基于内摆线原理的绘制椭圆装置设计

Design of Elliptic Drawing Device Based on the Hypocycloid Principle

根据内摆线原理,推导了内摆线及内次摆线的参数方程,当R=2r时,内摆线变为直线,内次摆线则变为椭圆。并经过Pro/E建模仿真验证,动圆上点的轨迹为直线,圆内、圆外点的轨迹为不同的椭圆,基于此种原理设计一种绘制椭圆的装置。

The parametric equation of the hypocycloid and hypotrochoid are derived based on internal cycloid principle. When R=2r, hypocycloid is transformed into straight line, hypotrochoid is transformed into elliptic. The modeling and simulation results in Pro/E prove that the po int trajectory on moving circle is straight line, external and internal point of circle are different elliptic. A kind of elliptic drawing device is designed based on above theory.