texts: Given Pitch and Roll in one Heading, convert to co-planar pitch and roll for North

texts:
I have been pouring through countless articles about Euler's angles, rotation matrices, Rodriguez Rotation Formula, Quaternions, trying to understand how to generate an algorithm for this problem and have as of yet been unsuccessful.  I am trying to figure out, given a pitch and roll along a particular heading, the manner in which one could determine the co-planar  pitch and roll along the magnetic North heading.

In the above image, I have the pitch and roll values at the currentHeading, and am trying to calculate the pitch and roll values of the blue line in the same plane but in the magnetic North direction.  Any help would be highly appreciated.


texts: An analytical expression to calculate the stress triaxiality for a single notch sample

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As far as I know, there is a formula (Bridgman) for the calculation of stress triaxiality for a sample having a notch on either side or for a flat grooved sample.
Now my question is, if I have a sample just having a single notch on one side can I use the Bridgman formula?


texts: Optimal size and shape for a steel target?

texts:
Problem

I'm building a steel target for long-range rifle shooting. For those unfamiliar, the purpose of the steel is to produce a loud "PING" when the bullet strikes the target. It's very fun.

Since I have a variety of materials to choose from, I'd like to know the ideal shape and size of a target to produce the loudest possible noise upon impact.

Materials

The steel grade is AR500 (very hard but not too brittle). Its density is ~0.281 lb/in3 (7.78 g/mL).

I can choose from three thicknesses: 1/4", 3/8" or 1/2".

The metal can be cut into any shape, and I'd like it to be somewhere in the neighborhood of 24"-36" in any dimension. The most convenient shapes would be rectangle, square or circle. It could be bent along one axis if there's a very good reason to, but preferably kept flat.

Parameters

The target will be placed 1000 yards from the shooting position (see why it needs to be loud?).

For the sake of discussion, the projectile will be a "6.5 Creedmoor" round: 6.5mm diameter, 140 grain (9 grams), 2700 fps (830 m/s) muzzle velocity, copper jacketed with a lead core. Ballistics calculations give us ~1200 fps (366 m/s) velocity at 1000 yds.

Question

How should I build my target to produce the most audible sound upon impact from 1000 yards away?

Bonus Nachos:  How should I mount the steel plate to a wooden post to reduce dampening? Options include bolts, metal hooks, chain, rubber cables, or nylon straps.


texts: Why is this box girder made of lattice on one side only?

texts:
Here's a zoomed piece of this image from Wikipedia

That's a close-up of a tower holding a railroad bridge. A and B are two of the four columns in the tower's corners. I assume that they are placed symmetrically, so arrow B points onto the typical "outerwards" surface and arrow A points onto typical "inwards" surface.

Note that where arrow B points the surface is solid and where arrow A points there's a lattice instead. Note the numerous rivets alongside each beam - the beams look like they are box girders assembled such that each of them has three solid surfaces and one lattice surface.

What would be the reasoning for having a lattice on one of the surfaces only?


texts: Plumbing Imperial units confusion - 3/4" is supposed to be around 19mm, right?

texts:
I'm really confused. I've only ever used metric in my life. Recently I'm trying to build a IOT device and there is plumbing and water involved.

I was looking for a 19mm fitting, but on Amazon and other sites it's always advertised in inches. John Guest 3/4" BSP x 1/4" Push Fit Tap Adapter

I did the conversion and 3/4 inch, according to my calculation, should be around 19mm. But whenever I order these fittings they always send me a larger size. The resulting size is always around 25mm when I measure it.

To me it seems like 3/4 inch doesn't actually mean 3 quarters of an inch?


texts: Swing safety: maximum load of beam (supported at one end, free with load on the other)

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My husband and his dad built a fort for our two boys. Coming off of one side of the fort is a 4x6 wooden beam with a tire swing attached at the end. It is supported on one side by the fort, but not supported at all on the side where the tire swing sits.
The beam comes out about 5 feet from the fort. My boys weigh about 45 and 35 pounds, respectively, and like to be on the swing together at the same time. I'd like to trust that they'll be fine, but I'd be much more comfortable if the math proved this to be true.
Can anyone help me figure out if the wooden beam can support their weight--especially when they are riding wild?
And if not, what can be done to make the swing more structurally sound?
Thanks in advance!


texts: I want to design a shaft for a motor test rig. The motor and generator are 48V and 1.5kW and the maximum torque produced by the motor is 18Nm. RPM varies from 2900-3100. What shall be my next steps? I also intend to use Lovejoy coupling.


texts: Selection Of coupling and determining size of motor to rotate heavy disc

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Following image is something I want to design. The uniform stainless steel round plate of diameter 1000mm and thickness 10mm is rotated by a stepper motor. But after every turn, a pressure of 3000 kg/cm^2 is applied at he edge of the plate by a hydraulic piston. Will my disc deflect? Does it need a support at bottom where pressure is applied? How should I couple my motor to the disc so that the coupling can withstand the load? Can my motor withstand such pressure?
Please help me with the design.After ever turn the plate stops and pressure is applied. Which stepper can withstand such load?


texts:
Consider a receiving dipole antennae of length $L$. If electromagnetic waves of power intensity $P$ W/m2 is incident on it, then open circuit voltage induced in the antenna is given by

$$V=\frac{L}{2}\sqrt{P\times 2\times 377}$$

where $V$ is independent of the wavelength of the electromagnetic waves.

Another fact is that dipole antennae are resonant at half wavelength.

How to reconcile these two facts? I mean to say a dipole of 6cm is resonant for 2.4GHz. But if one uses it for receiving 10 Mhz signal, what exactly will be problem as the open circuit voltage will be same irrespective of frequency (of course $P$ is constant)?

My understanding says following. While voltage induced will be same, what will depended on frequency is impedance of antenna. At half wavelength, the dipole will be resistive only. At lower frequencies capacitive reactance will be high while at high frequencies inductive reactance will be high, both these will reduce the current induced in the circuit.

Am I wrong? or, am I missing some aspect?


texts: Does a stove which has started emitting heat on the non-circled areas have something wrong with it?

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We have a electric stove which looks like it was designed in the late 1980s or early 1990s, and probably was made in ~1995.
It has physical knobs that you turn around to change the heat for each plate. Four plates. The plates are metallic and separated from the white "backplate". (That is, there is a height difference. It's not one of those fancy, modern stoves with a fully flat glass plate which were just starting to appear in ~1995.)
Anyway, a family member mentioned recently that she thought that it had started emitting heat in the front and generally "around" the designated metal circles. I have also noticed this, and verified it today by touching it with my finger, quite a bit away from the actual circle, and it was super hot. Not just a little warm. Really hot.
This seems like it's somehow got damaged. Is this a common problem? Is it dangerous? Perhaps critically lethal? Will it blow up any day now? Will it start electrocuting us soon?
I tried to search for this online but found nothing, but that says nothing because I never find anything no matter what I search for.
Would really prefer to not have to deal with buying a new stove or even have this one replaced. Perhaps it's always been like this and I've just not thought about it before she had to mention it?
It's this specific model: https://rensavinden.s3.amazonaws.com/datas/49040/original.jpg?1584311806 ("EKE 6100")


texts: what can replace high carbon steel as the raw material for sewing needle

texts: I am working on a project that need to redesign a sewing needle. Because I am planning to use a stainless steel loop to replace a needle's eye, using high carbon steel, which make all modern needles, would not be industrially profitable as it is hard to weld and might take a lot of time. I am wondering is there other material that can replace high carbon steel as the raw material for a needle? Or, is there other materials soft enough to be bented into any shape and can be joint with high carbon steel or whatever material that can replace it? Thanks a lot!


texts: I was trying to simulate the simplified model of RDC (AD2S90) provided in link . The issue is to design proper compensator for this model to track constant velocity with zero velocity lag. Not very clear how to proceed. As suggested in the data sheet (page No.9) I tried to add a compensator (100/s * (s+100)/(s+1000)) between demodulator and the VCO. But from simulation(step response), it appears to oscillate. Where am I going wrong? Almost all the data sheets that I came across recommend the compensator with the above mentioned transfer function, but in simulation, it does not work. How to proceed?


texts: My instructor sent this solving with program that I don’t know the name , does anyone know the name of the program ?


texts:
Suppose I have a rough 3d model of a building created it some CAD software. Now I want to change some portion of the model based on the following factors

Lighting
Energy consumption
Structural Load
Fire Safety
Heating & cooling load
etc.

Is there any Software that can provide these feature. I know there are some good software for each of the feature mentioned above, but how can we integrate their results into the 3d model. I am from a Computer science background so don't have much idea about this, Any suggestion would be of great help.


texts: I do not understand something about the "rule of mixtures". Specifically, between upper bound elastic modulus and lower bound elastic modulus calculations, I seriously do not understand what value to choose based on transverse or longitudinal loading and on the basis of iso-stress and iso-strain conditions. Some insight into making these decisions will certainly help me out!


texts: The mechanism of submerged hydraulic jump

texts: Is there a mathematical analysis of the submerged hydraulic jump, such as under what condition it is formed, the speed and trajectory of the circular flow therein, etc.? Is there a good mathematically sophisticated reference on this topic?


texts: Motor Torque Required in a Reciprocating Compressor

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I am working on a Univerity project involving a reciprocating compressor and I am having trouble verifying the motor's torque requirements. I am relatively happy with my calculation method, however, the motors torque requirments seem unreasonable when considering the motor that is used (see image).

My calculation method was as follows:

This is very much not my area of expertise and I am unsure if i have missed a step or just over simplified its workings, either way, any input would be very much appriciated.
Many thanks,
Scott


texts: Reinforcing beam and slab with correct steel bar structure

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This question might look silly. I am not knowing the correct engineering terms to use in this question. I am trying to explain using the words what I know in English.

We have been hired some construction workers for a work in our backyard. I have some doubt on reinforcing beam for slabs. I came through following 2 models

.

1. Model one

.

2. Model two

According to my perception, I believe the second one is much better in terms of strength. Because the beam is supporting the weight of slab. But my friend suggested me the first one is the right way. But I am not aware why the first one is better than the second. Could any one please help me out in this case to identify the better one.


texts: Why is Mach 0.3 the threshold separating compressible and incompressible flow?

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I've read that Mach 0.3 is pretty much the upper limit for treating air as an incompressible fluid.  The sources I've read seem to treat this as a given, without proof or justification.

Why is this the limit?  Is there a mathematical justification for this?  Also, does this limit only apply to air? If not, then what does the limit depend on?


texts: Generally speaking are inrunner motors better generators than outrunner motors or vice versa?

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Using a motor as a generator but  looking to test something
I understand that outrunners have a higher torque but would that be neccesarily good for generating electricity or not?


texts: How to identify a material without doing a destructive test or crystallography analyses

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I have a structure which I need to know some of its mechanical properties, using the standard values is good enough so looking into a mechanical properties chart of various materials would be ok.
The problem is that I don't know what is the material the structure is made and I cannot disassembly it and neither do a tensile test or a crystallography analysis

How can I identify the material of the structure?


texts: Protection against accidents when chainsaw chain breaks

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I've just bought myself an electrical chainsaw. Specifications of the chain velocity of my saw read 55 km/hr.
I've read online that many wood-cutters have encountered chain breaks and want to protect myself against unfortunate accidents.
So, my idea is to always cut with the underside of the blade. This way if a break occurs at the point of contact with the wood and since the direction of motion of the chain is towards me from the underside, the chain will move away from me when it snaps.
I am basing this on the fact that the saw has a small sprocket underneath giving motion to the chain. When it breaks the sprocket cannot pull it towards me anymore and given the momentum of the other outward sprocket on the head of the blade, the chain will be pulled outwards, up and away from me. All this supposing that I am always cutting with the underside of the blade.
I do not know if I am correct though! Do you know of any experiments that have been conducted to demonstrate this? Since this is a matter of life and death, I would expect much information about this, but I can't find any!


texts: Finding coefficients for a PID controller that minimize the integral of the squared error (ISE)

texts:
The problem

The problem is to find the coefficients for the P, I and D terms of a PID controller used to regulate the object that minimize the the integral of the squared error (ISE):

$$Q = \int_0^\infty \epsilon^2(t) \ dt  $$

The object being controlled is described by the transfer function:
$$ G(s) = \frac{1}{s^3 + 6s^2 + 5s} $$

My attempt

My idea was to find to find the expression for error in the s-domain, then perform an inverse Laplace transform to get the expression for the error in the time domain, then integrate the error from $0$ to $\infty$ and then find the values for the terms $K_1, K_2, K_3$ that will minimize the function. I apologize for the mistakes if I've made any as my knowledge of control theory is very basic.

What I managed to do:

The transfer function of a PID controller is:

$$ K(s) = k_1 + \frac{k_2}{s} + k_3 s $$

If $H(s)$ is the overall transfer function, $W(s)$ is the input, let's say it's the unit step function, the expression for error in the s-domain is, if I'm correct:

$$E(s) = W(s) - H(s)W(s)$$
$$E(s) = W(s)[1 - H(s)]$$
$$E(S) = \frac{1}{s}[1 - H(s)]$$

The overall transfer function will be given by:

$$ H(s) = \frac{K(s)G(s)}{1 + K(s)G(s)} $$

After substitution and simplification:

$$ H(s) = \frac{k_3 s^2 + k_1 s + k_2}{k_3 s^2 + k_1 s + k_2 + s^4 + 6 s^3 + 5 s^2} $$

Then, substituting for the expression for error:

$$E(S) = \frac{1}{s}[1 - \frac{k_3 s^2 + k_1 s + k_2}{k_3 s^2 + k_1 s + k_2 + s^4 + 6 s^3 + 5 s^2}]$$

I used Matlab ilaplace command to calculate the inverse Laplace transform of $E(s)$ and got:

$$ \epsilon(t) = \frac{\delta(t)}{t} - \frac{(exp[(- k_2 - t^2 k_3 - 5t^2 - 6t^3 - t^4)(t^2 + 6t + 5)]}{t} $$

I don't know if I've arrived at the correct result, what seems weird to me is that the resulting expression for $\epsilon(t)$ doesn't contain any $k_1$ term. But assuming this is correct, I would finish by finding the values of parameters $k_1$, $k_2$ and $k_3$ that minimize this integral: $Q = \int_0^\infty \epsilon^2(t) \ dt  $

Question

Now, I would be grateful if you could verify whether my approach and solution is correct and describe how you would find the values of the parameters that minimize this integral using Matlab i.e. what commands and how you would use them. I'm wondering if lack of closed-form solution to the integral would make finding the parameters impossible.

Or maybe, there is a simpler method of solving this problem, perhaps by avoiding computing the integral.


texts: What is the Source of the 10% Trailer Tongue Weight Recommendaton?

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Throughout the trailer, hitch, and tow vehicle industry a recommendation of 10% tongue weight for a tow-behind trailer and 15% for a 5th wheel trailer seem universal. They have even been changed to 10%-15% and 15%-25% recently.

Where did they come from? How were they determined? Was it to keep the trailer on the ball in all conditions? If so, a weight-distribution hitch dramatically increases the forces on the ball but there is no recommendation for lower tongue weights with a weight distributing hitch.

With all the GVWR, GAWR, and GCWR numbers are thrown about, the only one with a standard seems to be GCWR with the relatively recent (last 10 years) SAE J2807 standard. And that standard has been widely criticized as not accounting for basic factors such as steering ratio and wheelbase when specs talk about steering wheel angle.

So, where did the 10% recommendation come from?


texts: How to evaluate solenoid valve specifications

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I need to replace a solenoid valve, and I need help in identifying the specifications that I should check for an equivalent replacement.

This is a picture of the valve itself:

Click for larger image

If it matters, the valve is used to control water flow with a whole house humidifier.  The required inlet and outlet pipe sizes are understandably constrained by the existing piping.

This site provides a good overview of the terminology involved, but also mentions a few terms that aren't listed on the label.  Their review is echoed by this site, which covers many of the same terms.

My online searching has yielded a couple of suggested equivalent parts, as well as a different version of the value offered by the OEM of the humidifier.  Some of the suggested equivalent parts are roughly half the price of the OEM replacement part.  But I would like to make sure that I'm truly buying an equivalent part.

What specifications do I need to verify before purchasing a replacement solenoid valve?


texts: 12v relay to open and an close switch without sending power to switch

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Sorry if this is elementary but here's what I need.

I'm trying to power a relay via 12v DC (vehicle) to open a closed switch while the 12v power is sent to the relay. Essentially, when the blinkers blink, it will open the switch each time they blink. The switch must remain closed when the blinkers are not switched on (blinking).

In addition to that, I need to open the resting closed circuit without feeding power to it. I've attached an image as an example.

I realize the above example may not even exist, but I hope it helps you understand what we're trying to accomplish.

Thanks


texts:
When I'm looking at images / videos about the load supported by reinforced concrete slabs, I always see a compression at the top of the slab in every point that varies from the center to the edges:

But isn't there a tension on the slab near the edges caused by the fact that the slab is supported by the walls?

I mean, why I always see the first and not the second schema below?


texts: Measure the distance to a balsa wood strip with 1 mm accuracy

texts:
I am working on a project where I need to determine the density of a balsa wood strip.

I know the length and height of the strip. The two measures left to take are the weight and the thickness of the strip.

To achieve this, I am using an Arduino Uno. The weight measure must be accurate to 1 g; I achieved this with an HX711. In the thickness measurement I have problems, because it has to be accurate to 1 mm.

The strips are between 17 cm thick and 1 cm thick. I have tried using an IR sensor, ultrasonic sensor and laser sensor but all of them give me bad readings. This is because the environment where the machine has to work is in a balsa factory, where there is noise and dust.

How can I get this measurement as accurate as I need?


texts: How do I calculate the strength of a weld joining two crossed rods?

texts:
While considering this recent question, I started wondering how to determine the strength of the welds in the steel mesh. As AndyT points out in his comment:

  The welds at the connections are only intended to keep the bars at
  right angles during handling - they are not intended to take any load.

The intent of the manufacturer, of course, doesn't stop someone from using the product to support a load anyway. Just what sort of load can this type of weld support? What is/are the likely failure mode(s)?

This weld has different geometry and loading than fillet welds (which are the only type I'm at all familiar with). I think it's properly called a flare-v groove weld, though most of the examples I can find show that as joining a round bar to a flat bar or plate. The geometry is different enough that I suspect those are not equivalent, from a design standpoint.

This AWS technical manual says:

  2.3.3.2 Effective Weld Size (Flare Groove). The effective weld size for flare groove welds when filled flush to the surface of a
  round bar, a 90° bend in a formed section, or a rectangular tube shall
  be as shown in Table 2.1, except as permitted by 4.10.5.

Table 2.1 indicates the effective weld size is either 1/2 or 3/8 the radius of the outside surface of the weld. I'm still not sure this applies to the crossed bars geometry, though.

When I was learning about fillet welds, it was always assumed the weld would fail first in shear along its throat. Given that a square mesh has no cross-bracing and there is a single point of contact between the members (rather than a line or plane of contact), can I afford to make that assumption?

Especially in the case where there are only two rods rather than a mesh grid, this weld could be loaded in quite the variety of configurations. Let's consider only the cases of pure torsion, pure tension and pure shear. Assume the weld fails before the members.


texts: Is there an equivalent concept in engineering to CS's "search space reduction"?

texts:
I am looking to learn more about how engineers efficiently search for solutions to problems, particularly mechanical engineers.

Computer scientists sometimes speak of "search space reduction" when they are trying to make an algorithm more tractable. For example, if a search space is small, trial-and-error or "brute force" may be a very efficient method to implement because it is easy to execute.

Do engineers have a similar concept?


texts: Intuitive explanation for why doubling max speed is proportional to eightfold power

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I read that when you want to double the max speed of e.g. a boat you would have to increase the power eightfold! I could understand that you have to square it (= fourfold) because you are working against "a wall" of water which makes it an area (= power of two)... but why to the power of three?

Could you please give a physical/mathematical explanation but also an intuition on why this is the case.


texts: Rayleigh-Ritz method, calculating slope of beam?

texts:
For a simply supported beam with a UDL if the deflection is assumed to be:

$$V=a+bx+cx^2+dx^3$$

What is the formula for calculating the slope?

I thought it would be:

$$θ=dV/dx$$

However, working through examples where I calculate the values for the constants this does not appear to be the case. At the midpoint of the beam when I should be getting zero deflection, the value I get using dV/dx is completely wrong.

How do I obtain θ?


texts: How might I see through a completely solid plate of steel worn as a mask?

texts:
I have a solid plate of steel I need to see through, as a mask. I need a wide FOV (at least 210 degrees). I cannot have any obstructions in the image, so no pinhole meshes or anything like that.
Furthermore, I can drill no more than 4 small (pinhole) holes in it. It only covers my eyes and parts of my nose. Think ski goggle coverage.

I'm not well versed in optics, so I'd like to know how I could somehow "re-route" my vision, like a periscope, while maintaining a reasonable field of view. I've also looked into using VR headsets as a way to do this but none currently released have wide enough FOVs for my tastes.


texts:
I have a statics problem that I am running into some difficulties with. What is being asked here is to determine the support reaction at the points A and C. This would normally be no problem, but when I set up my equations (sum of the forces in the x-direction, sum of the forces in the y-direction, and total moment) I realize that there are too many unknowns for the problem to be solved.

Is there a way to assume something in order to eliminate one or two of the unknowns? (I am guessing it will be in the x-direction, but that's just a hypothesis.) Or should the problem be solved in a completely different way?
Thanks for the help!


texts: In case a plane stalls, what should stall first, the tip or the root of the Wing? Why?


texts: Supporting flexible square plate of uniform density in equilibrium with only 4 rolling contacts placed along the square's diagonals

texts:
Consider a flexible square of uniform density with vertices (0,0), (0,1), (1,0), (1,1). I need the 4 coordinates for rolling contacts along the diagonals that will stably support it. Someone could just test it. Open to all thoughts and ideas.

This seems to be similar to the Bessel Points problem, but now in 2D. Guessing the answer is around (.22, .22), (.22, .78), (.78, .22), (.78, .78). How can I find this answer?


texts: Why does use with air or water reduce the maximum temperature of certain high temperature / pressure hoses?

texts:
This example is a Parker Hannifin model 426/436 "SAE 100 R1 AT / SAE 100 R16 High Temperature Hose".
Here are the temperature specifications:

(Full data sheet)
Although there is an asterisk after the water/air notes, I can't actually find any corresponding explanation in the data sheet for that.
I am actually looking into hoses for a compressed air application, so I'd like to understand the reason for this reduction in performance.


texts: Calculating diameter of steel rod required to not bend over a given length

texts:
I want to use steel (or other material) rods to support weight over a 900mm cavity. The weight that needs to be supported is technically unknown, but I'd specify some rough guidelines as:

100KG (max) - some give, but no permanent deformity
<50KG - no real visible bend

I'm not hugely attached to the weights listed above as they could be dropped with max weight advisories etc but I'd say those are probably ideal. Exceeding them would be fantastic, reducing them isn't a huge issue. Ideally I'd be able to calculate myself and adjust the design to use a bigger rod if necessary.

The rod would be used to back a slat of wood which presumably would add to the strength of the unit, and there would be multiple slats (laid horizontally) covering an overall length of about 1.6m. I'd probably add an overlap between the slats also which I would assume would add strength to the system.

I'm trying to find my feet with CAD design and engineering principals so I'm very much new to the (seemingly) advanced maths I've seen glimpses of for this sort of calculation, so a resource I can read through or a breakdown of a calculation would be much appreciated!


texts: What does a Sad Face on a circuit board mean?

texts:
I have a Fisher and Paykel Washing Machine (model number WL80T65C, well past warranty) which got rained on (a lot) and one of the capacitors blew up. I've done an amateur replacement of the capacitor which might work but when taking the circuit apart I forgot to take a photo until half way through. I've managed to place everything except for two cables, one of which is Green/Yellow and coming from the mains. This is Australia so I presume it's a ground cable.

The only hint I can find as to which is the ground and which is the other is the sad face that's printed on the circuit board, as shown in the photo attached.

The cables connect to where the blue marks are, one on the left and one on the right.

So, is a frown face in a PCB a standard thing and does it tell me which is ground or are Fisher and Paykel mocking me? Is there a place where I can look for the schematics of this thing?

Edit: Here's a better photo of the sad face and its friend, taken in the day time.

NB: It's become apparent that the component was ground and it didn't matter which way around I fixed the cables but I'm still curious as to what the sad face means.


texts: Can we reduce pitch of a lead screw to reduce backlash of the lead screw?

texts:
In gear design, the backlash is introduced in the design itself (not by tolerances of manufacturing) to allow free meshing of the gears. The backlash in the design can be minimized by reducing the pitch of the gears. For example, If the pitch of a gear halved the designed backlash can also be halved. Though the reduced pitch also reduces the torque capacity of the gear.
Similarly, is it possible to reduce the pitch of the lead screw to reduce the backlash in the design?


texts: How to design a narrow bearing that supports shear direction load

texts:
I need to connect two flat bars of metal with some kind of bearing that doesn't increase the joint thickness by more than 2-3mm (the less the better), as shown here:

There are almost no axial loads but the peak lateral (shearing) stress on the bearing would be of order of 2000 N with 800 N sustained being the norm and the directions of the stress varies (although axial respective to the lower beam would be most common and strongest).

There is a serious restriction on thickness of the joint - the present 10 mm is already pushing the envelope; another 2-4 mm would be acceptable though unwelcome.

The bars will be steel or duraluminum. There are extra braces, etc., which prevent buckling and limit stress in the perpendicular direction to negligible levels, but the two bars need to carry axial stress and lateral stress "in the thick direction".

Moderate friction is acceptable - 5 N·m friction torque is still a reasonable value. Rotation is moderately fast, at most ~1 rev/s, usually much less. Also the range of rotation is limited; only 30-180 degrees angle between the two bars is needed (and even a little less than that if necessary). Lifetime doesn't need to exceed 1000 hours; less for the prototype.

This will be prototyped using a common DYI workshop without specialized machinery like CNC devices, also preferably no very expensive solutions - of course purchase of a pre-made bearing fitting the criteria would be perfectly acceptable if the price is not excessive.

What kind of bearing or joint would fulfill these prerequisites?

EDIT: Let me add a picture explaining the general layout of forces:

In general situation any common bolt, bushing (with flanged axis) etc. would be sufficient. Here the problem is getting it all to be narrow enough not to extend way out of the narrow plane occupied by the two bars, and not fall apart.


texts:
I have a design with two parts (at the moment):

a fixed 10cm ring with vertical tracks
a freely rotating block with a cut that may freely slide along that tracks:

I'm trying to find a low profile way to ensure that whenever the cut in the moving block faces upward vertically, the block is pushed up (almost) touching the inner face of the ring. That is, it returns to its "home position" whenever the cut faces up:

The block is just driven by a crank. Indeed, the crank can freely shift vertically. However, i'm hoping the block (along with the crank) to return to the home position whenever the cut points upwards.

The only way I could think of is to have a part like a leg sticking out from the bottom of the block so that it pushes against the ring or an external track (near the bottom of the ring) whenever the cut nears facing upward. The issue is that this leg will require quite a bit of extra space, e.g., when the cut faces down but the block is at the top, the leg will point upward. The method should not constrain the block's movement along the tracks or rotation.

Does anyone know of a better way?

Any thought appreciated.


texts: How does water flow in the water jet cutter nozzle?

texts:
Here is a schematic cross-section of a water jet cutter nozzle design:

As it is shown, the thin water jet grabs abrasive particles in the mixing chamber and the mix flows through the nozzle.

My question is: what makes the water flow through the nozzle despite the loss of kinetic energy due to the abrasive material and the friction inside the nozzle instead of filling up the mixing chamber and running up in the ambient pressured abrasive feeding tube?


texts: Why is it that utilizing clockwork motors never came into fruition as power sources for things like vehicles and bolt shooters, in place of compressed air and strings?


texts: Calculating gyro data from accelerometer, pitch, roll and yaw

texts:
I am currently collecting accelerometer and attitude data using smartphone sensors. Data is collected at 100Hz over 2.5 seconds. Of which there are 250 accelerometer points and 250 points representing the attitude of the device. I am looking to convert the attitude/accelerometer data to gyroscope Data. For example, 1 of the 250 segments look like;

For example,

Accelerometer

AccX = 0.08458628
AccY = -0.0586758144
AccZ = 0.273877382

Attitude

Pitch = 0.111681767
Roll = -0.8779668
Yaw = 1.91596484

How can I calculate the corrected gyroscope data from this data?


texts: Internal teeth involute gear pitch circles

texts:
I'm having some trouble figuring out how to design the corresponding internal gear for any particular spur gear. With spur gears, meshing is accomplished by having two gears with the same modulus (MOD) or, in the US, the same diametral pitch. The spacing between the two gears is such that their pitch circles touch.

Looking at an internal gear the tooth profile for an internal involute gear is the inverse of the external involute. However if I try to create such a system (in Fusion 360), I get some interference issues:

What I've done is create two spur gears, both MOD = 1, one with 24 teeth which I've just simply inverted to create an internal ring gear and the other with 12 teeth. My questions:

The pitch circles are marked in green. Is the pitch circle for the internal gear the same as the spur gear that I used in inverse to create it? Or is it moved somewhat. The proper relative gear positions should be where the pitch circles touch so that's a main issue.
Although it doesn't look too bad, the left and right teeth in the image are interfering. I think if the addendum of the internal gear's teeth was reduced this would help matters. It seems that the larger the ratios (eg: if the spur gear was 8 teeth instead) the more the gears would crash and perhaps the more the addendum should be reduced.
In addition I could add backslash, would this help the interference issue?

Are there specific rules to design an internal involute gear for a particular MOD?


texts: Where can I find a database of (n,n' gamma) and (n,gamma) reactions sorted by Isotope and Q value

texts:
I have some MCNP spectra with interesting gamma peaks. I can not for the life of me find a database that allows me to search for reactions by Q value or isotope, or both. I can't even find the Q value for Cl-35(n,p) reaction.
I have tried various databases like ENDF and EXFOR, but thus far cannot figure it out! I need to be able to sort by isotope and Q value so I can identify the peaks in the MCNP spectra.
Any help would be much appreciated!


texts: How much energy do mass drivers need to project 1lb of material 1km/second

texts:
I am working on a geoengineering project that, at the moment, seeks to use many mass drivers to project lunar regolith (lunar soil) or other materials into space to create targeted shading effects on the earth for specific purposes. The material would intersect the moon allowing for easy recollection of material for quick reuse. There are other space infrastructure implications that would allow sharing of resources and a lot that can be done to increase efficiency. The problem is I can't find anywhere to help with some of the basic calculations. I know that mass drivers can be 80-90% energy efficient on the higher end and the project will be in an extremely low atmosphere environment.

I would like some help with the basic math to calculate energy needs. Even links to find the information and explore it would be welcomed.

The idea is to constantly project small units, no more than 10lb but probably smaller, approximately 3km/second from a mass driver (the small size as I understand it should allow a faster rate of projecting material which should make the whole process easier).

My question is;

How much energy would it take to take per pound of material to travel per km/second assuming 80% energy efficiency? Browny points if you can give an estimation of the refractory period between projections or point me to how to calculate that.

P.S. This is a big complex project and I always get random questions going in every direction. I'm used to it and happy to answer any questions or add them to my list of questions that need answering, but please provide useful feedback instead of blank criticism and recognize that I only have so many characters per comment to respond.


texts:
I have trial version of STAAD.Pro software and I am trying to figure out why my calculation are not same as manual one. I have modeled simple structure. But I don't want to have beams 1,27,26,25,24. It is intended that all that beams are one beam and beams 6,11,16,21 are welded to that beam and central beam (there are also beams 3,5,10,15,20 and they are in reality one single beam).

Is that influencing results (Continues load is added to 8 middle beams). I have merged beams 1,27,26,25,24 into single beam , and beams 3,5,10,15,20 into single beam-  and beams 2,7,12,17,22 into single beam also - but than it says that I have multiple structures.

Top view of structure

Can someone explain how to model intended?


texts: Confused about information on a state transition table

texts:
I'm working with a State Transition table with a variable I can't identify.

Here's the table:

I'm pretty sure "a" is the present state. "b" is the next state and Sx and Sx+ are the inputs.

However, I'm not sure what "D" is. Does anyone have an idea of what D would be and then what the state diagram would look like? Here's what I got:


texts: Is there a difference between punching shear for columns on slabs vs slabs on columns?

texts:
Might there a difference in design approach for punching shear for the two scenarios? Or something to pay particular attention to?

Is the slope of the shear plane (normally 1:1) the same for both scenarios? I would assume that it is, since the two design codes I usually use (Eurocode and SABS) do not differentiate between the two scenarios.


texts: Supporting a Chain While Its Size is Varied

texts:
I am trying to model a machine that uses eyelets to support a piece of fabric, and this design uses a chain to hold the eyelets in a loop; the links are pictured below.

As this machine runs more and less of these links will be needed, and so I'm trying to design a support to keep the chain under tension. The ideas i have are segments of a circle to act as a hand to pull outward from outside, or a loop that is made to push outwards.

The circle segments could be good but there would need to be more of these segments when you increase the number of links. This means either the operator or machine would have to know when to add these supports and be able to.

The loop could be good as well, but it would need to able to range in size from ~1cm to 20cm in circumference. This would be difficult to make durably.

Is there any other way that machines have supported adjusting chains?


texts: Possible to suck water through manual bilge pump using a transfer pump?

texts:
I dug a shallow well (12' deep) on a remote off-grid Florida Property I own.  The well  is a simple 1-1/4 PVC Sand Point well I hammered in the ground.  I then used a rubber coupler to attach a cheap manual bilge pump.  The pump works surprisingly well filling a home depot bucket with just a few strokes.  However, my choice for the well location was about finding some out of the way low laying spot rather than convenience. I hit water on the first try.
My van has an onboard 12v transfer pump that claims it can pull water 40' up and an 8 gallon tank on the roof I want to fill. I am able to drive the van about 20' from the well, but my transfer pump says the line must be primed.  I have a 25' 3/8 recoiled hose and I can fit a garden end on the output of  the manual bilge pump. I suspect I will have no issue priming the line with the bilge pump, BUT,  I am wondering if I would be ABLE TO SUCK WATER WITH THE TRANSFER PUMP THROUGH THE BILGE PUMP?
Understanding the design of these pumps they are basically two one way check valves that should allow for water to move freely upward while maintaining prime. I'm just not sure if an external suction source will be able to do that THROUGH the manual pump and how much added pressure this will put on the electric transfer pump which sounds very powerful but is 20' away.


texts: Is it economical to use solar energy to manufacture solar panels?

texts: Estimates of area needed to be covered by solar panels to power all of the US using only solar are about equal to a 100 mile by 100 mile tract of land. But solar panels have a lifespan of only a few decades and need fossil fuels for their manufacturing. Was wondering why there are no solar manufacturing plants running on solar power and if such a facility will ever be feasible from a financial standpoint. How much time(in months/years) will it take for a solar plant powered by 10GW of solar panels(assume battery backup) to churn out 1 GW of solar panels?


texts:
I am having a hard time taking care of signs. Whether we’ve made the cut at right or at left. Whether should we make the rotation according to axis x, y or z.
In this case, they assumed that P was applied at the left of the axis of rotation and obtained M as negative. Why couldn’t we assumed that P is at right as well and with the calculations shown be positive?


texts: What is the relation between the angle of a bend along one axis and the length of a face perpendicular to that bend

texts:
Sorry if the title doesn't make sense, I just cant think of how to word it so I'm going to be using images to help.
Basically I have a piece of sheet metal that I have bent along one edge to give me a right angle, I then bend it down the middle, perpendicular to the previous bend, at 35 degrees, now I have already cut out a relief to account for this bend forcing my metal on the right angle into itself, but when I make the second bend, the length of one of the previously bent pieces has to be shortened to make the tip of its edge line up with the other edge.

The edges I'm talking about are the two right angle bends that are separated by a small relief, this relief allows the main bend of 35 degrees take place.

But as can be seen in the flat pattern, I have had to trim the edge of the sheet in one place to allow the bent piece to appear more uniform, if I left the edge untrimmed and the same length along its entirety, when bent, there would be an overhang.
So obviously there would be more or less overhang depending on the angle of the main bend, so my question is what is the relation/equation between the amount needed to be trimmed and the angle perpendicular to that face?
Is it to do with making the length of the hypotenuse match the width of the other piece? The lengths would be the same if I cut a relief out of both sides at an equal angle but maybe there are situations where that isn't viable?
Some numbers that might be helpful, the width of the right angle bend on the lower half is 12mm, the width of the trimmed piece is 9.5mm, this width gets me close to inline but it isn't perfect.


texts: Measuring distance to a non perpendicular surface

texts:
I am a Mechanical engineering student and i am completely new to arduino and need some advice. i have a project to measure the maximum deflection in a sailplane wing (up to 9 meters)

How do i measure distance using ultrasonic or light sensors to a non perpendicular surface

what hardware would measure such a large distance as ultrasonic have a max range of 4 meters

ANY HELP would be greatly appreciated
the attached


texts: Calculating correct motor torque for windmill

texts:
I am struggling calculating the correct torque needed to rotate a windmill object at the required speed. Suppose I have a windmill:

        ^
        |
     <- o ->
        |
        v

with a motor at the centre, and the four blades are 2.4m long, each weighing about 10kg. I'd like to calculate the torque needed to rotate the windmill at around 5 rpm.

I'd be fine calculating the torque needed if there were just one blade, but my intuition tells me that since everything is balanced and symmetric, ANY non-zero torque would be sufficient. However, this answer seems "too easy".

I'm not an engineer, just a meagre pure mathematician, so any pointers or tips (or even answers!) would be greatly appreciated.


texts: Operative Temperature in Underfloor Heating?

texts:
I am new to the Underfloor heating system, and a bit confused on the terminology for Operative Temperature.

Is this the temperature that is measured by the sensor or is this the set-point temperature on the thermostat?


texts: Modelling a refrigeration cycle in Excel

texts: Is it possible to model a heat pump cycle without using tools like EES, but using Excel? I am considering to use Refprop application as an add-in in Excel, and model a heat pump cycle. Another alternative would be to create a P-h database for various fluids, and go from very complicated series of equations to find pressure, temperature, and density values.


texts: Has anyone achieved significant energy savings by increasing the cooling setpoints in retrofit office buildings, in practice?

texts:
I have a simulation based research vs. practical experience type question:

There are a number of academic research papers available which claim 20% to 40% cooling energy savings by increasing the cooling setpoint by 5°F. The savings change by location. Some research papers also provide thumb rules like (approx.) 10% energy savings for 1°C rise in cooling setpoint. The studies I have come across are based on energy simulations.

On the other hand, some 'on the field' engineers (retro-commissioning/energy engineer) I have spoken to suggest, these savings are inflated or at least not achievable with just change in the cooling setpoint. To achieve these savings you have to make changes in VAV controls (basically reduce the minimum airflow) along with changing the cooling setpoint. But these changes (reduction in VAV min airflow during reheat) can not be applied in actual buildings for various practical reasons. These reasons vary from burning up the electric reheat coil, high diffused air temperature leading to stagnation, not enough diffusion due to low velocity, IAQ issues in conference rooms, supply fan stalling, low air throw length etc.. There are savings but of the range 2-5% for changing just the setpoint by 3F (no VAV controls change as it is impractical for reasons mentioned earlier).

However my sample size for 'on-field experience' is small (a couple of engineers), and there is at least half a dozen of research papers based on simulations I could find which give results as I mentioned earlier, which suggest a good potential in energy savings by increasing the cooling setpoint.

Has anyone actually implemented these retrofits (changing the cooling setpoints) in regular existing office buildings (20,000 sqft to 70,000 sqft)? If yes, which camp do you agree with?


texts: If the material is manufactured by 3D printing (laser sintering) then what will be change in its mechanical properties than the properties by casting and machined part? What would be appropriate failure criteria for it?


texts: Why does the frequency of a bottle filling up changes?

texts:
Today as I was filling up a bottle of water, and I could hear the distinctive change in pitch that signals that the bottle is near filling up, I started wondering what equation determines the frequency of the sound.
More specifically, I suspect this is fundamentally a problem in vibration dynamics. I suspect that there is some type of equation that changes the natural frequency of the cavity but I cannot put my finger on it.
Does someone know how to derive this equation? I suspect it will involve a lot more variables than the the natural frequency of the harmonic oscillator $\sqrt{\frac{k}{m}}$, or the pendulum frequency $\sqrt{\frac{g}{l}}$.
This is not for a project, just plain old curiosity, so I would be very happy for pointers to books or links.


texts: How To Deal With Hinges In Statically Indeterminate Structures?

texts: In a statically indeterminate structure, solving the beam using slope deflection method how to cater for the beams with hinges? How would i calculate the FEMS for such beam? Do i have to consider hinge as a Far End Pinned or else? Also If The load is applied directly on the hinge, then how to cater for such a scenario. I have an upcoming Exam and if someone can clear that doubt to me?


texts: Why aren't screens round instead of rectangular?

texts:
Screens on TVs and phones et cetera are always rectangular. Why? Why are they not round? Eyes are round. The Sun, the source of almost all of our light, is round. Telescopes have round lenses and mirrors. If a photon has a shape it would be round since it is described by sinus waves and interferometry. Sure, we have two eyes but that gives a 3D illusion of an oval rather than of a rectangular field of view.

In the corners of our unnatural rectangular computer screens' user interfaces, there are hidden stuff like the time of day and some abort/undo button. Stuff you don't want to see unless you actively search for it. Why have corners on a screen? Who came up with that idea? Cathode ray oscilloscopes were invented with circular displays, how did they acquire horns and corners?


texts: Not getting accurate readings from my multimeter

texts:
EDITED THIS POST FOR THE PEOPLE WHO PROVIDED ME WITH GREAT FEEDBACK

I have been building a few simple project circuits, mainly to analyze electronic theory.

The problem I'm having right now is that I'm using a cheap multi-meter from amazon that is giving me wild and inaccurate readings on DC current.

The case at hand is SIMPLE-CIRCUIT-A:

9V Battery(multimeter is only reading about 7.5 from across the terminals)
2x 200-ohm resistors in series, totaling for 400ohms
1 small piece of #22 wire
1 breadboard

If I listen to the mutimeters readings on the 9V battery as being only about 7.5V, then i should be pulling about 18.75mA at any point in the series circuit:

[![Circuit schematic and math][2]][2]

But this is what I'm actually getting:

Now you could say, "Maybe the battery really is applying 9V across the circuit.", that conclusion would give us a DC of 22.5mA, yet im getting at best a reading of 24.5mA, that's a 9% error margin!!!

Could there be an issue with my multimeter? On top of that, I can never get stable readings from the leads, is that common in all multimeters? Usually when I apply the leads to a component to read DC, the numbers will bounce all over the place.


texts: How to calculate principal moment of inertia of an unequal angle?

texts:
Is there a formula to calculate the moment of inertia of an unequal angle? I am not talking about x or y direction but the maximum and minimum moment of inertia about its rotated axes (usually labelled u and v) through its centroid.

I can get this using Massprop function in AutoCAD, but I would like to have a formula so that I can use it in excel.


texts:
I was reading through a research paper and they showed the following schematic:

I am not exactly sure what is meant by a 45 degree coupler so I looked online but there is no such thing as a 45 degree coupler. So I was wondering if a 45 degree coupler in this context is just a fibre optic cable that has been cut at a 45 degree angle?


texts: What's the history of the 345 kV voltage level in power transmission?

texts:
I'm interested in the history of the 345 kV power level for high voltage transmission in the United States. I've got two (and a half) questions:

According to this source 345 kV was first applied in 1953 by American Electric Power. Who has developed it and why have they chosen exactly this voltage? Because it is 3*115 kV and nearly 2*161 kV?
When you look on this power network map you will notice, that 345 kV is  still the most highest voltage for the transmission networks of the Midwest and Texas. Why does they still stick to 345 kV even for new-built power lines despite 500 kV would be much more economic (less losses at a similar right-of-way width)?

PS: I've thought that "Engineering" wouldn't be the right category for this question, but I was advised so at Meta.


texts: Using Integral gain for motor positioning

texts:
I'm struggling to see how Integral gain is used for motor positioning.

Suppose we have an AC motor (with a 2048PPR encoder on the shaft) connected to a winch which drives an object forwards and backwards. At 0 speed and 0 torque, there is no movement.

Now, using Proportional gain, we can drive the motor to a position and as it approaches the setpoint, the output to the motor decreases. The motor hopefully lands close to the setpoint.

If we use Integral gain, where the error accumulates, when we reach the setpoint the value of I is still high and the motor overshoots (even with very little ki). This wouldn't be a problem if the motor required a non-zero voltage to maintain its position (e.g. using the motor as a hoist).

The Integral may get very small, causing the motor to stop, but wouldn't it then rise up again after some time (depending on Ki), overshoot, and just oscillate around the setpoint infinitely?

A basic solution I've come up with is to use Integral gain to "push" the motor to its setpoint (effectively correcting the steady-state error), and when the motor is "close enough" to the setpoint, set the output to 0.

Is this a commonly used method? Are there any other approaches?


texts:
I am having a small 2.5cc methanol 2-stroke engine that I am building an electric starter mechanism for. From my research I was under the impression that for a 2-stroke engine like the one that I have which is completely mechanical using a port for fuel intake it should not matter what direction I am starting the engine, it will just continue to move in that direction.
Image of the engine:

In order to make sure my DC motor used to start the engine is not suddenly "powered" by the much faster methanol engine I am using a one way bearing on the gear connected to the methanol engine. When I did a test run I could hear the methanol engine engage (due to the noise), but it cut out practically immediately afterwards and I could see kinda heavy abrasion on the gear of the DC motor (it is 3d printed, not some metal gear). I am getting the feeling that the methanol engine starts but wants to turn into the opposite direction of how it got started and then dies out pretty quickly because of the resistance.
This goes contrary to my believe that these 2-stroke engines should be able to run in any direction. What are the parameters that influence this for an engine and how would I go about determining that direction except ruining my starter gear and do it empirically? How does this work with a pull start, i.e. how do they ensure that the motor never engages in the other direction?


texts: A clarifying question on Lasalle invariance principle

texts:
Given a nonlinear system \begin{equation}
\dot{x}=f(x),~x(0)=x_0 \tag{1}
\end{equation}
where $f\in{\mathcal{C}^{1}}:D\to\mathbb{R}^{n}$. The Lasalle invariance theorem statement goes as follows:
Let $\Omega\subset{D}$ be a compact set that is positively invariant with respect to (1). Let $V:D\to{\mathbb{R}}$ be a continuously differentiable function such that $\dot{V}(x)\leq{0}$ in $\Omega$. Let $E$ be the set of all points in $\Omega$ where $\dot{V}(x)=0$. Let $M$ be the largest invariant set in $E$. Then every solution starting in $\Omega$ approaches $M$ as $t\to\infty$.
Here $M$ is the largest invariant limit set (every invariant set is a subset of M) where $x(t)$ converges to at infinite time. My question is how is $M$ and $E$ different. Since $\dot{V}$ is zero at whole of $E$, then isn't $E$ itself the largest invariant set?


texts: Hinge or similar that breaks at a certain change in acceleration?

texts:
Suppose I have a rope that is capable of lifting 100 Kg without breaking. But I would like the rope to break if it is exposed to a sudden change in acceleration (jerk). So if the rope was lifting 10 Kg but was instantaneous exposed to 700 N impulse force, it must break. The numbers here are just examples.
[that edit should make the physics clearer]
So perhaps such ropes or similar exist? Or the rope could be divided in two with a hinge or something in between? Anything would work - just as long as it has these properties of breaking at some predefined change of acceleration...

Does something like this exist?

Thanks.


texts: Single shear bolt shear force and moment diagrams

texts:
I’m trying to determine what the shear and moment diagrams of a bolt in single shear look like. Before anyone says it, I know that it’s rare that a bolt will ever fail first in bending, and this is something that typically isn’t even checked for.
Anyway, I’ve assumed that the bolt is essentially a beam cantilevered at one end and guided at the other (guided end only allows vertical translation, no rotation). I’ve applied a distributed load acting downward over half the bolt length, and a distributed load acting upward over the other half. I found a website that uses these assumptions as well, and even provides a shear diagram (I’ve arrived at the same conclusion). Does the moment diagram I’ve drawn make sense?
Thanks!
Website (see figure 4.2.4)


texts:
I have a vertical load (F) acting at a distance from the edge of the cylinder. The load is acting on the cylinder via chunk of steel sliding across the surface of the roller. The coefficient of friction between the two objects is 0.25.

The shaft is fixed at both ends. The cylinder has seized and has become a part of the shaft.

I want to know the torque and the force at the yellow point.
You must state the variables you use.

I would also like an explanation of where the frictional force from the load is going.

Thanks!


texts: Reinforced concrete design: will there be extra nominal moment on column in a frame structure?

texts:
Say I have a simple reinforced concrete frame (3as shown below) with all beam ends pinned:

( the keyplan)

This is the detailing output:

The beam elevation detail ( left), beam cross section detail ( right)

Column cross section

I understand that due to the pins, all beam end moments will be 0. However, at the column joint, will there be any moment? I think no.

But one of my engineering friend think that because this is a reinforced concrete beam, and we design our beam reinforcement bars for the designed moment, this designed moment should somehow be transferred to column (even though the frame analysis shows that there is no moment at this beam joint), and thus the column joint will have moment.

In other words, the presence of reinforcement bars in the beam means that we need to design for moment in the column at the joint, as the reinforcement will create a moment in the column, even though in the analysis this "reinforcement induced" moment is simply not there ( and the analysis shows us that column moment at joint is a 0). Is this a common practice ( as stipulated by convention or demanded by code of practice), or is this something completely unheard of?

Could he possibly be right?


texts: Impact energy absorption with objects of varying geometry

texts:
Imagine two objects are being dropped from an arbitrary height. One object is prismatic, and the other object is spherical. Both are isotropic and made of the same material (perhaps even the same volume of material).

Force upon impact is a straightforward calculation for an arbitrary mass. This can be done by utilizing the energy imparted on the object through the complete transfer of potential to kinetic energy.

I'm interested in knowing how geometry affects the resulting distribution of forces, and how one can take this knowledge to better design objects braced for impact. Is this something that can be easily calculated by hand, or does it require a more thorough simulation (via ANSYS, et al) in practice?

Edit: My original post lacks assumptions & needs clarification.

I have no velocity or material in mind for the dropped objects.
Yes, by force distribution, I mean stress distribution. I would like to calculate resultant peak stresses from impact, then compare these values to various material yield strengths.
The objects fall on a flat surface.
The object can rebound and experiences elastic shock waves. Further, consider that the flat impact surface has infinite stiffness.
A "back of the envelope" estimate should suffice. This information is needed to better inform prototyping design.


texts:
So I understand that shear stress can be either in the the form of transverse or torsional or both at the same time.  And normal stress is due to the moment or a force normal to the surface. My question is why is it that sometimes when it asks for the max shear stress we use the $\tau_{max}= \sqrt{\left( \frac{\sigma}{2}\right)^2 + \tau^2}$ and sometimes we use $\tau_{max} = \tau_v + \tau_T$  to find the max shear stress?
Why sometimes do we consider the normal stress in calculating the max shear stress and sometimes we do not?
$\tau_{max}= \tau_v + \tau_T$" />


texts: An interpretation of the slope-deflection method (or displacement method)

texts:
I want to be sure that the way I like to think about the displacement method of analysis is correct.

Suppose that a beam as given by the figure below is to be solved.

Under this conditions, the only unknown is the rotation of joint $B$, $\alpha_B$.
As I see it, the steps taken to compute $\alpha_B$ are:

i) apply a moment $M_B^F$ at point $B$ of the beam such that no rotation of $B$ takes place. Such a moment is clockwise. Due to this, node $B$ is under the action of an equal and opposite moment of anticlockwise direction and, therefore, according to the standard conventions, of positive value $PL/8$, and, as such, not in equilibrium;

ii) for node B to be in equilibrium, as it effectively is in the original structure, apply at beam $B$ a moment whose value will depend on $\alpha$; Node $B$ will be subject to an equal and opposite moment $M(\alpha_B)$ such that $$M(\alpha_B)+ PL/8=0$$

Is this a correct interpretation of this method of analysis?


texts: How to find nodes of an undamped free-vibrating 2 DOF pitch and bounce system

texts:
I am working on a 2DOF non-forced pitch and bounce model for an engineering project.
I've found the values for my natural frequencies, and the initial conditions which make the system resonate in a certain mode.
I now want to find the system's nodes. Can nodes only exist if the system is resonating in a mode?
Or can I get nodes when the system's motion is composed of contributions from both modes?


texts:
I am using GRBL and UGS with an arduino uno and its CNC shield.

Once I send the $H command, the z motor is moving a little bit and then it goes crazy. I mean it's starts to hum and doesn't move anymore. After that, the machine is in ALARM state. ALARM:8.

Once I send $X command, the machine goes back to idle. So i am now able to use my cnc machine again. But why am I not able to set it to home position ?

config:

$0 = 10    (Step pulse time, microseconds)

$1 = 25    (Step idle delay, milliseconds)

$2 = 0    (Step pulse invert, mask)

$3 = 0    (Step direction invert, mask)

$4 = 0    (Invert step enable pin, boolean)

$5 = 0    (Invert limit pins, boolean)

$6 = 0    (Invert probe pin, boolean)

$10 = 1    (Status report options, mask)

$11 = 0.010    (Junction deviation, millimeters)

$12 = 0.002    (Arc tolerance, millimeters)

$13 = 0    (Report in inches, boolean)

$20 = 0    (Soft limits enable, boolean)

$21 = 1    (Hard limits enable, boolean)

$22 = 1    (Homing cycle enable, boolean)

$23 = 0    (Homing direction invert, mask)

$24 = 25.000    (Homing locate feed rate, mm/min)

$25 = 500.000    (Homing search seek rate, mm/min)

$26 = 250    (Homing switch debounce delay, milliseconds)

$27 = 1.000    (Homing switch pull-off distance, millimeters)

$30 = 1000    (Maximum spindle speed, RPM)

$31 = 0    (Minimum spindle speed, RPM)

$32 = 0    (Laser-mode enable, boolean)

$100 = 250.000    (X-axis travel resolution, step/mm)

$101 = 250.000    (Y-axis travel resolution, step/mm)

$102 = 250.000    (Z-axis travel resolution, step/mm)

$110 = 500.000    (X-axis maximum rate, mm/min)

$111 = 500.000    (Y-axis maximum rate, mm/min)

$112 = 500.000    (Z-axis maximum rate, mm/min)

$120 = 10.000    (X-axis acceleration, mm/sec^2)

$121 = 10.000    (Y-axis acceleration, mm/sec^2)

$122 = 10.000    (Z-axis acceleration, mm/sec^2)

$130 = 200.000    (X-axis maximum travel, millimeters)

$131 = 200.000    (Y-axis maximum travel, millimeters)

$132 = 200.000    (Z-axis maximum travel, millimeters)


texts: How to know what capacity of a compressor will suit the demand of machines in a plant?

texts: Suppose I have nine machines in total which require a continuous supply of air at 2.5-3 kg/cm2. So, can I get maximum safe working pressure of the compressor by working on the formula of circumferential and longitudinal stress for pressure vessels which requires parameters such as internal pressure, wall thickness and shell diameter. Secondly, how do I calculate the capacity and HP of compressor which would suit my requirement. Also, at some websites, the CFM(cubic feet per minute) is explained as mass of 1 cubic feet of air which a compressor breathes per minute. But isn't it volumetric flow rate ?


texts: What are the difference between open loop and closed hydraulic system?

texts: I'm trying to get informative resource material through this.


texts: What material can I use for a 5/8 inch keyboard lift that can be cut to fit under my keyboard?

texts:
For my birthday in February, my Partner got me an iMac.  (I specced it out to include what I thought was enough computing versus cost.)

We have a Physical Therapist who comes to our home and treats us.  She is also an Ergonomics expert.  I have the Mac on a desk, which has a keyboard tray / drawer, so that is good.

However, the keyboard sits about 5/8 inches too low on the desk, and I need something to raise it up.  (Currently, I am using a book that we found that just happened to meet the height requirement; Unfortunately, it doesn't meet the dimension requirements for this keyboard, which is the Apple Mac US English Keyboard with the Numeric Keypad.)

What I need is something that has just the slightest amount of 'give' to it, like rubber or something similar.  I would like to be able to contact whomever sells the material and order a piece cut to the dimensions I specify.

  For your reference, the dimensions are as follows:

Height:  5/8 inches
Depth:  4.5 inches
Width:  16 15/16 inches

I would appreciate very much if you could point me in the direction of a material that I might consider.


texts: On construction of a triangular interferometer like LISA

texts:
I am planning to do a project in which I plan to mimic the LISA interferometer. For this I use the fabric material, Lycra to mimic space time and use spherical balls, forming a couple and connected to a rotating shaft thus mimicking binary stars.

As the balls rotate, they would cause waves in the fabric. Further away from the binary system is the triangular interferometer, this system comprises of three discs, each having a laser and a sensor. When the laser in aligned with the second discs' sensor, and the laser of the second to the third's sensor and lastly the third's laser to the primary's sensor, the three form a equilateral triangular system.

The three discs would be placed on individual corks and each disc would be connected to a vertical shaft with a shock absorber( so that the disc can oscillate about its mean position when the spherical balls start to spin and thus produce ripples). The three shafts are connected and hence form a system where the individual components can oscillate about their mean position when ever a disturbance is caused in its surrounding fabric. When the individual components oscillate, the alignment of the lasers would change. I need this system to be sensitive to minute translational displacements, so that when the ripples hit the system, the contraction and expansion of relative lengths between the lasers can be measured by some device connected to this system.

  Below is an actual representation of LISA:

My question is regarding the position instruments I am to use/make, what sort of instruments and/or devices would be able to detect the minute changes in the position of the interferometers and measure the curvature of the wave when the wave propagates in the elastic medium?
Any help is appreciated.


texts: What's the second moment of a T beam with a heel?

texts:
The second moment of area of a rectangle is $I_{yy} = \dfrac{bh^2}{12}$

b : base
h : height

What is the second moment of area of a T beam like this one?


texts: (de facto) Standards for freehand technical lettering?

texts:
What de facto standards or otherwise exist that prescribe a style for freehand technical lettering?

With the ubiquity of CAD there is probably a diminished need for standardized handwriting.  Technical lettering was not part of my undergraduate engineering training yet was frequently mentioned and occasionally required by professors.  When "required"- the criteria presented were few; simply capital case, sufficiently 'black', and ruled (drawn on/between lines).  I am aware that true or traditional technical lettering has much greater complexity such as prescribing the order of strokes for drawing characters and their proportion.

I personally have sought to apply block lettering for readability and general aesthetic in handwritten drafts, but for lack of formal training apply personal habits of using dashed '7's and Z's and serif'ed 'I's- all of which I suspect are faux pas.  Nonetheless I'm curious as to where to look for historical consensus to develop my drafting.


texts: What does the torque curve of an engine mean?

texts:
I have been trying to understand the torque curve and power curve of an engine. From what I have read and understood I know that the torque curve and power curve is has a peak at a particular RPMs(RPM is different for torque curve and power curve). I also understand that when the engine is running at a particular RPM it will be producing a particular torque(drive torque) and if we increase the load on the engine(increase the load torque) then the RPM will start to decrease. To keep the RPM from decreasing, we can open up the throttle( which will increase the fuel burnt and so the energy produced at the power stroke) and so, increase the drive torque being produced to match the increased load torque.

What I am not able to understand is if the torque value at a particular RPM shown in the torque curve is the maximum possible torque at that RPM (i.e throttle valve fully open at that RPM) or if that torque curve is given for a particular external load(i.e we can still increase the load and to keep the RPM constant we can still open up the throttle valve). I am guessing that the curve shows the maximum possible torque at a particular RPM but I am not sure.


texts: Simulating linear momentum/KE through angular momentum/KE

texts:
I have undertaken a project where I need to design a brake system for a miniature locomotive. To test the effective of the brakes I have decided to create a rig where the brake system is attached to a flywheel which is spun to a certain angular speed in order to simulate the momentum of the locomotive as if it was on a track. I don't have a track available which is why I am doing this.

The mass of the locomotive is 800KG and assumed to be travelling at a const velocity of 4.2 m/s therefore will possess a linear momentum of 3,360 kg.m/s and a linear kinetic energy of 7065J.

I would like to simulate this momentum in the form of a flywheel, in order to determine its dimensions I need to know how much angular momentum the flywheel needs.

I am not sure how I can correctly mathematically/physically be able to "convert" linear momentum into angular momentum. I know that these two quantities are independent which is why I am asking this question.

Where I have ended up so far:

The energy in an object has two components: linear K.E. (El) and rotation K.E.(Er) Et = El + Er

El = 0.5*m*(v^2) , Er = 0.5*I*w^2, Et = total energy where, 'v' is linear velocity, 'w' is angular speed and 'I' is moment if inertia.

If I assume the locomotive only has linear component: 7065J and I assume that the flywheel only has rotation component - can I assume it to have 7065J of energy.

I question myself whether a linear joule is the same as rotational joule.

Any comment is helpful - i can work on from a hint


texts:
I am currently trying to design a rear gate to retrofit to an existing caged trailer (similar to image 3), with the goal of having a system where the rear gate can pivot down (on its bottom edge) to form a ramp, or from either side so that it can swing out of the way to the side.

Currently I have the following design mocked up (not to scale): images 1 & 2. In these images, parts are coloured as below:

Black: Existing trailer body
Grey: Hinges with removable locking pins, as seen in image 4. Horizontal pins would have some kind of extra or spring loaded locking to avoid loss during vibration. This part should be straightforward.
Blue/light blue: Ramp and attachment points
Yellow: Gas strut/damper or hydraulic ram (this is where the issue arises).

The current issues I am facing at this point:
 - How can I attach and detatch the strut from the bottom of the rear gate to allow the gate to swing open sideways, while reducing the risk of sudden release? I am thinking of some kind of mechanism where the strut slots in to the rear gate section.

The strut appears necessary as a method to dampen the rear gate movement, as it will likely have significant weight.

My end objective here is to be able to have the rear gate function as a ramp for loads up to approximately 500kg, as well as being able to swing out of the way for loads that are simply pushed off the back of the tray (e.g. gravel, rubbish dump runs).

Ground clearance ideally should not be reduced (below axle level), and a dependence on electricity should also be avoided.

So, my question is, how can I safely and efficiently detatch this strut to swing the gate open sideways with the above design, or should I consider an alternative design to achieve this?


texts: I am currently using a AI-6061-T6 plate measuring 750mmx370mmx6mm as a rack between two frames at about 3/4 meter above ground. The load on the plate would be about 8-12kg. How much load will be able to take before bending? And how would the plate react underwater at a depth of 3-4m? Please help.


texts:
I am a beginner in ProE and simulation. I would like to apply force in ProE simulation like below picture.

Could anyone explain how to put the payload on a remote point?


texts: In aluminum machining, what are the most common factors that might cause a machined component to have warping issues?

texts:
I am currently having an issue where features of my machined parts are warping. I am using Alloy 7050 Type I and Type III in this particular case. Using a feeler gauge and a certified, calibrated granite slab, I am getting out-of-flatness measurements up to .009, which is significantly out of tolerance relative to my requirements.

I have decided to construct a statistically-designed experiment (design of experiments) to find which specific factors are playing a role, but I want to ensure that I am including all of the factors which may contribute.  I don't want to lead the conversation too much by posting what I already listed, but I am looking for others' opinions on what might cause this kind of warping/deflection.


texts: Finding stability of open loop system connected to closed loop system

texts:
I have a simple cruise control closed-loop system with negative feedback and have no problem using the Nyquist stability criterion to find its stability. However, I have another function that describes the fuel consumption of the throttle in the closed loop. There is no feedback from the fuel consumption to the throttle or the speed.

In other words, I have an additional transfer function outside the loop from the plant to the fuel consumption and want to assess the stability of the fuel consumption.

Since the fuel consumption is just a function of the throttle which is inside the feedback loop, am I guaranteed stability if the closed loop system is stable?
Is it possible for the fuel consumption function to essentially add a gain that makes the consumption unstable even if the speed control is stable?
Should I treat the fuel consumption as a purely open loop problem from the throttle to the fuel?

Thank you


texts:
Does anyone know the required strength of the mounting points of a car seat? I'm working on a new sliding mechanism and don't want to damage the integrity of the seat mounting. "Child seats" have rather poisoned the search results for this.

No points for "don't do it" or "buy one in" - what I'm building simply isn't available - a 2-3' track extension into the rear of the vehicle. The extension is only while the vehicle is stationary so it's really down to the material which will probably be a little weaker than the thick, folded steel of the regular runners. I'm just looking for a baseline I can work from.

Mike.


texts: Will AC Motor Maintain Speed of Descending Object

texts: Suppose we have an AC motor which needs to lower an object at a set speed. We use a PID loop to determine and correct positional errors. Presumably the PID loop will keep the current low as most of the work will be done by gravity. By lowering or stopping the current, will the motor be able to maintain the set speed, or will gravity take over and descend the object at its own will?


texts: Find transfer function from bode diagram?

texts:
I've been given this bode diagram :

I've been asked to find the transfer function only by using the bode diagram.
It's the first time I'm doing this so here's what I thought.

The starting value is zero so the multiplying constant of the the transfer function has to be 1 and it is positive since the phase diagram starts from 0 degrees( it would start from 180 had it been negative)

From the fact that the starting degrees are 0 we derive that we have no pole or zero that is at the origin.

Also, the final degrees are -270 and the dBs are decreasing so I must have 3 poles.Am I correct?
Also ,I know that I can look at the curve , the dBs per decade at any point to see how many poles or zeros are acting. I can't get a good estimation though.It seems like it's 10 dBs per decade until the frequency reaches 10 rad/sec while I know it has to be a factor of 20 dBs. 60 dBs per dec mean 3 poles/zeros,40 dBs per dec mean 2 etc.

How do I know where the poles are if I can't tell where the angle of the curve changes? Is it clear and I can't see it?

By the way, I've been given the answer to check if I do it right in the end and it's as follows: $$ G=\frac{500}{s^3+20s^2+200s+500} $$ Also p =

-8.2390 + 8.6072i,
  -8.2390 - 8.6072i,
  -3.5220 + 0.0000i


texts: By what factor should I scale some tapered legs to make my harpsichord stable?

texts:
Not sure how to ask a question usefully, as I'm not an engineer, but here goes. I have a harpsichord, essentially a sort of triangular slab (I'm assuming a general answer, though I could provide specifics) for which I've turned 3 tapered legs, each set in some distance from the edges, and attached securely with 4 screws. But the instrument wobbles extremely easily: if you push it on a side with one finger it's easy to move it half an inch or more. So I'd like it to be "stable" instead of wobbly. Each leg is 2.75" square at the top and at the bottom is a circle with diameter .675". Here's an early version of the leg (its final dimensions are slightly different), but very close to the present version:

Here are the legs in context:

My question: By what factor do I need to scale the thickness of the present legs (height is constant) to make the instrument "stable?" I'm not sure how to define stable, but the point is, it should only wobble with "significant" effort, not minimal, one-fingered effort. I'm pretty sure that if the thickness was increased by a factor of 10 it wouldn't wobble easily, as it would be resting on tree trunks, practically. But what's a reasonable number? 1.5, 1.7, 2.3? I have no idea, but I'd be grateful for your suggestions.

Edit in response to the answer: I'd like to avoid redesigning with bracing. And I've already made a large plate, which is the bottom of the instrument. Assuming a rigid connection with the legs, wouldn't increasing the thickness improve stability?


texts: Control the rotation of multiple discs along the same axis

texts:
I have an engineering background, I'm an EE, but I know almost nothing about mechanics and that's why I'm writing here.

This is the challenge: how to control the rotation of multiple discs along the same axis? Assume you have a sliced cylinder. The ideal scenario would be to control every slice independently, but to make things easier I think it helps to consider that you can move them in a fixed number of combinations and on the same direction (e.g. a mechanism that enables to rotate the top and bottom cylinders at the same time and same direction - combination #1 - and the inner ones in the same way - combination #2 - but not as the same time as #1).

Any idea on how to accomplish this?

I though I could use something like a "key" along the axis/shaft/rod. By moving it up/down it would lock different discs/slices. Not sure if this is a good idea. One issue I can see with this one, is that the slices that weren't locked by the "key" could be rotating freely and I want them to be steady.


texts: How to prevent ice build up in a refrigerator?

texts:
There is ice build in my Samsung RF266 refrigerator. I have posted the following questions in Home Improvement Stack Exchange hoping to find a solution. The questions are as follows:

Samsung RF266 refrigerator not cooling - Fan making noise
Ice buildup inside Samsung RF266 refrigerator

Bel
below is an image of the ice build up

I believe the purpose of the fan is to circulated the cold air and coils are what generates the cold air. I don't believe the ice build up is normal.

Question: From an engineering standpoint, how is this suppose to work? What would cause the ice build up? What design feature are present in a refrigerator to prevent ice buildup?


texts:
What is the fundamental difference between the flute geometry of an end mill as opposed to a drill bit?
Obviously drill bits are not intended to cut horizontally so what difference about them makes them unable to do this efficiently?
Also, since end mills can cut vertically, why not just manufacture drill bits with the same flute geometry as end mills?


texts: Reloading Press Powder Dispenser Pressure

texts:
Yesterday my Lee powder dispenser to my reloading press popped off gunpowder everywhere
I had removed the top part of the container off and placed it back on, there is a "on" / "off" mechanism in the product design. I'm fairly confident the reservoir was tightly secured.
Is pressure able to be built in a plastic container? Has this happened to anyone else? Are there best practices to prevent gunpowder spills.


texts: What is a formula to approximate the change in relative humidity cause by a change in temp?

texts:
The moisture-carrying ability of air goes up as the temperature rises. So if I take a volume of air and heat it or cool it (allowing it to expand/contract so the pressure remains constant) how can I calculate the (approximate) relative humidity of the warmer/cooler air that contains the same amount of water vapor?

Say I blow 30°c air at 20% relative humidity over a cool object (but not cool enough to condense water out of the air.) The air is cooled to 20°. What would the relative humidity of the cooled air be if it contained the same amount of water vapor? How do I calculate that?

I am building an Arduino-based control for a warm air dryer for ski boots and bike gear. I will measure the temperature/humidity of the heated air as it comes out of the dryer, and then measure it again as it escapes the gear that I am drying. While the gear is still damp, the waste air should pick up additional moisture, and so its relative humidity should be higher that it would be if I simply cooled it down. When my gear is completely dry, the cooler waste air should contain the same amount of water vapor that it started with, so the relative humidity should be the amount calculated for the measured change in temperature.

I want a "good enough" solution, not one that's mathematically pure. If it gets me answers that are within a percent but involves less computation, that's better than an ideal solution that involves lots of time-consuming calculations. The Arduino microcontroller is fairly slow and cannot do high speed/high precision floating point calculations.

(Would this question be better on an engineering forum? I could see arguments either way.)


texts:
I have a set of little flywheels that have a magnet to break the motion of the system. I have one aluminum and several copper ones all water jet cut roughly to size. The copper and aluminum disks I have are all the same dimensions but bought from three different sources.
Yesterday I machined the Aluminum disc and three of the copper discs to the correct specs on the lathe.

I checked the amount of drag caused by these discs some time ago and found the copper was far more effective than the aluminum. Today I needed to check the operating distance of the magnet so repeated this test on the newly machined parts and was shocked to find the three copper discs provided so little drag it bearly registered. The aluminum and the other copper ones worked very well. The drag the magnet courses on the other copper wheels is considerable so the difference is huge, one copper disc brings the whole system to a halt immediately but with the other discs I machined yesterday I can barely feel any drag at all, at first I was unsure there was any until I spun it up faster then I could just about feel some slight resistance.

I thought the strength of the eddy currents produced was dictated by the conductivity of the metal used so I am now confused as to what happened here. As I said before the copper discs are from three different sources so maybe different coppers. Does anyone know what has gone wrong and if it's the copper which coppers are best for use in this job?


texts:
I need to have some beams fabricated with copes on the ends.   They will be set on top of existing steel trusses, and used to replace undersized purlins to shore up existing rafters (hence the need for the copes).

My structural engineer specified 4" long copes.  There is a cope at each end.  The distance between the edge of the flanges on the steel trusses is 186".

The question is a matter of practicality.  If I have the fabricator make the coped length of the beam exactly 186", I feel like I may have a difficult time getting the beams in place.   So I'd like to have a little tolerance to give me room to slide the beam above one truss and then pivot it into place above the other.

How much tolerance should I allow for to make this easy on myself, the installer of the beam, without diminishing the integrity of the design?  In the CAD drawing below, I have just arbitrarily chose to show that the coped end-to-coped end distance should give me 1/4" of play on each end of the beam.

I don't want to overthink this, but these suckers are heavy and installing them is going to be fun enough without having to fight tolerance problems.

Is there a tolerance rule of thumb for this situation?   What tolerance would you use?


texts: How do I calculate rolling resistance for tire on pavement?

texts:
First condition assuming perfect rolling, no slip, from what I understand is that the rolling resistance coefficient can be calculated as the displacement arm of the normal force the tire "feels", in which should be equal to the force about its center times the radius of the tire (essentially equating two moments?)

I am attempting to do a finite element analysis on a tire, solving for rolling resistance for the tire.

My approach is to take the sum of the shear in the contact patch, multiply it by contact area to result in total tractive force (Fundamentals of Vehicle Dynamics). If this force is then subtracted by static friction, shouldn't this result in total rolling resistance force?

Not sure if my conceptual understanding is correct.

What are industrial ways of getting rolling resistance of tires?


texts:
Say I have a ring with the center of mass G. Also I rotate the ring around a point P on the ring, and I have a "anything" moving along the ring at the same time with velocity v.

How would one explain the motion of the "anything"? Would one say that it's absolute velocity is the velocity of G + the relative velocity (velocity measured from P) + the rotational velocity of the entire system? Or is some of these terms zero?

Thank you.


texts:
I need to settle a discussion on the following question:

Part A:

Find the equivalent spring constant for springs in series
Use equations of motion, sum of torques to find natural frequency of the system

where:

$$\begin{gather}
\dfrac{1}{k_{eq}} = \dfrac{1}{k_1} + \dfrac{1}{k_2} + \dfrac{1}{k_3} \\
I_p\ddot\Theta = -(k_{eq} + k_4 + k_5 r^2 + k_6 r^2)\Theta
\end{gather}$$

Part B:

System in torsion therefore:

$$w_{nf}=\sqrt{\dfrac{k}{J}}$$

where:

$$J = \dfrac{mr^2}{2}$$

Issues

Solutions from my lecturer suggest adding the three strings in series and not using an equivalent

$$w_{nf}^2=\dfrac{k_1 + k_2 + k_3 + k_4 + k_5 r^2 + k_6 r^2}{J}$$

I believe you have to use the following, taking in to account the equivalent spring constant for the springs in series:

$$w_{nf}^2 = \dfrac{k_eq{} + k_4 + k_5 r^2 + k_6 r^2}{J}$$

Could someone please clarify whether the use of K123 being the equivalent is the right method. All literature suggests equating spring constants in series yet my lecturer appears to think differently.


texts: Explanation of network interdiction in layman terms

texts:
I am trying to understand network interdiction. I have read these papers, but it is still hard to get a clear understanding of what it exactly means:

Blind Network Interdiction Strategies - A Learning Approach
Network interdiction – models, applications, unexplored directions

Could someone explain it to me in layman's terms, using minimal technical language?


texts: GIM Mechanism Software (Kinematics / Analysis / Synthesis)

texts:
I've recently discovered a very awesome software tool for the synthesis and analysis of mechanisms.  The tool is called GIM, from Faculty of Engineering in Bilbao, Department of Mechanical Engineering, University of the Basque Country (UPV/EHU)  "The software is intended for educational purposes, in particular destined to the field of kinematic analysis, motion simulation and synthesis of planar mechanisms" as well as for the "static analysis of mechanical structures."  I'm doing some personal dynamic art work with six bar linkages (not for profit) so I think I'm okay here.

Link to download GIM software
Four Bar Tutorial Video
Synthesis Sample Video

I will say the interface wasn't totally intuitive.. after a few minutes in the users guide I was able to figure out the double click thing.  (Duh!  Read the messages on the bottom bar.)

I do have one issue that is driving me crazy.  I'm actually trying to easily compare different design alternatives. I'd just like to display coupler point output path, but I can't figure out how to do that.

Has anybody else used this tool?  Anybody know the secret to just showing a single output path?

Oh, and yes I'm aware of the www.saltire.com software and that would work for displaying output in a nice format, but I won't have the synthesis and full analysis tools available.


texts: How to generate a NACA 6-Series Airfoil analytically?

texts:
I asked this question over at Aviation.stackexchange but after that I figured it might be better to place it here. Especially since there were really good answers on the NACA 5-digit-Series airfoil generation.

I would like to calculate the profile NACA 64-2A015.
With the help of Aviation.stackexchange I learned that the A-Version of the profile was created to ease manufacturing by thickening the trailing edge-section (by a straight contour from 80% chord backwards).

However, I am struggling to plot the profile based on the equations given here and here.

The implementation in MATLAB looks like this:
Here is the Matlab code I used:

a = 0.4;
b = 1.0; % caution for NON-unity entries change the equation for h
% c = 1; to simplifiy the equation the chord is set to 1

cl = 1;

g = -1/(b-a) * (a^2 * (1/2  * log(a) -1/4) - b^2 * (1/2 * log(b) -1/4)); % g  = -1/(1-a) * (a^2 * (1/2 * log(a) -1/4) + 1/4)
h = 1/(1-a) * (1/2*(1-a)^2 * log(1-a) -1/4*(1-a)^2)+g; % simplified version for b = 1: h =  1/(b-a) * (1/2*(1-a)^2 * log(1-a) - 1/2 * (1-b)^2 * log(1-b) + 1/4*(1-b)^2 - 1/4*(1-a)^2) + g

x = (0:0.001:1);
y  = cl/(2*pi*(a+b)) * ( 1/(b-a) .* (1/2 * (a-x).^2 .* log(abs(a-x)) - 1/2 .* (b-x).^2 .* log(abs(b-x)) + 1/4 .* (b-x).^2 - 1/4 .* (a-x).^2) - x.*log(x) + g - h.*x); % y = cl/(2*pi*(a+1)) * ( 1/(1-a) .* (1/2 * (a-x).^2 .* log(abs(a-x)) - 1/2 .* (1-x).^2 .* log(abs(1-x)) + 1/4 .* (1-x).^2 + 1/4 .* (a-x).^2) - x.*log(x) + g - h.*x);

L6j01_x = [0, 0.005, 0.0075, 0.0125, 0.025, 0.05, 0.075, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1];
L6j01_y = [0, 0.01193, 0.01436, 0.01815, 0.02508, 0.03477, 0.04202, 0.04799, 0.05732, 0.06423, 0.06926, 0.0727, 0.07463, 0.07487, 0.07313, 0.06978, 0.06517, 0.05956, 0.05311, 0.046, 0.03847, 0.03084, 0.02321, 0.01558, 0.00795, 0.00032];

plot(x,y), axis equal, hold on
plot(L6j01_x, L6j01_y,'ro'), hold off

But the results do not match the data points from the Nasa-Reports
.

What did I miss to implement in the equation or is there another representation of the airfoil (excluding leading and trailing edge radius)?


texts: In the Panama Canal, how are the lock gates kept water-tight (at the hinges, middle, and bottom)?

texts:
The Panama Canal has these huge gates. They close so the locks can be flooded or drained.

They're swing gates, so 3 questions come to mind:

How are they water-tight at the hinges?
How are they water-right at the middle, where the two gates meet?
How are they water-tight at the bottom, where the gate drags across the floor?

Edit: Okay, they don't need to be perfectly water-tight. We can call them "decently sealed".


texts:
I have a trajectory which is a function of time that returns tuples of position, velocity, acceleration and jerk for each moment. So at every control loop iteration I would like the motion of my actuator to match these values. However it is not clear how to build a control system which will be able to follow position, velocity, acceleration and jerk commands altogether.

The actual question is that of control system input. In the vast majority of cases input is just a force which in context of PWM is just a number. Therefore natural question arises: should I anyhow map my 4 trajectory parameters to this one input of control system(if yes then how?) or is there any other way?


texts: How was Volkswagen able to trick the lab pollution test?

texts:
The recent Volkswagen pollution test cheating scandal has shocked many people with its widespread extent as well as how it was hidden for so many years.

  Last year, the International Council on Clean Transportation (ICCT) in
  Washington DC contracted scientists from the Center for Alternative
  Fuels Engines and Emissions at West Virginia University in Morgantown
  to test emissions from three light-duty diesel vehicles under
  more-realistic conditions than are possible in the lab. To do so, the
  scientists fitted cars with a portable emissions measurement system to
  gather a continuous stream of data over a variety of US road types.

  The tests found that the levels of NOx emitted by a Volkswagen Jetta
  were 15–35 times greater than dictated by the US standard (31
  milligrams per kilometre), depending on road and driving conditions.

How was this cheating program carried out, and why were the lab tests unable to detect the presence of this cheating program?


texts: Using two motors and belt drives to drive one shaft

texts:
I have an application where I need two motors to drive one shaft via the use of belt drives but I need help on how to arrange such a system. The system constraints are:

motor type - induction motors $(48\ \textrm{V}, 750\ \textrm{W})$
both motors will have pulleys of same dimensions
both motors will drive single o/p shaft with bigger pulley attached to it

Please see the image of my current work, and please let me know if with this arrangement I can have more output speed and torque. If you have any other ideas, please let me know.