1.Axonometric ProjectionAxonometric Projection Basic Knowledge of Axonometric ProjectionBasic Knowledge of Axonometric Projection Isometric ProjectionIsometric Projection Cabinet Axonometry ProjectionCabinet Axonometry Projection ExercisesExercises

2. 2 Basic Knowledge of Axonometric ProjectionBasic Knowledge of Axonometric Projection Definiens :Definiens : An axonometricAn axonometric projectionprojection is one in which the object is viewed inis one in which the object is viewed in such a position thatsuch a position that several faces appear in a single viewseveral faces appear in a single view.. Trait :Trait : Axonometric drawings areAxonometric drawings are excellent for showingexcellent for showing the third dimensionthe third dimension of objects, but it is difficult to drawing andof objects, but it is difficult to drawing and being transmutedbeing transmuted.. PurposePurpose :: Axonometric drawings are often used toAxonometric drawings are often used to supplement drawingssupplement drawings.. 3. 3 (1)(1) FormForm of axonometric projectionof axonometric projection 1.1. Form and characteristics of axonometric projectionForm and characteristics of axonometric projection Place a P-plane (a new singlePlace a P-plane (a new single view) in the three-view systemview) in the three-view system and select a proper direction ofand select a proper direction of projection. Project both theprojection. Project both the object and the coordinateobject and the coordinate system of the three-view systemsystem of the three-view system to the P-plane with parallelto the P-plane with parallel projection such that the newprojection such that the new projected drawingprojected drawing simultaneously reflects threesimultaneously reflects three coordinate planes. Such acoordinate planes. Such a projection is called axonometricprojection is called axonometric projection.projection. Basic Knowledge of Axonometric ProjectionBasic Knowledge of Axonometric Projection 4. 4 (2)(2) The Characteristics of Axonometric ProjectionThe Characteristics of Axonometric Projection 1)1) Parallel line segments on the object are still parallelParallel line segments on the object are still parallel with axonometric projection.with axonometric projection. 22)) If line segments on the object are parallel to coordinate,If line segments on the object are parallel to coordinate, they are parallel to coordinate on the axonometricthey are parallel to coordinate on the axonometric projectionprojection.. Basic Knowledge of Axonometric ProjectionBasic Knowledge of Axonometric Projection Characteristics ofCharacteristics of parallelityparallelity 5. 5 The coefficient of axial deformation of the X-axis is p = O1 A1 / OA. The coefficient of axial deformation of the Y-axis is q = O1 B1 / OB The coefficient of axial deformation of the Z-axis is r = O1 C1 / OC. 2. A2. Axes anglexes angle andand coefficient of axial deformationcoefficient of axial deformation Basic Knowledge of Axonometric ProjectionBasic Knowledge of Axonometric Projection (1)(1)AAxes anglexes angle (2)(2)CCoefficient of axial deformationoefficient of axial deformation Angles between axonometric projection axisAngles between axonometric projection axis are calledare called axes angleaxes angle.. The length ratio between line segments on axonometric axes andThe length ratio between line segments on axonometric axes and that on the corresponding space coordinate axes is calledthat on the corresponding space coordinate axes is called ccoefficient of axial deformationoefficient of axial deformation .. ZZ11 XX11 YY11 OO XX11OO11YY11 XX11OO11ZZ11 YY11OO11ZZ11 6. 6 DrawingDrawing methodmethod 1)) Coordinate method 3.3. Drawing forDrawing for axonometric projectionaxonometric projection 2) Union method 3) Subtraction method 4) Synthetic method Basic Knowledge of Axonometric ProjectionBasic Knowledge of Axonometric Projection 7. 7 1.1. Construction of isometric projectionConstruction of isometric projection Isometric ProjectionIsometric Projection 2. A2. Axes anglexes angle and cand coefficient of axial deformationoefficient of axial deformation To produce anTo produce an isometric projectionisometric projection, it is necessary to view an, it is necessary to view an object such that its principal edges are equally inclined to theobject such that its principal edges are equally inclined to the viewer and hence are foreshortened equally.viewer and hence are foreshortened equally. 120120 120120 3030 00 3030 XX 120120 YY ZZ (1)(1)AAxes anglexes angle (2)(2)CCoefficient of axial deformationoefficient of axial deformation p = q = r = 0.82p = q = r = 0.82 11 XXOOY:Y: 120120 XOZXOZ:: 120120 YYOOZ:Z: 120120 8. 8 Isometric ProjectionIsometric Projection 3.3. Isometric drawing for polyhedral solidsIsometric drawing for polyhedral solids CommonCommon drawing stepsdrawing steps (1)(1) Draw the isometric axes and position origins.Draw the isometric axes and position origins. (2)(2) Measure the size of lineMeasure the size of line segmentssegments onon XX ,,YY axesaxes andand drawdraw parallel line to theparallel line to the XX,,YY draw the lower base ofdraw the lower base of the solidthe solid.. (3)(3) From all end points draw lines parallel to theFrom all end points draw lines parallel to the ZZ axes, measure theaxes, measure the size of linesize of line segmentssegments equal to highequal to high,, construct top shapeconstruct top shape of the solidof the solid.. (4)(4) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines.. Example 1Example 1 Example 2Example 2 Example 3Example 3 9. 9 4.4. Isometric drawing forIsometric drawing for curved solidscurved solids CommonCommon drawing stepsdrawing steps (1)(1) Draw the isometric axes and position origins.Draw the isometric axes and position origins. (2)(2) Measure the size ofMeasure the size of DD ,construct diamond shape of the circle.,construct diamond shape of the circle. (3)(3) ConstructConstruct approximateapproximate ellipseellipse with a compass from four centerswith a compass from four centers.. (4)(4) DrawDraw the tangent and profile lines.the tangent and profile lines. (5)(5) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines.. Example4Example4 Example5Example5 Isometric ProjectionIsometric Projection The long and short axis of the corresponding iso-circle 10. 10 1. Construction of1. Construction of cabinet axonometry projectioncabinet axonometry projection Cabinet axonometry projectionCabinet axonometry projection 2. A2. Axes anglexes angle and cand coefficient of axial deformationoefficient of axial deformation When theWhen the axonometryaxonometry projectionprojection plane is parallel to a coordinate axis,plane is parallel to a coordinate axis, and theand the coefficientcoefficient of axial deformationof axial deformation of two axes that parallel to theof two axes that parallel to the coordinate plane are equal, thecoordinate plane are equal, the cabinetcabinet axonometryaxonometry is produced.is produced. (1)(1)AAxes anglexes angle (2)(2)CCoefficient of axial deformationoefficient of axial deformation p = r = 1 q = 0.5p = r = 1 q = 0.5 XXOZOZ:: 9090 XOXOY:Y: 135135 YYOOZ:Z: 135135 ZZ 9090 XX OO 4545 135135 YY 135135 11. 11 3.3.Cabinet axonometry projectionCabinet axonometry projection for polyhedral solidsfor polyhedral solids CommonCommon drawing stepsdrawing steps (1)(1) Draw oblique axes and position originsDraw oblique axes and position origins OO.. (2)(2) Measure the size of lineMeasure the size of line segmentssegments onon XX axes and measure theaxes and measure the size of linesize of line segmentssegments onon YY axesaxes withwith sizesize, and, and draw paralleldraw parallel line to theline to the XX ,,YY ,, draw the lower base ofdraw the lower base of the solidthe solid.. (3)(3)From all end points draw lines parallel to theFrom all end points draw lines parallel to the ZZ axes, measure theaxes, measure the size of linesize of line segmentssegments equal to highequal to high,, construct top shapeconstruct top shape of the solidof the solid.. (4)(4) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines.. Example 1Example 1 Cabinet axonometry projectionCabinet axonometry projection 12. 12 4.4.Cabinet axonometry projectionCabinet axonometry projection forfor curved solidscurved solids (1)(1) Define the oblique coordinate frame and position originsDefine the oblique coordinate frame and position origins OO.. (2)(2) Draw oblique axes and position originsDraw oblique axes and position origins OO, lay out the centerlines of the circles., lay out the centerlines of the circles. (3)(3) Draw all circles on the each planeDraw all circles on the each plane.. (4)(4) Complete the tangent and profile lines.Complete the tangent and profile lines. (5)(5) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines.. circles or arcs parallel to the projection planecircles or arcs parallel to the projection plane CommonCommon drawing stepsdrawing steps Example 2Example 2 Example 3Example 3 Example 4Example 4 The long and short axis of the corresponding iso-circle Cabinet axonometry projectionCabinet axonometry projection 13. 13 Exercises 1.1. Make an isometric drawing of the cylinderMake an isometric drawing of the cylinder.. 2.2. Make an cabinet axonometry projectionMake an cabinet axonometry projection of theof the composite solid.composite solid. 14. 15. 15 1.1. Make an isometric drawing of the right cylinder.Make an isometric drawing of the right cylinder.== 24 16. 16 2.2.Make an cabinet axonometry projection of the composite solid.Make an cabinet axonometry projection of the composite solid. 1/ 2 Y= 8 17. 17 z 0 X y 30 30 20 20 20 20 20 20 1. Make an isometric drawing of the cube1. Make an isometric drawing of the cube ((L=20L=20 cm)cm).. StepsSteps:: 1)1) Draw the isometric axes.Draw the isometric axes. 2)2) Draw the lower base ofDraw the lower base of the solid.the solid. 3)3)Construct top shape.Construct top shape. 4)4) Erase the unnecessary linesErase the unnecessary lines andand deepen the visible linesdeepen the visible lines.. 18. 18 2. Make an isometric drawing of the solid.2. Make an isometric drawing of the solid. StageStage 11 StageStage 22 StageStage 33 StageStage 44 19. 19 3. Make an isometric drawing freehand.3. Make an isometric drawing freehand. Draw a box Construct basic shape Line in the view StageStage 11 StageStage 22 StageStage 33 20. 20 32 15 15 O19 9 4 15 9 9 1 2 3 1 2 3 4 O2 15 2. Make an isometric drawing of the truncated ordinary cone.2. Make an isometric drawing of the truncated ordinary cone. DD11 =18=18mm,mm, DD22 =30=30mm,mm, HH=32=32mmmm oo11 oo22 Steps: (4)(4)DrawDraw the tangent.the tangent. (3)(3)Construct ellipseConstruct ellipse with four centerswith four centers.. (5)(5)Erase the unnecessary lines andErase the unnecessary lines and deepen thedeepen the visible linesvisible lines.. Four centersFour centers :: FindFind 11 22 33 44.. Draw arc.Draw arc. Draw tDraw the rest ofhe rest of arc.arc. (2)(2) Construct diamond shape of the circleConstruct diamond shape of the circle.. (1)(1) Draw the isometric axes.Draw the isometric axes. oo11(o(o22)) 21. 21 12 R8 R812 12 24 48 R8 1 2 1 2 R8 3. Make an isometric drawing of the3. Make an isometric drawing of the soleplatesoleplatea with round cornersa with round corners.. (2)(2)Construct top arc.Construct top arc. (1)(1)DrawDraw the rectangle soleplatethe rectangle soleplatea.a. StepsSteps: R8 24 48 12 (4)(4)DrawDraw the tangent.the tangent. (3)(3)ConstructConstruct basebase arc.arc. (5)(5)Erase the unnecessary lines andErase the unnecessary lines and deepen the visibledeepen the visible lineslines.. 22. 22 90 0 z X 20 y 20 20 45 1. Make an cabinet axonometry projection1. Make an cabinet axonometry projection of the cubeof the cube((L=20L=20 mmmm StepsSteps: (1)(1) Draw the oblique axes.Draw the oblique axes. (2)(2) Draw the lower base ofDraw the lower base of the solid.the solid. (4)(4) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines.. (3)(3) Construct top shape.Construct top shape. 23. 23 2. Make an cabinet axonometry projection2. Make an cabinet axonometry projection of the cube with a hole.of the cube with a hole. StepsSteps: (1)(1) Lay out the centre lines of the cube.Lay out the centre lines of the cube. (2)(2) Draw circles on the cube.Draw circles on the cube. (3)(3) Erase the unnecessary lines andErase the unnecessary lines and deepen the visible linesdeepen the visible lines.. 24. 24 8 01 16 02 3. Make an cabinet3. Make an cabinet axonometry projectionaxonometry projection of the component.of the component. StepsSteps: (2)(2)Draw circles and arc.Draw circles and arc. (3)(3)Complete the tangent and profile lines.Complete the tangent and profile lines. (4)(4)Erase the unnecessary lines andErase the unnecessary lines and deepen the visibledeepen the visible lineslines.. (1)(1)Draw the oblique axes.Draw the oblique axes. O2" O1" oo11(oo22) 16 R1515 28 20 30 4 10 24 25. 25 4. Make an cabinet axonometry projection4. Make an cabinet axonometry projection of the lever.of the lever. StageStage 11 StageStage 22 StageStage 33 StageStage 44 26. 26 P P S Construction of isometric projectionConstruction of isometric projection (1)(1) An projection planeAn projection plane PP is in front of a vertical plane.is in front of a vertical plane. (2)(2) Direction of projectionDirection of projection SS isis vertical to thevertical to the projection plane.projection plane. (3)(3) Change the relative positionChange the relative position betweenbetween a solid and thea solid and the projection plane.projection plane. 27. 27 P P S Construction ofConstruction of cabinet axonometry projectioncabinet axonometry projection (1)(1) An projection planeAn projection plane PP is in front of a vertical plane.is in front of a vertical plane. (2)(2) Direction of projectionDirection of projection SS isis incline to theincline to the projection plane.projection plane. (3)(3) Fixedness the relative positionFixedness the relative position betweenbetween a solid and thea solid and the projection plane.projection plane. 28. 28 Axonometric projectionAxonometric projection Orthogonal projectionOrthogonal projection Isometric projectionIsometric projection 29. 29 Circle toCircle to ellipseellipse Circle toCircle to ellipseellipse Rectangle toRectangle to rhombusrhombus Axonometric projectionAxonometric projection 30. 30 Axonometric projectionAxonometric projection 31. 31 Axonometric projectionAxonometric projection 32. 32 Axonometric projectionAxonometric projection 33. 33 ZZ XX YY Characteristics ofCharacteristics of parallelityparallelity XX ZZ YY YY 34. 34 RightRight ErrorError Positioning object relative to projection planePositioning object relative to projection plane Place the face of the objectPlace the face of the object containing circles or arcs parallel tocontaining circles or arcs parallel to the projection plane.the projection plane. Place the longest dimension ofPlace the longest dimension of the object containing circles or arcsthe object containing circles or arcs parallel to the projection plane.parallel to the projection plane. 35. 35 The long and short axis of the corresponding iso-circle (the ellipse) 36. 36 The long and short axis of the corresponding iso-circle (the ellipse) 37. 37 38. 38 39. 39 40. 40 41. 41 42. 42