Fractal properties of trajectories of a characteristic point at the working plane of lapping and polishing machine

The article deals with the results of modeling the trajectory of a characteristic point at the working plane of lapping and polishing machine, the layout structure of which is based on nonreverse double-joint manipulator. The kinematic scheme of the mechatronic complex of abrasive lapping is presented and the calculation scheme for determining the trajectory of characteristic point motion along the lapping surface of the detail is proposed. The peculiarity of the proposed technical solution is that the working trajectories of a characteristic point have different density of grinding traces, the control of which is possible by changing the kinematic parameters, namely the multiplicity of the lapping angular velocities and links of the manipulator. It is revealed that the received complex working trajectories of a characteristic point have a fractional dimension, which makes it possible to classify them using fractal geometry methods. We proposed a technique for determining the fractal dimension of some working trajectories.