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A constraint in
computer-aided design Computer-aided design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve c ...
(CAD) software is a limitation or restriction imposed by a designer or an engineer upon
geometric Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
properties of an entity of a design model (i.e. sketch) that maintains its structure as the model is manipulated. These properties can include relative length, angle, orientation, size, shift, and displacement. The plural form ''constraints'' refers to demarcations of geometrical characteristics between two or more entities or
solid modeling Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes '' (solids)''. Solid modeling is distinguished within the broader related areas of geometric modeling and ...
bodies; these delimiters are definitive for properties of theoretical physical position and motion, or displacement in
parametric design Parametric design is a design method in which features, such as building elements and engineering components, are shaped based on algorithmic processes rather than direct manipulation. In this approach, parameters and rules establish the relatio ...
. The exact terminology, however, may vary depending on a CAD program vendor. Constraints are widely employed in CAD software for
solid modeling Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes '' (solids)''. Solid modeling is distinguished within the broader related areas of geometric modeling and ...
, computer-aided architectural design such as
building information modeling Building information modeling (BIM) is an approach involving the generation and management of digital representations of the physical and functional characteristics of buildings or other physical assets and facilities. BIM is supported by vario ...
,
computer-aided engineering Computer-aided engineering (CAE) is the general usage of technology to aid in tasks related to engineering analysis. Any use of technology to solve or assist engineering issues falls under this umbrella. Overview Following alongside the con ...
, assembly modeling, and other CAD subfields. Constraints are usually used for the creation of 3D assemblies and
multibody system Multibody system is the study of the dynamics (physics), dynamic behavior of interconnected rigid body, rigid or flexible body, flexible bodies, each of which may undergo large Translation (physics), translational and rotational displacements. In ...
s. A constraint may be specified for two or more entities at once. For instance, two lines may be constrained to have
equal Equal(s) may refer to: Mathematics * Equality (mathematics). * Equals sign (=), a mathematical symbol used to indicate equality. Arts and entertainment * ''Equals'' (film), a 2015 American science fiction film * ''Equals'' (game), a board game ...
length or diameter of circles can be set to have the same dimension (e.g., radius or length). Moreover, the constraint may be applied to solid models to be locked or fixed in a specified space. Concept of constraints is applicable for both two- (2D)
three-dimensional In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (''coordinates'') are required to determine the position (geometry), position of a point (geometry), poi ...
(3D) sketches (including the ones used to create extrusions and solid bodies). The concept of constraints initially emerged in the 1960s and were further developed in the 1970-80s.


History

The original idea of "constraints" was introduced by
Ivan Sutherland Ivan Edward Sutherland (born May 16, 1938) is an American computer scientist and Internet pioneer, widely regarded as a pioneer of computer graphics. His early work in computer graphics as well as his teaching with David C. Evans in that subje ...
in 1975. It is derived from ideas employed in
Sketchpad Sketchpad (a.k.a. Robot Draftsman) is a computer program written by Ivan Sutherland in 1963 in the course of his PhD thesis, for which he received the Turing Award in 1988, and the Kyoto Prize in 2012. It pioneered human–computer interaction ...
system made in 1963. In his work he argued that the usefulness of a
technical drawing Technical drawing, drafting or drawing, is the act and discipline of composing drawings that visually communicate how something functions or is constructed. Technical drawing is essential for communicating ideas in industry and engineering. ...
made by a computer program relied on their structured nature. Compared to traditional drawings that lack this feature the virtual ones had advantages in keeping track of and recalculating dimensions of entities (lines, angles, areas etc.). These ideas were integrated into a CAD system that maintained this structure as a designer manipulated geometric model. In the 1970s the idea was further extended into
three-dimensional space In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values ('' coordinates'') are required to determine the position of a point. Most commonly, it is the three- ...
. In the 80s, a more generalized constraint-based programming language approach emerged and found some application in CAD software. At least one conceptual prototype was built in 1989.


Overview

The purpose of constraints in a design is to control and limit the behavior of the entities and bodies in relation to another entity, plane or body. Effective constraints or mates between two or more bodies may exist at the assembly level of these or between two or more entities in defining a sketch, but adding conflicting, unnecessary or redundant constraints may result in an overdefined sketch and an error message.


Degrees of freedom

Development of a good constraining system might be a time-consuming process. One approach to this situation may be referred as removing
degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinite ...
(DOF). The latter are often represented by (X,Y,Z) coordinates in space. The designer may quickly figure out whether an entity is constrained or not by counting the number of DOFs removed from it.


Types


Geometric constraints

There are several constraints that may be applied between entities or bodies depending on their actual natural geometry (may also be referred to as ’’mates’’):
collinearity In geometry, collinearity of a set of points is the property of their lying on a single line. A set of points with this property is said to be collinear (sometimes spelled as colinear). In greater generality, the term has been used for aligned ...
,
perpendicular In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', � ...
ity, tangency,
symmetry Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant und ...
, coincidency, and parallelism are ways of establishing the orientation of the entity.


Parametrics

More advanced 2D/3D CAD systems may allow application of mathematical relationships between constraints that help to save time on reshaping a model. By way of parametrics a complicated sketch can be adjusted in matters of seconds in predictable ways by only changing one or a few basic dimensions saving a fair amount of working time. Such systems are usually referred as parametric as they create parametric models. Parametrics may also be referred as a design intent, varying geometry, family tables, or as driving dimensions.


Assembly constraints

In assembly modeling, constraints are widely used to control or restrict design parts movements or relationships between each other. Some constraints forces models to respond to changes made in a separate part of a designed product. This enables the design to be responsive as a whole.


Implementations

Implementation of constraints functionality vary with given CAD system and may respond differently to how user applies them. When constraints are added into a sketch some system may be smart enough to apply additional ones based on pre-existing entities automatically. For instance, if the line is drawn next to another one the system may figure to constrain them into being in parallel relative to each other. This sometimes, however, may lead to unexpected results.


Geometric constraint solving

Constraint solver is a dedicated software that calculates positions of points of the 2D sketch based on geometric constraint specified by the user. The purpose of the constraint solver is to find all points' positions with respect to the said constraints. It also usually helps with identifying issues with constraining such as over-constraining etc. so the entire sketch is stable.


Example

Ideally, a rod will need to be ''
concentric In geometry, two or more objects are said to be ''concentric'' when they share the same center. Any pair of (possibly unalike) objects with well-defined centers can be concentric, including circles, spheres, regular polygons, regular polyh ...
'' to a hole drilled through the plate where it will be inserted, so the constraint "concentric" guarantees that the diameter of the rod and the diameter of the hole maintain a common centerline, thus "locking" the manner the rod relates to the hole in the plate; this means that the rod could still slide on either direction since the position of its ends has not been limited. Instance 2 illustrates that the rod may still rotate along its centerline while it slides up or down.


See also

* Constraint (classical mechanics) * Geometric constraint solving *
Geometric dimensioning and tolerancing Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a Symbolic language (engineering), symbolic language on engineering drawings and computer-generated Solid modeling, 3D models tha ...
*
Parametric modeling Procedural modeling is an umbrella term for a number of techniques in computer graphics to create 3D models and textures from sets of rules that may be easily changed over time. L-Systems, fractals, and generative modeling are procedural modeli ...
* Preliminary design & detailed design


References


Sources

* ''Introducing AutoCAD 2010 and AutoCAD LT 2010'' (pages 117-122), by George Omura. 2009; 1st. Edition. Wiley Publishing, Inc., Indianapolis, Indiana. Hard Cover; 384 pages. * ''Autodesk® Inventor® 2011 Essentials Plus'' (pages 312-341), by Daniel T. Banach; Travis Jones; Alan J. Kalameja. 2011; Delmar/Cengage Learning, Autodesk Press. Printed in the United States of America. ; {{ISBN, 1-1111-3527-4. New York. Computer-aided design software Computer-aided design Design engineering