Answer:
[tex]\mu_{min}[/tex]=[tex]26.38^{\circ}[/tex]
[tex]\mu_{max}[/tex]=[tex]71.79^{\circ}[/tex]
Explanation:
[tex]r_{1}[/tex]=7 in, [tex]r_{2}[/tex]=3 in, [tex]r_{3}[/tex]=9in
,[tex]r_{4}[/tex]=8 in
Transmission angle (μ ):
It is the acute angle between coupler and the output (follower) link.
Here we consider link [tex]r_{1}[/tex] as fixed link ,[tex]r_{2}[/tex] as input link ,link [tex]r_{3}[/tex] as coupler and link [tex]r_{4}[/tex] as output link.
As we know that
[tex]\cos\mu_{max}=\frac{r_{4}^2+r_{3}^2-r_{1}^2-r_{2}^2}{2r_{3}r_{4}}-\frac{r_{1}r_{2}}{{r_{3}r_{4}}}[/tex]
[tex]\cos\mu_{min}=\frac{r_{4}^2+r_{3}^2-r_{1}^2-r_{2}^2}{2r_{3}r_{4}}+\frac{r_{1}r_{2}}{{r_{3}r_{4}}}[/tex]
When link [tex]r_{2}[/tex] will be horizontal in left side direction then transmission angle will be minimum and when link [tex]r_{2}[/tex] will be horizontal in right side direction then transmission angle will be maximum.
Now by putting the values we will find
[tex]\cos\mu_{max}=\frac{r_{4}^2+r_{3}^2-r_{1}^2-r_{2}^2}{2r_{3}r_{4}}-\frac{r_{1}r_{2}}{{r_{3}r_{4}}}[/tex]
[tex]\cos\mu_{max}=0.3125[/tex]
[tex]\mu_{max}=71.79^\circ[/tex]
[tex]\cos\mu_{min}=\frac{r_{4}^2+r_{3}^2-r_{1}^2-r_{2}^2}{2r_{3}r_{4}}+\frac{r_{1}r_{2}}{{r_{3}r_{4}}}[/tex]
[tex]\cos\mu_{min}=0.8958[/tex]
[tex]\mu_{min}=26.38^\circ[/tex]
Hence, The minimum and maximum angle of transmission angle is 26.38° and 71.79° respectively.
