**Kris Kasprzak Applications Engineer Unigraphic Solutions Inc. Madison, Ala. kkasprza@ugsolutions.com**

The only thing constant in engineering is change. Take a look at the number of design iterations mechanical parts and assemblies endure during development. Designs begin changing almost from their conception. Even nonengineering groups, such as the marketing department, get involved making requests for durability and cost limits. Design methods must accommodate changes quickly and reliably. This capability is often the key to reducing the time to market for a new product.

Unfortunately, some engineers find themselves in an endless design loop because unreliable changes have compromised the original ideas. Consider how someone might invent a mechanical product. They first envision the product and then create CAD models of its parts and assemblies. Once complete, the model or prototype can be tested for operations and aesthetics. When the design is not up to expectations, the changes begin.

Most mature CAD systems include parametric features to help with the changes. The features maintain design intent by managing design variables. The technology simply lets users tell the CAD system how the model should react with changes. The whole idea behind the technology is to predict or control the outcome of a design change.

It works this way: As you create a CAD model, you apply constraints or relationships between geometric elements to define how they interact. Doing so defines design intent to the CAD system. It sounds simple enough. The difficulty comes in applying relationships to accurately control the intent of the design.

**Applying parameters**

A few examples can help explain the concept. The first one illustrates the problems of changing a part without constraints or a design intent. The illustration *A basic bearing pillow block* is constructed by extruding a 2D cross section into a thickness. Rounds and holes add detail. An experiment makes a simple change to the height of the left flange.

Typically the height of both flanges should change simultaneously. After the change, the illustration *Not the design plan* shows the irregular shape of the flanges. The reason for the end result is simple — the system didn’t know the design intent. Constraints or relationships can convey design intent to a model. A few CAD systems without constraints let users move geometry to required locations without establishing relationships. In a case this simple, it’s not difficult to imagine the number of steps required to change the flanges and support for the shaft. It will be necessary to establish associativity between the model elements to both simplify the process and maintain design intent after changes. Doing so first requires identifying the main design variables. For this type of part, they are the shaft diameter, mounting-hole spacing, and block width. For larger shaft diameters, the overall height and width must increase. The length and height of the mounting flanges are to remain equal and the shaft is to remain centered about the block. After defining independent variables, we can add relationships to the model that help control these dependent variables.

Constraints fall into geometric and dimensional categories. Start by adding geometric relationships. In the illustration *Applying relationships*, the plus-sign symbols tell the system and user the element is to remain either horizontal or vertical. Dotted lines applied to key points of some elements force them to remain aligned either horizontally or vertically. For example, to force the top arc to remain centered about the block, apply a vertical alignment relationship to the center of the arc and the midpoint of the base. In addition, the added equal-sign symbols force elements to remain equal in length. The equal symbols applied in conjunction with other relationships ensure that the face of the block is symmetric. The “O” at the endpoints of the arcs guarantee tangency. Most production CAD systems let users work with several types of geometric relationships such as parallel, perpendicular, connect, and concentric. There are different symbols for each of these.

The CAD system called Solid Edge produced the models in this article. It applied the constraints while a user constructed the geometry. For example, as the shaft hole was drawn, the system added a relationship connecting the center of the hole with the center of the arc. These relationships were deleted earlier to show what happens after making changes to underdefined designs.

With the relationships in place, we can make reliable design changes. For example, increasing the overall flange width keeps the upper and lower flange width equal and the shaft hole centered. Applying a few geometric constraints based on the design variables preserves the intent, somewhat. We have established design control from a geometric standpoint, but now need to add dimensions for additional control.

Dimension constraints fall into driving and driven categories. A driving dimension controls the model; a driven dimension is controlled by the model. From the pillow-block example, we need to control the size of the mounting flanges, top arc, shaft-hole size, and height of the shaft hole by applying driving dimensions to them.

The dimensions we don’t want to control, but would like to know the values of, are the overall height and angle of the face. Apply driven dimensions to them. The software places inspection boxes on both the angle dimension and the dimension to the silhouette edge in the illustration A parametric model.

With both geometric and dimensional constraints in place we can make predictable design changes. Dimensional changes now maintain the design intent and let users accurately predict how the rest of the model changes. The illustration A radical change under control, shows results from a design change in which the flange width and the shaft-hole height are modified. The changes maintain the integrity of the pillow block. Notice the significant difference in results from the design change in Not in the design plan and the last one.

Applying dimensional and geometric constraints has so far been a straightforward process. But as with most designs, a dimension may need to control more than just the element to which it’s applied. For example, if the shaft diameter were to control several other parameters, we could simply change one dimension and have the entire model correctly update. Consider the speed and flexibility in being able to enter some of the values for the design variables and have the system generate the part.

**Smart variables**

A few CAD systems include functions that assist in this process. The system used in this example also includes a built-in table similar to a spreadsheet. It allows establishing equations to drive dimensional constraints. This example sets up a few design parameters so the user simply enters a shaft diameter and the system generates a new pillow block.

For the pillow-block example, the block width equals 0.75 times the shaft diameter, and the distance between the arc and the shaft circle is 30 mm. The flange height is constant. The equations are entered into the formula column of the variable table in the first illustration. The flange thickness remains constant because no equation defines it. Thanks to parametric features, users need only change the shaft-hole diameter and the system does the rest. Additions might include equations that generate a model based on material parameters.

This is just a simple example of parametric design. Regardless of the application’s magnitude, the concepts are the same: identify design variables and apply model relationships to control or predict changes.

If your CAD system has parametric capabilities, creating intelligent models can be tis easy. Your job is to indicate what the design variables are and let the system manage the rest. This can be more challenging than it sounds because some CAD systems require complete constraint definition as designs develop. That means you must know the variables before you start. More advanced systems let you add relationships as design variables are recognized. Additional functions within some CAD systems let users create and store several designs within the same file (family of parts). Regardless of the methods, the end result of parametrics is the