11.1 - Initial Proposal
Introduction
In this paper, our team proposes a mechanism to consistently flip water bottles. While this may seem mundane and pointless, this task holds a large sentimental value to many individuals of our generation. Bottle flipping was a trend that exploded in popularity in the 2010s, with the majority of our generation reveling in the test of skill to impress our friends. The goal of bottle flipping is to toss a bottle in the air so that it completes a full rotation before landing flat on its bottom. We believe this problem is neither too easy nor too difficult and touches upon most of the content covered in this course, including position, velocity, and force analysis.
Figure 11.1.1. Demonstration of a Bottle Flip (Source: Alaxus)
Problem Description
A bottle flip is not a simple projectile motion problem because it involves complex rotational dynamics. The initial velocity and mass distribution control the bottle's rotational motion. The angular velocity of the bottle is governed by the moment of inertia, which is subject to change due to the constant shifting of the liquid inside the bottle. A wider mass distribution slows the rotation, while a concentrated mass increases it. For a successful landing, the bottle must contact the ground with most of its mass near the base so the momentum doesn't tip it over.
A simple joints mechanism lacks the motion coordination to flip a bottle consistently. Rather, the motion required to flip a bottle needs to begin with a horizontal sweeping-like motion to add some angular momentum followed by a vertical flick to provide the upwards speed necessary for the bottle to flip in the air. The primary technical challenge will be tuning the mechanism to provide the perfect amount of velocity in the correct direction so the bottle neither fails to flip completely nor flips too far and does not land upright.
Beyond the mechanism itself, we also must account for the design of the end-effector and the water bottle itself. To prevent there from being too many electronics, our end-effector must be passive and somehow hold and release the water bottle at the right moment. Additionally, the water bottle itself is prone to becoming damaged throughout the testing process, which we must account for while tuning the mechanism.
Proposed Mechanism
The sort of path we would need is one that has a sweeping motion at the bottom to create momentum and releases with a near-vertical velocity at the top to give it enough height to flip. Using a four-bar linkage we can create this type of motion. Link 3 will be a ternary link with the end-effector being attached to the third joint of this link. By rotating the grounded link and tuning the shape of the ternary link we will have a lot of freedom to customize the path to meet our needs.
Figure 11.1.2 below was created using MotionGen. The rightmost path is an example of the type of motion we are seeking. Please note that MotionGen swapped the labels for L3 and L4 in the exported GIF. Throughout the report, references to L3 refer to the ternary link.
Figure 11.1.2. A preliminary four-bar design for the bottle flipper.
Proposed Scope
Our project will be done in two parts: a prototype and a final version. The prototype will focus on just the flipping mechanism, making sure the four-bar linkage moves in the right way to flip the bottle. To do this, we’ll record and analyze real bottle flips to get a sense of what the position and velocity of the bottle should be at each moment from the initial grasp to the final release. We will then model our system in MATLAB and tune the link lengths and crank velocity to match up with the necessary position and velocity profiles as closely as possible. We will then use SolidWorks to CAD the links in order to fabricate them.
Once the prototype is built, we’ll experiment with various velocities to test its performance. Our main priority is getting the flipping motion right. However, if we’re able we would like to make it able to also pick the bottle back up after it lands for another flip. The design will be fully mechanical, so there won’t be any sensors or feedback systems, just careful tuning of the linkages and motor speed. By the end of the semester, we plan to have a working bottle-flipping machine.
Preliminary Design Ideas
The linkage in Figure 2 has the following dimensions:
L1 = 8.11 in
L2 = 1.93 in
L3 = 7.00 in
L4 = 3.76 in
δ = 11.3 degrees (angle of ternary link at the joint connecting L2 and L3 in Figure 2)
LAP = 8.81 in (length from the joint connecting L2 and L3 to the end-effector in Figure 2)
With the dimensions described above, some preliminary analysis can be done.
Gruebler Equation
Number of Links (L) = 4
Number of Full Joints (J1) = 4
Number of Half Joins (J2) = 0
M = 3(L - 1) - 2J1 - J2 = 3(4 - 1) - 2(4) - 0 = 1
Our mechanism will have 1 degree of freedom, which is all a mechanism like this needs.
Grahof Condition
Shortest Link (S) = 1.93 in
Longest Link (L) = 8.11 in
Other Links (P, Q) = 7.00 in, 3.76 in
S + L = 10.04 in
P + Q = 10.76 in
Because S + L ≤ P + Q, this linkage meets the Grashof condition, meaning at least one link can make a full rotation. This is ideal because we intend to control it with a single motor without sensors.
Kinematic Diagram Draft
Figure 3 below shows our current kinematic diagram. It’s merely a static version of Figure 2 with the ground more explicitly labeled.
End-Effector and Bottle Design Considerations
In addition to the mechanism itself we also have to consider the design of the end-effector and bottle. For the end-effector we are currently thinking of having two parallel bars that grasp the cap. As the mechanism moves, the bottle will simply slide off the bars, a passive release mechanism. For the bottle itself, we will either be printing a plastic protective cover for the bottom or fabricating our own bottle for more fine control. Figure 4 shows some sketches showcasing these two ideas.