Tag Archives: technical and engineering drawings

Constraint-based Modeling: Advantages, and Types of Constraints

The objects, results, or end products generated from constraint-based modeling software are derived from the dimensions and constraints that define the geometry of their features.

Whenever a modification or change has to be made, the modified or new part is re-created from the original part which is based on the original definitions.

Constraint-based modeling is also called feature-based modeling because its individual models consist of combinations of features.

The constraint model is made up of individual features and their relationships with other features, defined by dimensions and constraints.

Each feature (which is defined by specific properties) is a basic piece of a constraint-based solid model. To create a feature, you have to specify the geometric constraints that apply to it; then specify the size parameters and use them to generate the feature.

If a component, part, or element of the feature is modified or changed, the modeling software can be used to regenerate the modified feature in accordance with the constraints that define or are assigned to it.

Apart from defining relationships between features, constraint-based modeling software can be used to apply constraints and parameters across parts in an assembly or assembled structure (such as a group of machine parts that fit together to form a self-contained unit). As a result, when a part is changed, any related parts in the assembly can also be updated.

Because constraint-based modeling software can regenerate features and parts from the relationships stored in its database, the planning aspect of constraint-based relationships is crucial to generating useful and efficient constraint-based models that clearly reflect the design intent of products, parts, or objects.

Advantages of constraint-based model/modeling

  • During the evolution of designs, constraint-based models can be easily updated by altering the relationships and sizes that define them, respectively.
  • Categories of designs can be created because of the ease with which constraint-based models can be updated; also, it is possible to analyze, make changes, reanalyze, and make changes to the model again and again.
  • Constraint-based model makes it easy to update related parts to a new size after dimensions are changed.
  • Constraint-based model analyzes mass properties such as the weight and volume data during design so that the resulting structure behaves in the desired way.
  • Constraint-based model enhances the amount of time that can be used to optimize a design; this is possible because the model makes it possible for analysis to be incorporated earlier in the design process.
  • By focusing on the design intent for any product, constraint-based modeling helps modelers to be more imaginative, carefully consider or reconsider the function and purpose of the item being designed, and improve designs—thereby even resulting in better designs.

Types of constraints used to define and drive the constraint-based model geometry

Each object or product in a constraint-based model is defined by the constraints or dimensions/sizes and geometric relationships stored in the model and used to produce the object or product. Two basic types of constraints are used to define and drive the constraint-based model geometry:

  • Size constraints are the dimensions that define the model or its geometry. The type of dimensions chosen and how they are placed, respectively, are important aspects of capturing the design intent behind a model.
  • Geometric constraints determine the limits and maintain the geometric properties of a product or object, such as circularity, tangency, horizontality, verticality, etc. These geometric constraints are equally important in capturing design intent.

In constraint-based modeling, the term parameter refers to a named quantity that has a value that can be changed; just like a variable, it can be used to define other parameters.

However, unlike a variable, a parameter is not abstract—implying that it will always have or be assigned a value to represent a model.

For instance, the parameter called length can be assigned and defined by a value, such as 20. (Width is also a dimension but a different type of parameter.) On the other hand, the same length can be defined as having a value that is two times the width of the same object: the size or dimension of the length can be defined as: “2 × width”—meaning that, instead of assigned, the length parameter can be calculated using the width. In that case, if the value of the width is changed, the length would be automatically updated to the new value of “2 × width”.

The parameters that define and drive the object or model geometry are indicated on reproduced drawings. If the parameter value for the breadth, width, or length of a part of an object is changed, the whole object would be updated automatically.

It is important to note that the dimensions (used to define individual features) in a constraint-based model can behave in different ways. A dimension can be:

  • A parameter: this aspect is used in equations that “drive” the size of a model feature.
  • A reference dimension (often called driven dimension): this aspect derives its value from the model geometry; however, it is not a size constraint for the model.
  • A size constraint (often called driving dimension): this aspect of the model feature can be updated when the dimension is altered or modified.
  • A dimension: generally, this aspect is just any text whose value either has or does not have a relationship with the model geometry, regardless of whether or not it is included on a drawing or model view.
  • A combination of all the above.

Driving dimensions help to moderate the size of a feature element in the constraint-based model for an object or idea. Each driving dimension has two parts: a numerical value and a name. Each name makes it possible for the dimension it represents to be used in equations or relationships that define different parts of the model geometry. The numerical value, on the other hand, can be derived from an equation or represented by a number that defines the dimension.

Constraint-based modeling software lets users switch their display between the named and numeric dimensions in their respective models.

Like the geometric constraints used in constraint-based modeling, the size parameters can also establish relationships between features of the model component in formulas.

The operators used in the equations that express constraint-based dimensions are similar to those used in a spreadsheet or other types of programming notation.

In fact, many modelers have made it easy for users to import and export dimensions or numeric values from a completely different application; for instance, a spreadsheet.

When handling information from other applications, it is possible to use complex formulas to calculate the sizes in the other program; thereafter, the obtained results or values can then be imported back into the modeling package which, like others, has its own syntax and notation.


The Merits of Using Surface Models

One outstanding quality of surface models is the improved appearance of their surfaces and the ability to use its [appearance] complicated definitions for computer-aided manufacturing (CAM).

Evidence proves that customers purchase products, not only based on how they function, but also on their styling or how aesthetically pleasing they are, with or without visually expressing how their back edges actually appear.

By using lighting and different materials in most surface modeling softwares to create and present a realistically shaded model of a product to potential customers, you can actually evaluate their [customers’] reaction—pleasure, displeasure, or otherwise—to seeing it.

Many real-life consumer products often start out as a surface model and their interior parts are engineered to accommodate or somewhat conform to the shape of the exterior part(s).

Using surface models is cost-effective and could increase savings when used in place of physical prototypes or in place of actual products for promotional purposes. The cost-effectiveness of surface modeling depends on the complexity or difficulty of the surface, the level of accuracy it requires, and the potential purpose of the modeling.

The surface definitions of surface models eliminate the ambiguity that is inherent in some wireframe models: they make it possible for you to view the front edges or surfaces and holes by hiding the “invisible” parts of the model.

It is true that complex surfaces can be difficult to model, but it is possible to manufacture irregular shapes that are difficult to document systematically in 2D views if their complex surfaces, which are defined by a surface model, can be exported to numerically controlled machines.

Surface models (and solid models too) can be used to assess interference and fitness before a product is eventually manufactured. Oftentimes, solid models can be changed into surface models and vice versa.

Although surface models define surfaces and often provide information about the surface area of a part of a product, such information can save time, especially when a complex surface is involved. However, the accuracy of calculations in surface models may depend on the method employed by the software to store product surface data.

Basic Methods Used to Create Surface Models

Most surface modeling softwares are programmed with a matrix/list of an object’s or a part’s vertices and how they are linked to one another to form edges in the CAD database which can mathematically generate surfaces (from points, lines, and curves) between an object’s vertices.

During the process of creating surface models, some surface modelers save additional information that defines and indicates the inner/inside and outer/outside parts of a surface.

This is often accomplished by saving a “surface normal”—a leading or directional line that is normal or perpendicular to the outer part of the surface. This feature makes it easy to shade and render the model.

The basic methods used to create surface models, are as follows:

  • Extrusion and revolution
  • Mesh surfaces or meshes
  • NURBS-based surfaces, or spline approximations

1. Extrusion and revolution

It’s possible to define a surface by using a 2D shape or profile and the axis or course about which it revolves (circles around or moves about in an orbit) or extrudes (forms or takes shape by forcing through an opening).

Figures 1 and 2 below show a surface model that is created by revolution, and the axis of revolution and profile used to create it. Surface primitives (such as cylinders, planes, and cones) are sometimes used as building blocks and can be created from the revolution or extrusion of regular geometric entities.

Figure 1

Figure 1

Figure 2

Figure 2

The surface model (figure 1) above was created by revolving the profile (figure 2) about the axis (same figure 2). (Source: Technical Drawing with Engineering Graphics, 15th edition.)

2. Mesh surfaces or meshes

In the CAD database, vertices or matrix of vertices are used to define flat plane surfaces, and the 3D location of each vertex defines each individual mesh surface. Below, figure 5 shows the matrix/list of a mesh’s vertices, while figures 3 and 4 show the wireframe view and rendered view, respectively.

Mesh surfaces are very important in modeling uneven surfaces in which it isn’t necessary to use completely smooth surfaces. Instead of producing a mesh surface with a slightly bumpy appearance, some CAD modeling packages allow users to define surfaces by a smoothed representation.

Figure 3

Figure 3

Figure 4

Figure 4


593, 6177,5594

594, 6177,5596

595, 6177,6601

596, 6177,6611

597, 6177,6621

598, 6177,6621

599, 6177,6616

600, 6177, 6611

601, 6177,6606

602, 6177, 6611

603, 6177, 6631

604, 6177,6641

Figure 5

A Mesh Surface: A mesh surface comprises a series of planar surfaces that are defined by a matrix or list of vertices (figure 5), a wireframe view (figure 3), and a rendered view (figure 4). (Source: Technical Drawing with Engineering Graphics, 15th edition.)

3. NURBS-based surfaces, or spline approximations

The mathematics that is behind and guides non-uniform rational B-spline curves also forms the basis for the method which is used to create surface models and surfaces in most surface modelling systems.

A set of vertices (in 3D) that are used to mathematically define smooth surfaces, are also used to define non-uniform rational B-spline (NURBS) surfaces.

The advantage that the surface modelers who use NURBS have is that, because rational curves and surfaces can be used to generate both free-form curves and analytical forms (such as cylinders, planes, lines, and arcs), the CAD database doesn’t necessarily have to be equipped with different techniques for creating surfaces by using a surface primitive, revolution, extrusion, or mesh.

Some extruded and revolved surfaces can be “lofted” or “swept”, and spline curves can be used as program or input for extruded and revolved surfaces.

“Lofting” is a term used to define any surface that fits into a series of curves that don’t intersect or meet at any point with each other. On the other hand, “sweeping” is a process whereby a surface is created by sweeping a cross section or curve along one or more “paths”.

In both cases—lofting or sweeping—the overall surface merges from the shape of one curve to the shape of the next curve, as shown in figures 6 and 7 below.

Figure 6

Figure 6

Figure 7

Figure 7

A lofted surface (figure 6) merges a series of curves that don’t intersect into a smooth surface, while a swept surface (figure 7) sweeps a cross section or curve along a curved path and merges the characteristics of both into a smooth surface model (Source: Technical Drawing with Engineering Graphics, 15th edition.)

Figure 8

Figure 8

Figure 9

Figure 9

NURBS surfaces can also be created by meshing curves that are perpendicular or cut across each other, as shown in figure 8 and 9 above. (Source: Technical Drawing with Engineering Graphics, 15th edition.)


If you want to create a surface model, you don’t have to create an entire surface at once. Only entities (technically referred to as “patches”) would be enough, but you have to combine the entities or patches into a continuous model and to create complex surfaces.

Each patch can be approximated or interpolated just like a spline curve can, and surface patches are connected together by employing mathematical methods to merge the approximated edges of the patches and eventually create smooth joints.

It is important to note that sometimes or where necessary, trimming is used to create complex surface patches. For instance, a modeler might start out with a circular patch but trim it to a triangular patch and eventually merge it with other surface patches.

Some surface modeling systems use Boolean operations, while others don’t. It can be difficult to use the systems that don’t employ Boolean operations (or proficient tools for trimming surfaces) to create a feature such as a rectangular hole through a curved surface because the exact shape of the surface and hole has to be defined by assigning or fixing its edges.

Types of Models Used in Technical & Engineering Drawings and Designs

Generally speaking, a model is a representation or hypothetical description of a complex process, entity, system, device, or theory that helps to predict its behavior.

A model can also be defined as a small-scale object that is usually built to scale to represent the details of a much larger object.

Models are used in technical and engineering drawings and designs and also preliminary works or construction, as plans from which final products are created; for example a clay model can be created for a real or an eventual casting process.

Models in technical and engineering drawings and designs and preliminary works can be used in testing, perfecting, or honing a final product after understanding and being satisfied with how it behaves; for example, a test model can be created for a solar-powered vehicle.

This article discusses the following types of models used in technical & engineering drawings and designs:

1. Descriptive models

Descriptive models are used in technical and engineering drawings and designs to represent an object, system, entity, device, or process, in either words or pictures.

A descriptive model is a group of written specifications for a design, an object, a system, an entity, a device, or a process.

The major aim of a descriptive model is to describe and provide enough details that can express the image of the final design, object, system, entity, device, process, or product.

Sometimes, descriptive models use representations that are simplified, similar, or equivalent to something that can be more easily understood.

If all the specifications in a descriptive model are adhered to, the final design, object, system, entity, device, process, or product will perform as correctly as expected.

Sketching is another type of descriptive model for the design ideas that are expressed on paper. Two-dimensional (2D) and 3D computer-aided design (CAD) drawings are also descriptive models.

Although, in certain cases, a physical model or prototype is created to be smaller in scale, they are still regarded as another type of descriptive model.

2. Analytical models

Analytical models in technical and engineering drawings and designs help to mathematically or diagrammatically (schematically) represent and predict the future behavior of an object, system, entity, device, process, or product.

For example, an electrical circuit model or simple circuit design model can help to simulate or reproduce the behavior of an actual electrical circuit, or how it would function; therefore, an electrical circuit model is an example of an analytical model.

An effective analytical model helps to determine the best aspects of a system’s, an object’s, an entity’s, a device’s, a process’, or a product’s behavior that should be modelled.

A finite element analysis (FEA) model—such as that used to calculate important properties (for e.g., stresses, temperature, etc.) during the design of a real object, system, entity, device, process, or product—helps to simplify CAD models in a similar way.

A FEA model breaks a model into smaller elements and reduces a complex or complicated system into a series of smaller systems which helps to solve a problem, or understand and estimate certain properties more easily.

Understanding and applying an analytical model requires a good understanding of the difference between the model and the actual system, entity, device, process, or product, in order to be able to interpret any results correctly.

3. Two-dimensional (2D) models

Traditional paper drawings

Two-dimensional (2D) sketches and multi-view paper drawings represent designs for technical and engineering drawings and designs.

All the information that defines an object can be shown on paper drawing through sketch details, but may require many orthographic views which could take a long or longer time to create than CAD drawings would.

Because paper drawings are difficult to modify, the labor costs involved in producing them usually outbalance or outweigh equipment savings.

Paper drawings are not always highly accurate: their accuracy is approximately plus or minus one fortieth (1/40) of the drawing scale and makes paper drawings not particularly measurable.

2D CAD Models

Although two-dimensional (2D) CAD models share the visual characteristics of paper drawings, they are much more accurate than paper drawings and easier to modify.

CAD models represent the full size of objects, unlike paper drawings which usually don’t. Also, in CAD models you can “snap” to exact locations on objects, so as to be able to determine sizes and distances.

CAD systems have standard symbols which are easy to add and change; in addition, they have many editing tools that enable users to quickly edit and reuse drawing geometry.

Two-dimensional 2D CAD drawings can be easily and quickly printed to any desired scale, and different types of information can be singled onto several layers; this gives the model an advantage and makes it more flexible than paper drawing.

Computer-aided design accurately defines the positions of lines, arcs, and other geometry. If you query the AutoCAD database, it accurately returns information to you in the form it was originally created.

2D constraint-based modelling

Constraint-based modeling was originally started as a method to create 3D models. Constraint-based 2D models provide users with technical aspects that can help them define 2D shapes based on their individual geometry.

Users can add relationships like tangency and concentricity between entities in a drawing, and once a tangential or concentric constraint is added between two shapes or drawings (for e.g., circles), they will be constrained to remain tangential or concentric, and a user will be alerted if they attempt to make a change that will violate a selected geometric constraint.

The dimensions used in drawings constrain the sizes of the features of the drawings, and the relationships defined between components of the 2D model are retained by the software that is used when making changes to any drawing.

Geometric constraints are highly valuable tools, but must be applied with a proper understanding of basic drawing geometry if any benefit is to be derived from them.

Examples of constraints in AutoCAD 2016

The following are the constraints that define 2D objects’ respective geometry in AutoCAD:

  • “Vertical”: This constrains lines or pairs of points on objects to remain parallel to only the y-axis
  • “Horizontal”: This constrains lines or pairs of points on objects to remain parallel to only the x-axis
  • “Parallel”: This constrains two selected lines to remain parallel to each other
  • “Perpendicular”: This constrains two selected lines to be at an angle of 90° to each other
  • “Tangent”: This constrains two curves to be tangent to each other or to their extensions
  • “Smooth”: This constrains a spline to be contiguous and maintain G2 curvature continuity with another entity
  • “Concentric”: This constrains two arcs, circles, or ellipses to retain or maintain the same center point
  • “Coincident”: This constrains two points to stay connected to each other
  • “Collinear”: This constrains two or more line segments to remain along the same line
  • “Symmetric”: This constrains two selected objects to remain symmetrical about a specified line
  • “Equal”: This constrains selected entities to retain or maintain the same size
  • “Fix”: This constrains points, curve points, or line endpoints to stay in fixed position on the coordinate system
  • “Angular”: This constrains the angle between two lines to be retained
  • “Linear”: This constrains the distance between two points along the x- or y-axis to be retained
  • “Aligned”: This constrains a distance between two points to be retained
  • “Diameter”: This constrains the diameter of a circle to be retained
  • “Radius”: This constrains the radius for a curve to be retained

Icons for constraints in AutoCAD 2016

4. Three-dimensional (3D) models

Two dimensional (2D) models must be interpreted in order to correctly visualize 3D objects. Three-dimensional (3D) models are used to convey technical and engineering and designs to people who are unfamiliar with orthographic projection; in addition, they (3D models) are used to evaluate properties of drawings and designs that are undefined in 2D representations.

Physical models

Physical models serve as a source of visual reference and are also called “prototypes” whenever they are created in “full-size” or used to validate a nearly last or final design for production.

Physical models are good visual representations of designs; however, if they are not created from materials that would be used in a design, their weight and other features won’t match the final product.

Physical prototypes help to discover and correct many problems in designs and enable people to interact with physical models and understand how designs would eventually look like, and how they would function.

In certain cases, due to the size of a project, a physical model is created to be smaller in scale than how the final design would be. However, physical prototypes lack flexibility, and once they have been created, it is usually difficult, expensive, and time-consuming to modify or change them.

Therefore, it is advisable to use full-sized physical prototypes late in the design process, when major design changes are less likely to be made.

3D CAD models

Three-dimensional CAD models combine the characteristics of both descriptive models and analytical models and provide the benefits of both a 2D model and a physical (prototype) model.

Three-dimensional CAD models can generate standard 2D multiview drawings for visual representation, as well as rendered and shaded views.

Because 3D CAD models accurately depict the geometry of objects or devices, they can completely describe the shape, size, and appearance of objects or devices in the same way as a physical or scaled model would.

Virtual reality

Virtual reality (also called “VR”) refers to the process of interacting with a 3D CAD model as if it were real. In virtual reality, the model simulates how a user would interact with a real object, device, or system.

The term “virtual prototype” refers to 3D CAD systems that represent objects that are adequately enough to enable people, manufacturers, or designers to acquire the same type of information they would be able to acquire from creating and studying a physical model or prototype.

When a virtual reality display is used, users can be able to immerse themselves in the model and move about or through it and view it from several points of view.

If the conditions of a virtual object are altered, it would react in a certain way and provide feedback, or a sensation of its reaction would be provided to the user or person immersed in the virtual reality they subjected themselves to.

Types of Coordinate Systems for 2D and 3D CAD Modeling/Drawings

Computer-aided design (CAD) drawings are produced and stored in relationship to a coordinate system, especially Cartesian coordinate system, polar coordinate system, cylindrical coordinate system, and spherical coordinate system.

Regardless of the CAD software system that will be used in 2D and 3D CAD modeling or to produce CAD drawings, it is important to understand the basics of the most widely used coordinate systems in CAD softwares.

Majority of CAD systems use the right hand rule, as applied to coordinate systems. Although it is quite rare, some CAD systems use the left-hand rule.

To get a clear illustration of the right-hand rule, do this: as shown in Figure 1 below, stretch the thumb of your right hand—to represent the direction of the positive x-axis; stretch the index finger of your right hand—to represent the direction of the positive y-axis; and stretch the other remaining fingers of your right hand to represent the direction of the z-axis.

Figure 1: The right hand rule, as applied in coordinate systems (Source: Technical Drawing with Engineering Graphics, 15th edition.)

The right hand rule is also related to the popular Cartesian coordinate system which can be used to express drawings in 2D (x, y) and 3D (x, y, z). When using a computer for 2D (two-dimensional) or 3D (three-dimensional) modeling, the face of your computer screen represents the 2D or xy plane, and the z-axis represents the axis pointing directly towards you, as indicated in Figure 2 below.

Figure 2: Z-axis pointing towards your direction, as computer screen face represents the 2D or xy plane. (Source: Technical Drawing with Engineering Graphics, 15th edition.)

Two-dimensional (2D) CAD systems use only the x– and – coordinates of the Cartesian coordinate system, while 3D CAD systems use the x-, y-, and z– coordinates. When representing a 2D system in a 3D CAD system, the line of view is along the z-axis. Figure 3 below shows an orthographic view or 2D drawing produced with only x and y values, with the z-coordinate set at 0.

Figure 3: Computer screen face showing a CAD drawing in 2D or xy plane. (Source: Technical Drawing with Engineering Graphics, 15th edition.)

Orthographic views show only two of three coordinate directions, with the line of view generally considered to be along one axis—usually the z-axis. Two-dimensional CAD drawings are the same: they are produced with and represented by ­x and y coordinates, while the z-axis is the line of view.

As stated, in a CAD system, the 2D (xy)­ plane is aligned with the computer screen, while the z-axis is pointing horizontally and directly towards the person using the computer. However, in machining and many other applications, the z-axis is regarded as the vertical axis. Regardless of the name given to an axis, the coordinate axes (x, y, and z) must be perpendicular to each other (mutually perpendicular).

It is more important to understand how to use axes or coordinates in a model/drawing than to name the direction of default axes and planes. As shown in Figure 4 below, the structure of a 3D object is identified by its x, y, and z coordinates, with the location (0, 0, 0) taken as the starting point from which other points are plotted.

Figure 4: The coordinates for a 3D drawing (Source: Technical Drawing with Engineering Graphics, 15th edition.)

Coordinate systems/formats used to specify locations or points

Although 2D and 3D models/drawings are stored in a single Cartesian coordinate system, a CAD user may be drawn into a situation whereby they would be required to specify locations of some features using other coordinate systems.

The most distinctive of these CAD geometry coordinate systems or location methods are absolute coordinates, relative coordinates, polar coordinates, cylindrical coordinates, and spherical coordinates:

  • Absolute coordinates are locations or points that are at a distance from a common point of origin in a Cartesian System. Locations are established using values on the x-, y-, and even z– axes. For example, in Figure 4 above, the absolute coordinate (3.5, 8, 4) represents a location that is 3.5 units away from the x-axis origin (0), 8 units away from the y-axis origin (0), and 4 units away from the z-axis origin (0). In other words, we can say that the location is (3.5, 8, 4) away from the origin (0, 0, 0). In Figure 5 below, the point of origin (point B) is (0, 0) and there are five absolute coordinates located away from the point of origin (0, 0): A (0, ─4), C (─6, 3), D (6, 4), E (2, ─2), and F (─3, ─5). Generally, absolute coordinates express the position/location of the points of an object with respect to an origin of a given coordinate system.

Figure 5: Absolute coordinates in 2D (Source: Siyavula)

  • Relative coordinates are locations that are expressed in terms of their relative distances away from a reference point that is not the point of origin. Instead of specifying a location from the actual point origin, a relative coordinate can be used to specify a location in terms of the location’s distance away from a previous location.
  • Polar coordinates are 2D coordinate systems in which individual locations or points are defined in terms of an angle (in degrees) and distance away from an axis—the axis could be any of x, y, or z Polar coordinates are absolute if they express a location or point in terms of its angle away from an axis and distance from the origin; on the other hand, polar coordinates are relative if they express a location in terms of its angle and distance away from another location that is not the origin.

Figure 6: Polar coordinate (Source: Geogebra)

  • Cylindrical coordinates are locations that are specified in terms of a radius (r), an angle (θ), and distance a (z) which is usually in the z-axis direction. Any values attached to these terms are relevant for conveying information about locations or points that are on the edge of a cylinder. The radius tells the distance of the point from the center (or origin); the angle expresses the angular inclination of the point away from an axis (for instance, the x-axis shown in Figure 7 below) along which the point is located; and the distance expresses the height of the point on a cylinder. The difference between cylindrical coordinates and polar coordinates is that cylindrical coordinates include a height distance in the z-direction.

Figure 7: Cylindrical coordinate (Source: Mathinsight.org)

  • Spherical coordinates are locations that are expressed by a radius (ρ), an angle (θ) from the x-axis, and another angle () from a 2D (example: either yz or xy) plane. Spherical coordinates express the position of a point on a sphere, with the origin of the coordinate system at the center of the sphere, and the radius indicating the size of the sphere.

Figure 8: Spherical coordinate (Source: Millersville.edu)

How to Enhance Your Creativity in Technical & Engineering Drawings

Although some people are more naturally gifted in creating technical and engineering designs and drawings, everybody has the ability to create at least something significant, no matter how little, and enhance their level of creativity or design ability if they consistently use certain tools or apply certain techniques over a period of time.

Enhancing creativity in technical and engineering drawings is synonymous with enhancing creativity in any type of sport: study and practice is a necessary requirement. Everybody can start at any level of creativity and improve if they are willing to put in an appreciable amount of effort, both mentally and physically.

So, how can anyone develop new ideas or their creativity in technical and engineering drawings? By consistently and conscientiously engaging in technical or engineering drawing visualization, communication, and documentation and producing drawings (traditional and CAD), anybody can be able to develop a higher capacity to generate more ideas and become more creative and competitive in the world marketplace.

This article discusses the following five proven ways that can be used to enhance creativity in technical and engineering drawings, and make it easier to generate new ideas for drawings:

1. By consistently studying the natural world

The easiest way to enhance creativity is to be a student of the natural world: make it a regular practice to meditate on, ponder upon, and draw the objects that exist in the natural world.

By imagining and analyzing how objects are aligned and living things function and interact together in the environment, it would be possible to obtain so much information and inspiration from the natural world and set a firm foundation to unleash and enhance one’s creativity.

It’s important to note that objects such as spiderwebs and beehives have inspired many structural designs, and birds’ wings have inspired the design of aerodynamic structures. There is quite a lot to learn from nature, just by taking time to study living things and natural objects.

2. By learning from mentors or being part of design groups

In today’s world, most people handle technical and engineering drawings in working or team environments which usually have leaders, experts, or knowledgeable people who are usually more creative and familiar with design drawings.

Being part of a design group and having regular interaction with people who are very creative can play an important role in enhancing one’s own creativity and broadening their understanding of what it takes to generate new ideas.

3. By studying artificial or manufactured products

Artificial or manufactured products contain a great deal of information that can be interpreted by studying or observing them, regardless of whether their parts are assembled or dismantled.

By assembling or dismantling manufactured products, one can make evaluations and acquire a greater understanding of how their parts are designed and work together.

By being inquisitive and seeking how to do things differently or making improvements (in efficiency, performance, speed, etc.) in already-existing manufactured products, one could be well on the way to developing new ideas and enhancing their own creativity.

4. By conducting research on patent drawings

Patent drawings for products are great resources for ideas; researching on/studying patent drawings can enhance one’s creativity and broaden their imagination.

People still have access to patent drawings, even though patents, which are issued by governments, protect drawings and grant their respective owners certain rights to exclude other people from using, making, or selling their products for certain periods of time.

Anybody can search a government’s patent office—if available online—for the current design of a product or an idea. For instance, the USA Patent and Trademark Office’s website (www.uspto.gov), which has strict regulations on how drawings should be presented, contains design drawings that researchers can easily reproduce.

5. By surfing the Internet and examining designs or drawings

There are many outstanding sources for designs and drawings on the Internet (World Wide Web). By spending time to visit engineering and technology sites and read/study technical and engineering drawings, any interested individual can become more familiar with drawings and develop or enhance their own creativity.

The following websites can be useful for studying technical and engineering designs and drawings:

i. www.engineeringtoolbox.com

ii. www.practicalmachinist.com

iii. www.howstuffworks.com

iv. www.engnetglobal.com

v. www.mcmaster.com

Measurement Systems used in Technical & Engineering Drawings

Technical and engineering drawings consist of drawn objects or items that will be eventually produced, manufactured, or constructed in real life; the sizes and dimensions of objects are always expressed by using the units of a particular measurement system.

The two most widely used measurement systems are the “Metric System” (also known as the “International System of Units”), and the “United State Customary Units”; both measurement systems consist of a number of units.

Among the two measurement systems, the metric system is the standard that is mostly used around the world, especially for expressing the sizes and dimensions of the lengths, heights, and widths of objects on technical and engineering drawings.

Various professions use measurement systems in technical and engineering drawings to communicate and document their designs; some examples of professions include civil engineering, environmental engineering, mechanical engineering, architecture, landscape design, industrial design, and manufacturing.

1. The Metric System (International System of Units, or SI Units)

The present-day metric system is the “International System of Units” which is commonly referred to as “SI Units”—an acronym from the French phrase “le Système International d’Unités”.

The International System of Units is a measurement system that was established in 1960 after an international agreement was reached; it is presently the international standard used in expressing the sizes and dimensions of objects.

Although some countries still use U.S. Customary Units to a lesser or greater degree, all countries in the world have adopted the International System of Units.

The most widely used units of the Metric System (International System of Units) are the kilometer (mm), the meter (m), and the millimeter (mm). The centimeter (cm) and the decimeter (dm) are also among the units in the Metric System, but they are rarely used on technical and engineering drawings.

It’s quite common to see some industries using a dual dimensioning system to express the units of the sizes of the dimensions of objects on each of their drawings.

For example, they could use “millimeter” and “inch” together on one drawing, even though millimeter is a unit that belongs to the Metric System (International System of Units) and inch belongs to the U.S. Customary Units.

It has to be noted that using a dual dimensioning system to express the units of the sizes of the dimensions of objects can cause a bit of confusion because the sizes derived by using two different systems may contain rounding errors whenever one unit is converted to another.

Most creators of technical and engineering drawings use Metric System units on dimensions in order to maintain consistency between different units that belong to the same measurement system. In standard practice, the following Metric System units and relationships are often used:

1 kilometer (km) = 1000 meters = 10,000 decimeters = 100,000 centimeters = 1,000,000 millimeters

1 meter (m) = 10 decimeters = 100 centimeters = 1000 millimeters

1 decimeter (dm) = 10 centimeters = 100 millimeters

1 centimeter (cm) = 10 millimeters = 0.1 decimeter

1 millimeter (mm) = 0.1 centimeter = 0.01 decimeter.

2. The United States Customary Units

The United States Customary Units is a measurement system that was formalized in 1832 and has been commonly used in the United States since then.

The United States Customary System (USCS or USC) was derived from the English units that were being used in the British Empire before the United States became an independent nation.

The most widely used units in the United States Customary Units are the mile (mi.), the foot (ft.), the inch (in.), and the yard (yd.). The pica (P.) and the point (p.) are also among the units in the United States Customary Units, but they are rarely used.

Although technical and engineering drawings may use either measurement system (Metric System, or the United States Customary Units), they adhere to popularly accepted drawing standards.

The dimensions given in the United States Customary Units can be easily converted to Metric System units in decimal or fractional form. In standard practice, the following units and relationships are often used:

1 mile (mi.) = 1760 yards = 5280 feet = 1.609 kilometers

1 yard (yd.) = 3 feet = 0.9144 meters = 914.4 millimeters

1 foot (ft. or ′) = 12 inches = 0.3048 meters = 304.8 millimeters

1 inch (in. or ″) = 6 pica = 25.4 millimeters = 2.54 centimeters

1 pica (P.) = 12 points = 4.233 millimeters

1 point (p.) = 0.3538 millimeters.

Definition & Types of Technical Drawing (PDF Download Available)

This article defines technical drawing (drafting or projection) and uses different images to illustrate the meaning, and types of technical drawing widely taught in schools and practiced in industries. The eBook/technical drawing PDF document for this article is available for free download at the end of the article (along with a list of world-class technical & engineering drawing/graphics books in electronic form/PDF, available for sale at cheap prices). Both the article and eBook discuss the following topics:

  • 1.0  Definition of technical drawing
  • 2.0 Types of technical drawing: parallel projection (orthographic: first angle, and third angle; oblique: cavalier, and cabinet; axonometric: isometric, dimetric, and trimetric), and perspective projection (1-point, 2-point, and 3-point)
  • 3.0  Objectives of technical drawing
  • 4.0  Purpose of technical drawing
  • 5.0  Application of technical drawing

1.0 Definition of technical drawing

Technical drawing can be defined as the graphic representation of an object, concept, or idea using a universal language that consists of graphic symbols produced with the aid of drawing equipment/tools that can be used to measure straight and curved lines according to specified dimensions, scales, and codes of practice.

Technical drawing is used in many professions (engineering, architecture, manufacturing, construction, estate management, etc.) to draw or draft ideas and different views of physical objects like drainages, culverts, septic tanks, incinerators, houses, etc. Drawing—either artistic or technical—is one of the oldest forms of communication, and is believed to be older than verbal communication. Generally, there are two types of drawings: artistic drawing, and technical drawing:

Artistic drawing

Artistic drawing is the type of drawing that is abstract because its meaning is unique to the person/artist who creates it. In order to understand the meaning of an artistic drawing, one has to understand the artist’s point of view or motivation for producing a particular artistic drawing.

Sometimes, it is necessary to understand an artist in order to understand their artistic drawing because artists often take a unique/abstract approach when communicating through their drawings. This type of approach gives rise to various interpretations when their drawings are exposed to public view.

Regardless of how complex artistic drawings may appear, they express the clear feelings, beliefs, philosophies, and ideas of the artists who create them. Artistic drawings are generally freehand drawings or drawings made without the use of drawing instruments/tools.

Technical drawing

Technical drawing is the type of drawing that is not abstract because it doesn’t require an understanding of what its creator has in mind; rather, it requires an understanding that can only be gained by studying and using universally accepted tools, codes, and conventions applicable to technical drawing.

In addition to the previously stated definition of technical drawing, we can say that technical drawing clearly, precisely, and concisely communicates all important information conveyed by an idea produced in graphic form by the use of universally accepted codes of practice, tools, dimensions, notes, symbols, and specifications.

Download PDF: Types of Technical & Engineering Drawing Lines and Their Uses

Download PDF: Orthographic Drawing Definition, Types, Views, Tutorial & Practice

Technical drawing can be done manually on paper, or technologically on computers. When any idea or object is drawn on a computer, it is said to be drafted by computer-aided design (CAD). One major advantage of using CAD is that revisions can be easily and speedily carried out on any draft.

Any student, architect, engineer, etc., must understand the theory behind projections, dimensioning, and conventions if they wish to become proficient in drafting and interpreting drafts. It is very important for people to understand manual (traditional) drawing/drafting before exposing themselves to CAD softwares. Why? Because an understanding of manual drawings would make it easier to use CAD.

2.0 Types of technical drawing

Technical drawings are constructed on the basis of the fundamental principles of projection. There are two main types of technical drawing or projection: parallel projection, and perspective projection. (Note that each projection has various categories which will be illustrated further below.)

A projection is any drawing, draft, or representation of an idea or object that is carried out after considering views from various imaginary planes. Projections, which are quite similar to the direct views that one can see on televisions, can be used to represent actual objects if the following are employed:

  • the eye of the viewer looking at the object.
  • an imaginary plane of projection as dictated by the direction of the eye(s) of the viewer.
  • projectors or imaginary lines of sight.

The theories behind projection have been widely used to draft 3-dimensional objects on 2-dimensional media such as papers and computer screens. The theory of projection is based on two variables:

  • line of sight.
  • plane of projection: plane from which images can be projected—depending on the axis.
Figure 1: Lines of sight: parallel and perspective projections
Figure 1: Lines of sight: parallel, and perspective projections


Chapter 1_Figure_2_ planes of projection for parallel and perspective projectionssss.jpg
Figure 2: Planes of projection: parallel, and perspective projections

2.1   Parallel projection

Parallel projection is the type of projection in which the lines of sight or projectors are parallel to each other, and also perpendicular to the planes of objects or images. Parallel projection can be categorized or divided into orthographic, oblique, and axonometric projections.

(1) Orthographic projection

Orthographic projection (or drawing) is the type of projection in which 3-dimensional objects are represented in 2 dimensions by projecting planes (consisting of 2 major axes) of objects so that they are parallel with the plane of the medium they are projected on.

Orthographic projection can also be defined as the type of projection in which views are taken on different planes of objects and drawn (or represented) in 2 dimensions as illustrated by the principal views shown in the figures below:

Chapter 1_Figure_3_three major views of orthographic projection.jpg
Figure 3: Three major views in orthographic projection
Chapter 1_Figure_4_six general views of orthographic projection.jpg
Figure 4: Six general views in orthographic projection

There are two types of orthographic projection: first angle projection, and third angle projection:

In first angle projection (i.e., European/international system) the front view is placed at the top of a medium (paper, computer screen, etc.) along with the right side view which is placed at the left side of the front view, while the left side view is placed at the right side of the front view, and the plan (T) is placed alone beneath the front view.

In third angle projection (i.e., American system) the plan (T) is placed alone at the top, while the front view is placed beneath the plan, and the right side view is placed at the right side of the front view, while the left side view is placed at the left side of the front view. (Note that third-angle projection is more popular than first-angle projection.)

Chapter 1_Figure_5_first and third angle projections
Figure 5: First angle, and third angle projections

If you would like to read more details about orthographic projection or drawing, click here.

(2) Oblique projection

Oblique projection is the type of projection in which an object is drawn in 3 dimensions, with each of the 3 dimensions (or major planes) consisting of two lines (or major axes: either xy, or yz, or xz) perpendicular to each other (i.e. 90°), and one of the 3 planes parallel to the plane of paper, or computer screen, etc.

In addition, one of the 3 planes is projected at either 30°, 45°, or 60° to the x-axis. Oblique projection is of 2 types: cavalier, and cabinet projection.

Chapter 1_Figure_6_oblique_cavalier_cabinet projections.jpg
Figure 6: Oblique projection: cavalier, and cabinet projections

In cavalier projection, one of the 3 planes is drafted to represent a plane of an object “according to a given scale”, while in cabinet projection, one of the 3 planes is drafted to represent half of a plane of an object “according to half of a given scale”. A scale is any ratio (examples: 1:10, 1:100, 1:1000, etc.) of the size of an object on paper to the actual size of the same object in real life.

Chapter 1_Figure_7_oblique projection with orthographic views.jpg
Figure 7: Oblique projection of objects expressed in their respective orthographic views

(3) Axonometric projection

Axonometric projection is the type of projection that consists of three-dimensional drawings in which each of the 3 major axes (x, y, and z) of an object is drawn perpendicular to each other by either 30°, 45°, or 60°, and no plane of the object is drawn parallel to the plane of the medium—paper, computer screen, etc. Axonometric projection/drawing can be categorized into three types: isometric, dimetric, and trimetric projections.

Download PDF: Technical Drawing with Engineering Graphics and Design in Practice_Definitions, Importance, and Applications

Isometric projection is a method of projection/drawing in which the edges of 3-dimensional objects are represented by 3 axes perpendicular to each other and inclined to each other by 120° on the plane of media—paper or computer; also, 2 of the 3 axes are inclined at either 30°, 45°, or 60° to any imaginary x-axis on any medium. 

In dimetric projection, 2 angles between any 2 major axes are unequal, while in trimetric projection, the 3 angles between the 3 major axes are unequal. Two different angles are required to construct 2 planes of objects in dimetric projections, while 3 different angles are required to construct 3 planes of objects in trimetric projections.

Chapter 1_Figure_8_Axonometric projection_Isometric_dimetric_trimetric
Figure 8: Isometric, dimetric, and trimetric projections

2.2   Perspective projection

Perspective projection is the type of projection in which objects appear smaller as their distances from an observer increases: objects’ dimensions along a line of sight appear shorter than they actually are.

There are 3 types of perspective projections: 1-point, 2-point, and 3-point projections. One-point perspective projections consist of 1 vanishing point, while 2-point and 3-point perspective projections consist of 2 and 3 vanishing points, respectively.

A vanishing point is a point of convergence where all lines of sight meet.

Chapter 1_Figure_9_one point perspective projection
Figure 9: One-point perspective projection


Chapter 1_Figure_10_two point perspective projection
Figure 10: Two-point perspective projection


Chapter 1_Figure_11_three point perspective projection
Figure 11: Three-point perspective projection

3.0 Objectives of technical drawing

The general objectives of studying technical drawing include the following:

  • to develop skills in using universally accepted tools, symbols, scales, and conventions to draw any visible object or invisible idea on paper, and computer.
  • to understand orthographic and isometric projections and employ them in drafting/drawing ideas and objects using both projections, respectively.
  • to understand and interpret technical drawings, sketches, and working drawings.
  • to develop the ability to use imagination to observe, visualize and draft objects, ideas, or concepts.
  • to develop the ability to produce clean, accurate, neat, and informative drawings in a moderate amount of time.
  • to develop the ability to take on any projects and draw environmental health science, civil, and environmental engineering objects/structures.

4.0 Purpose of technical drawing

To draft and design objects or structures, and assess how they would appear in real life after they are manufactured, fabricated, assembled, constructed, or built. For example, houses, septic tanks, drainages, etc., must be designed and assessed before they are built.

5.0 Application of technical drawing

Technical drawings have wide applications in any field in which planning and designing are required, such as architecture, manufacturing, engineering, construction, environment, estate management, etc.

Sanitarians, surveyors, environmental scientists, and civil/environmental engineers use technical drawings to supervise the construction of layouts, structures, objects, and boundaries for various types of properties (houses, etc.).

Technical drawings are also used in situations where ideas/designs for objects and structures need to be modified, and different 2-dimensional views need to be assembled into 3-dimensional views.

Generally, technical drawings are used by a variety of professions, including but not limited to:

  • engineers
  • architects
  • contractors
  • inventors
  • technicians
  • teachers
  • etc.

If you are interested in downloading the eBook of this article for free, click here. It contains all the information in this article and extra important information on its last page which has a link to images of hundreds of various shapes and sizes of objects in 2 & 3 dimensions, and categorized under different types of projections.

Thank you for reading.


Interested in buying world-class technical and engineering drawing eBooks? Please, read on.

Knowledge is power. The more you read, study, and absorb, the more you can greatly magnify your visualization process and become better. There is no limit.

For further reading and study of topics on technical and engineering drawings/graphics—which is essential for your education/future as an engineer/technologist and—we advise that you make a habit of reading good books.

It’s possible to get a good book from a friend or purchase it either from a local bookstore (offline) or online. In case you’d be interested in purchasing, we have six high-quality technical & engineering drawings/graphics books (eBooks/PDF books) for sale at cheap prices.

Continue scrolling down and you’ll come across their respective titles, number of pages, and lists of chapters. Each book is available for purchase at a cost of $5 (or 2,500 Naira) per book; if you wish to purchase all books, you’ll get a discount of $5 (2,500 Naira) and purchase 6 books for $25 (12,000 Naira) instead of $30 (15,000 Naira).


For the past 3 years, until January 19, 2022, all the eBooks on this site were always available for free download (no payment). However, as from January 20, 2022, we introduced payments to be able to acquire, at least, little funds for the upkeep of our domain name and site maintenance for the benefit of present and future visitors who will read our articles on topics of their interest.

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(3) After confirming payment, we’ll provide you with access to the book(s) which is/are easy-to-read and contain(s) comprehensive coverage of technical and engineering drawing/drafting and design instructions that comply with present-day industry standards.

The titles of the books (arranged in decreasing order of priority [from 1 to 6]—based on our assessment) and their respective number of pages and titles of chapters are as follows:

1. Technical Graphics Communication, 4th Edition, by Gary R. Bertoline, Eric N. Wiebe, Nathan W. Hartman, William A. Ross (1335 pages), 2009

Chapter 1: Introduction to Graphics Communication, pg.5

Chapter 2: The Engineering Design Process, pg.27

Chapter 3: Design in Industry, pg.46

Chapter 4: The Role of Technical Graphics in Production, Automation, and Manufacturing Processes, pg.109

Chapter 5: Design & Visualization, pg.135

Chapter 6: Technical Drawing Tools, pg.187

Chapter 7: Sketching and Text, pg.237

Chapter 8: Engineering Geometry and Construction, pg.305

Chapter 9: Three-dimensional Modeling, pg.399

Chapter 10: Multiview Drawings, pg.488

Chapter 11: Axonometric and Oblique Drawings, pg.577

Chapter 12: Perspective Drawings, pg.631

Chapter 13: Auxiliary Views, pg.652

Chapter 14: Fundamentals of Descriptive Geometry, pg.691

Chapter 15: Intersections and Developments, pg.716

Chapter 16: Section Views, pg.759

Chapter 17: Dimensioning and Tolerancing Practices, pg.818

Chapter 18: Geometric Dimensioning and Tolerancing (GDT), pg.875

Chapter 19: Fastening Devices and Methods, pg.908

Chapter 20: Working Drawings, pg.949

Chapter 21: Technical Data Presentation, pg.1064

Chapter 22: Mechanisms: Gears, Cams, Bearings, and Linkages, pg.1105

Chapter 23: Electronic Drawings, pg.1146

Chapter 24: Piping Drawings, pg.1163

Chapter 25: Welding Drawings, pg.1187

2. Technical Drawing with Engineering Graphics, 15th Edition, by Frederick E. Giesecke, Shawna Lockhart, Marla Goodman, Cindy M. Johnson (1077 pages), 2016

Chapter 1: The World-wide Language for Graphic Design, pg.2

Chapter 2: Layouts and Lettering, pg.30

Chapter 3: Visualization and Sketching, pg.62

Chapter 4: Geometry for Modeling and Design, pg.124

Chapter 5: Modeling and Design, pg.170

Chapter 6: Orthographic Projection, pg.234

Chapter 7: 2D Drawing Representation, pg.284

Chapter 8: Section Views, pg.326

Chapter 9: Auxiliary Views, pg.362

Chapter 10: Modeling for Manufacture, pg.414

Chapter 11: Dimensioning, pg.502

Chapter 12: Tolerancing, pg.546

Chapter 13: Threads, Fasteners, and Springs, pg.592

Chapter 14: Working Drawings, pg.636

Chapter 15: Drawing Control and Data Management, pg.710

Chapter 16: Gears and Cams, pg.730

Chapter 17: Electronic Diagrams, pg.756

Chapter 18: Structural Drawing, pg.780

Chapter 19: Landform Drawings, pg.808

Chapter 20: Piping Drawings, pg.828

Chapter 21: Welding Representation, pg.846

Chapter 22: Axonometric Projection, pg.W870

Chapter 23: Perspective Drawings, pg.W900

3. Engineering Drawing & Design, 6th Edition, by David A. Madsen and David P. Madsen (1104 pages), 2017

Chapter 1: Introduction to Engineering Drawing and Design, pg.2

Chapter 2: Drafting Equipment, Media, and Reproduction Methods, pg.39

Chapter 3: Computer-Aided Design and Drafting (CADD), pg.61

Chapter 4: Manufacturing Materials and Processes, pg.109

Chapter 5: Sketching Applications, pg.162

Chapter 6: Lines and Lettering, pg.181

Chapter 7: Drafting Geometry, pg.205

Chapter 8: Multiviews, pg.228

Chapter 9: Auxiliary Views, pg.259

Chapter 10: Dimensioning and Tolerancing, pg.277

Chapter 11: Fasteners and Springs, pg. 347

Chapter 12: Sections, Revolutions, and Conventional Breaks, pg.387

Chapter 13: Geometric Dimensioning and Tolerancing, pg.409

Chapter 14: Pictorial Drawings and Technical Illustrations, pg.495

Chapter 15: Working Drawings, pg.526

Chapter 16: Mechanisms: Linkages, Cams, Gears, and Bearings, pg.561

Chapter 17: Belt and Chain Drives, pg.601

Chapter 18: Welding Processes and Representations, pg.617

Chapter 19: Precision Sheet Metal Drafting, pg.644

Chapter 20: Electrical and Electronic Drafting, pg.669

Chapter 21: Industrial Process Piping, pg.717

Chapter 22: Structural Drafting, pg.773

Chapter 23: Heating, Ventilating, and Air-conditioning (HVAC) and Pattern Development, pg.847

Chapter 24: Civil Drafting, pg.899

Chapter 25: The Engineering Design Process, pg.950

Engineering Drawing and Design Student Companion Website, pg.973

4. Engineering Design and Graphics with SolidWorks by James D. Bethune (829 pages), 2017

Chapter 1: Getting Started, pg.1

Chapter 2: Sketch Entities and Tools, pg.41

Chapter 3: Features, pg.123

Chapter 4: Orthographic Views, pg.225

Chapter 5: Assemblies, pg.299

Chapter 6: Threads and Fasteners, pg.375

Chapter 7: Dimensioning, pg.439

Chapter 8: Tolerancing, pg.509

Chapter 9: Bearings and Fit Tolerances, pg.605

Chapter 10: Gears, pg.639

Chapter 11: Belts and Pulleys, pg.699

Chapter 12: Cams, pg.725

Chapter 13: Projects, after pg.774

5. Interpreting Engineering Drawings, 8th Edition, by Theodore J. Branoff (530 pages), 2016

Unit 1: Introduction: Line Types and Sketching, pg.1

Unit 2: Lettering and Title Blocks, pg.11

Unit 3: Basic Geometry: Circles and Arcs, pg.15

Unit 4: Working Drawings and Projection Theory, pg.22

Unit 5: Introduction to Dimensioning, pg.39

Unit 6: Normal, Inclined, and Oblique Surfaces, pg.52

Unit 7: Pictorial Sketching, pg.67

Unit 8: Machining Symbols and Revision Blocks, pg.78

Unit 9: Chamfers, Undercuts, Tapers, and Knurls, pg.86

Unit 10: Sectional Views, pg.91

Unit 11: One- and Two-View Drawings, pg.110

Unit 12: Surface Texture, pg.117

Unit 13: Introduction to Conventional Tolerancing, pg.130

Unit 14: Inch Fits, pg.142

Unit 15: Metric Fits, pg.150

Unit 16: Threads and Fasteners, pg.161

Unit 17: Auxiliary Views, pg.181

Unit 18: Development Drawings, pg.190

Unit 19: Selection and Arrangement of Views, pg.196

Unit 20: Piping Drawings, pg.202

Unit 21: Bearings, pg.214

Unit 22: Manufacturing Materials, pg.220

Unit 23: Casting Processes, pg.232

Unit 24: Violating True Projection: Conventional Practices, pg.249

Unit 25: Pin Fasteners, pg.264

Unit 26: Drawings for Numerical Control, pg. 274

Unit 27: Assembly Drawings, pg.280

Unit 28: Structural Steel, pg.289

Unit 29: Welding Drawings, pg.294

Unit 30: Groove Welds, pg.305

Unit 31: Other Basic Welds, pg.315

Unit 32: Spur Gears, pg.328

Unit 33: Bevel Gears and Gear Trains, pg.337

Unit 34: Cams, pg.347

Unit 35: Bearings and Clutches, pg.353

Unit 36: Ratchet Wheels, pg.362

Unit 37: Introduction to Geometric Dimensioning and Tolerancing, pg.368

Unit 38: Features and Material Condition Modifiers, pg.380

Unit 39: Form Tolerances, pg.394

Unit 40: The Datum Reference Frame, pg.402

Unit 41: Orientation Tolerances, pg.415

Unit 42: Datum Targets, pg.432

Unit 43: Position Tolerances, pg.440

Unit 44: Profile Tolerances, pg.461

Unit 45: Runout Tolerances, pg.469

6. Architectural Graphic Standards Student Edition, 12th Edition, by The American Institute of Architects (689 pages), 2017

Chapter 1: Functional Planning, pg.3

Chapter 2: Environment, pg.31

Chapter 3: Resilience in Buildings. Pg.53

Chapter 4: Architectural Construction Documentation, pg.77

Chapter 5: Concrete, pg.93

Chapter 6: Masonry, pg.107

Chapter 7: Metals, pg.125

Chapter 8: Wood, pg.141

Chapter 9: Glass, pg.165

Chapter 10: Element A: Substructure, pg.176

Chapter 11: Element B: Shell, pg.203

Chapter 12: Element C: Interiors, pg.363

Chapter 13: Element D: Services, pg.427

Chapter 14: Element E: Equipment and Furnishings, pg.517

Chapter 15: Element F: Special Construction, pg.565

Chapter 16: Element G: Sitework, pg.581

Appendices, pg.627


Thank you.