Determination of Tooth Profile Curves of Variable Rack and Pinion Gears

Abstract

Variable rack and pinion gears are one of the mechanical transmission systems with non-constant speed ratio. The design methodology for variable rack and pinion gears tooth profile based on the gear meshing theory has not yet been well established, and achievable speed ratio and corresponding essential conditions to be satisfied are not clear. In this paper, a design methodology of the tooth profile curves of the variable rack and pinion gears which are capable of achieving a given input/output relationship and are geometrically valid is derived. First, design variables were defined, and geometric conditions to be satisfied were shown. In addition, a calculation method of a tooth profile curve of a variable rack which meshes with a pinion and achieves target speed ratio was formulated from the meshing theory and instantaneous kinematics. Furthermore, conditions that must be satisfied in order for gears to be geometrically valid was formulated. The relationship between geometric conditions and design variables was clarified by these equations to represent the conditions. This paper contributes to designer’s guideline for designing variable rack and pinion gears tooth profile curves that achieve target speed ratios.