Engineering Mechanics and Machines: Comprehensive Study Guide

Defining Machines and Engineering Disciplines

• Machine Definition: A machine is defined as an apparatus that transmits or modifies force or motion. It consists of several parts, each with a definite function, which work together to perform a particular task.

• Engineering Disciplines Related to Machines: The Institute of Engineers Australia (IEA) provides details on various disciplines via Engineers Australia (2019).

  • Biomedical Engineering:

    • Biomedical Engineers work alongside doctors and medical scientists to research and design methods to improve health care.

    • They utilize microcomputers, lasers, and other materials to develop and improve diagnostic medical research equipment.

    • They are involved in creating medical products to monitor and treat patients, as well as designing equipment for disabled people.

    • In hospital settings, they ensure the safe operation of monitoring, diagnostic, and therapeutic equipment, including catheters, CAT scanners, pacemakers, and kidney machines.

    • They design artificial joints and limbs and assist surgical teams in fitting these devices.

    • They develop assistive technology for those with difficulty walking, communicating, or performing daily tasks.

  • Electronic Engineering:

    • Electronic Engineers work for companies and government departments to design, construct, and test electronic devices, including computers.

    • They are responsible for the installation of these devices.

  • Mechatronics:

    • This is a rapidly developing field that associates digital computers with the control of machines and processes.

    • It is used to create products such as substitutes for human sensors and organs, as well as computer-controlled machine tools.

Engineering in Society

• Societal Impact: A society without engineers would be similar to a hunter-gatherer society focused purely on survival.

• Innovation: Innovation begins as soon as a member of society creates a tool, such as a spear, a trap, or an improved technique for smashing objects; this marks the birth of engineering.

• Modern Necessity: No country or society today can succeed without adopting engineering at some level, as it impacts every aspect of modern life.

Types of Motion

There are four primary types of motion: linear, rotary, oscillatory, and reciprocal.

• Linear Motion:

  • Definition: Motion in a straight line, which can be horizontal, vertical, or along an incline.

  • Examples: Cars, bikes, drones, and lathe belts.

  • Conversion: A car jack handle uses rotational motion to create linear motion to lift the vehicle.

• Rotary Motion:

  • Definition: Motion follows a continuously circular path about an axis.

  • Examples: Spur gears, wheels, fan blades, Ferris wheels, merry-go-rounds, and motor output shafts.

• Oscillatory Motion:

  • Definition: Repeated motion where an object moves over the same path repeatedly. In an ideal system without friction, this would continue forever, but real-world systems eventually settle into equilibrium.

  • Mechanical Examples: Simple pendulums, movement of a point on a wheel, spring movement, and vibrating strings of musical instruments.

  • Electrical/Natural Examples: Alternating current (AC), earthquake motion, and cosmological model oscillations.

  • Simple Harmonic Motion (SHM): A specific type of oscillatory motion often studied in Mathematics Methods.

  • Visual Example: The cone of a loudspeaker vibrates in an oscillatory motion.

• Reciprocal Motion:

  • Definition: Repetitive back-and-forth or up-and-down linear motion.

  • Cycles: Two opposite motions containing a reciprocation cycle are called strokes.

  • Conversion: A crank is used to convert circular motion into reciprocating motion.

  • Examples:

    • Rack and Pinion: Used in drills to move a table up and down a central pillar.

    • Scotch Yoke: Converts linear motion into rotational motion by coupling a piston to a sliding yoke.

    • Traversing Head Shaper: Moves a cutting tool across a surface, lifting it clear on the return stroke.

    • Sewing Machines: The movement of the needle.

    • Manual Labor: The movement of a saw and a person's arm when cutting wood.

    • Power Tools: Jigsaws use reciprocating blades.

Fundamental Mechanical Concepts

• Mechanisms: A system of parts (pieces of machinery) working together inside a machine.

• Inputs and Outputs:

  • Effort ($F_E$): The force exerted on the input side of the machine.

  • Load ($F_L$): The resistance to be overcome or the force on the output side.

• Mechanical Advantage (MA):

  • A measure of force amplification.

  • Formula: $MA = \frac{\text{load}}{\text{effort}} = \frac{F_L}{F_E}$

• Velocity Ratio (VR):

  • The ratio of the distance moved by the effort point to the distance moved by the load.

  • Formula: $VR = \frac{\text{distance moved by effort}}{\text{distance moved by load}} = \frac{d_E}{d_L}$

• Efficiency ($\eta$):

  • Definition: A measure of how much work done actually moves the target compared to the multiplication of force.

  • Formula: $\eta = \frac{MA}{VR}$

  • Expressing Efficiency: Usually shown as a fraction or a percentage ($\%\eta = \frac{MA}{VR} \times 100$).

  • Perfect System: In a 100% efficient machine, $MA = VR$.

Basic Machines

• Crow Bar:

  • Classification: First-class lever.

  • Description: An iron or steel bar, often wedge-shaped at the working end.

  • Purpose: Breaking concrete, prying wooden planks, or wedging under objects to lift/move them.

• Bicycle:

  • Classification: Simple machine made of mechanisms (wheels, gears, chains, crank shafts, bearings).

  • Description: Human-powered land vehicle with two wheels and pedals connected to cogs by a chain.

  • Purpose: Transportation, fitness, and recreation.

• Car Jack:

  • Classification: Simple machine used for lifting.

  • Description: A metal tool (often stored in a car boot) used as a screw-based lifting device.

  • Purpose: Raising a car to perform repairs or change tires.

Levers

Levers utilize a fulcrum (pivot point). Moments about the fulcrum determine the required effort or liftable load.

• Law of Levers: $\sum M_{\text{fulcrum}} = F_E l_E + F_L l_L = 0$. Assuming 100% efficiency, this is simplified to: $F_E l_E = F_L l_L$

• Lever MA Formula: $MA = \frac{F_L}{F_E} = \frac{l_E}{l_L}$

  • $l_E$: Length of the effort arm.

  • $l_L$: Length of the load arm.

• First-Order Levers (Type 1):

  • The fulcrum is located between the effort and the load.

  • If l_E > l_L, then MA > 1.

  • If l_L > l_E, then MA < 1 (mechanical disadvantage).

• Second-Order Levers (Type 2):

  • The load is between the effort and the fulcrum.

  • Effort always moves further than the load (l_E > l_L).

  • Mechanical advantage is always greater than 1 (MA > 1).

• Third-Order Levers (Type 3):

  • The effort is between the load and the fulcrum.

  • Load always moves further than the effort (l_L > l_E).

  • Mechanical advantage is always less than 1 (MA < 1).

Pulley Systems

• Definition: A wheel on an axle/shaft designed to support cable/belt movement, change direction, or transfer power.

• Fixed Pulley:

  • Attached to a rigid support.

  • Changes the direction of the effort but provides no mechanical advantage ($MA = 1$).

  • Example: Raising a bucket from a well.

• Moving Pulley:

  • One end of the cable is stationary; the load is attached to the pulley axis.

  • The effort required to hold the load is halved ($MA = 2$).

• Simple Pulley Systems:

  • Combinations of fixed and moving pulleys using a single rope.

  • Velocity Ratio ($VR$) for simple pulleys: Equal to the number of rope sections ($n$) directly supporting/lifting the load.

  • Formula: $VR = n$.

  • Formula for MA: $MA = \eta \times VR = \eta \times n$.

  • Friction: Axis rotation and cable-to-roller friction reduce efficiency, typically to the range of 80-95%.

• Compound Pulley Systems:

  • Involves two or more pulleys and more than one rope.

  • The VR calculation for compound systems with multiple ropes is different and not covered in this specific course.

• Conservation of Energy: The trade-off for high MA is that the effort must move a much larger distance than the load ($d_E = n \times d_L$). Energy is conserved.

Inclined Planes and Screws

• Inclined Plane (Ramp):

  • A device where the vertical distance moved by the load ($h$) is smaller than the distance moved by the effort ($l$).

  • Velocity Ratio: $VR = \frac{\text{distance moved by effort}}{\text{vertical distance moved by load}} = \frac{l}{h}$.

  • Calculations: If efficiency ($\eta$) is known, $MA = \eta \times VR$. To find effort, use $F_E = \frac{F_L}{MA}$.

• Screw:

  • A modified inclined plane wrapped around a shaft.

  • Pitch: The vertical distance between threads.

  • Distance of Effort ($d_E$): The circumference of the circle described by the effort application point (e.g., the handle of a wrench).

  • Velocity Ratio: $VR = \frac{2\pi r}{\text{pitch}}$.

  • Torque: Using a longer handle (increasing $r$) increases the rotational distance and torque, thereby increasing VR and MA.

Gears

• Definition: Mechanisms that mesh via teeth to transmit rotary motion between shafts.

• Key Measurements:

  • Root Radius (Minor Radius): Centre to the base of the teeth.

  • Pitch Radius (Addendum Radius): Centre to the outside of the teeth.

  • Pitch: Distance between equivalent points of adjacent teeth; must be identical for gears to mesh.

• Gear Terminology:

  • Driver Gear: The source of power/effort.

  • Driven Gear: The output gear turned by the driver.

• Types of Gears:

  • Spur Gears: Parallel shafts, straight teeth. Transfer power but reverse motion direction.

  • Idler Gears: Placed between driver and driven gears. They do not change VR but ensure the driver and driven gear rotate in the same direction.

  • Rack and Pinion: Pinion (circular) engages the rack (linear) to translate rotary motion into linear motion. Used in steering and lifting.

  • Worm Gears: Worm and gear (worm wheel) at 90 degrees. High reduction ratios in small spaces. They cannot be run in reverse due to high friction.

  • Worm Gear VR: $VR = \frac{\text{Number of teeth on worm wheel}}{\text{Number of threads on worm}}$.

• Velocity Ratio (Gear Ratio):

  • Formula: $VR = \frac{\text{Number of teeth on driven}}{\text{Number of teeth on driver}} = \frac{\text{Diameter driven}}{\text{Diameter driver}} = \frac{\text{Rotational speed driver}}{\text{Rotational speed driven}}$.

• Mechanical Advantage of Gears:

  • Formula: $MA = \frac{F_L}{F_E} = \frac{\text{torque}_{\text{driven}}}{\text{torque}_{\text{driver}}}$.

  • Trade-off: High MA (driven gear larger than driver) produces more torque but lower output velocity.