Formulation of Approximate Generalized Generated Database Model for Low-Speed Gear Box Developed Based on Double-Crank Inversion for a Four-Bar Chain

Abstract

AbstractAn analysis of double-crank inversion of a four-bar chain shows feasibility for adopting it as a gear box for low-speed applications. It is observed that any point on the coupler of a double-crank inversion of a four-bar chain describes very closely a complete circular path. This circular motion of some appropriately selected points on the coupler can be tapped out using link arrangement which will give output speed variation in the range of 8–12%. In the present paper, an attempt is made to consider many double-crank inversions of a class I four-bar crank with (a-b)/(c-d) ratio in the range of 0.1 to 0.6. Here, a, b, c and d are the link lengths of class I four-bar chain as per Harding’s notation. For each of these inversions, minimum 5–6 points on the coupler would be chosen which will generate circular motion with almost constant angular velocity but average value of angular velocity would be different for a different point on the coupler. Each of these inversions will precipitate a gear box with different range of very low angular velocity variation. There are some industrial operations which do need very low range of angular speed variation depending on properties of raw material being processed with that machine. A very popular example is of motorized shredder of plastics. For all such gear boxes for its output shaft, the expressions are derived for angular acceleration, jerk, pop and crackle. Each one of these expressions would be function of ratio of link lengths, location of point of reference on the coupler and angular velocity of driving crank. As these expressions are established based on generated data regarding kinematics of several inversions of double-crank of four-bar chain, the model formed is nomenclated as GENERALIZED GENERATED DATA-BASED MODEL.KeywordsMechanismsFour-bar chainDouble-crank inversionGear boxCoupler curves