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.
Wednesday, January 16, 2008
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.
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.
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