Technical Drawing in Photonics Lesson 6 Drawing of different cycloids. TAMOP-4.1.1.C-12/1/KONV-2012-0005 project „Preparation of the concerned sectors.

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Presentation transcript:

Technical Drawing in Photonics Lesson 6 Drawing of different cycloids. TAMOP C-12/1/KONV project „Preparation of the concerned sectors for educational and R&D activities related to the Hungarian ELI project” Dr. Zsolt István Benkő

Technical drawing in Photonics Lesson 6 A cycloid is a trajectory of a point which is fixed to the perimeter of a rolling circle. (The circle rolls on a line.) If the point is not on the perimeter but outside the circle the curve traced out is a prolate cycloid. If the point is not on the perimeter but inside the circle the curve traced out is a curtate cycloid. All the previously described curves can be referred as trochoids.

Technical drawing in Photonics Lesson 6 If the point is fixed to the perimeter of a circle which rolls inside of an other circle then the trajectory is called hypocycloid. If the fixed point is not on the perimeter of a circle which rolls inside of an other circle then the trajectory is called hypotrochoid. If the point is fixed to the perimeter of a circle which rolls outside of an other circle then the trajectory is called epicycloid. If the fixed point is not on the perimeter of a circle which rolls outside of an other circle then the trajectory is called epitrochoid.

Technical drawing in Photonics Lesson 6 Drawing of a cycloid.

Technical drawing in Photonics Lesson 6 Drawing of a cycloid.

Technical drawing in Photonics Lesson 6 Drawing of a cycloid.

Technical drawing in Photonics Lesson 6 Drawing of a cycloid.

Technical drawing in Photonics Lesson 6 Drawing of a cycloid.

Technical drawing in Photonics Lesson 6 Drawing of a cycloid.

Technical drawing in Photonics Lesson 6 Cycloid

Technical drawing in Photonics Lesson 6 Prolate cycloid

Technical drawing in Photonics Lesson 6 Curtate cycloid

Technical drawing in Photonics Lesson 6 Epicycloid The ratio of the radii is integer.

Technical drawing in Photonics Lesson 6 Epicycloid The ratio of the radii is a rational number. The curve is closing.

Technical drawing in Photonics Lesson 6 Epicycloid The ratio of the radii is an irrational number. The curve is never closing.

Technical drawing in Photonics Lesson 6 Hypocycloid The ratio of the radii is integer.

Technical drawing in Photonics Lesson 6 References 1.Ocskó Gy., Seres F.: Gépipari szakrajz, Skandi-Wald Könyvkiadó, Budapest, Lőrincz P., Petrich G.: Ábrázoló geometria, Nemzeti Tankönyvkiadó Rt., Budapest, Pintér M.: AutoCAD tankönyv és példatár, ComputerBooks, Budapest, 2006