*By Jaiprakash Pandey*

Geometry in parametric drawing is constrained with a set of mathematical and geometrical rules with respect to other geometries of the drawing. A parametric approach to design offers a big list of advantages over classical non-parametric design approach.

Consider a scenario where you have completed designing a part having complex geometry. Suddenly you realize that something needs to be changed in the drawing. Making that change will affect your complete design, and with each change you need to update its dependent component geometry manually.

That’s a tedious enough job by itself, but what if the same issue happens with an assembly drawing? You get the point; it will be a nightmare to update every part and then the overall assembly to ensure changes are properly reflected everywhere!

It’s also clearly apparent that this task will be error prone and it will cost you extra design hours.

Now, if the design is made with a parametric approach, then a design change will automatically update any dependent geometry, eliminating the chances for human error and, best of all, saving you lots of design editing time.

# Parametric Feature in AutoCAD

The parametric constraint feature was added to AutoCAD 2010, making drawing with AutoCAD much more efficient. With AutoCAD you can apply geometric and dimensional constraints to your drawing, and with the parameters manager you can also add formulas to your drawing. These formulas can be used to define relationships between different parts of the geometry.

I will explain the usage of parametric features on a sample 2D drawing. I will demonstrate it using both geometric and dimensional constraints, and also how to use the parameters manager for adding formulas to dimensional constraints.

# Applying Geometric Constraint

Let’s take, for example, this geometry where we have a circle inside a polygon in such a way that the circle is tangent to both the non-parallel sides of the polygon. This geometry is completely unconstrained and changing the length of any side of the polygon or radius of the circle will break the tangency in the geometry.

To ensure that the relationship between the circle and the non-parallel lines is maintained, I will apply a tangent geometric constraint between them.

Select the **Parametric** tab from AutoCAD’s drafting and annotation workspace and click on **Tangent Constraint** from the **Geometric** panel. Next click on circle, then on bottom horizontal line. A new tangent constraint will be added between the objects and a box containing an icon of tangential constraint will appear near the point of tangency. Repeat the process of applying a tangential constraint between the circle and top inclined line of the geometry.

Now the circle is constrained with respect to both lines but the polygon itself is not constrained. A change in the circle geometry will force the polygon to change.

In order to constrain the polygon, start with the **Fix** geometric constraint and click on the left endpoint of the bottom horizontal line. This will ensure that polygon’s bottom left point will remain fixed in space. To ensure that the bottom line remains horizontal, select **Horizontal** constraint and click on the bottom horizontal line of polygon.

To ensure that both vertical lines of the polygon remain perpendicular to the bottom horizontal line we need to apply a perpendicular constraint. Select **Perpendicular** from the **Geometric** panel and click on the left vertical line of polygon and then on the bottom horizontal line. Repeat the process with the right vertical line as well.

Now that all the relevant geometric constraints are in place, we need to apply dimensional constraints to make the drawing fully constrained.

# Applying Dimensional Constraint

As the name suggests, dimensional constraints will restrict dimensions of geometry to a specified value. When that value is subsequently changed, the geometry will also update itself to match.

Select **Linear** from **Dimensional** panel and now click on bottom horizontal line of polygon near left end, then click at right end of line and place the constraint at a convenient location. Repeat the process for both vertical lines of the polygon as well.

Now the geometry is almost completely constrained except for the circle in the middle; the radius of the circle is still not fixed and it can be changed. To constrain the radius of circle select **Radius** from **Dimensional** **Constraints** panel and click on circle, then place the parameter at a suitable point.

Now that the geometry is fully constrained, your final geometry after applying geometric and dimensional constraint will look like this:

# Using Formulas to Manipulate Geometry

Using formulas, the relationship between different parts of the geometry can be established in such a way that if the geometry changes, it does so in a controlled manner with respect to the formulas defined.

Let’s define some formulas so that all dimensional parameters of the drawing will be controlled with the radius of circle. Click on **Parameters Manager** on the **Manage** panel of the **Parametric** tab. Alternatively, you can also use the **PARAMETERS** command. Once the command is active, you will see a palette as shown below:

You will see a list of all dimensional constraints used in the drawing. Double click in the blank area under the last constraint and a new user parameter will be added with default name *user1*. Change the name of the parameter to A by double clicking on its name. Now double click in front of parameter A under expressions column and enter this expression: ((rad1*2)+1)/2.

This expression will define value of parameter A with respect to the value of rad1. Similarly, add one more user parameter, give it name B and enter expression (rad1^2)+1.

Then create a third user parameter, C, and assign an expression B*2. This expression will ensure that the value of parameter C will directly depend on parameter B, which is in turn is dependent on the value of rad1.

Now our drawing is ready for accepting user parameter values. Now go to the dimensional constraints in the **Parameters Manager** palette and double-click on the d1 constraint in the expression column and change its value to C. Similarly, change the value of d2 to A and d3 to B. After making all these changes, this is how parameters manager palette will look:

Now all of the dimensions of geometry are directly dependent on the value of rad1 parameter.

You will notice an fx symbol before the name of every dimensional constraint on the drawing. This symbol appears when a dimensional constraint references one or more user parameters. These constrains appear only in the drawing area; they will not appear in your plot. The fx symbol facilitates recognition of parameter-dependent constraints to avoid accidental changes of these values or to understand situations where you might over-constrain the geometry.

To test our drawing, change the value of the rad1 parameter by double clicking on it and assign a value 3 to it. You will notice that complete geometry changes according to the defined formulas or expressions of **Parameters Manager** palette.

# Conclusion

The parametric drawing feature of AutoCAD makes your drawing changes very efficient and fast. For a beginner it might be little confusing, but with practice this feature will add much value to your drawing.

With this feature, design change becomes a very seamless task and it also minimizes chances of making mathematical errors while doing manipulations. If you have not yet tried this feature, I recommend you give it a shot. I am sure you will not be disappointed with the results.

** **

## About the author

Jaiprakash Pandey is a CAD corporate trainer and designer currently working with the engineering design consulting company, Ramboll.

He is an Autodesk AutoCAD Certified Professional, Autodesk Expert Elite and mechanical engineer. He also develops video courses for many online tutoring platforms and occasionally writes for *AUGI World *magazine. You can reach him on his blog Thesourcecad.com.