Why this topic is important for ECET
Kinematics is the foundation of Theory of Machines (TOM). It deals with the study of motion of parts without considering forces. In ECET exams, questions from kinematics include velocity analysis, acceleration, types of pairs and links, mechanisms. If you master this, you can easily score direct marks and also solve advanced TOM problems.
📘 Concept Notes
🔹 What is Kinematics?
- Kinematics = study of relative motion between parts of a mechanism without considering the forces.
- Example: The motion of a piston in an IC engine cylinder. We don’t worry about combustion forces here, only motion.
🔹 Important Definitions
- Link/Element:
- A rigid or resistant body that connects other parts.
- Example: Connecting rod in IC engine.
- Pair:
- Two links in contact to allow relative motion.
- Types:
- Lower Pair (surface contact) → e.g., crankshaft bearing.
- Higher Pair (point/line contact) → e.g., cam and follower, gears.
- Kinematic Chain:
- When links are joined in such a way that motion is possible.
- Example: Four-bar chain.
- Mechanism:
- A kinematic chain where one link is fixed.
- Example: Slider-crank mechanism in engines.
- Machine:
- When a mechanism is used to perform useful work.
- Example: Lathe, drilling machine.
🔹 Types of Kinematic Pairs
- Sliding Pair → Piston and cylinder.
- Turning Pair → Crank and bearing.
- Rolling Pair → Ball and roller bearings.
- Screw Pair → Bolt and nut.
- Spherical Pair → Ball and socket joint.
🔹 Gruebler’s Criterion (Mobility of Planar Mechanism)
where:
- FFF = Degrees of freedom (mobility)
- nnn = Number of links
- jjj = Number of lower pairs (revolute/slider)
- hhh = Number of higher pairs
🔹 Inversion of Mechanism
By fixing different links of a kinematic chain, different mechanisms are obtained.
- Four-bar chain inversion → Crank-rocker, drag-link, double crank, double rocker.
- Single slider-crank inversion → Reciprocating engine, Whitworth quick return, rotary engine.
🔹 Example in Daily Life
- Fan regulator mechanism → Turning pair.
- IC engine piston-crank → Slider-crank mechanism.
- Bicycle chain & sprocket → Higher pair motion.
⚙️ Formulas
- Mobility of Planar Mechanism (Gruebler’s Criterion):
Kutzbach’s Criterion (general):
where
- LLL = Number of links
- J1J_1J1 = Lower pairs
- J2J_2J2 = Higher pairs
- Number of Pairs in Kinematic Chain:
🔟 10 MCQs
Q1. Kinematics is the study of:
a) Forces and motion
b) Motion only
c) Energy and motion
d) Work and power
Q2. A slider-crank mechanism is obtained from:
a) Double slider chain
b) Four-bar chain
c) Single slider-crank chain
d) None of these
Q3. Which of the following is a higher pair?
a) Piston and cylinder
b) Cam and follower
c) Shaft in bearing
d) Nut and screw
Q4. The mobility of a four-bar chain is:
a) 0
b) 1
c) 2
d) 3
Q5. If a mechanism has 6 links, 7 revolute pairs, and no higher pairs, then its DOF is:
a) 1
b) 2
c) 3
d) 0
Q6. A crank and lever mechanism is an inversion of:
a) Four-bar chain
b) Double slider chain
c) Single slider-crank chain
d) None
Q7. The number of instantaneous centers in a mechanism with 5 links is:
a) 5
b) 10
c) 15
d) 20
Q8. Which of these is NOT a kinematic pair?
a) Ball and socket
b) Bolt and nut
c) Belt and pulley (without slip)
d) Beam and load
Q9. Gruebler’s equation is valid only for:
a) 3D mechanisms
b) 2D planar mechanisms
c) Screw mechanisms
d) None
Q10. The Whitworth quick return mechanism is obtained by inversion of:
a) Double slider chain
b) Four-bar chain
c) Single slider-crank chain
d) None
✅ Answer Key
| Q | Ans |
|---|---|
| 1 | b |
| 2 | c |
| 3 | b |
| 4 | b |
| 5 | a |
| 6 | c |
| 7 | c |
| 8 | d |
| 9 | b |
| 10 | c |
🧠 Explanations
- Q1: Kinematics = study of motion only (forces are in dynamics) → (b).
- Q2: Slider-crank = obtained from single slider-crank chain inversion → (c).
- Q3: Cam and follower have line contact = higher pair → (b).
- Q4: Four-bar chain has 1 DOF → (b).
- Q5: Using Gruebler’s equation: F=3(6−1)−2(7)=15−14=1F = 3(6-1) – 2(7) = 15 – 14 = 1F=3(6−1)−2(7)=15−14=1 → (a).
- Q6: Crank and lever is inversion of single slider-crank → (c).
- Q7: n(n−1)/2=5(4)/2=10n(n-1)/2 = 5(4)/2 = 10n(n−1)/2=5(4)/2=10 → (c).
- Q8: Beam and load is not a pair (no relative motion definition) → (d).
- Q9: Gruebler’s criterion is for planar mechanisms only → (b).
- Q10: Whitworth quick return is from single slider-crank inversion → (c).
🎯 Motivation / Why Practice Matters
Kinematics is the base of Theory of Machines.
- ECET asks both direct definitions (pairs, links, DOF) and numericals (mobility, ICs).
- By practicing daily, you build speed in formula application and accuracy in conceptual clarity.
- Remember, fast recall of definitions = easy 2–3 marks in ECET 2026.
📲 CTA
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