Mechanism Design
We originally thought of building a 4-bar crank and rocker mechanism to archive a limited curved path. We wanted to retract the dart holder to reload it, then a quick stop so the dart slides out.
This original design was too simple and created a uniform curve, but the path that a dart taken when thrown by a human has a more logarithmic curve shape.
Therefore the team looked into 6-bar systems that would create a similar shape. We wanted a continuous rotating in the input link for the DC motor, and for the links to constraints the path for the output.
Below is the stevensons II six bar design, with the path of the top link.
The top half curve of the output link follows the desired path and fulfills the requirement for the input link to do a full rotation. We decided to edit this setting to get the desired output curve, resulting in the following mechanism design:
The adapted stevenson’s II mechanism edited the lengths of the links, and the orientation of the second link. It contains the requirement for full rotation on the input link, creates the natural curve of a dart throw, and completes a quickrelease when input rotates counterclockwise.
Calculating Mechanism Dimensions
Our team used the Planar Mechanism Kinematic Simulator to create the mechanism previously shown. This software returns the x and y coordinates of each of the joints. Therefore, the team had to calculate the link lengths and angles based on the provided coordinates. To do so, we wrote a MATLAB code that inputs the coordinates and maps out the mechanism.
Initializing Coordinates
Calculating link lengths
Calculating initial position angles
From the above MATLAB code, we calculated the below link lengths and angles.
| Link Names | Link Lengths (mm) | Link angles (deg) |
1 | "ground x" | "5.643" | "323.3201" |
2 | "ground y" | "-0.511" | "-29.27814" |
3 | "input" | "3.3625" | "100.6081" |
4 | "tri_top_bottom" | "7.3597" | "45.88632" |
5 | "tri_top_left" | "3.571" | "53.24242" |
6 | "tri_top_right" | "3.8454" | "39.05772" |
7 | "middle" | "2.4721" | "12.97377" |
8 | "output" | "5.045" | "150.92" |
9 | "tri_ground_top" | "5.0201" | "173.3195" |
10 | "tri_ground_left" | "7.4328" | "103.3482" |
11 | "tri_ground_right" | "7.4087" | "63.80848" |
This data was used to create a Solidworks model of the mechanism.
SolidWorks Model
The Soldiworks model encountered a few iterations discussed in Manufacturing and Assembly section.
In order to make the model more modular for future edits, all the link lengths relationships from joint to joints were linked to the global equations folder.
All the original lengths from the MATLAB code previously shown were saved in the equation and divided by a gain. The gain was to make the input link 10cm, then it would scale all other links to their respective proportions. It also allowed the team to change the overall shape of the links without affecting the integrity of the geometry. As can be seen in Manufacturing and assembly when the teams withced from high surface are to a bone structure.
The team was provided a high speed 12V pololu motor. The input link is directly connected to the motor. The spacing between the grounded links is also crucial fro the correct movement of the output. For such design, the motor had to be elevated to exactly 1 in, and the correct distance was positions with the holes on the base of the mechanism.
Its important to note that although the T and the top 3 link joint seem symmetric, they are not.
With the sides of the top 3 link bar having a 12 mm difference, adn the T-link a 1 mm difference. The orientations for these links was also taken into account when manufacturing.