S13 Design and analyse basic mechanical systems

Posted: October 10, 2010 in Systems and Control

Initial knowledge – 1

Current working level – 2

When I think of basic mechanical systems I automatically go back to my school days and a trip to the Museum of Automata  in York and constructing a simple mechanical toy in DT with the use of a single cam.  Of course mechanics and mechanisms play a massive part in our everyday life whether it be travelling in various automobiles or using an everyday household object such as a pair of scissors.  Mechanisms is an extremely broad subject and its uses are almost endless, so to understand the basics of designing and analyzing basic mechanisms it is probably best to start by looking at the types of movement that mechanisms can make and their types of motion.

There is linear motion which is a straight motion such as a rack and pinion and guillotine.  Rotary motion is a rotating movement such as a set of gears or a carousel.  Reciprocating is a continuous motion such as a saw going back and forward or the needle of a sewing machine continuously going up and down.  Finally there is oscillating motion which again goes back and forward but will move in a circular arc such as a pendulum.

There are three different classes of lever.  A class 1 lever has its fulcrum in the middle and operates like a see-saw.  The fulcrum is simply the levers pivoting point. A class 2 lever has its fulcrum at one end and the effort is applied at the opposing end like a wheelbarrow.  A class 3 lever again has its fulcrum at one end but the effort is applied in the middle such as a pair of tweezers.

There are 5 different types of linkage that can feature in different mechanisms including parallel linkage.  A parallel-motion linkage creates an identical parallel motion.   By pulling (or pushing) a linkage in one direction, it creates an identical parallel motion at the other end of the linkage.  There is also reverse motion linkage A reverse-motion linkage changes the direction of motion.   By pulling (or pushing) the linkage in one direction, it creates an exact opposite motion in the other direction. If the fixed pivot was not central, it would create a larger or smaller motion in the opposite direction.  Another form of linkage is a treadle linkage,  this linkage shows how linkages can be used to change one type of motion into another. In the case of treadle, the rotary motion of the cam moves a parallel-motion linkage. The parallel-motion linkage controls the identical side-to-side, or oscillating motion in windscreen wipers for example.  The final form of linkage is a bell-crank linkage, this linkage changes the direction of movement through 90°. A bell-crank linkage tends to look a little like an L shape.  For example, a bell-crank linkage could be used to turn a vertical movement into horizontal movement which is the sort of motion used in bike brakes.

To calculate a moment of force between two points the equation is M= FxD .  The moment is the force multiplied by the distance.

Other calculations I may need to make when analyzing mechanisms is its mechanical advantage.   Mechanical Advantage is the ratio of the existing weight or load to the acting force; or, the ratio of the distance through which the force is exerted to the distance the weight is raised. For example, a machine has a mechanical advantage of 5 if an applied force of 1 kg can counterbalance a weight of 5 kg.  Or in simpler terms the load is divided by the effort.  So the load ( or weight)  5kg is divided by the force (or effort) of 1 kg to equal a mechanical advantage of 5.

To work out a velocity ratio the equation is distance moved by effort divided by the distance moved by load.  I can calculate a velocity ratio by looking at pulley systems.  Pulleys are used to change the speed, direction of rotation or the turning force or torque.  A pulley system typically consists of two pulley wheels each on a shaft that will be connected by a belt.  This will transmit rotary motion and force from the input, or driver shaft, to the output or driven shaft.

If the pulley wheels are different sizes, the smaller one will spin faster than the larger one. The difference in speed is called the velocity ratio. This is calculated using the formula:

Velocity ratio = diameter of the driven pulley ÷ diameter of the driver pulley

So Velocity ratio = 120mm ÷ 40mm = 3

If the pulley system is a two pulley one or a four pulley one the distance moved by effort is multiplied by 2 an4 respectively

If you know the velocity ratio and the input speed of a pulley system, you can calculate the output speed using the formula:

Output speed = input speed ÷ velocity ratio

So the output speed = 100rpm ÷ 3 = 33.3 rpm

The velocity ratio of a pulley system also determines the amount of turning force or torque transmitted from the driver pulley to the driven pulley. The formula is:

output torque = input torque × velocity ratio.

To work out efficiency I have to use the equation: mechanical advantage divided by velocity ratio x 100%

Moving back to the days of the old cam driven toys at school  I can look at the different types of cams available.  A cam is used to change a motion ( commonly a rotary one) to a reciprocating or linear motion.    There are different shaped cams and these are the most common shapes:

Although there are of course many variations of these standard shapes.There are also different types of followers available:

a)  knife edge follower: In theory there is not a limit on the shape of cam that can be used with this follower

b)  Roller Follower: The roller follower has the advantage that the sliding motion between cam and follower is largely replaced by a rolling motion. Note that sliding is not entirely eliminated since the inertia of the roller prevents it from responding instantaneously to the change of angular velocity required by the varying peripheral speed of the cam. This type of follower also produces a considerable side thrust.  The roller follower demands that any concave portion of the working surface must have a radius at least equal to the radius of the roller.

c)  Flat of Mushroom Follower : These have the advantage that the only side thrust is that due to friction between the contact surfaces of can and follower. The relative motion is one of sliding but it may be possible to reduce this by off setting the axis of the follower as shown in the diagram. This results in the the follower revolving under the influence of the cam.

Flat faced Follower These are really an example of the mushroom follower and are used where space is limited. The most obvious example being car engines.

A spring can be attached to some followers to keep it in permanent contact with the cam and the cams motion caused by its shape can be tracked by a displacement graph or diagram.

Another mechanism that uses rotary motion is gears they can not only transmit motion but force also.  When gears are ‘meshed’ like this they can act in a similar way to levers.  Each tooth of the gear could be regarded as an individual lever with the fulcrum being at the centre of the gear.

To work out a gears mechanical advantage you divide the number of teeth on the driven gear by the number of teeth on the driver gear so in this instance it would be 18 / 8 = 2.25.

To work out the gears velocity ratio or gear ratio we divide the number of teeth on the driver gear by the number of teeth on the driven gear so again it is 18/8.

There are also numerous types of gears as well:

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