...
Figure 1: Open 4-bar configuration (Mechanism 1). Figure 2: Closed 4-bar configuration (Mechanism 2).
...
We further analyzed the velocity of the mechanism with these link lengths to better understand the end effector's motion.
Figure 5: Figure 5: The velocity analysis of the optimal mechanism 1.
The original value of the angle of link one was 0 degrees, which produced the first velocity plot shown above for the mechanism's end link. From our analysis in Motion Gen we know that the end-effector (attached to link 3 as shown in the photo above) interacts with the tab of the can when the crank angle is around 180 degrees. In the first plot we can see that with a theta1 = 0 degrees the velocity is decreasing as it pulls the tab up, but it is not the slowest that it could be. When we change our mechanism such that theta1 = 120 degrees, the lowest velocity is achieved where the end-effector needs to impart the most force.
Mechanical Advantage
Figure Figure 6: Analysis of the mechanical advantage after changing the angle of link 1.
Originally, with an initial angle of link 1 at 0 degrees, the greatest mechanical advantage was achieved when the crank angle was less than 80 degrees. As we adjusted the angle of link 1, the location of the peak mechanical advantage changed. With the angle of link 1 at 45 degrees, the mechanism will have the greatest mechanical advantage at a crank angle around 180 degrees and 330 degrees. This is closer to where the end effector will interact with the tab of the can allowing us to impart more force with less motor power. After the kinematic analysis of our open 4-bar mechanism, pictured below is the resulting final design modeled in MotionGen.
Figure 7: Final open 4-bar mechanism after kinematic analysis
Mobility and Grashof Analysis:
To verify our design we need to check the Grashof and mobility equations to ensure that the mechanism achieves the motion and position profile of our end effector link that will lift the tab of our can. The open 4 bar mechanism has 1 DOF and meets the Grashof condition.
[The Grashof and mobility equations were used to calculate if the preferred mechanism is able to have full continuous motion about the input joint. The mobility of the crossed 4-bar mechanism is 1, which is described by the rotational movement that is created. Furthermore, the mechanism is able to produce a continuous motion about the input link as it is Grashof. ]
Figure 7: Mobility and Grashof Calculations
Final Design
After the kinematic analysis of our open 4-bar mechanism, pictured below is the resulting final design modeled in MotionGen.
Figure 8: Final open 4-bar mechanism after kinematic analysis
Mechanism 2: Closed 4-Bar Configuration
...
Figure 89: 4-bar linkage model for human finger (Patent)
...
| Link within Patent | Lengths (cm) |
|---|---|
| Ground link (L1) | 0.85 |
| Crank Link (L2) | 3.5 |
| Coupler Link (L3) | 0.87 |
| Output Link (L4 | 3.5 |
Table 2: Link lengths given from patent
...
Figure 910: Position profiles of the Mechanism with varying lengths for a) Link 1, b) Link 2, c) Link 3, and d) Link 4
...
We found that by altering link 2 to 2.5 cm, the position profile creates a hooking motion that is able to curl under the tab and provide a lifting motion when under the tab. The position profile as further altered by changing the theta 1 position so that the lifting motion was direct more vertically. After multiple theta 1 values, we settled for an angle of 45 degrees to best model the hooking motion.
Figure 1011: Position Analysis with Theta 1 of 0 Degrees and 45 Degrees
...
For the velocity analysis, the team calculated the velocity profiles of the corresponding link length modifications and Figure X depicts the velocity profile for the different link lengths.
a) b)
c) d)
Figure 1112: Velocity Velocity profiles of the Mechanism with varying lengths for a) Link 1, b) Link 2, c) Link 3, and d) Link 4
The velocity profile of the configuration with the best link lengths was also plotted to describe the compare the motion between a theta 1 of 0 degrees and 45 degrees. In Figure x, the plots illustrate that the
Mechanical Advantage
minimum velocity after rotating link 1 by 45 degrees is approximately zero at 280 degrees.
Figure 13: Velocity Analysis with Theta 1 of 0 Degrees and 45 Degrees
Mechanical Advantage
For the mechanical advantage, we calculated the ratio between the angular velocity of the input link to the output velocity calculated in the above section and Figure X depicts the mechanical advantage as the link lengths are altered.
a) b)
c) d)
Figure 14: Mechanical Advantage of the mechanism with varying lengths for a) Link 1, b) Link 2, c) Link 3, and d) Link 4
The mechanical advantage of the configuration with the best link lengths was also plotted to describe the compare the motion between a theta 1 of 0 degrees and 45 degrees. In Figure x, the plots illustrate that the peak mechanical advantage after rotating link 1 by 45 degrees is above 300 at 280 degrees.
Figure 15: Mechanical Advantage with Theta 1 of 0 Degrees and 45 Degrees
Mobility and Grashof Analysis
Similar to the previous mechanism, we used the Grashof and mobility equations were used to check if the 4-bar crossed mechanism will produce the motion and position profile of our end effector link that will lift the tab of our can. Although it has the desired DOF, it does not meet the Grashof condition.
calculate if the preferred mechanism is able to have full continuous motion about the input joint. The mobility of the crossed 4-bar mechanism is 1, which is described by the rotational movement that is created. however, the preferred mechanism design is not Grashof, highlighted with the non-continuous motion. However, because we are looking for a hooking mechanism, this non-Grashoff design we created is still able to complete the goals we need.
Figure 16: Mobility and Grashof Calculations
Final Design
After the kinematic analysis of our crossed 4-bar mechanism, pictured below is an approximated final design modeled in MotionGen.
Figure 17: Final crossed 4-bar mechanism after kinematic analysis
Selected Design
Our team has chosen to continue with the open 4-bar design as the position profile is closely matching the continuous motion we described at the beginning. Not only is the path very similar, the distance that the end effector needs to travel when in contact with the can is more easily controlled with the open 4-bar. Furthermore, the velocity and resulting mechanical advantage from the best open 4-bar configuration provides a desirable location to apply a high force to the tab. Following this kinematic analysis is documentation of the prototype iterations we have created.
Iterative Documentation
Prototype #1: Cardboard
When starting our prototype, we began creating the mechanism with cardboard to map out the movement with physical pieces. We measured the the link lengths to approximately the desired lengths that were defined in Motion Gen. The goal for this prototype is to observe and understand the motion of the mechanism using physical components. However, cardboard is very flimsy and susceptible to breaking down after repetitive use.
Figure 18: Cardboard prototype of the open 4-bar mechanism
...
For this prototype, we tried recreating the same prototype with the desired link lengths using laser cut wood and rods. We will most likely use wood and rods to have more structural stability and support when developing the entire mechanism. We found that the motion is not as smooth as we desired and future iterations will have rods and bearings.
Figure 19: Laser cur prototype of our open 4-bar mechanism.
...
The final prototype is similar to the previous in that we laser cut linkages; however, we replaced the rods with M6 screws and mounted it to a board to produce smooth motion. In the gif below you can see that the position profile of the end-effector models the position profile we determined in our kinematic analysis.
Figure 20: Moving prototype of our open 4-bar mechanism.
Bill of Materials
Our bill of materials are given within this spreadsheet . We expect to collect all the parts by 4/15.
...