The mathematical model and mechanical properties of variable center distance gears based on screw theory

•Propose a variable center distance gear type.•Establish its mathematic model and investigate its mechanical properties•Find the “non-conjugation” feature of the pitch curves for this gear type.•Investigate the change rules of three basic substituting methods.•Propose three applicable gear trains within this gear type.

Currently, researches on planar gears (including cylindrical gear, noncircular gear) are primarily concerned with those of fixed center distance, that is, the center distance between two meshing gears remains unchanged during the driving process, while those of variable center distance are rarely touched upon. Although not widely applied as fixed center distance gear is, variable center distance gear can be found in noncircular gear shaping and high-torque hydraulic motor, exhibiting unique mechanical properties.This paper focuses on a systematic revelation of the driving principle and mechanical properties of this special variable center distance gear type. On the basis of screw theory, this paper first establishes its mathematical model, including kinematic relations, instantaneous screw axis, “non-conjugated” pitch curves, generator, envelope surfaces and generated surfaces. And then, the mechanical properties, forms as well as advantages of applicable variable center distance gear train are all discussed.