The precision calculating method of robots moving by the plane trajectories

Abstract

Robots with complex motion paths are very rarely designed. The main obstacle is the lack of the necessary mathematical apparatus, despite the fact that the theory was proposed by Newton. We managed to formulate a new method for obtaining linear transformation parameters. It can be used for ellipse, hyperbola, as well as for other complex flat differentiable curves. A theorem for receiving the values of a transformed curve is formulated in the general case. The theoretical algorithm and the results of experimental studies using the geometric modeling method are presented. The proposed method works for all test curves, but this does not mean that it can always be used. Separation of the characteristic equation imposes additional complexity. Additional research is necessary, but it can be applied to many mechatronic frameworks now.