TOM Acceleration Analysis

(WEEK 09)

Course Instructor

Engr. Uzair Khaleeq uz Zaman

400 parts, 30 cm long, 15 cm highused for arithmetic operations (Grant Calculating Machine - 1876)

Acceleration Rate of change of velocity with respect to time

- Linear:

A = dV / dt

Introduction

- Angular = d / dt

Tangential acceleration:

AtPA = p

Normal / Centripetal acceleration:

AnPA = p2

Acceleration Difference

/ Relative Acceleration

AP = AA + APA Absolute acceleration of point P is

equal to acceleration of P relative

to A plus acceleration of A relative

to ground

APA = AP - AA

Introduction (contd)

Motor attached at point O2 Main task is to find rate of change

of output velocities (3 and 4) given:

Value of input variable (2)

Value of input velocity (2)

Rate of change of input velocity (2)

Length of all the links

Need to know values of output variables (3, 4) and output velocities (3 , 4)

Need to perform complete position and velocity analysis(Chapters 4 and 6) before starting.

Analytical Acceleration Analysis

4-bar Pin Jointed linkage

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

From position analysis:

R2 + R3 R4 + R1 = 0

From velocity analysis:

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

Each term contains 2 functions of time and

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

Derivation of 3 and 4 is part of the HOMEWORK

Ex: Calculate the angular acceleration of Link 4, 4 , when the

input angular acceleration, 2 = 0 rad/s2 , 2 = 1 rad/s and 2

= 30

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

Ex: Calculate the angular acceleration of Link 4, 4 , when the

input angular acceleration, 2 = 0 rad/s2 , 2 = 1 rad/s and 2

= 30

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

Ex: Calculate the angular acceleration of Link 4, 4 , when the input angular acceleration, 2 = 0 rad/s

2 , 2 = 1 rad/s and 2 = 30

Find values of output variables (3, 4) and output velocities (3 ,4) first

Get above values by performing complete position analysis (Chapter 4) and velocity analysis (Chapter 6)

For Open Configuration: From Chapter 4: When 2 = 30 3 = 35.4 and 4 =

84.4 From Chapter 6: When 2 = 30 and 2 = 1 rad/s

3 = -0.54 rad/s and 4 = -0.075 rad/s

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

Repeat the same steps to obtain values for the Cross Configuration.

Ex: Calculate the angular acceleration of Link 4, 4 , when the input angular

acceleration, 2 = 0 rad/s2 , 2 = 1 rad/s and 2 = 30

Using a math program (MATLab), we can plot the output

acceleration (4) for all values of the input variable (0 2

360)

For instance when 2= 0 rad/s2 and 2= 1 rad/s:

Analytical Acceleration Analysis (contd)

4-bar Pin Jointed linkage (contd)

From position analysis:

R2R3R4 R1= 0

From velocity analysis:

Analytical Acceleration Analysis (contd)

4-bar Slider Crank

Analytical Acceleration Analysis (contd)

4-bar Slider Crank (contd)

Derivation of 3 and d (double

dot) is part of the HOMEWORK

The Coriolis component will always be present when there is

a slider sliding on a rotating link

It will automatically be accounted for as long as the

differentiation is correctly done.

Analytical Acceleration Analysis (contd)

4-bar Slider Crank Coriolis Acceleration

Rotating and changing length as system moves 2 DOF

2 inputs = and VP, slip

Analytical Acceleration Analysis (contd)4-bar Slider Crank Coriolis Acceleration (contd)

From position analysis:

R2R3R4 R1= 0

From velocity analysis:

Analytical Acceleration Analysis (contd)

4-bar Inverted Slider Crank

Analytical Acceleration Analysis (contd)

4-bar Inverted Slider Crank (contd)

Derivation of 4 and b (double

dot) is part of the HOMEWORK

Determine accelerations of points on the mechanism, instead of

accelerations of output variables

Can only be done once all output variables, output velocities and output

accelerations are found

Analytical Acceleration Analysis (contd)

Acceleration of a Point on a Linkage

Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)

Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)

Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)

Analytical Acceleration Analysis (contd)Acceleration of a Point on a Linkage (contd)