Simple Machines

Simple Machines

Definitions

Any mechanical or electrical device that transmits or modifies energy to perform or assist in the performance of human tasks..
A mechanical device that transmits, modifies, or changes the direction of force in order to help people do work..
A apparatus in which work is done on the machine by applying a force (Effort) at one part which results in work being done by the machine in overcoming an external force (Weight or Resistance). The advantage of using a machine is that a small force can be used to overcome a larger resisting force. Optionally a small movement can be used to cause the machine to generate a larger movement.

There are six basic simple machines..

 Incline Wedge Lever Wheel and Axle Pulley Screw

The Mechanical Advantage of a machine is the ratio of Force being moved W to the Effort F

The Velocity Ratio of a machine is the ratio of the distance moved by the Effort and the distance moved by the Force being overcome.

Velocity Ratio = Distance moved by Effort/ Distance moved by force

In the ideal frictionless/weightless machine

The efficiency of a simple machine

Efficiency = Work done by the machine / Work supplied to machine

The only parameter that can be determined from the machines dimensions is the velocity ratio.

Machines generally follow the linear rule..

F = a + b. W

Incline Plane

One of the simplest of machines is the inclined plane..

The force Force (F) is the effort required to move the Weight (W) up the slope.   A movement of the weight a distance x along the incline will result in a vertical displacement of x Sin(θ)).   Assuming that the incline is frictionless the F required to move the weight up the slope = W Sin(θ)).

Velocity ratio = 1 /Sin(θ)

Wedge

Velocity ratio (Single Wedge) = 1 /Tan(θ)
Velocity ratio (Double Wedge) = 2 /Tan(θ/2)

Lever

Velocity Ratio (First Class Lever) = B /A

Velocity Ratio (Second Class Lever) = (A+B ) /A

Velocity Ratio (Third Class Lever) = A / (A+B )

Wheel and Axle

Velocity ratio = R / r

Pulley
 Simple Pulley.. Velocity ratio = Number of ropes Note: A very simple 2-rope pulley is shown.  In practice there can be a number of rotating pulleys on the top and bottom blocks increasing the number of vertical ropes. Differential Pulley.. Velocity ratio = 2.R /(R-r) Note:Requires use of chain with engaging sprockets to prevent slip

Screw

Velocity ratio = R. 2.p / p