What is the velocity of the crosshead - crank, Mechanical Engineering

What is the velocity of the crosshead - crank:

In the slider crank mechanism shown in Figure, the crank is rotating clockwise at 120 revolution/minute. What is the velocity of the crosshead when the crank is in the 60o phase?

Solution

We have, crank AB = 200 mm = 0.2 metres.

ω AB  = 120 revolutions / minute

= 120 × 2 π /60

= 4 π rad / sec

As B rotates about A, vB  = AB . ω AB  = 0.2 × 4 π = 0.8 π = 2.51 m / sec , and vB is perpendicular to AB.

Crosshead C moves along the horizontal line as shown.

 We know vB fully, its magnitude and direction.

Consider Δ ABC,

AB /sin α   =    BC /sin 60o  =  AC / sin (120o  - α)

∴ sin α = (AB / BC ). sin 60o  = (200/900) × 0.866 = 0.1924

 ∴ α = 11.09o

 (i)        By Instantaneous Centre Method

Draw perpendiculars to vB at B and to vC at C. They meet at O.

Consider Δ BOC.

BC /sin 30o =   CO /sin 71.09 o = BO / sin 78.9o

∴ OC = 0.9 ×( sin 71.09 /sin 30o) = 1.702 m

OB = 0.9 × (sin 78.9 /sin 30o) = 1.76 m

∴ ωBC =  vB /OB =( 2.51/1.76) = 1.426 rad / sec

vC  = ωBC  × OC = 2.42 m / sec

 (ii)       By Velocity Diagram Method

From any point O draw a line perpendicular to AB to represent vB. From end of vB draw a line perpendicular to BC to represent vBC. Next, draw from O a line parallel to AC to represent vC.

∴          vB /sin 78.91o  =           vBC /sin 30o    = vC /sin 71.11o

∴ vC  = vB . (sin 71.11o /sin 78.91o)

= 2.42 m / sec

vC = vB.   (sin 30 o / sin 78.91o)

= (2.51 × 0.5 )/0.98

= 1.2806 m / sec

∴ ωBC    = vBC / BC

 = 1.2806 /0.9 = 1.423 rad/sec

Posted Date: 1/29/2013 2:10:33 AM | Location : United States







Related Discussions:- What is the velocity of the crosshead - crank, Assignment Help, Ask Question on What is the velocity of the crosshead - crank, Get Answer, Expert's Help, What is the velocity of the crosshead - crank Discussions

Write discussion on What is the velocity of the crosshead - crank
Your posts are moderated
Related Questions

(a) What do you understand by the following : (i) Open System (ii) Closed System (iii) Concept of ‘Work' (b) 0.014 m 3 gas at a pressure of 2070 KPa expends to a pressure of

Nitrides, Silicides and Sulfides Nitrides contain very high melting point but initiate to oxidize at low temperature. They have poor resistance also to chemicals. Boron nitrid

List and explain four different types of layouts for a factory.

Con e of Friction: When the body is having impending motion   in direction of P , the frictional force will be limiting friction and the resultant reaction R wil

Explain in detail about the Pile Foundations Where the support given by top soil is not sufficient and the load has to be carried deep down for purposes of stability and contro

Q. What is Extrusion defects? • Surface cracking - When the surface of an extrusion splits. This is often caused by the extrusion temperature, friction, or speed being too high

A flat belt, 8 mm thick and 100 mm wide transmits power between two pulleys, running at 1600 m/min. The mass of the belt is 0.9 kg/m length. The angle of lap in the smaller pulle

Symmetric Central Force A central force is spherically if the magnitude of the force does not depend on the direction (angles  θ , or  Ø ) of the particle but only on distance

Torque carried by the hollow shaft: A hollow and a solid shaft of similar material have the same weight when the inner diameter of the hollow shaft is half its outer diameter.