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21 sensor reduces hardware cost, but it necessitates signicant computational capability and more complex programming. Many robotic designs still prefer to use sensors because FOC does not provide the same level of condence, credibility, and robustness that using direct-sensor readout offers. Understanding Basic Robotic Configurations While the general public may associate the term "robot" with a mobile, life-like servant or assistant, most robotic systems in the industrial domain are stationary and use a variety of mechanical arms and congurations to perform tasks. Among the most common arrangements are: • The Cartesian robot, which has three linear axes of motion, one each in the x, y, and z-planes (Figure 2). This setup is used in pick and place machines, application of sealant, and basic assembly. • In a cylindrical robot, all motion is conned to a cylinder- shaped zone. It combines linear motion in the y plane, linear motion in the z plane, and rotational motion around the z-axis (Figure 3). This robotic arrangement is used for assembly, tool handling, and spot welding. • The spherical or polar robot combines two rotary joints and one linear joint, and the arm is connected to the base with a twisting joint (Figure 4). Motion is dened by a polar coordinates system and conned to a spherical zone. They are found in welding, casting, and tool-handling applications. The approaches cited here offer three degrees of freedom, using a combination of linear and rotary motion; however, some applications need only one or two degrees. More advanced robotic arms or articulated robots combine additional linear and rotary motion, for almost human-like dexterity and exibility (Figure 5). Some leading edge arms provide six, eight, or even more degrees of freedom. Other designs use special combinations of linear and rotary motion for application-specic situations, such as the parallelogram implementation; an implementation used for precise and rapid motion over short distances, for example, pick and place of tiny components. As the number of degrees of freedom increases, achieving rapid, smooth, accurate, and synchronized control along each of these degrees grows exponentially more challenging. Considering Trajectory Profiles The motion-control objective in robotics seems simple enough: have the end-effector optimally reach its target position as quickly and accurately as possible with the supported load. Of course, there are tradeoffs involved, as in all engineering decisions, depending on the priorities associated with the optimum result in the given application. For example, is it acceptable to accelerate and decelerate more quickly to more rapidly reach a higher velocity if the result is overshot and if there is even possible oscillation at the end point? Is it worth trading accuracy for speed, and to what extent? How are the choices of acceleration, velocity, and position related to the desired transition from position A to position B? What are the priorities and parameters that dene "optimum" in a particular application? Specialists in motion control for robotics and other motion applications have developed standard trajectory proles that provide various ways to implement the desired tradeoff solution for a given application. All choices involve signicant real- time calculation based on the present situation and feedback signal, but some impose a more substantial, high-resolution computation burden. These proles include: • The simple trapezoid, where the motor accelerates at a xed rate from zero to a target velocity, stays at that velocity, and then ramps down at a xed rate to zero velocity at the desired Figure 3: The cylindrical robot has motion along two linear axes and around one rotational axis. (Source: RobotPark) Figure 4: The spherical or polar robot combines motion around two rotary axes and along one linear axis, and it requires numerous calculation- intensive transformations between coordinate frames of reference. (Source: RobotPark) Figure 2: The Cartesian robot is the easiest to comprehend and control because it has the simplest equations and works in the x, y, and z planes. (Source:RobotPark) Figure 5: The articulated robot arm combines multiple rotation and linear motion modes for many degrees of freedom, but it also requires careful coordination among the actuators and arms. (Source: RobotPark) requires numerous calculation- between coordinate frames of reference. (Source: RobotPark)

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