CONICAL HELIX CURVES SIMULATING CONICAL GEARS By Cheddi
CONICAL HELIX CURVES SIMULATING CONICAL GEARS By Cheddi Charles and Amber Le. Croy Mentor: Dr. Guy Bernard Suggested by Dr. Salim Azzouz
A Continuously Variable Transmission � A CVT (continuously variable transmission) gives a constant RPM from a variable RPM. � No geared CVT currently.
Parametric Equations � Parametric Equations for surfaces � Parametric Equations for curves on these surfaces
Simple Cone �
Archimedean Spiral Surface �
Logarithmic Spiral Surface �
Project Direction � Place curves on a simple cone to simulate gear teeth. �Constant distance between curves �Constant curve angle
Helixes based on the cone radius � {
Simple Cone with Helixes based on the radius View Angle Side m = 0. 5 m=2
Helixes based on the cone length � {
Recommended Surface
Cone with Helixes based on the length This program placed ten curves at a distance of d = 0. 5 units apart along the length of the surface. This program placed fifty curves at a distance of d = 0. 1 units apart along the length of the surface.
New Shapes � Calculate equations that keep the angle of a helix constant. � Trace new surface in MATLAB. � Look a distance between curves.
Constant Angle Helixes Side view of acorn shaped surface. It has one constant angle helix curve placed upon it. � This is an angle view of the same surface. The single helix makes several turnings before reaching the end of the surface.
Future Research � Explore other parametric equations that will trace different surface shapes. � Simulate other types of gear teeth in the current MATLAB programs.
- Slides: 15