The Inverse Kinematics of the Plane System 2-3 in a Mechatronic MP2R System, by a Trigonometric Method

Robots have penetrated today in almost all industrial fields, being much more precise than humans in the execution of operations, but also faster, more dynamic, more stable and more resilient, working 24 h of the 24 h possible, in any season, breaks, holidays, vacations and especially without getting sick. The most important fact is that they can also perform special operations that man can’t do. So, for example, they can work in toxic, contaminated, mined, dangerous, or airless environments (in the cosmos, under water or underground), they can also position the parts very precisely so they can be used for fine, special processing at high precision operations, excellent mechanical processing, exceptional medical operations and even in all medical operations today, helping the doctor manage the patient's surgery with amazing precision, especially when it comes to open heart, brain, kidneys, liver, etc. Robots should not be fed and yet they can have an extremely long life. They can help us conquer both the underwater spaces and the cosmic spaces. Robots have stunning work precision and a faster execution speed than a man. In addition, their very precise positioning makes robot operations a great advantage, which can no longer be neglected. In repetitive and tiring work they are irreplaceable. The most commonly used anthropomorphic robotic mechatronic systems, which are currently being used, have been studied by eliminating the heavy, matrix 3D spatial system, the study being simplified in a plan by considering the main work plan of the system and the plan, the rotation required to restore the spatial parameters of the anthropomorphic 3D system. In other words, we can greatly ease the work of the anthropomorphic robot engineer by moving from 3D systems to a 2D system. In this study we will study the inverse cinematics of the plan system, 2D, as the most important one. In general, end effector positions are known (required) and the positions of the 2D module elements and the necessary rotations of the actuators for their creation must be determined. In the kinematics we know the kinematic parameters x_M and y_M, which represent the scaled coordinates of the point M (endeffector M) and must be determined by analytical calculations the parameters φ₂₀ and φ₃₀.