Akademik Veri Yönetim Sistemi
Studies on Scientific Developments in Geometry, Algebra, and Applied Mathematics, Ankara, Türkiye, 1 - 03 Şubat 2022, ss.112-113
A new mathematical method is investigated for solving nonlinear system of equations with three
unknown variables in three equations in a special format. The proposed method is based on finding
the roots of a second order algebraic equations (polynomials) which have a symmetry between the
unknowns. In this case the roots of any two of these equations are found in terms of one of these
unknowns. Afterwards these roots are substituted in the remaining equation, which leads to a 32
degree polynomial after some symbolic equations, while using the Bezout Elimination method, it
yields to a 16th degree polynomial by calculating symbolic determinants of 4x4 and 6x6 matrices
which is comparatively difficult. The proposed method is easy to implement while still provides all
roots. In the practice, the Stewart-Gough platforms used in the robotics/airplane simulators need
the solutions of this kind of system of equations. The presented technique can be used for the
forward kinematics problem to find possible manipulator assembly modes as well as any kind of
nonlinear systems of equations in the same format as given here by using only simple mathematical
operations that doesn’t need special mathematical techniques.