Engineering & Technology · Digital Design, Simulation & Prototyping
Parametric geometry, CAD models and design intent
Two digital plates look identical: each is 80 mm long with holes at 20 and 60 mm. One designer meant “keep the holes a quarter of the length from the ends”; another meant “keep a 20 mm end margin”. Their first images agree. Their next design changes will not.
Review sketches and models, measurement evidence and design decisions. The numerical lesson introduces its own midpoint calculation; no prior finite-element mathematics is assumed. The thermal expression is supplied to compare assumptions, not to prescribe an experiment or equipment setting.
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Express a simple geometric relationship as parameters and predict how two modelling choices respond to a change.
A model can store a rule as well as a shape
Computer-aided design, or CAD, represents geometry for design communication and further work. A parametric model lets selected dimensions and relationships determine geometry. A parameter is an explicitly identified value, such as the plate length L. A geometric constraint might preserve perpendicular lines; a dimension might drive a distance. A displayed measurement can also be a result rather than a driving input.
The rule is part of the design intent: what relationships should survive an edit? “Keep these holes symmetric” is different from “freeze their absolute coordinates”. Neither rule is universally better. Choose it from the function and interfaces, then make it understandable to someone who did not create the model.
An edit reveals a hidden assumption
Our original plate is 20 mm wide, with its hole centres on y=10 mm. Rule P sets x=L/4 and x=3L/4. Rule M keeps each centre 20 mm from its nearest end, so x=20 and x=L−20. With L=80 mm, both give 20 and 60 mm. With L=100 mm, P gives 25 and 75 while M gives 20 and 80.
The figure deliberately distinguishes the rules using different circle symbols. It does not specify different hole diameters. To judge which rule is appropriate, ask whether the mating system follows proportional spacing, a fixed end interface or something else. A regenerated shape can be internally consistent yet fail its intended interface.
Check geometry before asking it to prove performance
A sensible parameter range matters. At L=40 mm, Rule M places both centres at 20 mm; below 40 they reverse order. A model may need a domain restriction or a different rule. Trying boundary values exposes assumptions that one nominal image conceals. Saving a successful regeneration is useful evidence of a geometric check, with its tested parameter range.
A geometric model alone does not establish material strength, manufacturing capability, assembly variation or usability. A solid that looks complete may still omit tolerances, material data or important contacts. When exporting or simplifying it for analysis, check units, reference directions and the features retained. The analysis model is a further representation that needs its own justification.
Calculate the change before opening a CAD tool
Increase L from 80 to 100 mm while keeping W=20 mm. Under P, the first centre moves from 20 to 25 mm and the separation grows from 40 to 50 mm. Under M, the first centre stays at 20 mm, the second moves to 80 mm and separation grows to 60 mm.
If a companion part requires a fixed 60 mm hole spacing at the new length, M meets that one nominal coordinate condition. This does not establish overall fit: hole sizes, location variation, orientation and assembly conditions still need their own requirements and evidence.
Try the reasoning
Do matching initial pictures prove matching design intent?
Show the answer and reasoning
No. Different rules can produce the same nominal geometry but respond differently to a change.
At L=120 mm, what does Rule P predict?
Show the answer and reasoning
Centres at 30 and 90 mm, separation 60 mm. Rule M instead gives 20 and 100 mm, separation 80 mm.
Why try a parameter value near a limit?
Show the answer and reasoning
It can reveal collapsed, reversed or invalid relationships that a nominal successful regeneration does not expose.
What to carry forward
Choose and test the relationships that should survive change; a plausible shape is one part of the design evidence.
References
Teaching resources and research supporting this lesson’s explanations and examples.