The first step taken to justify the position analysis. For this, the path of the front leg, which is just an extension of R6, is plotted. Based on experience, the path should move directly away from R0, then curve up towards the end of its path.
The graph does not have a constant curvature. However, this still works, because the curved rocker on the chair has a pin joint attaching it to R0, and a pin joint for attaching the slider. The rocker can trace out any path without restrictions. As for how this relates to real life, the path agrees with how the slider extends, relative to R0. The starting point is below the base of the vector R0 (negative y-axis), and has a slight offset away from the vector R2 (negative x-axis). The motion of the slider is not straight, however it is mostly in the x direction. This is not exact proof, however this was enough to show that the MATLAB model's motion does correspond to the rocking chair in real life.
The results of the analysis focus on the mechanical advantage if a force is applied to the seat of a chair, and if a force is applied to the backrest, with the output as the slider portion of the front leg of the chair. The picture shown depicts the curved slider as grounded, however the vector loop analysis assumes that R0 is the grounded link. For the analysis on mechanical advantage, the magnitude of the mechanical advantage will not change, regardless of which link is chosen as the ground. Theta 2, or the toggle linkage, is set as the dependent variable.
The Mechanical Advantage is found using the angular velocities from the Velocity analysis.
| Latex formatting |
|---|
$$ MA = \frac {\omega_{in}}{\omega_{slider}} $$ |
For the mechanical advantage, the force out is increased for theta 2 > 135°. Theta varies from 15° to 165°, with 165° corresponding to the closed position. For the extended position, where the chair is open, the mechanical advantage is much lower. This means that forces applied to the backrest and seat have less of an effect on the slider when the chair is open. This is good for stability, since less force when the chair is open means that it is less likely to have the slider move and cause the chair to collapse.
...
Test Fits
Our project involved both 3D printed and laser cut pieces. Before printing and cutting all of our parts, we made some test pieces to determine the best sizing for shaft and bearing holes.
To determine the inner diameter of the bearing cups to be 3D printed, we printed 3 test pieces: 16mm, 16.5mm, and 17mm inner diameter. The 16mm inner diameter best held the ball bearings in place in the cup, so that is what we went with for all of the bearing cups. We also cut some pieces to determine the diameter of the laser cut holes for the bearing cups and shafts to be placed into. We determined that holes cut to the exact outer diameters–8mm shaft, 19mm bearing cup–provided a perfect fit that would allow the team to use super glue to keep these components in place in their holes. This laser cut test fit is shown in the video below.
3D Printing
We chose to 3D print bearing cups so that the interface holding the bearing in place would be PLA super glued to wood as opposed to metal to wood which would not hold as well. The bearing cups were printed with a 16mm inner diameter, 19mm outer diameter, and approximately ¼” height to properly hold the bearing in place and fit inside the laser cut pieces. The shaft link adapter (shown in the image below), was 3D printed with a hole for the shaft being 0.5mm larger than the 8mm shaft to provide room for insertion of the shaft but still have a tight fit.
For the quick return mechanism, we 3D printed the slider shaft holders, bearing cuffs, and bearing cap and riser. The focus of these pieces was making sure the pieces were designed with the appropriate height to ensure that the links experienced no out of plane motion. For the finger wagging mechanism, we printed the bevel gear box and mechanism adapter shown below.
Lastly, we also 3D printed some 8mm inner diameter shaft collars.
Laser Cutting
The motor mount and supports, shaft supports, links, and platforms were all laser cut using ¼” thick wood to provide better overall strength than ⅛” wood. The switch assembly was mostly cut from ¼” wood, with only the top piece that the switch attaches to cut from ⅛” wood. Washers were cut from ⅛” wood for use as needed to provide spacing between links.
We laser cut all our links with the appropriate shaft and bearing hole size that we previously determined using our test pieces: 8mm holes for shafts and 19mm holes for bearing cups. Super glue was used to attach the bearing cups into wooden pieces (links, shaft supports) to hold the bearings in place.
Timing Belt
We encountered many difficulties with setting up the timing belt. This belt is meant to connect the motor input shaft to the shaft of the finger wagging mechanism with a 1:1 gear ratio so the shafts rotate at the same rate. Because we required a custom distance between the two shafts (112mm, the ground link of the raise/lower mechanism), we were not able to purchase a prefabricated continuous loop timing belt and had to create our own out of a length of belt. To attach the ends of the belt together and create a loop, we first tried overlapping the ends of the belt slightly and stapling them together. However, every time the staples went over the gear, they had issues getting over the gear and bent/loosened. We then tried superglue but again, the motion was not smooth over the gears. Finally we ended up sewing the ends together.
In our attempts to fabricate the timing belt loop to get successful rotation transfer between the shafts, we noticed that the torque requirement and belt tension were big issues. The torque requirement to raise and lower the finger assembly was large, and the torque being provided by the small gears was not enough which resulted in the rotation stalling and gear teeth skipping at times. To provide more torque, we replaced the second gear (gear on the finger wagging shaft) with a larger gear which solved the torque problem. This provided adequate torque to raise and lower the finger assembly, but the belt was no longer a 1:1 timing belt (it had a 3:1 ratio). Additionally, without the right belt tension rotation did not transfer between the shafts. To address the tension issue, we created a makeshift tensioner using an allen key to pull the belt to the correct tension. The final timing belt assembly with a 3:1 ratio and tensioner is shown below.
Final Assembly
Once we had all our pieces 3D printed and laser cut, we began the final assembly. The team also took some time to look at the design of the final layout of the mechanism to determine the shaft lengths needed and cut these in the machine shop. We used wood glue to attach all the platform pieces to one another and attach the motor mount and supports to the platform. Super glue was used to keep the bearing cups and shafts in place in links to ensure that the attachments were rigid. Some images of the final assembly are shown below.
