Free-body Diagrams Helps to isolate and simplify a system (Like a boundary in systems theory) Is a line diagram that represents all of the forces acting.

Free-body Diagrams

• Helps to isolate and simplify a system

(Like a boundary in systems theory)

• Is a line diagram that represents all of the forces acting on a body

• This simplified diagram allows better understanding of how forces are effecting a structure

Fv

FbusFbridge

Fh

B e a m s

• Beams occur in almost every structure

• They are subject to forces and turning moments

• For a horizontal beam to be in equilibrium:

upwards forces = downwards forces

clockwise moments = anticlockwise moments

B e a m R e a c t i o n s • Beams are supported differently than levers

• Common examples are shown below:

MM

MM

Simple Built in

Built in at 1 end only Built in and simple

Example

• Determine the reactions R1 and R2 for the following simply supported beam

Take moments about R1

clockwise moments = anticlockwise moments

(10,000 N 2 m) + (500 N 2.5 m) + (6000 N 4 m) = R2 5 m

R2 = 20,000 Nm + 1250 Nm + 24,000 Nm = 9050N

5 m

Also upwards forces = downwards forces

R1 + 9050 N = 10,000 N + 500 N + 6000 N

R1 = 16,500 N – 9050 N= 7450 N

Therefore the reactions for the beam supports are R1 = 7450 N and R2 = 9050 N

2. A beam is simply supported at each end with a span of three metres. The beam carriesa small lifting device having a weight of 1 kN.

(a) Complete a suitable free-body diagram.(b) When the lifting device is positioned at the mid-point of the beam and carries a

casting weighing 2.5 kN, what are the reactions at R 1 and R2?(c) When the lifting device is positioned one metre from one end and carries a

machine component weighing 6 kN, what are the reactions at R 1 and R2?

LINKAGES

• Levers are often linked together to transmit force or motion. A linkage consists of two or more levers connected together. Linkages are useful for changing the direction of an input or for giving greater force or distance amplifications.

LINKAGES

• TASK: Open up the mechanisms software program Find the Likages section from the menu Construct a revision sheet based on the

information given in this section Remember to add sketches

LinkagesLinkages are an essential part of many mechanisms. They can be used to change direction, alter speed and change the timing of moving parts.In this example two linked linkages are used to convert the small linear movement of the drive shaft (bottom left) into first a rotational body movement and secondly a fast hammer movement. Compare the speed of the hammer with the speed of the drive shaft!

Linkages

• The basic 4 bar linkage. All four bars make up a parallelogram. Two, equal length orange shafts and the distance between the joints on the red moving bar and yellow fixed bar being equal. The movement of the top arrange shaft exactly shadows the movement of the lower orange bar.By changing these lengths and the lengths of the other bars different movements can be achieved.

Linkages

• This time, two different lengths of bar, the two long bars, yellow and red are the same length as before.Look at the tip of the red shaft, notice how it moves smothly until the last second then flips to the right.

Linkages

• Quite an extreme arrangement this! With the two long bars crossing over each other. A more extreme 'kick' in the orange bar this time at the end of the green bar's travel. Looks like a likely mechanism for a model!

Linkages

• http://www.robives.com/mechs

Have a look at this web site and try to find others which discuss linkages. Then construct a revision aid on linkages.