TITLE:
The Rectangular 2D Cartesian Plane Framework of Curve Functions Involving Radius of Curvature—Nonlinear Differential Equations with Application to Regular Wedge Cam Design
AUTHORS:
Shawn P. Guillory
KEYWORDS:
Radius of Curvature, Differential Equation, Simpson’s Rule, Three-Point Self-Centering Motion, Regular Wedge Cam Design, Design Optimization
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.9,
September
18,
2025
ABSTRACT: In the study of radius of curvature differential equations, a generalized closed-form analytical solution to the curve function
y(
x
)
in a rectangular 2D Cartesian plane is determined under the assumption that the radius of curvature function and initial conditions are known, specified quantities. Various mathematical examples are provided to demonstrate the validity of the differential equation solution. A more comprehensive application is then shown regarding a regular wedge cam mechanism design associated with three-point self-centering motion for its potential use when optimizing cam characteristics and associated machinery design related to curvature.