Parametric CAD tools are notoriously difficult to use. A lot of this
difficulty is essential; no matter what the software does, it can't save
you from understanding the geometry.
This tutorial is therefore very long, even though we are drawing
a trivial part. Many of the issues discussed here are not specific to
SketchFlat. They would apply for any CAD tool, or even for a drawing
that is dimensioned by hand.
On the drawing, the part is described with dimensions. A dimension
might indicate the length of an edge, or the angle between two lines,
or some other geometric relation (e.g., that two circles are concentric).
Given enough dimensions, the part is completely described. It's typical
to make the drawing approximately to scale, to give the viewer some
rough idea of what the part is supposed to look like, but that's just
a courtesy. The dimensions alone must describe the part completely.
Objective
We will start with a rough sketch of a part, and draw it in SketchFlat.
We will then export this drawing as a DXF. From there, we might send it
to a laser cutter, or to some CAM software for toolpath generation,
or to some other CAD tool.
This is our part:
I'll call it a trapezoid. (The word trapezoid has multiple
definitions. Here, I will use it to describe a foursided polygon, with
two edges parallel and the other two equal in length.) The two parallel
sides are horizontal; the bottom one is four inches long, and the
top one is five inches long. The trapezoid's altitude (i.e., the
distance between the two parallel edges) is three inches.
Of course, nothing in my pencil drawing says explicitly that the top
and bottom edges are parallel, or that the left and right edges are equal
in length. For a humanreadable drawing, we can assume that they are.
When we draw the part in SketchFlat, we will have to specify
this explicitly; the software cannot guess our intent.
Reference Coordinate System
I start with an empty sketch. The sketch will always contain two
datum lines. These lines intersect, and their intersection is
marked with a datum point. A datum line does not have endpoints;
it is infinitely long. In SketchFlat, datum lines are drawn dashed. One of
the datum lines is horizontal, and the other is vertical. The point is drawn
as a filled square.
These are our references. Everything in the drawing will be
dimensioned with respect to these two datum lines and that point. These
references form a coordinate system; the horizontal line is the xaxis,
the vertical is the yaxis, and the point is at the origin. It's not
possible to move or redefine the references. The references (and only
the references) are drawn in blue; other datum entities, that you can
define yourself, are drawn in green.
Ultimately, the coordinate system in which the part is described will
have physical meaning. The axes might correspond to the physical axes
of a CNC machine, and the origin to the machine's `home' position,
as measured with limit switches. When we're drawing the part, though,
we can probably choose the coordinate system for our own convenience,
and rotate or translate the part as needed before exporting the file. (In
SketchFlat, you can do that using a derived operation.)
A good choice of position and orientation will make the part easier
to draw. If the part has symmetry, then we might be smart to draw it
symmetric about one of the coordinate axes. In general, there will
be many different ways to draw and dimension a part; the choice is
subjective. A careful choice of dimensions will clearly show the
design intent.
Our dimensions are given in inches, so we should work in inches.
SketchFlat can work in either inches or
millimeters, and you can switch between the two freely. Choose View >
Dimensions in Inches, if it isn't selected already. Inch
dimensions are always given with three digits after the decimal point
(e.g., 1.500). Millimeter dimensions are given with two (e.g., 38.10).
Sketching the Part
To start, we will draw
a quadrilateral. SketchFlat provides various geometric primitives,
including line segments, circles, arcs of a circle, and cubic splines. In
this case, we want four line segments.
In SketchFlat, choose Sketch > Line Segment, and then click somewhere on
the drawing to start the line. Click three more times, to create the four
line segments. Before clicking the fifth time, move the mouse pointer
over the first point that you drew; this point will be highlighted
yellow. Then click the mouse; SketchFlat will automatically constrain
the lines that you just drew into a closed polygon, and stop drawing.
(So you've actually just drawn four line segments, and four
pointcoincident constraints, that constrain the line segments into a
closed polygon. You could have drawn the four lines separately, and then
added the constraints explicitly yourself—to stop drawing lines
before you've made a closed figure, hit Escape. But here, it's quicker
to let SketchFlat add the constraints automatically.)
You can pan the viewport by centerdragging with the mouse, and zoom
with the scrollwheel. To recenter and rezoom to make your sketch fill
the window completely, choose View > Zoom To Fit, or press `F'.
The small magenta circles represent the pointcoincident constraints.
If you drag one of the points, then the figure will stay closed, because
it is constrained that way. But aside from that, there are no constraints;
you can drag those four points anywhere that you want. This freedom is
indicated by the dark yellow tictactoe marks around each point. The
vertical
marks indicate that the point can be dragged vertically, and the
horizontal marks indicate that the point can be dragged horizontally.
In this case it has both, so the point has two degrees of freedom.
Once we start adding constraints, a point might have one or zero degrees
of freedom. A point with one degree of freedom will move, but only along
some line or curve. A point with zero degrees of freedom is locked, and
won't move at all.
Constraining the Part
I tried to draw my trapezoid approximately right, but it's not perfect;
to get the shape that we want, we must add our constraints. To start,
we observe that the finished trapezoid has one axis of symmetry. In this
case, I will choose to draw it with the vertical reference axis as the
axis of symmetry.
So we want to add a symmetry constraint. Hover the mouse over the
top left point, until it is highlighted in yellow; then click to select
it. The point is now highlighted in red, to indicate that it is selected.
Repeat this for the top right point, and for the vertical reference axis.
Then choose Constrain > Symmetric, or press `Y':
This constrains those two points to lie symmetric about the vertical
reference axis. (So if you printed out the drawing, and folded it along
the axis, then the points would be on top of each other.) The constraint
is indicated by the two magenta arrows. The top left point
still has two degrees of freedom, as indicated by the tictactoe marks,
but the top right point has none; the symmetry constraint forces its
position. If you drag the top left point with the mouse, then the top
right point will also move, in order to satisfy the constraint.
(Depending on whether you drew the quadrilateral clockwise or
counterclockwise, either the top left or the top right point might
be free. Look at the tictactoe marks to see which one you can drag
with the mouse, or look at the `Assumed Parameters' list in the panel
on the right. The label above this list is yellow, because there are
still unconstrained degrees of freedom.)
Repeat the process for the bottom two points, and add another symmetry
constraint. Now another point is fixed, in this case the bottom left one;
if you drag the bottom right point, then the bottom left will follow. Our
quadrilateral is now constrained to be a trapezoid:
Its rotation is fixed; the two parallel edges must be parallel to
the horizontal reference axis. Its horizontal position is fixed, by the
symmetry constraint, but its vertical position is free; you can drag it
wherever you want in that direction:
To constrain its vertical position, we might constrain one of the
bottom points to lie on the horizontal axis. Select the bottom right
point, and the horizontal axis. They now appear highlighted:
Choose Constrain > Coincident / On Curve, or press `O'. This
constrains the bottom right point to lie on the line. The bottom left
point moves as well, because the symmetry constraint still applies:
The top left point may be dragged freely; it still has two degrees of
freedom. The bottom right point now has only one degree of freedom,
its horizontal one; the vertical degree of freedom is restricted by the
pointonline constraint. The other two points are fixed, with no degrees
of freedom. Constraints remove degrees of freedom. Most constraints
remove one degree of freedom from the sketch, though some remove two.
So our trapezoid still has three degrees of freedom. We might further
constrain it by specifying the length of the top edge. Select the top
edge, and then choose Constrain > Distance / Diameter. This constrains
the length of the top edge; the constraint is indicated by a magenta
label drawn on the sketch. As we drew it, the top edge is 2.444 inches
long. (The label isn't in a very convenient place. If you hover the
mouse over the label, until it is highlighted, and then drag it, then
you can put the label wherever you want.)
From our specification, this edge is supposed to be five inches long.
To change the length, doubleclick the label. A text box appears on the
sketch. Type the new length, and hit Enter. The length of the line
changes, to respect the constraint; of course, all of the old constraints
are respected too.
Repeat the process for the bottom edge, and constrain that 4.000
inches long. We're now down to one degree of freedom. This is good,
because we have exactly one specification left, on the altitude between
the top and bottom edges. Select those two edges:
Then, choose Constrain > Distance / Diameter. As before, the distance
constraint is indicated on the sketch, by the label; right now the two
lines are 1.957 inches apart.
As before, you can type in the desired altitude, by doubleclicking
the label on the sketch. At this point, the sketch
is completely constrained. The label above the `Assumed Parameters'
list, that used to be yellow, is now green, and the `Assumed Parameters'
list is empty. This means that we're done.
Equivalent Drawings
Of course, we could have drawn the exact same trapezoid in many other
ways. Instead of finishing by constraining the trapezoid's altitude, we
might have constrained its side length.
Or, we might have kept the constraint on the altitude, but replaced the
top side length constraint with a constraint on one of the angles.
Or, we might not have used symmetry constraints to enforce the
trapezoidness; instead, we could have constrained the top edge
horizontal, the bottom edge's midpoint at the origin, and the left and
right sides equal in length. (The magenta circle at the origin represents
the atmidpoint constraint. The tick marks, which are highlighted in
yellow, represent the equallength constraint. The letter H represents
the horizontal constraint.)
Or, we might have constrained the length of a diagonal. To do this,
I added an extra line along one of the diagonals, and constrained that
line's length. I don't actually want that line in my figure, though; it's
just there to help me construct the geometry. To mark a `construction'
line, that will not appear when you export the part as a DXF or
whatever, select that line and then choose Sketch > Toggle Construction.
Construction lines are displayed in dark green.
A bit of high school trigonometry will show that all of these descriptions
are equivalent. We chose our initial set of constraints because they
mapped well onto the specifications that we had been given. If our
specifications had been given in a different form, then a different
set of constraints would have been appropriate.
Derive and Export
So at this point, we've drawn the part. Click on the `Derive and Export'
tab, at the top right of the window. A list of layers appears; in this
case, there is only one, with its default name, Layer00000001. A more
complicated sketch could have multiple layers, or `derived items' (like
the Boolean union of two layers, or a step and repeat), but ours does not.
To export the part, choose File > Export DXF or HPGL. If you choose
to export a DXF, then the units will be either millimeters or inches,
depending on the current display mode (View > Dimensions in ...). If
you choose HPGL, then the units are fortieths of a millimeter. If
different units are required, then scale the sketch (Derive > Scale)
before exporting.
The DXF or HPGL file will contain only line segments. All curves will
be broken down into piecewise linear segments. The chord tolerance is
determined by the zoom level of the part onscreen, at the moment that you
switch from sketch mode to derive mode; zoom in more to get smoother
curves. The exported file will contain all of the layers that
are currently visible. (To hide or show a layer, rightclick it in the
list. In this case, we have just one layer, so that's not very useful.)
This completes the tutorial. More complex parts are drawn by the same
process, just with more entities and constraints. As the sketch becomes
more complex, the program runs slower, because it takes more time to solve
for all the constraints. Depending on how the sketch is dimensioned,
SketchFlat can usually handle about a hundred points before it lags
noticeably.
Inconsistent or Nonconverging Constraints
In this tutorial, the sketch was always either underconstrained (when we
started), or exactly constrained. There is a third possibility: a sketch
can be inconsistently constrained. If we constrain the length of two sides
of a square, or all three angles of a triangle, then either one of the
constraints is redundant, or the constraints are inconsistent. In that
case, the solver cannot satisfy the constraints, and it signals an error.
It does this in two ways: the label in the status bar, at the bottom left,
turns red and says `can't solve, stopped'; and the label at the right,
that is usually yellow (underconstrained) or green (exactly constrained),
turns violet. At this point, the solver is off; the points are completely
free, and may be dragged in such a way as to violate the constraints.
It's necessary to fix the inconsistency before continuing.
As a convenience, SketchFlat lists all of the constraints that, if they
were removed, would make the sketch consistent again. These appear in the
list at the bottom right, labeled `Inconsistent Constraints'. Once the
sketch is made consistent, the solver will be reenabled. It's possible
to make extensive changes to the sketch with the solver disabled, but
almost certainly a bad idea; fix the problem before proceeding.
(Of course, it's also possible to make the sketch consistent again by
choosing Edit > Undo. This may be helpful if you're lost.)
A related but different error occurs if a constraint is not redundant
or inconsistent with other constraints, but still cannot be satisfied.
In that case, SketchFlat tries to solve, but the solver does not converge
to a solution. Consider the example below:
This is a triangle, with side lengths 3, 4, and 8. It's not possible
to construct this triangle, because 3 + 4 = 7 < 8. The solver is therefore
failing to converge.
As before, it's necessary to
delete constraints in order to bring the sketch back to a solvable state.
It might be simpler to just hit undo.
Multiple Solutions, and Initial Conditions
It's possible to manually disable the solver, even if the sketch is
consistent. This may be useful when multiple solutions exist, and you're
getting the wrong one. Consider our trapezoid:
The altitude is 3.000 inches, the bottom edge is 4.000 inches long, and
the left and right sides are both 3.041 inches long. SketchFlat reports
that this sketch is exactly constrained, and it is. But, there are three
other configurations that also meet the constraints: the sketch given
below, its mirror image, and a second trapezoid.
SketchFlat decides among these multiple solutions according to how the
lines are initially drawn, before they are constrained. If SketchFlat
picks the wrong solution, then you can disable the solver, drag the geometry
closer to what you want, and resolve.
To disable the solver, choose Constrain > Don't Solve. To reenable it,
choose Constrain > Solve Automatically. To run the solver once, but not
reenable it, choose Constrain > Solve Once Now. The solver status is
displayed in the status bar, at the bottom left.
It's also possible to choose among multiple solutions by shiftdragging
a point. This is equivalent to disabling the solver, dragging the point to
its new position, and then reenabling the solver.
It's important to draw the lines fairly close to the desired geometry
before constraining them. If you don't, then it's likely that the
solver will find an undesired solution, or even fail to converge. It's
possible to fix that after the fact, as described above, but painful in
a complicated sketch.
In general, it's a bad idea to draw all of your line segments, and
then dimension them. Instead, draw only a portion of your part, and
dimension that. Once the lines that you've drawn are fully constrained,
draw more lines, and dimension those. With fewer unconstrained points
at any given time, it's easier to keep track of what you're doing. This
process also guarantees that the system of constraint equations will
have a `nearlytriangular' structure; the solver can exploit this,
and work faster.
Desirability of Particular Constraints
Some constraints are `better' than others; they have a mathematical
form that makes them less prone to nonconvergence, or multiple solutions,
or other surprising behaviour.
Pointcoincident constraints are very easy to understand.
Horizontal and vertical constraints are also easy. It's better to
constrain a line segment horizontal or vertical than to constrain it
parallel to a coordinate axis, even though the geometric meaning is
equivalent.
Symmetry constraints are good. A symmetry constraint will actually
write two equations, so it fixes two degrees of freedom. This means
that each symmetry constraint fully constrains one point, which often
makes the sketch easier to understand.
Pointtopoint distance constraints (which include constraints on
the length of a line segment) are good, but they typically produce
multiple solutions; draw your lines fairly close to the desired
geometry before constraining them.
Equal length constraints are similar to pointtopoint distance
constraints. Equal radius constraints are either similar to
pointtopoint distance constraints (for arcs), or easy (for complete
circles).
Pointtoline distance constraints are good. They do not tend to
produce multiple solutions, because these distances are `signed'.
If a point is constrained to lie 20 mm above a horizontal line, then
the solver will reject the solution where the point is 20 mm below
the line. (Internally, the distance is either positive or negative.
The sign is not displayed on the sketch, but you can move the point
to the other side of the line by typing a negative distance.)
Linetoline distance constraints are equivalent to pointtoline
distance constraints. Lineline distance is meaningful only if the
two lines are parallel; it's necessary for some other constraint to
enforce that. Pointonline is equivalent to pointline distance with
a distance of zero, so that's good too.
Angle constraints are trickier, and more prone to unexpected
behaviour. Parallel and perpendicular constraints are special cases
of angles. Angle constraints apply modulo 180 degrees, and their sign
is not shown on the sketch. This means that a 135 degree angle is
equivalent to a 45 degree angle. It's arbitrary which number is displayed
on the sketch; to switch, select the constraint and then choose
Constrain > Other Supplementary Angle.
(The angles are signed internally, though.
As with the pointline distance, you can type a negative number to
flip the sign.)
If we wanted to draw a rectangle, then we would draw four line
segments, that form a closed polygon. We could then constrain
them, using:
 Two horizontal constraints, and two vertical constraints. This
is very good.
 Three symmetry constraints. This is also good.
 Two equal length constraints, on the top and bottom, and left
and right edges, plus a perpendicular constraint. Not as good,
but it works.
 Three equal length constraints, on the top and bottom, left and
right, and diagonals. (To constrain the diagonals, draw them in as
construction line segments.) That's a bit roundabout, but it works.
 Three perpendicular constraints. This is probably not the best
way to do it.
Example to Download
You can draw it yourself, but this is our trapezoid:
December 2007, near Seattle
