SME
Engineering Graphics & CAD
Assemblies and drawings
Use this for “A four-bar linkage has 4 links, counting the ground, joined by 4 pins. How many inputs does it need?”
Diagram
Gruebler: M = 3(n − 1) − 2j₁ − j₂ = 3 × 3 − 2 × 4 − 0 = 1.
M = 1: one input drives it.
This is an example. Type your own values to start a new problem.
M
=
3(
n
−
1)
−
2
×
j₁
−
j₂
Formulas
M
=
3
×
(
n
−
1)
−
2
×
j₁
−
j₂
1 = 3 × (4 − 1) − 2 × 4 − 0
Assumptions
•
The linkage moves in a plane; the ground (frame) counts as one of the n links.
•
Pins and sliders are full joints (j₁); a pin in a slot or a cam contact is a half joint (j₂).
•
Three links joined at one pin count as two full joints.
•
M = 1 needs one input, M = 0 is rigid, M < 0 overconstrained: a CAD assembly’s mates must bring M to 0, or 1 for a mechanism.
Step-by-step
WE KNOW
n = 4, j₁ = 4, j₂ = 0
FIND
mobility (M)
Step 1 · Find mobility (M)
Use M = 3 × (n − 1) − 2 × j₁ − j₂
Each link but the ground moves in x, y and turns: 3 DOF. A full joint takes away 2, a half joint 1.
M
=
3
×
(4
−
1)
−
2
×
4
−
0
M
=
3
×
3
−
2
×
4
M
=
9
−
8
M
=
1
Check
Put the numbers back in. Both sides should match.
1 = 3 × (4 − 1) − 2 × 4 − 0 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.