Development of surfaces
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The document discusses different methods for developing the surfaces of solids onto a plane. There are four main types of development - parallel-line, radial-line, triangulation, and approximate. Parallel-line development is used for prisms and cylinders, radial-line development is used for pyramids and cones, and triangulation development divides surfaces into triangles for transition pieces. The approximate method is used for objects with double curved or warped surfaces like spheres.
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Surface development 1
This document discusses the development of surfaces for various geometric shapes used in engineering. It provides instruction on how to construct parallel line and radial line developments of prisms, cylinders, pyramids and cones. It also covers how to construct developments of transition pieces using triangulation. The document contains 35 figures illustrating examples of developments for shapes including prisms, cylinders, pyramids, cones and various transition pieces.
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This document discusses the development of surfaces, which involves unfolding solid objects onto a flat plane. It describes several methods for developing different types of surfaces and solids, including parallel line development for prisms and cylinders, radial line development for cones and pyramids, and triangulation and approximate methods. It provides examples of developing cubes, prisms, pyramids, cones, and truncated solids. Developments allow sheet metal or other surfaces to be cut and folded into desired 3D shapes.
Surface Development
Department of Mechanical Engineering , E.D and Graphics Mehran University Of Engineering and Technology Jamshoro Sindh Pakistan
Development of surfaces
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This document discusses development of surfaces and isometric projection. It begins by introducing development of surfaces, including methods of development and developing the surfaces of right solids like cubes, prisms, cylinders, pyramids and cones. It then introduces isometric projection, including isometric axes, lines, planes and scale. It provides examples of developing different objects and drawing isometric views.
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The document discusses the development of surfaces, which is the process of laying out the entire surface of a 3D object onto a 2D plane. It describes various methods for developing different types of surfaces and solids, including parallel line development for prisms and cylinders, radial line development for cones and pyramids, and triangulation for more complex shapes. It then provides examples of developing specific objects like prisms, cylinders, pyramids, and cones.
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This document discusses the development of surfaces for various geometric shapes used in engineering. It provides instruction on how to construct parallel line and radial line developments of prisms, cylinders, pyramids and cones. It also covers how to construct developments of transition pieces using triangulation. The document contains 35 figures illustrating examples of developments for shapes including prisms, cylinders, pyramids, cones and various transition pieces.
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This document discusses the development of surfaces, which involves unfolding solid objects onto a flat plane. It describes several methods for developing different types of surfaces and solids, including parallel line development for prisms and cylinders, radial line development for cones and pyramids, and triangulation and approximate methods. It provides examples of developing cubes, prisms, pyramids, cones, and truncated solids. Developments allow sheet metal or other surfaces to be cut and folded into desired 3D shapes.
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Department of Mechanical Engineering , E.D and Graphics Mehran University Of Engineering and Technology Jamshoro Sindh Pakistan
Development of surfaces
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DEVELOPMENT OF SURFACES.docx
The document discusses the development of surfaces, which is the process of laying out the entire surface of a 3D object onto a 2D plane. It describes various methods for developing different types of surfaces and solids, including parallel line development for prisms and cylinders, radial line development for cones and pyramids, and triangulation for more complex shapes. It then provides examples of developing specific objects like prisms, cylinders, pyramids, and cones.
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This document provides examples and instructions for developing the surfaces of various solids using the radial line method. It begins with an overview of developing a square pyramid by opening up the triangular faces and drawing them as separate triangles connected by the base square. Several examples are then given of developing specific solids like pyramids, cones, and funnels that have been cut by various planes. Guidance is provided on drawing the projections, marking new points where edges intersect the cutting plane, and using radial lines to accurately trace the remaining portions on development. Tips are also included to first sketch the development lightly and then project and darken remaining sections.
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2. The development of lateral surfaces is covered for simple solids like prisms, pyramids, cylinders and cones, as well as solids with cut-outs and holes.
3. Examples are provided to illustrate obtaining the true shape of sections and developing the lateral surfaces of various solids through exercises.
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This document provides information about various types of quadrilaterals (four-sided shapes). It defines quadrilateral, rectangle, rhombus, square, parallelogram, and trapezium. For each shape, it describes the key properties like side lengths, angle measures, and how to calculate the area and perimeter. The goal is to explain these geometric concepts in a clear, step-by-step manner to make mathematics more accessible and enjoyable for students.
Understanding quadrilaterals chapter3 grade 8 cbse
This document defines and classifies polygons and quadrilaterals. It begins by defining curves and polygons, with polygons being plane figures bounded by three or more straight sides that meet at vertices. It then discusses the parts of polygons including vertices, sides, consecutive sides, and diagonals. Polygons are classified as convex or concave. Specific types of polygons are defined based on their number of sides. The document also discusses regular polygons, interior angles, and formulas for calculating polygon properties. Finally, it defines and provides properties of different types of quadrilaterals including rectangles, rhombi, squares, parallelograms, trapezoids, kites, and trapezoids.
Sections & Development of Surfaces_MAY 7 (3).pptx
1. A pentagonal prism with a 30mm base side and 50mm axis is resting on its base on the HP. One side of the base is perpendicular to the VP.
2. The prism is cut by a section plane inclined at 45 degrees to the HP, passing through the midpoint of the axis.
3. The development, true shape of the section, and sectional views (FV, TV, and side view) are drawn to show the remaining solid after cutting.
Presentation1 math
Types of pyramids include triangular, square, and pentagonal pyramids based on the shape of their base. A pyramid has triangular sides meeting at a single apex point directly above the center of its base. The surface area of a pyramid is the sum of the base area and half the perimeter multiplied by the slant height when the sides are equal triangles, or the sum of the base area and individual side areas when the sides are different shapes. The volume of any pyramid is one-third the area of the base multiplied by the height.
Presentation1 math
Types of pyramids include triangular, square, and pentagonal pyramids based on the shape of their base. A pyramid has triangular sides meeting at a single apex point directly above the center of its base. The surface area of a pyramid is the sum of the base area and half the perimeter multiplied by the slant height when the sides are equal triangles, or the sum of the base area and individual side areas when the sides are different shapes. The volume of any pyramid is one-third the area of the base multiplied by the height.
Presentation1 math
Types of pyramids include triangular, square, and pentagonal pyramids based on the shape of their base. A pyramid has triangular sides meeting at a single apex point directly above the center of its base. The surface area of a pyramid is the sum of the base area and half the perimeter multiplied by the slant height when the sides are equal triangles, or the sum of the base area and individual side areas when the sides are different shapes. The volume of any pyramid is one-third the area of the base multiplied by the height.
Presentation1 math
Types of pyramids include triangular, square, and pentagonal pyramids based on the shape of their base. A pyramid has triangular sides meeting at a single apex point directly above the center of its base. The surface area of a pyramid is the sum of the base area and half the perimeter multiplied by the slant height when the sides are equal triangles, or the sum of the base area and individual side areas when the sides are different shapes. The volume of any pyramid is one-third the area of the base multiplied by the height.
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The document discusses multiview drawings and orthographic projections. It defines key terms and concepts including: each view in a multiview drawing is based on orthographic projection; the three basic dimensions are height, width, and depth; the three regular views are front, top, and right side; the three principal planes of projection are frontal, horizontal, and profile; and the three visualization principles, three types of flat surfaces, characteristics of cylindrical surfaces, characteristics of fillets/rounds/runouts, and the difference between third-angle and first-angle projection.
Mensuration
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- Classifying three-dimensional figures according to their properties like faces, edges, and vertices.
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The document defines and describes various two-dimensional and three-dimensional shapes. It discusses properties such as faces, edges, vertices, parallel and perpendicular lines. Specific shapes described include cubes, cuboids, spheres, hemispheres, cones, cylinders, pyramids and prisms. Plane shapes such as polygons, quadrilaterals, rectangles, kites, rhombuses and trapezoids are also defined.
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Development of surfaces
- 3. INTRODUCTION When Surfaces of a solid are laid out on a plane the figure obtained is called DEVELOPMENT
- 4. METHODS OF DEVELOPMENT There are four main types of developments Parallel- line development Radial –line development Triangulation development Approximate Method
- 5. PARALLEL-LINE DEVELOPMENT It is employed in case of prisms and cylinders in which stretch –out-line principle Is used.
- 6. RADIAL-LINE-DEVELOPMENT It is used for pyramids and cones in which the true length of the slant edge or the generator is used as radial.
- 7. TRIANGULATION DEVELOPMENT This is used to develop transition pieces. This is simply a method of dividing a surface into a number of triangles and transferring them into the development.
- 8. APPROXIMATE METHOD It is used to develop object of double curved or warped surface as Sphere, Parabolic, Ellipsoid, Hyperboloid and the Helicoids.
- 9. WHAT IS CUBE In geometry a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
- 10. CUBE The development of the surface of the cube consist of six equal squares the length of the side of the squares being equal to the length of the edge of the cube