Mechanism and Machines

Mechanism

A mechanism is a combination of rigid or restraining bodies so shaped and connected that they move upon each other with a definite relative motion. Example: slider crank mechanism, type write.

Machine

A machine is a mechanism or a collection of mechanisms which transmits and modifies the available mechanical energy into some kind of desired work.

Kinematic Pair

According to nature of contact

1) Lower pair

A pair is said to be a lower pair when it having surface or area contact between members.

2) Higher Pair

When a pair has point or line contact between members, it is called as higher pair. e.g. cam and follower pair, gears, wheel rolling on a surface.

Wrapping Pairs comprise belts, chains, and other such devices.

According to nature of Relative motion

• Turning Pair: When one link can turn or revolve about a fixed axis of another link, the pair is known as turning pair. e.g. a shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine. A turning pair also has a completely constrained motion.
• Sliding Pair: When two links have sliding motion relative to each other, the pair is  called sliding pair. e.g. piston and cylinder, ram and its guides in shaper.
• Rolling Pair: When the link of a pair have rolling motion relative to each other. e.g. Ball and roller bearings. 
• Screw Pair: If two mating links have turning as well as sliding motion between them. e.g. lead screw, nut of lathe.
• Spherical Pair: When one link in the form of a sphere turns inside a fixed link. e.g. ball in socket.

According to mechanical constraint

• Closed Pair: When two elements of a pair are held together mechanically. e.g., all lower pair and some of higher pair.
• Open or Unclosed Pair: When two elements of a pair are not held together mechanically. e.g., cam and follower.

Types of Constrained Motions

• Completely Constrained Motion: When motion between two elements of a pair is limited to a definite(single) direction irrespective of the direction of force applied, It is known as completely constrained motion. For example, the piston and cylinder (in a steam engine) form a pair and the motion of the piston is limited to a definite direction relative to the cylinder irrespective of the direction of motion of the crank.
• Incompletely Constrained Motion: When the motion between the elements of a pair is possible more than one direction, then the motion is  called an incomplete constrained motion. e.g. cylindrical shaft in round bearing.
• Successfully Constrained Motion: When motion between the elements of a pair is possible more than one direction but made to have motion only one direction by some other means. e.g. piston reciprocating inside an engine cylinder, shaft in foot step bearing.

Kinematic Chain

A kinematic chain is a series of links connected by kinematic pairs. The chain is said to be closed chain if every link is connected to at least two other links, otherwise it is called an open chain.

Condition for kinematic chain

l = 2P - 4

where, l = Number of link

             P = Number of pair

2J = 3l - 4

where, J = Number of binary joint

l = Number of link

• If L.H.S. > R.H.S.  => Structure or frame or locked chain
• If L.H.S. = R.H.S.  => Kinematic chain or constrained chain
• If L.H.S. < R.H.S.  => Unconstrained chain

Types of Joins

• Binary Joint :  It two links are joined at the same connection.
• Ternary Joint : If three links are joined at the same connection. It can be considered as two binary joints.
• If n number of links are connect at a joint, it is equivalent to (n - 1) binary joints.

Degree of Freedom (DOF)

It is the number of independent variables that must be specified to define completely the condition of the system.

• DOF of a space Mechanism (3-D)

F = 6(L - 1) - 5P1 -4P2 -3P3 -2P4 - P5

F = Degree of freedom (DOF)

L = Total number of links

P1 = Number of pairs having one DOF

P2 = Number of pairs having two DOF

P3 = Number of pairs having three DOF

P4 = Number of pairs having four DOF

P5 = Number of pairs having five DOF

• DOF of plane (2 D) mechanism (Grabbler Criterion)

F = 3(L - 1) - 2P1 - P2

L = Total number of links

P1 = Number of pairs having one DOF

P2 = Number of pairs having two DOF

• Kutzback's Equation

F = 3(L - 1) - 2j - h

L = Total number of links

j = Number of binary joints

h = Number of higher joints

• Grubler's Equation

          For those mechanism which have single degree of freedom and zero higher pairs.

3L  - 2j - 4 = 0

Four Bar Mechanism

Grashof's theorem states that a four-bar mechanism has at least one revolving link if

and all three mobile links will rock if    s + l > p + q

Case	l+ s  vs  p + q	Shortest bar	Mechanism Type
1	<	Frame	Double Crank
2	<	Side	Rocker Crank
3	<	Coupler	Double rocker
4	=	Any	Change Point
5	>	Any	Double rocker

Mechanical Advantage

Mechanical Advantage (M.A.) = Output force or torque / Input force or torque

Power Input = Power Output
T2w2     = T4w4

• If α = 0  and 180 degree, w4 becomes zero thus MA will be infinity.
• Extreme position of linkage is known as toggle position.
• The angle β is called the "transmission angle"