SME
Kinematics of Mechanisms
Four-bar linkages
Use this for “A four-bar has links of 40, 90, 100 and 120 mm, with the 40 mm link as the crank and the 100 mm link fixed. Can the crank turn fully, and what kind of linkage is it?”
Chart
s: 40 mm
l: 120 mm
p: 90 mm
q: 100 mm
This is an example. Type your own values to start a new problem.
s
Shortest link
example · mm
l
Longest link
example · mm
p
Third link
example · mm
q
Fourth link
example · mm
S
Sum s + l
worked out (not typed) · mm
P
Sum p + q
worked out (not typed) · mm
G
Fixed link
example
T
Linkage type
worked out (not typed)
Formulas
S
=
s
+
l
160 = 40 + 120
P
=
p
+
q
190 = 90 + 100
T
:
if
S
<
P
,
a
crank-rocker,
double-crank
or
double-rocker
by
G
;
change
point
if
equal;
else
triple-rocker
160
<
190,
so
Grashof,
with
s
next
to
the
fixed
link,
so
crank-rocker
Assumptions
•
A planar four-bar with pin joints; each length is measured pin to pin.
•
“Turns fully” means a full turn relative to the fixed (ground) link.
•
s is the shortest link, l the longest, and p and q the other two.
Step-by-step
WE KNOW
s = 40 mm, l = 120 mm, p = 90 mm, q = 100 mm, G: next to s
FIND
sum s + l (S), sum p + q (P), linkage type (T)
Step 1 · Find sum s + l (S)
Use S = s + l
Add the shortest and the longest links: the pair Grashof tests.
S
=
40
+
120
S
=
160
mm
Step 2 · Find sum p + q (P)
Use P = p + q
Add the two middle links.
P
=
90
+
100
P
=
190
mm
Step 3 · Find linkage type (T)
Use T: if S < P, a crank-rocker, double-crank or double-rocker by G; change point if equal; else triple-rocker
Grashof,
and
s
is
next
to
the
fixed
link:
s
turns
fully
as
a
crank,
and
the
link
opposite
rocks.
160
<
190,
so
Grashof,
with
s
next
to
the
fixed
link:
crank-rocker
T
=
compare
S
with
P
,
then
see
where
s
sits
T
=
compare
160
with
190,
then
see
where
s
sits
T
=
crank-rocker
Check
Put the numbers back in. Both sides should match.
160 = 40 + 120 ✓
190 = 90 + 100 ✓
160
<
190,
so
Grashof,
with
s
next
to
the
fixed
link,
so
crank-rocker
✓
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Transmission angle at a crank position
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More problem types
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