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mm of travel length The workpiece holding spindle is a pneumostatic air bearing design The spindle is powered through the use of a brushless type DC motor and will run up to a maximum speed of 3,000 RPM [73] The high-speed aspheric grinding system is designed and manufactured for use on Precitech OPTIMUM machining systems This compact aspheric grinding system uses a high-speed, turbine driven, air bearing spindle The air bearing spindle is mounted onto a manually positioned mechanical slide assembly The slide is mounted onto a fabricated steel column such that the grinding Fig 441: A close-up of the grinding of a large diameter spindle is positioned in the vertical direction aspheric lens glass on a Toshiba ULG 100A, The grinding spindle operates over a two-axis ultra-precision turning and grinding speed range of 10,000 70,000 RPM The machine [72] turbine drive provides an extremely smooth friction-free spindle rotation The grinding system accommodates grinding wheels from 3 mm 15 mm in diameter The system has been designed primarily for small aspheric components, particularly lenses and lens moulds up to 30 mm in diameter Semi-ductile grinding followed by simple mechanical polishing is an economical process for producing a mirror-like surface for hard and brittle Pyrex A fine grit resonoid bond grinding wheel was used by Ong and Venkatesh [74] to generate a large number of ductile streaks to improve the surface finish and to reduce the polishing time The ground samples were polished with different slurries on Precitech s OPTIMUM 2800



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Moving beyond philosophical concerns, we return to the subject of learning. A mobile robot in an unknown environment has, as a primary concern, the need to develop a model of its environment. A map. Given a simplistic room like the one in Fig. 18-1, you would think it would be easy for a robot to learn the layout. One rst step is to try to tame the in nite spaces of this room. The robot has limited memory and we need to nd a way to store the layout of this room in it. One way is to lay a grid over the room (Fig. 18-2) and then record information in each grid square as we nd it. This grid layout mimics the memory structure of the computer and is easy to represent. As the robot wanders around the room, it notes what it nds in each grid square as it passes through it (Fig. 18-3). The robot has moved a long distance and it hasn t learned much about the room. What if we added the ability to see out to the sides of the robot There are optical sensors that can provide a type of visual bumper, returning





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Fig 442: A typical operation of Toshiba s ULG 100 [72]: (a) grinding of a tungsten carbide mould for glass

lenses (b) Form accuracy of an aspheric lens on a Taylor Hobson instrument (c) Surface roughness measurement using the form Talysurf instrument

o~tt ~)p) + rtt(p', p) -

the distance to an obstacle. Assuming we can see out to the sides of the robot by three squares, this same path may return more information, as shown in Fig. 18-4.

Nanotech 500FG (Figure 444) developed by Moore Nanotechnology Systems adopts the microgrinding technique The machine is capable of generating arbitrary confocal shapes on materials

Polishing reagent Thickness removed (1 m grit size) during polishing dT ( m) Polycrystalline diamond Monocrystalline diamond Cerium oxide 39500 3700 1623 Polishing pressure P (kPa) 5506327 3317041 1925292 Polishing time, dt (min) 45 65 30 Relative speed, ds/dt (m s 1) 282743 282743 141371 Preston coefficient, k (m2 N 1) 9397 10 13 1012 10 13 3313 10

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Mapping assumes that the robot has some way of knowing where it is as it travels. The simplest technique for this is dead reckoning, technically known as odometry, the measurement of distances traveled. The math behind odometry is surprisingly simple. It requires an accurate measurement of the distance each wheel has traveled. From this, it can calculate the change in position and rotation of the vehicle. Figure 18-5 illustrates the odometry math. The distance traveled by the left wheel is DL, and by the right wheel DR. The width of the robot, from where the left wheel touches the ground to where the right wheel touches the ground, is W. At time T 0 the robot is facing in the direction OT, which is speci ed in radians. If the robot turns during its travels, it ends up in a di erent

Fig 443: (a) Precitech s Optimum 2800 ultra-precision turning and grinding machine and a (b) close-up of the

Fig. 18-4.

grinding set-up for studying ductile streaks [73]

Fig 444: Moore s Nanotech 500 FG [75]

Fig. 18-5.

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