Nice to have a lot of vex parts around to use in FRC field element or robot element mock ups. This is a testing mockup of the touchpad which activates a light if any of the three posts holding the bottom plate are deflected at least 1/2 inch. The vex green rubber links provide the flexibility for any aluminum beam to be pushed without jamming in the holes of the top plate.
Nothing but Net 2015/2016 competition game involves shooting 4 inch balls that can have a 10% variation in mass. We know that trajectory range ,R = V^2/g*sin(2*theta) so it is dependent upon the square of the ball release speed , V, and shooter elevation, theta. Mass does not enter into the equation unless it affects V.
Ball release energy :
Suppose we use a Vex 5″ diameter wheel as a flywheel and rotate it a w_wheel angular speed. As the ball leaves the shooter, it will have a V = r_wheel*w_wheel/2. e.g. half of the flywheel tangential speed. The ball will have a spin rate , w_ball = V/r_ball. The energy of the ball, E_b , is the sum of the ball translational energy and rotational energy.
E_b = 1/2*m_ball*V^2 + 1/2*I_ball*w_ball^2
where I_ball = 2/5*m_ball*r_ball^2 (solid sphere of uniform density).
so Eb = 1/2*m_ball*V^2( 1+2/5) . (corrected 5/29 Was 1/2*m_ball*V^2( 1+4/5) So the rotational energy adds 40% more to the translational energy. Rewriting in terms of w_ball gives
E_b = .7*m_ball*w_ball^2*r_ball^2
E_wheel = .5*I_wheel*w_wheel^2. where
I_wheel = m_wheel*(r_wheel*.84)^2 (ref blog post https://vamfun.wordpress.com/2015/05/17/finding-the-moment-of-inertia-of-a-vex-wheel-using-parallel-axis-theorem/)
E_wheel_initial = E_wheel_final + E_ball This assumes that the wheel is not being powered by the motor during launch and that the extra energy needed for the ball comes from the flywheel. Also, friction and ball compression energy losses are assumed zero to simplify this analysis but can be significant in actual percentages derived. I am focusing on how increasing flywheel mass lowers the percentage range errors caused by ball mass variations.
E_wheel_initial/E_wheel_final = (1 + E_ball/E_wheel_final)
Lets expand E_ball/E_wheel_final
E_ball/E_wheel_final = (.7*m_ball*w_ball^2*r_ball^2)/(.5*I_wheel*w_wheel_final^2)
SInce m_ball = 60 g and m_wheel = 180 g m
_ball/m_wheel = 1/3
So E_ball/E_wheel_final = .165 for a single 5″ wheel flywheel .165/n for n flywheels. So the ball energy is almost equal to the 1/6 final energy of the wheel
Range Tolerance analysis:
So how does R vary with m_ball from all this. Well , we know the range is proportional to V^2 which is proportional to w_wheel_final^2 which is proportional to E_wheel_final.
From above E_wheel_final = E_wheel_initial/(1+ .4954*m_ball/m_wheel)
So due to proportionality of R and E_wheel_final we can say
R/R_0 = ((1+ .4954*m_ball_0/m_wheel)/(1+ .4954*m_ball/m_wheel))
where R_0 and m_ball_0 are the nominal values without errors.
We can use R range= R_0(1+ %e_r) and m_ball = m_ball_0*(1 + %e_m_ball) to work with % changes.
Then with some manipulation we can get %e_r as a function of %e_m_ball
%e_r = -%e_m_ball/(2.02*m_wheel/m_ball_0 +1 + %e_m_ball)
Now m_wheel = n*.180 kg and m_ball= .06 kg so we can write an approx.
%e_r = -%e_m_ball /( n*6.06 +1) where n is the number of 5″ vex wheels.
Lets put in a few numbers:
Assume %e_m_ball = 10% then the range error is
n = 1, %e_r = -1.42%
n = 2, %e_r = -.76%
n = 3, %e_r = -.52%
n = 4, %e_r = -.40%
n = 5, %e_r = -.32%
So you see the benefits of having a higher flywheel mass to ball mass ratio. The use of two 5″ wheels in a single wheel design can reduce a potential 10% range error from ball mass variations to 1% ( less than a ball radius). To keep the spin up time to a reasonable number of seconds requires about 2 393 motors per wheel so 2 wheels costs 4 motors. So there is a motor tradeoff to get that higher accuracy with heavier flywheels.
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.
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.
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.
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.
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.
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.
I 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.
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.
GHCHS Team 599 Robodox attended the 2014 Inland Empire Regional FRC competition. We collected the Engineering Design award and also the competition finalist award and medals. It was a well run competition and we had a great time. Once again we had a top performing robot that got beat by a stronger no 1 alliance. We made an operational mistake in the finals that cost us the first match by breaking communication during setup and causing our Crio to need resetting after the match started and we sat out the Autonomous plus some seconds. Our alliance partners 294 and 4139 were having functional problems in the second so we were soundly trounced by the winning alliance led by 1678 citrus circuits who teamed up 399 and 4161. The 2nd final match (see video) was a thing of beauty with 1678 and 399 performing two truss catches and racking up a 229 to 72 score. Hopefully we can redeem ourselves at our next regional in Sacramento where we will once again tangle with 1678 citrus circuits from Davis. Also, thanks again to 294 for selecting us for the direct eliminations.
Winning the engineering design award means a lot to us since this year we focused on doing a 3D Solidworks design supported by solid prototyping. All fabrication was done based upon automated drawings made from the 3D model. This the best looking robot we have done in years and clearly the most durable. See this post for picture.
Lots more pictures on my facebook page.
The choo-choo catapult reset mechanism performed well so long as we kept the linkages in good order. The high forces caused holes in the linkages to elongate after a day worth of shooting. This was anticipated so we brought three spares and used them all. We will use steel linkages rather than aluminum at our next competition so they should last longer.
Robodox also ran the robot First Aid Station and the spare parts booth. We also had on display our underwater ROV which will be used by Algalita Research Foundation to do plastic pollution exploration in the Pacific Gyre this summer.