tom

Theory of Machies

II Prepared by IIVimal Patel

Mechanical Engineering Department, SVNIT, Surat – 395007Ph. No. : +919099573650 E-mail : - [email protected]

` Practical Manuel

Theory of Machies Page 1 of 4

Sheet No :1 Types of CAMS

Mechanical Engineering Department, SVNIT, Surat – 395007Vimal Patel : +919099573650 E-mail : - [email protected]

`

[A] Types of cams according to Shape

1. Wedge and Flat cams

1 Types of CAMS




2. Radial or Disc Cams 3. Spiral Cams

4. Cylindrical Cam 5. Conjugate Cams




6. Globoidal Cams 7. Spherical Cam

[B] According to follower Movement

1. R-R-R 2. D-R-R-D 3. D-R-D-R-D 4. D-R-D




Terminology of Cam mechanisms:


Sheet No :2 Machines And Mechanisms


`

[A] Types of Constrained Motions1. Completely constrained motion

Fig. Square bar in a square hole. Fig. Shaft with collars in a circular hole.2. Incompletely constrained motion

Fig. Shaft in a circular hole. Fig. Shaft in a foot step bearing.

2 Machine and Mechanism




[B] Inversions of Four Bar Chain

Fig. Beam engine. Fig. Coupling rod of a locomotive.[C] Single Slider Crank Chain

Fig. Pendulum pump.




Fig. Oscillating cylinder engine. Fig. Rotary internal combustion engine.

Fig. Crank and slotted lever quick return motion mechanism. Fig. Whitworth quick return motion mechanism




[C] Inversions of Double Slider Crank Chain

Fig. Double slider crank Chain Fig. Scotch yoke mechanism.

Fig. Oldham’s coupling.


Sheet No :3 Velocity Analysis [Relative velocity Approach]


`

Ex.1 In a four link mechanism shown in fig.1, the dimensions of the links are as under:

AB = 50 mm BC = 66 mmCD = 56 mm AD = 100 mmAt the instant when angle DAB = 60º, the link AB has an angular velocity of 10.5 rad/s in the counter clockwisedirection. Determine,

i. Velocity of the point C.ii. Velocity of the point E on the link BC when BE=40mm.iii. Angular velocities of the links BC and CD.iv. Velocity of an offset point F on the link BC if BF = 45 mm, CF = 30 mm and BCF is read clockwise.v. Velocity of an offset point G on the link CD if CG = 24 mm, DG = 44 mm and DCG is read clockwise.vi. Velocity of rubbing at pins A, B,C and D when the radii of the pins are 30, 40, 25 and 35 mm respectively.

Answers:[i] 0.39 /cV m s[ii] 0.415 /eV m s

[iii]5.15 /

6.96 /cb

cd

rad s

rad s

[iv] 0.495 /fV m s

[v] 0.306 /gV m s

[vi] 0.626 /Br

V m s

0.303 /Cr

V m s

0.315 /Ar

V m s

0.244 /Dr

V m s

Figure 1 Velocity diagram

3 Velocity Analysis[Relative velocity Approach]


Sheet No :3 Velocity Analysis [Relative velocity Approach]


Ex.2 An engine crankshaft drives a reciprocating pump through a mechanism as shown in figure 2. The crank rotates in theclockwise direction at 160rpm. The diameter of the pump piston at F is 200 mm. Dimensions of the various links areOA = 170 mm (Crank) CD = 170 mm AB = 660 mmDE = 830 mm BC = 510 mmFor the position of the crank shown in the diagram, determine the,

i. Velocity of cross head E.ii. Velocity of rubbing at pins A, B, C and D, the diameters being 40, 30, 30 and 50 mm respectively.iii. Torque required at shaft O to overcome a pressure of 300 kN/m2 at the pump piston at F.

Answers:

[i] 0.54 /eV m s[ii] 0.26 /

ArV m s

0.107 /Br

V m s

0.05 /Cr

V m s

0.079 /Dr

V m s

[iii] 303.66T Nm

Figure. 2 Velocity Diagram


Sheet No :4 Velocity Analysis [Instantaneous Centre Method]


`

Ex.1 Figure 1 shows a six link mechanism. The dimensions of the links are OA = 100 mm, AB = 580 mm, BC = 300 mm, QC = 100mm and CD = 350 mm. The crank OA rotates in clockwise at 150 RPM. For the position when crank OA makes an angle of30º with the horizontal, determine:

i. Linear velocities of the pivot points B, C and D.ii. Angular velocities of the links AB, BC and CD.

Answers:[i] 2.66 /bV m s

1.33 /cV m s0.788 /dV m s

[ii] 5.88 /ab rad s 13.3 /bc rad s 2.66 /cd rad s

4 Velocity Analysis[Instantaneous Centre Method]

Figure 1Instantaneous centers

Solution


Sheet No :4 Velocity Analysis [Instantaneous Centre Method]


Ex.2 Figure 2 shows a sewing needle bar mechanismO1ABO2CD wherein the different dimensions are as follows:Crank O1A = 16 mm; ∠β = 45°; Vertical distance between O1 and O2 = 40 mm; Horizontal distance between O1 and O2 = 13mm; O2B = 23 mm; AB = 35 mm; ∠O2BC = 90°; BC = 16 mm; CD = 40 mm. D lies vertically below O1.Find the velocity of needle at D for the given configuration.The crank O1A rotates at 400 r.p.m.

Figure 2

Instantaneous centers

Solution


Sheet No :5 Acceleration Analysis


`

Ex.1 Figure shows the configuration diagram of a four link mechanism along with the lengths of the links in mm. The link ABhas an instantaneous angular velocity of 10.5 rad/s and a retardation of 26 rad/s2 in counterclockwise direction. Find:

i. The angular accelerations of the links BC and CD.ii. The linear accelerations of the points E, F and G.

[i] 234.09 /BC rad s 279.11 /CD rad s

[ii] 25.15 /ef m s24.42 /ff m s

23.9 /gf m s

5 Acceleration Analysis




Ex.2 In toggle mechanism shown in figure, the crank OA rotates at 120 rpm counter clockwise increasing at the rate of 60rad/s2. For the given configuration, determine,

i. Velocity of slider D and the angular velocity of link BD.ii. Acceleration of slider D and the angular acceleration of link BD.

[i] 2.54 /DV m s , 6.32 /BD rad s

[ii] 216.4 /Df m s , 2109.2 /BD rad s




`

Ex.1 Figure shows a link mechanism of a quick return mechanism of the slotted lever type, the various dimensions ofwhich areOA=400 mm OP = 200 mm AR = 700 mm RS = 300 mmFor the given configuration shown, determine the acceleration of the cutting tool at S and the angular acceleration ofthe link RS. The crank OP rotates at 210 rpm.

[i] 232.8 /sf m s , 252.3 / ( )RS rad s CW

6 Acceleration Analysis




Ex.2 In the swiveling joint mechanism shown in fig, AB is the driving crank rotating at 300 RPM clockwise. The lengths ofthe various links are,AD = 650 mm AB = 100 mm BC = 800 mm DC = 250 mm BE=CE, EF = 400mm OF = 240mm FS=400mmFor the given configuration of the mechanism, determine the acceleration of sliding of the link EF in the trunnion.

[i] 24.86 /f m s in trunioun


Sheet No :7 Cam Profile [Constant Velocity]


`

Ex.1 Cam with 100 mm as minimum diameter is rotating clockwise at a uniform speed of 1200 rpm and has to give themotion to knife edge follower as defined below:

i. Follower to complete outward stroke of 40 mm during 600 of cam rotation with uniform velocity.ii. Follower to dwell for 300 cam rotation.iii. Follower to return to its initial position during 800 of cam rotation with uniform velocity.iv. Follower to dwell for the remaining 1900 cam profile.

Layout the cam profile when:[a] The follower axis passes through the axis of cam[b] The follower axis is offset to the right by 20mm

Determine the uniform velocity of follower on the outstroke and the return stroke. Also draw displacement, velocity andacceleration diagrams.

7 Cam Profile[Constant Velocity]


Sheet No :8 Cam Profile [Constant Acceleration and Retardation]


`

Ex.1 Cam with 70 mm as minimum diameter is rotating clockwise at a uniform speed of 1200 rpm and has to give the motionto the roller follower of 20 mm diameter as defined below:

i. Follower to complete outward stroke of 40 mm during 1200 of cam rotation with equal uniform acceleration andretardation.

ii. Follower to dwell for 600 cam rotation.iii. Follower to return to its initial position during 900 of cam rotation with equal uniform acceleration and

retardation..iv. Follower to dwell for the remaining 900 cam profile.

Layout the cam profile when:[a] The follower axis passes through the axis of cam[b] The follower axis is offset to the right by 15mm

Determine:i. The uniform acceleration and retardation of follower on out stroke and return stroke.ii. Maximum velocity of follower during outstroke and return strokeiii. Acceleration / deceleration of follower after 300 of cam rotation after starting of accent period.iv. Draw displacement, velocity and acceleration diagrams.

8Cam Profile

[Constant Acceleration and Retardation]


Sheet No :9 Cam Profile [Simple Harmonic Motion]


`

Ex.1 Cam with 80 mm as minimum diameter is rotating clockwise at a uniform speed of 240 rpm and has to give the motionto the flat faced follower as defined below:

i. Follower to complete outward stroke of 36 mm during 1200 of cam rotation with Simple Harmonic Motion ofFollower.

ii. Follower to dwell for 300 cam rotation.iii. Follower to return to its initial position during 1000 of cam rotation with Simple Harmonic Motion.iv. Follower to dwell for the remaining 1100 cam profile.

Layout the cam profile when;[a] The follower axis passes through the axis of cam[b] The follower axis is offset to the right by 10mm

Determine:i. The maximum velocity and acceleration of follower during out stroke and return stroke.ii. Acceleration / deceleration of follower after 300 of cam rotation after starting of accent period.iii. Draw displacement, velocity and acceleration diagrams.

9Cam Profile

[Simple Harmonic Motion]


Sheet No :10 Cam Profile [Cycloidal Motion]


`

Ex.1 Draw the profile of a cam to give the following motion to the oscillating roller follower.i. Follower to move outwards by an angular displacement of 300 during 1200 of cam rotation with cycloidal motion.ii. Follower to dwell for 300 of cam rotation at end of out stroke.iii. Follower to return to its initial position during 1200 of cam rotation with constant acceleration during first half (up

to midway) and with constant velocity during second half (up to end).iv. Follower to dwell during the next 900 of cam rotation.

The distance between oscillating follower pivot center and cam axis = 115 mm. The distance between pivot and oscillating roller follower center or length of the follower = 100 mm Minimum radius of the cam = 50 mm Follower roller radius = 10 mm Speed of the cam = 500 rpm in anticlockwise direction.

Determine;i. Maximum linier velocity and acceleration during accent.ii. Constant acceleration and velocity during return.iii. Draw graph of linier displacement, velocity and acceleration with reference to cam rotation angle to the scale.

10Cam Profile

[Cycloidal Motion

tom

Documents

dtheory of machies page

angular velocity

types of constrained

link mechanism

link bc

flat cams1 types of

c single slider crank

theory of machiesii