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Conical Helix Curves Simulating Conical Gears

By Cheddi Charles and Amber LeCroy Mentor: Dr . Guy Bernard Suggested by Dr. Salim Azzouz. Conical Helix Curves Simulating Conical Gears. A Continuously Variable Transmission. A CVT (continuously variable transmission) gives a constant RPM from a variable RPM. No geared CVT currently.

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Conical Helix Curves Simulating Conical Gears

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  1. By Cheddi Charles and Amber LeCroy Mentor: Dr. Guy Bernard Suggested by Dr. Salim Azzouz Conical Helix Curves Simulating Conical Gears

  2. A Continuously Variable Transmission • A CVT (continuously variable transmission) gives a constant RPM from a variable RPM. • No geared CVT currently.

  3. Parametric Equations • Parametric Equations for surfaces • Parametric Equations for curves on these surfaces

  4. Simple Cone The equations for a simple conical surface.

  5. Archimedean Spiral Surface The equations for an Archimedean spiral surface.

  6. Logarithmic Spiral Surface The equations for an Logarithmic spiral surface.

  7. Project Direction • Place curves on a simple cone to simulate gear teeth. • Constant distance between curves • Constant curve angle

  8. Helixes based on the cone radius The 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. {

  9. Simple Cone with Helixes based on the radius

  10. 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. {

  11. Recommended Surface

  12. 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.

  13. New Shapes • Calculate equations that keep the angle of a helix constant. • Trace new surface in MATLAB. • Look a distance between curves.

  14. 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.

  15. Future Research • Explore other parametric equations that will trace different surface shapes. • Simulate other types of gear teeth in the current MATLAB programs.

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