5. According to the type of relative
motion between the elements
• Sliding pair
• Turning pair
• Cylindrical pair
• Rolling pair
• Spherical pair
• Helical pair or screw pair
6. According to the type of relative
motion between the elements
(a) Sliding pair [DOF = 1]
(b) Turning pair (revolute pair)
[DOF = 1]
7. According to the type of relative
motion between the elements
(c) Cylindrical pair [DOF = 2]
(d) Rolling pair [DOF = 1]
8. According to the type of relative
motion between the elements
(e) Spherical pair [DOF = 3]
Eg. Ball and socket joint
(f) Helical pair or screw pair
[DOF = 1]
9. According to the type of
contact between the elements
• Lower pair
• Higher pair
10. Lower pair
• The joint by which two members are
connected has surface contact.
11. Higher pair
• The contact between the pairing elements
takes place at a point or along a line.
12. According to the type of closure
(a) Self closed pair
(b) Force – closed pair
13. Kinematic Chain
• Group of links either joined together or
arranged in a manner that permits them
to move relative to one another.
14. Locked Chain or Structure
• Links connected in such a way that no
relative motion is possible.
15. Types of Joints in a Chain
• Binary joint
• Ternary joint
• Quaternary joint
16. locked / kinematic / unconstrained
chain
• In order to determine the nature of chain, i.e.
whether the chain is a locked chain (or structure)
or kinematic chain or unconstrained chain, the
following relation between the number of links
and the number of binary joints, as given by
A.W. Klein, may be used :
17.
18. Kutzbach criterion for movability
• A mechanism with l number of links connected by j number
of binary joints or lower pairs (i.e. single degree of freedom
pairs) and h number of higher pairs (i.e. two degree of
freedom pairs), then the number of degrees of freedom of a
mechanism is given by
• If there are no two degree of freedom pairs (i.e. higher
pairs), then h = 0, we have
20. Grubler’s Criterion for Plane
Mechanisms
• The Grubler’s criterion applies to mechanisms
with only single degree of freedom joints where
the overall movability of the mechanism is unity.
Substituting n = 1 and h = 0 in Kutzbach
equation, we have
21. Mechanism
• A mechanism is a constrained kinematic
chain. Motion of any one link in the
kinematic chain will give a definite and
predictable motion relative to each of the
others. Usually one of the links of the
kinematic chain is fixed in a mechanism.
22. Types of Kinematic Chains
• Four bar chain or quadric cyclic chain
• Single slider crank chain
• Double slider crank chain
23. Four bar chain or quadric cyclic chain
• AB (link 1) which is fixed is
known as frame.
• AD (link 4 ) make a complete
revolution relative to the other
three links is known as crank or
driver.
• BC (link 2) which makes a partial
rotation or oscillates is known as
lever or rocker or follower.
• CD (link 3) which connects the
crank and lever is called
connecting rod or coupler.
24.
25. Inversion of Mechanism
• A mechanism is one in which one of the
links of a kinematic chain is fixed.
Different mechanisms can be obtained by
fixing different links of the same kinematic
chain. These are called as inversions of
the mechanism.
26. Inversions of Four Bar Chain
• Beam engine
(crank and lever mechanism)
• Coupling rod of a locomotive
(Double crank mechanism)
• Watt’s indicator mechanism
(Double lever mechanism)
39. Double Slider Crank Chain
• A kinematic chain which
consists of two turning
pairs and two sliding pairs
is known as double slider
crank chain
• link 2 and link 1 form one
turning pair.
• link 2 and link 3 form the
second turning pair.
• link 3 and link 4 form one
sliding pair.
• link 1 and link 4 form the
second sliding pair.
