Vibratory soil cutting a new approach for the mathematical analysis

•Kinematics analysis of a vibratory soil tilling tool was the objective of this research.•A polar coordinate system was used instead of a Cartesian coordinate system.•A mathematical model was developed base on polar coordinate system.•The mathematical model was compared with previous experimental date and the previous reported models based on experimental data.•The model was in good agreement with previous experimental researches.

An Innovative method was introduced to analyze the displacement, velocity and force on oscillating tillage tools based on the polar coordinates system. A new mathematical model was also introduced to analyze the effect of some crucial design parameters on the performance of vibrating tillage tools. As a basis one of the suggested force models was regarded to investigate the effects of design parameters. Dimensionless terms were introduced to recognize the effect of design parameters on the tools performance. Results were in good agreement with previous experimental data.