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    Cylindrical Coordinate System
                     The Cylindrical Coordinate System is a three-dimensional system that is essentially a combination of the polar coordinate
                     system and a vertical Cartesian axis.

                     Description
                        A point is defined by three coordinates:
                     u
                            r (radius): The radial distance from the origin on the horizontal
                           l
                            plane.                                                                        y-axis   Z
                               (theta): The angle  from  a fixed  reference  direction  on the
                           l
                            horizontal plane.                                                                r          x-axis
                            z (height): The vertical distance from the horizontal plane along
                           l
                            the Z-axis.
                        A point is written as (r, ,z).
                     u
                     Application in Robotics

                     u   Cylindrical  Manipulators: Some  robotic  arms  are specifically  designed  to  work best  in  a  cylindrical  system.
                        Their movements are a rotation around a central axis (changing ‘ ’), a linear extension or retraction of an arm
                        (changing ‘r’), and a vertical up-and-down motion (changing ‘z’).
                        Drilling Robots: A robot designed to drill holes on the surface of a cylinder would find the cylindrical coordinate
                     u
                        system to be the most natural and efficient for describing its movements.
                        Mobile Robots with Vertical Lifts: A mobile robot that needs to move to a location and then raise an object to a
                     u
                        certain height might use a cylindrical system to plan its movement, as it separates the horizontal motion from the
                        vertical.
                     Advantages
                        Intuitive for Rotational and Vertical Motion: It is a natural fit for robots that have a dominant rotational joint and a
                     u
                        vertical linear joint.
                        Simplifies Certain Tasks: It simplifies the programming of tasks that involve moving around a central point and
                     u
                        changing height.
                     Disadvantages

                        Not a Universal System: Like the polar system, it is not as versatile as the Cartesian system for all types of motion.
                     u
                     Specification of Robots: Defining Performance Metrics

                     Resolution

                     Resolution refers to  the smallest incremental  movement  that  a robot  can detect  or achieve.  It is a measure  of the
                     granularity of the robot’s control system and sensors. Think of it like the pixel density of a digital image: a higher resolution
                     means more detail and a finer level of control. The resolution of a robot is determined by the resolution of its joint sensors
                     (encoders) and the precision of its motors.
                        Current Trends: Higher Resolution Encoders: Modern robotics is seeing a push toward higher-resolution encoders,
                     u
                        particularly in applications that demand exceptional precision, such as electronics or biomedical manufacturing.
                        These encoders can detect tiny changes in joint angles, allowing the robot to make incredibly small and precise
                        movements.
                            Real-time Example: In a semiconductor fabrication plant in countries like Taiwan, robots are used to place
                           l
                            microchips onto circuit boards. The robot’s joints are equipped with high-resolution encoders that can detect
                            rotational movements as small as a fraction of a degree. This allows the robot to place a microchip with a
                            resolution of a few micrometres, which is essential for ensuring the chip is perfectly aligned with the circuit
                            board’s contact points.

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                                                                                                              Mechanical System

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