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.

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Types of 3D Models Used in Technical & Engineering Drawings and Designs

There are three main types of 3D models or modeling methods integrated into CAD systems for a single software package, and each has its own strength and weakness: wireframe models/modeling, surface models/modeling, and solid models/modeling.

Although there are other types of 3D models that can be used in CAD systems for technical & engineering drawings/graphics and designs, most of them exist as a subset of the three main types of models, or they can be used individually for specific purposes.

1. Wireframe model

The Wireframe model/modeling method was the first 3D modeling method to be established. Wireframe models are often used as a starting point in 3D modeling since they eventually create a “frame” for 3D structures.

A wireframe is a three-dimensional model that only includes vertices and lines; it doesn’t contain surfaces, textures, or lighting like a 3D mesh. Instead, a wireframe model is a 3D image comprised of only “wires” that represent three-dimensional shapes.

Generally, “wireframe model/modeling” refers to any computer screen display of a model in regard to only the edges and contours of the object or artifact it represents.

Wireframes provide the most basic representation of a three-dimensional scene or object: using simple lines and curves, a wireframe model can represent a “skeleton” for building a 3D object.

Wireframe models express the contours and edges of objects by using circles, lines, and arcs orientated in 3D. The portrayal of contours and edges in the wireframe model was developed from 2D modeling practices.

The wireframe modeling method derived its name from the process of mentally or visually representing objects, sculptures, or carvings with wires as shown in Figures 1, 2, and 3 below.

Figure 1: The Wireframe model (lines, arcs, and curves in 3D) of an artefact (Source: Quora)

Figure 2: The Wireframe model of a car (Source: DepositPhotos)

Figure 3: The Wireframe model of the world (Source: PngEgg)

A wireframe model can be created in the same way a 2D CAD drawing is created. Simple geometric tools (such as circles, lines, and arcs) are drawn in 3D to express each edge where the surfaces on an object intersect.

Wireframe models don’t look as realistic or “close to reality” as some other models because they incorporate surfaces or boundaries that are often shaded.

A wireframe model can help to visualize 3D equipment which is more difficult to visualize when represented or expressed in 2D. In many cases, it is advisable not to overlook wireframe during the design of an object.

The major advantage of wireframe 3D models is that they provide a single and clear understanding of some shapes and make it possible for objects not to be represented unambiguously, especially when expressed using multi-views.

2. Surface model

CAD surface modeling/models specify limits and define an artifact or shape by using the stored information about its surface to create a realistic visual or mental picture or impression.

However, surface models do not assign any material thickness to surfaces, and the outer surfaces of objects (balls, boxes, cubes, etc.) can be shaded between or around the limits specified and defined by surface models.

Generally, surface models focus on modeling the outer/outside parts of objects, artefacts, shapes, or products, instead of the inner and mechanical parts within.

Figure 4: Surface modeling for Audi car (Source: GrabCAD)

The information (or definitions) about an artefact is stored in the CAD database. This information represents the outer or external boundaries of surfaces that could form part of the 3D model. (The process of storing the definitions of surfaces in the database is called “boundary representation” [BREP].)

To create a surface model, an entire surface doesn’t need to be created at once: only pieces or “patches” are combined into a continuous model. In summary, surfaces can be created from bits or pieces technically referred to as “patches”.

Each patch can be interpolated or approximated like a spline curve. A patch can be regarded as a “coon’s patch”—this refers to an interpolated surface that is defined by four boundary curves which have points that can be interpolated using mathematical methods.

The surface models employed in computer-aided manufacturing (CAM) need to operate at a high level of accuracy to produce really good and smooth surfaces that may require fewer control points to make their curves more fluid.

3. Solid model

The term “solid models or modeling” is a technique used by solid modelers or designers to create a representation (called a solid) of a solid object. Unlike surface and wireframe models, solid models ensure that objects are geometrically correct and all surfaces meet precisely. 

Solid models not only represent the edges, vertices, and surfaces of the part, they also help determine the locations of points in space within an object or outside it.

In terms of storing information concerning the volume occupied by an object of artifact, solid models go way beyond surface models. In fact, solid models record information about the vertex and edge of the 3D wireframe modeler, the surface modeler’s surface definitions, and volume.

Because many solid modelers store the operations used to produce features, it is possible to quickly edit features of objects and easily test, define, and refine the designs that solid models represent.

Figure 5: Three technical/engineering drawing projections and their corresponding solid (shaded) model (Source: ResearchGate)

Solid models are easy to understand and highly accurate and visual if modelled accurately. Some 3D solid models are often more capable of replacing physical models.

However, 3D solid models work better with analysis packages and contain all the information about the volumes of objects which are very important in many calculations.

During the refinement process of designs, the solid model can be used as a foundation from which centroid, mass properties, moments of inertia, and weight can be estimated as many times as may be needed.

Figure 6: Difference between Wireframe model and Solid Model (Source: LearnMech)

The behavior of an object or its system can be simulated from the information stored in the solid model which can further provide useful information that may be required for other analyses.

Because solid models define entire objects, their information can be used by finite element analysis (FEA) softwares to automatically generate FEA meshes and break up complex objects into smaller objects, thereby making it easier to even calculate material properties such strain, stress, and heat transfer.

Some solid modeling softwares and FEA are structured to provide this and similar types of analysis. Other modeling softwares even permit direct model optimization based on results from FEA, and could be used to produce a new version of the model which the modeler can review further.