Auxiliary views Descriptive geometry Section of solids Flóra Hajdu B406 hajdfl@sze.hu

Content Auxiliary views Descriptive geometry Section and intersection of solids 2019.04.26. Hajdu Flóra

Auxiliary views Many machine parts have surfaces that are not perpendicular or at right angles to the planes of projection (sloping or inclined surfaces) In regular ortographic views such surfaces appear to be distorted and their true shape is not shown When an inclined surface has important characteristics that should be shown clearly and without distorsion an auxiliary view is used Then the drawing completely and clearly explains the shape of the object 2019.04.26. Hajdu Flóra

Auxiliary views In many cases the auxiliary view will explain one of the regular views One of the regular orthographic views will have a line representing the edge of the inclined surface The auxiliary view is projected from this edge line at right angles and is drawn parallel to the edge line Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Auxiliary views Only the true-shape feature on the views need to be drawn The auxiliary view shows only the true shape and detail of the inclined surface or features a partial auxiliary view is all that necessary Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Construction of auxiliary views scan Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Construction of auxiliary views Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design scan 2019.04.26. Hajdu Flóra

Multi-auxiliary view drawings Some objects have more than 1 surface not perpendicular to the plane of projection An auxiliary view may be required for each surface Depends upon the the amount and type of detail lying on these surfaces Some objects require a secondary auxiliary view to show the true shape of the surface or feature The surface or feature is usually oblique (inclined) to the principal planes of projection scan Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Multi-auxiliary view drawings Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design scan 2019.04.26. Hajdu Flóra

Secondary auxiliary view Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design Secondary auxiliary view scan 2019.04.26. Hajdu Flóra

Revolved views when the true size and shape of inclined surface do not in a drawing Auxiliary view Keep using the regular reference planes while imagining that the object has been revolved Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design scan 2019.04.26. Hajdu Flóra

Descriptive geometry Major problem: find the true view of lines and planes Solve engineering problems with geometric elements Structures have 3D forms made up a combination of geometric elements The graphic solution of 3D forms require an understanding of the space relations that points, lineas and planes share in forming any given shape Problems that require mathematical solution can be solved graphically 2019.04.26. Hajdu Flóra

Points in space Normally identified by 2 or more projections scan 2019.04.26. Hajdu Flóra

Lines in space Lines are grouped into 3 classes depending on how they are positioned in relation to the reference lines Normal lines: perpendicular to the reference plane Inclined lines: appear inclined in one plane Oblique lines: appear inclined in all 3 views Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

True length of an oblique line Place an auxiliary reference line RL3 to any parallel oblique lines Transfer distances M and N shown in the regular views to the auxiliary view locating points A1 and B1 Join points A1 and B1 with a line A1B1 is the true length of AB Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Point on a line The line AFBF contains a point C Poject construction lines perpendiculat to reference lines RL1 and RL2 The construction lines are projected to line ATBT and line ASBS If C is to be located on the true lenght of line AB another reference line is required and the distances M and N are used to locate the true lenght of line A1B1 in the auxiliary view Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Planes in space Planes are considered to be without thickness and can be extended without limit May be represented or detemined by intersecting lines, 2 parallel lines, a line and point, 3 points or a triangle 3 basic planes are identified by their relationship to 3 principal reference planes Normal plane: surface appears in its true shape in the front view and as a line in the 2 other views Inclined plane: the shape of the triangular plane appears distorted in 2 views and as a line in the other view Oblique plane: shape appears distorted in all 3 views Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Locating a line in a plane Given triangular plane ABC and line RS RS Line RTST crosses over lines ATBT and and ATCT at points DT and ET Project points DT and ET down to the front view locating points DF and EF Extend a line through points DF and EF The length of the line can be found by projecting poits RT and ST to the front view locatong the end points RF and SF Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Locating a point in a plane Given triangular plane ABC and point R Draw a line from AT passing through point RT to s point MT on line BTCT Project point MT to front view locatong point MF Join points AF and MF with a line Project points RT to top view locating point RF Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Locating the piercing point of a line and a plane Given line UV passing through plane ABC Locate points DT and ET Project points DT and ET locating points DF and EF Connect points DF and EF with a line The instersection of lines DFEF is the piercing point Project OF to the other view locating point OT Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Locating the piercing point of a line and a plane Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Establishing visibility of lines in space Given 2 nonintersecting lines in space Label the crossing of lines ATBT and CTDT as 1 and 2 Project the cossing point to the other view establishing point 1 on line AFBF and point 2 on CFDF Point 1 on line AFBF is closer to the reference line, which means that line ATBT is visible Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Visibility of lines and surfaces Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Visibility of lines and surfaces Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Distance from a point to line Given front and side views. The shortest distance between line AB and point P is required Draw the primary auxiliary view Draw reference line RL2 at any convenient distance and parallel to line ASBS Transfer distances designated as R, S and U in the front view to the primary auxiliary view. The resulting line A1B1 is the true lenght of line AB Draw the secondary auxiliary view Draw reference line RL3 at any convenient distance and perpendiculat to line A1B1 Transfer distances designatet as V and W in the side view to the secondary auxiliary view, establishing points P2 and A2B2 The shortest distance between point P and line AB is shown in the secondary auxiliary view Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

Shortest distance between 2 oblique lines Given front and side views. The shortest distance between line AB and point P is required Draw the primary auxiliary view Draw reference line RL2 at any convenient distance and parallel to line AFBF Transfer distances designated as R, S and U in the other view to the primary auxiliary view to establish lines A1B1 (true length of line AB) and C1D1 Draw the secondary auxiliary view Draw a reference line at any convenient distance and perpendiculat to line A1B1 Transfer distances L, M and N from the front view to the secondary auxiliary view, establishing line C2D2 and the point view of line A2B2 The shortest distance between these 2 lines is shown in the secondary auxiliary view scan Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design 2019.04.26. Hajdu Flóra

The angle a line makes with a plane Draw a line parallel to the perpendicular reference plane RL1 Draw the primary auxiliary view Draw the secondary auxiliary view 1 Draw the secondary auxiliary view 2 Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design scan 2019.04.26. Hajdu Flóra

Edge lines of 2 planes Source: C. Jensen, J. D. Helsel, D. R. Short: Engineering Drawing&Design Given 2 planes ABC and ABD (intersection at line AB) Draw the primary auxiliary view Draw reference line RL2 at any convenient distance and parallel to line AFBF Project lines perpendicular to reference line RL2 from points AF, BF, CF and DF shown in the front view to the primary auxiliary view Transfer distances R, S and U shown in the top view to the primary auxuliary view area, establishing points A1, B1, C1 and D1 Join these points to establish the primary auxiliary view Draw the secondary auxiliary view Draw reference line Rl3 at any convenient distance and perpendicular to line A1B1 Project lines parallel to line A1B1 from points A, C and D shown the primary auxiliary view to the secondary auxiliary view Transfer distances L, M, and N shown in the front view to the secondary auxiliary view, establishing points A2, B2, C2 and D2 Join these points with lines Point A2B2 is a point-on-view of line AB, the true angle between the 2 planes is seen in this view scan 2019.04.26. Hajdu Flóra

Section of solids Pyramid cut by a plane Cylinder cut by a plane Cone cut by a plane Sphere cut by a plane scan 2019.04.26. Hajdu Flóra

Pyramid cut by a plane 2019.04.26. Hajdu Flóra

Cylinder cut by a plane 2019.04.26. Hajdu Flóra

Cone cut by a plane 2019.04.26. Hajdu Flóra

Sphere cut by a plane 2019.04.26. Hajdu Flóra

Intersection of solids Prism and pyramid Cone and cylinder Cylinders with different diameter and position scan 2019.04.26. Hajdu Flóra

Intersection of prism and pyramid 2019.04.26. Hajdu Flóra

Intersection of cone and cylinder 2019.04.26. Hajdu Flóra

Intersection of cone and cylinder 2019.04.26. Hajdu Flóra

Intersection of Cylinders with different diameter and position 2019.04.26. Hajdu Flóra

Summary Auxiliary views Descriptive geometry Points, lineas and planes in space Section and intersection of solids Next week: Basic dimensioning

Thank You for Your attention!