Solution of the inverse kinematics problem of the manipulator

There are a lot of methods for inverse kinematics problem of manipulator solution. But most of them include usage of transcendental equations, numerical methods, non-linear differential equations, and recursive calculations, which are very complicated for application in embedded systems. However, in real-time systems the speed and ease of algorithm are valued the most. These qualities are inherent for analytical solutions, which unequivocally connect the input coordinates of trajectory and generalized coordinates of kinematic scheme of manipulator, A.K.A angles of relative rotation of elements of manipulator. First, it is needed to solve the simple problem of identification of triangle angles, located in vertical plane. The sides of the triangle are known, as the dimensions of manipulator are given. After doing so, it is possible to use the principles of interplanar angle identification to reach the last generalized coordinates. Also, the method of identifying the angle between two vectors is useful in these calculations. After calculation of the generalized coordinates according to the described method, it is needed to apply constraints on the signs of the values of these coordinates depending on the desired position since the expressions include absolute value functions and trigonometric functions, which are not unambiguous.

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