1. Mechanisms : Around us we can see many moving objects and mechanisms that produce movement that we can also call motion. The most important element in all of them is the driving force that initiates the movement. The driving force can be a spring, an electric motor or our own muscles.

Are mechanisms that transmit motion and force in a straight line from one point to another. Examples include levers and fixed, mobile and compound pulleys.

2.1. Levers: A lever is a rigid bar that is supported by a fulcrum. "F" is the force or effort applied at one end of the bar. "R" is the resistance or load which acts at the other end of the bar. "d" is the distance from F to the fulcrum. "r" is the distance from R to the fulcrum. F x d = R x r.

Class 2: The resistance is between the fulcrum and the effort applied. The effect of the effort applied is always multiplied. (d>r)

Class 1: The fulcrum is between the effor applied and the resistance. The effect of the effort applied can be multiplied or reduced.

Class 3: The effort applied is between the fulcrum and the resistance. The effect of the effort applied is always reduced (d<r).

2.2. Fixed pulley : A fixed pulley is a wheel that has a groove around it into which a rope, chain or belt fits. It rotates around an axle that is fixed to an inmobile surface. A fixed pulley is balanced when the effort "F" is equal to the resistance of the load "R" , F = R. Uses : wells and gym equipment , for example.

2.3. Moveable pulley: A moveable pulley is a set of two pulleys, one is fixed while the other can move in a linear direction. A moveable pulley is balanced when it satisfies this equation: F = R : 2. The effort required to move a load with a moveable pulley is half the effort needed to move the same load with a fixed pulley.

2.4. Compound pullley: This is a system of fixed and moveable pulleys, often called block and tackle. F = R : 2n (n = number of moveable pulleys) . And if the mechanism is straight the following formula is used : R : 2n.
Uses: lifts, goods lifts and cranes.

These mechanisms transmit motion and effort in a circular way, from the input to the output. They include friction drives, pulley systems, gears and worm gears.

3.1. ⭐ Friction drives ⭐ : They are made up of two or more wheels that are in contact. The first wheel is called the primary drive wheel. When it moves, it turns or drives the second or output wheel , causing it to move as well. The output wheel rotates in the opposite direction of the primary wheel. If we use more than two wheels, each one rotates in the opposite direction to the one next to it. The ratio between the rotation velocity of the wheels or pulleys depends on the relative size of the wheels. (N1 x D1 = N2 x D2.) D1 : D2 = N1 : N2. N1 and N2 are the velocities of the primary drive wheel and the output wheel. These velocities are expressed in revolutions per minute, they are expressed in units of length. The ratio D1D2 is called the gear ratio.

3.2 ⭐ Pulleys with belt ⭐ : They consist of two pulleys or wheels that are a certain distance apart. Their axles are parallel and they rotate simultaneously due to the effect of the belt.

3.3 ⭐ Gear mechanisms and cogwheels ⭐ : Cogwheels are sets of wheels that have teeth called cogs. The cogs fit into the spaces between the cogs of another wheel, so that one wheel moves the other. They transmit a rotary motion between the two connected axles, which can be parallel, perpendicular or oblique. Gears can be cylindrical or conical. All the teeth must be the same shape and size. The two wheels and the two axles rotate in opposite directions . The ratio between the rotation velocities of the wheels depends on the number of teeth on each wheel. It is expressed by this equation: N1 x Z1 = N2 x Z2 . Z1:Z2 = N1:N2 : . N1 and N2 are the velocities of the corresponding wheels. Z1 and Z2 are the numbers of teeth.

3.4 ⭐ Worm gear ⭐ : This is a screw that moves a helical cogwheel that is set perpendicular to the screw. Each time the screw rotates, the gear moves forward as many teeth as there are grooves in the screw, usually a small number : 1, 2 or 3.This is used to reduce velocity as well as functioning as a brake system. A worm screw fulfils this equation: N wheel = N screw x Z grooves : Z wheel. N are the velocities and Z the number of grooves or teeth.

3.5 ⭐Gear mechanisms with a chain ⭐ : These are two cogwheels with parallel axles that are a certain distance apart, they rotate simultaneously by means of a metal chain or a toothed belt stretched over both wheels. The chain transmits the rotary motion of axle 1 to axle 2 by means of gears 1 and 2, and the two gears rotate in the same direction. This system transmits greater forces without losing velocity because the chain is attached to the gear teeth so there is no slippage between the chain and the wheel. Formula :N1 x Z1 = N2 x Z2 . Z1:Z2 = N1 = N2. N are de velocities of the corresponding wheels, Z are the number of teeth.

3.6 ⭐Gear train ⭐ : This is a system of more than two gears, connected together as shown in the diagram. The rotary motion of the first wheel direves the second wheel and so on. In this system, the rotary movement of the first axle is transmited to the second by means of wheels 1 and 2. Wheel 3 rotates with the same velocity as wheel 2 and drives wheel 4, to which it is connected. Each connected geared wheel rotates in the opposite direction to the wheel it is attached to. Formula: N4 : N1 = (Z1 x Z3 ) : (Z2 xZ4). N are the velocities of the drive wheel and the driven wheel. Z are the number of teeth on the wheels.

3.7 ⭐Pulley trains with belts ⭐: 1.The rotary motion of axle 1 is transmited to axle 2 by the belt that connects them.2. Pulleys 2 and 3 rotate at the same velocity. 3.The motion of pulley 3 is transmited to pulley 4 by the belt that connects them.4. A ll the wheels rotate in the same direction. The gear ratio between the drive pulley 1 and the driven pulley 4 depends on the relative size of the pulleys in the system . It is expressed as a function of their diameters. N is the respective velocity of the drive and driven pulleys. D is the diameter of each wheel.

Variation in velocity:Apart from transmiting force and motion, rotary transmission mechanisms allow velocity to vary. When the wheels and the gears have the same diameter or the same number of teeth, they rotate at he same velocity. When they are different sizes, the smallest rotates more quickly. The ratio of the velocities of the two wheels is given by the gear ratio.

4. Mechanisms that transform motion: There are two ways in which motion can be transformed: 1. From rotary into linear. 2.From rotary into reciprocating.

Rack and pinion system: This uses a pinion that is a small cogwheel, mounted on a rack that is a toothed belt or bar. When the pinion rotates, the rack advances in a linear motion. The ratio between the number of rotations of the pinion and the velocity of the movement of the rack is expressed by this equation : L = P x Z x N . L is the velocity of the movement of the rack in milimetres per minute. P is the distance between two consecutive teeth in milimetres. Z is the number of teeth in the pinion. N is the number of rotations per minute of the pinion.

Nut and bolt system: This consists of a bolt or threaded bar and a nut that has the same interior diameter as the diameter of the bolt. If the bolt rotates and the nut can't turn, the nut moves in a linear motion along the threaded axle. If the nut rotates in a fixed position, the bolt will move in a linear motion

Winch and crank handle: A crank is a bar attached to an axle that is used to turn it. A winch and crank handle system consists of a drum that rotates and a crank handle that allows to pull or lift objects. The effort needed to turn the winch is less than it would be if we tried to turn it without the crank handle. A winch is balanced when it satisfies this equation: F x d = R x r . F = R (R x r) : d F is the force applied , R, the resistance and r the radius of the winch and d, the length of the crank handle.

Crank link slider: This is composed of a crank and a rod called a connecting rod or link. This rod has articulated joints at each end, one is connected to the crank and the other to the slider. The slider produces a reciprocating motion. As the wheel rotates, the crank transmits the rotary motion to the connecting rod, which moves in a reciprocating motion. This crank link slider system can work in reverse, it can transform reciprocating motion or oscillating motion into rotary motion. This device was vey important in the development of stream engines.

Crankshaft: This is a set of connecting rods attached to a jointed axle. Each of the joints of the axle acts as a crank. A crankshaft transforms the rotary motion of an axle into a reciprocating motion with different connecting rods moving at different times. It can also transform the reciprocating motion of the rods into a rotary motion of the axle.

Cam: This is basically a rotating object that pushes a follower as it moves. We can change the shape and the usable profiles, the outside edge of the piece, that are more or less pointed to produce more complex movements. A cam transforms rotary motion into reciprocating motion in the follower or bar. A set of cams fixed on the same axle is called a camshaft.

Eccentric cam : This consists of a wheel with an off centre rotation axle that doesn't coincide with the centre of its circumference. It transforms the rotary motion of the wheel into reciprocating motion in the follower. The distance between the centre of the circumference and the rotation axle is called eccentricity.

5.1 Mechanisms for controlling and directing motion : The most typical mechanism of this type is the ratchet, which allows rotation in one direction but impedes it in the opposite direction, as you can see in the diagram. The mechanisms used to reduce velocity are called brakes. There are several types.

5.2 Mechanisms that store energy: Springs are devices that absorb energy. This energy can be released later, little by little or all at once. Springs work in different ways: : 1.By compression, the spring is compressed, in a chair for example. 2. By traction: The spring is stretched. in a bed frame for example. 2.By torsion, the spring is twisted, in a clothes peg for example.

5.3. Connecting mechanisms: 1. Clutches are mechanisms that allow axles or shafts to be connected or separated. 2. Fixed combinations are used to make permanent connections between axles and shafts. 3. Moveable connections are used to connect shafts that can move along the axle or at an angle to each other. There are two main types: Oldham joints and Cardan joints

5.4 Supports: Bushings and bearings: These mechanisms support shafts and transmission axles. 1. In bushings the axle or the shaft is inserted in a plain circular piece that is placed inside a housing to provide a bearing surface. 2. Bearings are made up of two concentric rings with balls or rollers between them. The inner ring joins or adjusts the axle or shaft and the outer ring is the support element.