RECAP ON GEOMETRIC FIGURES
Do you remember how to construct the indicated geometric figures?
Do you remember what the first theorem of Thales is?
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RECAP ON GEOMETRIC FIGURES
RECAP ON GEOMETRIC FIGURES:
Communication skills and Technology department
RECAP ON GEOMETRIC FIGURES
RECAP ON GEOMETRIC FIGURES:
Quiz
Draw a regular pentagon inscribed in a circle with a radius of 5cm.
Draw a regular pentagon with a side of 5cm.
Solution of the quiz:
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RECAP ON GEOMETRIC FIGURES
Solids and surfaces
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RECAP ON GEOMETRIC FIGURES
Warped surfaces
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SURFACE DEVELOPMENT
Definition:
The development of surface of an object means the unrolling and
unfolding of all surfaces of the object on a plane.
If the surface of a solid is laid out on a plain surface, the shape thus
obtained is called the development of that solid.
Development is a complete layout of all surfaces of a solid on a
plane or flat object. A surface is said to be developable if it can
be unfolded / unrolled to coincide with a plane. Surfaces of
polyhedral and single-curved surfaces are developable. But
warped surfaces and double curved surfaces are not developable
they may be developed by approximately dividing them into
developable sections.
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SURFACE DEVELOPMENT
Application:
Designers and manufacturers are frequently required to have knowledge
of development of surfaces of an object.
Principles:
Every line on the development should show the true length of
the corresponding line on the surface which is developed.
During making developments of surfaces, the following general rules
should by observed.
1. Developments of solids are usually made with the inside surfaces up to
facilitate bending or rolling during manufacturing.
2. It is possible to begin development of a solid from any edge desired,
however it is a good practice to start and end with the shortest edge to
provide strength of the final solid formed and ensure an economical
usage of fixing material like UHU for paper models and soldering,
welding and riveting for sheet metal model.
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SURFACE DEVELOPMENT
3. When making the development of a solid, elements should be labeled
using numbers or alphabet of letters in the clock wise direction.
4. Bend or fold lines should be clearly shown in the development so that
they will be used as guides for rolling or bending when making the
final product.
5. Extra material to be used as lap or seam should be provided at the end
element lines of the development where fixing or fastening is required.
The amount of material to be added varies depending on the thickness
of the material, the type of connection and production equipment.
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SURACE DEVELOPMENT
If you avoid the above principles you will end up with unacceptable outputs
as indicated below. X
XXXXX
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SURFACE DEVELOPMENT
Methods of development:
Parallel
-line
Radialline
Triangul
ation
Approxi
mate
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SURFACE DEVELOPMENT
Methods of development:
Parallel-line development
It is used for developing Prisms and single curved surfaces like
Cylinders, in which all the edges/generation of lateral surfaces
are parallel in each other.
The method divides the surface into a series of parallel lines to
determine the shape of a pattern. Example: Prism, Cylinder
Radial-line development
It is employed for Pyramids and single curved surfaces like Cones in
which the apex is taken as centre and the slant edge or generator
as radius of its development. Example: Cone, Pyramid.
The method uses lines radiating from a central point to construct
the expanded pattern of each three-dimensional shape.
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SURFACE DEVELOPMENT
Methods of development:
Triangulation development
Such developments are made from polyhedrons, single curved
surfaces, and wrapped surfaces. Example: Tetrahedron and other
polyhedrons.
The development involve subdividing any ruled surface into a series
of triangular areas.
If each side of every triangle is true length, any number of triangles
can be connected into a flat plane to form a development
Triangulation for single curved surfaces increases in accuracy
through the use of smaller and more numerous triangles.
Triangulation developments of wrapped surfaces produces only
approximate of those surfaces.
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SURFACE DEVELOPMENT
Methods of development:
It is used for developing transition pieces. Transition pieces are usually
made to connect two different forms, such as round pipes to square
pipes. These transition pieces will usually fit the definition of a non
developable surface that must be developed by an approximation.
This is done by assuming the surface to be made from a series of
triangular surfaces laid side-by-side to form the development
Approximate development
It is employed for double curved surfaces like Spheres, as they are
theoretically not possible to develop. The surface of the sphere is
developed by approximate method. When the surface is cut by a
series of cutting planes, the cut surface is called a zone.
In approximate development, the shape obtained is only
approximate. After joining, the part is stretched or distorted to
obtain the final shape. Example: Sphere, torus and ellipsoid
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SURFACE DEVELOPMENT
Methods of development:
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SURFACE DEVELOPMENT
Examples of developments:
Development of a Prism
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SURFACE DEVELOPMENT
Examples of developments:
Development of a right circular cylinder
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SURFACE DEVELOPMENT
Examples of developments:
Development of a right circular cone
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SURFACE DEVELOPMENT
Solution for class assignment 7
Development of right pyramid.
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•EN
Thank you for your patience and time.