Non-Circular Gear Tooth Profile for Constant-Speed Meshing
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Solution Overview
Problem
Conventional gear mechanisms experience speed variation issues due to one externally toothed gear wobbling while the other rotates at a constant speed.
Innovation Solution
A gear mechanism with an externally toothed circular gear and an externally toothed non-circular gear, where the non-circular teeth are shaped as an offset epitrochoid curve, ensuring that the circular and non-circular gear tooth side portions are designed to suppress speed variation by defining virtual circles and drawing points to achieve a stable rotational motion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional externally toothed gears are used, then the gear mechanism is simple in structure, but speed variation occurs causing one gear to wobble while the other rotates at constant speed
Solution Approach 1:
The patent applies asymmetry by designing the non-circular gear with an epitrochoid curve tooth profile instead of conventional symmetric circular teeth. This asymmetric tooth shape allows the gear to maintain constant angular velocity while meshing with the circular gear, eliminating speed variation and wobble without requiring complex additional mechanisms
Solution Approach 2:
The patent changes the geometric parameters of the gear teeth by using an epitrochoid curve defined by specific mathematical relationships (radii ratios, offset distances) rather than conventional circular arcs. This parameter change in the tooth profile geometry enables constant velocity transmission while maintaining a relatively simple single-gear structure
2Reliability
If the non-circular gear tooth side portion is shaped as an offset epitrochoid curve, then speed variation is suppressed and constant rotational speed is achieved, but the manufacturing precision requirements increase
Solution Approach 1:
The patent uses curved epitrochoid profiles for the non-circular gear teeth instead of straight or simple circular arcs. This curvature design allows the tooth flanks to maintain continuous contact with the circular gear teeth throughout the meshing cycle, ensuring smooth constant velocity transmission while the curved geometry can be manufactured using standard gear cutting methods
Data Source
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AI summary
A gear mechanism including an externally toothed circular gear having M circular teeth and rotating around a first central axis, and an externally toothed non-circular gear having N non-circular teeth and rotating around a second central axis separated by a predetermined distance D from the first central axis, wherein the circular teeth of the externally toothed circular gear have a circular gear tooth tip portion and a circular gear tooth side portion located on sides of the circular gear tooth tip portion and having a circular shape of radius r, the non-circular teeth of the externally toothed non-circular gear have a non-circular gear tooth tip portion and a non-circular gear tooth side portion located on the sides of the non-circular gear tooth tip portion and in contact with the circular gear tooth side portion, wherein the shape of at least a part of the non-circular gear tooth side portion is such that, when a virtual circle of radius D x N/(M + N) centered on the second central axis is taken as a fixed circle, a virtual circle of radius D x M/(M + N) centered on the first central axis is taken as a moving circle, and the center of the circular gear tooth side portion is taken as a drawing point, the epitrochoid curve drawn is an offset epitrochoid curve offset by a length r.