Non-Circular Gearing Analytical Design for Driven Slider-Crank Mechanisms Balancing

In this paper, a solution for a purely mechanical balancing of operated slider \u2013 crank mechanisms is proposed and analytically developed. The solution design provides the application of an unusual configuration of a pair of non-circular gears, together with the use of a standard flywheel. The pinion gear is mounted on the mechanism crank shaft, while the driven gear is keyed on a secondary parallel shaft, which does not participate directly in the transmission of motion and carries the flywheel. Therefore the working principia of the flywheel, that is to introduce an additive (inertia) torque, is applied in a renewed manner and amplified by the use of the non-circular gearing. The fundamental idea is to supply the cyclically time-variable balancing torque by means of the flywheel constant inertia through a cyclically time-variable gear ratio. With the wish for contributing in the development of non-circular gearing application, the gearing mathematical model is implemented, while system dynamics and new equation of motion are developed adopting a specific case study, which regards an agricultural reciprocating cutter mechanism previously analyzed by the authors. Finally, gearing constraints satisfaction in analyzed and discussed. This kind of non-circular gearing implementation, which can be thought as an amplifier of inertia momentums, is generally applicable to operated slider \u2013 crank mechanisms and avoids deep changes in the original system architecture. The paper represents the analytical preamble to the numerical analysis on which the authors are going to present results