Conic Sections
Teaching tool developed by Steve Hines as an independent project during the second year of college.
...This was the development of a device for drawing the conic sections (the hyperbola, parabola, ellipse, and in theory the circle). The conic sections represent a family of curves, varying in their ratio of the distance from a point on the curve to (1) the focus (distance R), and to (2) the directrix (the straight line, perpendicular to the curve's axis) (distance X).
...The first working model pictured below uses pairs of parallel wood dowels, a rubber band, and a ball-point pen ink cartridge with metal roller which spins freely on the ink cartridge, and which also supports and pushes the rubber band. One end of the rubber band (R) is fixed at the focus of the curve. The other end of the rubber band (X) is attached to a knuckle which slides vertically over the directrix between dowels, and is moved vertically by the horizontal pair of dowels, which are pushed along by the pen as the curve is drawn. The two crank arms, attached by thumbtacks at one end along the axis, simply keep the horizontal dowels horizontal while giving them the freedom to move vertically when pushed by the pen.
...The objective, while drawing each curve and stretching the rubber band, is maintain the original ratio R:X between the two sections of the rubber band. While drawing a curve, if the user is careful to not allow the rubber band to turn the roller, around the pen stylus, then the original ratio of ends of the rubber band will be maintained, and the correct conic section curve will be drawn.
...A more finished model, below, uses a steel bar at the directrix, and an additional roller (model airplane wheel) which is free to roll along the directrix pulled by the rubber band as the curve is drawn. The user draws the curve being careful to not let the roller rotate around the ink cartridge, to assure that the R:X ratio is maintained.
...For example, for a parabola R = X therefore the roller on the stylus is placed at the center of the rubber band to create equal lengths of the rubber band. The rubber band is marked at its midpoint, for drawing parabolas. Sections of the rubber band between the midpoint and the focus (R) are used for drawing ellipses. Sections between the mid point and the directrix (X) are used for drawing hyperbolas.
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...Circles cannot be drawn practically with this device because the distance R (point on the circle to the focus) = 0.
....This product is not for sale. Do not contact us to purchase this product. This project is shown only as an example of past industrial design services. HinesLab currently offers consulting in the area of industrial design, novel solutions to your problems as well as a variety of licensable technology.
