Derivation
MA =
\begin{vmatrix}
\frac{\omega_{crank}}{\omega_{out}}
\end{vmatrix}
\begin{vmatrix}
\frac{r_{crank}}{r_{out}}
\end{vmatrix}
The mechanical advantage of a system is defined by:
...
(Eq. 11)
For my case, the input radius and angular velocity comes from the crank itself, not link 2. The output angular velocity can either be ω4 or ω5. The output radius is the same for link 4 and link 5.
...
(Eq. 12)
I have solved for the angular velocity ratio for | ω2 / ωout | in the previous section. We can thereby solve for the equivalent angular velocity ratio for | ωcrank / ωout |:
...
(Eq. 13)
...
(Eq. 14)
Substituting equation 13 and equation 14 to equation 12 gives:
...
(Eq. 15)
Finally the total mechanical advantage is the summation of both end effector forces:
...
(Eq. 16)
Mechanical Advantage Plot
I input the following parameters from table 2:
| Parameter | Value |
|---|---|
| rin | 1.25 |
| rout | 1.875 |
| N2 | 40 |
| Ncrank | 12 |
Table 2, mechanical advantage parameters
