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Redwood Discovery Museum brachistochrone

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Abstract[edit]

The Redwood Discovery Museum in Eureka requested a Brachistochrone exhibit from our team of engineering students at Humboldt State University. Our team successful designed, tested, and built an exhibit that demonstrate the Brachistochrone question in a fun and educating way.

Brachistochrone2.gif

Background[edit]

The Redwood Discovery Museum, located in Eureka CA, is geared towards presenting scientific knowledge in a fun and engaging way to children of all age groups. The client required a functional demonstration of the Brachistochrone question and has contracted Team Schmotron of Humboldt State University’s Engineering: Introduction to Design Fall 2017 class to design the exhibit.


Problem Statement and Criteria[edit]

The objective of this project is to design and build a functional Brachistochrone exhibit and present the concept in a fun and educational method; while maintaining a sturdy, child-safe structure that is both aesthetically pleasing and engaging.

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Description of final project[edit]

Photos and Descriptions of the Brachistochrone Exhibit.

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Costs[edit]

Bracost.jpg

Testing Results[edit]

A Prototype of the Dual-Track Design

The results of the design prototypes led to the creation of a fully functional final design of the Brachistochrone exhibit. The final design is an educational tool capable of demonstrating the concept of the Brachistochrone path of quickest decent in an engaging, informative, and fun manner.


The initial track prototype, shown to the right, proved to be successful for use with balls and cars and was incorporated into the final design. The heights of the walls were slightly too tall in the prototype and were scaled down in the final design to allow balls to roll down the center gap without touching the walls.


The end gate prototype proved to be successful in accurately detecting the winning vehicle. A foamboard prototype was created to test the circuitry for the end gate. Components were then placed into the foamboard prototype, two tracks worth of circuitry was installed for testing. On the final design the circuitry is scaled up to four tracks and is able to reliably detect the winning vehicle, whether it be a car or a ball.

How to build[edit]

Construction of Track

Visuals of Tracks
Figure 5-1 Example of Possible Curve Layout

For the construction of the tracks one will need to cut all three sheets of plywood into 6 half inch 4’x4’ sheets of plywood by cutting each of the 4’x8’ sheets of plywood in half. One will then need to use a computer equipped with designing software such as AutoCAD or Autodesk inventor. On these programs one needs to replicate the dimensions of each 4’x4’ sheet of plywood including the width. On these programs one will then sketch the desired pair of slopes similar to those of Figure 5-1 making sure that only one pair of slopes of a track is that of a cycloid. You should have a design similar to Figure 5-8. Once you have these drawn in a design program they will need to be exported as a DWG or a DXF file so that the shapes of the tracks can be cut out by a CNC machine. Once all these shapes are cut out and you have 4 pairs of identical quadrilaterals, you will want to join each of these pairs to another one with a half inch gap in-between them as shown in Figure 5-8. These four tracks will then be given walls that start after the 1.5 inch space center at the centerline. All four built tracks then will be constrained to a total width of 15”. Within these bounds the tracks will be spaced evenly and then attached to the base which is another 4’x4’ sheet of plywood. Wood glue and screws will need to be used as necessary. The end product of the tracks on the base will look like that of shown in Figure 5-8.

Construction of Start

Level Pull Start Mechanism

Starting mechanism can be constructed with a door hinge and some plywood. A hinge links the rotating door/projectile housing to the body of the Brachistochrone. The lever should be at least a foot in length in order to give an enough torque for an easy open. Since each path starts at a different angle the projectile housing must be measured for each individual track. If the measurements are calculated and pieces of wood cut to dimensions then they can be put together with a drill and screws easily.


Construction of Finish

Figure 5-12 Arduino Finish Gate Base Plate

The finish line placement mechanism is constructed from wood, with a sturdy metal housing used for the gate portion. Begin by measuring the width of the metal box to be used as the gate housing. Cut a piece of ½” plywood that spans the width of the metal box to be used as a base, and extends 6” out of the back, and 2” out of the front. Draw a line across this board directly in the center of 6” metal housing, which is 9” from the back and 5” from the front. Drill 4 holes on the center line, starting at 2.4” from the side, then space each hole 3.5” from the previous hole, see Figure 5-12.

Figure 5-13 Finish Gate Front View

Construct a box to hold the Arduino, wiring, and LEDs which will be mounted above the base board. The box is to be positioned so that the infrared receiver and infrared transmitter are located within 4 inches of each other. Drill out 4 holes to mount the infrared transmitters located above the holes for the infrared receivers. Drill out 4 additional holes on the front face place of the box for the indicator LED’s. Cut 8 14” long, ½” wide strips of ½” plywood to be used as track, cut 8 14” long, ¾” wide strips of ½” plywood to be used as track wall. See image Figure 5-13. Glue the track strips so that there is a ½” gap in between, with the hole for the infrared receiver positioned in the center of the ½” gap. Glue the track wall strips on the outside of each track strip to form the dual use track.

Wire up all the electrical components for the circuit based on the provided schematic seen in Figure 5-14. I highly recommend creating a test circuit first using a solderless bread board before creating the final circuit. Begin final circuit by soldering 330Ω resistors to the anode of each indicator LED, the anode is the short leg on the indicator LED, then solder ground wire to the other side of the resistor, and color-coded wire to each cathode. The ground wire will lead to the main ground on the Arduino and each cathode wire will lead to PIN10,11,12,13 on the Arduino. Next solder 220Ω resistors to the cathode of each IR LED, the cathode is the long leg on the IR LED, with ground wire soldered to the other side of the resistors. Solder color-coded wire to each cathode of the IR LED and run them to PIN6,7,8,9 on the Arduino. Solder four 330kΩ resistor to the positive lead wire from the 5v port on the Arduino unit, then solder the other side of each 330kΩ resistor to both the wire connected to the cathode of each IR Phototransistor and to each wire that connects to PIN2,3,4,5 on the Arduino. The cathode is the long leg on the IR Photo-transmitters. Make sure to implement a quick disconnect on the wires that travel between the lower base plate (for the IR Phototransistors) to the upper box that houses the Arduino in order to be able to separate the two halves for maintenance, also leave extra slack on these wires to make for easy connection/disconnection. Label each side of the quick disconnects in order to ensure proper reconnection. Power the Arduino with a AC to DC transformer rated between 7.5-12V 600mah-1000mah DC.


Figure 5-14 Wiring Schematic for Ending Mechanism

Programming the Arduino:

In order to interface and program the Arduino the “Arduino IDE” must be downloaded onto a computer. The Arduino IDE can be found at https://www.arduino.cc/en/Main/Software and is available for Windows, Mac and Linux. Download and install the Arduino IDE. After the Arduino IDE is installed, connect the Arduino UNO Microcontroller to the computer via a USB cord. Once the Arduino is connected, open up the Arduino IDE program. At the top of the program, open the drop-down menu titled “Tools” and select “Board” and then select “Arduino / Genuine UNO”. Next, from the same “Tools” drop down menu, select “Port” and the select the port that the Arduino is connected to. If there are multiple ports listed make a note of the ports, then disconnect the Arduino and see which port disappeared, then reconnect the Arduino and select that port. The Arduino is now ready to be programmed. Copy Paste the Arduino code, located after this paragraph, into the Arduino IDE program. Select the “Check Mark” at the top of the screen to verify the code. The sketch will compile and should not result in any errors, if any errors are detected, make sure that you copied the code exactly, including all of the code located between the bolded “Arduino Code Starts Here” and before the bolded “Arduino Code Ends Here” statements. Next, click on the “Right Facing Arrow” icon that is located next to the verify button, that will transfer the code to the Arduino Microcontroller. The Arduino should now be programmed. Disconnect the Arduino from the computer, verify that all wires are correctly connected to the correct pins on the Arduino as instructed by the schematic, then connect a power source to the Arduino, the circuit should now function. The coding for the Arduino is displayed below, copy paste all of the code after the bolded “Arduino Code Starts Here” and before the bolded “Arduino Code Ends Here” statements.

Arduino Code Starts Here

/*

  • Finish Line Detector
  • Lights up LED 1, 2, 3, or 4 depending on which sensor is tripped first
  • Both LEDs light up in the case of a tie
  • /

const int ledPin1 = 13; const int ledPin2 = 12; const int ledPin3 = 11; const int ledPin4 = 10;

const int irledPin9 = 9; const int irledPin8 = 8; const int irledPin7 = 7; const int irledPin6 = 6;

const int sensorPin1 = 2; const int sensorPin2 = 3; const int sensorPin3 = 4; const int sensorPin4 = 5;

// Change this number to increase or decrease time LED stays lit const int TIMEOUT = 4000; // milliseconds - time LED stays lit

// Setup runs once, at start // Input and Output pins are set void setup(){

  pinMode(sensorPin1, INPUT);
  pinMode(sensorPin2, INPUT);
  pinMode(sensorPin3, INPUT);
  pinMode(sensorPin4, INPUT);
  pinMode(ledPin1, OUTPUT);
  pinMode(ledPin2, OUTPUT);
  pinMode(ledPin3, OUTPUT);
  pinMode(ledPin4, OUTPUT);
  pinMode(irledPin9, OUTPUT);
  pinMode(irledPin8, OUTPUT);
  pinMode(irledPin7, OUTPUT);
  pinMode(irledPin6, OUTPUT);

}

// Called repeatedly void loop() {

   // Turn on IR LED
  digitalWrite(9, HIGH);
  digitalWrite(8, HIGH);
  digitalWrite(7, HIGH);
  digitalWrite(6, HIGH);
 
  // Get the Sensor status
  int status1 = digitalRead(sensorPin1);
  int status2 = digitalRead(sensorPin2);
  int status3 = digitalRead(sensorPin3);
  int status4 = digitalRead(sensorPin4);
  // Set the output LED to match the sensor
  digitalWrite(ledPin1, status1);
  digitalWrite(ledPin2, status2);
  digitalWrite(ledPin3, status3);
  digitalWrite(ledPin4, status4);
  if (status1 == HIGH || status2 == HIGH || status3 == HIGH || status4 == HIGH) {
     // A sensor was tripped, show the results until timeout
     delay(TIMEOUT); // Wait for timeout
  }

}

Arduino Code Ends Here

Maintenance[edit]

The Arduino chip components of the finish line are rated to last many years of constant use, if however they do require replacement the price will range depending on the component. The Arduino UNO Microcontroller can be found for $12, the LED and Photoresistors tend to be $0.25 each. Repainting the design will all depend on how much damage the exterior takes from the kids playing with the design. If the damage is minor then painting over will only take a few minutes, costing around $5. To repaint the whole design will take longer. The hinge that is attached to the starting mechanism may have to be replaced depending on the amount of use it gets. Kids could pull the handle to hard and over time may become loose and need replacing. This is a simple replacement, and will only take about 5 minutes with a drill and cost around $5.00. Cleaning may need to be done depending on how much debris gets on the tracks, making it difficult for the vehicles to go down the track. A quick sweep or dusting will suffice and only take about 5 minutes. Hot wheel cars will need to be replaced as they are lost, stolen, or broken. These can easily be ordered online for nearly a dollar per car. Golf balls depending on what kind you buy can vary in price, but the cheapest can be found online for about $0.50 each.

Schedule[edit]

This is when to maintain what.

Daily
Clean/dust as needed.
Weekly

Clean/dust as needed.

Replace Lost/Stolen cars and balls.


Monthly
Clean/dust as needed.
Replace Lost/Stolen cars and balls.
Yearly
Replace hinges on start mechanism.
Replace burned out LED.
Touch up paint as needed.
Every 2 years
Replace burned out LED.
Touch up paint as needed.

Troubleshooting[edit]

Troubleshooting involved testing multiple types of vehicles for the ramps, starting mechanisms, ending mechanisms and xylophone ending sounds.

Discussion and next steps[edit]

We hope that children will be fascinated by the Brachistochrone and encourage them to learn about physics and mathematics. Also we would hope that the educational properties can be used by educators in the surrounding area.

Suggestions for future changes[edit]

The Arduino controlled finish line placement mechanism can be upgraded to monitor and display the descent time of the vehicles. The indicator LED's need to be replaced with digital displays. A closed circuit needs to be added to the Arduino that is connected to the start mechanism. When the start mechanism is raised it will break the circuit. The Arduino is programed to begin a timer when it detects the broken circuit, the timer will stop when the Arduino senses a vehicle cross the infrared beam. The time is then displayed on the digital display. The Arduino code will need to be updated for this feature.

References[edit]

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