Appendix. Springer International Publishing Switzerland 2016 A.Y. Brailov, Engineering Graphics, DOI /

Transcription

1 Appendix See Figs. A.1, A.2, A.3, A.4, A.5, A.6, A.7, A.8, A.9, A.10, A.11, A.12, A.13, A.14, A.15, A.16, A.17, A.18, A.19, A.20, A.21, A.22, A.23, A.24, A.25, A.26, A.27, A.28, A.29, A.30, A.31, A.32, A.33, A.34, A.35, A.36, A.37, A.38, A.39, A.40, A.41, A.42, A.43, A.44, A.45, A.46, A.47, A.48, A.49, A.50, A.51, A.52, A.53, A.54, A.55, A.56, A.57, A.58, A.59, A.60, A.61, A.62, A.63, A.64, A.65, A.66, A.67, A.68, A.69, A.70, A.71, A.72, A.73, A.74, A.75, A.76, A.77, A.78, A.79, and A.80. Springer International Publishing Switzerland 2016 A.Y. Brailov, Engineering Graphics, DOI /

2 296 Appendix Fig. A.1 Sketch of the product

3 Appendix 297 Fig. A.2 Three-dimensional parametric model of the product Fig. A.3 Two-dimensional parametric model of the product

4 298 Appendix Fig. A.4 Parametric drawing of the product

5 Appendix 299 Fig. A.5 Competing points. Axonometry Fig. A.6 Competing points. Front view Fig. A.7 Competing points. Top view

6 300 Appendix Fig. A.8 Competing points. Left view Fig. A.9 The horizontal level line. Axonometry Fig. A.10 The horizontal level line. Front view

7 Appendix 301 Fig. A.11 The horizontal level line. Top view Fig. A.12 The horizontal level line. Left view Fig. A.13 The plane of general position. Axonometry

8 302 Appendix Fig. A.14 The plane of general position. Front view Fig. A.15 The plane of general position. Top view

9 Appendix 303 Fig. A.16 The plane of general position. Left view Fig. A.17 The plane of general position. Right view

10 304 Appendix Fig. A.18 Cone right circular. Axonometry Fig. A.19 Sections of cone right circular

11 Appendix 305 Fig. A.20 Sections of the trihedral prism Fig. A.21 The trihedral prism. Axonometry

12 306 Appendix Fig. A.22 The truncated pyramid. Axonometry

13 Appendix 307 Fig. A.23 The truncated pyramid. Front view Fig. A.24 The truncated pyramid. Top view

14 308 Appendix Fig. A.25 The main lines of a plane. Axonometry Fig. A.26 The main lines of a plane. Front view

15 Appendix 309 Fig. A.27 The main lines of a plane. Top view Fig. A.28 The main lines of a plane. Left view

16 310 Appendix Fig. A.29 The theorem of a right-angle projection. Axonometry Fig. A.30 The theorem of a right-angle projection. Front view

17 Appendix 311 Fig. A.31 The theorem of a right-angle projection. Top view Fig. A.32 The theorem of a right-angle projection. Left view

18 312 Appendix Fig. A.33 The perpendicular to the plane. Axonometry Fig. A.34 The perpendicular to the plane. Front view Fig. A.35 The perpendicular to the plane. Top view

19 Appendix 313 Fig. A.36 The perpendicular to the plane. Left view Fig. A.37 The point of intersection of the straight line and the plane. Axonometry

20 314 Appendix Fig. A.38 The point of intersection of the straight line and the plane. Front view Fig. A.39 The point of intersection of the straight line and the plane. Top view

21 Appendix 315 Fig. A.40 The point of intersection of the straight line and the plane. Left view Fig. A.41 The method of sectional spheres. Axonometry

22 316 Appendix Fig. A.42 The method of sectional spheres. Front view Fig. A.43 The method of sectional spheres. Top view

23 Appendix 317 Fig. A.44 The method of sectional spheres. Left view Fig. A.45 The method of change of projection planes. Axonometry

24 318 Appendix Fig. A.46 The method of change of projection planes. Front view Fig. A.47 The method of change of projection planes. Top view

25 Appendix 319 Fig. A.48 The method of change of projection planes. Right view Fig. A.49 The rectangular triangle method. Axonometry Fig. A.50 The rectangular triangle method. Front view

26 320 Appendix Fig. A.51 The rectangular triangle method. Top view Fig. A.52 The rectangular triangle method. Left view

27 Appendix 321 Fig. A.53 The revolution method. The projecting axis. Axonometry Fig. A.54 The revolution method. The projecting axis. Front view Fig. A.55 The revolution method. The projecting axis. Top view

28 322 Appendix Fig. A.56 The revolution method. The projecting axis. Left view Fig. A.57 The revolution method. True length of segment. Axonometry Fig. A.58 The revolution method. True length of segment. Front view

29 Appendix 323 Fig. A.59 The revolution method. True length of segment. Top view Fig. A.60 The revolution method. True length of a segment. Left view

30 324 Appendix Fig. A.61 The true length of a segment. Axonometry Fig. A.62 The true length of a segment. Front view

31 Appendix 325 Fig. A.63 The true length of a segment. Top view Fig. A.64 The true length of a segment. Left view

32 326 Appendix Fig. A.65 The revolution method. The axis of level. Axonometry Fig. A.66 The revolution method. The axis of level. Front view

33 Appendix 327 Fig. A.67 The revolution method. The axis of level. Top view Fig. A.68 The revolution method. The axis of level. Left view

34 328 Appendix Fig. A.69 The true value of the triangle. Axonometry Fig. A.70 The true value of the triangle. Front view Fig. A.71 The true value of the triangle. Top view

35 Appendix 329 Fig. A.72 The true value of the triangle. Left view Fig. A.73 The method of coincidence. The true length of a segment. Axonometry Fig. A.74 The method of coincidence. The true length of a segment. Front view

36 330 Appendix Fig. A.75 The method of coincidence. The true length of a segment. Top view Fig. A.76 The method of coincidence. The true length of segment. Right view

37 Appendix 331 Fig. A.77 The method of coincidence. The true value of a triangle. Axonometry Fig. A.78 The method of coincidence. The true value of a triangle. Front view

38 332 Appendix Fig. A.79 The method of coincidence. The true value of a triangle. Top view Fig. A.80 The method of coincidence. The true value of a triangle. The result

39 Index A Algorithm for solving positional problems, Ambiguity, 9 Analytical model of plane, 52 of a point, of straight line, 36 Angle projection, 186, 272 Angle, 8, 179 Approximation, 233, 237 Archimedean spiral, 68 Auxiliary line, , 115, , 136, 143, , , , 161, 163, Axiom of reflexivity, 80 Axiom of symmetry, 80 Axiom of transitivity, 80 Axis of abscissas, 15 Axis of applicate, 16 Axis of ordinates, 16 Axis of revolution, 59 Axonometric coordinate axes, 250 Axonometric projections, algorithm of construction of, classification of, components of, 248 convertibility of, essence of method of axonometric projection, measurability of an axonometry, oblique-angled frontal dimetry, oblique-angled frontal isometry, oblique-angled horizontal isometry, Polke-Schwarz Theorem, 254 projection drawing, properties of, rectangular axonometric projections, rectangular dimetry, standard kinds of, visualization of, Axonometry basic equation, 253, 256, 261 Axonometry, B Base plane of projection, See Reference plane of projection Basic geometric figures, 80 Biunique conformity, 227 C Carcass surfaces, 58 Cartesian coordinate reference points, 19 Center of projection, 3, 7 Central projection, 7 properties of, 8 10 Change of projection planes, 193 Changeable (mobile) position, 192 Characteristic point of intersection, 130, 132, 137, 139, 144, 147, 152, 156, 161, 165, 170, 173 Characteristic points, 277, 279 Characteristics of the images, 179 Circle arc, 215 Closed torus, 73 Coincidence (incident) of points, 81 Coincidence method, 210 Coincidence of geometric image, 193 Coincident point, 216 Coincident zero frontal, 216 Coincident zero horizontal, 216 Collective property of plane of level, 42 of projecting plane, 47 Springer International Publishing Switzerland 2016 A.Y. Brailov, Engineering Graphics, DOI /

40 334 Index of projecting straight line, 32 Competing points, Complex drawing, 191 of geometrical image, 21 of level line, 31 of a plane of general position, of plane of level, 47 of projecting plane, 52 of projecting straight line, of straight line of general position, transformation, solving metric problems by, Components of method of axonometric projection, Cones, surface development, Conic surface, Conical projection, See Central projection Conoid, 65 Constructing development of curvilinear developed surface, methods of, 231 Constructive elements of a product, Convertibility of axonometric projections, 245, Coordinates of the point, 20 Criterion of development, 228 Curvilinear developed surface, Curvilinear projection, 7 Curvilinear surface, See Nonruled surface Cylinders, surface development, Cylindrical projection, See Parallel projection Cylindrical surface, Cylindroid, D Descriptive geometry, 1 4 aims and problems of, 2 geometric figures and objects, types of, 2 geometric image, determinant of, 3 projecting method, 3 4 subject matter of, 1 2 Determinant, of geometric image, 3 algorithmic part, 3 geometric part, 3 identifier, 3 Developable surfaces, 59 Development of surfaces, See Surface development Dihedral angle, 190 Dimetrics axonometry, 255 Direct problem, 81 95, 105 Direction of projection, 3 Directional lines, 59 Distance, 179 Distortion factor, 252 Double incidence, 115, 129, 161, 170 E Edge of regression, 63 Edges of surface, definition of, 25 Elementary image, 80 Ends of line, definition of, 25 Equivalence, 80 Essence of method of axonometric projection, F Fractional numbers, 253 Frog prospect, 275 Frontal axonometry, 254 Frontal plane of projections, 15 Frontal projection, 19 G Gaspard Monge, method of, General position, of geometric image, 206 Generating lines, 59 Geometric figures, 2, 80. See also Geometric objects Geometric image, See also Geometric objects, Geometric figures, Linear geometric images Geometric images, mutual intersection of, algorithm for solving positional problems, choice of intermediary, plane and a surface, line of intersection of, point of intersection of straight line and a plane, positional problems, classification of, 109 straight line and a surface, points of intersection of, two planes, line of intersection of, two surfaces, line of intersection of, Geometric models, of plane of frontal plane of level, of frontally projecting plane, 49 50

41 Index 335 of horizontal plane of level, of horizontally projecting plane, of plane of general position, 41 of plane of level, of profile plane of level, of profiled projecting plane, of projecting plane, Geometric models, of straight line of frontal level line, of frontally projecting straight line, of horizontal level line, of horizontally projecting straight line, of level line, of profile level line, of profiled projecting straight line, of projecting straight line, of straight line of general position, 27 Geometric objects, 2 compound, 2 linear, 2 nonlinear, 2 Geometrical models, three dimensional, two-dimensional, 21 H Helicoid, closed, 68 convolute, 69 eccentricity of, 69 minimal, 69 oblique, 68 open, right, 68 Helix, 69 Horizontal axonometry, 254 Horizontal plane of projections, 15 Horizontal projection, 19 Hyperbolic paraboloid, I Incidence of geometric images to solve engineering problems, 98 Intermediary, 109 Intersection, 19 Invariable (motionless) position, 192 Inverse problem, 81 97, 100, Isometric axonometry, 255 Isometry, 255 K Kinematic surfaces, 59 L Laws of projective connections, 22 Length, Line segment, ways of representation for, 26 Line, definition of, 25 Linear geometric images, mutual location, intersection and belonging of, planes to each other, point and a plane, point and a straight line, point and a surface, points to each other, straight line and a plane, straight lines to each other, Lines of projective connections, 21 M Major axis of an ellipse, Measurability of an axonometry, 245, Measurement system, 16 Meridian plane, 70 Method of concentric spheres, 158 Method of cutting spheres, 157 Method of eccentric spheres, 158 Method of normal, 239 Method of plane-parallel moving, Method of rectangular triangle, 180 Method of section by planes of general position, 157 Method of triangulation, 233 Method of unreeling, 236 Metric characteristics, 179 Metric problems, angle between a straight line and a plane, angle between planes, angles between straight lines, 186 perpendicularity of a straight line and a plane, perpendicularity of straight lines, perpendicularity of two planes, solving, by complex drawing transformation, changeable (mobile) position in space,

42 336 Index geometric image, method of plane-parallel moving, motionless geometric image, solving, without complex drawing trasformation, theorem of a right-angle projection, Military (antiaircraft) prospect, 275 Minimum radius, 158 Minor axis of an ellipse, Mutual belonging, 79 80, 90 91, 96, 108, 180 Mutual intersection, 79 80, 90 91, 96, Mutual location, See also Geometric images, mutual intersection of Mutually perpendicular planes, 15 N Name of the method, 157 Natural factors of distortion, 257 Non-coincidence (non-incident) of points, Nonruled surface, 59 O Oblique plane, See Hyperbolic paraboloid Oblique-angled any trimetric axonometry, 255 Oblique-angled axonometry, 254 Oblique-angled frontal dimetry, Oblique-angled frontal isometry, Oblique-angled horizontal isometry, Oblique-angled projection, properties of, Octant definition of, 15 formation of complex drawing, Gaspard Monge, method of, Open torus, 72 Operation of connection, 3, 4 Operation of intersection, 3, 4 Operations of method of axonometric projection, Origin, 15 Orthogonal coordinate reference points, See Cartesian coordinate reference points Orthogonal projection, 12, 277, 279 P Parallel projection properties, 7 8 parallel oblique-angled projection, parallel rectangular projection, 12 Perpendicularity of a straight line and a plane, of straight lines, of two planes, Plane analytical models of, 52 determinants of, of general position, 39 geometric models of, main lines of, of special position, ways of representation in complex drawing, Plane of Parallelism, Plane of projection, 3 Plane of rotation, 214 Plane surface, definition of, 25 Plane-parallel movement, 193 Point of regression, 63 Point of the general position, 22 Point of triple incidence, 117, , 171 Points, 22 definition of, 25 of double incidence, 156 of general position, 22 of special position, 22 Polke-Schwarz Theorem, 254 Positional problems, See also Geometric images, mutual intersection of classification of, 79 competing points, concept of, 79 linear geometric images, See also Individual entry Positional properties, 180 Primary axonometric coordinates, 278 Primary projection, 250 Primary reference point, 251 Principle of constructing development, 228 Principle of one image, 246 Principle of two images, 246 Principles of construction of a drawing, Prismatic surface, 61 Prisms, surface development, Problem of visibility, 79, Profile axonometry, 254 Profile plane of projections, 15 Profile projection, 19 Projecting angle, 254 Projecting method, descriptive geometry, 3 4

43 Index 337 components of, 3 operations of, 3 4 Projecting plane, 40 Projecting rays, 3 Projection drawing, construction, convertibility, 245 measurability, 245 requirements for, visualization, 245 Projection of point, 3 Projection, types of, 7 12 central projection, 7 parallel projection, 7 8 Property of displacement, 69 Proportion angle, 274 Pyramidal surface, Pyramids, surface development, R Rectangular axonometric projections, Rectangular axonometry, 254 Rectangular dimetry, Rectangular horizontal isometric axonometry, 255 Rectangular projection, properties of, 12 Rectangular triangle method, 197 Rectangular triangle, 193 Rectilinear projection, 7 Reference plane of projection of level line, 31 of plane of level, 47 of projecting plane, 52 of projecting straight line, 35 Reference points, 19. See also Cartesian coordinate reference points Relative positioning, Resultant factors of distortion, 253 Revolution of a geometric image, 193 Rotation method, Rotation of a geometric image, 193 Ruled developable surfaces, Ruled surface, 59 Ruled undevelopable surfaces with three directional lines, 67 with two directional lines, S Screw lines, 69 Screw surfaces, 60, developable, 69 pitch of, 69 step of, 69 Secondary axonometric coordinates, 278 Secondary projection, 250 Secondary reference point, 251 Sign (semiotic) model, 117, 125, 131, , 147, 155, 164, 173, 206, 210, 216 Sphere, 72 Straight line, 25 analytical models of, 36 determinants of, 26 of general position, 26 geometric models of, of special position, 26 Straight line, 7 Surface, 57 analytical models of, carcass, 58 classification of, conic, contour, 60 cylindrical, definition of, 25 description and mapping, 58 development, basic properties, condition of, 228 cones, curvilinear developed surface, cylinders, prisms, pyramids, geometric models of, indication of point belonging to, 73 kinematic, 59 nonruled, 59 of parallel transposition, 59 of parallel transposition, 59 prismatic, 61 pyramidal, of revolution, 59, ruled, 59 screw, sketch, 60 surface contour, 60 surface sketch, 60 surfaces of revolution, topographical, 58

44 338 Index torso, 63 way of representing in complex drawing, 60 ways of formation, 57 Surfaces of Catalan, 64 System of coordinates, 15 T Theorem of a right-angle projection, Theorem of perpendicularity of two planes, 185 Three-dimensional geometric model, to two-dimensional geometric model, 21 Three-dimensional object, 19 Topographical surfaces, 58 Torso surface, 63 Trimetric axonometry, 255 Two-dimensional geometric model, 21 to three-dimensional geometric model, 21 U Unambiguity, 202, 280 Undevelopable surfaces, 59 V Variant of combination of positions, , 137, 141, 150, 159, 168 Vectorial projection, 275 Visualization of axonometric projections, 245, Z Zero frontal straight line, 210 Zero horizontal straight line, 210 Zero profile straight line, 210