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Figure 1.2 (a) A simple planar arm manipulator with two links (l1 , l2 ), and two revolute joints (J0 , J1 ). The robot base coincides with joint J0 and is xed in 2D space. This 2 DOF manipulator can bring its end effector to any point P (x, y) within its workspace; the end effector s orientation at each such point will then be de ned by the orientation of link l2 . (b) Same arm with added third revolute link (hand), l3 ; now the end effector can be put in any arbitrary position of workspace with arbitrary orientation, P (x, y, 3 ).

Improperly resetting a RAM can have a catastrophic impact on the area. Table 2.4 Resource Utilization for BRAM with Synchronous and Asynchronous Resets Implementation Asynchronous reset Synchronous reset Slices slice 3415 0 Flip- ops 4112 0 4 Input LUTs 2388 0 BRAMs 0 1

job; this can be some kind of a gripper, a screwdriver, a paint or welding gun, and so on. The arm end effector may have its own DOF. To use tools, the end effector needs to be put not only in a particular position but also at a particular orientation: For example, not only the screwdriver s blade has to be in the screw s slot, but its axis has to be perpendicular to the surface into which a screw is driven. In the human arm, it is of course the hand that handles the tool orientation, a relatively compact device, compared with the rest of the arm, with its own (many) DOF. A similar organization of kinematics is common to robot arm manipulators: The robot s DOF are divided into the major linkage, relatively long links whose function is to bring the end effector to the vicinity of the job to be done, and the more compact minor linkage (called the wrist or hand), which is the end effector proper. Although from the theoretical standpoint such division is not necessary, it is useful from the design considerations. Often a real arm s major linkage consists of three DOF, and its minor linkage presents a 3-DOF hand. The values of all robot arm DOF de ne its coordinates in physical space. A given position plus orientation can be described via two coordinate (reference) systems: Cartesian coordinates and joint (joint space) coordinates. The latter are also called con guration space coordinates. As long as both systems describe the robot con guration that is, position plus orientation in a unique way, they are equivalent. For the 3-link 3-DOF arm manipulator shown in Figure 1.2b, its

Mr Johnson was still yelling when I snapped back into the present tense He was blabbering about some lost file, some letter that surely demanded legal redress for the wrongs done to our firm s client blah blah blah When Herbie was really upset, he growled, and his growling increased as he talked It s the most important file in this whole damn office, Banes It s the Anderson case, the trader The bonus discrimination case He said this as if I actually cared about Anderson, or his case, or whether the file had been shredded with the receipts of Herbie s gifts to his mistress I did care about trading, though, and when Mr Johnson said, trader, it made me even more excited to go check with Scott to see what had happened.

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Most FPGA vendors have a variety of ip- op elements available in any given device, and given a particular logic function, the synthesis tool can often use the set and reset pins to implement aspects of the logic and reduce the burden on the look-up tables. For instance, consider Figure 2.11. In this case, the synthesis tool may choose to implement the logic using the set pin on a ip- op as shown in Figure 2.12. This eliminates gates and increases the speed of the data path. Likewise, consider a logic function of the form illustrated in Figure 2.13. The AND gate can be eliminated by running the input signal to the reset pin of the ip- op as shown in Figure 2.14. The primary reason synthesis tools are prevented from performing this class of optimizations is related to the reset strategy. Any constraints on the reset will not only use available set/reset pins but will also limit the number of library elements to choose from.

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For instance, consider the following implementation in a Xilinx Spartan-3 device:

I wrote some notes down on the pad of paper that Scott had given me while Mr Johnson continued his tirade I didn t have to take any notes about the case, which Mr Johnson was now describing in the most specific detail I knew this case because it was on the front pages of every New York business section We were representing a Wall Street firm one of the biggest securities firms in the world The firm was accused of paying a smaller bonus to a physically handicapped trader, or something like that, to force the trader out of the firm I didn t know all the details, but I knew that the case was Herb s, that it was producing huge amounts of filing work, and that meant that it was producing huge fees.

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