Untitled Quiz

Theory of Machines Module 1

• Mechanics of Machines: A branch of engineering dealing with relative motion and forces between machine elements.
• Classification of Mechanics: Two main categories are:
  • Statics: Analyzing forces and their effects on stationary machine parts.
  • Dynamics: Analyzing forces and their effects on moving machine components. Further divided into:
    • Kinematics: Studying relative motion without considering forces.
    • Kinetics: Studying forces due to mass and motion of machine elements.
• Mechanism: A combination of interconnected bodies where the motion of one body determines constrained motion in other bodies. Examples: typewriters, automobile wiper mechanisms.
• Machine: A mechanism that transmits and modifies available energy into useful work. Examples: Internal combustion engines, automobiles, lathes.
• Structure: An assemblage of resistant bodies with no relative motion, designed to carry loads with straining action. Examples: railway bridges, roof trusses, machine frames.
• Difference between Machine and Structure:
  • Machine parts move relative to each other, structure members do not move relative to each other.
  • Machines transform energy into useful work, structures do not transform energy.
  • Machine links transmit power and motion; structure members transmit forces only.
• Comparison between Mechanism, Machine & Structure:
  • Mechanisms have relative motion between parts. Machines modify energy and perform work. Structures have no relative motion between members and transmit forces only.
• Kinematic Link or Element: A part of a machine that has relative motion with another part and is a resistant body. Resistant bodies transmit forces without significant deformation.
  • Characteristics: Must have relative motion and be a resistant body.
• Classification of Links: Categorized based on the number of joints.
  • Singular Link: Connected to only one other link.
  • Binary Link: Connected to two other links.
  • Ternary Link: Connected to three other links.
• Classification of Links (Driver & Follower to Transmit Motion):
  • Rigid Link: A rigid link does not deform during motion transmission.
  • Flexible Link: A flexible link can deform without affecting motion transmission (belts, ropes, chains).
  • Fluid Link: Energy is transferred through fluid pressure or compression.
• Types of Constraint Motion:
  • Completely constrained motion: Motion limited to a definite direction regardless of force direction. Example: piston and cylinder.
  • Incompletely constrained motion: Motion possible along more than one direction, the direction may change with applied force. Example: shaft in a circular hole.
  • Successfully constrained motion: Motion occurs only if another force constrains is applied elsewhere on the parts. Example: load on a shaft preventing its movement.
• Kinematic Pairs: Connecting elements resulting in relative motion. If relative motion is completely constrained, they're kinematic pairs.
  • Different types of kinematic pairs (according to relative motion):
    • Prismatic pair (sliding pair): Elements can only slide longitudinally. Also has completely constrained motion. Examples: piston and cylinder, guides.
    • Revolute/turning pair: Rotation around a fixed axis only (turn/revolve). Example: Shaft with collars, crankshaft. Also has completely constrained motion
    • Rolling pair: Two members roll over each other. Example: Ball & roller bearings.
    • Screw pair: One member turns around the axis imposed by the other member (through screw threads). Example: lead screw, bolt & nut.
    • Spherical pair: One element swivels freely about the center of the other fixed element. Examples: Ball and socket joint, car mirror mount.
  • Lower pairs (surface contact when moving): Sliding, turning, screw pairs.
  • Higher pairs (point or line contact when moving): Friction discs, gears.
• Self-closed pair: mechanically connected allowing desired motion.
• Force-closed pair: mechanically separate but kept together by external forces.
• Kinematic Chain: Coupling of kinematic pairs where the last link is connected to the first. Forming a closed kinematic chain: required motion is completely constrained.
• Reciprocating Engine: Example of a kinematic chain. Includes crankshaft, connecting rod, piston, and cylinders.
• Conditions of Kinematic Chain: 1=2p-4 and j=((l-1)*3)/2

• Types of Joints (Binary or Ternary): Relations between link numbers/binary/ternary joints to determine chain nature (locked or kinematic).

  • Binary Joint: Connection between two links.
  • Ternary Joint: Connection between three links (considered equivalent to two binary joints).
  • Quaternary Joint: Connection between four links (considered equivalent to three binary joints).

• Mechanism: A mechanism with a fixed link in a kinematic chain used to transmit or transform motion.

  • Simple (Four links): Four bar mechanism
  • Compound (More than four links)

• Four Bar Mechanism: Four links connected by turning pairs (A, B, C, D).

  • Grashof's Law: Sum of shortest & longest link length ≤ sum of other two links for continuous relative motion. Shortest + Longest < or = remaining 2 links

• Important Concepts in Link Mechanisms:

  • Crank: Link that rotates relative to the frame.
  • Rocker: Link that oscillates relative to the frame.
  • Coupler: Link that connects the crank and rocker.
  • Frame: Fixed link in the mechanism.

• Possible Combinations of 4-Bar Mechanisms:

  • Crank-Rocker: Short link rotating, long link oscillating.
  • Double-Crank: Both short links rotating.
  • Double-Rocker: Both short links oscillating.

• Kinematic Diagrams: Diagrams showing link connectivity without dimensions for visualizing mechanism.

• Degree of Freedom (DOF): Number of independent coordinates required to define the position.

• Mobility of Mechanisms: The number of independent motions a mechanism can have.

• Kutzbach Criterion: For planar mechanisms, n = 3(L - 1)- 2J1 - J2-Fr Where:

• L = Total links

• J1 = One degree of freedom joints (pins,slider)

• J2 = Two degree of freedom joints (higher pairs)

• Fr = Degrees of redundancy (extra degrees of freedom)

• Grubler's Criterion: A method for analyzing the degrees of freedom when the mechanism only has single degrees of freedom joints and the overall movability is unity DOF = 3 (L - 1) - 2 J1 - J2

• Special Cases - Redundant DOF: If a mechanism has more constraints than the theoretical minimum, and particular links can move without the rest of the mechanism changing motion.

• Steering Gear Mechanisms:

  • Ackerman: Simpler mechanism (turning pairs), front wheels turn about same instantaneous center.
  • Davis: More complex mechanism (sliding pairs), correct steering at all angles (higher wear).

• Inversions of Mechanisms: Obtaining different mechanisms from the same kinematic chain by fixing different links in turn.

• Straight-Line Motion Mechanisms: (Mechanisms creating linear motion)

  • Peaucellier: Creates exact straight-line motion
  • Hart: Exact straight-line motion.
  • Scott Russel: Exact and specific straight-line motion.

• Approximate Straight-Line Motion Mechanisms: (Giving more or less straight motion)

  • Watt's: Approximate straight-line motion.
  • Modified Scott-Russell: Approximate straight-line motion.
  • Grasshopper: Designed to give a long stroke with a short crank.

• Coupler Curve: The path traced by a point on a coupler link during the motion of the mechanism.

• Transmission Angle: The angle between the output link and the coupler link.

• Mechanical Advantage: Ratio of output force to input force

• Double Slider Crank Chain - Double crank and double slider.