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Parametric sketching with Apple Pencil

A parametric sketch is one where the sizes and relationships drive the shape. Change a number and the drawing follows. It’s how every CAD program builds parts, and it works just as well in 2D on an iPad, with a Pencil instead of a mouse.

Dimensions and constraints

Two things pin a sketch down. Dimensions set sizes: a length, a radius, a diameter or an angle. Constraints set relationships: this line is horizontal, these two are equal, that arc is tangent to this line. A dimension that controls the geometry is a driving dimension. Edit it and the geometry moves to match.

The usual constraints are much the same in every program:

Degrees of freedom

Every point in a 2D sketch can move two ways, across and up. Each constraint or dimension takes away one or more of those freedoms. When none are left, the sketch is fully defined: nothing can move unless you change a number. Fully defined sketches are the ones that behave when you edit them later.

A rectangle with horizontal and vertical constraints on its sides, a width of 80 and a height of 40, and its lower-left corner fixed, so it is fully defined H H V V 80 40 0 degrees of freedom: fully defined
Four corners have 8 freedoms. Horizontal and vertical take 4, the two sizes take 2, and fixing a corner takes the last 2.

Over-constrained

Add one constraint too many and the sketch can’t satisfy all of them, such as a rectangle with a width of 80 and its top and bottom set equal to two different lengths. Good tools tell you which constraint is in the way, rather than just refusing. Remove or replace the one you care about least.

A good order to work in

  1. Shape first. Horizontal, vertical, parallel, equal and tangent. These rarely change.
  2. Then sizes. Dimension from one edge or a centreline, not from feature to feature, so a change doesn’t ripple.
  3. Then position. Fix one point, or tie the sketch to a datum.
  4. Don’t double up. If two lines are equal, dimension one of them.

Parametric sketches in PencilCAD

PencilCAD reads the marks you’d make on paper, so you can constrain a sketch without leaving the Pencil.

  1. In Settings → Tools, choose CAD. Sketch with Line and Shape, or turn on Hold to make lines and hold a scribble still to turn it into lines.
  2. Pick Constrain. Write a size beside a line, such as 120, 3 1/2, 2′6″, R20, ⌀40 or 45°. It becomes a driving dimension and the shape resizes.
  3. Draw marks: two ticks for equal, arrows for parallel, a corner box for square, a loop around two ends to join them. Or tap Constrain again to pick from all thirteen constraints.
  4. Tap Finish to add whatever the sketch is missing, at the sizes it has now. A fully defined sketch turns green.
  5. If a new constraint clashes, the card names the one in the way. Tap Replace to swap them in one undo step.

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