1. Mechanism & Synthesis Mechanisms & synthesis
In kinematic analysis, a given mechanism is investigated based on the mechanism geometry plus other known characteristics (such as input angular velocity, angular acceleration, etc.). Kinematic synthesis, on the other hand, is the process of designing a mechanism to accomplish a desired task. Both choosing the types as well as the dimensions of the new mechanism can be part of kinematic synthesis

2. Mechanism & Synthesis
If one of the links of the kinematic chain is fixed , then it forms a mechanism.
Mechanism is used to transmit rotary or reciprocatory motion.
Mechanism with four links is known as simple mechanism and with more than four links is called compound mechanism.
When a mechanism is designed to produce power or do some work then it a machine.

3. Degrees of freedom for plane mechanisms
Mechanism & Synthesis
Degrees of freedom for plane mechanisms
It is defined as number of input parameters that has to be individually controlled in order to bring the mechanism into useful engineering purpose.
The definition of the degrees of freedom of a mechanism is the number of independent relative motions among the rigid bodies.
Number of degrees of freedom is one.

4. Mechanism & Synthesis F = total degrees of freedom in the mechanism
n = number of links (including the frame)
l = number of one degree of freedom pairs
h = number of two degrees of freedom pairs
This equation is also known as Gruebler's equation.
The number of degrees of freedom of a mechanism is also called the mobility of the device.
The mobility is the number of input parameters (usually pair variables) that must be independently controlled to bring the device into a particular position.
The Kutzbach criterion, which is similar to Gruebler's equation, calculates the mobility.

5. Mechanism & Synthesis
A four bar linkage comprises four bar-shaped links and four turning pairs
output Link
Coupler Link
Input Link
Fixed Link

6. s + l <= p + q Mechanism & Synthesis Terminology
In a four-bar linkage, we refer to the line segment between hinges on a given link as a bar where:
s = length of shortest bar
l = length of longest bar
p, q = lengths of intermediate bar
Grashoff's theorem states that a four-bar mechanism has at least one revolving link if
s + l <= p + q

7. Terminology Mechanism & Synthesis
Crank: A side link which revolves relative to the frame is called a crank.
Rocker: Any link which does not revolve is called a rocker.
Crank-rocker mechanism: In a four bar linkage, if the shorter side link revolves and the other one rocks (i.e., oscillates), it is called a crank-rocker mechanism.
Double-crank mechanism: In a four bar linkage, if both of the side links revolve, it is called a double- crank mechanism.
Double-rocker mechanism: In a four bar linkage, if both of the side links rock, it is called a double- rocker mechanism.

8. Synthesis of four bar mechanism
Mechanism & Synthesis
Synthesis of four bar mechanism
Let us consider a four bar mechanism for three different positions as shown in the figure.

9. Synthesis of four bar mechanism
Mechanism & Synthesis
Synthesis of four bar mechanism
Let the three positions of the input link AB are known and the three positions of the output link CD are also Known.
To determine the dimensions of the links a,b,c and d given the three kinown angular positions of the input link and output link.
The freudenstien equation:
K1 cosθ + K2 cosΦ+k3= cos(θ – Φ)
Where K1 = d/a, k2=d/c, k3= (a2 -b2 + c2 + d2 )/ 2ac

10. Mechanism & Synthesis K1= Δ1/Δ , k2= Δ2/Δ , K3= Δ3/Δ.
Assuming the value of either a or d other values are obtained.
Here link dimensions are determined and the mechanism is graphically drawn on the canvas with the dimensions of the links.

11. Mechanism & Synthesis Interactivity Input parameters Output parameters
Enter values of theta
Enter values of phi
theta1 30
phi1 60
theta2 45
phi2
Enter values here
theta3
phi3
Grey cells are input cells
delta Matrix
0.5
0.866 1
delta1 Matrix
Do not touch
0.707
Output cells
delta k1
2.7802
delta2 Matrix
Formual cells do not touch
delta 1 k2
delta2
delta3 k3
-2.932
delta3 Matrix a =
0.36 b
1.42 c d
Input parameters
Θ1 , θ2 and θ3
Φ1, Φ2 and Φ3.
Output parameters
a,b,c,d the dimensions of the links of four bar mechanism.

12. Mechanism & Synthesis
Animation

13. Quality Management Quality Engineering Management
In a four bar mechanism the lengths of input , floating and output links are respectively 300 mm, 400 mm and 150 mm. To have continuous motion with the designed mechanism the length of the fixed length should be
> 550 mm
<= 550 mm
750 mm
325 mm

14. Quality Engineering Management
Quality Management
In a double crank mechanism, the rotation of input link is 360 degrees then the rotation of output link is
180 degrees
360 degrees
450 degrees
90 degrees

15. Quality Management Rotational, Rotational/ reciprocating, Rotational
Quality Engineering Management
Quality Management
The motion of input link, floating link and output link are of the following type respectively:
Rotational, Rotational/ reciprocating, Rotational
Linear , Linear, Linear
Reciprocating, Rotational, Reciprocating
Both reciprocating and rotary for all the three links.

16. Quality Management Quality Engineering Management
Four bar mechanism is a
Open loop kinematic linkage
Closed loop kinematic linkage
Open loop with 2 Degrees of freedom
Is not a machine and mechanism

17. Mechanism & Synthesis Resources Books:
Theory of machines by Thomas bevan
Erdman & Sandor 84)Erdman, A. and Sandor, G., Mechanism Design: Analysis and Synthesis, Prentice-Hall, New Jersey, 1984.
Reference Links: