Assignment #3: Plotter Pen Mechanism
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Goal:
The goal of this project is to create a 1 degree-of-freedom linkage mechanism that moves an initially vertical pen positioned on a piece of paper to its vertically pen cap which is 1-cm above its initial position. Students must create a multi-body simulation of this mechanism on SOLIDWORKS. Additionally, the mechanisms motor's speed and torque necessary to perform a start to finish mechanism in 500 milliseconds must be calculated based on the geometry and material parameters.
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Constraints:
The following constraints must be considered when designing the linkage mechanism:
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The mounting surface is 1-cm above the paper/pen tip.
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The pen is initially vertically positioned on top of the paper.
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Then pen cannot extend below the paper.
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The mechanism cannot be attached or mounted to the paper or the mounting surface.
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There cannot be any permanent fixtures to any surface.
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The mechanism is actuated by a servo motor or a stepper motor.
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The links must be made of AISI 1020 Steel.
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The mechanism must be executed in 500 milliseconds.
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Information and Assumptions on the Pen and Pen Cap:
The pen chosen for this project is a BIC black pen. The cap itself has a length of 4-cm and the radius of the hole is 1-cm. The part of the pen to be capped (referred as the pen tip for the rest of this project) is also 4-cm. To obtain realistic results of the mechanism working, the pen cap is assumed to be held in place such that contact with the tip of the pen would not cause it to topple over and will be at the edge of the mounting surface. The mounting surface will also act to help secure the final position when the tip is coming into the cap. Additionally, the pen tip has a triangular geometry so approaching the pen cap at an angle becomes feasible. Furthermore, the pen tip cannot faze through the pen cap since the cap is solid, therefore the pen tip must approach the entrance of the pen cap hole 4-cm above the bottom of the pen cap. This will be visually shown in the initial design through Math Illustrations to clarify the explanation. Finally, the links must not interfere/obstruct the path of other links because in real prototype design, this will not work even though it might work in a simulation.
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Mechanism Design:
Image Source: ME360 Product Design, Assignment #3 - Plotter Pen Mechanism, ESGW, 3/23/2021
Figure 1: The design of the mechanism which works to transition the pen tip (AB) to the pen cap (A'B')
Design of Mechanism in SOLIDWORKS:
M
L
P1
I
H
B
A
Figure 2: The assembly of the linkage mechanism, where the links are dimensioned based off values from the Mathworks Illustration figure
Motor Torque and Speed Specification:
Calculations of the Motor Torque and Speed:
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Assume that the lead of the screw is 2.5*10^-3 m.
The path the pen takes is the square root of (5cm)^2+(1cm)^2, so the distance it must travel from stop-to-stop 500 milliseconds is 5.1cm.
Using the formula A=1/2*b*h, where A is 5.1cm, b is the 500 milliseconds, and h is the maximum velocity gives a maximum velocity of 0.204 m/s.
The acceleration is calculated using the solved maximum velocity, 0.204 m/s divided by half the time it takes to complete the mechanism, 250 milliseconds, which solves out to 0.816 m/s^2. Since gravity is considered, 9.81 m/s^2 must be added to the acceleration. This gives an acceleration of 10.63 m/s^2
Physical Prototype of Linkage Mechanism:
By using the dimensions of each link from Math Illustrations, a physical prototype can be built to check if the design would work in real life.
Since the incorrect Arduino kit was provided (which was missing the links and screws), the links and fixed support were created using a foam board and exacto knife.
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Figure 1, shown on the left, is a picture of the pen mechanism at the position that it is stopped.
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Note that the fixed support holding the links would be attached to a nearby wall and that pins are used to represent the joints.
Conclusion and Future Work:
A 1-DOF linkage mechanism that could move a pen to the two stop-to-stop positions was successfully created. In all three cases (Math Illustration, SOLIDWORKS, and physical prototype), the mechanism performed the same course of movement consistently.
The next steps to improve this mechanism would be to attach clasps that would grab and release the pen in 500 milliseconds so that the pen could be released when inserted into the pen cap. Additionally, the weight of the links should be considered into the calculations of the motor torque, since the additional weight would contribute to additional torque needed. Furthermore, another step to consider the hole and clearance tolerance for the pen cap - thus design the BIC pen cap so that the mechanism would guarantee that the pen tip would fit every time the mechanism is performed. Another next step to take would be to redesign this mechanism with other types of mechanisms such as 2-DOF systems instead of solely using linkages.
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Citations:
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BIOVIA, Dassault Systèmes, SOLIDWORKS Education, 2020, San Diego: Dassault Systèmes, Accessed March 23, 2021.
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Saltire Software, Math Illustrations, 2020. Accessed March 23, 2021.