Optimum inverse kinematic method for a 12 DOF manipulator

In General, there are two methods to analyse the inverse kinematic of manipulators, one of which can be selected with respect to the conditions and the type of the manipulator. One of the methods is the closed solution which is based on the analytical expressions or forth degree or less polynomial solution in which the calculations are non-repetitive. The other method is the numerical solution. In the numerical solutions, the numbers are repeated and generally it is much slower than the closed solutions. The slowness of this method is so noticeable in such a way that principally there is no interest to use the numerical solutions to solve kinematic equations. The purpose of the present paper is to present a compound method that is made up of the numerical and the closed solutions which does not have the problems of the current methods and can be generalized to similar robots with different degrees of freedom. The method which will be presented is based on the connecting lines between the pairs of links and the conditions under which the size of the connecting lines are created. The inverse matrix equations are not applied in this analysis. However, the positions of all links are expressed based on the geometrical position of the interfaces and the use of the mathematical function.