Wednesday, January 16, 2008

Math and Science Calculations

Rov Arm Calculations
The calculations used in determining the correct components for the hydraulic system are shown below. I needed a hydraulic system that would divide the force at the arm, as only a small force is needed compared to the usual forces used in hydraulic systems. Most hydraulic systems are used to gain a mechanical advantage, such as raising a car with a minimal amount of force. In the case of the Rov, a force of only 2 pounds is needed to clamp onto the heaviest object, and to safely secure it for a trip to the surface a force of 3 pounds would suffice. By examining Pascal’s principle I can prove that my design will function.

Force Required To Operate Arm:
One of the major concerns addressed in my presentations was a kink in the hydraulic line on my model. While a complete kink will cut off flow and make it difficult for the arm to function, minor bends and very long hydraulic lines have no effect. Pascals Equation P1=P2 proves that in a closed system the pressure at any point is equal to the pressure at all other points. Therefore by applying pressure at the control station, the pressure will be transmitted with full efficiency to the Rov arm. Since pressure equals force per unit area the following equation also holds true; F1/A1=F2/A2.
The master piston has a surface area of 1.227 square inches found by using the equation pi x r squared, or ((pi) x (.625)(.625)). The slave piston, found on the Rov, has a surface area of .785 square inches determined using the same formula, or ((pi) x (.5)(.5)). Since a force of 3 pounds is needed at the slave piston the previous equation can be used to determine the force required at the master piston.
F1/A1=F2/A2
(F1)/(1.227)=(3)/(.785)
(F1)/(1.227)=(3.8216)
(F1)=(1.227)x(3.8216)
F1= 4.6891

This equation proves that to deliver a force of 3 pounds at the Rov arm, a force of 4.6891 pounds must be applied at the control station. The airline tubing, which has the lowest maximum pressure rating of all the components, is capable of holding 22 psi. Therefore the system is capable of withstanding the 4.6891 pound force, and is capable of much more.

Distance Pistons Must Move:

Pascals Principle also states that that V1=V2, which means that the volume of fluid displaced on one side is equal to the volume of liquid that will appear on the other side. Since volume equals area x distance the following equation can be substituted. A1/D1=A2/D2. Since the areas have already been calculated, I can determine the distance we must depress the master piston to close the Rov arm. According to the current designs the arm will have to move a maximum of 1.8 inches to move the arm from a fully open position to a fully closed position.
A1=1.227” squared(master piston)
A2=.785” squared (slave piston)
D2= 1.8” ( distance moved by slave piston)
D1= ? (Distance the master piston is required to move)

A1/D1=A2/D2
(1.227) x (D1)=(.785) x (1.8)
(1.227) x (D1)=(1.413)
(D1)=(1.413)/(1.227)
(D1)=(1.1516)
D1= 1.1516”

This equation proves that to fully close the arm which requires the slave piston to extend 1.8 inches, seen in Figure 2, the master piston must be depressed 1.1516 inches, the same holds true when extracting the master piston to reopen the arm.
Figure 2 (Hydraulic Arm)

Mechanical Advantage:
By rearranging the previous equation, the mechanical advantage lost or gained by using a larger piston at the control station than the piston on the arm can be found. This equation is D1/D2=A2/A1=IMA.

D1=1.1516”
D2=1.8”
A2=.785” squared
A1=1.227” squared
IMA=? (Mechanical Disadvantage)

D1/D2=A2/A1=IMA
1.1516/1.8 = .785/1.227 =IMA
.6397=.6397 = IMA

This means that the mechanical advantage is .6397, since this number is less than one there is a disadvantage to using this system. This however was done purposefully to increase the closing speed of the robotic arm.

Math, Science, and Technology Analysis

Rov Arm Math, Science, and Technology Analysis

My final solution for the Rov arm is a simple design that relies on the basic laws of hydraulics to function. Through calculations, seen on the attached document, I have determined the size of tubing and syringes I need to not just make my design functional, but also make it strong enough to complete the tasks. I also have decided to use polycarbonate sheeting for the main material to construct my arm.
Hydraulic System:
The original purpose of choosing hydraulics was to reduce the electricity needed by the entire Rov. After researching the laws and properties many more advantages became apparent. The main difference between hydraulics and pneumatics involves the tendency of the substance that fills the system to compress. A pneumatic system involves the use of air which can easily be compressed, thus requiring greater pressure to accomplish a task. In a hydraulic system the fluid, often oil, will not compress and therefore transfers all energy with very minimal loss. This also shows why it’s very important to remove all air from a hydraulic system. Due to the high efficiency of a hydraulic line there is almost no force lost to friction. This is defined by Pascals law which states “when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.”(Pascals Principle), or defined by the equation P1=P2. Therefore a hydraulic tube can be led through all sorts of bends and over large distances without any sacrifice in performance.
My hydraulic system will also make use of force multiplication. At the control station I will use a 2oz syringe as the hydraulic pump, while a 1 oz syringe will be attached onto the arm. Force multiplication is determined by comparing the surface areas of the pistons. The equation to be used is pi * r^2. If piston B has a surface area 10 times greater than piston A, then any pressure applied to piston A will show up 10 times greater on piston B, although the distance the piston must travel will also be larger. This is shown in Figure 1 below with piston A being represented by F1 and piston B being represented by F2.
For my design I have divided the force rather than multiplied it. The main pressure will be applied by hand from the control station piston, called the master piston, and approximately two thirds of the force will be delivered to the piston on the Rov, called the slave piston. This also means that for every inch the master piston is depressed, the slave piston will extend 1.5652 inches. While it may seem odd that I am purposefully lowering the force delivered to the slave piston, it fits in context with the contest tasks. The maximum weight that must be lifted will be 2 pounds, although this is a stretch and the most likely weight will be closer to 1 pound or less. By decreasing the force I am making it harder for myself, or any other controller, to accidentally overload the arm. If too much pressure is applied the hydraulic system may simply break as it has only been designed according to the specifications of needing to hold a maximum weight of 5 pounds. The control line also is in danger of rupturing at a pressure greater than 22 psi.. I also believe that it will be more important to have a swift moving arm as it is unknown how stable the platform will be under water, and it may be necessary to quickly grab the objects rather than slowly clamp onto them. To apply a force of 3 pounds to pick up the heaviest contest object, the “black smoker rocks”, a force of 4.6891 pounds must be applied at the control station which is well within the capabilities of the system. This is explained on the attached calculations sheet.

Rov Arm Materials:
I have decided to use polycarbonate sheeting with a thickness of ½” as the main material in my design. It will be used to construct the arms as well as the top mounting block. The reason for this was the lightweight and impact resistant properties of the material. Polycarbonate has many other uses as well which show its strength. Polycarbonate is used to make bulletproof glass, shop safety goggles, and water bottles. It is also very easy to cut with a band saw. I had also considered using fiberglass but the initial cost of materials is nearly three times larger and it will require at least 3 days of extra construction time. Since my design only requires rectangular shapes and no intricate designs, this material seemed to be the best choice.

Conclusion:
Overall my design has shown through both a working model presented in class and calculations on the attached sheet that it is capable of completing the competition tasks. Using the laws of a closed hydraulic system I was able to void many of the concerns associated with my design. I believe that once constructed my final design will once again prove itself effective and complete all the required tasks.

Tuesday, December 18, 2007

Materials List

3 eyehooks, 1 ½” long

2 Hex screws 4 inches long, ¼” wide

25 inches balsawood block, 1” by 1”

6 inches of plastic sheeting, ½” thick and 1” wide

2 Paint brushes, 1” wide

1/4” drill bit

1/16” drill bit

1/8” drill bit

2’ metal rod, 1/8” thick

4 metal washers, ¼” opening, 1” wide

2 hex nuts for ¼” screw

3” rubber grip ¼” thick

½” by 12” by 6” polycarbonate sheeting

Friday, December 14, 2007

Plan of Procedures

Plan of Procedures


1. Cut a polycarbonate sheet 1/2” thick into four pieces 12” by 1” by ½”.

2. Take the four pieces and cut triangles of ½” by 2” off the edge that match up to each other.



3. Glue two pieces together so that the triangular cuts line up.

4. Repeat step 3 for the remaining two pieces, this will be the main arms measuring approximately 12” by 1” by 1” with the triangular cut taken out.




5. Place arms next to each other so that the triangular cuts are on the inside. Make a mark 4” from the back edge centered 1/2” for each side on each arm.

6. Drill a 1/8” pilot hole vertically through the marks on each arm.


7. Drill a ¼” hole vertically through the 1/8” pilot holes previously drilled.

8. Using sandpaper level the inside of the triangular cuts so that the top and bottom section are even.


9. Cut a polycarbonate sheet 1/2” thick into a 1” by 6” section, which will become the top mounting block.

10. Drill 1/4” holes through the top mounting blocks centered ½” from the 1” edges.

11. Sand all rough edges off the plastic block and run sandpaper through the drilled holes to remove any rough edges.


12. Drill two ¼” holes through the front PVC edge of the Rov frame, centered 5 inches from the middle of the PVC tube. Care must be taken to assure the holes line up exactly with the top mounting block and that both the top and bottom hole are completely vertical. The top mounting block may be used as a guide to mark the holes.

13. Insert two eye hooks into the Rov arms, one on each, centered on the inward facing sides ½” from the back edge.


14. Drill a pilot hole 1/16” wide through the center of the back plunger of the hydraulic syringe.

15. Carefully insert a third eyehook into this hole, applying a small amount of thread sealant onto the threads.


16. Mark the center line of the top mounting block 3 inches from each side. The mark should extend the entire 1 inch length of the mounting block and should be placed on the bottom side.




17. Using sandpaper, sand down the area ½” to either side of this line in an arched shape, so that the deepest point is where the mark previously was. The hydraulic syringe should fit into this cavity.

18. Insert two 4”hex screw ¼” wide through the top mounting block, insert two washers below the mounting block. Thread the Polycarbonate arms onto the screws, applying a small amount of Dow 33 grease. Place two more washers below the arm.


19. Temporarily thread two matching hex nuts onto exposed screws to secure the assembly.

20. Slide the hydraulic syringe into place and adjust to a position so that the arms may close fully with a minimum of 1 and ½” clearance between the tip of the syringe and the closest closed part of the arm. The syringe should not extend farther forward then the point where the last nonmoving section of the syringe lines up with the back edge of the mounting block.


21. Mark the points on the cylinder which will show what point will rest directly under the top mounting block.

22. Using a fine sandpaper go over this section to create a slight texture.


23. Place the hydraulic syringe into the previously marked location.

24. Measure the distance between the eyehook on the syringe and the eyehooks on the arm when the syringe is fully empty and the arms are opened at about 15 degrees past parallel. The distance should be the same on both sides.




25.Cut two metal rods of approximately 1/8” thickness into lengths of the previous measurement plus 1 and ½”.

26. Place a metal rod into a clamp and bend the last ¾” upwards at a 90 degree angle. Both sides should be pointing in the same direction.


27. Repeat step 26 for a second rod.

28. Check to make sure both pieces still have the same length, that of the previous measurement.


29. Remove the hydraulic syringe, making sure the marks are still present.

30. Thread one metal rod into the eyehook on the hydraulic syringe and using pliers bend it back towards the center of the metal rod. Use caution so that no more than the ¾” extra is used to make the loop. The loop should close in onto itself so that the metal rod will not unattach itself from the hook.


31. Repeat step 30 for the second metal rod.

32. Place the hydraulic syringe back into its marked location and epoxy in place. Allow to dry.


33. Thread the loose end of a metal rod into one of the eyehooks on the polycarbonate arms. Repeat the process used in step 30 to secure it in place.

34. Repeat step 33 for the second metal rod.


35. Test the movement of the polycarbonate arms and make any adjustments necessary.

36. Cut a 3 foot section of hydraulic line and insert a connector onto one end. The connector must be able to secure the other section of hydraulic line which will run through the tether.


37. Tighten a metal hose clamp around the space where the hose overlaps the connector.

38. Fill the hydraulic syringe with the hydraulic fluid until the arms are fully closed.

39. Thread a second metal hose clamp onto the hydraulic line so that it may be used later, do not tighten.


40. Place the open end of the hydraulic line onto the tip of the hydraulic tip and secure with the metal hose clamp.

41. Open the polycarbonate arms and close the syringe so that the hydraulic fluid is pushed through the hydraulic line. Hold the opposite end of the hydraulic line elevated above the syringe and work all the air out of the system. Using a plug, close the still open end of the hydraulic line.


42. Fill a 2 oz syringe fully with hydraulic fluid.

43. Connect the 2 oz syringe to a piece of hydraulic line approximately 35 feet long. This line will be placed inside the 30 foot tether. 1 foot of tubing will extend past the tether on the Rov end and 4 feet will extend past the tether on the control box end.


44. Slowly close the syringe so that the tube fills with hydraulic fluid. The end of the tubing must be elevated above the syringe. Carefully remove all air from the system. If there is not enough fluid to fill the line, clamp the line near both ends and refill the syringe with fluid. Continue this process until the line is completely filled with hydraulic fluid, void of air bubbles, and there is a minimum of 1 oz of fluid left in the syringe.

45. Using a metal hose clamp secure the tube to the 2 oz syringe.


46. Thread the hydraulic line through the tether.

47. Once the tether has been permanently connected to the Rov, remove the plug on the 3 ft section of tubing with the connector attached. Thread a metal hose clamp onto the hydraulic line that is built into the tether.


48. Attach the tether line to that of the one on the Rov by using the connector. Slide into place and attach with a metal hose clamp.

49. Test the movement of the arm by closing the 2 oz syringe and opening the 2 oz syringe. This should fully open and close the arm. The 2 oz syringe will not need to fully fill and empty, but only move a few centimeters.

Monday, December 3, 2007

Final Solution Exploded View


Parts list, Item, Description, QTY, Size, Remarks

1-Polycarbonate Arm, 2, 12” x 1” x 1”,Made for left and right

2-Hydraulic Syringe, 1, 1 oz, Used on Rov arm

3- Plastic Mounting Block, 1, 6” x 1” x ½”

4-Stainless Steel Hex Screw, 2, 4”x ¼”, Runs vertically through arm

5-Stainless Steel Hex nut, 2, ¼”

6-Stainless Steel Washers, 4, ¼” I.D. , 1”O.D., Placed above and below arms

7-Rubber Grips, 2, 2”, Glued to end of arms

Monday, November 26, 2007

Monday, November 19, 2007

Tuesday, November 13, 2007

Monday, October 29, 2007

Model



I have designed and built my model at a scale of 1:2. The main arms and top supporting block is made of plywood. The bottom base is made from a piece of PVC tubing, similar to the final design. The hydraulic arm is slighlty larger than the 1:2 scale but was the smallest available. This causes the slight kink of the tubing seen in the pictures. The tubing is standard aquarium airline tubing rated to a pressure of about 20 psi. The black grips shown are modeled using balsa wood but will be made of rubber in the final design. The model is also functional and is capable of holding large amounts of weight. The only noticable problem is picking up very thin items, as the model arm does not close completely.


Figure 1: Overall view



Figure 2: Arm fully closed

Figure 3: Arm half open


Figure 4: Arm fully open

Figure 5: Rear view



Figure 6: Overall view

Friday, October 12, 2007

Selection Rejection Report

To compete in the MATES Rov competition the Rov requires an arm capable of completing all the tasks that will be released on November first. I must design the Rov arm to be able to complete any tasks that could possibly be chosen. This requires a powerful universal arm which has no major limitations and is not prone to breaking. It is important to keep the arm simple, while still being complex enough that it is able to work in all the tasks. A major problem I noticed during the competition of previous years was failure of very important components that stopped the team from having any chance of winning. I must be sure that the design has no major flaws that would cause a failure such as this

My first alternate solution is a simple design run off a hydraulic arm. As the arm is retracted due to a negative pressure in the line the arm closes. This makes it very easy to close the arm. The negative pressure in the arm can cause a problem as it is limited by how much pressure can be applied. As the pressure becomes lower, and more force is applied to the arm, outside water may be pulled into the line through small leaks. This will cause the pressure to slowly change and may eventually lead to the arm being useless, as there will be too much liquid in the hydraulic line to close all the way. It is very useful in that it has a large opening which can be used to grab items. It also has a compact design and can be mounted very securely so there is little risk of it separating from the Rov. The design of the arm also makes it hard for the pads to close directly against each other and at an angle instead.

The second alternative solution uses an electric motor as power. Due to the gearing system the motor will be capable of exerting large amounts of force; however it can not sustain this force for extended periods of time. Running the motor for anything longer than short fifteen second intervals runs the risk of burning out the motor, which will leave the Rov useless. This arm will not be good for carrying items to the surface as it may take up to a minute to reach the surface and remove the item. It is useful for moving heavy items short distances, such as picking up a rope off the bottom of the pool and moving it to the side. This design will be very stable as it has one stationary and one mobile arm. The stationary arm will be mounted in multiple locations so that there is little chance that it will separate from the Rov. This design is also good because it can open to a very large degree.

The third alternate solution also uses hydraulics but relies on a positive pressure to close rather than a negative pressure like design one. This design is very useful for grabbing small items as it has a small pointed tip, but may be restricted in how wide it can be opened. This can be adjusted by how far away the pivot points on each arm are mounted. The positive pressure of the hydraulic line lowers the chance of water leaking into the line as only a slightly negative pressure will be used to open the arms. A larger amount of pressure can then be applied to the object, up to 40 psi according to the competition rules. The positive pressure can create a problem in that if the pressure is too high the line may break, rendering the system useless. This can be solved by installing a pressure gauge in the line, and researching the maximum pressure the tubing used can hold, which for normal aquarium silicon tubing is 30 psi. Due to the length of this design its mounting may become inadequate if a large load is used. It is possible that the entire arm could break from the mounting and fall off the Rov, rendering it useless.

Alternate Solution 4 also uses a hydraulic arm as power, but can easily be adapted to use a servo or electric motor. This design is based off that of a slide ruler and is good in that it has a large surface area which it can use to grab an item. The physics of the actual arm allow the arm to close tightly and lock into place. A problem with this design is that it has a very small opening space between the claws, which makes it difficult to grab large items. This design will be very stable due to its stationary arm and multiple mounting locations. Its narrow profile is also useful for reaching into small areas.

As discussed each idea has its pros and cons but only one can be selected for the competition. I have decided on design three as it is capable of performing the widest variety of tasks. Many of the issues associated with the design can be easily remedied, unlike the others. I believe that in the competition I will need to pick up both large and small items, and I believe design three is capable of both. The use of a positive pressure in the hydraulic line allows me to vary the pressure I exert on the payload and the design of the arms allows for a secure fit on any item.