Degrees of freedom and constraints

When you first draw a geometric object, it has some specific number of degrees of freedom (DOF); that is, ways it can move or change. For example, a completely unconstrained line has 4 DOF, which may be thought of as its length, its horizontal and vertical locations, and its angle.

Each geometric object has a characteristic number of DOF. Note: To check on the remaining number of DOF and/or flag underconstrained geometry, use the DOF tools located in the upper right corner of the Concept window. DOF is also displayed next to the model name in the Model Explorer.

Geometry	Degrees of freedom
point	2
circle	3
line	4
circular arc	5

Similarly, any figure composed of a set of geometric objects has a number of DOF determined by the sum of DOF of the individual objects less the ways they constrain each other.

Putting a constraint on an object removes one or more DOF. For example, putting a fixed point on one end of a line removes 2 DOF. You can then change only the line's angle or length. Setting a line at angle constraint on the same line removes another degree of freedom, so that it has 1 DOF remaining and only its length is modifiable. Placing a length dimension on the line removes the last DOF. With zero DOF, the line is fully constrained.

You cannot place any further constraints on fully constrained geometry. (However, to change the geometry you can delete constraints and modify the values of dimensions and some constraints.) Similarly, you cannot over-constrain geometry. For example, if the geometry has only 1 DOF and you attempt to add a constraint that removes 2 DOF (such as a fixed point constraint), Concept will display an error message and will not add the constraint.

Keep this in mind as you constrain geometry, and use the appropriate constraints to maintain zero DOF as you progress through sketching a model. To add a constraint to fully constrained geometry, or to add a constraint that would otherwise over-constrain the geometry, remove an existing constraint. Dimensions also act as constraints, reducing the DOF (degrees of freedom). However, unlike other constraints (those found in the Constraints toolbar in the Sketch view), you can apply dimensions to fully constrained models. Therefore, one good option may be to remove one or more dimensions, apply the needed constraint(s), then reapply the dimensions.

The following table can help you decide which constraint to use based on the number of DOF the constraint removes.

Constraint	Values set or DOF reduced
parallel	1
perpendicular	1
collinear	2
tangent to	1
equal to	1
concentric	2
coincident point	2
point on object	1
point on midpoint	2
line at angle	1
fixed point	2