David Anderson. Gill & Macmillan

Transcription

1 One Volume Edition David nderson 3 and 4 Online Worksheets Ideal as homework exercises Will save students time as the problems are already set up on the page Worksheets are referenced in the text The material covered in the worksheets closely matches the material covered in the text Sheets are laid out to allow space for the student s solutions Many of the sheets also contain CD generated 3-D representations of the solution Gill & Macmillan

2 uxiliary Elevations Sheet 1.1 x y 35 The drawing shows the plan of a cylinder resting on the horizontal plane. The cylinder has been cut by a simply inclined plane. Project the elevation. Draw a new elevation that will show the true shape of the cut surface. R pictorial drawing of an object is shown. Given the plan and elevation of this object project a new elevation of the solid that will show the true shape of surface R 10 Ø y x 1 uxiliary Elevation 12 2 x 1 Front Elevation y uxiliary Elevation Front Elevation 90 y 1 x 1 Plan Plan

3 uxiliary Plan Sheet 1.2 S The elevation and plan of a cylinder which has been cut by a simply inclined plane are shown. (i) Project an end elevation of the cylinder. (ii) Project a new plan of the cylinder that will show the true shape of the cut surface. The elevation and plan of a shaped solid are shown. (i) Project an end elevation of the solid. R R (ii) Construct an auxiliary plan of the solid that will show the true shape of surface S. Truncated cylinder y x Front Elevation End Elevation x Front Elevation End Elevation y x S 3 d y 1 90 c b Plan a Plan y 1 x 1 uxiliary Plan uxiliary Plan

4 True Shapes Sheet 1.3 n equilateral prism has been cut as shown. (i) Use an auxiliary elevation to find an edge view of the cut surface. (ii) Using a second auxiliary plan project a view of the solid to show the true shape of cut surface. hexagonal-based pyramid has been cut by a plane. Three points, 1, 2 and 3, are given. (i) Using the three given points find an auxiliary elevation which shows the cut surface as an edge view. (ii) Hence determine the remaining points on the cut surface and complete the elevation and plan. (iii) Find the true shape of the cut surface. 3 x x Elevation y y 1 s Level line t x End Elevation Front Elevation 2 y Plan True length t 3 1 s

5 50 18 Solids in Contact Sheet 3.1 The diagram shows the plan of a rectangular-based pyramid of 55 mm height. sphere of 20 mm radius is in contact with the horizontal plane and the pyramid. lso shown is a point P on the surface of the pyramid. (i) Draw the elevation and plan of the two solids showing the point of contact. (ii) Show the plan and elevation of a sphere that rests on the horizontal plane and is in contact with the pyramid at point P. x y 30º P R20 60 x y p

6 Solids in Contact Sheet 3.2 The elevation of a sphere S is shown with two points on its surface, points P and Q. (i) Draw the plan and elevation of the sphere and points. (ii) Draw the plan and elevation of a sphere of radius 25 mm that has point P as its point of contact with sphere S. (iii) Draw the plan and elevation of a sphere of radius 11 mm that has point Q as its point of contact with sphere S P R38 P 20 S Q Q 18 x y x y

7 Solids in Contact Sheet B The diagram shows the elevation of a cone and two spheres B and C. The three solids are in contact. (i) Draw the given elevation and project a plan. (ii) Show the points of contact in both views. Ø60 25 C Ø50 x Ø100 y x y

8 Solids in Contact Sheet 3.4 x R40 y The diagram shows the plan of a right cone in contact with a sphere B. The cone s altitude is 55 mm. Both solids rest on the horizontal plane. The position of a point P on the cone s surface is also given. (i) Draw the cone and sphere B in plan and elevation showing the point of contact. (ii) Locate point P in elevation. (iii) nother sphere C is placed on the horizontal plane and is in contact with cone at the point P. Draw this sphere in plan and elevation. The plan of a cylinder and a cone B of altitude 60 mm are shown. Both solids rest on the horizontal plane and are in mutual contact. (i) Draw the plan and elevation of the two solids and show the point of contact. (ii) sphere C rests on the horizontal plane and is in contact with the cone B and the cylinder. Sphere C has a radius of 15 mm. Project the views of this solid and show all points of contact. x 90 B y Ø58 Ø66 45º 25 P B R20 20 x y x Elevation y B p

9 Isometric Projection Sheet 5.1 R27 28 R 46 Elevation R40 R28 W Fullsize portions of the elevation and plan. Isometric View Plan

10 24 44 Isometric Projection Sheet The plan and elevation of a shaped solid are shown. Complete the full-sized plan and use this to help produce an isometric view of the solid Elevation 10º Plan Isometric View Full-size plan

11 xonometric Projection Sheet squa R Front Elevation End Elevation Complete the axonometric view of the bracket shown above.

12 xonometric Plane Sheet 5.4 R 40 R40 56 Elevation R Plan Draw a true isometric of the solid shown using the axonometric plane method.

13 xonometric Projection Sheet 5.5 Given the axonometric view of an object. Find the front elevation, end elevation and plan of the solid.

14 Trimetric Projection Sheet 5.6 Using the axonometric plane method draw a trimetric projection of the given solid. The angles for the axes are given R Elevation Plan 115º 120º 125º

15 7 5m 4 5m 12m 6m 4 5m Perspective Projection Sheet 6.1 Given the plan and elevation of a building. Make a perspective view of the building when the spectator is 10 m from the corner, the picture plane touches corner and the horizon line is 8 m above the ground line. 12m 6m 30º 60º S 10 5m VP2 3m Horizon Line Ground Line 2m VP2 2 5m Picture Plane Scale 1:100 VP1 Spectator VP1

16 Perspective Projection Sheet c VP2 b d a e Partial Elevation VP1 S Elevation Make a two-point perspective of the object shown. The picture plane is to pass through the corner GL to HL = 60 mm S

17 Picture Plane uxiliary Vanishing Points Sheet Using auxiliary vanishing points complete the perspective of the shape shown. 20 θ α Elevation VP1 30 Plan VP2 Lines which are sloping upwards as they go away from the spectator will have an auxiliary vanishing point above the horizon. Lines which are sloping downwards as they go away from the spectator will have an auxiliary vanishing point below the horizon. VP1 S VP2 Horizon Line Ground Line

18 uxiliary Vanishing Points Sheet x y Incomplete Elevation VP1 VP2 Picture Plane Given the solid shown above. Draw a two-point perspective of this solid when the position of the spectator is as shown and the horizon line is 30 mm above the ground line. Use auxiliary vanishing points where appropriate S S VP1 VP2 Horizon Line Ground Line

19 uxiliary Vanishing Points Sheet 6.5 x D D C C E Partial Elevation B B y VP1 VP2 Picture Plane VP3 VP1 VP2 Horizon Line VP3 S Ground Line 2.4m 1.8m 1.4m 0.7m 4.3m D D The plan of the structure shown is based on semi-hexagonal prisms. Using auxiliary vanishing points construct the perspective of the object. The picture plane passes through corner. The picture plane, ground line and horizon line are arranged as shown. Scale 1:100 C C 30º 7.5m E 2.2m 3.6m 30º Elevation Plan 30º B B S 60º

20 uxiliary Vanishing Points Sheet 6.6 B Make a perspective view of the structure shown. The picture plane passes through corner. The spectator is 7.5 m from corner and the horizon line is 7.5 m above the ground line. Use auxiliary vanishing points where appropriate. 0.6m 2.2m 2.2m 2.2m B 20º 1.8m 1.8m 1.5m 2.4m Picture Plane 5m 70º 2.4m 2.8m 3.2m S 7.5m Scale 1:100 S 20º Horizon Line Ground Line

21 Parabola Sheet The elevation of a cone cut by a plane is shown. Complete the plan and find the true shape of the cut surface. Name the ten parts of the parabola labelled in the diagram Directrix Vertex Focus Focus xis Using the eccentricity method construct a parabola. Eccentricity: Focus to point Point to directrix Directrix F to P P to DD Eccentricity of a parabola equals 1. W7.2 Make a freehand sketch showing the focal sphere and cuffing plane for a parabola

22 Parabola Construct a parabola in the rectangle shown. Given the focus and directrix, construct the parabola. Sheet 7.2 Vertex D xis Focus Directrix D Construct a tangent to the given parabola at point P 1. Using a different method construct another tangent at point P 2. Construct a tangent from point P 1 to the given parabola. Using a different construction method draw a tangent to the parabola from point P 2. D D P 1 P 1 + F F P 2 + P 2 D D

23 Ellipse Sheet 7.3 Using the concentric circle method construct an ellipse. Locate the focal points. Major xis Major xis Minor xis Minor xis Using the rectangle method construct an ellipse. P + P Construct a tangent at point P. Show the construction to locate the point of contact for the given tangent. Tangent Construct two tangents to the ellipse shown from the given point P.

24 Ellipse Sheet The elevation of a cone cut by a plane is shown. Complete the plan and find the true shape of the cut surface Name the ten parts of the ellipse labelled in the diagram. Directrix Given that the eccentricity of an ellipse is 0.75, construct a portion of the curve. Focus Vertex Focus xis Eccentricity: Focus to point Point to directrix Directrix Focus Vertex F to P P to DD Directrix Eccentricity of an ellipse is always <1. Make a freehand sketch of a cone cut by planes as shown. Include the focal spheres and the cut section.

25 Hyperbola Sheet 7.5 V 1 C V 2 Construct a double hyperbola in the given rectangles. F 1 V 1 C V 2 F 2 Given the axes, foci and vertices of a double hyperbola draw the double curves. xis

26 uxiliary Elevations Sheet cone has been cut as shown. Find the true shape of the cut surface Label the eight parts of the double hyperbola shown. F xis Given the focus, axis and directrix of a hyperbola of eccentricity 1.2. Construct a portion of the curve. Eccentricity: Focus to Point Point to Directrix F to P P to DD Eccentricity of a hyperbola >1. Directrix Make a neat freehand sketch showing how the double cones are cut to produce a double hyperbola.

27 Evolutes Sheet 7.7 Complete the evolute to the parabola shown. D F xis F 1 F 2 D Complete the evolute to the ellipse shown.

28 Oblique Plane V Sheet 8.1 T x y x P 1 T y The plan of an object resting on an oblique plan is shown. Complete the elevation. Given the plan of an object resting on an oblique plane. lso given is the elevation of point P. Find the vertical trace and complete the elevation. P H V H Given the elevation of an object resting on an oblique plane. The plane makes a true angle of 60 to the vertical plane. Complete the elevation. T x y x T y Given the plan of a figure resting on an oblique plane. The plane makes a true angle to the horizontal of 35. Complete the elevation. H

29 Oblique Plane Sheet 8.2 V x 1 y 1 x T y H Given the plan and elevation of a cone which is to be cut by the oblique plane VTH. Complete the plan and elevation of the cut solid.

30 Oblique Planes Sheet 8.3 V x 1 x T y y 1 Given the plan and elevation of a sphere. Draw the plan and elevation of the solid when it is cut by the plane VTH. H

31 Oblique Plane Sheet 8.4 V x 1 x T y y 1 H The elevation and plan of a regular hexagonal prism. The solid is cut by the oblique plane VTH. Draw the plan and elevation of the solid when it is cut by the plane. Draw the true shape of the cut surface.

32 Oblique Plane Sheet 8.5 The plan and elevation of a solid which is to be cut by the oblique plane VTH is shown. Complete the drawing to show the cut surface. Find the true shape of the cut surface. V x 1 x H T y y 1

33 Planes in Space Sheet 8.6 C D E B C D E B Determine the line of intersection between the two given planes. Determine the dihedral angle between the planes. Draw the projections of a line on the plane BC that passes through and makes an angle of 70 with edge BC.

34 Planes in Space Sheet 8.7 B D C E x C D y E B Given the projections of two planes BC and DE. (i) Determine the line of intersection between the two planes. (ii) Determine the dihedral angle between the planes. (iii) Determine the projection of a line drawn from E which is inclined at 30 to the HP, is 28 mm long and touches the plane BC.

35 Planes in Space Sheet 8.8 B D F C E D F B C E (i) Find the projections of the line of intersection between the two planes. (ii) Determine the dihedral angle between the planes. (iii) Draw a line from E which is 22 mm long, and is parallel to both BC and the vertical plane.

36 Skew Lines Sheet 8.9 C B D B C C D B D x D B y C Given two skew lines B and CD. Show the projections of the shortest horizontal line between them. Given the two skew lines B and CD. Show the projections of the shortest distance between them.

37 Intersection of Solids Sheet 9.1 Given the plan and end view of two intersecting prisms. Complete the front elevation of the solids. Front Elevation End Elevation Plan

38 Intersecting Solids Sheet 9.2 Given the elevation and plan of a sphere and a cone which intersect each other. Find the line of intersection and complete both views. x y

39 Intersecting solids Sheet 9.3 x Elevation y Plan

40 Developments Sheet 9.4 Elevation Plan Given the plan and elevation of two intersecting cylinders. Draw a surface development of the curved surfaces.

41 Developments Sheet 9.5 X Elevation Plan Given the plan and elevation of a cylinder intersecting with a square prism. Find the development of the curved surface of the cylinder and the two faces of the prism affected by the interpenetration. X X

42 Interpenetration of Solids Sheet 9.6 x Elevation y square-based prism is being intersected by an equilateral triangular prism as shown. Complete the plan and elevation of the solids showing all lines of interpenetration. Plan

43 Interpenetration of Solids Sheet 9.7 Find the line of intersection between the two solids shown. Elevation Plan

44 Intersection of Solids Sheet 9.8 The partial plan and elevation of a shaped solid intersected by an equilateral triangular prism is shown. Complete the plan and elevation showing all lines of intersection. x 1 y 1

45 Developments Sheet ,11 2,10 3,9 4,8 5, Base Given the plan and elevation of a truncated cylinder. Draw the complete surface development of the solid.

46 Developments Sheet ,12 3,11 4,10 5,9 6, Plan 4 5 Base Given the plan and elevation of a truncated cone. Find the complete surface development of the solid.

47 Envelopments Sheet 10.3 Label Elevation Given the plan and elevation of a cylinder and the development of an elliptical label. Complete the elevation of the cylinder when the label is wrapped around it. Plan

48 Envelopments Sheet 10.4 P Elevation P P Plan Given a cone and the development of a label. Draw the elevation and plan of the cone when the label is in position.

49 Developments Sheet 10.5 x Elevation y Draw the surface development of the given truncated oblique cylinder.

50 Developments Sheet O Elevation O 3 4 Plan 5 Given the projections of an oblique cone. Find the development of the curved surface of the cone.

51 Envelopments Sheet P 1 P 1 1 P Q Given the plan and elevation of an oblique cylinder and the development of a label to be wrapped around it. Complete the plan and elevation when the label is in position. Point P on the label is to be placed on P on the cylinder xis. PQ is to line up with line 1,1 on the cylinder.

52 Envelopments Sheet Elevation 1 1 Plan Complete the elevation and plan of the oblique pentagonal prism when the elliptical label is wrapped around it. The minor axis is to line up with edge 1,1.

53 Dimensioning Sheet 11.1 Fully dimension the two given shapes.

54 Dimensioning Sheet 11.2 Fully dimension the two given shapes.

55 Freehand Sketching Sheet 12.1 Given the views of an object. Produce a neat pictorial sketch of the solid. Shade the sketch.

56 Freehand Sketching Sheet 12.2 Make neat, freehand pictorial sketches of the given objects. Shade with colour.

57 Freehand Sketching Sheet 12.3 Given the plan and elevation of an object. Produce a neat isometric sketch of the object. Use shading to enhance the drawing.

58 Freehand Sketching Sheet 12.4 Given the front and end elevation of an object. Complete an isometric sketch of the object.

59 Freehand Sketching Sheet 12.5 Given the pictorial views of three objects. In each case make neat freehand orthographic views of the object showing all hidden detail.

60 Freehand Sketching Sheet 12.6 For each object make a neat, freehand sketch showing a front elevation, end elevation and plan.

61 Freehand Sketching Sheet 12.7 Hatching Crosshatch Scribbling Stippling

62 Shadow and Shade Sheet 12.8

63 Colouring Pencils Sheet 12.9

64 Tone and Texture Sheet Use a variety of pencil techniques to apply tone and texture to the objects above.

65 Epicycloid Sheet 13.1 C P Rolling circle Plot the locus of point P as the small circle rolls without slipping around the outside of a fixed circle. Centre of stationary circle

66 Hypocycloid Sheet 13.2 P Plot a hypocycloid given point P on the small rolling circle.

67 Trochoids Sheet 13.3 Plot the locus of point P as the circle rolls without slipping along the line. P Superior Trochoid P Inferior Trochoid

68 Inferior Epitrochoid Sheet 13.4 Fixed circle P Plot the locus of point P as the circle rolls without slipping along the fixed circle.

69 Superior Epitrochoid Sheet 13.5 Plot the path of point P as the circle rolls without slipping along the outside of the fixed circle. Fixed circle P Rolling circle

70 Inferior Hypotrochoid Sheet 13.6 Plot the locus of point P when the circle rolls without slipping along the inside of the fixed circle. circle Fixed P C

71 Superior Hypotrochoid Sheet 13.7 Plot the locus of point P as the circle rolls without slipping inside a fixed circle. Fixed circle P Rolling circle

72 Link Mechanisms Sheet 13.8 P B C D Crank B rotates for a complete revolution. Link DC rotates about fixed centre D. Plot the locus of point P for the movement.

73 Link Mechanisms Sheet 13.9 B P C D Crank DC rotates about D. rm B can rotate about and is linked to the crank by BC. Plot the locus of point P for one full turn of the crank.

74 Link Mechanisms Sheet E D B C P Crank B rotates clockwise. During one turning of the crank, D slides at a constant speed to E and back to D again. C and B are pivot joints. Plot the locus of point P for one rotation of the crank.

75 Link Mechanisms Sheet D C B O 2 O 1 Crank O 1 rotates about O 1. rm O 2 B rotates about O 2. Points, B and C are pin joints. D slides along the path indicated. (i) Plot the locus of C for one rotation of the crank. (ii) Draw a displacement diagram for slider D.

76 Cams Sheet Plot the follower displacement diagram for an in-line knife-edge follower in contact with the cam profile shown. Rotation

77 Cams Sheet Given the cam profile construct the follower displacement diagram. The follower is an in-line, flat follower and extends 8 mm each side of the centre line.

78 Cams Sheet Given the cam profile construct the follower displacement diagram. The follower is an in-line roller follower of 16 mm diameter. Rotation

79 Involute Gears Sheet Draw 5 teeth of an involute gear. The gear is to have 16 teeth, a module of 10 and a pressure angle of 20. PCD = m x t ddendum (a) = m Tip circle = PCD + (2 x a) Base circle diameter equals PCD x COS (20 ) Dedendum (d) = 1.25 x a Root circle = PCD (2 x d) Circular pitch (p) = πm Pitch angle = 360 /t Involute profile Circular pitch Dedendum Base circle ddendum Pitch circle Tip circle Tooth thickness Pitch circle

80 Pitch circle Pitch circle Involute Gears Sheet Pitch Circle Driver Gear Module (m) = 10 No. of teeth (t) = 20 Pressure angle = 20 Pitch circle diameter = m x t Base circle diameter = PCD x Cos Ð ddendum (a) a = m Dedendum (d) 1.25 x a Pitch angle = 360 /t = 18 Root circle diameter = PCD d d Driver Gear Module (m) = 10 No. of teeth (t) = 15 Pressure angle = 20 PCD = m x t Pitch angle = 360 /t = 24 Tip circle diameter = PCD + a + a Pitch Circle Draw two involute gears showing the gears in mesh. Show five teeth on each gear. The gear ratio is 4:3. Driver gear details: module 10, 20 teeth and pressure angle 20.

81 Involute Gears Sheet Pitch circle Tip circle circle Pitch circle Base circle Root Involute construction Wheel 15º Line of action Involute 20º Tip line Pitch line Root line 20º P ddendum Dedendum Pitch line Rack n involute gear wheel has 20 teeth, a pressure angle of 20 and a module of 12. It is in mesh, with a rack. Show five teeth on the gear and five teeth on the rack. Gear wheel Module (m) = 12 No. of teeth (t) = 20 Pressure angle Ð = 20 Pitch circle diameter = m x t = Base circle diameter = PCD x Cos Ð ddendum (a) a = m = Dedendum (d) 1.25 x a = Clearance = d a = Tip circle diameter = PCD + 2a = Root circle diameter = PCD 2d Circular pitch (p) π x m = Pitch angle = 360 /t = Tooth thickness = P/2

82 Cycloidal Gears Sheet Wheel Module (m) = 10 No. of teeth (t) = 18 PCD = m x t = ddendum (a) = m = Dedendum (d) = 1.25 x a = cycloidal gear wheel with 18 teeth and a module of 10 is in mesh with a cycloidal pinion gear with 15 teeth and a module of 10. Draw the gears in mesh showing five teeth on each gear. Each gear should have radial dedenda. Cb Ca Generating circle for epicycloid on pinion Cc Cd d c b a a Wheel Pinion Wheel d b c 15º 15º 10º 10º Pinion Generating circle for epicycloid on wheel C1 C2 C C4 C5 Pinion Module (m) = No. of teeth (t) = PCD = m x t = ddendum (a) = m = Dedendum = 1.25 x a =

83 Rack and Pinion Pinion details Circular pitch (p) π x m = Sheet Module (m) = 12 No. of teeth (t) = 16 Pitch circle diameter = m x t = Tooth thickness = P 2 = Pitch angle = 360 t = Pressure angle = 20 Base circle diameter = PCD x Cos 20 = Rack details Root circle Pitch circle ddendum (a) = m = Module (m) = 12 ddendum = Tip circle Dedendum (d) = 1.25 x a = Clearance = d a = Dedendum = Clearance = Tip circle diameter = PCD + 2a = Tooth thickness = Root circle diameter = PCD 2d Pinion Tip line Pitch line Root line cycloidal pinion with 16 teeth and a module of 12 is in mesh with a rack. Draw full size the rack and pinion in mesh. The pinion is to have radial dedenda. Rack

84 Hyperboloid of Revolution Sheet 14.1 x Elevation y Plan Given the base circle, throat circle and height of a hyperboloid of revolution. Construct the shell structure using elements. c b a x y Elevation c b a Plan

85 Hyperboloid of Revolution Sheet B B C V1 V2 symptote x Elevation y x Elevation B y x Elevation y x Elevation y B Plan Plan Plan Plan With the information given construct the hyperboloid of revolution on the left using the rectangle method and the one on the right using the asymptote method.

86 Hyperbolic Paraboloid Sheet 14.3 The diagram shows the outline plan of two adjoining hyperbolic paraboloid roof surfaces BCD and DEF. The corners B, C, E and F are at ground level. The corner is 3 m above ground level and the corner D is 20 m above ground level. (i) Draw the given plan and project the elevation. (ii) Project an end elevation of the roof. (iii) Find the true shape of the section S S. (iv) Draw a new auxiliary of roof BCD that will show the true length of edge CD. Scale 1:200 F S E x Elevation E y 14 m D F 4.4 m B 13 m S 90º C D B Plan C

87 Hyperbolic Paraboloid Sheet 14.4 X y c b e d a f Given the outline plan of two adjoining hyperbolic roof surfaces abcd and abef. The corner a is at ground level and corner b is 1 m above ground level. Corners d and e are 4 m above ground level and corners c and f are 11 m above ground level. (i) Draw the given plan and project an elevation. (ii) Project an end view. (iii) Find the curvature of the roof along a line joining c to f. Scale 1:100

88 Hyperboloid of Revolution Sheet 14.5 Shown is the elevation of a hyperboloid of revolution. The sides of the V-cut are elements of the hyperboloid. The true length of full length elements is 6 m. (i) Draw the plan and elevation of the solid. (ii) Project an end view. Scale 1: m 5 m x Ø3.6 m y x Elevation End view y Plan

89 Hyperboloid of Revolution Sheet 14.6 R x Front Elevation End Elevation y 11 m Ø3.8 m 60º x 4.6 m y Scale 1:100 Plan The elevation of a hyperboloid of revolution is shown. n equilateral triangular hole is cut through the bottom section and the top has been cut as shown. (i) Draw the plan and elevation of the building. (ii) Project an end view.

90 Plane Director Sheet 14.7 V c b a d a d T b Given two skew line directrices of a hyperbolic paraboloid ab and cd. lso given the traces of the plane director VTH. Determine five elements on the surface of the hyperbolic paraboloid. c H

91 Hyperbolic Paraboloid Sheet 14.8 o c b f d a e x Elevation y e f o c d b a Plan g h e o f k b a 12 m 32 m c d The diagram shows the outline plan of a roof made up of nine adjoining hyperbolic paraboloid surfaces. The outline is an equilateral triangle and the three internal surfaces make a regular hexagon in plan. (i) Draw the plan and elevation of the three surfaces abcd, cdef and bcfo. (ii) Determine the curvature of the roof along a line joining a to c. (iii) Determine the plane director for the elements cf and de. Find the traces of the plane director having its horizontal trace passing through e. Scale 1:200 i j l

92 Hyperbolic Parabaloid Sheet 14.9 x y E D F C Given the outline plan of a roof. The semi-circular plan is an extension of the hyperbolic paraboloid surface BCD. Lines EB and FCB are elements of the roof with E and F at ground level. Corner B is 10 m above ground level and corner D is 20 m above ground level. (i) Draw the plan and project the elevation. (ii) Determine the plane director for the elements B and CD. Show the traces of the plane director containing the element B. (iii) Show the curvature of the roof along the line joining D and B. Scale 1:200 B

93 Hyperbolic Parabaloid Sheet D B E x End Elevation Front Elevation Parabola C y D B E 22 m 8 m 20 m C E D E F 11m 11 m 6 m Scale 1:200 The structure is generated by translating the parabola BC in a vertical position along the parabola DE whose vertex is at E. (i) Draw the given plan and elevation. (ii) Project an end view. (iii) Find the true shape of the curve EF. Plan

94 Hyperbolic Parabaloid Sheet B B B D Parabola BC x C Front Elevation End Elevation y E 18 m B D B F 60º D E 8 m 25 m F 25 m C Plan pictorial view of a shell structure is shown. Six of these units are combined to form a total roof surface. The surface of the unit is generated by translating the parabola BC in a vertical position along the parabola BC whose vertex is at D. (i) Draw the plan and elevation of the unit. (ii) Project an end view of the unit. (iii) Find the true shape of curve DF. Scale 1:200

95 Mining Geometry Sheet 15.1 The map shows ground contours at 10 m vertical intervals. lso shown are the outcrop points, B and C on a stratum of ore. (i) In the space provided draw the profile of the line EF. (ii) Find the strike and dip of the stratum of ore. 30 C 40 N B 50 E F Scale 1:1000

96 Mining Geometry Sheet 15.2 The map shows ground contours at 10 m vertical intervals. lso shown are the outcrop points, B and C on a stratum of ore. (i) In the space provided draw the profile along the line DE. (ii) Find the strike and dip of the stratum of ore. N B D E C Scale 1:1000

97 Mining Geometry Sheet 15.3 The map shows ground contours at 10 m vertical intervals. Points, B and C are outcrop points. (i) In the space provided draw the profile of the line DE. (ii) Find the strike and dip of the stratum. (iii) Determine the outline of the outcrop between and C D E B 10 C N Scale 1:1000

98 Mining Geometry Sheet 15.4 The map shows ground contours at 10 m vertical intervals. Vertical boreholes at, B and C strike a stratum of ore at altitudes of 90 m, 60 m and 50 m respectively. (i) Determine the strike and dip of the stratum. (ii) Find the complete outline of the outcrop C N B Scale 1:1000

99 Mining Geometry Sheet 15.5 The map shows ground contours at 10 m vertical intervals. Points, B and C are outcrop points on the headwall of a stratum of ore and D is an outcrop point on the footwall. 50 (i) Find the strike, dip and thickness of the stratum. (ii) Find the outline of the outcrop. N 40 D C B Scale 1:1000

100 Cut and Fill Sheet Cut 1:1 = 5:5 1 Formation Level rises as you move away from the road Fill 1:1.5 = 5: Formation Level falls as you move away from the road. B The map shows ground contours at 5 m vertical intervals. B is in the line of a proposed roadway. The road is to have the following specifications: (i) Formation width 16 m. (ii) Formation level 75 m. (iii) Side slopes for cuttings 1:1. (iv) Side slopes for embankments 1:1.5. Show the earthworks needed to accommodate the roadway. Scale 1:1000

101 Earthworks Sheet Cut Formation :1.5 5:7.5 Levels rise as we move away from the road. B Embankment Formation 1 2 1:2 5:10 Levels fall as we move away from the road The map shows ground contours at 5 m vertical intervals. B is the line of a proposed roadway. The road is to have the following specifications: (i) Formation width 14 m. (ii) Formation level 85 m. (iii) Side slopes for cutting 1:1.5, side slopes for embankment 1:2. Show the earthworks necessary to accommodate the roadway. Scale 1:1000

102 Earthworks Sheet Cut B Formation :1.5 4:6 Levels rise as we move away from the road. Embankment Formation 1 C 1:2 4:8 Levels fall as we move away from the road. 2 o The map shows ground contours at 4 m vertical intervals. BCD is the centre line of a proposed roadway with the centre for the curve at O. The road is to have the following specifications: (i) Formation width 14 m. (ii) Formation level 52 m. (iii) Side slopes for cutting 1:1.5. (iv) Side slopes for embankment 1:2. Show the earthworks needed to accommodate the roadway. Scale 1:1000 D

103 Earthworks Sheet O D B C The map shows ground contours at 2 m vertical intervals. BCD is the centre line of a proposed roadway with the centre for the curve at point O. The road is to have the following specifications: (i) Formation width 14 m. (ii) Formation level 40 m. (iii) Side slopes for cutting 1:2, side slopes for embankment 1:2.5. Show the earthworks necessary to accommodate the roadway. Scale 1:1000

104 Earthworks Sheet Cut C Formation 1 2 1:2 2:4 Levels rise as we move away from the road. D F 112 Embankment Formation E B 1:2.5 2:5 Levels fall as we move away from the road The map shows ground contours at 2 m vertical intervals. B shows a proposed roadway with CDEF being a car park. The car park is level and at the same level as the road. The road and car park are to have the following specifications: (i) Formation width 12 m. (ii) Formation level 110 m. (iii) Side slopes for cutting 1:2. (iv) Side slopes for embankment 1:2.5. Show the earthworks necessary to accommodate the road and car park. Scale 1:1000

105 Earthworks Sheet D C E B 88 F 92 Scale 1:1000 The map shows ground contours at 4 m intervals. B shows a proposed roadway with CDEF being a car park. The car park and road are at the same level. Formation width 12 m, formation level 100 m. Side slopes for cutting 1:1.5, side slopes for embankment 1:1. Show the earthworks necessary to accommodate the road and car park.

106 Sloping Roads Sheet B The map shows ground contours at 5 m vertical intervals. B is the line of a proposed roadway. The road has the following specifications. (i) Formation width is 12 m. (ii) Formation level at is 70 m. (iii) Gradient to B is 1 in 15 rising. (iv) Side slopes for cuttings 1 in 2. (v) Side slopes for embankments 1 in 1.5. On the drawing supplied, show the earthworks necessary to accommodate the roadway. Scale 1:1000

107 Sloping Roads Sheet C B The map shows ground contours at 5 m vertical intervals. BC is the line of a proposed roadway. The road has the following specifications. (i) Formation width is 12 m. (ii) Formation level at is 50 m. (iii) Gradient to B to C is 1 in 15 falling. (iv) Side slopes for cutting 1 in 1.5. (v) Side slopes for fill 1 in 1. On the drawing show the earthworks necessary to accommodate the roadway. Scale 1:1000 Scale 1:1000

108 Sloping Roads Sheet B C D Scale 1:1000 The map shows ground contours at 5 m vertical intervals. BCD is a proposed roadway that widens from C to D. The road has the following specifications. (i) to C formation width of 12 m. (ii) Formation level at B is 205 m. (iii) to B is 1 in 10 rising, B to D is 1 in 15 rising. (iv) Side slopes for cutting 1 in 2. (v) Side slopes for embankment 1 in 1.5. On the drawing show the earthworks necessary to accommodate the roadway. Scale 1:1000

109 Surface Geometry Sheet 16.1 D 9 m E C 4 m B 6 m 6 m x y Scale 1:100 The plan of a roof is shown above. Surfaces C and D have a pitch of 50. Surface has a pitch of 70, surface B of 40 and surface E of 60. (i) Draw the plan and elevation of the roof. (ii) Develop surfaces and C. (iii) Find the dihedral angle between and D. (iv) Find the dihedral angle between B and C.

110 Surface Geometry Sheet 16.2 x y 1.8 m B C D 8.4 m E F 1.8 m 6.8 m 5 m The diagram shows the plan of a roof. Surfaces, B, C, E and F have a pitch of 50 and surface D has a pitch of 60. (i) Draw the plan and elevation. (ii) Develop surfaces and E. (iii) Find the dihedral angle between surfaces D and E. (iv) Find the dihedral angle between surfaces and C. Scale 1:100

111 Surface Geometry Sheet 16.3 The diagram shows a Y joint between three 50 mm diameter pipes. Develop the surface of the section marked.

112 Surface Geometry Sheet 16.4 P pipe P intersects a larger pipe at right angles. Find the line of intersection to complete the front elevation. Develop the surface of pipe P. Develop the top half of pipe.

113 Surface Geometry Sheet 16.5 Shown is a T-junction joining a 40 mm dia. pipe and a 50 mm dia. pipe. Complete the elevation to show the line of intersection. Develop the surface of the smaller pipe. lso develop enough of the 50 mm dia. pipe to show the true shape of the hole to be cut in it.

114 Surface Geometry Sheet 16.6 c d,c c Elevation a,d b d Plan a b Find the surface development of the transition piece shown connecting a circular and a rectangular pipe on the same axis.

115 Surface Geometry Sheet 16.7,D B,C x Elevation y D C Plan B B C Shown is a transition piece starting as a rectangle and ending as a circle. The circle is off centre. Draw the complete surface development of the surface of the transition piece. Edge BC is given as a starting point.

116 Surface Geometry Sheet 16.8 seam line D, C,B Elevation B D Plan C D C The plan and elevation of a transition piece are given. It joins a square duct to a circular duct which lies on a different axis, Make a development of the surface of the transition piece when the seam line is midway between and B.

117 ssemblies Sheet 17.1 Ø70 Ø56 Ø º M R16 2 HOLES M8 70 X X R15 x y R Plan 4 HOLES Ø12 The diagram shows the plan and elevation of a vertical support bracket. (i) Draw the given plan. (ii) Project a sectional elevation on X-X. (iii) Project an end view looking in the direction of arrow. (iv) Insert four leading dimensions and the first-angle projection symbol.

118 ssemblies Sheet 17.2 x y REF DESCRIPTION QTY 1 BSE 1 R Fillet radii 6 mm and 3 mm Ø19 25 Ø32 2 RM 1 3 PIN 1 Q Ø BUSH 1 5 WSHER (Ø44 X 3 THICK) 1 B Ø58 Ø º Ø35 Ø48 6 HEX NUT M X Ø22 Ø Ø20 X Ø28 M22 Ø Ø35 Given the details of a ROCKING RM in the diagrams with a parts list tabulated. Make the following drawings of the assembled parts with the arm resting on Q: (i) Sectional elevation on X-X. (ii) Sectional plan on -. (iii) n end view in the direction of arrow B. (iv) Insert leading dimensions, the title and the ISO symbol.

119 ssemblies Sheet 17.3 Ø M6 M R30 x y The object shown is to have a 30 mm long M12 HEX HD bolt inserted in the top. (i) Draw the given plan and elevation with the bolt included and inserted 15 mm into the threaded hole. (ii) Draw a sectional end elevation on plane -. (iii) Insert four leading dimensions, the projection symbol and the title BSE PLTE ND UPRIGHT.

120 ssemblies Sheet 17.4 Index Part Quantity 1 Base 1 2 Sliding Jaw 1 3 End Plate 1 4 Clamping Screw 1 5 Grub Screw 1 6 Cheese Head Screw 2 M10 x 35 mm long M º 60º º Ø º 45º Tap M R Holes M Ø8 Ø6 Ø8 M Ø40 M8 5 Ø 10 C BORE 20 8 deep 3 Ø Details of a clamping device are shown. The parts list is tabulated. (1) Make the following drawings of the assembled parts: (i) sectional front elevation on section plane -. (ii) full plan. The moveable jaw should be shown in the mid-position. (2) Insert the following on the drawing. (i) Title: CLMPING DEVICE. (ii) ISO projection symbol. (iii) Five leading dimensions. x y

121 ssemblies Sheet M12 x 2 30 R4 2 2 x 45 Ø R R Ø30 Ø12 Ø30 Ø x Ø12 15 c Ø10 R3 6 7 Ø30 10 Ø Ø R M12 25 Ø Ø Part No. Description Required 1 Frame 1 2 Top roller 1 3 Bottom roller 1 4 Bottom Bearing block 2 5 Top bearing block 2 6 djusting screw 2 7 Dowel 2 x y Details of BENCH ROLLS are given above. The parts list is tabulated also. Draw a full-size sectional elevation - showing the parts assembled. Insert item reference numbers to identify the parts. dd the title BENCH ROLLS, the ISO projection symbol and four leading dimensions.

122 ssemblies Sheet 17.6 x y 1 S 2 Ø M Ø20 10 Part No. Description Required 1 Body 1 2 Clamping screw 1 3 Sliding vee 1 4 Securing screw Q32. Details of PIPE VICE are given with the parts list tabulated. (i) Draw a full-size sectional elevation on cutting plane - showing the parts completely assembled. (ii) Insert item reference numbers to identify the parts and add the title PIPE VICE. M8 M Ø Ø º 45º 2 Ø12 Ø Ø16 R70 R30 R15 R S 70 Fillets = R Ø12 45º 45º M16 Ø8 10 HLF SECTION SS R