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The term degrees of rotation refers to the extent to which a robot joint, or a set of robot joints, can turn clockwise or counterclockwise about a prescribed axis. Some reference point is always used, and the angles are given in degrees with respect to that joint. Rotation in one direction (usually clockwise) is represented by positive angles; rotation in the opposite direction is specified by negative angles. Thus, if angle X 58 degrees, it refers to a rotation of 58 degrees clockwise with respect to the reference axis. If angle Y 274 degrees, it refers to a rotation of 74 degrees counterclockwise. Figure 34-2 shows a robot arm with three joints. The reference axes are J1, J2, and J3, for rotation angles X, Y, and Z. The individual angles add together. To move this robot arm to a certain position within its work envelope, or the region in space that the arm can reach, the operator enters data into a computer. This data includes the measures of angles X, Y, and Z. The operator has specified X 39, Y 75, and Z 51. In this example, no other parameters are shown. (This is to keep the illustration simple.) But there would probably be variables such as the length of the arm sections, the base rotation angle, and the position of the robot gripper (hand).

Project building has seen a recent resurgence in the last few years, and the STAMP 2 controller is a very powerful and often-used building block STAMP 2 has been discovered by engineers, technicians, and hobbyists alike and has made project building a dream The beauty of the STAMP 2 is its reduced instruction set and its ability to perform tasks quickly and efficiently with a decent amount of memory The STAMP 2 can run off a standard 9-V transistor radio battery and consumes little power Utilizing the STAMP 2 microprocessor allows project designs to be powerful, flexible, and have a much lower parts count than a discrete IC design The STAMP 2 allows project designs to be upgradable and to evolve as more features and complexity are needed try that with discrete logic.

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The word articulated means broken into sections by joints. A robot arm with articulated geometry bears some resemblance to the arm of a human. The versatility is defined in terms of the number of degrees of freedom. For example, an arm might

The STAMP 2 has had a long and varied evolution and has developed a cult status as it has become popular and widely utilized Since their inception, the STAMP 1 and 2 have allowed many electronics-minded persons to construct all types of electronic projects and systems from simple light-emitting diode (LED) followers to more complex Internet interfaces The STAMP 2 has had a large following over its life to date and consequently has created an extensive library of expertise and software, so that many newcomers can benefit from all the combined experience There are very helpful newsgroups, web ring, and e-mail groups dedicated to helping STAMP 2 newcomers Many STAMPERs are readily available and willing to help newbies The STAMP 2, since it has had a long evolution, has many support chips, interfaces, and sensors available for those wishing to build modern complex circuits.

34-2 Degrees of rotation. Angles X, Y, and Z are measured relative to axes J1, J2, and J3. This robot arm employs articulated geometry.

The DCF valuation approach applies to all assets: financial assets such as bonds, mortgages and stock; real assets such as buildings and real estate, art and antiques, and rare coins; and human assets such as a college education and the economic value of a person s life (Many jurisdictions use DCF valuation techniques to determine the economic value of a life in a wrongful death court case) For financial assets with fixed payments such as bonds and mortgages, it s relatively simple to apply the DCF approach Adapting this approach to common stocks (or an individual s life) is considerably more difficult We address how to overcome these difficulties in the chapters that follow..

have three degrees of freedom: base rotation (the equivalent of azimuth), elevation angle, and reach (the equivalent of radius). If you re a mathematician, you might recognize this as a spherical coordinate scheme. There are several different articulated geometries for any given number of degrees of freedom. Figure 34-2 is a simplified drawing of a robot arm that uses articulated geometry.

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