(Ellipse) المنحني الناتج من الحركة التدحرجية للشكل الاهليجي على منحني (الليث -اويد) دراسة في حالة نقطة ثابتة على المحيط الخارجي للشكل الاهليجي

Abstract

This work studies a new type of open curves which resulted from the non-slippery motion of an elliptic shape rolled on a specific path . This investigation was done by using cycloid drawing method which depends on rolling a cycle on a specific path . The curve was drawn by studying the motion of a stationary point on the ellipse circumference during one or more ellipse cycles . The percentages , of the resulted curve was studied by the analysis of a specific point on the ellipse circumference on both large and small axles . These two cases are taken in moving the ellipse on given length straight path equals to the ellipse circumference. The other studied case was rolling the ellipse on the outer circumference of the Laith-oid curve , which is a new case of curves that resulted from the motion of a stationary point on the outer circumference of a circle which rolls in a non-slippery motion on a straight line with a length equals to twice its diameter .The case of the ellipse rolling on one complete Laith-oid curve was studied . Another case was the rolling on two adjacent curves . The possibility of generating closed or open surfaces from the resulted curve was studied with their characteristics .