The analysis that will need to be performed prior to fabrication is for the motion and force profiles of the coupler point. The analysis was done using MATLAB. The desired motion profile was successfully derived through the transition of our manual experimentation to the linkage simulation.
We realized that this mechanism would essentially be replicating an arm digging. After trial and error, we designed a four bar with a coupler point. 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.
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 attack 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.
Design Process
Shown below is the development of our project. In V1 we were coming up with a mechanism that could rotate fully and was capable of digging. Clearly, our motion path was not settled yet. The angle of attack was not ideal and it would get stuck if it hit the ground that way. We found that a fixed height would work best for our situation as well. We changed things for V2. This was now the mechanism we wanted with the ideal infinty motion path and 45 degree angle of attack into the ground. It would traverse the ground pick up dirt and come back. To do this we added the coupler point with two more linkages and elavated our input link. We took this to prototype. Our prototype was made of acrylic and mounted on a wooden beam. When tested it performed just as expected. We took suggestions that improved our design from this point as well. We opted to use wood for the final version because it was faster to work with and adaptable. We found that the coupler point could be done with rigid triangular-like body. There was no need to have it as linkages so we modified this accordingly. Thanks to this, we were able to incorporate a seed dropping maze within the thickness of the triangular body. 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. When making the final prototype we found that the yellow shovel design was collided with the ground and linkages. Instead of making spacers, we opted for the easy alternative of offsetting the shovel so it would not collide with the ground. This fixed the issue and our mechanism was now flush and met all requirements. Beyond this, we wanted to implement a way for the mechanism to move forward to another piece of land for our final version. This was done with a gear system connected to the motor and a long shaft that drived our wheels using rubber band belts with the same rotation of the motor. 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. As shown in the picture, the mechanism would move along the box of dirt and plant. Ultimately, this was unsuccessful due to a gear that was too tight and didnt fit properly on the motor. However, our final version is still mounted on these wheels and gears.
V1
V2
Acrylic Prototype
Seed Maze
Offset Shovel
Final Version
Kinematic Analysis
Plots and Description of Ideal Motion Profile
MotionGen Image: Ideal Motion Profile Plot -
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.
MotionGen Image with Drawn Descriptions -
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. In our final project, we will include the water and seed dropping into the soil in between steps two and three.
Mobility
MotionGen Image with Drawn Mobility
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.
Position Analysis
Matlab Position Analysis Plot
In order to do a position analysis of our prototype, we chose to break up our analysis into three steps. In our first step of analysis, we designated link two as our crank, link six as our coupler link, link three as our output link, link one as our fixed link, and link four as our coupler extension. Because our input angle for our shovel is 45 degrees into the ground (below the y-axis), we have designated our coupler extension angle to be 45 degrees. We also know that our system will rotate from 0 360 degrees. In section two, we calculated our output angles and accounted for an offset due to our bar being a six-bar linkage system rather than a four-bar linkage system. Once we calculated these values, we plotted the position analysis in the x and y-direction of our shovel head. Attached below is our code for this analysis.
Matlab Position Analysis Code
Mechanical Advantage
Matlab Mechanical Advantage Plot
In our linkage system, it is important that we have a mechanical advantage greater than one. If our value of mechanical advantage is less than one, then our linkage system will not be able to rotate and move the way we intended. If our ratio of output force to input force is at least great than one, then we know that our linkage system will be able to rotate completely and that our shovel head will also have enough force to break through the dirt. As seen in our mechanical advantage plot, we maintain a mechanical advantage greater than one throughout our input angles. Because of this, we know we have enough output force to overcome the input forces our linkage system has to overcome. Attached below is our code for this analysis.
Matlab Mechanical Advantage Code
Brief Analysis of Other Mechanisms Used
Rack and Pinion on Prismatic Joint Design Drawing
This design is intended for our final demonstration. Similar to our second build assignment, we will create a prismatic joint, except we will include a rack and pinion mechanism to create a way to time the rotation of our six bar linkage system. The sizes of the slots on the rack and the number of teeth on the gear will help us leave a necessary gap in between each cycle of the shovel looped path. This gap will allow enough time for us to deposit the water and the seed with our described tube method in our proposed mechanism summary.
Animation of Linkages
MotionGen Animation
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 returns to its starting position and the cycle continues for as long as we move the prismatic joint.