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DMD_poster(5)
1
DYNAMIC MATHEMATICAL DISPLAY ABSTRACT It is often forgotten students are learning to build a better future. As a group of students, we are looking to create a form of innovative technology that provides a learning experience through two of the most important learning methods: visual and kinesthetic. To provide hands on learning experience, we have created the Dynamic Mathematical Display (DMD). The DMD is a device with pins placed within a three by three grid. The pins are 150 mm length, 12.5 mm width, and each controlled by individual motors and slide potentiometers. The dynamic movement of each pin is measured by the potentiometer's linear resistance, which is monitored electronically by a computer program. That program will engage the pin to move to a given point projected from 3D graph. The main purpose of the DMD project is to create a morphing table that will allow a user to visualize complicated 3D graphs with all their components such as depths and peaks. These components will be represented by light emitting diodes (RGB LEDs), which are attached to each pin. The LED's are programmed to provide color based on the physical location of the pin at the time according to the projected graph. Both instructors and students will have the option to manipulate the brightness and color of the LEDs. While the pins provide kinesthetic information to a graph, the LEDs provide additional visual information similar to a topographic map, enhancing the learning experience of a student by presenting more realistic and information-rich representations of physical models. INTRODUCTION HYPOTHESIS There are multiple methods in which multivariable equations can be visualized. Many of the traditional methods of visualizing these complex equations is on a two dimensional format. In order to display multivariable graphs in a three dimensional format, the Dynamic Mathematical Display coordinates a three by three grid of pins to move to different depths and peaks to imitate a three dimensional model. RGB LEDs are placed inside of each pin to enhance depth perception of the three dimensional graph. METHODOLOGY During the planning of the Dynamic Mathematical Display, it was challenging to immediately find the right materials to make the desired apparatus. Initially, the stepper motor was used to move the pins, however based on the errors received from the prototype it was clear that a new solution was needed. The final prototype consisted of the slide potentiometer’s DC motor, and new pin design. The control system for the RGB LEDs is consisted of Python coding language and Raspberry PI microcontroller. The primary control system for the pins consisted of JAVA, Arduino Uno and coding platform. Originally, the two systems above were thought to affect the function of the apparatus, but after several run of both systems on the apparatus, no conflicts occurred. SYSTEM ANALYSIS The leveling position in which the DMD displays the pins ranges from 0, 50 and 100. Although, the graph formed by the pins could be interpreted into equations other than the equation originally input. For proof of accuracy, several equations were calculated based on ideal modeling versus what the graph would look like in pins formation. The comparison between the ideal graph and actual graph formed by the pins has little error margin (FIG 1 and FIG 2). The slide potentiometer’s DC motor is controlled by a motor- shield, an Arduino and Arduino coding language. As the primary motor for the pins, the potentiometer receives feedback by the force put on by the weight of the pins. The constructed system that drives the pin has a total of 98% accuracy and 2% error in positioning. COMPONENTS PINS (FIG 3) The DMD consists of nine 3D printed pins (150mm length and 12.5mm width). The pins are placed in a acrylic table top with laser cut to fit this size of the pins. SLIDE POTENTIOMETER (FIG 6) The movement of the pins is controlled by slide potentiometer’s DC Motors. The pins and the motors are connected by linkages. As the motors have a side to side motion, they are mounted vertically on acrylic plate. There are three rows of acrylic plates within the apparatus and three motors on each acrylic. ARDUINO - MOTOR SHIELD (FIG 5) The DMD used Arduino Uno to micro control the movement of the pins. The Arduino Uno works together with three Adafruit motor shields, which allows the Arduino to drive the motor, controlling the speed and position the pins. RGB LEDs – RASPBERRY PI (FIG 3 & 4) The RGB LEDs are assistive elements of the DMD projection of mathematical graphs. The lights are controlled by the Raspberry PI. The coding for this component is done in Python coding language. CODING METHOD The controls of the slide potentiometer was programmed in Arduino coding language. The movement of the pins according to a mathematical equation is based off of the JAVA coding language. Frame (FIG 6) The frame of the apparatus is made out of wood. The total dimension of the interior frame is 24” by 7.375”. The dimension of the foot and the top is 9” by 9”. CONTACT: Chelsie Zamelis (lead)- [email protected] Hamzeh Musleh - [email protected] Ni Nguyen [email protected], Andrew Ruiz [email protected], Alexandra Serdyuk- [email protected] Matthew Ferro – [email protected] Michael Madalina - [email protected] San Min Liew - [email protected], Christopher Dombrowski - [email protected], Jesslyn Budiman - [email protected] CONCLUSION The Dynamic Mathematical Display was able to successfully model several forms of multi-variable equations. The RGB LEDs worked very well in enhancing the depth perception of the graph. The motor system that drives the pin yielded only 2% in error in positioning. The apparatus provided sufficient examples of tangible multivariable graphs. However, the three by three grid is too low in resolution, the DMD can only graph simple equations. ACKNOWLEDGEMENTS Tom Flemming (advisor), Engineering Physics Jason Sawatski, Engineering Department Patrick Burnett, Engineering Department FIG 1 : General equation Z(m,n) = ℬ((x + m) 2 + (y + n) 2 ) + ∝ FIG 2 : Actual equation Z(m,n) = 50((x + m) 2 + (y + n) 2 ) + 0 FIG 4 : Raspberry PI and circuit board mounted on acrylic side frame FIG 3 : RGB LEDs mounted inside of pins FIG 5: Left, three motor shield mounted on top of the Arduino Uno. Right, linkages and pins placed in the acrylic table top FIG 6 : Dynamic Mathematical Display fully assembled.
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Transcript of DMD_poster(5)
DYNAMIC MATHEMATICAL DISPLAY
ABSTRACT It is often forgotten students are learning to build a better future. As a group of students, we are looking to create a form of innovative technology that provides a learning experience through two of the most important learning methods: visual and kinesthetic. To provide hands on learning experience, we have created the Dynamic Mathematical Display (DMD). The DMD is a device with pins placed within a three by three grid. The pins are 150 mm length, 12.5 mm width, and each controlled by individual motors and slide potentiometers. The dynamic movement of each pin is measured by the potentiometer's linear resistance, which is monitored electronically by a computer program. That program will engage the pin to move to a given point projected from 3D graph. The main purpose of the DMD project is to create a morphing table that will allow a user to visualize complicated 3D graphs with all their components such as depths and peaks. These components will be represented by light emitting diodes (RGB LEDs), which are attached to each pin. The LED's are programmed to provide color based on the physical location of the pin at the time according to the projected graph. Both instructors and students will have the option to manipulate the brightness and color of the LEDs. While the pins provide kinesthetic information to a graph, the LEDs provide additional visual information similar to a topographic map, enhancing the learning experience of a student by presenting more realistic and information-rich representations of physical models.
INTRODUCTION HYPOTHESIS There are multiple methods in which multivariable equations can be visualized. Many of the traditional methods of visualizing these complex equations is on a two dimensional format. In order to display multivariable graphs in a three dimensional format, the Dynamic Mathematical Display coordinates a three by three grid of pins to move to different depths and peaks to imitate a three dimensional model. RGB LEDs are placed inside of each pin to enhance depth perception of the three dimensional graph. METHODOLOGY During the planning of the Dynamic Mathematical Display, it was challenging to immediately find the right materials to make the desired apparatus. Initially, the stepper motor was used to move the pins, however based on the errors received from the prototype it was clear that a new solution was needed. The final prototype consisted of the slide potentiometer’s DC motor, and new pin design. The control system for the RGB LEDs is consisted of Python coding language and Raspberry PI microcontroller. The primary control system for the pins consisted of JAVA, Arduino Uno and coding platform. Originally, the two systems above were thought to affect the function of the apparatus, but after several run of both systems on the apparatus, no conflicts occurred. SYSTEM ANALYSIS The leveling position in which the DMD displays the pins ranges from 0, 50 and 100. Although, the graph formed by the pins could be interpreted into equations other than the equation originally input. For proof of accuracy, several equations were calculated based on ideal modeling versus what the graph would look like in pins formation. The comparison between the ideal graph and actual graph formed by the pins has little error margin (FIG 1 and FIG 2). The slide potentiometer’s DC motor is controlled by a motor-shield, an Arduino and Arduino coding language. As the primary motor for the pins, the potentiometer receives feedback by the force put on by the weight of the pins. The constructed system that drives the pin has a total of 98% accuracy and 2% error in positioning.
COMPONENTS PINS (FIG 3) The DMD consists of nine 3D printed pins (150mm length and 12.5mm width). The pins are placed in a acrylic table top with laser cut to fit this size of the pins.
SLIDE POTENTIOMETER (FIG 6) The movement of the pins is controlled by slide potentiometer’s DC Motors. The pins and the motors are connected by linkages. As the motors have a side to side motion, they are mounted vertically on acrylic plate. There are three rows of acrylic plates within the apparatus and three motors on each acrylic.
ARDUINO - MOTOR SHIELD (FIG 5) The DMD used Arduino Uno to micro control the movement of the pins. The Arduino Uno works together with three Adafruit motor shields, which allows the Arduino to drive the motor, controlling the speed and position the pins.
RGB LEDs – RASPBERRY PI (FIG 3 & 4) The RGB LEDs are assistive elements of the DMD projection of mathematical graphs. The lights are controlled by the Raspberry PI. The coding for this component is done in Python coding language.
CODING METHOD The controls of the slide potentiometer was programmed in Arduino coding language. The movement of the pins according to a mathematical equation is based off of the JAVA coding language. Frame (FIG 6) The frame of the apparatus is made out of wood. The total dimension of the interior frame is 24” by 7.375”. The dimension of the foot and the top is 9” by 9”.
CONTACT: Chelsie Zamelis (lead)- [email protected] Hamzeh Musleh - [email protected] Ni Nguyen [email protected], Andrew Ruiz [email protected], Alexandra Serdyuk- [email protected] Matthew Ferro – [email protected] Michael Madalina - [email protected] San Min Liew - [email protected], Christopher Dombrowski - [email protected], Jesslyn Budiman - [email protected]
CONCLUSION
The Dynamic Mathematical Display was able to successfully model several forms of multi-variable equations. The RGB LEDs worked very well in enhancing the depth perception of the graph. The motor system that drives the pin yielded only 2% in error in positioning. The apparatus provided sufficient examples of tangible multivariable graphs. However, the three by three grid is too low in resolution, the DMD can only graph simple equations.
ACKNOWLEDGEMENTS Tom Flemming (advisor), Engineering Physics Jason Sawatski, Engineering Department Patrick Burnett, Engineering Department
FIG 1 : General equation Z(m,n) = ℬ((x + m)2 + (y + n)2 ) + ∝
FIG 2 : Actual equation Z(m,n) = 50((x + m)2 + (y + n)2) + 0
FIG 4 : Raspberry PI and circuit board mounted on acrylic side frame
FIG 3 : RGB LEDs mounted inside of pins
FIG 5: Left, three motor shield mounted on top of the Arduino Uno. Right, linkages and
pins placed in the acrylic table top FIG 6 : Dynamic Mathematical Display fully
assembled.
