Finding the moment of inertia of a Vex wheel using parallel axis theorem

May 17, 2015

vex 5 in wheel

The new Vex game “nothing but net” might involve rotating shooter wheels.  We know that if all the mass of a wheel was located on its rim then the moment of inertia about its rotating axis  (I_rim) would be

I_rim = r^2 * m   where m is the mass of the wheel and r = radius of wheel.   But we know that the wheels actually  have mass that is unevenly distributed along the radius so the moment of inertia I_wheel will be less than I_rim.

Easy experiment to determine I_wheel if we know its mass.

We can determine I_wheel experimentally using the parallel axis theorem and the dynamics of a pendulum.

Parallel axis theorem says that any object that is rotated about an axis parallel to and a distance , d, from an axis going through the centroid of the object will add an amount =  m*d^2 to the moment of inertia about its centroid.  I.e.

I_parallel = I_centroid + m*d^2 .

Suppose we now swing the mass, m,  about the parallel axis like a pendulum  using just the torque from gravity pulling on the mass.      It is easy to show that the period, T , of the pendulum is related to the distance , d, and the moment of inertial , I_parallel, by the following formula:

T = 2*pi*sqrt(I_parallel/(d*m*g))     .   g is gravitational constant and assumes swing angles smaller than say 10 degs from the lowest point on the pendulum path. 

If we measure the period of the pendulum we can rearrange the equation and find I_parallel

I_parallel = T^2*d*m*g/(2*pi)^2 

Once we have I_parallel, we can now use the parallel axis theorem to determine I_wheel.

I_wheel = I_parallel –  d^2*m  =  d^2*m * (T^2*g/d/(2*pi)^2 -1)

(This assumes  that the string has negligible mass relative to the mass of the wheel)

Vex 5 in Wheel experiment:

Given….r_wheel = 2.5 inches ,

wheel mass,   m = 180 gm (0.180  kg)

The pendulum is created by suspending the wheel with a thread 2.75 inches from its center so

d =. 07 m (approx. 2.75 inches)

The average period  T = .668 sec

I_wheel  = d^2*m*(T^2/d*9.8/(6.28)^2 -1)

     = d^2*m*( .248*T^2/d -1)

     = .07^2*.180*(.248*.668^2/.07 -1) = 0.00051 kg m^2

Equivalent radius with a rim only mass r_e

r_e = sqrt( I_wheel/m) = .0533 m ( 2.1 inches)  

This  means that the wheel behaves as if the mass if located at 84 %  of the radius of the wheel which one could almost guess by looking at it.


Team 2826 ,Wave Robotics, built one of my favorite robots for 2015 FRC Recycle Rush

May 10, 2015

Nice engineering of “Depthcharge” to play this years  FRC Recycle Rush game.  Produced some of the highest scores but got knocked out in the finals of worlds in St. Louis.   The main difference was their team mates inability to snare extra recycling bins from the center step during autonomous.

Congrats guys… loved it.     You built what I sort of dreamed of at the beginning of the game to achieve a high score during autonomous.


Vex Note: Motor power required to launch balls

April 23, 2015

The new vex game , Nothing but Net, could utilize a design similar to a two wheel tennis ball launcher.

Question: how many motors are required on the launcher?

The after a launch, the energy lost from the spinning wheels is transformed into ball kinetic energy and heat due to friction and ball compression.

After each shot the wheels are brought back to initial spin speed by the power of the motors.   The maximum time allowed for respinning is the cycle time of the firing sequence.    Lets take a look at the Vex game derived requirements:

Ball mass, m = 60 grams

Ball launch Speed, v =  6 m/s

Ball kinetic energy:K =  1/2*mass*v^2 = .5*.06*6^2 = 1.08 joules

Energy loss due to compression : E_c

Energy loss due to friction :  E_f

Time between shots: 1 sec

Average power required  p_avg = ( K + E_c + E_f)/ t

Force on ball during acceleration:

F =  d(m*v)/dt    or the change in momentum of the ball over the time of acceleration., dt.

dt can be approximated as the contact distance / tangential speed of the wheel , v.

The contact distance is about 3 cm so

dt= .03/6= .005 s

d(m*v) = .06*6 = .36 kg*m/s

hence F = .36/.005 =   72 newtons

Normal force on ball F_n = F/u_friction .    The normal (compression)  force on the ball is then

F_n = 72 newtons  assuming a u_friction = 1 which is possible with a sticky wheel.

The assumed  compression distance is about 1 in or 2.54 cm.  (To be verified later)

Hence Ec = F_n*d/2 = 72*.0254/2 = .91 joules. 

With good design, the friction loss in the drive train can be small (maybe .1 joules) so lets assume that E_c + E_f  are about equal to the K= 1.06 j so

p_avg = 2*K/t = 1.06*2= 2.12 watts   or 1.06 watts per motor.

We know the vex 393 motors have a max power = max_speed*max_torque/4 or about 4.5 watts  but they will overheat if run continuously at this power.   The PTC fuses will stop the motors if they run continuously with currents equivalent to more than  25% maximum torque (speeds less than 75% max speed).    At this operating point, the motors only deliver  3/4 max power or 3.4 watts.

There are also friction losses from the teeth of the spur gears.   I usually assume about 5% per 5:1 ratio.    A shooter wheel with a 25:1 gearing would lose 10% torque or energy at a given speed.

So the net power to the shooter wheel will be  .9*3.4 =  3.0 watts which is more than the 1 watt that we require.         

Extra friction?    

If the gear train has pressure on the axles from bearing blocks and possibly the collars are too tight so the wheels slow down quickly when coasting with motors disconnected, then over heating can easily occur.   e.g.  if friction uses up just 15% of the available torque, the motors will have to provide about 1 watt extra. which cuts our margin considerably.

Faster shot rate?

We assumed 1 shot per second…what happens with 2 shots per second….   Well, the power requirements almost double since we are using twice as much energy per unit time.    We would likely have to add extra motors.


Reblog:New scientific study on plastic entering the ocean

February 13, 2015

Reblog from Algalita Blog

http://www.algalita.org/much-plastic-entering-ocean/

How much plastic is entering the ocean?

An important article has come out in Science Magazine. This is the first scientific study to systematically estimate the amount of plastic going into the ocean from land. It also highlights the geographies that contribute the most and provides insights into the relative impact of different mitigation strategies.

ballona-creekOne thing we have learned from this article is the estimated amount of plastic going into the ocean is far greater than most previous estimates. Yet, overwhelming amount of plastic going into the ocean today pales in comparison to what scientists estimate for the future. I have been studying this area for 15 years and it’s gone up by two orders of magnitude – it is approximately one hundred times worse than what I measured in 1999. This article is stating they expect an increase of ten in the next ten years.

Habitats are normally damaged by removing valuables from them, such as animals, plants and minerals. In a complete turnaround, we are destroying our ocean habitat by inserting our valuable polymer plastics. This leads us to a clear understanding of why the status quo HAS to change by adopting a zero waste circular economy—if we don’t, it will be ten times worse than it is now, or a thousand times worse than I found it in 1999.

Plastic consumption in developing countries is increasing and because many of these countries do not have sufficient waste collection, more plastic is entering our ocean each day. We keep hearing Mismanaged Waste. That implies that burning waste in an incineration or burying it in a landfill is properly managed waste, but it’s not. We believe in Zero Waste. This so-called managed waste is composed of precious resources that need to be recovered.

algalita-global-estimate-plastic-pollutionThe quantity of plastic in the global ocean’s five accumulator gyres has reached a level that is destroying their fragile ecosystems. It is reasonable that plastic manufacturers, who profit from externalizing the cost of dealing with their products that become waste, take some responsibility for the destruction of gyre habitat and help remove some of the tonnage of plastic causing the damage. Additionally, this would incentivize manufacturers of plastic products to design them to be easy to recycle and help create the infrastructure to process the collected plastics.

In 2013 International Coastal Cleanup Day had 648,015 volunteers from 92 countries combing coastlines around the world. In one day they gathered about 12.3 million pounds (about 6,000 tons) of trash, much of which was plastic. Even if it was all plastic, it would only be a third of what goes into the ocean each day, based on a mid-range estimate from the Jenna study. We would have to have a worldwide clean up 3 times a day, every day of the year to clean up what is ending up in the ocean, although much of the world’s coastal areas were not covered by the volunteers.

north-pacific-gyre-sample

In the North Pacific Gyre this summer, Algalita researchers took plankton samples from 10 meters below the surface. In our lab, we found that every spoonful of plankton looked at under a microscope had tiny plastic fibers in it. Gyres were pristine areas where virtually nothing floated for long. The creatures there think anything floating is something to eat. The plastic is being consumed in high quantities, has no nutritional value, and is toxic. On top of all this, floating garbage in the pristine ocean is UGLY and constitutes an aesthetic. An ugly world, poisoned by our waste, is not a world we want to live in, and bequeath to our progeny.

What can we do? Single use disposables are the biggest culprit. Targeting waste from “use once and toss” plastics is the key. We can’t solve the ocean plastic problem at scale without addressing waste management in developing countries. We can change habits and behavior. People are rational if they are given rational reasons for changing their habits.

As members of the Trash Free Seas Alliance, Algalita is happy to see that this information has been made available through Science Magazine. This is an important study and we must act on the information it provides, or we will see the status quo based prediction of exponential increase in marine plastic pollution by 2025 come true.

Read the article here.


60 in double reverse 4 bar linear linkage example

June 8, 2014

Here are some pictures of how a double reverse 4 bar using Vex 35 hole link arms. The main challenge is constructing a stable geometry. The lift has a middle link gear train to move the upper 4 bar in sync with the lower 4 bar.

Torque

Approx torque (inlb) required = 2*l_arm*(W_payload_lbs + W_lift_lbs + W_manipulator_lbs)*cos(angle)

height_delta = 2*l_arm*( sin(angle_finish) –  sin(angle_start))

where l_arm is the distance between pivots of the arms in inches, W_payload_lbs is game piece weight, W_lift_lbs  is the weight of the 3 arms used in the lift , W_manipulator_lbs  is the weight of the gripper attached to the upper arm and angle is defined relative to the horizontal.  The max torque occurs when the arms are horizontal or angle • 0 .

If you want to lift 4 1 lb Skyrise cubes with a 3lb lift weight , a 1 lb  gripper and a l_arm of 16 in you would need about 256 in lbs of torque.

As a rule of thumb I use 6 inlb of torque per motor for sizing  the number of motors.  This assumes 2  inlbs of elastic support , 1 inlb of friction and 3 inlbs from active current (about .9 amps) hold per motor used.   With these assumptions a 10:1 gearing and 4 393 motors might do the job.    The lift would take about 5 seconds to go full travel.  I’ll show a more exact torque derivation later.

Height change

With an  angle_finish = 75 deg and the angle_start= -60 deg  a 16 in arm reaches 59 in.  A 16.5 in arm reaches 61 in.   With a chain bar you could  clear an in or two more.20140608-214047.jpgSo 20140608-214101.jpg 20140608-214114.jpg


OpenROV debuts during Algalita 2014 POPS International Youth Summit at Dana Point Ocean Institute

April 5, 2014
IMG_6275

The Team with Capt Moore

IMG_6315

OpenROV going into demo tank

IMG_6311

OpenROV on Display

Our Robodox Algalita OpenROV build team attended the subject conference and gave Captain Charles Moore and crew their first look at the OpenROV that will be used to survey fish habitat located in plastic pollution during their July expedition to the Pacific Gyre.   See this video for Capt Moore interview.

Here is a link to the team summit report posted in our blog “Robodox Engineering ROV for ORV”

We had a short tank demo with a missing thruster… but at least we were able to go in circles:) Thanks to Dave L. for trying to get us new motors on the spur of the moment. We now have things back to normal and will proceed with salt water testing next week.

I was excited to finally get onboard the Alguita ORV and see how we might deploy the ROV. The girls on the team were more excited to see surfer-singer Jack Johnson!

Chris

Here are all the images from the conference…. sure was a beautiful place to meet.

 

OIMG_6150 IMG_6152 IMG_6153 IMG_6155 IMG_6156 IMG_6158 IMG_6161 IMG_6162 IMG_6163 IMG_6166 IMG_6168 IMG_6171 IMG_6172 IMG_6173 IMG_6174 IMG_6177 IMG_6178 IMG_6179 IMG_6181 IMG_6184 IMG_6185 IMG_6186 IMG_6187 IMG_6188 IMG_6189 IMG_6190 IMG_6191 IMG_6193 IMG_6196 IMG_6197 IMG_6198 IMG_6199 IMG_6200 IMG_6203 IMG_6207 IMG_6208 IMG_6209 IMG_6210 IMG_6211 IMG_6213 IMG_6214 IMG_6216 IMG_6217 IMG_6218 IMG_6219 IMG_6223 IMG_6224 IMG_6225 IMG_6226 IMG_6228 IMG_6231 IMG_6233 IMG_6234 IMG_6235 IMG_6238 IMG_6244 IMG_6245 IMG_6246 IMG_6248 IMG_6249 IMG_6250 IMG_6251 IMG_6252 IMG_6254 IMG_6255 IMG_6256 IMG_6257 IMG_6258 IMG_6259 IMG_6260 IMG_6261 IMG_6262 IMG_6263 IMG_6264 IMG_6265 IMG_6266 IMG_6268 IMG_6270 IMG_6272 IMG_6273 IMG_6275 IMG_6276 IMG_6277 IMG_6278 IMG_6283 IMG_6285 IMG_6287 IMG_6288 IMG_6289 IMG_6290 IMG_6292 IMG_6295 IMG_6297 IMG_6298 IMG_6300 IMG_6301 IMG_6302 IMG_6303 IMG_6309 IMG_6311 IMG_6312 IMG_6313 IMG_6315 IMG_6316 IMG_6317 IMG_6318 IMG_6320 IMG_6333 IMG_6337 IMG_6338 IMG_6339 IMG_6346 IMG_6347 IMG_6350 IMG_6352 IMG_6353 IMG_6355 IMG_6356

 


Homemade sea water for testing an ROV

March 16, 2014

Our GHCHS Algilata OpenROV project is not located near the ocean.   The OpenROV community has found that salt water operation can be flakey compared to fresh water due to low resistance between the salt water and  external wires that connect the battery tubes and the motors.     This post deals with making simulated sea water for testing the OpenROV in the lab.

Sea water conducts electricity due to the dissolved salts that produce ions for transporting charge between conductors submerged into the water.   Typical sea water has 35 parts per thousand  by weight of salt in water.    Since water at standard conditions weighs 1000 grams/liter then we can say that sea water has 35g of salt per liter.

I wanted to use just a cup measure to make a batch of sea water.     So I weighed one cup some Himalayan salt and found that it weighed 8 oz.  So we can estimate the weight of salt using this ratio…about 1  avoirdupois oz weight per 1  fluid oz .   Of course this will vary with the granularity of the salt due to variations in packing density but it should be good enough for conductivity testing.

Given that there are 28.3 grams per avoirdupois oz and  33.8 fluid oz per liter the sea water concentration of 35 gm per liter converts to  1.24 avoirdupois oz per 33.8 fluid oz or

1 avoirdupois oz per 27.2 fluid oz.

Since 1 cup (8 fl oz) of Himalayan salt weighed 8 avoirdupois oz then I would need to mix this with 217.6 fluid oz of water or 27.2 cups of water (1.7 gallons)

So I now have a simple rule of thumb for adding granulated salt to water using a volume measure:

volume ratio salt:water  1 : 27.2 

Other useful equivalents:   5.7 oz salt per gallon of water

                                              1/4 cup salt to 6 3/4  cup water

                                             1 tablespoon  salt to  1.7 cups water

Measuring salinity using conductivity:

Scientist often use conductivity to estimate salinity.   Standard units of conductivity are Siemans/meter  (S/m).    The electrical conductivity of 35 ppt salt water at a temperature of 15 °C is 42.9 mS/cm  (ref).   Thus 35 ppt equates to 42.9 mS/cm.

File:Conductimetrie-schema.png

Taken from wikipedia

Conductivity measurements assume that there are two parallel electrical plates of area A in water at a distance L apart.   If a voltage (V) is put across the plates and the current flow (I) measured then the conductivity  k = I/V*L/A =  L/(R*A)  where R is the resistance V/I.    Under ideal conditions the conductivity between the ROV wires and the water should be very low (high resistivity) but if a small area of copper is exposed  then conduction can occur. eg  some OpenROV forum members are finding resistance on the order of kiloohms rather than megohms.

Practically, if you put two probes from an ohm meter into water, the measured resistance will depend upon the area of the probe submerged and the distance between them.   You can use this as a reference to test your simulated sea water at home.

conductivity plug testerI made a simple  crude conductivity  instrument out of a two prong to three prong electrical plug adapter.   The plug prongs are separated by 1 cm and the exposed area between the prongs is almost exactly 1 sq sm.  I covered the non-facing sides with tape or you  could use paint or nail polish to insulate the surfaces from water.   See photo.

In the field,  dip the plug tester prongs into the water and measure the resistance between them.  Note the temperature since conductivity varies a lot with temperature.

Theoretical  plug conductivity prediction for sea water.

k = L/(R*A)  = 1/R            S/cm

= 1000/R    mS/cm

Typically sea water resistance in ohms for this homemade instrument  at 15 deg C would be

R_ohms = L/(A*k)= 1cm/(1cm ^2)/(42.9 mS/cm) = 1000/42.9 = 23.3 ohms

When creating your simulated sea water at  home you would like to have similar conditions.   You would add salt to your water tank/tub until the resistance level matched.

Testing:

I did a quick conductivity test by dissolving 1 tablespoon of Himalayan sea salt in 1 3/4 cups of water.   The measured resistance  using my plug conductivity tester was around 3 kohms with a VOM meter and using the voltage / current method the resistance was 230 ohms.     So it is reading much higher than the theory.    The test was done at 70F (21C).   Temperature changes the conductivity about 2% per degree.  The measurement was 6 deg C higher so at most we would expect a 12%  increase over the 15 C reference.

The absolute measurements can vary too much with conductivity so I would recommend just using the 35g/kg  salt/water mixing method or just doing relative conductivity measurements..i.e.  matching field conductivity to home conductivity under similar conditions.


Follow

Get every new post delivered to your Inbox.