Helix Curve
0 likes652 views
This document defines and describes helical curves. A helix is a curve generated by a point moving around the surface of a cylinder or cone while advancing along the axis at a constant rate relative to its rotational speed. The document explains how helices are formed on cylinders and cones, provides examples of drawing helices with given specifications, and discusses applications of helical curves such as screws, springs, and cam shapes.
Helix Curve
- 1. Helix Curve By Prof. A.J.More Department of Engineering Sciences SlideNo-1Prof.A.J.More AISSMS's IOIT Pune
- 2. Contents • Define- Helix • Helix on cylinder • Helix on Cone • Applications of Helix Prof.A.J.More AISSMS's IOIT Pune SlideNo-2
- 3. Helix • IT IS A CURVE GENERATED BY A POINT WHICH MOVES AROUND THE SURFACE OF A RIGHT CIRCULAR • CYLINDER / CONE AND AT THE SAME TIME ADVANCES IN AXIAL DIRECTION • AT A SPEED BEARING A CONSTANT RATIO TO THE SPPED OF ROTATION. Prof.A.J.More AISSMS's IOIT Pune SlideNo-3
- 4. Helix on Cylinder • It is curve generated by a point which moves around the surface of a right circular cylinder and at same time advances in the axial direction at a speed which bears constant ratio to the speed or rotation. Prof.A.J.More AISSMS's IOIT Pune SlideNo-4
- 5. 1 2 3 4 5 6 7 8 P P1 P P2 P3 P4 P5 P6 P7 P8 1 2 3 4 5 6 7 HELIX (UPON A CYLINDER) PROBLEM: Draw a helix of one convolution, upon a cylinder. Given 80 mm pitch and 50 mm diameter of a cylinder. (The axial advance during one complete revolution is called The pitch of the helix) SOLUTION: Draw projections of a cylinder. Divide circle and axis in to same no. of equal parts. ( 8 ) Name those as shown. Mark initial position of point ‘P’ Mark various positions of P as shown in animation. Join all points by smooth possible curve. Make upper half dotted, as it is going behind the solid and hence will not be seen from front side. SlideNo-5Prof.A.J.More AISSMS's IOIT Pune
- 6. It is a surface generated by moving a Straight line keeping one of its end fixed & other end makes a closed curve. What is Cone ? If the base/closed curve is a polygon, we get a pyramid. If the base/closed curve is a circle, we get a cone. The closed curve is known as base. The fixed point is known as vertex or apex. Vertex/Apex 90º Base
- 7. If axis of cone is not perpendicular to base, it is called as oblique cone. The line joins vertex/ apex to the circumference of a cone is known as generator. If axes is perpendicular to base, it is called as right circular cone. Generator Cone Axis The line joins apex to the center of base is called axis. 90º Base Vertex/Apex
- 8. P 1 2 3 4 5 6 7 P P1 P2 P3 P4 P5 P6 P7 P8 P1 P2 P3 P4 P5P6 P7 P8 X Y HELIX (UPON A CONE)PROBLEM: Draw a helix of one convolution, upon a cone, diameter of base 70 mm, axis 90 mm and 90 mm pitch. (The axial advance during one complete revolution is called The pitch of the helix) SOLUTION: Draw projections of a cone Divide circle and axis in to same no. of equal parts. ( 8 ) Name those as shown. Mark initial position of point ‘P’ Mark various positions of P as shown in animation. Join all points by smooth possible curve. Make upper half dotted, as it is going behind the solid and hence will not be seen from front side. SlideNo-8Prof.A.J.More AISSMS's IOIT Pune
- 9. Prof.A.J.More AISSMS's IOIT Pune SlideNo-9
- 10. Prof.A.J.More AISSMS's IOIT Pune SlideNo-10 Applications: •Helical Stair case •External and internal threads •Worm •Shape of Springs •Helical grooved cam for automation
- 11. Prof.A.J.More AISSMS's IOIT Pune SlideNo-11
- 12. Thank You SlideNo-12Prof.A.J.More AISSMS's IOIT Pune