The calculations of Jordan curves trajectory of the robot movement

Abstract

Calculation of the moving mechanism on a trajectory described by a planar differentiable curve is challenging. The difficulty arises in compliance with high-precision movement. The new method of calculation based on the intrinsic properties of the plane is proposed. The method is based on mathematical linguistics and relational algebra. First, these disciplines are applied to analyze the intrinsic properties of the Euclidean plane. Calculation of classic and new methods for moving point for the flat rod is shown for comparison. Analytical formulas for Jordan curves can be obtained in some cases. The experiments in the areas of geometric modeling and control of a robot are listed briefly. The analytic solution was obtained by nontraditional methods not only for centrally symmetric conic sections but also for Jordan curves.