Team:Washington-Software

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Abstract

LegoRoboBricks for Automated BioBrick Assembly

Commercial Liquid Handling Systems are extremely expensive, and are typically beyond the reach of the average molecular biologist interested in performing high throughput methods. To address this problem, our project consists of the design and implementation of a liquid handling system built from commonly accessible Legos. We demonstrate a proof-of-principle use for this system to perform BioBrick assembly by transferring colored dye solutions on a 96-well plate.

We introduce a new concept called LegoRoboBrick. The liquid handling system is build by designing and implementing 3 LegoRoboBrick modular components: ALPHA (Automated Lego Pipette Head Assembly), BETA (BioBrick Environmental Testing Apparatus), and PHI (Pneumatic Handling Interface). We will demonstrate that the same BioBrick assembly software can run on multiple plug-and-play LegoRoboBrick instances with different physical dimensions and geometric configurations. The modular design of LegoRoboBricks allows easy extension of new laboratory functionalities in the future.

Project Goals

• Implement a simple and cheap way to handle liquids in normal genome lab operations(portable genomic science lab)
• Only uses lego mindstorm bricks
• Document entire process so it can easily be replicated

Project Summary

Hardware

• Lego Bricks
  • Commonly accessible industry standard

Firmware

• RobotC
  • Made in CMU Robotics Academy
  • Enables floating point precision

Software

• ALPHA module
  • Precise reverse triangulation using Rotational Matrix
  • Controller of Master-Slave Synchronization
  • Accurately positions pipette head
• PHI module
  • Pneumatic control to suck and dispense fluid
  • Compression pump to "air-clean" system

Mathematical Modeling

Alpha

Problem

Given the following construction and point p, or (x,y,z) find the angles θ₁, θ₂, and θ₃.

Note that positive z is the down direction.

Constants

• TR
  • Top radius
• BR
  • Bottom radius
• L
  • Linkage
• CA
  • Control Arm
• φ₁ and φ₂
  • Two angles

Construction

From the top to the bottom:

• A circle centered at the origin with radius TR, named O
• Make three lines A₁, A₂, and A₃ such that:
  • The lines A_x are perpendicular to a tangent of O and a radius of O,
  • The angle between the radii of A₁ and A₂ is φ₁, and
  • The angle between the radii of A₂ and A₃ is φ₂.
• Make a circle centered at point p with radius BR, named P
• Find three points P₁, P₂, and P₃ such that:
  • They are on the circumference of P,
  • The angle between the radius which touches P₁ and the radius that touches P₂ is φ₁,
  • The angle between the radius which touches P₂ and the radius that touches P₃ is φ₂,
  • The ray from the center of P to P_x is parallel to the ray from the center of O to the point which is on A_x and O 's circumference, for all x.
• Construct three line segments CA₁, CA₂, and CA₃ such that:
  • CA_x is in the same plane as A_x, for all x, and
  • The angle between CA_x and A_x is θ_x, for all x.
• The distance between P_x and the end point of CA_x that is not on A_x is L, for all x.

Solution

1. Note that the control arms can only move in a circle, while linkage can move in a sphere.
2. We will calculate θ₁ first, which only involves the points, circles and lines p, CA₁, A₁, and P₁.
3. Find the plane where CA₁ 's circle resides in. Use it to cut the sphere around P₁. For future reference, call CA₁ 's circle C₁ and the circle resulting from the cut C₂
4. Define x_o1, for x offset, for the difference in the x coordinates of the center of C₁ and the point P₁.
   • x_o1 = TR - (BR + x)
   • x_o1 = TR - BR - x
5. Define D₁ to be the distance between the center of C₁ and C₂. It will also be the line connecting the centers.
   • D₁ = sqrt(x₁² + z²)
6. Obviously, D₁, CA₁, and linkage form a triangle. The angle between CA₁ and D₁ is a close approximation to θ₁, but it is not exact. We will call this angle θ₁₁. We use the law of cosines to calculate θ₁₁.
   • L² = CA² + D² - CA * D * cos(θ₁₁)
     
     
   • θ₁₁ = cos^-1((D² + CA² - L²)/(2*D*CA))
     
     
7. One endpoint of D₁ is on A₁. Thus, we can make another triangle, and the angle between D₁ and A₁ is the difference between θ₁ and θ₁₁. We will call this angle θ₁₂. If we have the length of the side on A₁ be z, then the last side will be x_o and the triangle will be a right angle triangle. Since only x_o1 changes sign in the good interval, we should use a trigonometric function that involves x_o in the numerator. Thus,
   • θ₁₂ = sin^-1(x_o1/D₁)
     
     
   • θ₁ = cos^-1((D² + CA² - L²)/(2*D*CA)) - sin^-1(x_o1/D₁)
8. You just have to rotate the model φ₁ degrees counterclockwise for θ₂, and another φ₂ degrees for θ₃ using the two dimensional rotational matrixes

   {cos(φ2),-sin(φ2)}
R1={                }
   {sin(φ2)  cos(φ2)}

   {cos(φ3) -sin(φ3)}
R2={                }
   {sin(φ3)  cos(φ3)}

LegoRoboBrick Modules

Module ALPHA

ALPHA stands for Automatic Lego Pipet Head Assembly.

• Created 8/21/2009
• Consists of 3 double-jointed arms.
  • One joint is connected to the motor, and is controlled entirely by the motor. This is also referred to as the control arm.
  • The other joint moves in a sphere, and is loose. The end of this attaches to the platform which holds the pipet tip. This is referred to as linkage.
• Videos
  • [http://www.youtube.com/watch?v=Lqp5Ebsu8GQ&feature=channel Robot in Action]
    • This video shows that the module has high accuracy and precision. The stand is module Beta.
  • [http://www.youtube.com/watch?v=w3gM0UWEjjQ&feature=channel Two Robots]
    • This video shows that the same code can be used for other versions of ALPHA. The only difference is 6 physical constants:
      1. Top Offset
      2. Bottom Offset
      3. Control Arm Length
      4. Linkage Arm Length
      5. Inter-arm Angle
      6. Gear Ratio
  • [http://www.youtube.com/watch?v=bsu2nNNU34g&feature=channel_page Old Video]

Module BETA

BETA stands for Biobrick Enviroment Testing Apparatus.

• Consists of a telescoping frame, and a big lego plate.
  • The telescoping frame is used for holding ALPHAs and PHIs.
  • the big lego plate is where you put the 96-well plates and petri dishes.

Module PHI

PHI stands for Pneumatics Handling Interface.

• PHI is the pipette. It consists of three motors.
  • Motor A.
    • This motor controls the flow of the air. If you look at it from the side when the switch is visible:
      • When the switch is to the left, there is a direct flow from the pipet head to the air. This makes it possible to use the second motor (motor B) to suck without sucking any liquid, and enabling it to blow extra air out.
      • When the switch is in the middle, there is no connection.
      • When the switch is to the right, the pressure built up in the air tank is released into the pipette head.
  • Motor B.
    • This motor is connected to a piston, so it can suck and dispense liquid.
  • Motor C.
    • This motor is connected to to compressors compressing air in the air tank. It runs for 7 seconds once the air is released.
• Videos
  • [http://www.youtube.com/watch?v=WCM2kRFt-w4&feature=channel_page Phi in action]
    • This video shows Phi running by itself.

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