SlideShare una empresa de Scribd logo
1 de 26
Descargar para leer sin conexión
Velocity analysis of any mechanism can be carried out by

various methods.

     1. By graphical method

     2. By relative velocity method

     3. By instantaneous method
By Graphical Method

The following points are to be considered while solving problems

by this method.

1. Draw the configuration design to a suitable scale.

2. Locate all fixed point in a mechanism as a common point in

  velocity diagram.

3. Choose a suitable scale for the vector diagram velocity.
r
4. The velocity vector of each rotating link is       to the link.

5. Velocity of each link in mechanism has both magnitude and

   direction. Start from a point whose magnitude and direction is

   known.

6. The points of the velocity diagram are indicated by small letters.
To explain the method let us take a few
specific examples.


1. Four – Bar Mechanism:                                                 C
                                                             15 cm
In a four bar chain ABCD link AD is fixed        B
                                                                             8 cm
and in 15 cm long. The crank AB is 4 cm                    wBA
                                                     60o
long rotates at 180 rpm (cw) while link CD   A                                  D
                                                                 15 cm
rotates about D is 8 cm long BC = AD and         Configuration Diagram

| BAD = 60o. Find angular velocity of link

CD.
Velocity vector diagram
                                         2πx 120
           Vb = r =   ba          x AB =         x 4 = 50.24 cm/sec
                                           60

Choose a suitable scale
          1 cm = 20 m/s = ab
                              r              C   Vcb
                                  to CD

               a, d                               r
                                                      to BC
                          r
                              to AB

                                                       b
Vcb = bc

          Vc = dc = 38 cm/s = Vcd


We know that V = ωR
          Vcd =   cD   x CD
                  Vcd 38
          WcD =          4.75 rad/s (cw)
                  CD 8
Velocity of mechasnism_by_graphical
Learning Outcomes:


 • This session deals with velocity vector
   diagrams for      determining the velocity at
   different points in different mechanisms like IC
   engine Mechanism and Crank and slotted Lever
   Mechanism.
•Introduction.
•Definition of Displacement, Velocity and
Acceleration.
•Difference between absolute Velocity and
Relative Velocity.
•Steps to construct Velocity Vector diagram.
•Velocity Vector diagram for a Four Bar
Mechanism
1. Slider Crank Mechanism:
In a crank and slotted lover mechanism crank rotates
of 300 rpm in a counter clockwise direction. Find
  (i)    Angular velocity of connecting rod and
  (ii)   Velocity of slider.
                        A
             60 mm              150 mm

                  45o
                                                    B

                        Configuration diagram
Step 1: Determine the magnitude and velocity of
point A with respect to 0,
                              2 x 300
            VA = O1A x O2 A =          x 60
                                 60
                = 600 mm/sec

Step 2: Choose a suitable scale to draw velocity vector diagram.
                                                     a   Va
Vab = ab
      Vba                                r
                                             to AB               r
                                                                     to OA
 ba =           r/s
      BA 150
Vb = ob velocity of slider
                                             b
                                                                     O
                                                 Along sides B
Note: Velocity of slider is along
       the line of sliding.            Velocity vector diagram
3. Shaper Mechanism:
In a crank and slotted lever mechanisms crank O2A rotates
at   r/s in CCW direction. Determine the velocity of slider.
                         6
                          D                Scale 1 cm = x m/s
                                   5

                                                       C

                                       W           3
                              O2                   B
                                   2



                                           4




                              O1

                       Configuration diagram
Scale 1 cm = x m/s                         a
                                               VAO2 = VA
                                     VBA
                             c
                                     b
                                   VBO1
                VDC
                         d                      O1O2
                             Velocity vector diagram

                                           O1b     O1c
           Va =      2   x O2 A
                                           O1B     O1C

                                                       O1C
           To locate point C                   O1c O1b
                                                       O1B
To Determine Velocity of Rubbing

Two links of a mechanism having turning point will be connected

by pins. When the links are motion they rub against pin surface.

The velocity of rubbing of pins depends on the angular velocity of

links relative to each other as well as direction.
For example: In a four bar mechanism we have
pins at points A, B, C and D.
              Vra =       ab    x ratios of pin A (rpa)

+ sign is used            ab   is CW and W bc is CCW i.e. when angular
velocities are in opposite directions use + sign when angular
velocities are in some directions use             -   ve   sign.
           VrC = (    bc   +     cd)   radius r
           VrD =     cd    rpd
Problems on velocity by velocity vector method (Graphical
Problems on velocity by velocity vector
method (Graphical solutions)


  Problem 1:
In a four bar mechanism, the dimensions of the links are as given
below:
      AB = 50 mm,                     BC = 66 mm
      CD = 56 mm            and       AD = 100 mm

At a given instant when |DAB       60 o the angular velocity of link
AB is 10.5 r/s in CCW direction.
Determine,
i)    Velocity of point C
ii)   Velocity of point E on link BC when BE = 40 mm
iii) The angular velocity of link BC and CD
iv) The velocity of an offset point F on link BC, if BF = 45 mm, CF
      = 30 mm and BCF is read clockwise.
v)    The velocity of an offset point G on link CD, if CG = 24 mm,
      DG = 44 mm and DCG is read clockwise.
vi) The velocity of rubbing of pins A, B, C and D. The ratio of the
      pins are 30 mm, 40 mm, 25 mm and 35 mm respectively.
Solution:
Step -1: Construct the configuration diagram
selecting a suitable scale.

 Scale: 1 cm = 20 mm                       C

                                                   G
                      B

                                       F



                    60o
             A                                 D
Step – 2: Given the angular velocity of link AB and its direction of

rotation determine velocity of point with respect to A (A is fixed

hence, it is zero velocity point).

            Vba =   BA x   BA

                 = 10.5 x 0.05 = 0.525 m/s
Step – 3: To draw velocity vector diagram
choose a suitable scale, say 1 cm = 0.2 m/s.
     First locate zero velocity points.
                   r
     Draw a line       to link AB in the direction of rotation of link AB
     (CCW) equal to 0.525 m/s.               b

                                                              Vba = 0.525 m/s
                                                 e, g

                                                                         a, d
                                       f
                                                 C      Ved
r                                   r
From b draw a line       to BC and from d. Draw d line       to CD

to interest at C.

Vcb is given vector bc Vbc = 0.44 m/s

Vcd is given vector dc Vcd = 0.39 m/s
Step – 4: To determine velocity of point E (Absolute
velocity) on link BC, first locate the position of point E
on velocity vector diagram. This can be done by taking
corresponding ratios of lengths of links to vector
distance i.e.
be    BE                  BE         0.04
                     be =    x Vcb =       x 0.44 = 0.24 m/s
bc    BC                  BC         0.066

Join e on velocity vector diagram to zero velocity points a, d
vector de = Ve = 0.415 m/s.
Step 5: To determine angular velocity of links BC and CD, we
know Vbc and Vcd.
               Vbc = WBC x BC
                       Vbc    0.44
               WBC =                 6.6 rad / sec . (cw)
                       BC    0.066
Similarly,   Vcd = WCD x CD
                     Vcd       0.39
               WCD =                    6.96 r / s (CCW)
                     CD       0.056
Step – 6: To determine velocity of an offset point F
                    r
      Draw a line       to CF from C on velocity vector diagram.
                        r
      Draw a line           to BF from b on velocity vector diagram to

      intersect the previously drawn line at ‘f’.

      From the point f to zero velocity point a, d and measure

      vector fa/fd to get Vf = 0.495 m/s.
Step – 7: To determine velocity of an offset point.
                    r
      Draw a line       to GC from C on velocity vector diagram.
                        r
      Draw a line           to DG from d on velocity vector diagram to

      intersect previously drawn line at g.

      Measure vector dg to get velocity of point G.

            Vg = dg         0.305 m / s
Step – 8: To determine rubbing velocity at pins
  Rubbing velocity at pin A will be
  Vpa =        ab   x rad of pin A      = 10.5 x 0.03 = 0.315 m/s

  Rubbing velocity at pin B will be
  Vpb = (      ab   +   cb)   x rad of point at B.
           [   ab   CCW and          cbCW]

  Vpb = (10.5 + 6.6) x 0.04 = 0.684 m/s.
  Rubbing velocity at point D will be
     cd   x rpd of pin D
  = 6.96 x 0.035 = 0.244 m/s

Más contenido relacionado

La actualidad más candente

Theory of machines solution of exercise
Theory of machines solution of exerciseTheory of machines solution of exercise
Theory of machines solution of exerciseSaif al-din ali
 
ICR Velocity Analysis Graphical Method, Theory of Machine
ICR Velocity Analysis Graphical Method, Theory of MachineICR Velocity Analysis Graphical Method, Theory of Machine
ICR Velocity Analysis Graphical Method, Theory of MachineKESHAV
 
Mechanism synthesis, graphical
Mechanism synthesis, graphicalMechanism synthesis, graphical
Mechanism synthesis, graphicalMecanismos Ucr
 
Velocity & acceleration diagrams
Velocity & acceleration diagramsVelocity & acceleration diagrams
Velocity & acceleration diagramssherin_ginige
 
Unit 2 Design Of Shafts Keys and Couplings
Unit 2 Design Of Shafts Keys and CouplingsUnit 2 Design Of Shafts Keys and Couplings
Unit 2 Design Of Shafts Keys and CouplingsMahesh Shinde
 
Module 2 instantenous center method
Module 2 instantenous center methodModule 2 instantenous center method
Module 2 instantenous center methodtaruian
 
Gyroscope.pptx 2.pptxfinal
Gyroscope.pptx 2.pptxfinalGyroscope.pptx 2.pptxfinal
Gyroscope.pptx 2.pptxfinalYashwadhan Sahi
 
009 relative acceleration
009 relative acceleration009 relative acceleration
009 relative accelerationphysics101
 
Unit 2.7 instantaneous center method
Unit 2.7 instantaneous center methodUnit 2.7 instantaneous center method
Unit 2.7 instantaneous center methodDr.R. SELVAM
 
Kinematic analysis of mechanisms analytical methods
Kinematic analysis of mechanisms  analytical methodsKinematic analysis of mechanisms  analytical methods
Kinematic analysis of mechanisms analytical methodsajitkarpe1986
 
straight line motion mechanism
straight line motion mechanismstraight line motion mechanism
straight line motion mechanismAbhishek joshi
 
Relative velocity method, velocity & acceleration analysis of mechanism
Relative velocity method, velocity & acceleration analysis of mechanismRelative velocity method, velocity & acceleration analysis of mechanism
Relative velocity method, velocity & acceleration analysis of mechanismKESHAV
 

La actualidad más candente (20)

Mechanism synthesis, graphical
Mechanism synthesis, graphicalMechanism synthesis, graphical
Mechanism synthesis, graphical
 
Theory of machines solution of exercise
Theory of machines solution of exerciseTheory of machines solution of exercise
Theory of machines solution of exercise
 
7.velocity analysis
7.velocity analysis7.velocity analysis
7.velocity analysis
 
Beam engine
Beam engineBeam engine
Beam engine
 
ICR Velocity Analysis Graphical Method, Theory of Machine
ICR Velocity Analysis Graphical Method, Theory of MachineICR Velocity Analysis Graphical Method, Theory of Machine
ICR Velocity Analysis Graphical Method, Theory of Machine
 
Mechanism synthesis, graphical
Mechanism synthesis, graphicalMechanism synthesis, graphical
Mechanism synthesis, graphical
 
Velocity & acceleration diagrams
Velocity & acceleration diagramsVelocity & acceleration diagrams
Velocity & acceleration diagrams
 
Unit 2 Design Of Shafts Keys and Couplings
Unit 2 Design Of Shafts Keys and CouplingsUnit 2 Design Of Shafts Keys and Couplings
Unit 2 Design Of Shafts Keys and Couplings
 
Ch.08
Ch.08Ch.08
Ch.08
 
Module 2 instantenous center method
Module 2 instantenous center methodModule 2 instantenous center method
Module 2 instantenous center method
 
Lecture 2. linkages
Lecture 2. linkagesLecture 2. linkages
Lecture 2. linkages
 
3.share gear-trains
3.share gear-trains3.share gear-trains
3.share gear-trains
 
Gyroscope.pptx 2.pptxfinal
Gyroscope.pptx 2.pptxfinalGyroscope.pptx 2.pptxfinal
Gyroscope.pptx 2.pptxfinal
 
Chapter 6 - Gyroscope Notes.pdf
Chapter 6 - Gyroscope Notes.pdfChapter 6 - Gyroscope Notes.pdf
Chapter 6 - Gyroscope Notes.pdf
 
009 relative acceleration
009 relative acceleration009 relative acceleration
009 relative acceleration
 
Unit 2.7 instantaneous center method
Unit 2.7 instantaneous center methodUnit 2.7 instantaneous center method
Unit 2.7 instantaneous center method
 
Kinematic analysis of mechanisms analytical methods
Kinematic analysis of mechanisms  analytical methodsKinematic analysis of mechanisms  analytical methods
Kinematic analysis of mechanisms analytical methods
 
DYNAMICS OF MACHINES UNIT-1 BY Mr.P.RAMACHANDRAN/AP/MECH/KIT/CBE
DYNAMICS OF MACHINES UNIT-1 BY Mr.P.RAMACHANDRAN/AP/MECH/KIT/CBEDYNAMICS OF MACHINES UNIT-1 BY Mr.P.RAMACHANDRAN/AP/MECH/KIT/CBE
DYNAMICS OF MACHINES UNIT-1 BY Mr.P.RAMACHANDRAN/AP/MECH/KIT/CBE
 
straight line motion mechanism
straight line motion mechanismstraight line motion mechanism
straight line motion mechanism
 
Relative velocity method, velocity & acceleration analysis of mechanism
Relative velocity method, velocity & acceleration analysis of mechanismRelative velocity method, velocity & acceleration analysis of mechanism
Relative velocity method, velocity & acceleration analysis of mechanism
 

Destacado

Destacado (20)

Gear and Gear trains ppt
Gear and Gear trains pptGear and Gear trains ppt
Gear and Gear trains ppt
 
Design of machine elements
Design of machine elementsDesign of machine elements
Design of machine elements
 
Electric motor basics
Electric motor basicsElectric motor basics
Electric motor basics
 
J3010 Unit 6
J3010   Unit 6J3010   Unit 6
J3010 Unit 6
 
Unit 2b Power Transmission by Belts
Unit 2b Power Transmission by BeltsUnit 2b Power Transmission by Belts
Unit 2b Power Transmission by Belts
 
Design_of_Machine_Elements_Spo
Design_of_Machine_Elements_SpoDesign_of_Machine_Elements_Spo
Design_of_Machine_Elements_Spo
 
Dinesh machine design
Dinesh machine designDinesh machine design
Dinesh machine design
 
THE NATURE OF MATERIALS
THE NATURE OF MATERIALSTHE NATURE OF MATERIALS
THE NATURE OF MATERIALS
 
Mechanical Engineering : Engineering mechanics, THE GATE ACADEMY
Mechanical Engineering  : Engineering mechanics, THE GATE ACADEMYMechanical Engineering  : Engineering mechanics, THE GATE ACADEMY
Mechanical Engineering : Engineering mechanics, THE GATE ACADEMY
 
Study of Gear Technology
Study of Gear TechnologyStudy of Gear Technology
Study of Gear Technology
 
Instantaneous centre
Instantaneous centreInstantaneous centre
Instantaneous centre
 
Theory of Machine and Mechanisms (Gears)
Theory of Machine and Mechanisms (Gears)Theory of Machine and Mechanisms (Gears)
Theory of Machine and Mechanisms (Gears)
 
Gears and Gear Trains
Gears and Gear Trains Gears and Gear Trains
Gears and Gear Trains
 
Gear
GearGear
Gear
 
Theory of machines
Theory of machinesTheory of machines
Theory of machines
 
Design of machine_elements_
Design of machine_elements_Design of machine_elements_
Design of machine_elements_
 
Gear train
Gear trainGear train
Gear train
 
Course Outcome and Program Outcome Calculation(new method)
Course Outcome and Program Outcome Calculation(new method)Course Outcome and Program Outcome Calculation(new method)
Course Outcome and Program Outcome Calculation(new method)
 
Types of gears
Types of gearsTypes of gears
Types of gears
 
242713764 theory-of-machines-r-k-bansal
242713764 theory-of-machines-r-k-bansal242713764 theory-of-machines-r-k-bansal
242713764 theory-of-machines-r-k-bansal
 

Similar a Velocity of mechasnism_by_graphical

Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)
Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)
Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)MUHAMMAD USMAN SARWAR
 
Velocityofmechasnismbygraphical 130217105814-phpapp02
Velocityofmechasnismbygraphical 130217105814-phpapp02Velocityofmechasnismbygraphical 130217105814-phpapp02
Velocityofmechasnismbygraphical 130217105814-phpapp02MUHAMMAD USMAN SARWAR
 
Velo & accel dia by relative velo & accl method
Velo & accel dia by relative velo & accl methodVelo & accel dia by relative velo & accl method
Velo & accel dia by relative velo & accl methodUmesh Ravate
 
Chapter#3 Met 305 2-_velocity_relative
Chapter#3 Met 305 2-_velocity_relativeChapter#3 Met 305 2-_velocity_relative
Chapter#3 Met 305 2-_velocity_relativehotman1991
 
116 coriolis acceleration
116  coriolis acceleration116  coriolis acceleration
116 coriolis accelerationAravind Mohan
 
Mechanics of Machines MET 305
Mechanics of Machines MET 305Mechanics of Machines MET 305
Mechanics of Machines MET 305hotman1991
 
lec09_part1.pptx PLANAR KINEMATICS OF RIGID BODIES
lec09_part1.pptx  PLANAR KINEMATICS OF RIGID BODIESlec09_part1.pptx  PLANAR KINEMATICS OF RIGID BODIES
lec09_part1.pptx PLANAR KINEMATICS OF RIGID BODIESShyamal25
 
EE301 Lesson 15 Phasors Complex Numbers and Impedance (2).ppt
EE301 Lesson 15 Phasors Complex Numbers and Impedance (2).pptEE301 Lesson 15 Phasors Complex Numbers and Impedance (2).ppt
EE301 Lesson 15 Phasors Complex Numbers and Impedance (2).pptRyanAnderson41811
 
Lecture16 5
Lecture16 5Lecture16 5
Lecture16 5Aims-IIT
 
Accelerations in Slider Crank mechanism
Accelerations in Slider Crank mechanismAccelerations in Slider Crank mechanism
Accelerations in Slider Crank mechanismAkshay shah
 
L15 analysis of indeterminate beams by moment distribution method
L15 analysis of indeterminate beams by moment distribution methodL15 analysis of indeterminate beams by moment distribution method
L15 analysis of indeterminate beams by moment distribution methodDr. OmPrakash
 
Ejercicios resueltos-vectores-2016
Ejercicios resueltos-vectores-2016Ejercicios resueltos-vectores-2016
Ejercicios resueltos-vectores-2016RodrigoSalgueiroLlan
 
Oscilloscope tutorial -phasemeasurement
Oscilloscope tutorial -phasemeasurementOscilloscope tutorial -phasemeasurement
Oscilloscope tutorial -phasemeasurementcyberns_
 
A some basic rules of tensor calculus
A some basic rules of tensor calculusA some basic rules of tensor calculus
A some basic rules of tensor calculusTarun Gehlot
 

Similar a Velocity of mechasnism_by_graphical (20)

Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)
Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)
Velocityofmechasnismbygraphical 130217105814-phpapp02 (1)
 
Velocityofmechasnismbygraphical 130217105814-phpapp02
Velocityofmechasnismbygraphical 130217105814-phpapp02Velocityofmechasnismbygraphical 130217105814-phpapp02
Velocityofmechasnismbygraphical 130217105814-phpapp02
 
Velo & accel dia by relative velo & accl method
Velo & accel dia by relative velo & accl methodVelo & accel dia by relative velo & accl method
Velo & accel dia by relative velo & accl method
 
Chapter#3 Met 305 2-_velocity_relative
Chapter#3 Met 305 2-_velocity_relativeChapter#3 Met 305 2-_velocity_relative
Chapter#3 Met 305 2-_velocity_relative
 
116 coriolis acceleration
116  coriolis acceleration116  coriolis acceleration
116 coriolis acceleration
 
Mechanics of Machines MET 305
Mechanics of Machines MET 305Mechanics of Machines MET 305
Mechanics of Machines MET 305
 
lec09_part1.pptx PLANAR KINEMATICS OF RIGID BODIES
lec09_part1.pptx  PLANAR KINEMATICS OF RIGID BODIESlec09_part1.pptx  PLANAR KINEMATICS OF RIGID BODIES
lec09_part1.pptx PLANAR KINEMATICS OF RIGID BODIES
 
7807139.ppt
7807139.ppt7807139.ppt
7807139.ppt
 
EE301 Lesson 15 Phasors Complex Numbers and Impedance (2).ppt
EE301 Lesson 15 Phasors Complex Numbers and Impedance (2).pptEE301 Lesson 15 Phasors Complex Numbers and Impedance (2).ppt
EE301 Lesson 15 Phasors Complex Numbers and Impedance (2).ppt
 
Lecture16 5
Lecture16 5Lecture16 5
Lecture16 5
 
Accelerations in Slider Crank mechanism
Accelerations in Slider Crank mechanismAccelerations in Slider Crank mechanism
Accelerations in Slider Crank mechanism
 
Vertical Curves (Part 2)
Vertical Curves (Part 2)Vertical Curves (Part 2)
Vertical Curves (Part 2)
 
99992505.pdf
99992505.pdf99992505.pdf
99992505.pdf
 
L15 analysis of indeterminate beams by moment distribution method
L15 analysis of indeterminate beams by moment distribution methodL15 analysis of indeterminate beams by moment distribution method
L15 analysis of indeterminate beams by moment distribution method
 
Vertical Curves (Part 1)
Vertical Curves (Part 1)Vertical Curves (Part 1)
Vertical Curves (Part 1)
 
Ejercicios resueltos-vectores-2016
Ejercicios resueltos-vectores-2016Ejercicios resueltos-vectores-2016
Ejercicios resueltos-vectores-2016
 
Svpwm
SvpwmSvpwm
Svpwm
 
Oscilloscope tutorial -phasemeasurement
Oscilloscope tutorial -phasemeasurementOscilloscope tutorial -phasemeasurement
Oscilloscope tutorial -phasemeasurement
 
A some basic rules of tensor calculus
A some basic rules of tensor calculusA some basic rules of tensor calculus
A some basic rules of tensor calculus
 
Ch03 ssm
Ch03 ssmCh03 ssm
Ch03 ssm
 

Velocity of mechasnism_by_graphical

  • 1. Velocity analysis of any mechanism can be carried out by various methods. 1. By graphical method 2. By relative velocity method 3. By instantaneous method
  • 2. By Graphical Method The following points are to be considered while solving problems by this method. 1. Draw the configuration design to a suitable scale. 2. Locate all fixed point in a mechanism as a common point in velocity diagram. 3. Choose a suitable scale for the vector diagram velocity.
  • 3. r 4. The velocity vector of each rotating link is to the link. 5. Velocity of each link in mechanism has both magnitude and direction. Start from a point whose magnitude and direction is known. 6. The points of the velocity diagram are indicated by small letters.
  • 4. To explain the method let us take a few specific examples. 1. Four – Bar Mechanism: C 15 cm In a four bar chain ABCD link AD is fixed B 8 cm and in 15 cm long. The crank AB is 4 cm wBA 60o long rotates at 180 rpm (cw) while link CD A D 15 cm rotates about D is 8 cm long BC = AD and Configuration Diagram | BAD = 60o. Find angular velocity of link CD.
  • 5. Velocity vector diagram 2πx 120 Vb = r = ba x AB = x 4 = 50.24 cm/sec 60 Choose a suitable scale 1 cm = 20 m/s = ab r C Vcb to CD a, d r to BC r to AB b
  • 6. Vcb = bc Vc = dc = 38 cm/s = Vcd We know that V = ωR Vcd = cD x CD Vcd 38 WcD = 4.75 rad/s (cw) CD 8
  • 8. Learning Outcomes: • This session deals with velocity vector diagrams for determining the velocity at different points in different mechanisms like IC engine Mechanism and Crank and slotted Lever Mechanism.
  • 9. •Introduction. •Definition of Displacement, Velocity and Acceleration. •Difference between absolute Velocity and Relative Velocity. •Steps to construct Velocity Vector diagram. •Velocity Vector diagram for a Four Bar Mechanism
  • 10. 1. Slider Crank Mechanism: In a crank and slotted lover mechanism crank rotates of 300 rpm in a counter clockwise direction. Find (i) Angular velocity of connecting rod and (ii) Velocity of slider. A 60 mm 150 mm 45o B Configuration diagram
  • 11. Step 1: Determine the magnitude and velocity of point A with respect to 0, 2 x 300 VA = O1A x O2 A = x 60 60 = 600 mm/sec Step 2: Choose a suitable scale to draw velocity vector diagram. a Va Vab = ab Vba r to AB r to OA ba = r/s BA 150 Vb = ob velocity of slider b O Along sides B Note: Velocity of slider is along the line of sliding. Velocity vector diagram
  • 12. 3. Shaper Mechanism: In a crank and slotted lever mechanisms crank O2A rotates at r/s in CCW direction. Determine the velocity of slider. 6 D Scale 1 cm = x m/s 5 C W 3 O2 B 2 4 O1 Configuration diagram
  • 13. Scale 1 cm = x m/s a VAO2 = VA VBA c b VBO1 VDC d O1O2 Velocity vector diagram O1b O1c Va = 2 x O2 A O1B O1C O1C To locate point C O1c O1b O1B
  • 14. To Determine Velocity of Rubbing Two links of a mechanism having turning point will be connected by pins. When the links are motion they rub against pin surface. The velocity of rubbing of pins depends on the angular velocity of links relative to each other as well as direction.
  • 15. For example: In a four bar mechanism we have pins at points A, B, C and D. Vra = ab x ratios of pin A (rpa) + sign is used  ab is CW and W bc is CCW i.e. when angular velocities are in opposite directions use + sign when angular velocities are in some directions use - ve sign. VrC = ( bc + cd) radius r VrD = cd rpd Problems on velocity by velocity vector method (Graphical
  • 16. Problems on velocity by velocity vector method (Graphical solutions) Problem 1: In a four bar mechanism, the dimensions of the links are as given below: AB = 50 mm, BC = 66 mm CD = 56 mm and AD = 100 mm At a given instant when |DAB 60 o the angular velocity of link AB is 10.5 r/s in CCW direction.
  • 17. Determine, i) Velocity of point C ii) Velocity of point E on link BC when BE = 40 mm iii) The angular velocity of link BC and CD iv) The velocity of an offset point F on link BC, if BF = 45 mm, CF = 30 mm and BCF is read clockwise. v) The velocity of an offset point G on link CD, if CG = 24 mm, DG = 44 mm and DCG is read clockwise. vi) The velocity of rubbing of pins A, B, C and D. The ratio of the pins are 30 mm, 40 mm, 25 mm and 35 mm respectively.
  • 18. Solution: Step -1: Construct the configuration diagram selecting a suitable scale. Scale: 1 cm = 20 mm C G B F 60o A D
  • 19. Step – 2: Given the angular velocity of link AB and its direction of rotation determine velocity of point with respect to A (A is fixed hence, it is zero velocity point). Vba = BA x BA = 10.5 x 0.05 = 0.525 m/s
  • 20. Step – 3: To draw velocity vector diagram choose a suitable scale, say 1 cm = 0.2 m/s. First locate zero velocity points. r Draw a line to link AB in the direction of rotation of link AB (CCW) equal to 0.525 m/s. b Vba = 0.525 m/s e, g a, d f C Ved
  • 21. r r From b draw a line to BC and from d. Draw d line to CD to interest at C. Vcb is given vector bc Vbc = 0.44 m/s Vcd is given vector dc Vcd = 0.39 m/s
  • 22. Step – 4: To determine velocity of point E (Absolute velocity) on link BC, first locate the position of point E on velocity vector diagram. This can be done by taking corresponding ratios of lengths of links to vector distance i.e. be BE BE 0.04 be = x Vcb = x 0.44 = 0.24 m/s bc BC BC 0.066 Join e on velocity vector diagram to zero velocity points a, d vector de = Ve = 0.415 m/s.
  • 23. Step 5: To determine angular velocity of links BC and CD, we know Vbc and Vcd. Vbc = WBC x BC Vbc 0.44 WBC = 6.6 rad / sec . (cw) BC 0.066 Similarly, Vcd = WCD x CD Vcd 0.39 WCD = 6.96 r / s (CCW) CD 0.056
  • 24. Step – 6: To determine velocity of an offset point F r Draw a line to CF from C on velocity vector diagram. r Draw a line to BF from b on velocity vector diagram to intersect the previously drawn line at ‘f’. From the point f to zero velocity point a, d and measure vector fa/fd to get Vf = 0.495 m/s.
  • 25. Step – 7: To determine velocity of an offset point. r Draw a line to GC from C on velocity vector diagram. r Draw a line to DG from d on velocity vector diagram to intersect previously drawn line at g. Measure vector dg to get velocity of point G. Vg = dg 0.305 m / s
  • 26. Step – 8: To determine rubbing velocity at pins Rubbing velocity at pin A will be Vpa = ab x rad of pin A = 10.5 x 0.03 = 0.315 m/s Rubbing velocity at pin B will be Vpb = ( ab + cb) x rad of point at B. [ ab CCW and cbCW] Vpb = (10.5 + 6.6) x 0.04 = 0.684 m/s. Rubbing velocity at point D will be cd x rpd of pin D = 6.96 x 0.035 = 0.244 m/s