DOF solved problems#
This page presents some examples of determining the number of d.o.f. of a mechanism using Grübler’s formula, as seen in the previous section.
Example 1#
(Image credits: [AI14])
Solution
Two valid solutions:
\[n= 4, p_I=3, p_{II}=1 \rightarrow g=2\]
or
\[n= 5, p_I=5, p_{II}=0 \rightarrow g=2\]
Example 2#
(Image credits: [AI14])
Solution
Two valid solutions:
\[n= 12, p_I=15, p_{II}=0 \rightarrow g=3\]
or
\[n= 11, p_I=13, p_{II}=1 \rightarrow g=3\]
Example 3#
(Image credits: [AI14])
Solution
Count neither the disk at the bottom nor the belt transmission. Grübler fails with belts and gears, so we must leave them out.
\[n= 6, p_I=7, p_{II}=0 \rightarrow g=1\]
or (counting the cam as a type II joint instead):
\[n= 5, p_I=5, p_{II}=1 \rightarrow g=1\]
Example 4#
(Image credits: [AI14])
Solution
\[n= 10, p_I=12, p_{II}=0 \rightarrow g=3\]
Example 5#
(Image credits: [AI14])
Solution
\[n= 5, p_I=4, p_{II}=2 \rightarrow g=2\]
or
\[n= 7, p_I=8, p_{II}=0 \rightarrow g=2\]
Example 6#
(Image credits: [AI14])
Solution
\[n= 6, p_I=5, p_{II}=2 \rightarrow g=3\]
or:
\[n= 8, p_I=9, p_{II}=0 \rightarrow g=3\]
Example 7#
(Image credits: [AI14])
Solution
\[n= 9, p_I=9, p_{II}=2 \rightarrow g=4\]
or:
\[n= 11, p_I=13, p_{II}=0 \rightarrow g=4\]