Solving the Forward Position Problem of an In-Parallel Planar Manipulator in the Gauss Plane
This work addresses a kinematic modeling problem for robotic manipulators, but it appears incremental as it applies known algebraic methods to a specific manipulator geometry.
The paper tackles the forward position problem for an in-parallel planar manipulator with specific joint configurations by constructing an ideal in complex numbers and using self-inversive polynomials, resulting in single-variable polynomials derived from Groebner bases that are self-reciprocal.
We study determining the posture of an in-parallel planar manipulator, which has three connectors composed of revolute, prismatic and revolute joints, from specified active joint variables. We construct an ideal in the field of complex numbers, and we introduce self inversive polynomials. We provide results for an in-parallel planar manipulator, which has a base and moving platform in right triangular shape. Using Sage computer algebra system, we compute its Groebner bases. We illustrate that the single variable polynomials obtained from the Groebner bases are self reciprocal.