Kinematic Analysis Of a Mechanism
Brief introduction about mechanisms
According to engineering, Mechanism is a thing which converts one/set of inputs into one/set of outputs, which can do a effective task. Forces, movements, motions are the most common types of inputs and output types in these mechanisms. To do these conversions moving parts / components are used in these mechanisms. Followings are some examples for moving parts/ components in mechanisms.
- Linkage
- Cam and followers
- Gear trains
- Belts
- Friction devices
Power can be defined by combination of forces and movements. In mechanisms there is a method to gain the forces and movements, which we need as output, by managing power effectively. Commonly machine is known as a set of multiple mechanism. But sometimes an entire machine is considered as a mechanism. Examples:
➢ Steering mechanisms
➢ Winding mechanisms etc.Now let us consider about the examples of mechanisms. In below some examples of mechanisms are mentioned.
- Differential in vehicles-gear trains mechanism
- Double wishbone suspension in chassis-linkage (four bar) mechanism
- Wall clocks-cam and follower
Description about two possible applications of four bar linkage mechanisms
Usage1: Oil Pumps
In above images figure of oil pumps are shown. In second image it is clearly shown the four bars of the oil pump by naming those bars as “A-B-C-D”. In this case CD bar is the input link. AD is the coupler link. AB is the output link. BC is the fixed link. This mechanism is activated by rotating CD bar around fixed point C.
Usage 2: Bicycle Riding
In this image it is shown that a man who rides a bicycle. But we cannot see four bar linkage in this mechanism explicitly. But if we see the naming “A-B-C-D” we can see a four-bar linkage mechanism in this figure. In here AB shows the input link. AD shows the coupler link. DC shows the output link. BC shows the fixed link. This mechanism is activated by rotating AB bar around fixed point B.
Effectiveness of four bar linkage mechanism, in terms of mechanical efficiency
We know that in mechanical engineering many mechanisms are used but among those mechanism linkage mechanism is the one of the prior mechanisms. When we considering mechanical efficiency of linkage mechanism with gears trains, it is clear that in some points gear is effective than linkages. Some of them are,
- By using gear train, we can form large velocity in minimum space.
- Long life and mechanically strong.
- Maintaining is easy.
But in some cases, linkage is effective than gears. Some of them are,
- Gears do noisy operations.
- Gears are not flexible.
- Gears cannot do transition over long distances.
When we considering mechanical efficiency of linkage mechanism with cam and follower, in some cases linkage is less effective.
- Power reduction due to friction is low.
- Any desired motion program can be exactly reproduced by cam
In some cases, like below, linkage is more effective,
- Cam and followers can have high noise.
- Cam and followers are expense to manufacture.
- Cam and followers are relatively low high-speed capability.
Discussing two important mechanisms with applications
1: Cam and followers
This is also known as “track follower”. A cam is a rotating part in a linkage which drives a mating component known as a follower. In here follower is the driven member. In this mechanism cam gets the input and follower gives the output. Usually cam do a rotational motion while follower do a translational motion.
There are various types of cams are used in present as expected outputs and given inputs are varying. Some of the cam types are mentioned in below.
- Plate or Disk Cams: This is the simplest and common types. This is show in above figure This is formed on a disk or plate
- Cylindrical or Drum Cams: This is shown in above. This is formed on a cylinder.
- Linear Cam: This is show in above figure. This is formed on a translated block.
We can also divide followers into many types. Those types are mentioned below.
1.In-line, knife edge followers.
2.Pivoted, roller followers.
3.Offset, flat-face follower.
4.Pivoted, spherical-face follower.APPLICATIONS
- In paper cutting machine / Cutting machine
In this cutting machine it is used two cams and followers. The cam ‘A’ is input, and output of the follower related to cam ‘A’ do cutting. The cam ‘B’ is also input and output of the follower related to cam ‘B’ do placing cut items.
2. Shaft in Engines
In this case cams is used to move the push rod, which acts as the follower.
In here we can see cam is used to do a movement / push the rod with cam’s frequency. By this mechanism rotational motion has converted to transnational motion.
3. Textile industry (Weaving Machines)
2: Gear Trains
This mechanism is designed to ensure the pitch circles of engaging gear rolls on each other without slipping, providing a smooth transmission of rotation from one gear to the next.
In other words, more than one gear is arranged for transmitting torque or power from one system to another system then the arrangement is called a gear train.
- In here, rotational motion input gives a rotational motion output as the result.
- teeth are used to avoid slipping.
Types of Gear Trains
- Simple Gear Train: in this type only a pair of gear is engaged with each other.
- Compound Gear Train: more than one gear is fixed to one shaft for the compound gear train.
- Reverted Gear Train: compound gear trains, where the input shaft and output shaft are collinear to each other.
- Variable Gear Train: Variable gear train is a compound gear train, which has variable reduction ratio.
- Sun and Planet Gear Trains: Different gears are arranged in a cyclic manner instead of the linear manner.
APPLICATIONS
- Gear Box of Automobiles
In here a set of gears enclosed in a box. Gear box is used to maintain engine speed at all conditions of load and vehicle speeds. In here speed is controlled by using gears which has different ratios.
2. Differential in Vehicles
When a vehicle goes on a curve. It is necessary to rotate two wheels in two corners in different speeds. To this we must divide power to those wheels in different ratios. To this engineers use a mechanism called ‘Differential’ in automobile engineering.
To do this task, engineers mainly use gear trains in differential.Discussing the mobility of linkage systems
• Mobility of a linkage is related to its degrees of freedom.• Mobility is related to Degree of freedom• Depend on the number of independent parameters• To calculate the mobility of a planar mechanismGruebler’s equation
F=3(N-1)-2L-H
N=number of kinematic elements
L=number of lower pairs
H=number of higher pairs
MOBILITY OF DIFFERENT KIND OF LINKAGES
kinematic chain needs at least one link to be fixed in order to facilitate relative motion of other links. When we choose different link as fixed, each time we get different characteristic of motions. Same arrangement of links with a different frame has a different path of motion.
WE USE GRASHOF CRITERIA TO STUDY MOTION OF FOUR-BAR-LINKAGE
Four Bar Linkage Analysis with Grashof’s Criteria
Grashof’s theorem tells that a four-bar linkage always has the smallest link as revolving link. When,
s=shortest link
l=longest link
p, q =intermediate links
s + l ≤ p + q happens
Three types of motion can be identified:
- Crank Rocker Mechanism-where s Is the input link
- Double Crank Mechanism-where s is the fixed link
- Double Rocker Mechanism-where s is the coupler link
However, when s + l > p + q:
All three moving links do rocking motion.
