MDME: MANUFACTURING, DESIGN, MECHANICAL ENGINEERING

# FREE BODY DIAGRAMS

A Free-Body Diagram (FBD) is a sketch of an object with everything else stripped away, and replaced with all the forces acting on the body. This makes it easier to understand the forces, and allows us to analyse the stresses within the object.

Tutorial Notes FBD.pdf    FBD.one

### Which Force?

According to Newtons 3rd law, every action has an equal and opposite reaction.

If the object is in equilibrium the two opposite forces cancel out. But when it comes to drawing a FBD we must choose one of them! Which one?

Answer: The one that acts ON THE BODY.

(Same as...What does it do TO the body)

## Definition of the FBD

A free body diagram consists primarily of a sketch of the body in question and arrows representing the forces applied to it (TO the body)  Another way is to say the force of something ON the body. The selection of the body to sketch may be the first important decision in the problem solving process. For example, to find the forces on the pivot joint of a simple pair of pliers, it is helpful to draw a free body diagram of just one of the two pieces, not the entire system, replacing the second half with the forces it would apply to the first half.

### What to include

The sketch of the free body need include only as much detail as necessary. It is usually best to outline the body and avoid any confusing internal details. In some cases (concurrent forces), the body can be a single point!

Only the forces acting on the BODY are included. These may include forces such as friction, gravity, normal force, drag, or simply contact force due to pushing. It is usually easy to determine the point of application of each force - contact points and the centre of gravity.

Try to guess the direction of the force and show by the direction of the arrow. If you guessed wrong it won't matter - you simply get a negative answer in the end which means opposite direction. However, known forces (like gravity or other applied forces) must have the correct direction.

### What to leave out

Don't draw anything other than the body. It is often best to draw the body as an outline to avoid confusion with internal parts. Do not include forces which the free body applies to other objects think... "TO THE BODY").

For example, if a ball rests on a table, the ball applies a force to the table, and the table applies an equal and opposite force to the ball. The FBD of the ball only includes the force that the table causes ON THE BALL, and the force of gravity ON THE BALL. Internal forces, forces between varies parts that make up the system that is being treated as a single body, are omitted.

Examples:
Notice how the 'body' is drawn as an outline.

## How to Draw a Free Body Diagram

### 1. Isolate Body

There must be only 1 body.  Make sure you isolate the body exactly – as if you cut it out in a silhouette or outline. It is important to be very clear about the boundary you have made around the body.

### 2. Find Force locations

Forces are applied by contact, gravity or inertia. Identify all the points where forces are applied to the body. Gravity always acts through the centre of mass, pressure acts through the centre of pressure.

The only forces to consider are those that CROSS THE BOUNDARY. Ignore all other forces.

### 3. Line of Action of Forces

• Point contact: ‘Smooth’:  No friction. Force can only be applied perpendicular to smooth surface.Wheels:  Perpendicular to surface and acting through centre of axle.
• Cable. Force can only be tensile (pulling). Force must be along direction of cable.
• Pin Joint: Force can be any direction but no moment around pin.
• Other Joints: Solid:  Force in any direction, moment in any direction. Slider:  Moment any direction. Force perp to slider
• Gravitational. Centre of gravity
• Inertial. Centre of inertia (not always the same as C.O.G). These are due to acceleration.
• Fluid pressures. Usually taken as a single resultant force in statics calculations, acting through the centre of pressure.
• Other. Magnetic, electrostatic (charge) etc. These are pretty rare outside of electric equipment design.

### 4. Direction of the Forces

Include all the forces acting TO THE BODY. The direction is determined by thinking TO the body, or ON the body.  Eg Gravity acts down ON the body, floor pushes up ON the body, what does the road do TO the wheel…etc.

## Worked Example 1: Wheelbarrow

### 1. Isolate Body

Draw a FBD for a wheelbarrow full of dirt.

The wheelbarrow is three dimensional. For simplicity we will treat the problem as two dimensional by combining the handles together.

Now isolate the body (where body = wheelbarrow + dirt). It is best to draw a silhouette (only showing the outline). This helps to avoid confusion with internal components that should have been included (combined) with the body.

### 2. Find Force locations

In statics questions like this, look for contact points where forces are applied, and the centre of gravity of the BODY. Both the hand force and Ground force cross the boundary of the body.

### 3. Line of Action of Forces.

"Wheels:  Perpendicular to surface and acting through centre of axle."  Since ground is flat, the force must be vertical.
Gravity: Always vertical
Hand: Mostly vertical - especially if the ground is flat and we are standing still without friction.

### 4. Direction of the Forces

Gravity: Gravity is always down. What does GRAVITY do to the body.? It pulls down.
Ground: What does the ground do to the body/ It pushes up.
Hand. What does the hand do to the body? It pulls up.

(At this stage there is no difference between pushing or pulling. All the forces below are drawn as if the are pushing because it is clear on the diagram. We will be important later when we go to add the forces up.)

## Worked Example 2: The Handle of the Wheelbarrow

### 2. Find Force locations

Watch out for the boundary here, the force must cross the HANDLE boundary, or outline.

### 3,4. Line of Action of Forces + Direction of the Forces

Wheel Axle: Vertical, applied through centre of axle. Since ground is flat, the force must be vertical.
Handle Gravity: Always vertically down
Load Force: Applied along the whole length of the tray, but take an average force through the centre of mass. It is a gravity force so vertically down (as always).
Hand: Vertical by default (no friction or acceleration) What does the hand do to the body (Handle)? It pulls up.

Free Body Diagram for Handle

#### FBD practice exercises

 A wooden ball on a table; (a) Body is the ball (b) Body is the table Two people balanced on a see-saw; (a) The body is the beam of the see-saw Car stationary; (a) Body is the whole car Car & trailer stationary - trailer is slightly loaded towards the front (a) Body is the whole car (b) Body is the whole trailer A person is using a spanner to tighten a bolt (clockwise). (a) The spanner A machine is supported by a lifting eye. (a) The eye-bolt (not including the nut. Hammer pulling out a nail; (a) Hammer (b) Nail (c) Small block under the hammer Ball in a V groove - (a) Ball (b) The V block A bolt tightened inside a tube. (a) the whole bolt and nut  (b) the nut (c) the tube Pliers clamping on a pipe. (a) the pipe (b) the whole pliers (c) the finger lever (d) the hand lever Object held by G clamp. (a) The ‘G’ frame (b) the screw   (c) the object being clamped Bow and arrow with the archer ready to shoot. (a) The bow only (b) The string only (c) The bow, string & arrow together A kite (flying but not moving): (a) the kite (frame, cloth together) Piston engine: Mid-stroke during a compression test at very low speed (ignore inertia). (Drawn from side view - looking down the axis of the crankshaft) (a) Connecting rod (b) Piston (c) Crankshaft Bicycle under power: (a) Whole bicycle (b) Back wheel only (c) Crank under load (d) A single chain link Manuallly operated Jib crane with load. (a) Jib (b) Cylinder (c) Mast (d) The whole crane as shown (with load, includes person pushing on crank) Scissor Jack supporting a car. (a) The whole jack (b) The screw (c) The Foot (d) One of the upper arms An insulator that supports the overhead cable. (a) The clevis pin (b) The insulator component (it is a ceramic insulator integrated with the steel clevis assembly)

#### Detailed practice exercise

(Note The above practice questions and this detailed exercise are have similarities with assessment questions.)

Vise-Grips: (the engineer's nutcracker)

Assumptions:
• The nut is under load (a tough nut to crack)
• Parts are in the position shown
• Hand forces are applied with approximate position and direction as shown (in blue)

Draw a FBD for each of the following;
1. Screw
2. Handle
3. Spring
5. Jaw
6. Grip
7. Release
8. Walnut

##### Resources
• Internet Search Engine Tip: "Free body Diagram"