Mutual tectonics mechanism of working outlines between inner and outer of node-circle based on the same convex-rotor

ObjectiveThe convex-rotor outline has attracted much attention because of its characteristics that directly determine the product performance; whereas the structure of it is also relatively complex due to the conjugate operation of the two rotor outlines. Therefore, a simple construction method based on a single rotor is proposed to effectively reduce the difficulty of outline-construction.MethodsFirstly, for the rotor-pair consisting of two identical convex-rotor, from the simple nodal symmetry relationship of rotor-pair outlines when the node was conjugated and its synchronous conjugate rotation law, the conjugate outline relationship of the rotor-pair was derived when the node was non-conjugated. Secondly, from the simplified reciprocal relation between the inner and outer working outlines of node-circle on the same convex-rotor, the bi-axial sequential symmetry mechanism of the node-axis and the instantaneous-center tangent-axis between the inner and outer working outlines of node-circle was revealed. Finally, with the rotation-angle of node-circle as a direct variable, the conjugated normal-length and transmission-angle as two indirect variables, the dimensionless construction-equation of the inner and outer working outlines of node-circle and its bi-axial symmetry matrix were quickly constructed.ResultsThe results of circular-arc as working outline show that the bi-axial symmetry relationship facilitates the efficient construction for convex-rotor outline, which makes the complex conjugate-relationship between the two convex-rotor outlines be transformed into the simple mutual relationship between inner and outer working outlines of node-circle based on the same convex-rotor. The dimensionless construction-equation and following bi-axial symmetry matrix are correct and reliable. The bi-axial sequential symmetry mechanism has the application-value for any profile-construction of convex cylindrical-gear and cylindrical-rotor, so as to provide a foundation for subsequent further popularization and application.