Robotics 2 E Part 13 doc

350 Manipulators FIGURE 9.23f) Idea of a "trunk" made of Stewart-platform-like elements. This idea belongs to Dr. A. Sh. Kiliskor. 9.4 Grippers In previous sections we have discussed the kinematics and dynamics of manipu- lators. Now let us consider the tool that manipulators mainly use—the gripper. To manipulate, one needs to grip and hold the object being manipulated. Grippers of various natures exist. For instance, ferromagnetic parts can be held by electromag- netic grippers. This gripping device has no moving parts (no degrees of freedom and no drives). It is easily controlled by switching the current in the coil of the electro- magnet on or off. However, its use is limited to the parts' magnetic properties, and magnetic forces are sometimes not strong enough. When relatively large sheets are handled, vacuum suction cups are used; for instance, for feeding aluminum, brass, steel, etc., sheets into stamps for producing car body parts. Glass sheets are also handled in this way, and some printing presses use suction cups for gripping paper sheets and introducing them into the press. Obviously, the surface of the sheet must be smooth enough to provide reliability of gripping (to seal the suction cup and prevent leakage of air and loss of vacuum). Here, also, no degrees of freedom are needed for gripping. The vacuum is switched on or off by an automatically controlled valve. (We illustrated the use of such suction cups in the example shown in Figure 2.10.) Grippers essentially replace the human hand. If the gripping abilities of a mechan- ical five-finger "hand" are denoted as 100%, then a four-finger hand has 99% of its ability, a three-finger hand about 90%, and a two-finger hand 40%. We consider here some designs of two-fingered grippers. In the gripper shown in Figure 9.24, piston rod 1 moves two symmetrically attached connecting links 2 which in turn move gripping levers 3, which have jaws 4. (Cylinder 5 can obviously be replaced by any other drive: electromagnet, cable wound on a drum driven by a motor, etc.) The jaws shown here are suitable for gripping cylindrical bodies having a certain range of diameters. Attempts to handle other shapes or sizes of parts may lead to asymmet- rical gripping by this device, because the angular displacements of jaws may not be parallel. To avoid skewing in the jaws, solutions like those shown in Figure 9.25a) or b) are used. In Case a) a simple cylinder 1 with piston 2 and jaws 3 ensures parallel 9.4 Grippers 351 FIGURE 9.24 Design of a simple mechanical gripper. FIGURE 9.25 Grippers with translational jaw motion. displacement of the latter. In case b) a linkage as in Figure 9.24, but with the addition of connecting rods 6 and links 7 with attached jaws 4, provides the movement needed. These additional elements create parallelograms which provide the transitional move- ment of the jaws. Various other mechanical designs of grippers are possible. For instance, Figure 9.26 shows possible solutions a) and b) with angular movement of jaws 1, while cases c) and d) provide parallel displacement of jaws 1. In all cases the gripper is driven by rod 2. All the cases presented in Figure 9.26 possess rectilinear kinematic pairs 3. Intro- duction of higher-degree kinematic pairs are shown in Figure 9.27. In case a) cam 1 fastened on rod 2 moves levers 3 to which jaws 4 are attached. Spring 5 ensures the contact between the levers and the cam. In case b) the situation is reversed: cams 1 are fastened onto levers 3 and rod 2 actuates the cams, thus moving jaws 4. Spring 5 closes the kinematic chain. In case c), which is analogous to case b), springs 5 also play the role of joints. In case d) the higher-degree kinematic pair is a gear set. Rack 1 (moved by rod 2) is engaged with gear sector 3 with jaws 4 attached to them. Cases a) to d) have dealt with angular displacement of jaws. In case e) we see how the addition of parallelograms 5 (as in the example in Figure 9.25b)) to the mechanism shown in Figure 9.27d) makes the motion of the jaws translational. The last two cases do not need springs, since the chain is closed kinematically. 352 Manipulators FIGURE 9.26 Designs of grippers using low-degree kinematic pairs. FIGURE 9.27 Designs of grippers using high-degree kinematic pairs. 9.4 Grippers 353 To describe these mechanisms quantitatively we use the relationships between: 1. Forces F G which the jaws develop, and the force F d which the driving rod applies; and 2. The displacements S d of the driving rod and the jaws of the gripper S G . Figure 9.28 illustrates these parameters and graphically shows the functions S G (S d ) and F G /Fd=flSj for a gripper. This discussion of grippers has been influenced by the paper by J. Volmer, "Tech- nische Hochschule Karl-Marx-Stadt, DDR, Mechanism fur Greifer von Handhaberg- eraten," Proceedings of the Fifth World Congress on Theory of Machines and Mechanisms, 1979, ASME. We should note that the examples of mechanical grippers discussed above permit a certain degree of flexibility in the dimensions of parts the gripper can deal with. This property allows using these grippers for measuring. For instance, by remembering the values of S d by which the driving rod moves to grip the parts, the system can compare the dimensions of the gripped parts. When the manipulated parts are relatively small and must be positioned accurately, miniaturization of the gripper is required. A solution of the type shown in Figure 9.29 can be recommended, for example, in assembly of electronic circuits. Here, the gripper FIGURE 9.28 Characteristics of a mechanical gripper. 354 Manipulators is a one-piece tool made of elastic material that can bend and surround the gripped part, of diameter d, to create frictional force to hold the part, and then to release it when it is fastened on the circuit board. The overlap h = Q.2d serves this purpose. Three-fingered grippers are also available (or can be designed for special purposes). Figure 9.30 shows a concept of a three-fingered gripper. Part a) presents a general view and part b) shows a side view. Here, 1 is the base of the gripper and 2 the driving rod, which is connected by joints and links to fingers 3. When rod 2 moves right, the fingers open, and when it moves left, they close. This gripper (as well as some considered earlier) can grip a body from both the outside and the inside. (Such grippers are pro- duced by Mecanotron Corporation, South Plainfield, New Jersey, U.S.A.) One of the most serious problems that appears in manipulators equipped with dif- ferent sorts of grippers is control of the grasping force the gripper develops. Obviously, there must be some difference between grasping a metal blank, a wine glass, or an egg, even when all these objects are the same size. This difference is expressed in the dif- ferent amounts of force needed to hold the objects and (what is more important) the limited pressure allowed to be applied to some objects. Figure 9.31 shows a possible solution for handling tender, delicate objects. Here, hand 1 is provided with two elastic FIGURE 9.30 Three-fingered gripper. FIGURE 9.31 A soft gripper for grasping delicate objects. 9.4 Grippers 355 pillows 2. When inflated by a controlled pressure, they develop enough force to hold the glass, while keeping the pressure on it small enough to prevent damage. (The small pressure creates considerable holding force due to the relatively large contact area between the glass and the pillows.) It is a satisfying solution when modest accuracy of positioning is sufficient. A more sophisticated approach to the problem of handling delicate objects is the Utah-MIT dextrous hand which is described in the Journal of Machine Design of June 26, 1986. This is a four-fingered hand consisting of three fingers with four degrees of freedom and one "thumb" with four degrees of freedom. The "wrist" has three degrees of freedom. The thumb acts against the three fingers. Thus, the hand consists of 16 movable links driven by a system of pneumatically operated "tendons" and 184 low- friction pulleys. The joints connecting the links include precision bearings. The problem of air compressibility is overcome by use of special control valves. Figure 9.32a) shows a general design of one finger. Here links A, B, and C can rotate around their joints. The space inside the links is hollow and contains the pulleys and the tendons, which go around the pulleys and are fastened to the appropriate links. Figure 9.32b) shows the drive of link C. Tendons I and la run around pulleys 7, 8, and 9 and are fastened to the center of pulley 6. Thus, pulling tendons I and la causes bending and straighten- ing of link C. Figure 9.32c) shows the control of link B by tendons II and Ha, and Figure 9.32d) shows the control of link A by tendons III and Ilia. A pair of tendons IV and IVa are used for turning the whole finger around the X-Xaxis, as shown in Figure 9.32e). The Utah-MIT hand has 16 position sensors and 32 tendon-tension sensors. Thus its grasping force can be controlled, and the object handled by the gripper with a light or heavy touch. For simpler grippers (as in Figures 9.24, 9.28, and 9.30), force-sensitive jaws can be made as shown in Figure 9.33. Here, part 1 is grasped by jaws 2 which develop grasp- ing force F G . The force is measured by sensor 3 located in base 4 which connects the gripper with drive rod 5. The latter moves rack 6 and the kinematics of the gripper. Force F d , which is developed by rod 5, determines grasping force F G . Sensor 3 enables the desired ratio F G /F d to be achieved. The sensor can be made so as to measure more than one force, say, three projections offerees and torques relative to a coordinate axis. These devices help to control the grasping force; however, its value must be pre- determined (before using the gripper) and the system tuned appropriately. Serious efforts are being devoted to simulating the behavior of a human hand, which "knows" how to learn the required grasping force during the grasping process itself. This ability of a live hand is due to its tactile sensitivity. Next, we consider some concepts of arti- ficial tactile sensors installed inside the gripper's fingers or jaws. Figure 9.34 illustrates a design for a one-dimensional tactile sensor. laws 1 develop grasping force F G which must cause enough frictional force F u (vertically directed) to prevent object 2 from falling due to gravitational force P. The sensor consists of roller 3 mounted on shaft 4 by means of bearings. Shaft 4 is mounted on jaw 1 by flat spring 5, which presses roller 3 against object 2 through a window in the jaw. When F u < P, slippage occurs between the gripper and object, and the object moves downward for a distance X, thus rotat- ing roller 3 (see the arrow x in the figure). This rotation is translated into electric signals (say, pulses, due to an encoder located between shaft 4 and the inner surface of hollow roller 3), which cause the control system to issue a command to increase force F G until the slippage stops (but no more than that, to prevent any damage to the object). In 356 Manipulators FIGURE 9.32 Design of the Utah-MIT dextrous hand: a) General view of one finger; b) Drive of link C; c) Drive of link B; d) drive of link A; e) Turning around the X-X axis. addition, the control system also gives a command to lift the gripper for a distance Y to compensate for the displacement X due to the slippage. For two-dimensional compensation, the concept shown in Figure 9.35 can be pro- posed. Here conducting sphere 1 (instead of a roller) is used. The surface of this sphere is covered with an insulating coating in a checkered design. Three (at least) contacts 2,3, and 4 touch the sphere and create a circuit in which a constant voltage V ener- gizes the system. When slippage occurs between object 5 and the gripper, the sphere 9.4 Grippers 357 FIGURE 9.33 Design of a grasp-force-sensitive gripper. FIGURE 9.34 One-dimensional tactile sensor. rotates and voltage pulses V 1 and V 2 correspond to the direction of the slippage vector S relative to the X- and Y-coordinates. A layer of soft material 6 is used to protect the sphere from mechanical damage. The jaws or fingers discussed in this section can be provided with special inserts and straps to better fit the specific items the grippers must deal with. For handling tools like drills, cutters, probes, etc., the straps must go round their shaft and provide 358 Manipulators FIGURE 9.35 Two-dimensional tactile sensor. accuracy and reliability of grasping. The same idea is used for making the jaws corre- spond to other specific shapes, dimensions, and materials of items being processed. Special devices can be considered for holding exchangeable grippers, say, to replace a two-finger gripper with a three-finger one during the processing cycle, which may be effective in some cases. 9.5 Guides The problem of designing guides is mainly specific for X-Y tables which, accord- ing to our classification, belong to Cartesian manipulators with two degrees of freedom. However, the concept of guides can be generalized and applied more broadly (except for translational movement) also to polar or rotating elements as well as to spiral guides (screws). Guides must provide: • Stable, accurate, relative disposition of elements; • Accurate performance of relative displacements, whether translational or angular; • Low frictional losses during motion; • Wear resistance for a reasonable working lifetime; • Low sensitivity to thermal expansion (and compression) to maintain the required level of accuracy. These properties must be achieved within the limits of reasonable expense and tech- nical practicality. The designer faces contradictory conditions in trying to meet these requirements. In certain cases the weight of the structure must be minimized, e.g., for moving links such as manipulator links. For accuracy, the guides must be rigid to prevent deflections. For heavier loads, the area of contact between the guide and the moving 9.5 Guides 359 part must be larger. To prevent excess wear, the guides must apply low pressure to the moving part, which also entails a certain width of the guide and length of the support (to create the required contact area). It is important to mention that, above all, wear of the guides depends on the maintenance and operating conditions. Wear varies from 0.02 mm per year for good conditions to 0.2 mm per year for careless operation. We discuss here some ideas and concepts for overcoming some of these technical obstacles. Figure 9.36 shows a typical example of a Cartesian guide system for a lathe and the scheme of forces acting in the mechanism. Guides 1 along axis X-X (main guides of the bed shown in projection b)) and guides 2 along axis Y-Yin dovetail form (its cross section is shown in projection a)) direct the support 4 of cutter 3. The cutter develops force P at the cutting point. Decomposition of this force yields its three components P x , Py, and P z . Together with the weight G of the moving part, these forces cause the guides to react with forces A, B, and Cin the Z-Fplane and frictional forces f A , f B , and f c along the X-axis (when movement occurs). Statics equations permit finding the reac- tive forces A, B, C, and Q: FIGURE 9.36 Two-dimensional Cartesian guide system and forces acting in it. [...]... and the other wheels are braked, the vehicle travels around point O as illustrated in Figure 9.55d Here, the stopped wheels roll in the directions perpendicular to their planes In the intermediate cases, when the wheels are driven at different speeds, the motion of the vehicle will respond correspondingly All wheeled vehicles or bogies require specially prepared areas to function properly Wheels are not... plane of the wheels When two of the wheels are driven as shown in Figure 9.55b) with equal speeds V^ and V2 and the third wheel is immobile, the vehicle moves in the direction V3 (The barrel-like rollers do not resist sideways movement of a wheel.) When all three wheels are driven as shown in Figure 9.55c) so that Vl = V2 = V3, the vehicle turns around center O When one wheel is driven with speed V2... by screw 5 Shields 6 and 7 keep the guides clean Rolling guides have much lower friction than sliding guides, and therefore the Fsr values are much smaller However, these guides employ more matching surfaces: between the housing and the rolling elements, and between the rolling elements and the moving part In addition, deviations in the shapes and dimensions of the rolling elements affect the precision,... three-wheeled device, combined with greater maneuverability, are found in the Stanford Research Institute robot vehicle (Figure 9.55) The vehicle FIGURE 9.53 Three-wheeled bogie: a) General view; b) Two-wheel drive: c) Drive of the steering wheel 9.6 Mobile and Walking Robots 373 FIGURE 9.53d) General view of a three-wheeled cart that automatically follows a white stripe drawn on the floor This device corresponds... wheel 2 as the driving one Motor 6 is installed for this purpose The direction of the bogie is determined by steering fork 3 which is driven, say, by special motor 7 controlled by the control unit In this case wheels 1 roll freely A three-wheeled bogie has the advantage of theoretical stability Three points determine a flat plane; thus, three wheels are stable on every surface However, this bogie can... ahead, while in view b) the behavior of the device depends on the direction of the wheels' rotation When they all rotate in one direction and stay strictly parallel, the device moves sideways When the pairs of wheels rotate in opposite directions, the device rotates in place around point 0 (The wheels in this case must be oriented tangentially to a circle with radius R.) The advantages of a three-wheeled... the vehicle so that it follows the strips In addition, another sensor counts the number of intersections of strips, while a program in the system controls the steering wheel A wheel-revolution counter stops the vehicle when a certain distance has been travelled Thus, the vehicle reaches the required table Instead of painted guides, metallic strips or wires can be installed under the floor or carpet... robots However, a short review of mobile robots, including some walking problems, seems to be necessary to complete this book First some ideas for wheeled mobile systems will be considered The simplest concept is a three-wheeled bogie (truck, cart) such as in Figure 9.53a) Two wheels 1 rotate in one plane (parallel to the longitudinal axis symmetry of the bogie) and a third wheel 2 is placed in steering... the guides and are shown in Figure 9.36 The obtained pressure values are average values, and the real local pressure might not be uniformly distributed along the guides The allowed maximum pressures depend on the materials the guides are made of and their surfaces, and are about 300 N/cm 2 for slow-moving systems to 5 N/cm 2 for fast-running sliders Obviously, the lower the pressure, the less the wear... complete the algorithm, angle 0 must be expressed in terms of the steering angle iff From Figure 9.57b) it follows that where L is a constant parameter for each vehicle In changing y/, one changes the radius r of the trajectory S Thus, 376 Manipulators FIGURE 9.57 a) Layout of a three-wheeled vehicle in an absolute-coordinate system; b) The relation between the steering angle and the trajectory slope . Obviously, there must be some difference between grasping a metal blank, a wine glass, or an egg, even when all these objects are the same size. This difference is expressed in the dif- ferent . therefore the F sr values are much smaller. However, these guides employ more matching surfaces: between the housing and the rolling elements, and between the rolling elements and the moving. projections offerees and torques relative to a coordinate axis. These devices help to control the grasping force; however, its value must be pre- determined (before using the gripper)