18.1 - Project Proposal

Introduction

We propose our robot, called DSLR (Do sketch Like Real), which creates complex motions to draw the object. Many types of drawing robots have been introduced publicly such as wire-based robots connected to wires that allow unconstrained motions, simple linkage robots that either can only draw curves using one motor or draw both curves and lines with the help of at least two motors. Our team’s goal is to design a mechanism that can generate the motion for the sketch which involves curves and lines using one motor. Specifically, the main mechanism of DSLR comes with the integration of cam and crank-slider systems that can handle non-linear and linear motion respectively.

Problem Statement

Complexities with Motion

The DSLR robot will need to be able to move with 2-3 DOF depending on the level of complexity of the machine. At its most basic level, the robot will need to move the drawing implement in the X-Y plane to draw figures. Additional levels of complexity would include:

The ability for the robot to lift the drawing implement on and off the page along the Z axis to start and stop drawing.
The ability for the robot to interchange implements or use multiple implements at once.

Complexities with Construction

To successfully produce drawings with high aesthetic quality and replicability, we will need to introduce high levels of control. This will include reducing or eliminating jamming, backlash issues, and slippage in the gears. With the linkages, we will need to avoid any possible locking or flipping at toggle points. Lastly, the cams will need to be carefully fabricated, as any errors in their construction will be seen in the pathing of the mechanism.

When successfully controlling for these factors we will be able to produce either the same drawing every time, or a high-quality drawing using the same set of motions. These drawings will have smooth curves, straight lines, and recognizable geometric shapes.

Need for Non-Joint Solution

This task could not be achieved using only simple linkages because we plan to use the robot to draw complex shapes and designs within a set boundary. The pathing for linkages and cranks consists primarily of repeated circles, curves, and straight lines. To use only linkages for drawing of the complexity that we plan would require complex digital control or a large unruly machine that could not be easily adapted to a different drawing. The issue with using only linkages is heightened, when considering that the complex motions needed to produce the drawing will need to be produced using a single motor.

Mechanism

The main challenge of this project is encoding a drawing into a physical mechanism. Joint based mechanisms alone become incredibly complex with harder shapes. However, wave-based functions can create all sorts of shapes, and thus are still desirable. CAM-follower systems are thus a great method of encoding our desired drawing of a longhorn logo, as they use an eccentrically shaped cam to encode motion for the rolling follower to execute as the cam rotates. It is this system we seek to use, where the CAM and follower are oriented horizontally and the follower holds a marker. Specifically, the CAM-follower system would be spring-loaded such that the follower stayed attached to the CAM profile. The main issue to solve with this system is that some shapes are complex for one CAM - and thus some sort of CAM hybridization will likely be necessary. Further, precision in the mechanism is highly desired, and thus choosing the right types of CAM and follower methods with correct tolerancing will be required.

Proposed scope

Design and prototype mechanisms for drawing primitives

Straight lines
Curved lines

Design and prototype mechanisms for transitions between primitives
Run analyses and simulation to create a specific drawing by combining primitives and transitions
Design a non-motor driven mechanism to raise and lower the drawing platform

Preliminary Design

While the final sketch will be determined by a process of iterative design, prototyping, and assessment of feasibility, the basic set of mechanisms which we will use to control this form remain consistent throughout and reflect the description found in the mechanism section. The key will be in how we combine these individual mechanisms over the same work area to produce the sketch.

To more effectively discuss this combination, we will examine a few preliminary thrusts that we will explore to decide which sets of mechanisms will benefit the final design most through such things as smoothness of motion, ease of manufacture, and replicable motion.

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

(2) A plot showing the path of point P and the flower petal shape that would be produced when the input link completes one full revolution

Gruebler’s Equation for the pictured 4-bar mechanism: M = 3*(4-1) - 2*4 = 1

Grashof Condition: Class I

S + L = L2+L4 = 4 + 9.32 = 13.32

P + Q = L1 + L3 = 6 + 8.88 = 14.88

Figure 3: An example of a slider crank mechanism which follows along a rail, by attaching a drawing implement this mechanism could be used to draw straight lines

Gruebler’s Equation for slider-crank: M = 3*(4-1) - 2*4 = 1

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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