Unit 02 · Lecture 3
Geometric constraints: tangent, parallel and concentric (Part 2)
Dimensions alone can’t lock every sketch. This lesson moves on to relationship constraints, rules such as “these two lines are parallel” or “this circle touches that line”, and explains the idea behind all constraining: removing degrees of freedom.
Video 14:32Reading 8 minUpdated 26 October 2026
What you will build
A 500 × 500 mm square centred on the origin, with a 10 mm square, a Ø10 circle, a hexagon and a triangle in its four quadrants, each fully constrained. You will reuse this sketch in the next lecture.
You will learn
- Inscribed vs. circumscribed polygons and when each is useful
- Degrees of freedom in a 2D sketch
- Parallel, horizontal and vertical constraints
- Coincident, tangent and concentric constraints
Before you start
Finish Understanding constraints (Part 1). You should be able to fully constrain a rectangle and circles with dimensions.
Step by step
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01
Draw two hexagons with the Polygon tool
0:45Start a new part from Standard (DIN).ipt and sketch on the XY plane. A rectangle is part of the polygon family, so open Polygon and draw two six-sided polygons, one with each option.
Dimension both with 60. They come out different sizes and rotated differently, even though they have the same number.
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02
Compare them against circles
2:15Draw a Ø120 circle on the centre of each polygon. The first polygon sits inside its circle with its corners on the circumference. That is inscribed, measured from the centre to a vertex. The second wraps around its circle with its sides touching it. That is circumscribed, measured from the centre to the middle of a side, so it comes out larger.
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03
Set up the exercise sketch
4:24In a new sketch, draw a Two Point Center rectangle of 500 × 500 mm on the origin. In the four quadrants, add a 10 × 10 mm square, a Ø10 circle, a circumscribed hexagon with 5 mm from centre to side, and a triangle (set the side count to 3), also circumscribed at 5 mm.
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04
Dimension each shape 15 mm from the corner
5:57Place each shape 15 mm from the two nearest sides of the big square. The square and the circle become fully constrained. The polygon and the triangle don’t, because they can still rotate about their centres. Rotation is a degree of freedom that no position dimension removes.
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05
Lock rotation with parallel and horizontal
7:23Choose Parallel, click a vertical side of the hexagon, then a vertical side of the big square. The hexagon can no longer rotate.
For the triangle, use Horizontal on its base. Horizontal doesn’t relate the line to another sketch line. It aligns the line with the sketch’s own X axis. Vertical aligns a line with the Y axis.
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06
Try point relationships: vertical, horizontal, coincident
9:31Draw a 100 mm horizontal line and a 150 mm vertical line that don’t touch. Apply Vertical to their end points and they line up one above the other. Add Horizontal to the same pair and they occupy the same spot. Coincident does both in one step.
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07
Tangent and concentric
11:44Draw a Ø60 circle and apply Tangent between it and the horizontal line. Move the line and the circle follows. Add a second tangent to the vertical line and all three move as one.
Draw a Ø30 circle (press D for Dimension) and apply Concentric with the Ø60 circle so they share a centre.
Degrees of freedom
Three things can move in a 2D sketch
A shape can slide in X, slide in Y and change size. Rotatable shapes such as polygons can also turn. A sketch is fully constrained when every one of those freedoms is removed, whether by a dimension or a relationship. “Three dimensions per shape” is a starting rule. The real test is whether anything can still move.
Why circumscribed polygons are useful
In 3D printing, a round pocket for a magnet often comes out undersized because of sagging filament. A circumscribed hexagon pocket touches the magnet on six flat sides and leaves room in the corners for excess material, so the magnet still fits.
Common mistakes
- Dimensioning an inscribed polygon when the drawing gives the size across flats. Check which option you picked before you type the number.
- Thinking the hexagon is constrained because it has a position. It can still rotate until you add a parallel or horizontal constraint.
- Adding a constraint that repeats an existing one. Inventor warns that the sketch would be over-constrained. Cancel and leave it out.
Practice exercise
Draw a Ø40 circle on the origin and a circumscribed hexagon of 20 mm (centre to side) concentric with it. Make one side of the hexagon horizontal. Add a horizontal line tangent to the bottom of the circle and fully constrain everything.
Bonus: switch the hexagon to inscribed and note how its size changes.
Check yourself
A hexagon touches its circle at the middle of each side. Is it inscribed or circumscribed?
Circumscribed. It lies around the circle.
Which constraint makes a line follow the sketch’s X axis?
Horizontal.
What single constraint replaces vertical plus horizontal between two points?
Coincident.
Two circles must share a centre. Which constraint?
Concentric.
Want the graded version? Take the 5-question lesson quiz in the course player after the video.
Written by the CADsmit instructor from the lecture recording and checked in Autodesk Inventor Professional 2027. Last updated 26 October 2026. Spotted an error? Tell us.