SME
Engineering Graphics & CAD · Problem type
Is the sketch fully defined
Use this for “A rectangle sketch has 2 horizontal, 2 vertical, a width, a height and a corner fixed at the origin. Is it fully defined?”
Diagram
f = 2p + 3c = 2 × 4 + 3 × 0 = 8.
Each point slides in x and y, and each circle also grows.
DOF = f − r = 8 − 8 = 0.
The sketch is fully defined: it keeps its shape when a dimension changes.
This is an example. Type your own values to start a new problem.
f
=
2
×
p
+
3
×
c
DOF
=
f
−
r
Formulas
f
=
2
×
p
+
3
×
c
8 = 2 × 4 + 3 × 0
DOF
=
f
−
r
0 = 8 − 8
Assumptions
•
A point in a plane sketch moves in x and y: 2 DOF. A circle adds a radius: 3 DOF.
•
A line is set by its two end points, so it adds no DOF of its own.
•
Each constraint or dimension removes the DOF it fixes: a fixed point removes 2.
Step-by-step
WE KNOW
p = 4, c = 0, r = 8
FIND
starting DOF (f), DOF left (DOF)
Step 1 · Find starting DOF (f)
Use f = 2 × p + 3 × c
Each point slides in x and y; a circle’s center does too, and its radius can grow.
f
=
2
×
4
+
3
×
0
f
=
8
Step 2 · Find DOF left (DOF)
Use DOF = f − r
The constraints and dimensions fix what they remove; 0 left means fully defined.
DOF = 8 − 8
DOF = 0
Check
Put the numbers back in. Both sides should match.
8 = 2 × 4 + 3 × 0 ✓
0 = 8 − 8 ✓
Topic check
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