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Rube Goldberg Engineering Analysis |
Engineering Analysis
Note: The energy conversions can be seen via our functional block diagram (see appendix 1).
Introduction
Table D3's contribution to black lab's Rube Goldberg device is as follows;
Our section will contain (5) steps, with the possibility of adding in one mini-step to ensure compatibility. An outline of the steps is best described as: Team D4's ball drops from a height of 1 foot. The ball that is dropped falls down a funnel and the energy is directed into the pushing of a pencil down (1) to activate the button on a pre-programmed mindstorms robot. The robot will then proceed forward (2) according to it's coding and trigger the 'popping-up' of a pre-winded jack in the box. Jack in the box will then trigger (3) a set of dominos (4) that will later trigger a pendulum swing either directly or by redirection with a mouse trap. The pendulum will then swing (5) to the preset height of 9 inches in order to transfer kinetic energy to group D11's device.
Compulsory design features incorporated are, but not limited to:
-Lego Mindstorm (robot)
-Energy transfer (in steps like chemical battery > kinetic)
-Biomimetics (wave design of domino track, 'arm' of robot)
-Function of energy storage (spring potential in jack in the box, gravitational potential of pendulum)
The funnel step
The first step of the device consist of a 50g ball bearing dropping done a funnel of 10cm in outer diameter extending to the tube of 5cm in diameter. At the end of the funnel, the ball would collide with the eraser tip of a pencil of 4.5cm in diameter. The other end of the pencil would then exert the force onto the on/off switch of the robot.
The potential energy of the ball can be calculated in the formula:
E = mgh
Where :
m = mass of the ball
g = acceleration due to gravity (9.81m/s2)
h = height of the drop in relation to its target
Work
E = (0.05kg)(9.81m/s2)(30.48m)
E = 0.147J
The force can then be calculated:
F = mg
Where :
m = mass of the ball
g = acceleration due to gravity (9.81m/s2)
Work
F = (0.05kg)(9.81m/s2)
F = 0.49N
Idealistically, according to the conservation of energy, the maximum magnitude of the potential energy is equal to the magnitude of the maximum kinetic energy. Therefore the ball would idealistically be assumed to exert 0.49N when it comes in contact with the mechanical pencil. Since only 0.02N is required to press the button by measuring with a force meter, and 0.49>>0.02N (again assuming in ideal conditions), the on/off button of the robot is pressed.
The Jack in the box step
To activate the jack in the box handle, one must exert a force of 1.96N (found using a force meter) to the handle. The force output by the flap of the jack in the box is 1.18N (again found by measuring using a force meter attached to a hook on the flap).
The efficiency of the jack in the box is therefore calculated using the formula:
Eff = output/input *100%
Eff = 1.18N/1.96N *100%
Eff = 60.2%
Lego mindstorms
Note: The flow chart of the program can be found in appendix 2
From the back of the power supply, the lego mindstorm needs a voltage of 9V and has a resistance of 120 ohms [1] (referenced on internet).
From the jack in the box section, we know that a force of 1.96N is needed to activate the mechanism. We need the robot to move a 10cm distance to achieve this affect.
The energy needed for this affect is:
E = Fd = 1.96N(0.1m) = 0.196JE = energy (J) F = force (N) d = distance (m)
The power produce by the robot is
P = V2/R = 92V2/120ohms = 0.675WP = Power (W) V = Voltage (V) R = Resistance (ohms)
The time it takes is found by using this formula:
E = Pt t = E/P = 0.196J/0.675W = 0.290sP = Power (W) t = time (s) E = energy (J)
The current is found to be:
I = V/R = 9V/120ohms = 0.075AI = Current (A) V = Voltage (V) R = Resistance (ohms)
Dominos step
The Dominos will first be triggered by the swinging motion of the jack in the boxs lid. The dominoes will be placed on a platform that raises them to be flush with the top of the jack in the box top. The track that the dominos are placed on will be constructed of lego and translucent sheet plastic. The object of the dominos is mainly to transfer kinetic motion through means of stored gravitational potential energy, from one side of our given space to the other. The raised dominos will incorporate a biomimetics wave design nearing the end of the track. Once the last domino has been triggered, it will transfer its motion, into knocking the pendulums ball off of a stand. The last domino will likely have added weight to give it extra punch in continuing the kinetic movement to the next step of the device.
For dominos, there is no equation governing the force output of the dominos when they drop. The dominos are also not heavy enough to register a force on any of the force measuring devices that we have available to us. Thus it is only possible to estimate the force based on the weight of the dominos and the speed at which they are falling. To ensure that this step is reliable enough, we must compare our estimates with estimates concerning how much force or energy will be required to trigger the next step. As a side note, if we are unable to trigger motion in the pendulum swing with dominos, an intermittent step will be required. For this we will use a mousetrap; which will have more than sufficient stored spring potential energy to trigger the pendulum swing.
Pendulum step
The pendulum ball will be raised to a height of 12 inches to match the height of the domino track. The ball will most likely be a tennis ball or something of similar mass. It will be placed on the end of the track to be knocked off by the last domino, and will swing into an arc that ends in a height of 9 inches (as requested by team D11, the team we must set into motion. Once the pendulum is engaged by the domino and set into movement, it will transfer kinetic energy though means of stored gravitational potential energy.
The calculation we had to do to determine the energy we would have according to gravitational potential is
Ek= mgh
Using this formula and estimating the mass of the ball to be around 50 grams we have determined the energy output to be:
(0.050g)(9.81m/s^2)(0.09m) = Ek
Ek = 0.045 J
Reference
[1] Harkin Educational Group, Montana education, "Mindstorm Robot Outline" February 2005, cs.montana.edu/harkin/courses/cs445/topics/5-mindstorms/outline.pdf.
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