2. Kinematic Analysis and Design Process

Design Process

Images of Design Ideas in Order from Left to Right

Our design process had many different iterations over time before coming to a final design decision. Our original design (leftmost) was a simple four-bar mechanism, a tube of water, and a seed attached to it. We originally had planned for the tool to be a hoe rather than a shovel. After realizing that the hoe wouldn't be able to redistribute the soil across the platform, we turned to look at a shovel head. While we knew this was a great start to our design process, there was some complexity missing from our design. In the second iteration of our design, we came up with the idea of mounting our linkage onto a prismatic joint system to move it across in the x-direction. We chose not to continue with this design because the linkage system had more than one degree of freedom. In the last iteration, we completely changed the design of the linkage system but realized that our new design would be too difficult to mount to the prismatic joint. Each iteration of our design helped us understand what we want in our system as well as what to avoid in our system to achieve an intended functionality. Our third initial proposal design MotionGen image is shown below.

Image of MotionGen for our Initial Proposal in the Design Process

In the initial design proposal, we came up with a mechanism that could rotate fully and was capable of digging. The angle of digging for our original design was not ideal to shovel the most amount of dirt with the greatest force, and it would get stuck if it hit the ground. We found that a fixed height for our design would work best for our situation, so we came up with our final prototype design. This was now the mechanism we wanted with the ideal looped motion path and 45-degree angle for digging into the ground. It would traverse the ground, pick up dirt, and return to its original position. To do this we added the coupler point with two more linkages and elevated our input link. This image can be seen below. 

Image of MotionGen for our Final Prototype in the Design Process

Our initial prototype was made of acrylic and mounted on a wooden beam.  We took suggestions that improved our design from this point as well. From our feedback, we were able to incorporate a seed dropping maze within the thickness of the triangular linkage in our design. This 3D printed maze takes a seed when the mechanism's input link is at 90 degrees. The seed then falls into the maze and drops in the soil when the angle is steep enough. This happens after the shovel digs a hole and lifts the dirt away. An image of the maze within our design is shown below.

Image of the Seed Maze Used in the Final Prototype

Brief Analysis of Other Mechanisms Used

For our design, we also created a 3D printed shovel head to dig into the dirt. Our other main mechanism used was a gear system connected to the motor and a long shaft that drove wheels using rubber band belts with the same rotation of the motor. This design was to allow our mechanism to move along multiple areas of soil to repeat the planting process. The idea was that the mechanism would dig, plant, move forward and repeat. Our gear system ensured that the mechanism completed the seed planting before it moved the whole thing over. This was done using gear ratios for timing. As shown in the picture, the mechanism would move along the box of dirt and plant. Ultimately, this was unsuccessful due to a wear in the gears that caused slipping. The mechanism incorporated into our final prototype can be seen in our demonstration video. 

Animation of Linkages

From the MotionGen animation above, we can see that our joint attached to the motor rotates 360 degrees. Our loop starts at the left point just above the dirt. After the shovel head breaks into the ground at a 45 degree angle, we continue to dig deeper into the dirt. As the shovel collects dirt underground, it also pushed dirt to the right side of the first loop. Once the shovel comes out of the ground at the right side, it deposits the excess dirt and then immediately reverses its direction to push dirt back into hole that was dug out. As it does this, it moves to another fresh patch of dirt to repeat the planting process in a new spot. The animation for our final prototype can be seen below.

MotionGen Animation of our Final Design

Analysis of Final Prototype Design from MotionGen 

For our prototype, we know that we needed to have a complex motion based on the criteria of what seed we will be planting. For this project, we have specifically chosen to work with a sow bean due to its planting criteria. After reading instructions on how to plant a sow bean online, we learned that our linkage system must be able to dig between one to two inches deep into the dirt for our seed. We also learned that each seed that we plant needs to be at least three inches apart. For our prototype that only focuses on the depth of the shovel into the ground, we did not need to account for the three inches apart criteria.  We also researched that the best angle to shovel at was between 35 to 45 degrees. A sow bean must also be planted loosely with dirt, so our shovel does not need to tightly compact the dirt. With this in mind, we decided that a figure eight motion for our linkage system would work well for the planting motion with the shovel that we wanted. The purple circle on the image represents the location of the motor or rotation. In the final project, this will be the location of the gear that is on the side of the prismatic joint. An image of our final prototype design in MotionGen can be seen below.

MotionGen Image: Ideal Motion Profile Plot - 

To better analyze our motiongen, we have drawn on our image to make sure our criteria for planting a sow bean correctly are met. From our starting position right above the ground of dirt on the left side, we begin digging at about a 45 degree angle. We then continue to dig deeper into the ground and approach a less intense angle over time until we are about 1.5 inches deep into the soil. After we have met our depth criteria, the shovel brings the dirt out of the ground until it is just above the ground surface. In our third step, the back of the shovel head pushes back dirt into the whole. In the final step, the shovel head returns to its initial starting position. An image of these descriptions can be seen below. 

MotionGen Image with Drawn Descriptions - 

Mobility and Linkage Lengths

In terms of mobility, our prototype must be able to cover a large area in the x-direction to account for the at least three inches in gap between each seed. Our prototype is able to rotate from 0-360 degrees at theta at the location of the motor. In terms of lengths, our prototype is able to reach a depth of 1.75 inches into the dirt and move a total of 2.25in in height to account for the depth of 1-2 inches needed. Our shovel works with about 8.75 inches across the dirt in the x-direction to account for the large gap between seeds needed. From our MotionGen, we are able to determine the lengths (in inches) of each link we will need. These lengths are as follows: L1 = 5.387in, L2 = 3.093in, L3 = 5.761in, L4 = 4.824in, L5 = 7.982in, and L6 = 6.824in. An image of this can be seen below. 

MotionGen Image with Drawn Mobility

Kinematic Analysis

The kinematic analysis was done using MATLAB. The desired motion profile was successfully derived through the transition of our manual experimentation to the linkage simulation. Performing kinematic analysis before manufacturing is vital to view our motion and force profile to determine if our proposed design will fail or be successful. To begin the analysis, we took the link measurements from Motiongen. We found that our mechanism could be treated as a four-bar instead of a six-bar for our analysis (This was a major change from our prototype to our final design). Yet, our project had some differences from a traditional four-bar. As mentioned earlier, our mechanism has a coupler point. We want the motion profile of that point because our shovel translation and angle of attack will be attached here and follow it. We found that an offset was required to obtain the adequate digging motion. We found that that the most optimal offset was around -70% in the x axis and -160% in the y axis. The angle of attack was set at -45 degrees based on research. After this, we used the equations of motion for a four-bar and attached that offset for every calculation. We ran these calculations taking in the input angle, which was free to rotate fully, as a limit of iteration. Every coordinate was then plotted. Our mechanism must be able to cover a sufficient area in the x-direction to account for digging and lifting dirt of the way. Additionally, our mechanism must reach a depth of at least 1.75 inches into the dirt to account for the depth of 1-2 inches needed to plant a seed. As shown on the plot below the shovel travels 6.08 inches across the dirt in the x-axis and has a range of 2.06 inches for height. An image of our position analysis can be seen below. 

Matlab Position Analysis of our Final Design

The second part of this analysis was the mechanical advantage. Again, we used the equations for mechanical advantage of a four-bar. Here we were interested in the range of angles between 90 and 270 degrees. This is when our shovel will dig the dirt and lift it out of the way. As shown in our mechanical advantage plot, we maintain a mechanical advantage greater than one throughout our input angles. This means our shovel head will have enough force to break through the dirt. From the plot, the mechanical advantage seems to be reasonable from 90 to 180 and then increases exponentially and approaches infinity. This is because the four bar reaches a toggle point. Despite this, its important to note that our linkage maintains a mechanical advantage above one throughout the movement. An image of our mechanical advantage can be seen below.

Matlab Mechanical Advantage Analysis of our Final Design