1) Completely Constrained Motion- when the motion between a pair is limited to a definite direction irrespective of the direction of force applied. Example- the motion of a square bar in a square hole.
2) Incompletely Constrained Motion- when the motion between a pair can take place in more than one direction. Example- a circular bar in a circular hole where the bar can either rotate or slide in the hole.
3) Successfully constrained motion- when the motion between a pair is such that the constrained motion is not completed by itself but by some other means. Example- piston reciprocating inside an engine cylinder.
KINEMATIC CHAIN-
It is defined as a combination of kinematic pairs joined in such a way that each link forms a part of two pairs and relative motion between the links is completely or successfully constrained. When any one link is fixed then the kinematic chain becomes a mechanism.
Relation between no. of pairs (p) and no. of links (l)
l= 2p – 4
Relation between no. of links (l) and no. of joints (j)
j = 3/2 l – 2
klein’s formula,
j + h/2 = 3/2 l – 2
When L.H.S > R.H.S, then the chain is locked.
When L.H.S < R.H.S, then the chain is unconstrained chain.
When L.H.S = R.H.S, then the chain is a kinematic chain.
MECHANISM-
When one of the links of a kinematic chain is fixed then the chain is called a mechanism. It transmits and modifies motion. The process of obtaining different mechanisms by fixing different links in a kinematic chain is known as inversion of the mechanism.
KINEMATIC CHAINS AND THEIR MECHANISMS-
- Four bar chain or Quadric cycle chain- It consists of four links and each of them forms a turning pair. The inversions of four bar chain mechanism,
o Crank and lever mechanism (oscillatory motion) – Here the crank is able to rotate completely but the follower can only give an oscillatory motion. Example- beam engine.
o Double crank mechanism- Here in this inversion there is a complete rotation of the crank and the follower. Example- coupling rod of a locomotive.
o Double lever mechanism- example- watt’s indicator mechanism, pantograph.
- Slider crank mechanism- It consists of three turning pairs and one sliding pair. It converts rotary motion into reciprocating motion and is found in reciprocating steam engines. The inversions of slider crank mechanism,
o 1st inversion- Example- Internal combustion engine, pump, reciprocating steam engine.
o 2nd inversion- It is obtained by keeping the connecting rod fixed. It is called as crank and slotted lever mechanism. Example- oscillating cylinder engine.
o 3rd inversion- It is obtained by keeping the crank fixed. Example- Whitworth quick return motion mechanism. This mechanism is used in shapers.
- Double slider crank chain mechanism- It consists of two sliding pairs and two turning pairs. The inversion of double slider crank chain mechanism,
· Elliptical trammels
· Scotch yoke mechanism
· Oldham’s coupling
