Easy Reading: Fortunately, the Milk

TGIF! What a nice day it was to go down to the local library and get some easy reading material. I heard about Fortunately, the Milk from Neil Gaiman's Tumblr (Nice marketing, Mr. Gaiman!), and had wanted to get my hands on one ever since its publication last month. Imagine my excitement when I found out that the library already have several copies and I can place a hold for one (They circulate fast and were all checked out.). Now imagine what it's like to finally get a message after a week's waiting:

The following item(s) you requested are being held for you:
Gaiman, Neil.
Fortunately, the milk /
The item will be held until: 11/04/2013

It was heavenly! Skipping down the streets with my headphone on, I couldn't be sure if the silly grin was due to the giddiness of knowing what I was about to pick up or the cheerful audio book playing on my headphones (The book was Chitty Chitty Bang Bang narrated by David Tennant.) was simply too much fun.

With all these excitement, I finished the book in no time. And I am happy to say, it absolutely lived up to my expectations. The story was most curious. 10 years ago I would find it fantastic. Now, nearly an adult, I find it cute and silly. I nearly forgot how good it is to read adventure stories without having to feel anxious about the characters. Another great element of children's books are the illustrations. How I adore them! People with curly fingers, animals standing on their hind legs, strange creatures with big eyes.... Fortunately, the Milk has become one of my all time favorite children's books. It is something I would love to share with my younger cousins and probably read to them when I have the chance.

Review: Flappers and Philosophers

Romance rarely top my list of enjoyable stories. Recall seeing lovebirds engage in passionate kisses with hands over the place at public places and make everyone present uncomfortable? The show off cannot compare to the sight of the couples holding hands with shyness and a hint of a smile lingering on both sweet faces. Love stories can be like that: Showy but unconvincing or subtle and sweet. When two people fell in love in a story, it should be believable. Let readers feel the love! The audience should not be merely the spectator. They should be engaged in a relationship.

What I love most about Fitzgerald's love stories is their realness. The characters can do incredibly romantic things or be madly in love with one another, with good reason. There are ups and downs in the relationship - just like in real life! His characters have very distinctive personality. Some are proud, some strong, some shy, some bold. They might not be perfect, but they feel like real human beings. One would worry about them when they made the wrong judgement and cheer them on when they did the right thing. They are people we can relate to, be it pain or joy. We see ourselves in their shoes.

Overall I find Flappers and Philosophers a fun and charming. It is a collection of very different types of romance. I read the book on my kindle. Having no knowledge of the construction of the book and no physical volume as hint. I did not expect The Offshore Pirate, my favorite story in the collection, to end where it did. The result was a wonderful surprise at the plot twist I would otherwise have guessed. (I have long since learned not to read book descriptions just to leave myself at the mercy of surprise.) It was a romantic journey as impacting as first love.

Review: Casino Royale (A James Bond Novel)

Casino Royale is the first James Bond novel by Ian Fleming. Instead of boring and tedious background stories, readers get to learn about the mysterious spy the way one would when making new acquaintances: We judge him by his actions and beliefs. The outcome was not bad. Even with a negative view, James Bond's emotions were easy to connect with. One can almost feel sentimental about his situations. To conclude, the book is believable and invites the reader to experience the thrill without the danger.

Gathering from the discussions and glimpses of the movies, the double 0 agent has always seemed, to me, to be a the cold-blooded machine that never make mistakes on a mission and his seductive qualities merely material supplied for the purpose of spicing up the plot to suit the taste of audiences. For years, I have refused to read the story believing in, and disgusted by, the amount of male chauvinism involved. But I was surprised to find that, the book is actually action packed with a storyline filled with glorious peaks as well as bitter pitfalls. James Bond is a believable character with many talents. He may misjudge a dire situation, and expresses fear in the face of danger. He is not a superhuman hero but a man good at his job. Although he does hold somewhat offensive views of women, his line of thinking is understandable. Mercifully, the romance never got in the way of the plot, as I had previously assumed it would. Instead, it gives much insight to the making of the man living a dangerous and lonely life. He is far from heartless, although he has a touch too much of manly pride (from my prideful point of view of a lady).

This is the first Bond novel I've read. As popular as the various movie adaptations are, I have watched few and understood less. Spy stories used to be too political and complicated for me. I am thankful that, without plot spoilers from the movies, my experience with this book is completely fresh and exciting.

Review: Endymion

Endymion is a poem by John Keats. It is based on the Greek mythology of Endymion, the shepherd beloved by the moon goddess Selene. The poem is divided into four books. It starts with beautiful descriptions of the woods and the merry gathering of shepherds in honor of Pen. However, readers will soon learn that Endymion heeded nothing, being terribly lovesick after his encounter with the moon goddess. He set out in search of his loved one. The journey and adventures he undertook was described in colorful details. The hero's dreams and his fantastical encounters were hard to distinguish, one as wondrous as the other. As readers follow Endymion's footsteps, they will be kept curious of what the next page brings. Be it sorrow, joy, wonder, or pain?

Sidenote: As one unfamiliar with poetry, reading Endymion has been quite a challenge. Reading out loud helped me stay focus on the meaning of each sentence (which usually takes several lines). It was a tremendous joy to listen to the words rolling off the tongue. I strongly recommend readers to try.

Review: To Kill A Mockingbird

There is profound clarity when serious issues are viewed from a child's innocent eye. Without prejudiced ideas about rank and race in a society they make judgements solely on the happenings of an event. Although Scout often asked her father, Atticus Finch, about the happenings around her, she was far from an ignorant child. She was most often puzzled by the folly of the ways of the grownups. Children understands much more than grownups often assumes, as was pointed out constantly throughout the story.

To Kill A Mockingbird is a book ahead of its time. Even when viewed in the 21st century, where humankind has advanced so much since the 1930s, the story can still call its readers to reflect upon the issues of bully, racism, and government. Interestingly, to readers of different ages, the effect it have would be as different as the land and the sea. It preaches about morality, how to face assaults, and how to stand in other people's shoes;

"The one thing that doesn't abide by majority rule is a person's conscience."

It captured the horror of racism and yet does not despair in the state of events; It is a story about how there are people that uses what power they can to change the things that were wrong;

"Simply because we were licked a hundred years before we started is no reason for us not to try to win."

It tells of successful parenting (Even though Atticus Finch had been continuously accused of letting his children "run wild," readers will not object to his being a real moral model); It allows us a peek of the life in a Southern town in the 30s; It is a story of how normal people are heroes many different ways.

As a first time reader, and knowing nothing in advance about the plot, the story line caught me by surprise. What started out as an innocent looking, child narrated, summertime events in a quiet little Southern town, turned into a thought provoking roller coaster ride. I regret not having read it in my teens. Because of the many layers contained, this book is worth rereading every ten years. With every new built experience one will view the story at a new level, yet be constantly reminded of how to be a human being.

Review: Of Mice and Men (spoilers)

Of Mice and Men is a novella[1] written by John Steinbeck. Overtime there has been many adaptations to the famous story. I learned about the story from the radio play by BBC 4. It has left me feeling extremely emotional. Never suspecting the sad nature of the story I treated it as a bedtime story. The result was many heartbroken, cold sleepless minutes under the bed covers and later uneasy dreams. It left me feeling so broken that, even though the story fascinated me to the point that I wish to read the original, I will not be doing that anytime soon. Feelings need time to heal.

The main characters were George Milton and Lennie Small. The topic revolves largely on their strong friendship throughout the story. Lennie was a large and physically strong being, but his mental disability made him fragile and unable to take care of himself. Despite his appearances, Lennie was kind-hearted and always attracted to soft things. From the very beginning we learned that he had been with George for a long time and George has always took care of him. They were fleeing from a ranch they worked at previously because of misunderstandings caused by Lennie's love of soft things. On the way to find a new workplace, Lennie urged George to talk about their shared dream to one day save enough money to buy a piece of land and live their own happy lives. It was very sweet except their dream was already overshadowed by the dangers caused by Lennie's strength.

The play vividly introduces its audiences to the various characters George and Lennie met on the new ranch. Everyone had a story to tell; Everyone was lonely for one reason or another; And everyone dealt with their discontent differently. Some get together and took care of each other, others used bad means to satisfy themselves, still others took their rage out on everyone else. Unfortunately for Lennie, he became the victim of unfortunate times.

The tragic ending was not the reason the story utterly broke my heart. It was the cruelty of having had my hope risen up by the possibility that George and Lennie's dream were so close to realization, only to be plunged into deep sea when the fatal accident happened. But that was not the end of it. Naively, I hold on to the hope that George will find Lennie (Of course he did.) and together they will fled into the night once again. Alas, I did not understand that there was no running away again. I realized too late that George had to do what he did to save Lennie from a cruel and painful death. When George instructed Lennie to look away I did I understood with horror what he was doing, and I screamed internally: "Please don't do it... Please don't do it...." The sound of gunshot was far more painful than it should be to my mind. The only comfort to the audience was knowing that Lennie had probably died painlessly and escaped gruesome treatment and Lennie at least had another friend who understands him to keep him company.

Having finished the story, the most puzzling thing remaining is the title of the story. It was meaningless until I did some research on Wikipedia[2]. It was taken from a poem by Robert Burn:

The lest laid schemes o' mice and men
Gang aft agley. (often go awry)

All the plans George made all came to naught when the accident happened. What could he do when even the best laid plans can go wrong?

Math Tool: A Java Program

This page (copyrighted by John Polking) is a wonderful resource for studying differential equations. There are two programs: One for graphing the direction field of first-order differential equations in the form: x' = f(t,x); One for graphing the phase portrait for system of differential equations of the for dx/dt = f(x,y), dy/dt = g(x,y). Below are some screenshots of what the program looks like:

Control window for phase plane graphing.

The result window.

Another result.

I find these programs very helpful not to mention IMMENSELY fun to play around with. As a bonus, they had the Matlab versions on their page too!

Centroid of a Linkage (Part I)

Point I in Figure 1 is an instantaneous centroid of the four-bar linkage. The centroid of a linkage is important in mechanical design because when the mechanism is subjected to a combined force that passes through the centroid, it will act like a rigid structure. That is, the system will not deform.

Figure 1

In a design related course, the class was asked to find both the fixed (space) centroid and the body (moving) centroid of a mechanical structure. The fixed centroid is the locus of the instantaneous centroid of the structure at different geometry configurations. The body centroid, on the other hand, is the position of the fixed centroid when viewed from the joint of the stricture (in the case of the four-bar linkage shown in Figure 1, the body centroid is viewed from points (e, f) or (g, h)).

Figure 2

The meaning of this definition will be apparent as we explore more on the subject in Part II. First, we will get familiar of the subject by an example of what the centroid locus look like when drawn in the same picture. Figure 2 is an example of the centroid calculated for the particular linkage. The body centroid (red) will move with the linkage (blue). At each given instant, one of the points of the body centroid will coincide with a point on the fixed centroid. Again, how the calculation is done will be covered in Part II.

Work of a Ski Lift

I wanted to post this example because I used to forget that when the ski lift accelerates to its operating speed it also rises the chairs. Hence, the total power required at start-up equals the sum of the power needed for acceleration as well as the power needed for the upward lift. It was such a silly mistake to make and, though harmless in problem-solving at school, can cause a lot of damage in real life situations. It is extremely important to consider the problem thoroughly before attempting to solve it.

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Problem 2-32 (Thermodynamics - An Engineering Approach 7th Edition)

A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart. The lift is operating at a steady speed of 10 km/h. Neglecting friction and air drag and assuming that the average mass of each loaded chair is 250 kg. Estimate the power required to accelerate this ski lift in 5 s to its operating speed when it is first turned on.

Power is needed for (1) acceleration and (2) lifting the loaded chairs. This two parts can be calculated separately and then added together.

(1) Power for acceleration:

The final speed of the lift is

$V=\left( 10\ km/h \right)\left( \frac{1\ h \times 1000\ m}{60\ sec \times 1\ km}\right)=2.887\ m/s$.

Then the power needed is

$P_a=\frac{1}{2}m\left(V^2-V_0^2\right)/\Delta t=\frac{1}{2}\left(50\times 250\ kg\right)\left(2.778\ m/s\right)^2=9.6\ kW$.

(2) Power for lift

Assume that the acceleration is constant (i.e. power supply is constant), its value will be

$a=\frac{\Delta V}{\Delta t}=\frac{2.778\ m/s}{5\ s}=0.556\ m/s^2$.

Then the vertical lift during acceleration will be

$\left(\frac{1}{2}at^2\right)\times\left(\frac{200}{1000}\right)=1.36\ m$.

Hence, the power needed to increase the potential energy of the lift is

$P_g=\frac{mg\Delta h}{\Delta t}=\left(50 \times 250\ kg \right)\left(9.89\ m/s^2\right) \left(1.36\ m \right)/ \left(5\ s \right)=3.41\ kW$.

Then the total Power required is

$P_{total}=P_a+P_g=9.6+34.1=43.7\ kW$.

Newton-Raphson Method: Application

This is an application of the Newton-Raphson method for finding the joint angles of a mechanism. This was adapted from a note I made in a class called Mechanics of Machines in my sophomore year. It has proven useful to me for numerous times since then. The Newton-Raphson method can be used on any closed-loop mechanisms, including non-inverted and inverted slider-crank mechanisms. It also converges relatively fast in many common cases which makes it such a convenient tool. Throughout the years the Newton-Raphson method one of my favorite tools as a ME student. 

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Consider the double-loop mechanism:

Link 1 is the input, i.e. the rotation angle of link 1 is specified. Since this mechanism have one degree of freedom the positions of all other links can be found. Realizing that the two loops shown in the figure are in fact two four-bar linkages, we can solve them independently.

First of all, to find the joint angles of the 4-bar linkage made by links 1, 2, 3, and the ground link,notice that the vectors R₁, R₂, R₃, and R₆' have the following relationships:

$R_1+R_2-R_3-R_6=0$.

This is the loop equation for Loop 1. One must be aware of the direction of the vectors. Rewriting this equation in terms of link lengths r₁, r₂, r₃, r₆', and joint angles $\theta_1,\ \theta_2,\ \theta_3,$ and $\phi_6'$, it becomes:

$r_1\cos\theta_1+r_2\cos\theta_2-r_3\cos\theta_3-r_6\cos\phi_6=0$

$r_1\sin\theta_1+r_2\sin\theta_2-r_3\sin\theta_3-r_6\sin\phi_6=0$.

There are two unknowns, $\theta2$ and $\theta3$. The goal here is to find solutions to these two equations:

$F_1(\theta_2,\ \theta_3)=r_1\cos\theta_1+r_2\cos\theta_2-r_3\cos\theta_3-r_6\cos\phi_6$

$F_2(\theta_2,\ \theta_3)=r_1\sin\theta_1+r_2\sin\theta_2-r_3\sin\theta_3-r_6\sin\phi_6$

Here we will apply the Newton-Raphson method.

1. Find estimated values $\theta_2$ and $\theta_3$. Let's call them $\theta_2'$ and $\theta_3'$.
2. The partial differivative of F1 and F2 with respect to $\theta1$ and $\theta2$ are
   
   $\frac{\partial F_1}{\partial \theta_2}=-r_2\sin\theta_2$,    $\frac{\partial F_1}{\partial \theta_3}=r_3\sin\theta_3$
   
    $\frac{\partial F_2}{\partial \theta_2}=r_2\cos\theta_2$,   $\frac{\partial F_2}{\partial \theta_2}=-r_3\cos\theta_3$.
3. Since the values are estimated, it is highly unlikely that they will be the exact solution to F1 and F2. That is, F1 and F2 will not be zero when substituting these values into the equations. We write:
   
   $F_1(\theta_2',\ \theta_3')=\epsilon_1'$
   $F_2(\theta_2',\ \theta_3')=\epsilon_2'$.
4. Then Newton-Raphson method yields that
   
   $-r_2\sin\theta2'\times(\Delta\theta_2)+r_3\sin\theta_3\times(\Delta\theta_3)=\epsilon_1-\epsilon_1'$
   $r_2\cos\theta2'\times(\Delta\theta_2)-r_3\cos\theta_3\times(\Delta\theta_3)=\epsilon_2-\epsilon_2'$

   where $\epsilon_1=\epsilon_2=0$ in this case (the cost of F1 and F2).
5. Solving the equations in 4. gives the change for $\theta_2$ and $\theta_3$.
   .
6. The new estimation for the two values are $\theta_2''=\theta_2'+\Delta\theta_2$ and $\theta_3''=\theta_3'+\Delta\theta_3$, respectively. Using these new values we can start the process from step 3 and find new values again. The values will converge to the exact value of  $\theta_2$ and $\theta_3$. Once the values are withing tolerance, the procedure is terminated and we had our answer.

The procedure for Loop 2 is the same as that described above. Just use the Newton-Raphason method again to find  $\theta_4$ and $\theta_5$.