1. MINOR II 1 Date: Friday, 25/03/2011. Time: 11 am to 1 pm (including first 30 min. for quiz). Syllabus: All topics covered from lab 4 to lab 8 (including all conic sections-ellipse, parabola, and hyperbola). Instruments: All drawing instruments except mini-drafter. The 90 o scale of the mini-drafter may be used. Drawing sheets will be provided.

2. 2 MEL 110 Intersection of surfaces

3. 3 A machine component having two intersecting cylindrical surfaces with the axis at acute angle to each other. Intersection of a Cylindrical main and Branch Pipe. Pump lid having shape of a hexagonal Prism and Hemi-sphere intersecting each other. Forged End of a Connecting Rod. A Feeding Hopper In industry. An Industrial Dust collector. Intersection of two cylinders. Two Cylindrical surfaces. SOME ACTUAL OBJECTS ARE SHOWN, SHOWING CURVES OF INTERSECTIONS. BY WHITE ARROWS.

4. 4 More examples

5. 5 Intersection of surfaces Objects constructed may have constituent parts, the surfaces of which intersect one another in curves which are called CURVES OF INTERSECTON. The intersection between two flat surfaces is a straight line. If one of the surfaces is curved, the intersection may form a line or a curve. The intersection of two curved surfaces always forms a curve. When one solid completely penetrates another, there will be two curves/lines of intersection. The dimensions and shapes of the curves of intersection are required during manufacturing processes.

6. 6 Construction rules Problems involving 2 geometric surfaces, both of which are plane- – Locate points through which the edges of each of the two geometric shapes pierce each other. – Join these points to get the lines of intersection Problems where one or both surfaces are curved- – Draw elements (generator lines) on the lateral surface of one geometric shape in the region of the line of intersection – The points where these elements intersect the True Shape view of the other surface are points on the line of intersection – A curve traced through these points will represent the required intersection

7. 7 X Y 1 2 3 4 a” g” c” e” b” f” d” h” 4” 1”3”2” 1’ 2’4’3’ a’ b ’h’ c’g’ d’f’ e’ CASE 1. CYLINDER STANDING & CYLINDER PENETRATING Problem: A cylinder 50mm dia.and 70mm axis is completely penetrated by another of 40 mm dia.and 70 mm axis horizontally Both axes intersect & bisect each other. Draw projections showing curves of intersections. 45 o

8. 8 X Y a” d” b” c” 4” 1”3”2” 1’ 2’4’3’ 1 2 3 4 a’ c’ b’, d’ CASE 2. CYLINDER STANDING & SQ.PRISM PENETRATING Problem: A cylinder 50mm dia.and 70mm axis is completely penetrated by a square prism of 25 mm sides.and 70 mm axis, horizontally. Both axes Intersect & bisect each other. All faces of prism are equally inclined to Hp. Draw projections showing curves of intersections. 45 o

9. 9 30 o Cylinder through another cylinder- intersection line will be curved Divide the cross section into certain number of equal parts. Draw corresponding generator lines along the surface. Divide the cross section here too into the same number of equal parts and at the same positions as FV Join corresponding points of intersection to get the elliptical face of the cylinder in TV T F Draw one line tangent to the vertical cylinder in order to get the point where curve changes direction Line of intersection will be around this circle where it intersects the surface of the other cylinder Intersection curve Intersection curves shown in RED 1 3 2 4 6 5 8 7 9 10 11 12 1 7 4 10 6 5 8 9 3 2 12 11

10. 10 Vertical triangular prism intersecting a cone For front faces- visible part For front faces- hidden part behind cone generators For back face Visible up to this point Intersection curve on back face Hidden behind cone generator Draw concentric circles on the cone in the TV to generate different height positions One circle should be inscribed in the prism and one should circumscribe it in order to generate the top and bottom- most points of intersection Intersection curves shown in RED T F