Domino effect - Its more than just a fall

There is none who hasn't heard of the domino effect. Its the chain reaction triggered by one falling object on the other (dominoes) which in turn fall on the other and so on. Simple isn't it? But when I was surfing the net reading about the energy conversions involved in a domino effect, I was amazed to see how naive I have been in thinking that the effect is nothing but a successive fall of dominoes. Here are some of the interesting aspects of a domino effect that I came across

1) The speed

The speed of the domino effect depends on the distance between the successive dominoes. The farther they are placed apart, the slower is the progression because it takes a longer time for the falling domino to knock down the next one - common sense. 

2) An Infinite arrangement of dominoes

An infinite dominoes set poses some interesting questions. Will the system continuously lose energy continuously through heat and sound and eventually come to a halt? The answer is no. The energy of the system comes from the potential energy of each of the dominoes that was stored while setting them up in a metastable position. An initial trigger to the first domino will convert its potential energy into kinetic energy while falling and a fraction of this kinetic energy will push the next domino to an unstable position thereby making it fall and converting its potential energy into kinetic. Thus the system is self sustained and never comes to a stop. In fact, as the first domino pushes the next at a speed, the second one falls faster than the first. This in turn topples the next one even faster and thus the progression is actually accelerated.

So, if the progression is accelerated, will an infinite dominoes system reach the velocity of light at one point? the answer is no again. Consider this analogy - a ball falling towards the earth's surface from about a height of 1000 km should ideally reach a velocity of 42 km/sec when it reaches the surface. But that does not happen because the atmospheric air dampens its acceleration and makes it reach a "terminal velocity" which will be constant till it touches the ground. Here energy is lost by friction and buoyancy and an equilibrium is reached. In a similar way, in a domino-effect, the energy is lost during the impact through heat and sound. this energy loss is more when the speed of impact is more. Thus the system reaches a point in time when the acceleration and energy loss reach an equilibrium and the progression will be at a constant velocity from then on.

There may be still more to a domino-effect when you consider the size and geometry of the dominoes. May be I'll look for more on this topic and write about it sometime later. From now, when you witness a domino effect, remember, there is more to it than what meets the eye! ;)

References: Wikipedia, www.physicsforums.com

Project Euler

My friend has told me long ago about Project Euler. It took me almost half a year to check out what it is. Project euler hosts some 275+ problems which are mostly mathematical and analytical. Well, though they are mathematical, its impossible to solve them without the help of a computer program.

Some of the problems are as simple as find the sum of all multiples of 3 or 5 less than 1000. There is one problem which asks u to find the pythagorean triplet a,b,c such that a+b+c=1000. There are also freakin big probs like find the last five digits before the trailing zeroes of factorial(1,000,000,000,000).

I just started coding for few problems. You too check those probs @ projecteuler.net

Get a head start on simple robotics

I'm back to posting something almost after a month. Still I'm lazy enough to post the same thing which i've wriiten for CSAU's(Computer Society of Anna University) next edition of cursor magazine. Its about simple robotics and here it goes... 


check out this moving butterfly robot

‘Robotics’ is a very common word among the guys and girls of CEG. Many people misinterpret this term as something big and hi-fi. Yeah, even for me the first thing that comes to my mind when I hear the word ‘robot’ is ASIMO! In reality, the bots we actually make at college level are quite simple and fascinating. In fact, making robots will make a great hobby. I was fortunate enough to have seniors who helped me a lot in gaining some insight into this field. In this article, I’ll discuss some theoretical aspects for building a manual radio-controlled bot.

Invariably, all the bots that we make at college move on wheels (on belts or chains too) and DC motors drive them. As Wikipedia defines a robot as an Electro-Mechanical entity, we have to primarily design a robot on Electronic and Mechanical point of view.

The mechanical design includes the chassis design, drive system and the mechanism to complete its objective. The chassis design is simple. You just have to decide where to place the motors (2 or 4 according to the bot’s objective), battery and the circuit boards. Make sure that the centre of gravity of the robot is as low as possible for greater stability. For the drive system, there are two major types

· Steering drive

· Differential drive

The steering drive is the drive system used in cars. A rack and pinion arrangement is used to steer the front wheels. This type of drive can be used in building bots for which speed is of great importance as the bot can be driven forward as well as be steered to any one direction simultaneously. But the great disadvantage is that building a precise steering mechanism is highly complicated. So, we practically don’t use this system for most projects.

Differential drive is used in almost all simple robots. In this system, a left or right turn is achieved by the differential motion of the left and right wheels. The turns can be achieved in more than one way.

Left turn – 1) Right wheels rotating in forward direction while the left ones aren’t moving (Arc turn)

2) Right wheels rotating in forward direction and the left wheels in the reverse (Spot turn)

3) Right wheels rotating faster than the left wheels. (This type is not in practice)

The right turn can be achieved in a similar way. The great advantage of this system is that it is very easy to build the electronic control. However, the bot has to stop moving forward every time it needs to turn.

There is another type of drive – the pivoted drive. This method is used for making precise turns. This is fit for use only in autonomous robots and hence I am not discussing that now.

Additional mechanisms are based on the bot’s mission. It may be a hand to pick objects, a wedge in front for sumo bots or event rack and pinion arrangements to lift objects. These things can be designed according to your choices. Often simple ingenious designs work better than complex mechanisms as greater the complexity, greater the chances for failure.

Electrical design

For a radio controlled bot, we require a transmitter and receiver module. We need not design these components. The transmitter and receiver module can be hacked from a RC toy car. I’ve given a layout of the electrical design below

The Receiver module operates at 5V whereas the motors we usually use are rated at 12V. So, in simple words, the motor driver converts the 5V output signals from the receiver to 12V and gives them to the various motors used. This driver circuit is the only circuit that we make originally for a simple bot. A typical transmitter-receiver module handles 4 signals. I’ll write on how to hack a receiver module from a toy car and how to use those four signals to effectively operate the bot in the next post.