Mechanical Fundamentals and Simple Machines

Course Overview

  • Course Name: Mechanical Maintenance I

  • Subject: Mechanical Fundamentals and Simple Machines

  • Institution: Brightpoint Community College

  • Department: Mechanical Engineering Department

  • Course Duration: Fall 2025

Agenda

  1. Mechanical Concepts

    • Force

    • Torque

    • Pressure

    • Motion

  2. Newton's Laws

    • First Law

    • Second Law

    • Third Law

  3. Work and Energy

  4. Simple Mechanical Machines

Mechanical Concepts

Force

  • Definition:

    • A force is something that changes or tends to change the state of rest or motion of a body.

  • Newton’s Second Law:

    • Mathematically defined as F = m imes a where

    • F = force

    • m = mass

    • a = acceleration

  • Units of Measurement:

    • Force is measured in Newtons (N) or pounds-force (lbf).

  • Gravitational Force:

    • For falling objects: F = mg where g = 9.81 ext{ m/s}^2 (or g = 32.2 ext{ ft/s}^2).

Job Examples of Force

  • Applications:

    • Wrench applying torque to a bolt

    • Crane lifting HVAC unit

    • Hydraulic press forming metal

Force Vectors

  • Direction and Magnitude:

    • Forces have both direction and magnitude.

    • Force vectors mathematically represent force accounting for both aspects, essential in applications:

    • Crane operations: Resultant forces from multiple cables.

    • Structural support: Analyzing load distribution.

    • Belt/chain systems: Tension forces at angles.

Adding Forces

  • Same Direction:

    • Total Force: F1 + F2 = ext{Total Force}

  • Opposite Directions:

    • Net Force: F1 - F2

  • At Angles:

    • Use vector addition.

    • Example Scenario: Two technicians pulling a motor:

    • Technician A: 150 lbs east

    • Technician B: 100 lbs east

    • Total force calculation and variation when direction is reversed.

Resolving Forces into Components

  • Understanding Angled Forces:

    • In real-world applications, single forces act at angles rather than perfectly aligned.

  • Components:

    • If F is the force and heta the angle (from the horizontal),

    • Horizontal component: F_x = F imes ext{cos}( heta)

    • Vertical component: F_y = F imes ext{sin}( heta)

The Unit Circle

  • Description:

    • A Unit Circle is one with a radius of 1 and diameter of 2.

  • Quadrant Sign Representation of Coordinates:

    • Quadrant I: (+, +)

    • Quadrant II: (-, +)

    • Quadrant III: (-, -)

    • Quadrant IV: (+, -)

Angles, Sine, and Cosine

  • Definition of Angles:

    • Defining angle heta between the positive x-axis and radius.

  • Components of the Angle:

    • Length of horizontal line: distance along x-axis

    • Length of vertical line: distance along y-axis

Sine and Cosine Relationships

  • Cosine (Cos):

    • ext{Cos}( heta) = rac{x}{r}

  • Sine (Sin):

    • ext{Sin}( heta) = rac{y}{r}

Coordinate Relationships

  • Opposite and Adjacent Definitions:

    • ext{Sin}( heta) = rac{ ext{Opposite}}{ ext{Hypotenuse}}

    • ext{Cos}( heta) = rac{ ext{Adjacent}}{ ext{Hypotenuse}}

Measuring Forces

Equipment & Applications

  • Tools:

    • Spring scales: Measure cable and belt tension.

    • Load cells: Measure crane capacity, structural loading.

    • Force gauges: Used for quality control, material testing.

Force Assessment and Problems

  • Name three tools for measuring force.

  • Importance of direction in equipment installation and effect of misalignment.

    • Misaligned forces can lead to uneven loading, wear, unsafe conditions, and failure

  • Basic Calculations:

    • Example problem calculating net force with given directional forces.

    • Example of force calculations, including conversions from lbf to Newtons.

Torque

  • Definition:

    • Torque is generated by a force acting on a point of rotation at a perpendicular distance.

  • Units of Measurement:

    • Measured in Newton-meters (Nm) or foot-pounds (ft-lbf).

  • Equation:

    • Mathematically represented as T = F imes r where

    • T = torque

    • F = force applied

    • r = distance from the point of rotation.

Measuring Torque

Tools Used

  • Torque Wrenches:

    • Used for precise screw and bolt specifications (in ft-lbs).

Pressure

Definition

  • Pressure is defined as force per unit area.

  • Example: A piston is used to illustrate the conversion between pressure and force.

Units of Measurement

  • Pressure is measured in Pascals (Pa) or pounds-per-square-inch (psi).

  • At Sea-level Atmospheric Pressure:

    • 1 ext{ atm} = 14.7 ext{ psi} = 101.325 ext{ kPa}.

  • Relation:

    • P = rac{F}{A}

Types of Motion

Four Key Types

  1. Linear Motion:

    • Examples: Conveyor belts, hydraulic cylinders, elevators.

  2. Rotational Motion:

    • Examples: Motors, fans, pump impellers.

  3. Oscillating Motion:

    • Examples: Reciprocating compressors, vibrating screens.

  4. Complex Motion:

    • Examples: Robotic arms, crane operations.

Describing Motion

Speed vs Velocity

  • Speed:

    • Measured in units like 60 mph, 1800 RPM.

  • Velocity:

    • Speed with direction (e.g., 60 mph north).

  • Acceleration:

    • Defined as change in velocity over time.

Acceleration

Definition

  • a = rac{v2 - v1}{t}

Critical Applications

  • Elevator safety, motor starting, conveyor loading impacts.

Newton's Laws

First Law (Law of Inertia)

  • “Objects at rest stay at rest, and objects in motion stay in motion unless acted upon by an unbalanced force.”

Second Law

  • Fundamental Formula:

    • F = m imes a

  • Units in pounds and slugs or Newtons and kilograms.

  • Rule of Thumb:

    • Applications and calculations assessing force needed for specific inertia scenarios.

Third Law

  • “For every action, there is an equal and opposite reaction.”

  • Illustrated with examples in various equipment operations.

Work and Energy

Definition of Work

  • Work is defined as the product of force and the distance over which it acts.

  • W = Fd

Energy Forms

  • Kinetic, Potential, Thermal, Chemical, Nuclear, Electrical, Electromagnetic energy.

Conservation of Energy

  • Total mechanical energy remains constant ignoring external factors like air resistance.

Examples of Energy Calculations

  • Work done against gravity leads to potential energy gain described mathematically as PE = mgh for lifting.

  • Kinetic Energy Equation:

    • KE = rac{1}{2} mv^2

  • Investigating energy transfers and conversions in mechanical systems.

Simple Machines

Overview of the Big Six Simple Machines

  1. Lever: e.g., wrenches, crowbars, bolt cutters

  2. Pulley: e.g., cranes, hoists, flagpoles

  3. Wedge: e.g., chisels, axes

  4. Wheel & Axle: e.g., steering wheels, winches

  5. Inclined Plane: e.g., ramps, screws

  6. Screw: e.g., jacks, clamps

Mechanical Advantage (MA)

  • Definition: How much a machine multiplies input force.

  • Formula:

    • MA = rac{ ext{Output Force}}{ ext{Input Force}}

    • MA = rac{ ext{Input Distance}}{ ext{Output Distance}}

Lever Classifications

  • Class 1: Fulcrum in the middle (e.g., crowbars).

  • Class 2: Load in the middle (e.g., wheelbarrows).

  • Class 3: Effort in the middle (e.g., tweezers).

Pulley Systems

Force and Distance Trade-offs

  • Types: Fixed, Movable, Compound.

  • Key Relationships:

    • Input force calculation and distance increases based on MA.

Inclined Planes & Screws

  • General applications and their respective advantages.

Wheel & Axle Systems

  • Applications: Steering wheels, winches - mathematical illustrations of mechanical advantage.

Practice Problems

  • Numerous calculations for forces, work, and energy scenarios across various mechanical concepts.

  • Real-world applications integrated with uniform problem-solving.

Exam Announcement

  • Coverage: Weeks 1 to 6

  • Format: Theoretical (Multiple choice, Computation, and descriptive questions) and Practical (Hands-on labs).

  • Further information to be posted by the following week.