mechanism & synthesis mechanisms & synthesis in kinematic analysis, a given mechanism is...

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


1. If one of the links of the kinematic chain is fixed , then it forms a mechanism.

2. 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.


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.


• 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.

http://www.cs.cmu.edu/~rapidproto/mechanisms/chpt3.html


A four bar linkage comprises four bar-shaped links and four turning pairs

Input Link

Coupler Linkoutput Link

Fixed Link


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


Terminology• 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.


Synthesis of four bar mechanism

Let us consider a four bar mechanism for three different positions as shown in the figure.


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


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.


Interactivity

• 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.

Enter values of theta

Enter values of phi

theta1 30 phi1 60theta2 45 phi2 45

Enter values here theta3 60 phi3 30Grey cells are input cells

delta Matrix

0.5 0.866 1 delta1 Matrix

0.866025

0.866025

1

Do not touch 0.70710678

0.707 1 1 0.707107

1

Output cells 0.8660254

0.5 1 0.866025

0.5 1

Do not touch delta -0.017638

1

k1 2.7802

delta2 Matrix

0.5 0.866025

1

Formual cells do not touch

0.707107

1 1

delta 1 -0.049038

1

k2 2.7802

0.866025

0.866025

1

delta2 -0.049038

1delta3 0.051712

26k3 -2.932 delta3

Matrix0.5 0.86602

50.86602

50.70710

70.70710

71

0.866025

0.5 0.866025

a = 0.36b = 1.42c = 0.36d = 1


Animation

Quality ManagementQuality 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

o> 550 mm

o<= 550 mm

o750 mm

o325 mm


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


The motion of input link, floating link and output link are of the following type respectively:

oRotational, Rotational/ reciprocating, Rotational

oLinear , Linear, Linear

oReciprocating, Rotational, Reciprocating

oBoth reciprocating and rotary for all the three links.


Four bar mechanism is a

oOpen loop kinematic linkage

oClosed loop kinematic linkage

oOpen loop with 2 Degrees of freedom

oIs not a machine and mechanism


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:

http://www.cs.cmu.edu/~rapidproto/mechanisms/

http://www.softintegration.com/chhtml/toolkit/mechanism/fourbar/fourbar_ani.html

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