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The real mechanical advantage of any machine is the load force divided by the effort force. Usually, the mechanical advantage is greater than 1 (there is an advantage). In some cases (third class lever, wheel being driven) the mechanical advantage is less than 1 (there is a dis-advantage). This is done to get a greater range of motion at the expense of needing a bigger applied force.
For each type of simple machine, the ideal mechanical advantage is the ratio of two distances. Which two distances depends on the simple machine in question.
Often, the system is assumed to be friction-less and hence free of loss. In this case, the real mechanical advantage is equal to the ideal mechanical advantage
For a pulley system, the mechanical advantage is the number of lines (ropes) on the moving block (pulley).
When you lift a weight, the distance the weight is lifted becomes LR and the amount of rope you have to pull becomes LE.
If you push an object up a ramp (inclined) plane. The amount of force you have to exert (E) is less than the weight (R) of the object by the ratio of the ramp length (L) to its height (H).
A wedge is an inclined plane that is stuck on the short side to produce a splitting force.
Where: L is the length of the long side and H is the length of the side being stuck
A screw is an inclided plane wrapped around an axle. The Pitch of the screw is how far it advances into the wood (or the nut) for one complete revolution. The Thread Count is the number of threads per inch on the screw. So:
The long side (L) of the inclined plane is the circumference of the screw, or π times the diameter
The pitch (P) becomes the height in the equation.
Three types of catapults are the Mangonel, the Ballista, and the Trebuchet
A Floating Arm Trebuchet out of Popsicle Sticks
In absence of wind resistance (a very real phenomenon) baseballs, basketballs, and other projectiles travel in a parabola.
a = constant
V = V0 + a t
D = D0 + V0 t + ½ a t2
X0 = 0
a = 0
V0X = V0 cosine (θ)
a = g = -32.2 ft/sec2
V0Y = V0 sine (θ)
X = X0 + V0X t
Y = Y0 + V0Y t + ½ g t2
VX is constant
= V0Y + g t
X = V0 cosine (θ) t
Y = Y0 + V0 sine (θ) t + ½ g t2
A floating arm Trebuchet from popsicle sticks
See how tractor engineering is applied full-scale to real life competitions. Though model tractors and simple designs provide a basic understanding of how tractors work, here you will find some enormous, professionally built models with real brute strength.
Just to get a glimpse of how popular tractor pulling has become, check out some of the many tractor pulling clubs and organizations across the world.
It is common knowledge that a good gear reduction is essential to a good tractor. Without it, the axles would spin with much less torque and the tractor would be unable to pull nearly as much weight. Here you will find some general information about how gears work and how to construct some functional gear trains.
For a fundamental explanation of gears and how they work please visit www.howthingswork.com/gears.htm
Here is another, easier, explaination at Badlinks
Here are some examples of some amazing, real-life gears and gear trains that are used by companies today: http://www.dgsteel.com/
Another effective method of system reduction involves the usage of pulleys. For information on pulley reduction and an example of a modern pulley system, please visit http://www.robotics.com/reducers.html and http://www.robotics.com/pr23.html
If you are interested in a local high school engineering challenge, your project will probably involve the design and construction of what is known as a micro-tractor. Just as the term tractor pulling refers to real-life, full-scale tractors, mini-tractor pulling refers to more of a lawnmower-sized, medium tractor. Smaller than normal tractors and beyond a mini-tractor comes the micro-tractor: a model tractor usually no larger than a football. Here you will find general information, concepts, and possible designs related to micro-tractors and the realm of micro-pulling.
The Lego Design PageWill help you get started
For information about Legos™ visit www.lego.com or "My Lego Projects"
Here's something that you can't do Nine to One Gear Reduction
Last updated on 22 January 2009 by P. A. Wiedorn