Post on 31-Mar-2015
CONICAL HELIX CURVES
SIMULATING CONICAL GEARS
By Cheddi Charles and Amber LeCroy
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
The equations for a simple conical surface.
Archimedean Spiral SurfaceThe equations for an Archimedean spiral surface.
Logarithmic Spiral Surface
The equations for an 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 radiusThe equations for the conical helixes based on the cone’s radius.
Where m is a constant that can stretch or compress the helix.
These equations were then programed in a MATLAB program.
{
Simple Cone with Helixes based on the radius
View m = 0.5 m = 2
Angle
Side
Helixes based on the cone length
The equations for the conical helixes based on the cone’s length.
Where α changes the cone
angle and n changes the
distance between lines.
These equations were also programed into MATLAB.
{
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 singlehelix makes several turningsbefore 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.