MECHANISMS AND ITS INVERSION

1. UNITI MECHANISMS
Definition – Machine and Structure – Kinematic link, pair and
chain – classification of Kinematic pairs – Constraint & motion
– Degrees of freedom - Slider crank – single and double –
Crank rocker mechanisms – Inversions, applications –
Introduction to Kinematic analysis and synthesis of simple
mechanisms – Determination of velocity and acceleration of
simple mechanisms.

2. Problem - 1
•The crank of a slider crank mechanism rotates
clockwise at a constant speed of 300 rpm. The
crank is 150 mm and the connecting rod is 600
mm long. Determine the linear velocity of the
mid point of the connecting rod and angular
velocity of the connecting rod at a crank angle of
45° from inner dead centre position.

3. Space Diagram

4. Velocity Diagram
𝜔𝐵𝑂 =
2𝜋300
60
= 31.42 𝑟𝑎𝑑/𝑠
𝑣𝐴𝑂 = 𝑜𝑎 = 4.02 𝑚/𝑠
𝑣𝐷𝑂 = 𝑑𝑜 = 4.05 𝑚/𝑠

5. Problem - 2
• The dimensions and configuration of the four bar
mechanism shown in figure are as follows: P1A = 300
mm, P2B = 360 mm, AB = 360 mm and P1P2 = 600 mm.
The angle AP1P2 = 60°. The crank P1A has an angular
velocity of 10 rad/sec clockwise. Determine the
angular velocities of P2B, and AB and the velocity of
the point B.

6. Space Diagram

7. Velocity Diagram
𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑃2𝐵, 𝜔𝑃2𝐵 =
𝑣𝐵
𝑃2𝐵
= 6.11 𝑟𝑎𝑑/𝑠 (𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒)
𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝐴𝐵, 𝜔𝐴𝐵 =
𝑣𝐵𝐴
𝐴𝐵
= 6.028 𝑟𝑎𝑑/𝑠 (𝑎𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒)

8. Problem - 3
• In a toggle mechanism shown in figure, the slider D is
constrained to move on a horizontal path. The crank
OA rotates in the counter clockwise direction at a
speed of 180 rpm. The dimensions of the various links
are as follows: OA = 180 mm, CB = 240 mm, AB = 360
mm and BD = 540 mm. For the given configuration,
find velocity of slider D and angular velocity of BD
using relative velocity method.

9. Space Diagram

10. Velocity Diagram
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑣𝐴𝑂 = 𝑣𝐴 = 3.4 𝑚/𝑠
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑣𝐷𝐵 = 𝑣𝑒𝑐𝑡𝑜𝑟 𝑏𝑑 = 2.38 𝑚/𝑠
𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑣𝐷 = 𝑣𝑒𝑐𝑡𝑜𝑟 𝑐𝑑 = 2.012 𝑚/𝑠
𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝜔𝐵𝐷 =
𝑣𝐷𝐵
𝐵𝐷
= 4.408 𝑟𝑎𝑑/𝑠

11. Inversions of Mechanisms
• A mechanism is formed by fixing one of the links of a
chain.
• When different links of the same chain are chosen to
become frame-link, different mechanism will arise
• This process is known as kinematic inversion

12. Properties of Inversion
• Number of inversions possible for a kinematic chain
equals the number of links in the parent kinematic
chain
• Relative motions between any two links does not
change with inversions
• Absolute motion of points on various links may
however change drastically from one inversion to the
other

13. Types of kinematic chains
•The following three types of kinematic chains
with four lower pairs are important from the
subject point of view :
•Four bar chain or quadric cyclic chain,
•Single slider crank chain, and
•Double slider crank chain.

14. Four bar mechanism
• According to Grashof ’s law
for a four bar mechanism,
the sum of the shortest and
longest link lengths should
not be greater than the sum
of the remaining two link
lengths if there is to be
continuous relative motion
between the two links.

15. Inversions of Four bar mechanisms

16. Inversion of Four bar mechanism
• Crank – Crank or Double
Crank Mechanism
• Crank – Lever (Rocker)
Mechanism
• Rocker – Rocker or
Double Rocker
Mechanism

17. Crank – Rocker Mechanism
• Beam engine

18. Double Crank Mechanism
• Coupling rod of a locomotive

19. Double Lever Mechanism
• Watt’s Indicator Mechanism

20. Inversions of Slider Crank Mechanism
• It has four binary links, three
revolute pairs, one prismatic
pair
• By fixing links 1, 2, 3 in turn
we get various inversions