u03c8\u0307H(t) = 0 simultaneously to stabilize the position and direction of the head", " 6(b), PN is traveling to the tangential direction at velocity v, and the following equation holds true. y\u0307N (t) = sin\u03c8N (t) \u00b7 v (18) (18) is strictly true on the above assumption about slip. Now we assume the stabilization of head direction is conducted and (14) holds true. Then we obtain the following equation substituting (14) to (18). y\u0307N (t) = \u2212 sin{ \u222b sH sN \u03ba(s, t)ds} \u00b7 v (19) Where variables in the right-hand side of (19) are known. While the following equation about the head position holds true as known from Fig. 5. yH(t) = yN (t) + \u222b sH sN sin{ \u222b s sN \u03ba(s, t)ds+ \u03c8N (t)}ds (20) Differentiate (20) with respect to t and substituting (12), we obtain the following equation. y\u0307H(t) = y\u0307N (t) \u2212 \u222b sH sN sin{ \u222b sH s \u03ba\u0307(s, t)ds}ds (21) From (19) and (21), y\u0307H(t) = 0 holds true if \u03ba(s, t) satisfies the following equation.\u222b sH sN sin{ \u222b sH s \u03ba\u0307(s, t)ds}ds = \u2212 sin{ \u222b sH sN \u03ba(s, t)ds} \u00b7 v (22) The control method we propose is to calculate \u03ba(s, t) so that it satisfies (22). Next we determine \u03ba(s, t) concretely to implement the control on a real robot" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003154_1077546310362450-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003154_1077546310362450-Figure3-1.png", "caption": "Figure 3. Model of lubrication film in a meshing tooth pair: (a) its geometric illustration and lubrication film thickness; (b) its equivalent stiffness, Ko;i, and damping factor, Co;i\u00f0t\u00de.", "texts": [ " The Reynolds equation for the hydrodynamic- lubrication theory can be given as (Williams, 1994) q qx h3 12m0 qp qx \u00bc u qh qx \u00fe _h; \u00f09\u00de where p is the pressure distribution of the lubrication film, h is the lubrication film thickness, u is the entraining speed at the contact point, m0 is the absolute viscosity of the lubricant and a constant value as assumed here, and x is the coordinate centered at the contact point. In addition, _h, accounting for the squeezed-film effect, is a partial derivative of the time variable, i.e., _h \u00bc qh=qt. Then, integrating equation 9 leads to h3 12m0 qp qx \u00bc uh\u00fe _hx\u00fe c1; \u00f010\u00de where c1 is the integration constant. Rearranging equation 10, we get qp qx \u00bc 12m0\u00f0 u 1 h2 \u00fe 1 h3 _hx\u00fe 1 h3 c1\u00de: \u00f011\u00de Then, as illustrated in Figure 3(a), the film thickness, h, in the hydrodynamic lubrication model can be represented as h \u00bc hc \u00fe x2 2Req ; \u00f012\u00de where hc is the minimum thickness of the lubricant film which is separately calculated and is described next, while the second term accounts for the profile properties of the mating surfaces. According to Williams (1994), calculation of the minimum film thickness between two cylinders is briefly given as follows: hc \u00bc ReqHmin \u00f013\u00de In this study, the dimensionless film thickness, Hmin, is given as Hmin \u00bc g1 g3 g 2 : \u00f014\u00de The parameters in equation 14 are g1 \u00bc m0 u E0 Req ; g2 \u00bc wi E0Reqb ; and g3 \u00bc 1:6549g0:54 4 g0:06 5 ; \u00f015\u00de where wi is the contact loading on the ith mating surface pair, b is the face width, and E0 is the effective modulus", " In addition, the solutions for the three integral terms in equation 19 can also be analytically derived and are respectively given as\u00f0 dx hc \u00fe x2=2Req 2 \u00bc \u00f02Req\u00de2\u00bd x 4Reqhc\u00f0x2 \u00fe 2Reqhc\u00de \u00fe 1 2\u00f0 ffiffiffiffiffiffiffiffiffiffiffiffiffi 2Reqhc p \u00de3 tan 1\u00f0 xffiffiffiffiffiffiffiffiffiffiffiffiffi 2Reqhc p \u00de ; \u00f020\u00de \u00f0 xdx hc \u00fe x2=2Req 3 \u00bc 2R3 eq \u00f0x2 \u00fe 2hcReq\u00de2 ; and \u00f021\u00de \u00f0 dx hc \u00fe x2=2Req 3 \u00bc R2 eq hc \u00bd x \u00f0x2 \u00fe 2Reqhc\u00de2 \u00fe 3x 4Reqhc\u00f0x2 \u00fe 2Reqhc\u00de \u00fe 3 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x2 \u00fe 2Reqhc\u00de3 q tan 1 xffiffiffiffiffiffiffiffiffiffiffiffiffi 2Reqhc p : \u00f022\u00de Subsequently, the lubricant film load capacity per unit face width for the ith tooth pair can be expressed as wi \u00bc \u00f0Req Req p\u00f0x\u00de cos bdx: \u00f023\u00de Therefore, as illustrated in Figure 3(b), the equivalent stiffness, Ko;i, and the damping factor, Co;i, of the lubrication film in the ith meshing tooth pair can be obtained by taking partial derivatives of equation 23 as Ko; i\u00f0t\u00de \u00bc qwi qh \u00bc \u00f0Req Req qp\u00f0x\u00de cosb qh dx and \u00f024\u00de Co; i\u00f0t\u00de \u00bc qwi q _h \u00bc \u00f0Req Req qp\u00f0x\u00de cosb q _h dx: \u00f025\u00de To simplify the model, the stiffness relating to the lubrication film in equation 24 was not included. Therefore, only the damping formulation expressed in equation 25 was investigated and is extensively described below" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003645_1.4005527-Figure11-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003645_1.4005527-Figure11-1.png", "caption": "Fig. 11 Kinematic sketch to determine the cubic of stationary curvature and the inflection circle", "texts": [ "org/about-asme/terms-of-use \u2022 Point W is joined with the particular point C; \u2022 A line orthogonal to the line joining C and W is traced up to intersect in the particular point S the line across points B and W; \u2022 Repeating the same graphical construction for other rays across the origin X\u00bcB, the whole Jer\u030ca\u0301bek\u2019s curve can be traced. The moving centrode or Jer\u030ca\u0301bek\u2019s curve is a closed or open curve, when the point C falls inside or outside the circle a, respectively, while a circle is obtained for the Scott-Russell mechanism, when C falls on the circle a, as shown in Fig. 10. The method of instantaneous invariants in instantaneous kinematics was invented by Oene Bottema (1901\u20131992) and further developments were made by his favorite pupil, Geert Remmert Veldkamp, as reported in Refs. [23,24]. Referring to Fig. 11, the position of the moving frame f \u00f0X; x; y\u00de with respect to the fixed frame F\u00f0O;X;Y\u00de can be given by the Cartesian-coordinates of the origin X and by the oriented angle u. Similarly, the position of the canonical moving frame ~f \u00f0I; ~x; ~y\u00de with respect to the canonical fixed frames ~F\u00f0I0; ~X; ~Y\u00de can be given by the Cartesian-coordinates of the origin I and by the oriented angle #. The n-order derivatives of the Cartesiancoordinates ~XI and ~YI of the instantaneous center of rotation I with respect to the oriented angle # that the canonical moving frame ~f \u00f0I; ~x; ~y\u00de makes with respect to the canonical fixed frame ~F\u00f0I0; ~X; ~Y\u00de, are the instantaneous geometric invariants", " For the convenient starting configuration of the mechanism, where d and # are equal to zero and I\u00bc I 0\u00bcC, the first five instantaneous geometric invariants are given by a0 \u00bc a1 \u00bc a2 \u00bc 0 b0 \u00bc b1 \u00bc 0 (39) while b2, a3, and b3 can be expressed as b2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2XX du 2 \u00fe dYX du 2 \u00fe d2YX du 2 dXX du 2 s (40) a3 \u00bc 1 b2 d3XX du 3 \u00fe dXX du d2YX du 2 dXX du \u00fe and d3YX du 3 \u00fe dYX du d2XX du 2 \u00fe dYX du (41) b3 \u00bc 1 b2 d3XX du 3 \u00fe dXX du d2XX du 2 \u00fe dYX du \u00fe d3YX du 3 \u00fe dYX du d2YX du 2 dXX du (42) where u, XX, and YX are the oriented angle and the Cartesiancoordinates of the origin X of the moving frame f \u00f0X; x; y\u00de that is attached to the coupler link BC, with respect to the fixed frame F\u00f0O;X;Y\u00de. Therefore, the first, second, and third derivatives of XX and YX of Eqs. (40)\u2013(42) can be developed by referring to Fig. 11. In fact, the position vector rOX of Cartesian-coordinates XX and YX coincides with vector r, which is expressed through the first of Eqs. (4), while the oriented angle u is given by Eq. (5), as function of the crank angle d. These geometric invariants are very useful to express the cubic of stationary curvature C and the inflection circle IC with respect to the canonical moving frame ~f \u00f0I; ~x; ~y\u00de, which is attached to the moving plane of the coupler link BC. The origin of this frame is coincident for each instant, with the instantaneous center of rotation I, the ~x-axis is tangent to the fixed centrode p and the ~y-axis is oriented toward the center of the inflection circle IC, as shown in Fig. 11. The diagrams of the instantaneous geometric invariants b2 (continuous line), b3 (pointed line) and a3 (dashed line) for a given slidercrank/rocker mechanism can be obtained with respect to the driving crank angle d, as reported in the examples of Figs. 12 and 13, which refer to a centered and an offset slider-crank mechanism (Type A), respectively. In particular, b3 and a3 are equal to zero for d equal to 0 deg and 180 deg (dead-point positions), while they tend to infinity for d equal to 90 deg and 270 deg, as shown in Fig", " 4, FEBRUARY 2012 Transactions of the ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use community by Allen S. Hall, since representing the locus of the coupler points whose paths have, at least, four contact points with their osculating circles, which means to have a stationary curvature. Moreover, this geometric locus corresponds to an algebraic curve of third order (cubic). In particular, points B and C of the slider-crank mechanism of Fig. 11 have stationary curvature because they trace a circle path and a straight segment path, respectively. Thus, they belong to the cubic of stationary curvature C, which can be formulated, conveniently, by using the instantaneous geometric invariants of Eqs. (39)\u2013(42). In particular, the curvature k of a generic point of the moving plane attached to the coupler link BC can be expressed by referring to the canonical fixed frame ~F\u00f0I0; ~X; ~Y\u00de as follows: k \u00bc d ~X d# d2 ~Y d#2 d2 ~X d#2 d ~Y d# d ~X d# 2 \u00fe d ~Y d# 2 \" # 3=2 (43) where angle # gives the orientation of the canonical moving frame ~f \u00f0I; ~x; ~y\u00de with respect to ~F\u00f0I0; ~X; ~Y\u00de", " First, second, and third derivatives of the ~X and ~Y Cartesian-coordinates of a coupler point Q can be expressed with respect to angle # as follows: d ~X d# \u00bc a1 ~x sin# ~y cos# d ~Y d# \u00bc b1 \u00fe ~x cos# ~y sin# (47) d2 ~X d#2 \u00bc a2 ~x cos#\u00fe ~y sin# d2 ~Y d#2 \u00bc b2 ~x sin# ~y cos# (48) and d3 ~X d#3 \u00bc a3 \u00fe ~x sin#\u00fe ~y cos# d3 ~Y d#3 \u00bc b3 ~x cos#\u00fe ~y sin# (49) where a1, b1, a2, b2, a3, and b3 are the instantaneous geometric invariants given by Eqs. (39)\u2013(42). Thus, the geometric locus of the points of the moving plane having a stationary curvature is given in implicit form by the following third order algebraic equation: 3 b2 ~x \u00f0~x2 \u00fe ~y2 b2 ~y\u00de \u00fe \u00f0~x2 \u00fe ~y2\u00de\u00f0a3 ~x\u00fe b3 ~y\u00de \u00bc 0 (50) This, oblique strophoid is an unbounded connected curve with a single singular point (node) and a single asymptote. Referring to Fig. 11 and with the aim to express this geometric locus with respect to the fixed frame F\u00f0O;X;Y\u00de, which can be more useful than the canonical frame, a generic point Q of the cubic of stationary curvature C can be referred to ~f \u00f0I; ~x; ~y\u00de by means of the position vector r I Q \u00bc h cos w h sin w 1\u00bd T (51) where h and w are, respectively, the magnitude and the oriented angle of vector rIQ. Thus, the ~x and ~y Cartesian-coordinates of rIQ can be substituted in Eqs. (50) to give the parametric form of Eq. (51) in the canonical frame ~f ; \u00f0I; ~x; ~y\u00de as 1 h \u00bc 1 N sin w \u00fe 1 M cos w (52) where M \u00bc 3b2 2 b3 and N \u00bc 3b2 2 a3 \u00fe 3b2 (53) Thus, the position vector of point Q of the cubic of stationary curvature C can be expressed in F\u00f0O;X; Y\u00de as rOQ \u00bc TIO r I Q (54) where the position vector rIQ is given by Eq", " (50) takes the form 3 b2 ~x \u00f0~x2 \u00fe ~y2 b2 ~y\u00de \u00bc 0 (58) when the instantaneous geometric invariants a3 and b3 become equal to zero. For example, this can be demonstrated by referring to Eqs. (39)\u2013(42) and developing their derivative terms by taking into account the first of Eqs. (4) and (5) for d\u00bc 0 deg. In fact, Eq. (58) can be decomposed in the following: ~x \u00bc 0 ~x2 \u00fe ~y 2 b2 ~y \u00bc 0 (59) which are the equations of the ~y-axis (line) and the circle of diameter b2 and center of Cartesian-coordinates (0, b2 /2) in the canonical moving frame ~f \u00f0I; ~x; ~y\u00de, when I\u00bc I0 for d\u00bc 0 deg. Referring to Fig. 11, the inflection circle IC is the instantaneous locus of the coupler points R, which show in the same instant an inflection point in their paths. As reported in Beyer [27], Ludwig Burmester (1840\u20131927) named the inflection and return circles as De La Hire circles, who discovered these geometric loci and their properties. The equation of the inflection circle IC can be obtained by still using the instantaneous geometric invariants and by referring to Eq. (43), which expresses the curvature k for a generic point of the moving plane attached to BC" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003517_s00170-012-4481-9-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003517_s00170-012-4481-9-Figure1-1.png", "caption": "Fig. 1 Schematic illustration of LENS deposition process [23]", "texts": [ " Obielodan Mechanical Engineering Department, University of Wisconsin \u2013 Platteville, Platteville, WI 53818, USA B. Stucker (*) Industrial Engineering Department, University of Louisville, Louisville, KY 40292, USA e-mail: brent.stucker@louisville.edu materials delivered to the focus of the laser beam upon a substrate that is mounted on an x\u2013y stage. The stage moves in a raster fashion according to the tool paths generated from the sliced CAD models. The fabrication takes place under a controlled, inert atmosphere in a glove box. The process is schematically illustrated in Fig. 1. Some of the important process parameters are laser power, powder flow rate, layer thickness, hatch width, deposition speed, and oxygen level in the glove box. The capabilities of LENS for multi-material fabrication have been demonstrated. It is used for composite material fabrication [14, 15], functionally gradient structures [11\u201313], multi-materials processing [10] surface cladding for corrosion resistance [11], and wearresistant material coatings for biomedical applications [16, 17]. Most of the earlier works on multi-material fabrication using laser metal deposition processes were characterized using microstructure studies" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001459_jsvi.1998.1988-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001459_jsvi.1998.1988-Figure6-1.png", "caption": "Figure 6. Reduction unit with an idler gear (type B).", "texts": [ " Upon assuming that mesh stiffnesses and contact lengths are nearly proportional, a partial contact index l defined as the actual average mesh stiffness to the nominal mesh stiffness ratio at low speed (\u2018\u2018nominal\u2019\u2019 refers to a full contact from engagement to the end of recess) will be subsequently used as an indicator of the contact condition quality with respect to the ideal situation (full contact). For a multi-mesh system with intermediate gears simultaneously in contact with two other pinions or gears (see Figure 6), the excitation functions associated to each mesh are not independent because they are controlled by the power circulation and the corresponding relative orientations of the base planes. The method introduced by Velex and Flamand [16] for epicyclic drives is applied and illustrated in Figure 7 by an example of mesh stiffness functions for three different relative orientations of the base planes (double stage gear set). The principles of the methodology can be found in references [16, 29]. A particular stable solution of equation (14) is sought as a linear combination formed by the static solution X o of equation (14) superimposed on a truncated linear T 3 Gear data 1st stage 2nd stage ZXXXXCXXXXV ZXXXXCXXXXV Pinion Gear Pinion Gear Number of teeth (Z1, Z2) 27 63 25 69 Width (mm) 72 72 100 100 Module (mm) 4 6 Pressure angle (degree) 20 20 Helix angle (degree) 0 (spur) or 16 (helical) 0 (spur) or 12 (helical) Addendum coefficient 1\u00b70 1\u00b70 1\u00b70 1\u00b70 Dedendum coefficient 1\u00b74 1\u00b74 1\u00b74 1\u00b74 Shift profile coefficient 0\u00b70 0\u00b70 0\u00b70 0\u00b70 T 4 Shaft, bearing data Left side length Right side length External diameter (mm) (mm) (mm) Input shaft 233\u00b755 98\u00b743 80\u00b700 Intermediate 1st stage 211\u00b781 76\u00b769 90\u00b700 shaft 2nd stage 92\u00b743 196\u00b707 90\u00b700 Output shaft 96\u00b777 366\u00b770 133\u00b735 Bearing For all bearings, radial stiffness kp =4\u00d7108 N/m T 5 Gear data Pinion Idler gear Gear Number of teeth (Z1, Z2) 23 39 67 Width (mm) 60 60 60 Module (mm) 6 Pressure angle (degree) 20 Helix angle (degree) 0 (spur) or 12 (helical) Addendum coefficient 1\u00b70 1\u00b70 1\u00b70 Dedendum coefficient 1\u00b74 1\u00b74 1\u00b74 Shift profile coefficient 0\u00b70 0\u00b70 0\u00b70 T 6 Shaft, bearing and load machine data Left side length Right side length External diameter (mm) (mm) (mm) Input shaft 350\u00b700 100\u00b700 80\u00b700 Intermediate shaft 150\u00b700 100\u00b700 100\u00b700 Output shaft 150\u00b700 300\u00b700 120\u00b700 Bearing For all bearings, radial stiffness kp =4\u00d7108 N/m Load and motor inertia Im =6 kg m2, If =6 kg m2 combination of modeshapes [F] of the linear time-averaged system (pseudo-mode shapes): i" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003029_j.cma.2009.01.009-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003029_j.cma.2009.01.009-Figure6-1.png", "caption": "Fig. 6. System set up.", "texts": [ " From the last row of Table 1 it is evident that a B-spline interpolation scheme over a \u00f050 37\u00de grid does not introduce significant errors in the surface description and thus it can be used for tooth contact analysis purposes. We use now the closed form interpolated surface obtained in the previous section to perform the tooth contact analysis between the pinion and the gear tooth surfaces. Consider a hypoid drive and denote by C1 and C2 the pinion and gear tooth surfaces respectively. The B-spline approximations of the two surfaces are indicated by eC1 and eC2. We establish a fixed space E3 f and denote by eCf 1 and eCf 2 the two B-spline surfaces expressed in it. Consider Fig. 6: the two mating members rotate about their respective rotation axis e1 (pinion) and e2 (gear). We denote by u1 and u2 the rotations of the two members about e1 and e2. The position vectors of a generic point of eCf 1 and eCf 2 with respect to a common point Of are denoted by sf 1\u00f0u1;v1;u1\u00de and sf 2\u00f0u2; v2;u2\u00de, respectively. Their expressions are given by sf 1\u00f0u1;v1;u1\u00de \u00bc R\u00f0R\u00f0s1\u00f0u1;v1\u00de; e4; c\u00fe a\u00de; e1; u1\u00de \u00fe Pe1; sf 2\u00f0u2;v2;u2\u00de \u00bc R\u00f0s2\u00f0u2; v2\u00de; e2;u2\u00de \u00fe Ge2 \u00fe Ee3; \u00f015\u00de where R\u00f0 \u00de is the rotation operator as in [16], c is the transmission angle,3 and \u00f0E; P;G;a\u00de are the assembly error values (for brevity we assumed zero offset)" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003594_icra.2013.6630868-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003594_icra.2013.6630868-Figure1-1.png", "caption": "Fig. 1. Idealized model and control for robust swing leg placement (A) Conceptual double pendulum model of leg swing with point masses at the ends of massless segments of equal length ls. (B) Sequence of natural control tasks for reaching a target leg angle \u03b1tgt from an initial angle \u03b10 while guaranteeing foot ground clearance lclr .", "texts": [ " To compare the identified control with human swing leg behavior at the level of muscle activations, and to prepare a transfer to powered prosthetic legs that react like human limbs, we here develop a neuromuscular model of the human leg in swing and interpret the identified control with local muscle reflexes. We first summarize the previously identified control (Sec. II), then interpret it with the neuromuscular model (Sec. III), and finally compare and discuss the resulting leg placement performance with respect to the previous control and to human data on swing leg motions in walking and running (Sec. IV and V). The previously identified control [17] is based on the double pendulum analogy of the human swing leg (Fig. 1A) and takes advantage of the natural pendulum dynamics to achieve robust swing leg placement without enforcing predefined 978-1-4673-5643-5/13/$31.00 \u00a92013 IEEE 2169 reference trajectories of the foot. The control uses a target leg angle \u03b1tgt and a clearance leg length lclr as inputs, and it implements a natural sequence of three control tasks which comprise flexing the leg to the clearance length, advancing the leg to the target angle, and extending the leg until ground contact (Fig. 1B). In addition to taking advantage of passive dynamics for energy efficiency, the control is separated between the hip and knee as much as possible to enable modular implementation in artificial legs that replace only part of human limbs. The hip portion of the control is realized as a proportionalderivative control \u03c4h = k\u03b1p (\u03b1tgt \u2212 \u03b1)\u2212 k\u03b1d \u03b1\u0307+ \u03c4 iiih , (1) where \u03c4h is the commanded hip torque, \u03b1 and \u03b1\u0307 are the current leg angle and angular velocity, and k\u03b1p and k\u03b1d are proportional and derivative gains. Note that a positive input tends to extend the hip (Fig. 1A). The additional torque component \u03c4 iiih results from biarticular actuation that is commanded by the knee control during the last, leg extension task of the control sequence. It is the only interaction control between the two joints. The knee portion is divided into three parts which follow the natural control sequence. In the first part, the knee actively flexes in proportion to how fast the leg moves forward, \u03c4 ik = { ki\u03b1\u0307, \u03b1\u0307 \u2264 0 0, \u03b1\u0307 > 0 , (2) where \u03c4 ik is the resulting knee torque and ki is a proportional gain" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003235_j.actaastro.2010.09.014-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003235_j.actaastro.2010.09.014-Figure3-1.png", "caption": "Fig. 3. Schematic representation of projection onto the van der Pol plane.", "texts": [ " This method can be used to examine either predominant motion or sub-harmonic motion, but cannot be used to examine both motions at the same time. The coordinate can be converted from \u00f0y, _y\u00de to (u,v) by using the following reversible equations: y\u00f0t\u00de \u00bc u\u00f0t\u00de cos t v\u00f0t\u00de sin t \u00f08\u00de \u00f01=x\u00de _y\u00f0t\u00de \u00bc u\u00f0t\u00de sin t v\u00f0t\u00de cos t \u00f09\u00de where x is a scaling parameter. The new coordinate (u, v) defines the van der Pol plane, in which the coordinates q(u, v) rotate at a rotational speed t\u00f0 \u00bc t=T0\u00de with respect to \u00f0y, _y\u00de, as shown in Fig. 3, where T0 is the period that will be removed from each periodic solution. If the orbit has only one stable periodic pendulum oscillation, then the trajectory can be projected on the van der Pol plane as a single point, using the period of the solution and appropriate scaling parameter x. On the other hand, if the orbit consists of not only dominant motion but also sub-harmonic motion, then the trajectory projected on the van der Pol plane does not become a single point, but forms a closed trajectory, the high-frequency cusp behavior of which is smoothed out when the period of low frequency of the solution is used for T0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001562_s1388-2481(00)00137-5-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001562_s1388-2481(00)00137-5-Figure1-1.png", "caption": "Fig. 1. Modi\u00aeed micro \u00afow cell from electrocell AB. 1: anodic and cathodic compartments (T eflon\u00e2); 2: outlet; 3: volumic electrodes; 4: electric connections; 5: inlet; 6: Te\u00afon grid used to isolate the membrane from the electrodes; 7: ion exchange membrane, 8: gaskets (Viton\u00e2).", "texts": [ " Quantitative analyses were carried out by isocratic HPLC (Knauer) equiped with a di erential refractom- * Corresponding author. Tel.: +33-549-45-3731; fax: +33-549-45- 3580. E-mail address: el.mustapha.belgsir@univ-poitiers.fr (E.M. Belg- sir). 1388-2481/01/$ - see front matter \u00d3 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 8 - 2 4 8 1 ( 0 0 ) 0 0 1 3 7 - 5 eter (Knauer) and an UV detector (Gilson) setted on line. The partition was performed on a resin-exchange column (HPX87H from BioRad) with 6:66 10\u00ff3 N sulfuric acid ultra-pure aqueous solution as eluent. Modi\u00aeed Micro Flow Cell from ElectroCell AB (Fig. 1) was used to electrolyse a batch of 10 g of methyla-D-glucopyranoside in 250 cm3 sodium carbonate bu er solution pH 10 . The electrolyte was percolating through the graphite felt cathode and the TMGF anode at 5 ml min\u00ff1. The potential was controlled through a band from the separating membrane dipped in saturated KCl solution. Fig. 2 represents stable cyclic voltammograms of a TNGF electrode. In supporting electrolyte only (dotted lines) oxidation and reduction waves characteristic of R2NO =R2NO couple are observed at 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001877_s0022-0728(00)00177-7-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001877_s0022-0728(00)00177-7-Figure4-1.png", "caption": "Fig. 4. Cyclic voltammograms of a poly 1 electrode (G1=6.7 nmol cm\u22122) in CH3CN+0.1 M TBAP; scan rate=100 mV s\u22121. Potentials measured vs. the Ag Ag+ in CH3CN electrode.", "texts": [ "4 to 0.75 V for 1, results in the continuous growth of the cyclic voltammetric peaks as shown in Fig. 3. This indicates the formation of an electrogenerated polymeric film on the electrode surface. The increase in the peak system corresponds to the increase in the reversible one-electron oxidation wave of 1 and the appearance and the increase of the reversible oxidation wave of the polypyrrolic backbone. Electropolymerization of 1 was also carried out by the controlled-potential oxidation at 0.75 V. Fig. 4 shows the cyclic voltammogram exhibited by a modified electrode obtained by controlled potential electrolysis (1 mC) upon transfer into a CH3CN+0.1 M TBAP solution free of monomer. The poly 1 film presents in the negative region the electrochemical response of the one-electron reduction of the macrocycle and, in the positive region, those of the polypyrrolic matrix and the one-electron oxidation of the deuteroporphyrin ring. As previously described for other functionalized polypyrrole films [22], the cyclic voltammogram shows intense prepeaks at the foot of the macrocycle reduction wave (Epc= \u22121" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003430_978-0-85729-898-0-Figure9.9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003430_978-0-85729-898-0-Figure9.9-1.png", "caption": "Fig. 9.9 Workspace of the cooperative manipulator system and desired trajectory", "texts": [ " The conclusion is that, in this case, the robust controllers present practically the same position tracking performance than the hybrid position/force controller, but with less control effort. We also experimented with controlling the underactuated cooperative manipulator with the nonlinear H1 neural network-based adaptive controller developed in Sect. 9.6. The load parameters, presented in Table 9.4, represent those of a 9.7 Examples 219 force-torque sensor attached to the manipulators\u2019 end-effectors. Figure 9.9 shows the workspace of the cooperative manipulator and the desired trajectory for the set of experiments presented next. The desired trajectory is an arc of circle centered at C \u00bc \u00f00:24; 0:08\u00de m and with radius R \u00bc 0:26 m. The arc spans from xo\u00f00\u00de \u00bc \u00bd0:1 m 0:3 m 0 T to xd o\u00f0T\u00de \u00bc \u00bd0:38 m 0:3 m 0 T ; where T \u00bc 3:0 s is the desired duration of the motion. The reference trajectory for the x-axis is a fifth-degree polynomial, and for the y-axis it is defined by the reference arc. The following external disturbances are introduced to verify the robustness of the proposed controllers: sd1 \u00bc 0:01e \u00f0t 1:5\u00de2 0:5 sin\u00f02pt\u00de 0:01e \u00f0t 1:5\u00de2 0:5 sin\u00f02:5pt\u00de 0:01e \u00f0t 1:5\u00de2 0:5 sin\u00f03pt\u00de 2 664 3 775; sd2 \u00bc 0:02e \u00f0t 1:5\u00de2 0:5 sin\u00f02pt\u00de 0:02e \u00f0t 1:5\u00de2 0:5 sin\u00f02:5pt\u00de 0:01e \u00f0t 1:5\u00de2 0:5 sin\u00f03pt\u00de 2 664 3 775: 0 1 2 3 4 5 0", "5 compares the values ofL2\u00bdex ; E\u00bds ; and E\u00bdhoS when all three controllers presented in this chapter are applied to the 0 1 2 3 4 5 \u22120.4 \u22120.3 \u22120.2 \u22120.1 0 0.1 0.2 0.3 0.4 Time (s) Sq ue ez e fo rc e (N ) With squeeze force control Without squeeze force control Fig. 9.8 Squeeze force control Mass mo \u00bc 1:45 kg Length lo \u00bc 0:120 m Center of mass ao \u00bc 0:060 m Inertia Io \u00bc 0:0026 kg m2 222 9 Robust Control of Cooperative Manipulators 9.8 Neural Network-Based Adaptive Controller 223 fully-actuated cooperative manipulator system following the desired trajectory of Fig. 9.9. Note that the neural network-based H1 controller presented significantly better performance both in terms of trajectory tracking error and energy usage, while its performance in terms of squeeze forces is equivalent to the other two. When applying the neural network-based adaptive controller to the underactuated configuration, we again assumed that joint 1 of arm A is passive and the desired values for the squeeze forces are cd sc \u00bc \u00bd0 0 T : The gains are K \u00bc diag\u00bd3:42I3; 0:38I6 ; Table 9.5 Performance indexes, fully-actuated configuration Controller formulation L2\u00bdex E\u00bds (N m s) E\u00bdhos (N s) Neural network-based 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002048_rob.4620080505-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002048_rob.4620080505-Figure5-1.png", "caption": "Figure 5.", "texts": [ " In addition to these data, one of the joint parameters 07, 02, or 9, will be specified to reduce the problem to an equivalent 1-dof device. In the first analysis, it is assumed that 0 7 is specified or locked in a given position. The resulting 6-dof manipulator is illustrated in Figure 4, and the calculated input parameters are the position vector & and the orientation vectors s6 and 867. In the second analysis, the user might specify O2 in addition to the desired end effector position and orientation. A new equivalent six-dof manipulator was formed and shown in Figure 5 . It should be pointed out that the angle a12, and the offset distances S1 and S2 for the equivalent mechanism, must be solved for by simple projection in terms of the given parameter 0 2 . This second strategy has a distinct advantage over the former. The angle O2 directly positions the parallel planes containing links u34 and u4s, which are perpendicular to the vector S4. Since links u34 and u45 are much larger in magnitude than the remainder of the mechanism, the operator can orient the planes containing these links so as to avoid obstacles in the workspace", " 650 Journal of Robotic Systems-1 991 A unique value of ( 9 3 can be computed from eqs. (41) and (42) for each set of values of 07, 0 6 , 02, 01, 04, and 05. At this point the first analysis of the SSRMS is complete. It has been shown that eight assembly configurations can be determined through the solution of three successive quadratic expressions. CASE 2: 0 2 SPECIFIED The input parameters for this analysis are the position vector R7, the orientation vectors S7 and a78, and the angle 02, as shown in Figure 2. The equivalent six-axis manipulator for this case is shown in Figure 5. It should be noted that the mechanism parameters S1, S2, and aI2 of the equivalent six-axis manipulator are functions of 02. The following analysis is for the equivalent manipulator as illustrated in Figure 5. It is important to recognize that the joint angle values of the actual SSRMS will be distinguished from the joint angle values of the equivalent six-axis manipulator by writing the actual angles with an additional subscript a. For example, the fourth joint angle of the actual SSRMS will be written as 04a. The symbol O4 will refer to the value of the fourth joint angle of the equivalent sixaxis manipulator. Calculation of +la can be written The vector loop equation of the equivalent closed loop spatial mechanism This equation can be projected onto the vector SZ (see ref" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure6.1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure6.1-1.png", "caption": "Fig. 6.1 Soil preparation devices. a Wooden and stony Li Ze (\u6728\u7930\u790b, \u77f3\u7930\u790b) (Wang 1991). b Liu Zhe (\u78df\u78a1) (Wang 1991). c Gun Zhou (\u8f25\u8ef8) (Wang 1991). d Dun Che (\u7818\u8eca) (Wang 1991). e Shi Tuo (\u77f3\u9640) (Pan 1998). f Structural sketch", "texts": [ " They are pulled by animals, and their wooden or stone cylinders are used to roll on farms for breaking mud blocks and flatenting lands. One of their functions is to mix various degrees of humid soils. The stone roller is suitable for flattening dry land, while the wooden type is for wet land. Each of these devices is a Type I mechanism with a clear structure and can be identified as a mechanism with two members and one joint, including a wooden frame as the frame (member 1, KF) and a roller member (member 2, KO) that is set on the wooden frame. The roller member is connected to the frame with a revolute joint JRy. Figure 6.1f shows the structural sketch. K.-H. Hsiao and H.-S. Yan, Mechanisms in Ancient Chinese Books with Illustrations, History of Mechanism and Machine Science 23, DOI: 10.1007/978-3-319-02009-9_6, Springer International Publishing Switzerland 2014 109 There are seven harvest and transportation devices with roller members, including Xia Ze Che (\u4e0b\u6fa4\u8eca, a swamp-used cart), Da Che (\u5927\u8eca, a large cart), Tui Lian (\u63a8\u942e, a hand reaper), Mai Long (\u9ea5\u7c60, a wheat storage cart), He Gua Da Che (\u5408 \u639b\u5927\u8eca, a four-wheel cart), Nan Fang Du Tui Che (\u5357\u65b9\u7368\u63a8\u8eca, a single-wheel 110 6 Roller Devices cart), and Shuang Qian Du Lun Che (\u96d9\u9063\u7368\u8f2a\u8eca, a dual-driven wheel barrow) as shown in Figs" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003752_001872086300500106-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003752_001872086300500106-Figure2-1.png", "caption": "Fig. 2. Orientation of vectors.", "texts": [ "0175r$~ (5) the point E can be expressed by the vector equation where the first product is tangential acceleration, and the second product of three terms is normal acceleration. The product of two perpendicular vectors produces a third vector whose direction is mutually perpendicular to the A, = ii;*E+B*8*ST The algorithm continues with similar equations for the upper arm. = (8;+l- 8,-1)/0.0596 (6) (8) 8' = (8j+2+8i-2-283)/0.0036 (7) Bit- 8i+ 0.0 175 80 SE, = (s) sin Bi EY = -(SF) cos 8i The position of the upper arm as shown in Fig. 2 is established by - (9) (10) and the components of elbow acceleration are then determined by A,, = -e'*3zy-8*(8*SZ~) (11) A,, = +e'*sE,-B*(8*sE,) (12) multiplier and multiplicand vectors. The magnitude of this product vector is 18'1 * lSEl +(sine of the angle between vectors 8 and E). The direction of the vectors 8 and e' is normal to the plane of rotation. Thus, in Fig. 2, the 8 and 8 vectors are always parallel to the 7 axis. By dealing with x andy components of all vectors, the angle between vectors is always 90\"; the sine of the angle between factors is always one, and all vectors are oriented to the x , ~ , ? coordinate system. The necessity of coordinate transfer is eliminated. The vectors may now be expressed in terms of their components by use of unit vectors ?J, A, respectivelyin directions, x,y, and 7. Hence the quantities in the equation for A-, become e'= *fj" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002414_tia.1987.4504992-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002414_tia.1987.4504992-Figure2-1.png", "caption": "Fig. 2. Rotor cross section of buried-type PM machines. (Points 1, 2, 3, and 4 denote same parts of rotor as in Fig. 3).", "texts": [ " MAGNETIC EQUIVALENT CIRCUIT OF A PM MACHINE The idea of magnetic equivalent circuits of electric machines is based upon analogies between the stationary values of electric and magnetic fields, i.e., J= uE meances have the same meaning in both types of circuits. These relationships are formal because the product of voltage and current in an electric circuit has no analogy in a magnetic circuit. The permanent magnet as a flux source is represented in magnetic equivalent circuits in the manner shown in Fig. 1. The rotor cross section of the PM machine studied in this paper is shown in Fig. 2. The stator of the machine is a normal three-phase ac machine stator structure. The difference between the PM machine and the induction machine studied in [61 is in the rotor yoke. Supposing that the flux in the parts of the rotor between the magnets and slots is only radial, one can draw the magnetic equivalent circuit of one rotor pole of a PM machine in the way shown in Fig. 3. The node potential equations for the circuit from Fig. 3 are (1)Ipn (P5 - 6 ) = Tp1772 (ap)n 4bpMn + bptll ) A66 P6+A65'P5=-T-Pm,2 4'1'l A55 5+A54 oP +A56 6 TP\"24Pn7 A q +A 4 @03 + A45 y5 = Tpm1 4zr A32P2\u00b1+A 33(3 +A 3p4< =Fz A21PI + A22 2 + A233 - 4ws (2) (3) (4) (5) (6) (7) The symbols in the equations above are the same as those used in [61, except - Ipm is defined as and B= tH" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003411_iros.2011.6094663-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003411_iros.2011.6094663-Figure8-1.png", "caption": "Fig. 8. The local coordinate system of section i\u2019s circle", "texts": [ " 7), depending on the directions of l12 and l23; that is, the following equation must be satisfied: sin(\u03b11) = sin(\u03b12) (11) For the case that l12 and l23 are parallel, then Constraint 1 is satisfied since l12 \u00d7 l23 = 0 (12) and Constraint 2 can be expressed as: (p2 \u2212 p1) \u00b7 l12 = 0. (13) Since p1 and p2 are on section 1\u2019s circle and section 3\u2019s circle respectively, each can be expressed in terms of a scalar angle as derived below. Define a local coordinate system for section i\u2019s circle, as illustrated in Fig. 8, such that its origin is at the circle center ci, and two unit vectors ui and vi form the 2by the definition of cross product. orthogonal axes on the circle plane. ui and vi are functions of yi; Denote ri = 1 |\u03bai| as the radius of the circle for section i. Thus, since p1 is on the section 1\u2019s circle, its position vector (in the robot base frame) must satisfy: p1 = c1 + r1cos(\u03b81)u1 + r1sin(\u03b81)v1 (14) where \u03b81 is the angle from the vector u1 to p1 \u2212 c1. Similarly, since p2 is on the section 3\u2019s circle, its position vector must satisfy: p2 = c3 + r3cos(\u03b83)u3 + r3sin(\u03b83)v3 (15) where \u03b83 is the angle from the vector u3 to p2 \u2212 c3" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure4.7-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure4.7-1.png", "caption": "Fig. 4.7 A water-driven pestle, a Original illustration (Pan 1998), b Chain", "texts": [ "5 A simple cam mechanism 70 4 Ancient Chinese Machinery Cam mechanisms also appeared in water-driven pestles. The publication Huan Zi Xin Lun\u300a\u6853\u5b50\u65b0\u8ad6\u300bduring the latter part of the West Han Dynasty (206 BC\u2013 AD 8) records a water-driven pestle that \u201c\u2026used water to pestle\u2026\u201d \u300e\u2026\u5f79\u6c34\u800c \u8202\u2026\u300f (Huan 1967). Complex water-driven pestles appeared as early as the Jin Dynasty (\u6649\u671d, 265\u2013 420 AD). The book Jin Zhu Gong Zan\u300a\u6649\u8af8\u516c\u8b9a\u300b (Jin 1972) states: \u201cDu Yu and Yuan Kai constructed water-driven pestles.\u201d \u300e\u675c\u9810\u3001\u5143\u51f1\u4f5c\u9023\u6a5f\u6c34\u7893\u300f There are also many records of water-driven pestles in the literature of the later periods. Figure 4.7a shows a water-driven pestle described in the book Tian Gong Kai Wu (Pan 1998). This is a typical simple cam mechanism with three members and three joints. The water wheel is connected to a long shaft with paddles as an assembly (member 2). When water drives the water wheel, the cam effect on the assembly causes the tilted hammers (member 3) to produce work. Member 2 is connected to the frame (member 1) with a revolute joint (JRx; joint a). The paddle is connected to one end of the tilted hammer with a cam joint (JA; joint c). The tilted hammer is connected to the frame with a revolute joint (JRx; joint b). Figure 4.7b shows its corresponding chain. This device is a planar mechanism consisting of three members (1, 2, and 3), two revolute joints (JRx; joints a and b), and one cam joint (JA; joint c). Therefore, NL = 3, CpRx = 2, NJRx = 2, CpA = 1, and NJA = 1. Based on Eq. (3.1), the number of degrees of freedom, Fp, of this mechanism is: Fp \u00bc 3 NL 1\u00f0 \u00de NJRxCpRx \u00fe NJACpA \u00bc 3\u00f0 \u00de 3 1\u00f0 \u00de 2\u00f0 \u00de 2\u00f0 \u00de \u00fe 1\u00f0 \u00de 1\u00f0 \u00de\u00bd \u00bc 6 5 \u00bc 1 4.3 Cam Mechanisms 71 The bell and gong mechanism on the hodometer (\u8a18\u91cc\u9f13\u8eca) is also a cam mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002240_j.precisioneng.2002.12.001-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002240_j.precisioneng.2002.12.001-Figure1-1.png", "caption": "Fig. 1. Quasi-kinematic (A) and kinematic (B) couplings.", "texts": [ " Keywords: Kinematic coupling; Quasi-kinematic coupling; Plastic deformation; Exact constraint; Fixture; Repeatability; Stiffness; Assembly; Photonics; Automotive assembly; Over constraint; Precision optics The need to improve performance has forced designers to tighten alignment tolerances for next generation assemblies. Where tens of microns were once sufficient, nanometer/micron-level alignment tolerances are becoming common. Examples can be found in automotive engines, precision optics and photonic assemblies. Unfortunately, the new alignment requirements are beyond the practical capability (\u223c5 m) of most low-cost alignment technologies. The absence of a low-cost, sub-micron coupling has motivated the development of a new class of coupling interface, the quasi-kinematic coupling (QKC) (Fig. 1A). To understand the need for a new class of precision fixtures, it is necessary to understand why the cost and performance characteristics of current technologies are incompatible with the dual requirements of low-cost and sub-micron precision. We will first examine coupling types used in traditional manufacturing. The most common type, the pinned joint, is formed by mating pins from a first component into corresponding holes or slots in a second component. Obtaining \u2217 Tel.: +1-617-452-2395; fax: +1-509-693-0833", " micron-level precision with these couplings is impractical due to the micron-level tolerances that are required on pins, holes and pin\u2013hole patterns. Other well-known couplings such as tapers, dove\u2013tails and rail\u2013slots would also require micron-level tolerances. They also require expensive finishing operations to reduce the effect of surface finish on alignment performance. Let us now consider exact constraint couplings that are well known in precision engineering, but less frequently used in manufacturing. A common type of exact constraint coupling, a kinematic coupling (see Fig. 1A), routinely provides better than 1 m precision [1] alignment. Unfortunately, they fail to satisfy three low-cost coupling requirements that are common to many manufacturing processes: 1. Low-cost generation of fine surface finish: micron-level kinematic couplings must use balls and grooves with ground or polished surfaces [2]. Although balls with fine surface finish are generally inexpensive, grooves with fine surface finish are expensive. The finishing operations used to prepare groove surfaces add considerable cost to kinematic couplings", " Section 2 discusses the concept of the QKC and shows how it satisfies the low-cost coupling requirements in Section 1.2. Section 3 provides the theory used to predict coupling stiffness and provides a metric that can be used to minimize over constraint in QKCs. Section 4 discusses the theory as implemented in a MathCAD program and Section 5 provides experimental results that show QKCs can provide performance comparable to exact constraint couplings. The implications of coupling cost are covered in Section 6. Appendices are provided to cover the details of the theory and the design tool. From Fig. 1, we see that kinematic and QKCs share similar geometric characteristics. A kinematic coupling consists of balls attached to a first component that mate with v-grooves in a second component. The balls and grooves form small-area contacts. QKCs consist of axisymmetric balls attached to a first component that mate with axisymmetric grooves in a second component. Here the balls and grooves form arc contacts. Two examples of axisymmetric geometries that form arc contacts are shown in Fig. 3. The orientation of joints in both couplings is also similar" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003535_detc2012-70621-Figure5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003535_detc2012-70621-Figure5-1.png", "caption": "Fig. 5 The reconfiguration of an R\u030bR\u0304R\u0304R\u0304R\u030b-R\u0304R\u0304R\u030bR\u030bR\u030b-R\u030bR\u030bR\u030bR\u0304R\u0304 PM", "texts": [ " The use of compositional units and virtual chains [9] guarantees that all the PMs with both planar and 3T1R operation modes obtained have finite motion in each operation mode. By selecting four R joints as actuated joints, which are de- Base Moving platform Leg 1 Leg 2 Leg 3 noted by R, we can obtain PMs with both planar and 3T1R operation modes from these parallel kinematic chains. Three (or four) of the selected actuated joints should satisfy the validity condition for planar parallel manipulators ( [22]) (or the 3T1R PMs [4, 9]). The R\u030bR\u0304R\u0304R\u0304R\u030b-R\u0304R\u0304R\u030bR\u030bR\u030b-R\u030bR\u030bR\u030bR\u0304R\u0304 PM with both planar and 3T1R operation modes shown in Fig. 5(b) is obtained from the parallel kinematic chain in Fig. 4.2 Figure 5 shows the reconfiguration of the R\u030bR\u0304R\u0304R\u0304R\u030b-R\u0304R\u0304R\u030bR\u030bR\u030bR\u030bR\u030bR\u030bR\u0304R\u0304 PM with both planar and 3T1R operation modes shown in Fig. Fig. 5(b). The PM switches from the RR\u0304R\u0304R\u0304R-R\u0304R\u0304R\u0300R\u0300R\u0300R\u0300R\u0300R\u0300R\u0304R\u0304 planar operation mode [Fig. 5(a)] to a transitional configuration [Fig. 5(b)], and then to the R\u030bR\u0300R\u0300R\u0300R\u030b-R\u0300R\u0300R\u030bR\u030bR\u030b-R\u030bR\u030bR\u030bR\u0300R\u0300 3T1R operation mode [Fig. 5(c)]. In the RR\u0304R\u0304R\u0304R-R\u0304R\u0304R\u0300R\u0300R\u0300R\u0300R\u0300R\u0300R\u0304R\u0304 planar operation mode [Fig. 5(a)], the axes of rotation of the moving platform is parallel to the axis of the first R joint in leg 2. In the R\u030bR\u0300R\u0300R\u0300R\u030b-R\u0300R\u0300R\u030bR\u030bR\u030b-R\u030bR\u030bR\u030bR\u0300R\u0300 3T1R operation mode [Fig. 5(c)], the axes of rotation of the moving platform is parallel to the axis of the first R joint in leg 1. In the transitional configuration [Fig. 5(b)], the sum of all the leg-wrench systems is a 1-\u03b6\u221e-system in which the direction of the basis \u03b6\u221e is perpendicular to the axes of all the R\u0304 and R\u030b joints, and the moving platform has five instantaneous DOF which includes the planar 2The R\u030bR\u0304R\u0304R\u0304R\u030b-R\u0304R\u0304R\u030bR\u030bR\u030b-R\u030bR\u030bR\u030bR\u0304R\u0304 PM is discarded since the motion of the mov- ing platform in the planar operation mode cannot be controlled by any three of the four actuated joints. 6 Copyright 2012 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use with both planar and 3T1R operation modes. motion and the 3T1R motion. It is noted that the R\u030bR\u0304R\u0304R\u0304R\u030b-R\u0304R\u0304R\u030bR\u030bR\u030b-R\u030bR\u030bR\u030bR\u0304R\u0304 PM with both planar and 3T1R operation modes in the R\u030bR\u0300R\u0300R\u0300R\u030b-R\u0300R\u0300R\u030bR\u030bR\u030b- R\u030bR\u030bR\u030bR\u0300R\u0300 3T1R operation mode [Fig. 5(c)] is in fact a partially decoupled 3T1R PM [24, 25] since the translation of the moving platform along the Z-axis is controlled by the actuated joint in leg 2 while the remaining three DOF of motions are further controlled by the remaining three actuated joints. Although a 5-DOF PPPU= (PPPU equivalent) PM (Chapter 12, [9]) or 6-DOF PM can be used to carry out the task of the PM with both planar and 3T1R operation modes, one or two more actuators are needed than the PM with both planar and 3T1R operation modes", " Together with [19, 22], this work lays the foundation for the type synthesis of other classes of PMs with multiple operation modes. The optimal type selection of PMs with multiple operation modes and the method for switching a PM from one operation mode to another are still open issues. The author would like to thank the Engineering and Physical Sciences Research Council (EPSRC), United Kingdom, for the support under grant No. EP/I016333/1 and the Royal Society, United Kingdom, through an International Joint Project No. JP100715. Thanks to X He for creating the CAD model in Figure 5. [1] Herve\u0301, J.M. and Sparacino, F., 1991, \u201cStructural Synthe- sis of Parallel Robots Generating Spatial Translation,\u201d Proceedings of the fifth International Conference on Advanced Robotics, Pisa, Italy, Vol. 1, pp. 808\u2013813. [2] Li, Q.-C. and Huang, Z., 2003, \u201cType synthesis of 4-DOF parallel manipulators,\u201d Proceedings of the 2003 IEEE international conference on robotics and automation, Taipei, pp. 755-560. [3] Angeles, J., 2004, \u201cThe Qualitative Synthesis of Parallel Manipulators,\u201d ASME Journal of Mechanical Design, 126(4), pp" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003153_cca.2009.5281045-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003153_cca.2009.5281045-Figure2-1.png", "caption": "Fig. 2. A schematic diagram of the pendulum system", "texts": [ " The purpose of given work is an advancement of control approaches offered in [1] \u2013 [9], but in contrast to known analogs the adaptive scheme of pendulum control is obtained allowing to solve mentioned task in conditions of the full parametric uncertainty without the preliminary identification procedure. II. PROBLEM STATEMENT The mechanical part of plant represents a single-link pendulum fixed at the pivot pin with the reaction wheel situated at the opposite end of the pendulum. The platform of the pendulum is movable (see Fig. 2). Moving of the pendulum is provided by changing a direction and rate of turn of the reaction wheel. Wheel rotation is controlled by regulating an input voltage in DCmotor fixed together with the wheel. It is necessary to note, that platform of the system possesses a high inertia in comparison with the pendulum itself. We use a mathematical model describing a physical character of the mechanical part of the plant without movement of the platform and it looks like the following system of differential equations: \u00bd \u00c4\u03bc(t) + a sin \u03bc = \u00a1bp(\u00b9u\u00a1 f); \u00c4\u03bcr = br(\u00b9u\u00a1 f); (1) where \u03bc \u2013 an angle of the pendulum, \u03bcr \u2013 a wheel angle, a = mgl J , bp = ku J , br = ku Jr \u2013 unknown complex parameters of the pendulum, m \u2013 a combined mass of the rotor and the pendulum, l \u2013 the distance from pivot to the center of mass of the pendulum system, J \u2013 a combined moment of inertia of the pendulum system, Jr \u2013 a moment of inertia of the wheel and the rotor of electric motor about its center of mass, ku \u2013 a transfer constant of the DC-motor, g \u2013 the acceleration of gravity, f \u2013 a torque of friction forcing in the motor, j\u00b9uj 6 10 \u2013 a control signal" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001894_ac991182m-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001894_ac991182m-Figure4-1.png", "caption": "Figure 4. Cyclic voltammogram of the poly-NDGA-modified GC electrode in the absence (a) and presence (b) of 0.5 mM NADH. Electrolyte, as in Figure 1. \u0393 \u223c1.5 \u00d7 10-10 mol cm-2. Scan rate, 10 mV s-1.", "texts": [ " As was proved by Laviron,26 if \u2206Ep >200/n mV and Ep is linearly proportional to log(v), the standard rate constant ks and the charge-transfer coefficient R for the surface-immobilized redox species can be easy determined. In the case studied, the appropriate conditions were achieved over the range 4000-10 000 mV s-1. E\u00b0 \u2032 was taken as the average of the cathodic and anodic peak potentials at the lowest scan rate applied (2 mV s-1), where no kinetic effects are apparent. Using the equations derived by the author, we calculated ks and R values to be 43 s-1 and 0.44, respectively. The value of ks is higher that those for related systems reported so far.16,17,21,22 Mediated Electrooxidation of NADH. Figure 4. shows cyclic voltammograms of the poly-NDGA-modified electrode in buffer solution in the absence (a) and in the presence (b) of NADH, respectively. It can be seen that there is a great increase in the anodic peak of the QH2/Q couple in the presence of coenzyme. The reason is that electrochemically generated quinone is reduced back to hydroquinone by NADH species diffusing from the solution bulk to the electrode surface according to the equatiom For the same reason the cathodic peak of the QH2/Q couple is lowered" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001646_s0043-1648(00)00448-8-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001646_s0043-1648(00)00448-8-Figure2-1.png", "caption": "Fig. 2. Big and small specimen rings (dimensions in mm).", "texts": [ " The initial surface roughness and the final surface roughness after the wear test are measured by Talysurf. Therefore, the surface roughness Ra of the specimens at different time intervals during the wear test can be inferred. In order to verify the validity of the optical technique used in wear tests, the on-line measurements using the new optical technique were compared with surface roughness data measured using Talysurf by stopping the wear test at different time intervals. The pair of specimen rings are sketched in Fig. 2. The small and big specimen rings were made of bearing steel and mild steel, respectively. The elastic modulus of the specimens rings are 210 GPa. The hardness of the small ring is 1.75 times greater than that of the big ring (see Table 1) and the wear occurs mainly at the surface of the softer specimen ring. The small contact length between the specimen rings is to minimise the side effect of line contact and the effect of misalignment of the two disks. Furthermore, the contact length (2.5 mm) is close to the measuring length of the optical technique (2 mm), such that almost the complete contact area was measured" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001536_s0167-6911(00)00105-5-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001536_s0167-6911(00)00105-5-Figure1-1.png", "caption": "Fig. 1. Coordinate frames.", "texts": [ " We use the Routh two-dimensional impact model [10,11] which models the material deformation normal to the impact and relative sliding in the tangential direction. We show that the reachable set depends fundamentally on whether or not relative sliding between the puck and mallet terminates during the impact event which restricts the size of the reachable set. We show that the system satis1es a type of accessibility property if and only if the coe4cient of friction between the puck and mallet is nonzero. Consider the setup in Fig. 1 showing a circular puck with tangential and normal impulses Pb and Pn, respectively, acting on the puck at the origin of a coordinate frame (b; n), whose orientation is with respect to a base frame (x; y). We assume that the puck is a uniform thin disk of mass m, radius r, and moment of inertia, I = mr2=2, about its central axis. The con1guration q(t) of the puck at time t is given as q(t) = (x(t); y(t); (t))T, where x(t); y(t) are the coordinates in the base frame of the center of mass of the object, and (t) is the orientation of the object measured relative to the x-axis of the base frame" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003006_aero.2010.5446985-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003006_aero.2010.5446985-Figure9-1.png", "caption": "Figure 9. Sample Acquisition and Caching system deployed on the MER rover.", "texts": [ " At the end of the paper, we present sensitivity of the system to larger number of cores (31) and larger cores (1.1 cm x 8 cm). 8 Measure the sample to within 10mm. 9 Minimize vibration from the sampling tool to instruments. 10 Minimize sample contamination to satisfy Planetary Protection and Contamination Control requirements 11 Provide brushing & abrading of the surface similar to the functionality provided by the Rock Abrasion Tool of the Mars Exploration Rover mission. *Current Best Estimate Figure 9 shows the proposed Core Acquisition and Caching system in its deployed position on the MER size platform. The MER+ and MSL platforms used the same architecture. The only difference between the 3 rover platforms is the larger size of the robotic arm on the MSL rover, driven by the requirement to survive and recover from the catastrophic slip condition. This architecture as mentioned earlier has been developed specifically to reduce the risk associated with core acquisition and aching. Another approach developed by NASA JPL, on the other hand, focused on reducing the mass of the returned cache [10, 11]. The system components of the proposed architecture are shown in Figure 9 and include: 1. Drill 2. Sample Cache 3. Bit Carousel 4. 5 DOF Robotic Arm 5. Rock Abrasion and Brushing Tool (RABBit) The core acquisition and caching sequence takes only 4 steps as follow: 1. Drill docks with the Bit Carousel and acquires a new Bit (Figure 10). 2. Robotic Arm preloads the Drill against a target rock. The Drill commences its core acquisition operation: it drills to a target depth, breaks off and captures the core, and retracts the bit from the hole (Figure 11). 3. Robotic Arm positions the core bit in front of the camera (PanCam, HazCam etc" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002075_j.talanta.2005.01.044-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002075_j.talanta.2005.01.044-Figure1-1.png", "caption": "Fig. 1. Amperometric cell. (A) Frontal view, (B) top view of the open cell, (C) lateral view; (a and b) inlet and outlet of the carrier stream, (c and d) counter and reference electrodes. The working electrode is placed perpendicular to inlet, i.e. wall-jet configuration.", "texts": [ " The electrochemical cell was omposed of three electrodes (all from Bioanalytical Systems nc., BAS, USA): working (glass carbon with inner diameter nd length as 3 mm and 7.5 cm), reference (Ag/AgCl; 3 M aCl with length 7.5 cm) and counter (platinum wire with -cm length and gold connector). Experiments with flow injection analysis (FIA) were realzed using a programmable system from Ismatec (Zurich, witzerland) composed of two peristaltic pumps (fix and ariable), injection valves, tubing (0.7 mm, i.d., wall thickess < 0.2 mm), \u201cwall-jet\u201d electrochemical cell (Fig. 1) and ther accessories. .3. Procedure The electrochemical cell was filled with a 1.0 M Na2SO4 olution, and the glassy carbon electrode was submitted to 50 cycles (from 200 to 900 mV versus Ag/AgCl) with scan ate = 1 Vs\u22121. After that, the working electrode was manually olished with alumina (Al2O3, 1 and 0.3 m, Nuclear/Brazil) ntil the formation of a mirror surface and then left in sonicaion for 5 min (in a 1:1 mixture of water/alcohol) to eliminate icro particles of alumina adsorbed on the electrode surface", " The FIA system (initially used for evaluation of the PB film) was employed to verify the performance of the biosensor; in this case, a standard glucose solution (0.6 mM in R3) was used. 2.4. The flow-injection system The sample was injected into the FIA system by a 100 L sampling loop and pushed by its carrier stream (0.25 M KH2PO4 + 0.13 M K2HPO4 \u2212 reagent R3) at 0.8 mL min\u22121. This flowed through a 25 cm coiled reactor towards the detector with fixed applied potential at working electrode = \u221250 mV versus Ag/AgCl. The passage of the sample through the cell (Fig. 1) produced a transient signal with a peak current proportional to the glucose content in the sample. Precision was expressed as relative standard deviation calculated after successive measurements. 3. Results and discussion The steps realized for the film preparation were of great importance to improve the stability of the films. In fact, the performance of the amperometric sensor increased by about 25% compared with the one without these steps; moreover, it important to explain that any trace of fat or alumina adsorbed onto surface electrode before the deposition step decreases or eliminated the possibility to create a stable film of Prussian Blue" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003862_1350650112441747-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003862_1350650112441747-Figure1-1.png", "caption": "Figure 1. Contact model of the bearing.", "texts": [ " In the model, the diameter of each roller was a variable that can be same as or different from each other. Contact judgments between all of the rollers and the raceways were done constantly in the solution process, so that compatibility of deformation of the rollers and raceways need not be considered, which was different from other traditional methods. Thus, the unloaded roller in the loaded zone of the bearing could be found. Effects of the off-sized rollers on the load distribution in the bearing could be analyzed. Figure 1 shows the contact between the rollers and the raceways. First, there were some assumptions as follows: (a) the rings were flexurally rigid and underwent only local deformation due to the stresses in contacts; (b) the form errors of the raceways and rollers were too small to be taken into account; (c) the friction force in the raceway was omitted; (d) there were no axial manufacturing errors in rollers and raceways; (e) deformations occurred according to the Hertzian theory of elasticity; and (f) contact forces between rollers and the cage were negligible because only static load distribution was studied. at LAURENTIAN UNIV LIBRARY on December 9, 2014pij.sagepub.comDownloaded from The coordinate system and roller number The outer ring was fixed, but on the contrary, the inner ring was free in the plane (Figure 1). A coordinate system was set up on the outer ring. The coordinate origin was at the center O of the outer ring. The x-axis was downward vertically. The y-axis was perpendicular to the x-axis and rightward. Similarly, another coordinate system was also set up on the inner ring. Its coordinate origin located at the center O0 of the inner ring. The x0- and y0-axes were parallel with those of the coordinate system on the outer ring, respectively. All the rollers were equispaced in the bearing and counterclockwise numbered from 0 to n, where no. 0 roller was at the bottom of the outer raceway. The corresponding centers of the rollers were numbered from C0 to Cn. Initially, the bearing was unloaded. The inner raceway (a dashed arc in Figure 1) was concentric with the outer raceway. Also, the inner raceway did not contact the rollers. However, all the rollers just contacted with the outer raceway at first. In the coordinate system on the outer ring, the position angle j of each roller, which was the included angle between the x-axis and the line OCj, was calculated using equation (1) j \u00bc j: 360 Z \u00f01\u00de Then, the inner ring was loaded with a downward radial force Fr. Finally, The center of the inner ring shifted from O to O0. The displacements of the center along x- and y-axes were u and v, respectively", " Thus, the center of the roller displaced from Cj to Cj 0 by oj. It was explicit that Qij and Qoj were not collinear and there was an included angle among them. Thus, their relationship can be expressed as equation (2). However, forces on the roller cannot be in equilibrium in the strict sense. Here, Qij was assumed to be equal to Qoj considering the fact that was so small enough that cosine is extremely close to 1 Qij \u00bc Qoj cos \u00f02\u00de As the relative positions of the bearing components were determined, key points in Figure 1 could be defined in the coordinate system of the outer ring (Table 1). at LAURENTIAN UNIV LIBRARY on December 9, 2014pij.sagepub.comDownloaded from Raceway diameters Di and Do were calculated from equation (3) in which the plus was for the outer raceway and the minus the inner raceway Di,o \u00bc Dm d Pr 2 \u00f03\u00de When the roller just contacted the inner raceway with no contact force, the distance l1j between the center of the inner ring and the center of the roller can be determined by equation (4) l1j \u00bc 1 2 \u00f0Di \u00fe d\u00fe dj \u00de \u00f04\u00de Assumed that the inner raceway had shifted to O0(u, v) but all the rollers had not displaced, the distance l2j between the centers O0 and Cj was determined by equation (5)", " Furthermore, the rollers in the upper half of the bearing were considered without off size because there were no contact forces between these rollers and the raceways. Thus, at most ten rollers with off size in the lower half of the bearing are considered. The detailed distribution of the off-sized rollers in the bearing are listed in Table 4. Roller position changed. The effects of the position of one off-sized roller on the contact forces in the bearing were analyzed. There were five positions (nos 0\u20134 positions presented in Figure 1) that were taken into account. The off size was 0.005mm. The contact forces between at LAURENTIAN UNIV LIBRARY on December 9, 2014pij.sagepub.comDownloaded from the rollers and the inner raceway are displayed in Figure 4. It was very explicit that the position variation of the off-sized roller greatly affected the contact forces and the number of carrying rollers. When the off-sized roller was at no. 0 position, the off-sized roller was loaded most of the radial force Fr because the inner raceway contacted it first and the x0-axis effective component of its contact force was the maximal due to the minimal position angle 0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002640_bit.260250203-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002640_bit.260250203-Figure2-1.png", "caption": "Fig. 2. Typical response of the L-lysine electrode as pC0, with time.", "texts": [ "02M phosphate buffer (pH 6.8) for 3 min. The membrane was rinsed by immersion in stirred buffer solutions. When not in use, the electrode was stored at 4\u00b0C in buffer containing 10W3M PLP. Gelatin was selected as the inert protein for copolymerization with enzyme because of its mechanical properties, which avoid direct contact of the enzyme with glutaraldehyde and thus protect the enzyme against denaturation during the crosslinking process. Electrode responses to different lysine concentrations were registered (Fig. 2) and the calibration curve obtained by plotting the slope d p C 0 2 / d t at the inflexion point against lysine concentration (Fig. 3). Normally, 10-15 rnin are required to reach a steady-state response. By considering the dynamic state, both the response time and the rinsing time are considerably reduced. RESULTS AND DISCUSSION Choosing the optimum conditions for the enzyme electrode required careful consideration of the properties of the enzyme itself. The lysine decarboxylase, a pyridoxal 5\u2019-phosphate (PLP) enzyme, is known to contain 10 mol PLP/mol enzyme" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002901_0278364909348762-Figure8-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002901_0278364909348762-Figure8-1.png", "caption": "Fig. 8. A variety of configurations to make the robot stand at the height H while the total torques for standing are all the same.", "texts": [ " In turn, it is necessary to minimize the power to achieve the switch with smoothness. In this section, we consider kinetics related to torque at joints Jh and Jk in order to make the robot stand or sit at a certain height H . By referring to Figure 3(a), we have Th Wdh W r cos r l sin (16) Tk Wdk Wl sin (17) H r sin r l cos (18) where H is defined in the range R H r l (19) However, the configuration to make the robot stand at the height H is not unique. For instance, there are two stationary configurations of I and II shown in Figure 8(a) making the sum of motor torque of Jh and Jk same. This is clear because the distance a2 is equal to the sum of a1 and 2b1. The same thing can be said about the three cases marked with I, II, and III in Figure 8(b) because of a1 b1 b1 a2 b2 b2 a3 b3 b3. Even when the payload factor ratio is assigned as a fixed value, the configurations are infinitive. Horizontally flipped configurations in Figure 8(a) and (b) are also the candidates to keep H the same. Obviously, the motor for driving Jk in case I of Figure 8(a) requires more power than that in case II. Therefore, the payloads of the two motors become different and the configurations are not always practical because motor power is available within a specified capacity in the design. Then it is recommended to distribute the necessary power to the motors equally in terms of a payload factor for generating quite natural power together. These considerations imply that the optimal configuration is determined by minimizing the power together with the payload factor", " However, it is difficult to solve the equation, since Th and Tk change their signs, in general. Therefore, we simplified the equation as follows by supposing that Th and Tk are positive: Eb Th c Tk (26) Insert (16)\u2013(18) into Eb r 0 to obtain r2 B 1 sin2 r 2B Hr sin r B H2 l2 r2 0 (27) where B c 1 2. Hence, we find sin r B H B2l2 B H2 l2 r2 r2 r B 1 (28) Since (28) gives two configurations, we choose one satisfying Th cTk. Introducing sin r into (18) yields . Conditions such as 0 bi ai or ai bi 0 (see Figure 8) validate that this method is applicable. Therefore, H is limited in l2 r2 H l r (29) In fact, this method remains only in this analysis since its use is limited in a small range of H . Transition control of switching the locomotion type from one to another is illustrated as a sequence in Figure 10. In order to control the locomotion delicately so that the switching proceeds effectively without excessive rotation of Jh, we speculate the control in three phases. at Afyon Kocatepe Universitesi on May 15, 2014ijr" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003965_iemdc.2011.5994834-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003965_iemdc.2011.5994834-Figure4-1.png", "caption": "Fig. 4 Loss distribution for each motor at rated condition", "texts": [ "57%, while the rotor speed estimation using the vibration spectrum technique achieved an accuracy of within 0.16%. It was observed that the estimated values of the no load losses were an under estimate for the larger 11kW and 15kW motors. In contrast the estimated values displayed an over estimate for the 7.5kW motor. This can be explained by considering the distribution of loss components. The total percentage of losses relative to the input power for the individual loss components obtained from the IEC Std 34-2-1 for each motor, at rated load, is shown in Fig. 4. As depicted, the combined friction and windage loss and core loss (no load loss) for the 11kW and 15kW motors, amounts to 3.73% and 3.98% of rated input power respectively. Consequently, the empirical estimate of 3.5% of input power indicates an under estimate. For the 7.5kW motor however, the total no load loss contribution is 2.44% of input power. This is a lower value than the empirical 3.5% of input power and therefore, the empirical values provide on over estimate of no load losses. This suggests the questionability of the estimation of no load loss for smaller sized motors" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003491_20120905-3-hr-2030.00031-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003491_20120905-3-hr-2030.00031-Figure1-1.png", "caption": "Fig. 1. Scheme of the modified quadrotor with the pivoting joints.", "texts": [ " 5 reports some results obtained by simulations, showing the features and capabilities of the UAV, while Sec. 6 concludes with final comments and future work. 978-3-902823-11-3/12/$20.00 \u00a9 2012 IFAC 192 10.3182/20120905-3-HR-2030.00031 In order to obtain an UAV able to fly decoupling linear and rotational movements, thus allowing operations that are not usually possible with standard flying vehicles, the proposed quadrotor has some structural differences with respect to standard devices. The most important difference is shown in Fig. 1, where a scheme of the proposed quadrotor is reported. As it can be seen, an actuated rotational (pivot) joint ri is installed on each arm of the vehicle, thus allowing to rotate the corresponding propeller by the angle \u03b1i. In this manner, the force Pi generated by the propeller may be directed along any direction in a plane orthogonal to the corresponding arm (the plane \u03c0i in Fig. 2). Another difference with respect to a standard quadrotor is the rotating direction of the thrusters. In fact, as shown in Fig", " On the other hand, this configuration allows the UAV to translate by simply rotating two opposite propellers. Anyway, due to the redundancy of the proposed system (eight actuators), both configurations can be chosen for the propellers rotating directions. In order to define the dynamic model of the quadrotor, an inertial reference frame Fw and a frame Fb rigidly connected with the quadrotor body are assigned. The axes xb and yb of Fb are directed along the arms connecting the body with propeller 1 and 2 respectively, while zb is oriented to complete the frame, see Fig. 1. For simplicity, the UAV is considered as a rigid body whose position and orientation with respect to Fw depends on the propulsion forces generated by the four rotors. Then, the dynamic model is obtained by applying the Newton-Euler equations of motion of a rigid body in the configuration space SE(3) = R3 \u00d7 SO(3). Let p = [x, y, z] T be the position of the center of mass of the quadrotor, and R the rotation matrix that describes its orientation, both expressed in Fw. Then, the dynamic model can be computed as { mp\u0308 = Rf b +mg J\u03c9\u0307 = \u2212\u03c9\u00d7J\u03c9 + \u03c4 b (1) where J = diag([Jx, Jy, Jz]) is the inertia diagonal matrix expressed in the body reference frame, m is the total mass of the vehicle, g = [0, 0, \u2212 g] T (with g = 9", " (1) can be defined by considering that the corresponding propeller affects the dynamics of the quadrotor in two ways: by generating a propulsion force Pi orthogonal to the propeller itself, and by generating a counteracting torque \u0393i (see Fig. 4). In particular, as described in (Pounds et al., 2010), it is possible to consider these two contributions as: Pi = kf,i\u03b3 2 i (3) \u0393i = k\u03c4,i\u03b3 2 i + Ir,i\u03b3\u0307i (4) where Ir,i is the motor inertia and kf,i, k\u03c4,i are two parameters that depend on the air density and on geometrical properties of the i-th propeller (see (Pounds et al., 2010)). The term f b = [fb,x, fb,y, fb,z] T in Eq. (1) represents the forces generated by the propellers on the quadrotor body. By considering the model in Fig. 1, it can be calculated as: [ fb,x fb,y fb,z ] = [ P2S\u03b12 \u2212 P4S\u03b14 P3S\u03b13 \u2212 P1S\u03b11 P1C\u03b11 + P2C\u03b12 + P3C\u03b13 + P4C\u03b14 ] = [ 0 S\u03b12 0 \u2212S\u03b14 \u2212S\u03b11 0 S\u03b13 0 C\u03b11 C\u03b12 C\u03b13 C\u03b14 ] P =Bf \u00b7 P (5) where P = [P1, P2, P3, P4] T is the vector collecting the thrusts generated by the four propellers, and S\u03b1i = sin(\u03b1i), C\u03b1i = cos(\u03b1i). The term \u03c4 b in Eq. (1) can be written as the sum of two contributions, namely \u03c4 b = \u03c4m + \u03c4 c (6) where \u03c4m and \u03c4 c represent the momenta generated by the forces P on the body frame and the counteracting torques generated by the rotors, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002048_rob.4620080505-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002048_rob.4620080505-Figure1-1.png", "caption": "Figure 1.", "texts": [ " Their derivation was different than that of Lee and Liang. It is well established that a reverse kinematic analysis of robot manipulators with six axes can be performed by closing the loop with a hypothetical joint. Details of this procedure are given2,\u2019 and will not be repeated here. Briefly, an equivalent closed-loop spatial mechanism of mobility one is formed, and the displacement analysis of this mechanism is essentially the reverse analysis of the robot manipulator. The SSRMS, which is illustrated in Figure 1 , has seven axes and, therefore, a reverse analysis of the type just outlined cannot be performed, because the equivalent spatial mechanism has mobility two. In this article, three distinct reverse analyses are performed that have proved to be useful in an animated environment in employing the SSRMS to perform a wide variety of space-servicing tasks. In order to discuss these analyses it is first necessary to produce a kinematic model of the SSRMS (Fig. 2). The axes of the seven revolute joints are labeled with unit vectors S; 0\u2019 = 1,2, " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003181_10402004.2010.492925-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003181_10402004.2010.492925-Figure4-1.png", "caption": "Fig. 4\u2014Schematic representation of the load distribution on the inner raceway Fi (\u03c8) and the outer raceway Fo (\u03c8) for a bearing under pure radial load Fr. Loaded zones: inner raceway (I), outer raceway (II, III).", "texts": [ " Subsequently, the equations for the side flow rate and the layer thickness are given. According to Harris (20), in most cases the load distribution in a rolling element bearing may be approximated by the load distribution in a statically loaded bearing. Subsequently, in order to obtain the dynamic load distribution, the centrifugal force acting on the rollers can be added to the static load distribution on the outer raceway. A schematic representation of the different contributions to the load distribution, for a bearing under pure radial load Fr, is shown in Fig. 4. \u03c8denotes the angular position along the circumference of the bearing. Depending on the angle \u03c8, three regions can be distinguished in which different contributions act: 1. Static load distribution on the inner raceway \u03c8\u2208 [\u2212\u03c8l, \u03c8l]. 2. Static load distribution and centrifugal force on the outer race- way \u03c8\u2208 [\u2212\u03c8l, \u03c8l]. 3. Centrifugal force on the outer raceway \u03c8\u2208 [\u03c8l, 2\u03c0 \u2212 \u03c8l]. The static load distribution, that is, the load distribution on the inner raceway, for a rigidly supported bearing subjected to a radial load Fr was given by Harris (20): Fi (\u03c8) = Fmax ( 1 \u2212 1 2\u03b5 (1 \u2212 cos (\u03c8)) )n , [1] where Fmax is the maximum static load, and \u03b5 is the load distribution factor determining the size of the load zones I and II; that is, 2\u03c8", " This can be explained by the effect of the load on the side flow rate in the EHL contacts. The load on a rolling element due to the centrifugal force Fc is considerably smaller than the static loading Fmax. Due to the exponential viscosity\u2013pressure dependence, larger loads, that is, larger pressures, result in larger viscosities and a reduced side flow. This effect is shown in the theoretical and experimental results presented in van Zoelen, et al. (18). Consequently, in the bearing the side flow due to the centrifugal force (zone III in Fig. 4) is considerably larger than the side flow in the heavily loaded zone (I and II). As a result, the layer thickness decay period tcr is mainly determined by the flow in zone III, which is determined by the centrifugal force Fc and thus the angular velocity. Finally, it is found that the predicted times tcr in Table 2 are very short compared to the observed grease life in actual bearings, which is generally of the order of thousands of hours. The assumed critical layer thickness h\u0303cr may be smaller in practice, which will give longer times tcr", " At the boundaries of the levees a discontinuity in the layer thickness occurs. Depending on the rotational speed, the front of the levee has moved out of the domain after 1 or 2 h. The main difference between the solutions for the different rotational velocities is in the width of the furrow and the levees, both of which are larger for larger rotational speeds. The appearance of the furrow and the levees can be explained by the effect of the relatively large side flow in the lightly loaded zone (zone III in Fig. 4). The Hertzian contact width is relatively small in this zone. In fact, it is equal to the furrow width. The side flow outside the furrow is smaller, because the layer in this area is only forced in the relatively heavily loaded zones (I and II). Therefore, liquid from the furrow accumulates in this area, resulting in the appearance of the levees. The contact size in zone III is larger for larger centrifugal forces; thus, the width of the furrow increases for higher velocities. The model is based on mass conservation", " Kn is the load deflection factor, which is a combination of the deflection factors of the contacts on the inner raceway (Ki) and the ones on the outer raceway (Ko) according to: Kn = ( K\u22121/n i + K\u22121/n o )\u2212n . [A2] For a circular or elliptical contact Ki and Ko are defined by (see Eq. (2.13) in Wijnant (25)): Ki/o = 2 3 E\u2032 \u221a 2R\u03c02E/(4\u03ba2K3). [A3] For the definition of the variables in Eq. [A3], the reader is referred to the Nomenclature. The load distribution factor \u03b5 is a function of the radial load Fr and the number of rollers nr and can be solved from the static load equilibrium: Fr = nr 2\u03c0 \u222b \u03c8l \u2212\u03c8l Fi (\u03c8) cos (\u03c8)d\u03c8, [A4] where \u03c8l is the angular location of the boundary of the load zones (see Fig. 4): \u03c8l = { acos (1 \u2212 2\u03b5) \u03c0 0 \u2264 \u03b5 < 1 \u03b5 \u2265 1 . [A5] Fig. A1\u2014The load distribution factor \u03b5 as a function of the radial load Fr, the number of rollers nr, the load deflection factor Kn, and the diametral clearance Pd. Values of \u03b5 > 0.5 only occur for negative diametral clearances, which is uncommon. This is shown in Fig. A1, where the load distribution factor \u03b5 is given as a function of the radial load Fr, the number of rollers nr, the load deflection factor Kn, and the diametral clearance Pd. The solution of \u03b5 is obtained by solving Eq" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure3.5-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure3.5-1.png", "caption": "Fig. 3.5 Examples of representation of joints", "texts": [ " Since an unconstrained pairing element has six degrees of freedom including three translational and three rotational degrees of freedom, a joint is represented as: J Pxyz Rxyz in which superscript Pxyz denotes that it can be translated as a prismatic joint (JP) along the x, y and z axes; and, subscript Rxyz denotes that it can rotate as a revolute joint (JR) about the x, y and z axes. When a pairing element connects to another pairing element and forms a joint, a constraint is imposed and the motion of the original member is reduced by one or more degrees of freedom. Hence, a joint has a maximum of five degrees of freedom and a minimum of one degree of freedom. For example, a joint denoted as JRx represents that a pairing element of a joint can rotate about the x-axis with respect to the other pairing element, as shown in Fig. 3.5a. A joint denoted as JPx represents that a pairing element of a joint can translate along the x-axis with respect to the other pairing element, as shown in Fig. 3.5b. A joint denoted as JPx Rx represents that a pairing element of a joint not only translates along the x-axis but also rotates about the x-axis with respect to the other pairing element, as shown in Fig. 3.5c. Figure 3.6a shows a two-member mechanism with a joint from the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b(Pan 1998). Since the illustration is not clear, the link (KL) is connected to the frame (KF) with an uncertain joint. Considering the type and the direction of motion of the link, the joint has three possible types. First, the link rotates about the z-axis only, denoted as JRz. Second, the link not only rotates about the z-axis but also translates along the x-axis, denoted as JPxRz . Third, the link not only rotates about the y and z axes but also translates along the x and z axes, denoted as JPxzRyz " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002519_arso.2005.1511621-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002519_arso.2005.1511621-Figure3-1.png", "caption": "Figure 3 A serpentine robot ' S o y In' by Shigeo Hirose (Tokyo Inst. Tech. and IRS).", "texts": [ " Snake bodies have multiple ways of motion: sbaight crawler motion, wriggle motion, rolling-about motion, head-up motion, U and lambda motion, etc. This variety assures robustness against various terrains and conditions to recover fkom deadlocks. It is not necessary that such robots move autonomously. The important points are final performance as a system and its effectiveness to the rescue problems. Some types of serpentine robots have been developed. Even in the DDT Project, Soryu In, KOHGA, MORA, UMRS-V-KSW, 3D Snake, etc. are being researched. Soryu TI1 shown in Fig. 3 (a) is a practical platform on the basis of improvement of S o y I and I1 by Shigeo Kirose (Tokyo Institute of Technology and WS). Its size is 1210 mm long, 122 mm high and 145 mm wide, and the weight i s 10 kg. Typical gap size in Hanshin Awaji (Kobe) Earthquake was 300 x I50 mm, and the size of S o p 111 is slightly too high. The radius of turning is 410 mm, the trench width of crossing is 590 mm, the height of avoidable cave is 264 mm, the step height of ascending is 483 mm, and the maximum speed is 370 m d s ", " A CCD camera, an infrared camera (FLIR) and two-way audio are installed at present. In addition, some human sensors such as CO2 sensor and some navigation sensors such as a laser range finder are planned for external sensing. Rotation sensors of crawlers, rotation angle sensors for each joint, inclination sensors for each body, etc. are used for internal sensing. It has tether for the best quality of video image, and safety from lost. Experiments in the realistic test field in Kobe and those at under-floor examination of houses as shown in Fig. 3 (b) and (c) demonstrated its potential of mobility. 5.2 Aero Robot (Intelligent Helicopter) Rapid global surveillance and information collection right after incidences is very important for disaster managers make decision of countermeasures. Helicopters are effective for this purpose, but the following problems exist. I ) It is difficult for human pilots to be prepared 24 hours 2) Manned helicopters need flight admission. 3) Noise of large helicopters is so loud that human ground rescuers cannot hear victims' voice" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003821_j.jsv.2013.02.035-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003821_j.jsv.2013.02.035-Figure2-1.png", "caption": "Fig. 2. Free body diagram of the follower in the sliding contact regime.", "texts": [ " (1) and rearranging, \u03c8i (t) and \u03c8j(t) are evaluated as \u03c8 i\u00f0t\u00de \u00bc \u03c70sin\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de\u00fe rc\u00fe wb 2 \u00f0cos\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de\u22121\u00de \u00fee\u00bdsin\u00f0\u03b1\u00f0t\u00de\u00fe\u03980\u00de\u2212sin\u00f0\u03b1\u00f0t\u00de\u00fe\u0398\u00f0t\u00de\u00de , (6) \u03c8 j\u00f0t\u00de \u00bc \u03c70 1\u2212cos\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de \u00fe rc\u00fe wb 2 sin\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de \u2212e\u00bdcos\u00f0\u03b1\u00f0t\u00de\u00fe\u03980\u00de\u2212cos\u00f0\u03b1\u00f0t\u00de\u00fe\u0398\u00f0t\u00de\u00de : (7) Next, differentiate Eqs. (6) and (7) with respect to time to yield the following: \u03c8_ i\u00f0t\u00de \u00bc \u03c70cos\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de\u03b1_\u00f0t\u00de\u2212 rc\u00fe wb 2 sin\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de\u03b1_\u00f0t\u00de \u00fee\u00bdcos\u00f0\u03b1\u00f0t\u00de\u00fe\u03980\u00de\u03b1_\u00f0t\u00de\u2212cos\u00f0\u03b1\u00f0t\u00de\u00fe\u0398\u00f0t\u00de\u00de\u00f0\u03b1_\u00f0t\u00de\u00fe _\u0398 \u00f0t\u00de\u00de ; (8) \u03c8_j\u00f0t\u00de \u00bc \u03c70sin\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de\u03b1_\u00f0t\u00de\u00fe rc\u00fe wb 2 cos\u00f0\u03b1\u00f0t\u00de\u2212\u03b10\u00de\u03b1_\u00f0t\u00de \u00fee\u00bdsin\u00f0\u03b1\u00f0t\u00de\u00fe\u03980\u00de\u03b1_\u2212sin\u00f0\u03b1\u00f0t\u00de\u00fe\u0398\u00f0t\u00de\u00de\u00f0\u03b1_\u00f0t\u00de\u00fe _\u0398\u00f0t\u00de\u00de : (9) Fig. 2 shows the free body diagram of the follower in the sliding contact regime. The moment balancing about P yields the following equation of motion for the follower in the sliding contact regime, where IPb is the mass moment of inertia of the follower about P: IPb\u03b1\u20ac\u00f0t\u00de \u00bc \u2212Fs\u00f0t\u00dedx\u00feFn\u00f0t\u00de\u03c7\u00f0t\u00de\u22120:5Ff \u00f0t\u00dewb: (10) The elastic force (Fs(t)) from the follower spring is given by the following, where Lus is the un-deflected length of the follower spring: Fs\u00f0t\u00de \u00bc ks\u00bdLus\u2212dy\u00fedxtan\u00f0\u03b1\u00f0t\u00de\u00de\u22120:5wbsec\u00f0\u03b1\u00f0t\u00de\u00de : (11) The normal contact force (Fn(t)) is given by Fn\u00f0t\u00de \u00bc\u2212k\u03bb\u00f0\u03c8 i\u00f0t\u00de\u00de\u03c8 i\u00f0t\u00de\u2212c\u03bb\u00f0\u03c8 i\u00f0t\u00de\u00de _\u03c8 i\u00f0t\u00de: (12) The Hertzian theory [32] for line contact is used to define k\u03bb(\u03c8i(t)) as follows, where l\u03bb is the length of line contact, and Y is the equivalent Young's modulus (with subscript e denoting equivalent) k\u03bb\u00f0\u03c8 i\u00f0t\u00de\u00de \u00bc \u03c0 4 Yel\u03bb: (13) The equivalent Ye of the two materials in contact is calculated based on the Hertzian theory [32] as well Ye \u00bc 1\u2212\u03bd2c Yc \u00fe 1\u2212\u03bd2b Yb \" #\u22121 : (14) Here, \u03bd is the Poisson's ratio of the material, and the subscripts b and c represent the follower and cam, respectively", " As such, the response of the system with the alternate friction models is found not to vary significantly as long as vr(t) stays in the same direction. Consequentially, a change in direction in vr(t) is introduced (twice per revolution of the cam) by increasing e to 0.7rc as observed from Fig. 12; the system is verified to be in the sliding contact regime at 50 rev/min, using the inverse kinematics [36]. The force time histories Ff(t) and Nx(t) (dynamic bearing force along horizontal direction) are shown in Fig. 13 (a) and (b), respectively, for the alternate dry friction models. Note that Nx(t) is calculated from Fig. 2 as, Nx\u00f0t\u00de \u00bc Ff \u00f0t\u00decos\u00f0\u03b1\u00f0t\u00de\u00de\u00feFn\u00f0t\u00desin\u00f0\u03b1\u00f0t\u00de\u00de (35) As seen from Fig. 13 the forces Ff(t) and Nx(t) with friction model I (with mm\u00bc0.3) are discontinuous during the change in direction of vr(t) followed by some high frequency oscillations. This discontinuity is smoothened by using a small value of s\u00bc10 for friction model II, but the result of the friction model II should be close to that of the friction model I for a high value of s. Next, it is assumed that the cam oscillates with a particular frequency (\u03c9c); the motion of the cam is described by \u0398(t)\u00bc\u0398 (0)\u00fe0" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001440_60.921474-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001440_60.921474-Figure1-1.png", "caption": "Fig. 1. Circuit connection of single-phase SRSEIG using a three-phase induction machine.", "texts": [ " The investigation showed that best generator performance was obtained using the Steinmetz connection, provided that the excitation capacitance was connected across the lagging phase. In this paper, series capacitance compensation is incorporated in the above generator configuration to give a single-phase self-regulated self-excited induction generator (SRSEIG) with reduced voltage regulation and increased power output. The theoretical analysis will be verified by experimental results on a small laboratory machine. Fig. 1 shows the circuit connection of the single-phase SRSEIG based on the Steinmetz connection. The single-phase load is connected across phase A (the reference phase), while the excitation capacitance is connected across phase B (the lagging phase). Besides providing the reactive power for initiating and sustaining self-excitation, also acts as a phase balancer. The compensation capacitance is in series with the load and provides additional reactive power when the load current increases. To facilitate analysis, all the voltages and the equivalent circuit parameters have been referred to the base (rated) frequency by introducing the following parameters: 1) Per-unit frequency , defined by: (Actual frequency)/(Base frequency) 2) Per-unit speed , defined by: (Actual rotor speed)/(Synchronous speed corresponding to base frequency) 0885\u20138969/01$10.00 \u00a9 2001 IEEE III. STEADY-STATE ANALYSIS Referring to Fig. 1 and adopting the motor convention for the direction of currents, the following \u201cinspection\u201d equations can be written [11]: (1) (2) (3) (4) In (3), is the complex admittance of the excitation capacitance given by (5) Solving the above equations using symmetrical components analysis, the positive- and negative-sequence voltages are determined as follows: (6) (7) The input impedance of the induction generator across terminals 3 and 4 can be expressed as: (8) Details of the positive-sequence impedance and negativesequence impedance are given in Appendix I" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002867_icma.2009.5246352-FigureI-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002867_icma.2009.5246352-FigureI-1.png", "caption": "Fig. I. Previous gravity compensation systems [10], [11]", "texts": [], "surrounding_texts": [ "In step with the aging of the population, many patients suf fer from the disease on the legs. To alleviate their suffering, for the patients with muscle weakness, various kinds of power assist devices, which can compensate their body weight, have been developed by now. On the other hand, for the patient with a heavy arthralgia, the replacement arthroplasty to the prosthetic joints is provided. By the replacement treatment, many patients can recover the walking ability . However, since some muscles must be cut partly in the replacement arthroplasty, the patients have the severe muscle weakness after the surgery . Thus, the rehabilitation after the surgery is important. For such the patients, the rehabilitation devices which can compensate the body weight are highly required. Thus, a large number of the gravity support devices and the rehabilitation equipments have been developed by now[ I], [2], [3]. One type of them is the device to lift the patient's body from the ceiling or the brace member, which is used in the hospital for the rehabilitation of the patients with heavy leg malfunction[4], [5], [6], [7]. Another one is the power assist devices which make up for the poor athletic performance of the patients[I], [8]. However, the former ones restrict the patient's sphere of the activity considerably and may discourage the patients from continuing the long term rehabilitation, whereas the later ones are inconvenient for the continuous use by the limit of the battery life and have the 978-1-4244-2693-5/09/$25.00 \u00a92009 IEEE 943 risk to harm the patients by the malfunction of the electrical devices. For the rehabilitation equipments, the safety and the fitness for the continuous use must be assured. Therefore, it is preferable that the gravity support mechanisms embedded in the rehabilitation system are composed of the passive mechanical elements. Such the passive gravity compensation systems, have been studied for a long term[9] . In the early stages , they were developed in the robotics to reduce the load exerting on joints and realize the smooth manipulation of the heavy robots . Especially, in the humanoid robot manipulation, the improve ment of the torque/weight ratio is the most crucial problem. For this problem, Shirata et al. proposed a simple power assist mechanism composed of the passive spring stretched over the knee joint and achieved the smooth manipulation of the humanoid robots [17]. On the other hand, Morita et al. proposed an alternative mechanism[lO] as shown in Fig .I , which can compensate the gravitational moments perfectly and they apply it to the underactuated robot [11] and wheelchair[I2] . Such the passive gravity compensation systems have been well studied and many types of the gravity compensation devices were (2) developed by now. Though these devices work successfully to compensate the gravitational moment, they have the risk to injure the patients, when they are applied to the wearable rehabilitation systems since the springs and wires are barely stretched from the one link to another. In contrast with them, Herder et al. proposed a wheelchair with the gravity compensation system[16j, in which the safety of the patients is secured by bearing off the springs from the arm link using the parallel linkage. The usefulness of this system was shown in some clinical practices. However, this mechanism can not be applicable to the wearable gravity compensation equipment. Thus, this paper proposes a new gravity compensation system to establish a safe wearable rehabilitation system . In the new mechanism, the drive members are embedded completely inside the link itself, so that it never disrupts the motion of limbs and can be used safely as a wearable rehabilitation systems. In Section 2, a basic gravity compensation mechanism is introduced. In Section 3 and Sect ion 4, we examine the ef fectiveness of the proposed system through some experiment and computer simulations. The device introduced in Sect ion 2 can not generate the enough moment to cancel out the whole gravitational moment of the patients. Thus, in Section 4, we introduce the new gravity compensation mechanism which can amplify the generated gravity compensation moment arbitrarily by changing the gear ratio of the gear in the system . The effectiveness of the system is shown in Section 6 through some experiments using the prototype." ] }, { "image_filename": "designv10_13_0003528_045008-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003528_045008-Figure2-1.png", "caption": "Figure 2. Bending principle of the SBFA.", "texts": [ " Each of the three chambers of the SBFA consists of a BFA [13\u201315] with 120\u25e6 isosceles triangle cross section. Figure 1 illustrates the structure of the SBFA where the three obtuse angles of each of the BFAs join together to cover the full 360\u25e6. It should be noted that the chambers in the SBFA are numbered from 1 to 3 in figure 1. Similarly to the FMAs presented in [5\u20138], the SBFA bends due to the anisotropic elongation between the three chambers. If one or two chambers are pressurized to elongate, the SBFA bends away from the elongated chambers as illustrated in figure 2. Due to the presence of an inextensible polyester string along the center of the SBFA, simultaneously pressurizing the three chambers would not allow the SBFA to elongate. The winding channel walls in each SBFA chamber limits expansion along the radial direction of the SBFA. Prototypes were fabricated to demonstrate the feasibility and assess the performance of the proposed SBFA. Due to the complexity of the design, the molding technique proposed in [13] was not suitable to fabricate the SBFA. Each chamber was molded separately by using molds consisting of two parts, which were manufactured through an InVision 3D printer" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001883_1.1739244-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001883_1.1739244-Figure4-1.png", "caption": "Fig. 4 Sketch of roller-plate contact model", "texts": [ "91 In case of a roller contacting a flat plate, the latter expression in ~11! simplifies to drp52.66\u2022~ t !0.09 \u2022S Q\u2022~12n2! E\u2022L D 0.91 (12) It should be noted that this equation is independent of the roller diameter, a fact that confirms Palmgren\u2019s results. It is, however, still dependent on the thickness of the plate, which Palmgren did not consider. In order to validate the new relationship, an FE model of an un-profiled roller contacting a flat plate was set up. A sketch of the problem is presented in Fig. 4. Due to symmetry, only 1/8 of the roller and 1/4 of the plate had to be modeled. All degrees of freedom ~DOF! at nodes located on the lower surface of the plate Transactions of the ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F were fixed to ground. For the roller diameter and length, values of D5L510 mm were chosen. The materials of plate and roller were assumed to be the same, having an elastic modulus and a Poisson\u2019s ratio of E52.08\u2022105 MPa and n50.3, respectively. The ratio of plate-thickness-to-roller-diameter was varied in the range of t/D54 " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001837_robot.2003.1241896-Figure3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001837_robot.2003.1241896-Figure3-1.png", "caption": "Fig. 3. I module", "texts": [ " In order to show the validity of the proposed methods, we constructed a snake like robot called SMA (Super-Mechano Anaconda). Using the experimental system, we show that the winding pattern with which the robot can avoid singular postures is generated automatically, and head position and head configuration converge to desired ones. 11. MODEL OF A ROBOT A. Model assumptions are introduced. A Model of robot is set as show in Fig.4, and the next . The robot is multi-link structure which consists of a rigid body. . Each angular value is relative one, and 0 value means that a robot is like a straight line. One module (Fig.3) consists of 2 links. It has a vertical rotation joint at middle, and horizontal one at both sides. 0-7803-7736-2/03/$17.00 02003 IEEE 2055 All joints are able to be actuated. The considered robot consists of 9 modules. A module has passive wheels ,on the same axis with vertical jointand it touches a floor with only them. . The friction force to tangential direction is zero, to normal one is infinity. . The links before r F , a middle vertical rotating joint, have 3 dimensional motioR and those after it, have 2 dimensional movement" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003718_s12008-012-0163-y-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003718_s12008-012-0163-y-Figure4-1.png", "caption": "Fig. 4 Optional machine tool kinematic motions", "texts": [ " It takes into account fourteen settings: the machine center to cross point, the machine root angle, the sliding base, the work offset, the radial distance, the swivel angle, the tilt angle, the tool rotation angle and the six modified roll coefficients of the cradle rotation angle. The modified roll method consists of a representation of the machine settings in higher order polynomials in terms of the workpiece increment angle. It enables accurate modifications of the tooth flank topographies. Figures 3 and 4 describe the machine tool kinematic model. The machine tool kinematic motions shown in Fig. 4 are not really used to generate face-milled spiral bevel gears. The swivel angle, the tilt angle and the tool rotation angle are set to zero. Nevertheless, all of them are implemented in the tooth flank generation algorithm. The present work is illustrated with an example of spiral bevel gear manufactured with the face-milling method. The machine tool architecture enables recreating the meshing motion between the workpiece and an imaginary generating gear as shown in Fig. 5. The tool materializes a gear tooth and thus follows the same trajectory" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002048_rob.4620080505-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002048_rob.4620080505-Figure2-1.png", "caption": "Figure 2.", "texts": [ " Briefly, an equivalent closed-loop spatial mechanism of mobility one is formed, and the displacement analysis of this mechanism is essentially the reverse analysis of the robot manipulator. The SSRMS, which is illustrated in Figure 1 , has seven axes and, therefore, a reverse analysis of the type just outlined cannot be performed, because the equivalent spatial mechanism has mobility two. In this article, three distinct reverse analyses are performed that have proved to be useful in an animated environment in employing the SSRMS to perform a wide variety of space-servicing tasks. In order to discuss these analyses it is first necessary to produce a kinematic model of the SSRMS (Fig. 2). The axes of the seven revolute joints are labeled with unit vectors S; 0\u2019 = 1,2, . . . ,7). The directions of the common normals between pairs of successivejoint axes are labeled aij ( i j = 12,23, . . . ,78) and the common normal link lengths are labeled aij. The twist angles between Crane, Carnahan, and Duffy: Kinematic Analysis of SSRMS 639 successive pairs of joint axes are labeled aii40 ml/min, helped to maintain a turbulent flow profile through the fibres and minimized concentration polarization" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002240_j.precisioneng.2002.12.001-Figure14-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002240_j.precisioneng.2002.12.001-Figure14-1.png", "caption": "Fig. 14. Geometry characteristics of quasi-kinematic coupling joints.", "texts": [], "surrounding_texts": [ "This paper has provided the theory and a mechanics-based metric that can be used by designers to minimize the degree of over constraint in QKCs. The theory used to model coupling stiffness has been implemented in MathCAD and tested. Experimental results show that properly designed QKCs can provide precision alignment that is comparable to kinematic couplings. Characteristics such as low-cost, ease of manufacture, ability to form sealed joints and sub-micron performance will make the coupling an enabling technology. This will be particularly important for high-precision, high-volume assemblies in automotive, photonics, optical and other general product assemblies. Subsequent research activities will include developing the means to estimate alignment errors due to the kinematic effects that result from mismatch between ball and groove patterns." ] }, { "image_filename": "designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.29-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002431_b978-0-444-86396-6.50011-8-Figure5.29-1.png", "caption": "Fig . 5.29. Schemati c drawin g of th e Laserglaze \u2122 process .", "texts": [ " As a consequence of the high cooling rate, ultra-microcrystalline or amorphous microstructures have been obtained, as documented above. 276 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Kear Typical apparatus for laserglaze processing has involved use of continuous, multikolowatt C 0 2 lasers, although the effect is dependent on power density and can thus be achieved at power levels below 1 kW. Both Gaussian and unstable resonator output beams have been used. A typical experimental setup is schematically illustrated in fig. 5.29, and pictured in action in fig. 5.30. In fig. 5.29, a nominal 7.5 cm diameter beam from the laser is directed toward and focused upon the workpiece by reflective optics. In a typical test, a 46 cm focal length mirror would be used to provide an effective minimum spot diameter of 0.05 cm at the workpiece. At 3.0 kW, these optics would provide a maximum incident power density of approximately 1.5 X 106 W/cm 2 , a power density equivalent to that provided by a black body thermal radiative source at 22 800\u00b0C. This high power density is essential for localizing the energy input at the material surface, and further promotes effective coupling of the laser energy with the material, despite the initially high reflectivity of metallic surfaces to the 10.6 \u00ec\u00e9 \u00e7 wavelength of carbon dioxide laser radiation. The 3 kW power level is a convenient one, in that it promotes effective beam coupling, but does not create significant plasma generation problems. As noted in fig. 5.29, plasma suppression is accomplished by means of an inert gas shield, which further prevents atmospheric contamination of the melt. Cooling due to the inert gas flow was estimated to be negligible, in comparison with the heat-sinking effects of the unheated substrate material. Rapid solidification laser processing 111 278 \u00c5. \u00cc. Breinan, \u00c2. \u00c7. Rear A range of laserglaze melt depths may be achieved by varying the translational speed of the workpiece under the focused beam. Linear speeds of from 150 to greater than 6000 cm/min are attained by using a variable speed rotating disk with specimens located at a fixed radius on the disk surface" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003318_indin.2012.6300840-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003318_indin.2012.6300840-Figure1-1.png", "caption": "Figure 1. The force analysis of tiltrotor U", "texts": [ " Using the rigid body dynamics and kinematics theory ,we can get the mathematical model in the body coordinate as follows[10]: 978-1-4673-0311-8/12/$31.00 \u00a92012 IEEE 248 where, m is the mass of the tiltrotor UAV, Ix\u3001 the rotational inertia and inertia product, Vxt\u3001 three components of ground velocity in the body \u3001\u03c9 \u3001\u03c9 are the components of the angular v \u3001 \u3001 \u3001 \u3001 are the forces and torq tiltrotor\u2019s body\uff0c \u3001 \u3001 \u3001 \u3001 forces and torques caused by the rotors and their Considering the different forces and torques UAV and conventional fixed wing UAV, we wi the example UAV showed in Fig 1. From Fig. the UAV's actual control surfaces include eleva rudder \u03b4 ,average value of the throttle \u03b4 , the of the throttle \u03b4 ,the average value of tilt a differential value of tilt angle \u03b4 . Besides control surfaces such as elevator, rudder and aile rotors and corresponding tilting mechanisms in main wing, and grid plates tilting synchronously reduce the downwash resistance in the helicopter From Fig 1 we can see that the rotor location both sides of the body ,and the distance between center of gravity is ,the lateral distance is .Ta for example ,we define the direction of the left axis, define Y axis perpendicular to the surfac meets the right hand law. The transition matrix f coordinate to the body coordinate is .We def left rotor coordinate as ,which will generate When the body attack angle is \u03b1, left tilt angle the compounded velocity with the velocity speed \uff0cthen the angle between and gr defined as \uff1a 1 sin( ) tan cos( ) k L sL HL k L V V V \u03b1 \u03c4 \u03b1 \u03b1 \u03c4 \u2212 + = + + \u239b \u239e \u239c \u239d \u23a0 Consequently we can get the lift of left b resistance ,the pitching moment ,the trans the left grid board air coordinate to the left roto \u3002Then, we can get the definition of the right pa ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2 2 xt z yt y zt xb xT yt x zt z xt yb yT zt y xt x yt zb zT x x z y y z xy z x y y y x z z x xy y z x z z y x x y xy x y z m V V V F F m V V V F F m V V V F F I I I I M I I I I M I I I I M \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u2212 + = + \u2212 + = + \u2212 + = + + \u2212 + \u2212 = + \u2212 \u2212 + = + \u2212 \u2212 \u2212 = \u23a7 \u23aa \u23aa \u23aa\u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa\u23a9 (1) Iy\u3001Iz and Ixy are Vyt\u3001Vzt are the coordinate\uff0c\u03c9 elocity, \u3001 ues caused by the \u3001 are the tilt mechanisms" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.10-1.png", "caption": "Fig. 7.10 A pumping tube (\u7389\u8861). a Original illustration (Shi 1981), b Structural sketch, c1 Feasible design 1, c2 Feasible design 2", "texts": [ " Figures 7.10a1\u2013a4 show the geometric graphics of its some parts (Shi 1981). Since the lever arm is the input link of the two Heng Sheng simultaneously, it can cause the two horizontal wooden boards to rise and fall alternatively. Yu Heng can lift water more efficiently than a Heng Sheng. Since Yu Heng has a symmetrical structure, only one side of the device is sufficient for analysis. The structure of Yu Heng is the same as Heng Sheng and is a Type II mechanism with uncertain types of joints. Figure 7.10b shows its structural sketch, and Figs. 7.10c1\u2013c2 show the atlas of feasible designs. 148 7 Linkage Mechanisms There are seven grain processing devices with linkage mechanisms, including Shi Nian (\u77f3\u78be, a stone roller), Niu Nian (\u725b\u78be, a cow-driven roller), Shui Nian (\u6c34\u78be, a water-driven roller), Gun Nian (\u8f25\u78be, an animal-driven roller), Long (\u7931, a mill), Mian Luo (\u9eab\u7f85, a flour bolter), and Yang Shan (\u98b6\u6247, a winnowing device). Each of them is described below: 7.3.1 Shi Nian (\u77f3\u78be, A Stone Roller) Nian (\u78be, a roller) is usually used to remove rice husk or wheat bran" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003419_tec.2012.2227058-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003419_tec.2012.2227058-Figure1-1.png", "caption": "Fig. 1. Calculated loss distributions (f = 333 Hz, V = 190 V). (a) No load (s = 0.00%). (b) Loaded (s = 5.00%).", "texts": [ " These waveforms mainly include following components [9]: 1) fundamental rotational magnetic field; 2) stator-phase-band harmonics; 3) stator- and rotor-slot harmonics; 4) inverter-carrier harmonics. Table II lists the spatial order k and the time order n of the major harmonics included in these waveforms when the slip s is 5%. In this table, n is defined to be the harmonic frequency per f . \u03b4 is the function whose value is +1 and \u20131 for the forward and backward rotational fields, respectively. Fig. 1 also indicates that not only the loss density of the rotor bar but also that of the stator and rotor core increase due to the load. Fig. 4 and Table III show the variation in the decomposed electrical losses caused by (a)\u2013(d) with s and f. A harmonic loss decomposition method reported in [9] and [10] is applied. The stator core loss is caused by the fundamental rotational field, inverter-carrier harmonics, and rotor-slot harmonics. On the other hand, the rotor core and cage losses are caused by the fundamental rotational field varying with the slip frequency sf, inverter-carrier harmonics, stator phase-band harmonics, and stator-slot harmonics" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003721_icmech.2011.5971317-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003721_icmech.2011.5971317-Figure1-1.png", "caption": "Fig. 1 Stewart platfonn manipulator", "texts": [ " The intact relations for the inertia tensors of different elements of the manipulator and the justifiable direction of the reaction moment on the pods are taken into account in deriving the new formulation. In this study, in order to compare the results of the newly-solved formulation with the previously-introduced ones, the formulation has been implemented in a programme written in MATLAB for kinematics and dynamics of the manipulator. The fmdings of the new formulation are more accurate than the previous ones. II. STEWART PLATFORM DESCRIPTION The mechanism under investigation consists of a moving platform, a stationary platform and six extensible pods (Fig. 1). Each pod connects to the platform at its connection point a; through a spherical joint, and to the base at its connection point b; through universal joint (i=1 to 6 for six pods). Each pod consists of two parts: the upper part and the lower part, which connect to each other through prismatic joint. Therefore, it is referred to as the 6-UPS Stewart platform. This familiar manipulator is actuated by motors located on the prismatic joints. The location and orientation of the moving platform frame {P}, is specified according to the base frame {W} " ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003558_iros.2011.6094799-Figure6-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003558_iros.2011.6094799-Figure6-1.png", "caption": "Fig. 6. (Left) A model of a two-link underactuated robot where only the second joint has a torque input \u03c4 . (Right) Optimized swing-up and locomotion movement of the robot. The robot swings up from the suspended posture using the swing-up controller and moves towards the right by switching into the locomotion controller. In these maneuvers, the time-optimal control laws obtained in Sections III-B.1 and III-B.2 are used.", "texts": [ " As shown in Fig.3(c), using time-varying optimal stiffness achieves more energy efficient control (J = 0.4421) requiring smaller control commands than using constant optimal stiffness (J = 2.219). In this section, we apply the presented framework to the control of an underactuated system which has fewer actuators than the number of degrees of freedom. As an example plant, we consider a planar two-link robot arm under the influence of gravity where only the second joint has a control input (see Fig. 6 (left)), as seen in the Acrobot [23] and the brachiating robot [24], [25]\u2014with characteristics similar to a gymnast on a high bar. The dynamics take a standard RBD form (11) with q \u2208 R 2 and \u03c4 \u2208 R with no actuation on the first joint. Control of underactuated systems with passive joints is a challenging problem\u2014this is because, while it is imperative to exploit system dynamics for task achievement, the control theory of such systems has not been well-established yet. Specifically, we consider the tasks of (i) swing locomotion from handhold to handhold on a ladder (ii) swinging-up from the suspended posture by pumping up the energy in an appropriate manner to reach the target bar", " We use the following cost function in both the locomotion and swing-up tasks considered here: J = (y \u2212 y\u2217)TPT (y \u2212 y\u2217) + \u222b T 0 Ru2dt (34) where y = [ r, r\u0307 ]T \u2208 R 4 is the position and velocity of the gripper in the Cartesian coordinates, y\u2217 denotes its desired values when grasping, PT is a positive definite matrix, u is the elbow joint torque u = \u03c4 and R is a positive scalar. In the following tasks, we consider temporal optimization to achieve energy efficient maneuvers to find the locally optimal duration of the movement in addition to finding the optimal control command u. We use the model of the robot (Fig. 6 (left)) with m1 = 1,m2 = 3, l1 = l2 = lc1 = lc2 = 1, I1 = I2 = 0 and d1 = d2 = 0.05. In the following simulations, the initial control sequence u(t) used in ILQG is chosen to be zero. 1) Locomotion: Consider the task of moving from one to the next handhold by swinging the arms (from the left to right in Fig. 6). The distance between the handhold is dist = 1.2 (m). We optimized the duration of the movement T and obtained the optimal control command u. Fig. 4 (left) depicts the optimized movement of the robot moving from the left to the right to grasp the target bar. Fig. 4 (center, right) overlays the joint trajectories and control commands of the fixed time horizon T = 1.3 \u223c 1.55 (sec) at the interval of 0.05 seconds and the optimized T = 1.421 (sec). With the fixed time horizon, the cost ranged between J = 1", " 2) Swing-up Task: The swing-up task considers the movement from an initial suspended posture at rest with the aim to catch the next bar. This task is characterized by the necessity to move away from the desired goal in order to pump energy into the system combined with precise spatiotemporal control for grasping. Here, we added an additional term to the cost that was linear in the movement duration T as J \u2032 = J + wTT , where J is the original cost function given in (34), and wT is a trade-off term that we choose as wT = 10. Fig. 6 (right) illustrates the obtained swing-up sequence of the robot followed by the locomotion behaviour. Fig. 5 shows the joint trajectories and elbow torque with fixed movement duration T = [3.0, 3.5, 4.0, 4.5, 5.0] (sec) and with optimized movement duration T = 4.437 (sec). Spatiotemporally optimized trajectories (lowest cost) were obtained, suggesting the suitability of the framework in even highly dynamic movements. In this paper, we present a systematic method for stiffness and temporal optimization in periodic movements, with an emphasis on exploiting the intrinsic dynamics of the plant to realize efficient control" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure4.16-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure4.16-1.png", "caption": "Figure 4.16-Planar ferrite cores representing a new generation oflow profile cores From Huth, J.F. III, Proc. Coil Winding Conf. Sept. 3D-Oct. 2, 1986", "texts": [ " Surface mount design lends itself to high speed automatic component placement on the PC board. A surface mount bobbin with gullwing terminals is shown in Figure 4.15. The place ment on the PC board is also shown. 4.6-PLANAR TECHNOLOGY Continuing with the low-profile design tendency particularly with PC board mounting has led to a completely new generation of cores called planar cores. Huth(l986) reported on this earlier and now, most ferrite companies offer planar cores in several varieties. Some of the arrangements are shown in Figure 4.16. Either the E-E or E-I configuration is used. The I core is actu ally a plate completing the magnetic circuit. In many cases the windings are fabricated using printed circuit tracks or copper stampings separated by insu lating sheets or constructed from multilayer circuit boards.(See Figure 4.17 ) MAGNETIC COMPONENTS FOR POWER ELECTRONICS 120 121 CORE SHAPES FOR POWER ELECTRONICS In some cases, the windings are on the PC boards with the two sections of the core sandwiching the board. Philips (1998) claims the advantages of this ap proach as; 1" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003500_j.scient.2011.08.005-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003500_j.scient.2011.08.005-Figure4-1.png", "caption": "Figure 4: Free body diagram of elliptical contact surface.", "texts": [ " (10) Input traction coefficient tin and output traction coefficient tout are expressed by: tin = Tin mnFN r1 , (11) tout = Tout mnFN r3 , (12) tin = \u00b5in + \u03c7in sin(\u03b8 + \u03b3 ), (13) tout = \u00b5out \u2212 \u03c7out sin(\u03b8 \u2212 \u03b3 ), (14) where Tin, Tout, n andm are input torque, output torque, number of rollers and number of disks, respectively, and \u03c7in and \u03c7out are both spin momentum coefficients and \u00b5in and \u00b5out are traction coefficients (effective friction coefficients between FT and FN ). Finally power transmission efficiency of CVT can be calculated by: \u03b7 = Pout Pin = r1Tout r3Tin r3\u03c93 r1\u03c91 = tout tin (1 \u2212 Sp). (15) Obviously, strength of contact surfaces is limited, so by studying the stress in contact point of disk and roller, a constraint between equivalent Von misses stress and dynamic parameters was developed. Contact surface of disk and roller is an elliptic [10,12]. Figure 4 shows the free body diagram of elliptical contact surface. The values of ax and ay can be obtained using geometry of bodies, normal force at contact point, elastic modulus, E and Poisson\u2019s ratio, \u03c5 of disks and roller [10]. Critical points which bearing the maximum stresses are A, B and C . The value of stresses at point A, can be obtained as follows [12]: \u03c3z = \u2212 3 2 FN \u03c0axay . (16) Shear stress on the elliptical area: \u03c4zx = 4 3\u03c0 FT axay = 4\u00b5 3\u03c0 FN axay . (17) Von misses equivalent stress: \u03c3eq = \u03c3 2 z + 3\u03c4 2 zx = FN \u03c0axay 9 4 + 16 3 \u00b52" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002335_1.2406088-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002335_1.2406088-Figure1-1.png", "caption": "Fig. 1 Elastic foundation m", "texts": [ " These foundations are made of the superposition of bending and shearing elements resting on independent springs, thus materializing virtual beams or plates and introducing elastic convectivity between a loaded sector and the neighboring parts. The foundation model applies to each individual tooth in mesh allowing the simulation of pinions and gears of different face widths, and of the buttressing effect caused by the unloaded parts beyond the contact lines. A pair of mating teeth is therefore assimilated to two different foundations one for the pinion tooth, the other one for the gear tooth linked by a series of independent springs which simulates the elasticity of the contact Fig. 1 . In such a representation, contact convectivity interactions between any loaded point and the neighboring points is neglected as opposed to the structural one, implying that the number of discrete elements along the foundations is sufficient 16 . Rather than trying to a priori determine equivalent beams or plates which reproduce tooth deflections, a semi-heuristic approach was used with the foundation characteristics being adjusted based on 3D finite element results. The simplest way to account for deformable gear bodies consists in using two node shaft elements which have to be connected 2007 by ASME Transactions of the ASME x", " The pinion is supposed to be solid as is the case in most practical applications. In such conditions, a two node finite element in bending Timoshenko beam , torsion and traction is employed to simulate body deflections 16 and is connected to the mesh interface model. Basically, the proposed approach consists in slicing the pinion in the face width direction into a series of discrete thin gears and in connecting their degrees-of-freedom by using the two-node element shape functions. The connection with the Pasternak foundations which simulate mesh elasticity Fig. 1 is ensured by the continuity of the displacement fields at the pinion\u2013foundation interface. Assuming that any originally plane transverse section j of the pinion remains plane after deformation, its displacement field is characterized by a screw of coordinates 1j u1j O1j 1j 2 where u1j O1j =translational degree of freedom vector at O1j, center of the shaft jth cross section; and 1j =rotational degree of el for a pair of mating teeth eling of the teeth od rs for pinion-gear meshes FEBRUARY 2007, Vol", " 3 ; b is the base helix ngle; t the apparent pressure angle; Rb1 the base radius of the inion; and x1j represents the coordinate of a potential point of ontact Mij as described in Fig. 3. All the auxiliary degrees of freedom in q1j are condensed by sing the shape functions of the two-node shaft element and 1 Mij is finally expressed in terms of the three translations and hree rotations at the two nodes of the shaft element vector X1 as 1 Mij = V1 Mij T P1 O1j X1 4 ith P1 O1j , the shape function matrix expressed in O1j Displacements 1 Mij are then imposed at the free ends of the pring elements on the pinion side in Fig. 1 which materialize ooth structural stiffness and contribute to the mesh strain energy s developed in Eq. 9 . 2.3 Gear Model. Instead of a simple shaft model, a 3D finite lement approach is used to simulate gear body deflections. The isplacement vector at Mij, a potential point of contact on one ear tooth, can be expressed in terms of the degrees of freedom at pij; the point of the same slice j, located at the intersection of he gear root cylinder and of the neutral line of the slice Fig. 2 as u2 Mij = u2 Mpij + 2 MpijMij 5 Mpij is not necessarily a point corresponding to a node of the nite element grid but its displacements can be approximated by nterpolation using the FE shape functions and the displacements 8n at the eight nodes surrounding Mpij on the upper face of the nite element as 86 / Vol" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002167_978-1-4615-0871-7-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002167_978-1-4615-0871-7-Figure4-1.png", "caption": "Figure 4. 19-Exarnple of Integrated Magnetic From Bloom (1994)", "texts": [ " current, the inductor, usually in combination with a capacitor, serves as a smoothing choke to remove the ac ripple in a D.C. supply. This is often done in the output circuit ofthe supply after rectification. Since there are large D.C. and smaller superimposed a.c. currents, they usually need gaps to prevent saturation. In addition to the increase in current and possible catastrophic fail ure at saturation, the incremental permeability drops close to zero and there fore, the required inductance specification is not met. With the gap, the mag netization curve is skewed to avoid saturation (See Figure 4.11). With regard to the ac component, the permeability of the gapped core is larger than one operating at saturation. The amount of gap depends on the maximum D.C. current, the shape and size of the core and the inductance needed for energy storage. The a.c. ripple is usually on the order of 10% of the D.C. signal. To estimate the maximum current, 1m, an extra 10% or more safety factor for transients is inserted in the design making 1m on the order of 1.2-1.3 10 , In some power inductor applications, as in the common mode choke, the magnetic core must sense the small difference between 2 magnetic cur rents and a high permeability toroid or ungapped shape must be employed", "1-FERRITE CORE SHAPES Ferrite cores possess one advantage over other magnetic materials in that they come in a large variety of shapes. This feature is made possible by the part-forming process in which the ferrite powder is pressed in a die before sintering to final dimensions. The die can be complex as long as the pressed part can be ejected from the die. Some parts such as round-leg E-cores must be pressed with legs up which creates a need for a minor adjustment. A vari ety of ferrite shapes for power applications are shown in Figure 4.1 4.1.1 Pot Cores Pot cores are sometimes used ungapped in power applications with a solid center post since there is no need for the adjustor found in telecommuni cation applications. The shielding to protect a low-level telecommunication signal in LC circuits is not necessary. There may be some advantage to the shielding in that it does provide the lowest leakage inductance. Besides cost, MAGNETIC COMPONENTS FOR POWER ELECTRONICS 106 from the windings to escape. Since pot core dimensions all follow IEe stan dards, there is interchangeability between manufacturers. 4.1.2-Double Slab Cores In slab-sided solid center pot cores, a section of the core has been cut off on each side parallel to the axis of the center post. This opens the core considerably. These large spaces accommodate large wires and allow heat to be removed. In some respects, these cores resemble E-cores with rounded legs. See Figure 4.2 107 CORE SHAPES FOR POWER ELECTRONICS 4.1.3-RM Cores and PM Cores RM cores (See Figure 4.3) were originally developed for low power, telecommunications applications because of the improved packing density. They have since been made in larger sizes without the center hole. Their large wire slots are an advantage while still maintaining some shielding PM cores are large RM-shaped cores specifically for power applications. Zenger(1984) feels that the geometry and self-shielding of RM cores make them useful at high frequencies. Roess (1986) points out that the stray field from an E-42 core is 5 times higher than that of an RM core", "4-E Cores These cores are the most common variety used in power transformer applications. As such they are used ungapped. There are some variations that we shall discuss here. Their usefulness is based on their simplicity. Initially, E- cores were made from metal laminations and the early ferrite E cores were made to the same dimensions and were called lamination sizes. However, as 109 CORE SHAPES FOR POWER ELECTRONICS the ferrite industry matured, E core designs especially useful for power ferrite applications were developed.( Figure 4.4). Many standard E-cores have bob bins that permit horizontal mounting. Some of the smaller sizes also are avail able in surface mount design with gull-wing terminals. 4.l.S-E-C Cores E-C cores are a modification of the simple E core. The center post is round similar to a pot core and since round center bobbins wind easier and are more compact than square center bobbins, this is an advantage. The length of a tum on the round bobbin is 11 percent shorter than the square bobbin that means lower winding losses", " The legs of these cores have grooves to accom modate mounting bolts. (Figures 4.5 and 4.6) 4.1.6-ETD Cores ETD cores are similar to E-C cores. They have a constant cross sec tion for high output power per unit weight and simple snap-on clips for hold ing the two halves together. They also have a bobbins which provides for creepage for mains (line) isolation and have enough space for many terminals. Zenger( 1984) suggests that the constant cross section of the ETD is an im portant attribute for high frequency at\"~ high drive levels. (Figure 4.5) These cores are available only in the large s:z~;, and thus are not used with surface mount bobbins. 111 CORE SHAPES FOR POWER ELECTRONICS 4.1. 7-E-R Cores These cores combine high inductance and low overall height. They have a round center post and surface mount bobbins available with the smaller sizes. 4.1.8-EP Cores EP cores are a modification of a pot core but the overall shape is rec tangular. A large mating surface allows better grinding and lapping, preserv ing more of the material's permeability. The EP core is usually mounted on its side with the bobbin below it facilitating printed circuit mounting. The best advantage of this core is in high permeability material. Shielding is very good. Some sizes of E-P cores (EP7 and EP13) are available with surface-mount bobbins with gull-wing terminals. Figure 4.7 shows an assortment of EP cores with the mounting accessories. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 112 4.1.9-PQ Cores TDK says it stands for Power and Quality. These are one of the new est types of cores for power ferrites for switched mode power supplies. The lowest core losses in a transformer usually exist when the core losses equal the winding losses. The geometry in a PQ core is such as to best accomplish this requirement in a minimum volume. The clamp is also designed for a more efficient assembly. A more uniform cross sectional area is also achieved so that the flux density is uniform throughout the core so that the temperature will not vary much. See Figure 4.8. 4. 1. 10-Toroids Toroids are sometimes used as power shapes because they take full advantage of the material permeability. Since there is no gap, leakage is very low. The toroid's main disadvantage is the high cost of winding as compared to an E or pot core. (Figure 4.9). Engelman (1989) constructed a multi-toroid power transformer that provides digital control. 40 toroids were used. 113 CORE SHAPES FOR POWER ELECTRONICS Bates (1992) reported on a new SMP core technology combining new high frequency ferrite power materials as toroids in a matrix transformer that can deliver 2000 watts at 5V D.C. It has the advantage of being low profile, has low leakage inductance excellent winding isolation and higher thermal dissi pation due to increased surface area. 4.1.11-EFD Cores Probably the newest design in miniature power shapes is the EFD cores which stands for E- core with flat design. (See Figure 4.10) The center leg was flattened for the extra low profile needed for PC board mounting. Simple clips are available. As expected surface mount bobbins are available. Mulder (1990) has written an extensive application note on Design of Low Profile High Frequency Transformers. He finds an empirical relation between effective volume and the thermal resistance of a magnetic device with which a MAGNETIC COMPONENTS FOR POWER ELECTRONICS 114 CAD program can be constructed to develop the optimum range of EFD cores for the frequency band 100KHz to 1 MHz", " For gapped cores, the dimensions and magnetic properties must be modified to the effective parameters The toroid was described as a closed magnetic circuit with uniform cross section. Even in a toroid, however, the magnetic path length varies from the circumference formed by the ID and to that formed by the OD. The mean length is often taken as the circumference of the average diameter [ Ie = n( do + dj)/2]. Where there is a large variation between the OD and ID, the average 115 CORE SHAPES FOR POWER ELECTRONICS Figure 4.10- EFD Cores for Power Applications value is invalid and a more complex method involving integration of all the paths is necessary. The situation on other shaped components is usually not as simple. First, the circuit may have an air gap (intentional or that formed by mating surfaces). The permeability of the magnetic circuit will be; Jl e == JlJ{1+ JlJllm } [4.1] where; Jle == Effective permeability of gapped structure J.1o = permeability of the un gapped structure Ig == length of gap 1m = length of magnetic path It is very important for us to appreciate the impact of this relationship espe cially in high permeability materials", " These often occur when there is a threat of saturation that would allow the current in the coil to build up and overheat the core catastrophically. The gap can either be ground into the cen ter post or a non-magnetic spacer can be inserted in the space between the mating surfaces. The gapped core is extremely important in design of filter inductors or choke coils. We shall discuss this application later in this chapter. The basis of the gapped core is the shearing of the hysteresis loop shown in Figure 4.11a and 4.11b where 4.11a represents the ungapped and 4.l1b the 117 CORE SHAPES FOR POWER ELECTRONICS gapped core. The effective permeability, J.le, of a gapped core can be ex pressed in terms of the material or ungapped permeability, J..l, and the relative lengths of the gap, Ig, and magnetic path length, 1m : [4.5] With a very small or zero ratio of gap length to magnetic path length, the ef fective permeability is essentially the material permeability. However, when the permeability is high(lO,OOO), even a small gap may reduce the perme ability considerably. For a power material with a permeability of 2,000 and a gap factor of .001, the effective permeability will drop to 1/3 of its ungapped value. When each point of the magnetization curve is examined this way, the result is the sheared curve shown in Figure 4.11. Ito(1992) reported on the design of an ideal core that can decrease the eddy current loss in a coil by the use of the fringing flux in an air gap. The design includes a tapering of the core at the air gap. The reduction in temperature rise will depend on the oper ating frequency, the gap length and the wire diameter. 4.3.1-Prepolarized Cores Another variation of the gapped core is one that is prepolarized with a permanent magnet. If the transformer operates in the unipolar mode and the polarity of the magnet is opposite to the direction of the initial ac drive, the starting point for this induction change will not be the remanent induction as is usually the case but a point much lower down on the hysteresis loop and in MAGNETIC COMPONENTS FOR POWER ELECTRONICS 118 the opposite quadrant", " With this device, he more than doubled the volt-amp rating of the transformer. Nakamura (1982) re ported a 70% increase in the figure of merit namely the U 2. Thus, size and weight was reduced. The losses were not significantly higher under these conditions. Sibille (1982) also reported on several different geometries to im plement the prepolarized core. Prepolarized cores are especially useful in flyback and inductor appli cations with high DC components. Huth (1986) has described a clever way of biasing a core using orthogonal winding techniques. (See Figure 4.12 ). 119 CORE SHAPES FOR POWER ELECTRONICS 4.4-LOW-PROFILE FERRITE POWER CORES F or low power ferrite applications, the past 5-10 years have seen the introduction of low profile cores in several configurations. One reason for this change is explained in the section in which the permeability is maximizes by having the winding length large and the cross section small. This condition can be accomplished in a low profile or low height core. The other reason (also mentioned in Chapter 1) is the growing use of PC (printed circuit) boards on which to mount the magnetic cores", " This method of attaching cores is even more important in the power ferrite area than in the low power tele communications area since PC technology is increasingly placing the power supply for a circuit on the same PC board as the other circuit components. The space between the boards is one half inch so the power ferrite core must be designed to fit in that space with the bobbin and mounting hardware. The availability of low profile cores has been discussed under the sections dealing with the various core shapes. A low-profile EFD core is shown in Figure 4.13. 4.S-SURF ACE-MOUNT DESIGN IN POWER FERRITES The use of surface mount design has been used for low power ferrite applications. The motivation was the development of PC board technology surface-mount design (SMD. As with the low profile cores, the application has been widespread mostly in the power ferrite application. The use of low profile ferrite cores can be complemented to a large degree by surface-mount technology. The two terminal mounting types used for power ferrites are the gullwing and the J-type terminals shown in Figure 4.14. The gull wing form is used when thin wire up to .18 mm in diameter is used. The J-type design is used in wire sizes greater than .8 mm. Surface mount design lends itself to high speed automatic component placement on the PC board. A surface mount bobbin with gullwing terminals is shown in Figure 4.15. The place ment on the PC board is also shown. 4.6-PLANAR TECHNOLOGY Continuing with the low-profile design tendency particularly with PC board mounting has led to a completely new generation of cores called planar cores. Huth(l986) reported on this earlier and now, most ferrite companies offer planar cores in several varieties. Some of the arrangements are shown in Figure 4.16. Either the E-E or E-I configuration is used. The I core is actu ally a plate completing the magnetic circuit. In many cases the windings are fabricated using printed circuit tracks or copper stampings separated by insu lating sheets or constructed from multilayer circuit boards.(See Figure 4.17 ) MAGNETIC COMPONENTS FOR POWER ELECTRONICS 120 121 CORE SHAPES FOR POWER ELECTRONICS In some cases, the windings are on the PC boards with the two sections of the core sandwiching the board. Philips (1998) claims the advantages of this ap proach as; 1. Low profile construction 2. Low leakage inductance and inter-winding capacitance. 3. Excellent repeatability of parasitic properties. 4. Ease of construction and assembly 5. Cost effective 6. Greater reliability 7. Excellent thermal characteristics-easy to heat sink", " Brown (1992) replaced the traditional copper wire with a winding from the PC board or stamped copper sheet and using a low-profile ferrite core improved the performance and manufacturability of HF power supplies. Huang (1995) described design techniques for planar windings with low resistance. Three representative pattern types were explored; circular, rectangular and spiral. Gregory (1989) has described the use of flexible cir cuits to work with new planar magnetic structures. He claims that printed cir cuit inductors reduce losses and increase packing density making them an ex cellent choice for high-frequency magnetics. Figure 4.18 shows a collection of low-profile and planar cores. MAGNETIC COMPONENTS FOR POWER ELECTRONICS 122 MAGNETIC COMPONENTS FOR POWER ELECTRONICS 124 4.7-INTEGRATED MAGNETICS Bloom (1994) has shown the application of planar-type \"integrated\" magnet ics wherein the transformer and inductor element can be combined on the same core with separate wing. An example of this technique is shown in Fig ure 4.19. The use of folded windings on printed circuit boards with flexible fold lines is shown in Figure 4.20. 125 CORE SHAPES FOR POWER ELECTRONICS 4.8- CORE SHAPES FOR METAL STRIP MATERIALS Metal strip materials as discussed here for power electronics applica tions include; 1. Thin gage Si-Fe alloys (0.001-0.004 inches) 2. NiFe Alloys (Permalloys) 3. CoFe Alloys (Supermendur) 4. Amorphous Alloys 5. Nanocrystalline Alloys The shapes of the into which these alloys are formed are; 1. Tape-Wound Cores 2. Tape-Wound Cut Cores 3. Stacked Laminations For the power electronic applications, stacked laminations are rarely used since the metal thicknesses of laminations are normally greater than those compatible with high frequency operation" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002736_j.jmatprotec.2008.03.065-Figure9-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002736_j.jmatprotec.2008.03.065-Figure9-1.png", "caption": "Fig. 9 \u2013 Coordinate systems for tooth contact analysis.", "texts": [ " The basic uantities of the first kind of (4) are E4 = (\u2202r4/\u2202 3) \u00b7 (\u2202r4/\u2202 3) F4 = (\u2202r4/\u2202 3) \u00b7 (\u2202r4/\u2202 1) G4 = (\u2202r4/\u2202 1) \u00b7 (\u2202r4/\u2202 1) (31) and the basic quantities of the second kind of (4) are \u23a7\u23aa\u23a8 \u23aa\u23a9 L4 = n4 \u00b7 (\u22022r4/\u2202 2 3) M4 = n4 \u00b7 (\u22022r4/\u2202 3\u2202 1) N4 = n4 \u00b7 (\u22022r4/\u2202 2 1) (32) Then, the primary principal direction and curvature of (4) are \u23a7\u23a8 \u23a9 e (4) I = \u2202r4 \u2202 3 / \u221a E4 (4) I = L4/E4 (33) and the secondary principal direction and curvature of (4) are \u23a7\u23a8 \u23a9 e (4) II = n4 \u00d7 e (4) I (4) II = ( E4N4 \u2212 2F4M4 + G4L4 E4G4 \u2212 F2 4 ) \u2212 (4) I (34) 3. Mathematical models of tooth contact analysis 3.1. Tangent conditions of tooth faces A pair of regular surfaces being in contact continuously means that they are always in tangent over time without separation and intrusion. As shown in Fig. 9, to perform tooth contact analysis, the input gear tooth face (1) rotates with an independent variable \u01311 and the output gear tooth face (2) is driven Sf (xf, yf, zf) connects rigidly to the gear housing. When surfaces (1) and (2) are in tangent, their position and unit normal vectors considered in Sf must be equal, which can be represented 10 j o u r n a l o f m a t e r i a l s p r o c e s s i n g by the following equations: { r (1) f \u2212 r (4) f = 0 n (1) f \u2212 n (4) f = 0 (35) where\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 r (1) f = r (1) f ( 1, v, \u01311) = Mf 1(\u01311)r1( 1, v) r (4) f = r (4) f ( 3, 1, \u01314) = Mf 4(\u01314)r4( 3, 1) n (1) f = n (1) f ( 1, v, \u01311) = Lf 1(\u01311)n1( 1, v) n (4) f = n (4) f ( 3, 1, \u01314) = Lf 4(\u01314)n4( 3, 1) The first vector equation in Eq", " By regarding the parameter \u01311 as an independent variable, based on the theory of existence of implicit functions, the other five parameters can be solved as implicit functions as follows: {\u01314(\u01311), 1(\u01311), v(\u01311), 3(\u01311), 1(\u01311)} (36) After obtaining \u01314 (\u01311), the actual transmission error is defined by \u01314 = \u01314(\u01311) \u2212 ( N1 N2 ) \u01311 (37) Whether there are assembly errors or not, the tangent conditions in Eq. (35) are applicable. The influence of assembly errors on meshing can be analyzed by conducting the assembly errors into the coordinate transformation matrices Mf1 (\u01311) and Mf4 (\u01314). As shown in Fig. 9, center distance error c, axial distance error a, vertical angular error , and horizontal angular error h are considered. The coordinate t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 3\u201313 transformation matrices Mf1 (\u01311) and Mf4 (\u01314) are determined by the following successive multiplication of matrices: { Mf 1(\u01311) = Ry(\u2212 h) \u00b7 Rx(\u2212 v) \u00b7 Tz( a) \u00b7 Rz(\u01311) Mf 4(\u01314) = Ty(C + c) \u00b7 Rz(\u2212\u01314) (38) 3.2. Contact ellipse As the contacting surfaces are elastic bodies rather than rigid ones, the contact point will expand as a small elastic deformation area under load" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003272_tmag.2009.2024641-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003272_tmag.2009.2024641-Figure4-1.png", "caption": "Fig. 4. The 3-D mesh for the IPM motor.", "texts": [ " The motor coil is subject to a current with a fundamental frequency of 320 Hz generated from an inverter power supply with a carrier frequency of 7 kHz and a direct current voltage of 500 V. The current waveform shown in Fig. 3 is obtained from the coupled 2-D magnetostatic analysis of the motor and a circuit analysis that considers the controlling circuit in the power supply. To investigate the effect of the division of the PM on the accuracy of the proposed method, we analyzed two models in which the PM is not divided and is equally divided into five segments in the thickness direction. In the full 3-D analysis, we analyze the half region of one segment of the PM. Fig. 4 shows the 3-D mesh without the division of the PM. In the proposed method, a mesh with the same subdivision in the plane is used for the 2-D analysis of the motor. The meshes used for the 3-D eddy current analyses of the PM with Methods 1 and 2 are also the same as shown in Fig. 5. The widths and are 0.1 and 0.2 mm, respectively. For each model, the period of steady state is analyzed in steps of electrical angle of degrees. In this section, we investigate the method for determining the gap width in Method 2" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001375_1.2834123-Figure10-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001375_1.2834123-Figure10-1.png", "caption": "Fig. 10 Springs caused by elastic contact of raceways and balls", "texts": [ " The spring constant k per unit length of the distributed normal springs can be written as: k = Z,K (13) where Zt is the average number of balls existing in load zone in one circuit of the recirculating balls, t is the length of the load zone in one circuit of the recirculating balls, K is the discrete normal spring constant. The discrete normal spring con stant K is related to the vertical spring constant Ky of the LGT recirculating linear ball bearing itself by the relation: K = Ky AZ, sin^ a (14) where a is contact angle. By substituting Eq. (14) into Eq. (13), k becomes k = Kv 4li sin a (15) 4.3.2 Frequency Expressions for Rigid-body Natural Vibra tion of Carriage. The coordinates for the carriage supported by the distributed normal springs having the spring constant k per unit length are shown in Fig. 10. In this figure, origin o of the coordinates oxyz coincides with the position of the center of gravity of the carriage while it does not vibrate. Although the ;c-axis is not seen in Fig. 10, it is parallel to the longitudinal direction of the profile rail. Since the x-axis is also parallel to the driven direction of the carriage, the displacement of the carriage along x-axis is not considered, u and v are the displace ments of the carriage in the y- and z-axis. 4>, 6 and i// are the angular displacements of the carriage around the x-, y-, z-axis, respectively, a is the distance from the origin o to the contact point of the upper circuits of the recirculating balls of the car riage and the distributed normal spring in the direction parallel to the z-axis" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001473_s0967-0661(96)00205-5-Figure1-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001473_s0967-0661(96)00205-5-Figure1-1.png", "caption": "Fig. 1 A mobile platform with an onboard manipulator", "texts": [ " In Section 3, the mobile manipulator system trajectory-generation problem is formulated as an optimisation problem with torque minimisation, manipulability maximisation and obstacle avoidance. In Section 4, an efficient genetic algorithm is proposed to search for optimal trajectories for the simultaneous motions of the mobile platform and the onboard manipulator. Various simulations for a system including a threelink manipulator mounted on a mobile platform are presented in Section 5 to demonstrate the central ideas and the efficiency of the proposed method. Finally, some conclusions are drawn in Section 6. A mobile platform with an onboard manipulator as shown in Fig. 1 is considered in this paper. The manipulator has one rotational link and two planar links. The platform has two driving wheels (the centre ones) and four passive ones (the comer ones). The two driving wheels are independently driven by two motors. Dynamic Modelling and Trajectory Generation for Mobile Manipulators 41 - ~sin0+ ~cos0 = 0 (2) i.e., the platform must move in the direction of the axis of symmetry. Note that the position (z, x) and the heading angle 0 of the platform are not independent of one another, due to the non-holonomic constraint. In order to apply the Newton-Euler equations to derive the dynamic modelling, it is convenient to visualise the platform as a planar joint having three degrees of freedom. Any multiple degree-of-freedom joint, such as the planar joint, can be synthesised by an appropriate number of single-degree-of-freedom joints with zero link length and zero link mass (Craig, 1989). Here, the platform is modelled as a serial chain of two prismatic joints and one revolute joint, as shown in Fig. 1. Consider the inertial reference flame in the (Z o, X o) plane, and choose a point P along the axis of the driving wheels on the mobile platform whose frame is (X3,Y3) in this plane. The mobile platform at point P can be described by three variables (z, x, 0 ), where (z, x) denotes the Cartesian position and 0 describes the heading angle measured between X 3 and Z 0 (see Fig. 2) respectively in the world frame. For the manipulator, the joint angles of the three links are 04,05 ,06 \u2022 q = (ql .q~.q3.q , .%.%) T (1) where ql, q2 and q3 denote the platform position (z, x) and the heading angle 0 , respectively (see Fig. 2), and q, , %, and q6 denote the manipulator joint angles 0,, 05 and 06, respectively. The platform is subject to the following nonholonomic constraint: The coordinate systems for the composite mobile manipulator system are given in Fig. 1. By applying the Newton-Euler equations (Fu, et al., 1987), all the joint torques can easily be obtained through iteration. Because the platform is subject to the non-holonomic constraint, a centripetal force is exerted on the two fictitious prismatic links; therefore, the input forces at these two links are fpz = f, ~ z, + Nc sin0 (3) fox = f2 T Zl . N~ c o s 0 (4) where f~ and f: are the external forces exerted on the fictitious links 1 and 2; fp~ and fpx are the input forces at these two links in the z-direction and the xdirection, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0001948_robot.2001.932980-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0001948_robot.2001.932980-Figure4-1.png", "caption": "Fig. 4: A non-solvable 6-DOF robot", "texts": [ " After it is obtained, the rest of the joint angles can be obtained through subproblems. Enumeration of solvable robot configurations The number of solvable robot configurations are estimated based on the type of tNists, connection sequence of the twists and the intersection of the revolute twists. Table 3 summarizes the solvable non-redundant robot configurations and the way they are solved. Detail enumeration and estimation procedures are provided in [15]. For non-solvable configurations, other inverse kineniatics methods need to be applied. Fig.4 shows a robot configuration with one prismatic joint and five revolute joints that can be solved through none of the method mentioned above. Though this configuration has 2 intersecting axes, the reduced POE equation is still a 4th problem. The NRJ approach ,does not apply either because the total number of revolute joints is 5. ,\", NRJ Non-solvable 4.2 Transformation of POE equations The reduced POE equations may not be in the canonical form defined by the subproblems. In the NRJ approach, a POE equation like this may be encountered : A h ," ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003227_j.cma.2010.01.023-Figure4-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003227_j.cma.2010.01.023-Figure4-1.png", "caption": "Fig. 4. Installation of the shaving-cutter.", "texts": [ " (16) and (24) allows determination of the geometry of an ideal modified helical gear to be finished by plunging. 3. Determination of the shaver tooth surfaces 3.1. Applied coordinate systems The basic idea for determination of the geometry of the plungeshaver tooth surfaces is the consideration that the to-be-shaved gear, with the ideal geometry represented in the previous section, is the imaginary generating tool of the shaver. Following this idea, the shaver and the to-be-shaved gear will be in lineal contact in their process of meshing, while shaving of the gear is performed. Fig. 4 shows the installation of the plunge shaver with respect to the to-be-shaved helical gear. The crossing angle \u03b3 between the shaver and the to-be-shaved helical gear is determined as \u03b3 = \u03b2g\u2212\u03b2s \u00f025\u00de where \u03b2g and \u03b2s are the helix angles of the to-be-shaved gear and the shaver on the tangent plane. The usual values of crossing angle \u03b3 in plunge shaving are in the interval from 10 to 20\u00b0. Fig. 4 shows the pitch cylinder of the to-be-shaved gear and that of the shaver are in tangency at point M0, the instantaneous center of rotation of the gear drive. The velocities at point M0 has to satisfy the relation vg\u2212vs = \u03bcit \u00f026\u00de where vs and vg are the linear velocities of the shaver and the gear in the pitch tangent plane, it is the unit vector directed along the common tangent to the helices of the shaver and the to-be-shaved gear in the pitch tangent plane, and \u03bc is a scalar factor. Eq. (26) indicates that the relative velocity at point M0 has to be collinear to the unit vector it" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0003982_978-3-319-02009-9-Figure7.3-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0003982_978-3-319-02009-9-Figure7.3-1.png", "caption": "Fig. 7.3 A flail (\u9023\u67b7). a Original illustration (Wang 1991; Pan 1998), b Structural sketch, c Atlas of feasible designs, d Imitation of original illustration (Hsiao and Yan 2010)", "texts": [ " The operator uses one hand to place the forage or mulberry under the knife, and the other hand presses the handle down to cut them up. It is a linkage mechanism with two members and one joint, including the base as the frame (member 1, KF) and a knife as the moving link (member 2, KL). The knife is connected to the frame with a revolute joint JRz. It is a Type I mechanism with a clear structure. Figure 7.2c shows the structural sketch. 7.1.3 Lian Jia (\u9023\u67b7, A Flail) To separate the seeds from their pods, grains may be simply hit with a Lian Jia (\u9023 \u67b7, a flail) after harvesting as shown in Fig. 7.3a (Wang 1991; Pan 1998). The seed pods are spread on the hard ground, and the flail is applied by swinging the handle. After the seeds have been flailed, the pods and leaves are blown off with a 140 7 Linkage Mechanisms 7.1 Levers 141 winnowing device. This is followed by sieving. Thus, the good seeds are made ready for storage in the barn. It is a linkage mechanism with two members and one joint including the handle as an input link (member 1, KI) and the wooden rod as a moving link (member 2, KL). The input link is connected to the moving link with an uncertain joint J\u03b1. It is a Type II mechanism with uncertain types of joints. Figure 7.3b shows its structural sketch. Considering the types and the directions of motion of the moving link, uncertain joint J\u03b1 could be a revolute joint JRz, a spherical joint JRxyz, or a pin joint JPxRz . By assigning each possible type (JRz\u3001JRxyz\u3001JPxRz ) into the structural sketch, the atlas of the feasible designs can be obtained as shown in Figs. 7.3c1\u2013c3. Figure 7.3d shows an imitation of the original illustration of how to use the flail in the book Tian Gong Kai Wu\u300a\u5929\u5de5\u958b\u7269\u300b. 7.1.4 Quan Heng (\u6b0a\u8861, A Weighing Balance) A rope is hung on a lever as a fulcrum, from one end of the lever hangs a heavy object, and from the other end hangs weights or Cheng Chui (\u79e4\u9318, the sliding weight of a steelyard). The function of such a device is to measure weights and is called a Quan Heng (\u6b0a\u8861, a weighing balance) or Heng Qi (\u8861\u5668). Quan means weights or Cheng Chui, and Heng means scale beam" ], "surrounding_texts": [] }, { "image_filename": "designv10_13_0002247_07468342.2004.11922095-Figure2-1.png", "original_path": "designv10-13/openalex_figure/designv10_13_0002247_07468342.2004.11922095-Figure2-1.png", "caption": "Figure 2. The graph of wew", "texts": [ " Recall that in the \u201cno resistance\u201d case we set y(t) = 0, found a nonzero solution for the impact time t , and evaluated x(t) at this time to express the horizontal range as a function of \u03b8 , g, and v. Looking at the form of y(t) that results when resistance is present, we see that finding a nonzero root may be a daunting, if not impossible, task. Indeed, the presence of t and e\u2212kt in an expression does not bode well for isolating t . The stage is now set for a dramatic rescue, so let us introduce the new function that will come to our aid. The Lambert W function The Lambert W function can be defined as an inverse of the function T (w) = wew (see Figure 2). A look at the graph of T indicates that this function is strictly decreasing on (\u2212\u221e, \u22121] and strictly increasing on [\u22121, \u221e). So T has an inverse when restricted to each of these intervals, as indicated in Figure 3. We denote these inverses by W : [\u2212 1 e , \u221e) \u2192 VOL. 35, NO. 5, NOVEMBER 2004 THE COLLEGE MATHEMATICS JOURNAL 339 [\u22121, \u221e) and W\u22121 : [\u2212 1 e , 0) \u2192 (\u2212\u221e, \u22121], respectively. In this paper we will restrict our attention to the function W . The evolution of W began with ideas proposed by J" ], "surrounding_texts": [] } ]