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    Joints: These are the connections between the links that allow relative motion. In planar mechanisms, the most
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                        common joints are:
                            Revolute Joint: Allows two links to rotate relative to each other, like a hinge.
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                            Prismatic Joint: Allows two links to slide relative to each other along a straight line.
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                        Frame: One of the links is a fixed link, called the Frame, to which all the other links are connected. This provides a
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                        stable reference point for the entire mechanism’s motion.
                     Characteristics of Planar Mechanisms

                     1.  Two-Dimensional Motion: All points on the mechanism move within or parallel to the same plane. This simplifies the
                        mathematical analysis from three dimensions to two, primarily using coordinate geometry.
                     2.  Links and Joints: Like a robotic arm, a planar mechanism consists of rigid links connected by joints. The most
                        common joints are:
                            Pin Joints (Revolute Joints): Allow rotation in the plane, like a hinge.
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                            Slider Joints (Prismatic Joints): Allow linear motion (sliding) in the plane, like a piston moving in a cylinder.
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                     3.  Kinematic Analysis: The behaviour of a planar mechanism can be fully described by its kinematics—the study of
                        its motion (position, velocity, and acceleration) without considering the forces involved. This is significantly easier to
                        perform for planar systems than for three-dimensional systems.
                     4.  Degrees of Freedom: The degrees of freedom of a planar mechanism refer to the number of independent variables
                        needed to completely define its position. For a mechanism with one input motion (like a crank), the degrees of
                        freedom are typically one.

                                                          Robots are Already Helping Doctors Save Lives
                                          Medical robotics is one of the most inspiring applications of AI and robotics. The Da Vinci
                                       Surgical System, for example, allows surgeons to operate with robotic arms that moves more
                          BRAINY      precisely than a human hand. These systems can perform minimally invasive surgeries, reducing
                           FACT
                                       recovery time and risk for patients. Robots are also used in telemedicine, where doctors in one
                                          country can operate on a patient in another, thanks to robotic precision and fast internet
                                                 connectivity. It’s science fiction becoming everyday healthcare reality.

                     Real-Life Examples of Planar Mechanisms

                     Planar mechanisms are everywhere around us, demonstrating their practicality and effectiveness in solving specific
                     mechanical problems.
                     Windshield Wipers

                        Mechanism: A classic example is the windshield wiper mechanism in a car. It uses a motor to drive a crank (a
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                        rotating link). This crank is connected to a series of other links that translate its continuous rotational motion into the
                        back-and-forth oscillating motion of the wiper blade across the windshield.
                        How it Works: The motor rotates in a circle, but the linkage system ensures that the wiper blade moves in a controlled
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                        arc, covering the windshield efficiently. The entire system operates in a single plane, the surface of the windshield.

                     Scissors
                        Mechanism: A pair of scissors is a simple two-link planar mechanism. Each blade is a link, and they are connected
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                        by a single revolute joint (the pivot point).
                     u   How it Works: When you apply force to the handles, the blades rotate around the pivot in a single plane to cut paper
                        or cloth. The motion is entirely restricted to the plane of the scissors.

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                                                                                                              Mechanical System

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