Theory of Machines
What is Theory of Machines?
An assembly of links and joints designed to transmit motion and power.
Key formula / rule: Degrees of Freedom (Planar Mechanism)
Key points
- Analyze the motion of machine parts.
- Determine the forces acting on machine components.
- Understand the principles of vibration and balancing.
- Design and analyze common machine elements like gears and cams.
Common exam trap
Confusing kinematics with dynamics.
Definitions
- Term
Mechanism
- Meaning
An assembly of links and joints designed to transmit motion and power.
- Term
Kinematics
- Meaning
The study of motion of machine parts without considering the forces that cause the motion.
- Term
Dynamics
- Meaning
The study of motion of machine parts considering the forces that cause the motion.
- Term
Degrees of Freedom (DOF)
- Meaning
The minimum number of independent parameters required to completely define the position and configuration of a mechanism.
- Term
Balancing
- Meaning
The process of designing machine parts such that the resultant forces and moments due to inertia are zero, ensuring smooth operation.
Learning objectives
Analyze the motion of machine parts.
Determine the forces acting on machine components.
Understand the principles of vibration and balancing.
Design and analyze common machine elements like gears and cams.
Apply kinematic and dynamic analysis to solve practical engineering problems.
Formulae
- Name
Degrees of Freedom (Planar Mechanism)
- Note
l = number of links, j = number of joints. Assumes simple joints.
- Expression
DOF = 3(l-1) - 2j
- Name
Velocity Ratio (Gears)
- Note
N = speed, T = number of teeth. For simple gears.
- Expression
N1/N2 = T2/T1
- Name
Centrifugal Force (Balancing)
- Note
m = mass, ω = angular velocity, r = radius of rotation.
- Expression
Fc = mω²r
- Name
Condition for Primary Balancing
- Note
For balancing of reciprocating masses.
- Expression
Σmi ri cos(θi) = 0 and Σmi ri sin(θi) = 0
- Name
Condition for Secondary Balancing
- Note
For balancing of reciprocating masses.
- Expression
Σmi ri cos(2θi) = 0 and Σmi ri sin(2θi) = 0
Prerequisites
Engineering Mechanics (Statics and Dynamics)
Basic concepts of Calculus and Differential Equations
Understanding of Forces, Moments, and Equilibrium
Common mistakes
Confusing kinematics with dynamics.
Incorrectly applying Gruebler's criterion, especially for spatial mechanisms.
Overlooking the effect of inertia in dynamic analysis.
Misinterpreting velocity and acceleration diagrams.
Errors in calculating forces in mechanisms, especially with friction.
Keywords
Mechanism
Kinematics
Dynamics
Degrees of Freedom
Gruebler's Criterion
Vibration
Balancing
Gears
Cams
Linkages
Inertia
Practice preview
Which of the following best defines a kinematic pair?…
easy
What is the primary function of a gear train in a machine?…
easy
Which of the following mechanisms is an inversion of the single slider-crank chain?…
medium