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ranging from optical glass and infrared materials to non-ferrous metals, crystals, polymers and ceramics The microground surface typically requires little or no post-polishing (Figure 445) The machine temperature is maintained stable to less than 05 C Grinding is done in a flood-cooled environment Namba and Abe [76] developed an ultra-precision surface grinder and succeeded in stabilizing their grinding process by using a spindle rotor made from zero-thermal glass-ceramic expansive material This machine has two vertical spindles with a hydrostatic bearing of high precision and rigidity It can machine at extremely fine depths of cut (01 ( m), and at submicron flatness and nanometre surface roughness (5 nm Rmax) on optical glass (NbF1), it is capable of producing Mn-Zn ferrite and electronic materials using diamond abrasive grinding wheels McKeown et al [77] of the Cranfield Unit for Precision Engineering (CUPE) also developed a three-axis ultra-precision grinding machine (Nanocentre) which can perform diamond turning, grinding, polishing and is capable of measuring complex machined profiles through a 125 nm resolution interferometry They also suggested that as a rule of thumb, the machine must have a static loop stiffness between the tool and the workpiece of at least 300 N/ m in order to establish safe conditions for ductile grinding Suzuki and Murakami of the Toyoda Machine Works developed another example of an ultraprecision grinding machine for machining non-axisymmetric aspheric mirrors This is a five-axis machine having a feedback resolution of 10 nm, and a laser rotary encoder with a resolution of 000002 degree, controls the rotational positioning It is clearly seen that machine rigidity, high dynamic stiffness, high thermal stability, precise and smooth feedback resolution control, ability to achieve fine depths of cut and the use of special tooling play a vital role in producing very smooth surfaces under the sub-nanometric level in ultra-precision machining.



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orientation OT 1. This new orientation is calculated as a ratio of the wheel s relative motions with the robot s width: OT 1 OT DR DL W 18-1

Fig 445: A close-up of the grinding and the turning of an aspheric lens glass on a Moore s nanotech 500FG

The straight-line distance the robot traveled is the average of the two wheels travel distance: D DL 18-2 DT R 2 The new position of the robot in the X,Y grid is then approximated by: XT 1 XT DT cos OT 1 18-3 YT 1 YT DT sin OT 1 The catch is that this motion is only a straight-line approximation of the actual curved path.

ultra-precision turning and grinding machine [75]





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Free-form surfaces are not new to mankind, and sculptured idols and monuments bear testimony to human skills They have been pervasive in manufacturing due to their exceptional performance and properties Novel optical systems with free-form optical surfaces were developed for the Polaroid X-70 instant camera They have found applications in the eyewear, electro-optics, defence and automotive industries Mirrors for surveillance, LTV lenses for lithography, X-ray mirrors for X-ray lithography, laser rods and windows are some of the important defence and commercial applications of free-form optics Free-form surfaces offer numerous advantages Among other benefits offered by free-form surfaces to optical systems are improvements in aerospace designs such as in the field of view, aerodynamics, detectability, and cost It is possible that semiconductor, lithography and imaging technologies can also benefit from free-form surfaces

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Even if we used better, more complicated, math there would be errors recording the motion. The wheels don t contact the oor in a precise mathematical point so there is some error in W. If there is any slipping or shifting of the wheels, the measured distances do not match the actual distance traveled. Also, the sensor used to measure the wheel motion is not in nitely precise, which adds some uncertainty into each measurement. All of this adds up to errors, especially errors in calculating the robot s turns. There are also errors in the sensors, so they don t report the exact truth of the situation. Even if we blur the information returned from the sensors, the odometry errors can still put us out of the ballpark. Figure 18-6 represents this. This is a tricky diagram. The wide path is where the robot thinks it is going. The narrow path illustrates the actual path through the environment. The blurred sensor marks show how the robot s sense of the environment varies from the actual environment it is distorted and inaccurate. The more the robot travels, the more distorted its map becomes, until it s a useless blur. Researchers who use odometry spend a bunch of their time correcting for these built-in errors. One of the lessons to learned from this is that robotic tasks are never as simple as they seem at rst glance.

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