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The first area to explore will be linkage mechanisms, such as the 4-bar and slider crank mechanisms. While neither is suitable for the task alone, we would be able to create a simple flower design with the two linkage mechanisms in the figures below. The accompanying equations are used to characterize the system and will be necessary for each permutation of the design.
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Figures 1&2:(1) A 4-bar mechanism to which a pen would be attached at point P
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Gruebler’s Equation for slider-crank: M = 3*(4-1) - 2*4 = 1
Figure 4:
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Another promising mechanism that we plan to test is that of a cam and follower. By shaping the cam we are able to change the shape of the curve produced by the follower traveling along the surface. The use of a cam will allow us to draw more complex curves than would be possible with the path of a joint in a mechanism. We show a tool being used which allows for the manipulation of the shape of a cam (Figure 4), while also showing its path (Figure 5). Using this tool, we were able to create a cam with a path which approximates the UT longhorn logo as an example.
https://www.desmos.com/calculator/lsqv4ouwov
Figures 4 & 5: (4) A plot showing the shape of a proposed cam design
(5) A plot showing the curve generated by a follower traveling along the surface of the cam
The first stage of creating the preliminary design will be the design and prototyping of proof of concept mechanisms for the mechanisms displayed. This will be followed by deciding on how we will automate the interchange between these mechanisms. At this stage we will explore mechanisms such as a planetary gear system or a gear shift system, similar to that seen on a bicycle. Once this is decided we will move on to the analysis stage to formally decide on a set of mechanisms and an interchange system.
An additional consideration is that of how we will start and stop the machine from drawing. The simplest solution of this using a single motor would be a manual system for lifting and dropping the pen before supplying the machine with power. We have include an figure for the screw-based mechanism we would use to attach the drawing implement to the rest of the machine.
Figure 6: A screw-based mechanism used to manually prepare or disengage the drawing implement, and attach it to the rest of the robot