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.