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ature reading Linear four-bar linkages transmit the motion to and from the cams, which are held in contact by gravity The basic spiral contour cam mechanism has been used in instrumentation where it was necessary to generate such quantities as trigonometric functions, ballistic functions, logarithms, probability functions, etc For example, in multiplication, the input is converted to logarithms, added, and then reconverted to a linear scale by antilogs This cam contour (Fig 1448) is the simplest, most ef cient, most accurate means for linearizing input and output shafts where the motion relationship is a nonlinear function Contacting spirals, which are generally used, have pure rolling action and are reversible Also, for pure rolling, the contours of one curve must have an increasing radius and those of the other must be a decreasing one In other words, the curves will not have a minimum or maximum point within the range needed The surfaces may be plain, have cross-tapes, or have gear teeth As stated previously, the given related variables are nonlinear and it is necessary to make scale readings equidistant For example, measurement of ow of a uid may be determined by the pressure drop across an ori ce In the control eld, the proportional mechanisms for control are linear, and therefore for best results we must again have equal scale measurements Let us derive the basic relations for this contour In Fig 1448 we see the two curves in contact Let q0 qi r0 ri ce = angle rotated by the output driven member, deg = the angle rotated by input driver, deg = radius to point of contact at angle q0, in = radius to the point of contact at angle qi, in = r0 + ri = distance between centers of rotation, in

Based on conversations (August 2002) and subsequent e-mail communications between Frederic Biarnes of Sagem Morpho and the author

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Both the radii and the length of periphery are important Furthermore, as shown for pure rolling action the point of contact P must lie on the line of centers We know that the angle of the driven member q 0 = f (q i ) Differentiating, (1426)

(1427)

Figure 3-2

The velocity of point P as a point on either body is equal to radius r multiplied by the angular velocity dq/dt of the respective body u p = pi Solving, dq 0 ri = dq i r0 (1428) dq i dq = r0 0 dt dt

Unity is a latecomer to the DI container field, but it provides a simple and minimal approach that can be easily learned and used by beginners. Advanced users may find it lacking, but it certainly answers my 80-20 rule: it provides 80 percent of the features you look for most of the time. Unity is open source by Microsoft, and it has good documentation. I d recommend it as a starting point for working with containers. You can get Unity at www.codeplex.com/unity.

Solving Eqs (1427) and (1428) simultaneously and knowing that ce = ri + r0 gives radii r0 = ce ce = in dq 0 1 + f (q i ) 1+ dq i ce (1429)

ness since 1989; by 1991, Sonda installed a prototype system in the Chelyabinsk Department of Home Affairs Sonda claims its systems are in operation in more than 120 cities around the world Fingerprint technology was developed during the end of the 1980s and the beginning of the 1990s in Hungary, Russia, and China Several universities developed the technology in Hungary and Russia, and several dozen small-scale AFIS installations are running in China Cogent technology originated, in part, from work done at a Chinese university Today, Cogent is a well-established American AFIS vendor with systems in many countries South Korean companies have developed large-scale AFIS technology and are leaders in smart card use a field where they see strong demand for fingerprint verification Several South Korean companies are involved in the single-finger side of the automation of fingerprint identification Likewise, several Indian companies are entering this market at the single-finger end of the spectrum

(1430)

B.3.3

Equations (1429) and (1430) are the design equations for the contours of mating cams in terms of each radius r and angle q It is not necessary that the relationship be represented by any mathematical function The calculations can be performed by approximations from a table of numerical values

EXAMPLE Find the pro le equations for the following exponential relationship where A and B are constants:

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