# A Rapid and Inexpensive Method for Finding the Basic Parameters of Involute Helical Gears
## 4 Conclusions  
The paper is a progression of a recent work of the authors [25] concerning the accurate determination of the three basic parameters of an actual spur gear with involute teeth (number of teeth, module, profile shift coefficient) where an expedited method and the related measuring device are presented.  
The current study introduces a rapid, straightforward, and inexpensive approach for identifying the basic parameters of helical gears. In addition to the three parameters mentioned above, for helical teeth, another basic parameter occurs: the angle of tooth inclination--the helix angle on the pitch cylinder.  
For helical gears, due to the inclination of the teeth, the method proposed for the spur gear is inapplicable. Therefore, the rolling bodies introduced between the teeth of the gear to be measured are no longer pins, but balls; thus, the contact with the surfaces of the measuring device is of the point type.  
Another consequence of the slanted tooth of the gear is the existence of two profiles: a normal one, where the module has standard values identical to the values of the module of the basic rack, and a transverse one, defined in a section normal to the axis of the wheel. The entire gearing can be studied in the frontal section, similarly to a spur gear, but without the necessity of a standard module. Concerning the control method, the condition that the centre of the ball occupies an imposed position is required. Additionally, we have the condition of positions of the contact points between the balls and the flanks of the teeth. Two sets of balls of different sizes are necessary for a measurement, and the selection of  
Figure 16: The helix angle of the tooth \(\beta_{a}\) on the addendum cylinder, obtained via lateral scan.  
Figure 17: The helix angle of the tooth on the addendum cylinder, measured on a lateral photo.  
the radii of the balls is made in a manner to ensure the contact point with the flanks on the involute surface of the flank.  
Subsequent to the measurements, a system of four equations is obtained, with five unknowns: the pressure angles of the involute profile on the circles passing through the contact point ball-flank, the normal module, the normal profile shift coefficient, and the helix angle on the pitch cylinder.  
The research demonstrates that for gears with a typical number of teeth and profile shift coefficient, the helix angle of the tooth on the pitch cylinder can be approximated to be the angle from the top land, which can be conveniently determined through experimental measurements. Therefore, the system becomes compatible and allows for finding, with some approximation, all the basic parameters of the gear. Then, the normal module is adopted as the closest standard value compared to the solution obtained from the system. Further, by employing the standard value for the module, the system of four equations is resolved, leading to the precise determination of the fundamental parameters: the profile's pressure angle at the points of ball-tooth contact, the helix angle on the pitch cylinder, and the normal profile shift coefficient.  
The method is then exemplified for a concrete situation.  
Conceptualization, SA. and I.D.; methodology, S.A., F.-C.C. and C.B.; software, S.A. and I.-C.R.; validation, I.-C.R. and I.T.; writing--original draft preparation, F.-C.C. and C.B.; writing--review and editing, I.-C.R. and I.T.; visualization, LT; supervision, I.D., C.B. and F.-C.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Data are contained within the article.  
The authors declare no conflicts of interest.