Kinematic Inversions of 4-bar chain and slider crank chains:
· Types of Kinematic Chain: 1) Four bar chain 2) Single slider chain 3) Double Slider chain
· Four bar Chain:
The chain has four links and it looks like a cycle frame and hence it is also called quadric cycle chain. It is shown in the figure. In this type of chain all four pairs will be turning pairs.
By fixing each link at a time we get as many mechanisms as the number of links, then each mechanism is called ‘Inversion’ of the original Kinematic Chain.
Inversions of four bar chain mechanism:
There are three inversions: 1) Beam Engine or Crank and lever mechanism. 2) Coupling rod of locomotive or double crank mechanism. 3) Watt’s straight line mechanism or double lever mechanism.
· Beam Engine:
When the crank AB rotates about A, the link CE pivoted at D makes vertical reciprocating motion at end E. This is used to convert rotary motion to reciprocating motion and vice versa. It is also known as Crank and lever mechanism. This mechanism is shown in the figure below.
2. Coupling rod of locomotive: In this mechanism the length of link AD = length of link C. Also length of link AB = length of link CD. When AB rotates about A, the crank DC rotates about D. this mechanism is used for coupling locomotive wheels. Since links AB and CD work as cranks, this mechanism is also known as double crank mechanism. This is shown in the figure below.
3. Watt’s straight line mechanism or Double lever mechanism: In this mechanism, the links AB & DE act as levers at the ends A & E of these levers are fixed. The AB & DE are parallel in the mean position of the mechanism and coupling rod BD is perpendicular to the levers AB & DE. On any small displacement of the mechanism the tracing point ‘C’ traces the shape of number ‘8’, a portion of which will be approximately straight. Hence this is also an example for the approximate straight line mechanism. This mechanism is shown below.
· 2. Slider crank Chain:
It is a four bar chain having one sliding pair and three turning pairs. It is shown in the figure below the purpose of this mechanism is to convert rotary motion to reciprocating motion and vice versa. Inversions of a Slider crank chain:
There are four inversions in a single slider chain mechanism. They are:
· 1. Reciprocating engine mechanism :
In the first inversion, the link 1 i.e., the cylinder and the frame is kept fixed. The fig below shows a reciprocating engine.
A slotted link 1 is fixed. When the crank 2 rotates about O, the sliding piston 4 reciprocates in the slotted link 1. This mechanism is used in steam engine, pumps, compressors, I.C. engines, etc.
· 2. Crank and slotted lever mechanism:
It is an application of second inversion. The crank and slotted lever mechanism is shown in figure below.
In this mechanism link 3 is fixed. The slider (link 1) reciprocates in oscillating slotted lever (link 4) and crank (link 2) rotates. Link 5 connects link 4 to the ram (link 6). The ram with the cutting tool reciprocates perpendicular to the fixed link 3. The ram with the tool reverses its direction of motion when link 2 is perpendicular to link 4. Thus the cutting stroke is executed during the rotation of the crank through angle α and the return stroke is executed when the crank rotates through angle β or 360 – α. Therefore, when the crank rotates uniformly, we get
This mechanism is used in shaping machines, slotting machines and in rotary engines.