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Lesson 5.8: Variables, Expressions, and Equations

Technical Context​

An isolated dimension records a value but not the relationship that produced it. The model also has no way to know which other dimensions should change with that value.

Variables and equations record those relationships so one intentional change can update the dependent geometry.

Variables​

A variable is a named value defined once and used everywhere.

Instead of typing 3.2 into eleven holes, define #clearanceM3 = 3.2 mm and use #clearanceM3 in all eleven. When you discover the printer runs tight and you need 3.4, you change one line.

Name variables for what they mean, not what they equal. #plateThickness survives a change from 3 mm to 4 mm. #three_mm becomes a lie.

The variables worth defining in nearly every FTC part:

VariableWhy
#plateThicknessAppears in extrudes, ribs, fillets, and every mating part
#clearanceM3Every clearance hole, changed in one place when tolerance shifts
#railPitch15 mm on 15 mm extrusion; drives every pattern spacing
#motorBoltCircleVendor-defined; a variable stops it being remembered wrongly

Expressions​

An expression is a calculation in a dimension field rather than a typed result.

Onshape evaluates arithmetic wherever a number is accepted, so #plateThickness * 2 is a valid entry. This matters because the expression records the relationship. A pocket depth entered as #plateThickness - 1 mm stays 1 mm from breaking through when the plate changes thickness. Entered as 2 mm, it breaks through the moment the plate becomes 2 mm.

Units are part of the value. #railPitch is 15 mm, not 15. Onshape will refuse to add a length to a bare number, which is a feature, not an obstacle: it is catching the unit error before the part is made.

Type the reason, not the answer

If you find yourself doing arithmetic on paper before typing a dimension, type the arithmetic instead. The number is the same today and it stays correct tomorrow.

Equations Between Dimensions​

An equation links dimensions so one drives another. This is where a model starts encoding design rules rather than a single design.

Useful relationships in FTC:

  • Hole edge distance = #holeDiameter * 1.5, so holes never end up too close to an edge to hold
  • Rib thickness = #wallThickness * 0.6, a standard ratio that avoids sink and keeps the rib printable
  • Pattern instance count = floor(#railLength / #railPitch), so the hole count follows the length automatically

The last one is worth dwelling on. A rail that gets 60 mm longer should gain four holes. With an equation it does. With a typed count of 12 it does not, and nobody notices until the rail is cut.

A Worked Example​

A gearbox plate, driven properly:

#plateThickness  = 3 mm
#clearanceM3     = 3.4 mm
#boltCircle      = 31 mm          // vendor spec for the motor face
#edgeMargin      = #clearanceM3 * 1.5
  • The plate extrudes #plateThickness symmetric about the mid-plane
  • The motor bolt holes are a circular pattern on #boltCircle
  • The holes are hole features of #clearanceM3
  • The plate outline is #boltCircle / 2 + #edgeMargin from the centre

Change the motor and you change #boltCircle. The pattern moves, the outline grows to keep the edge margin, and the plate is still correct. Nothing else is touched.

A model with no variables is a drawing

If changing one number requires visiting eleven features, the model has recorded a single design rather than the rule that produced it. That is fine for a part that will never change, and no FTC part never changes.

Fill-in-the-Blank Practice​

  1. A named value defined once and reused throughout a model is a __________.
  2. Entering #plateThickness - 1 mm in a depth field rather than a typed number records the __________ between the two dimensions.
  3. In Onshape a length variable must carry its __________, so 15 mm rather than 15.
  4. Making a pattern's instance count follow the length of a rail requires an __________ rather than a typed count.
Show answers
  1. variable
  2. relationship
  3. units
  4. equation
Practice

Graded exercises with hard numbers and self-checks are in CAD Practice Exercises.

Exercise​

Take a plate you have already modelled and replace every typed number with a variable or an expression. You should end with three or four variables at the top and no bare numbers below them.

Then change #plateThickness by 1 mm. Everything that should have moved should have moved, and nothing else.

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