Numericals on Klein's Construction

Hello everyone , today i am going to solve some numericals on Klein's Construction. Previously i have explained you how to apply this method on single slider crank mechanism. If you are first time here then i insist you to view the first part on this topic here : farooq blogs kleins construction

In first numerical there is center of gravity of connecting rod given and we have to calculate the angular acceleration of CG of connecting rod. In second numerical the crank length and connecting rod are given in the form of stroke and obliquity ratio , first we have to calculate length of crank and connecting rod .

Ques 1. Determine the velocity and acceleration of each link in a single slider crank mechanism by using Klein's Construction method .Also determine the acceleration of center of gravity of connecting rod.
Crank length= 90 mm
Connecting Rod length= 450 mm
Crank angle from IDC= 30 deg.
Center of gravity of connecting rod from crankpin= 180 mm
Speed N=600 rpm in Clockwise direction.

Ans.
as the given dimensions are quite large we need to scale it down.
let 450 mm=15 cm on paper
and 90 mm= 3 cm on paper
hence we have scaled down by 3

    ω=2πN/60
⇒ ω=2*3.14*600/60= 62.83 rad/s

This is configuration diagram of given question

For simplicity i have drawn velocity and acceleration diagram separately.

               













There is an additional information of center of gravity of connecting rod in question .
Center of gravity of connecting rod from crankpin= 180 mm
as per our scale
180 mm=180 mm/3=6 cm from crankpin .
locate CG at 6 cm from crankpin A.

to find acceleration of center of gravity of connecting rod

join the ends of radial and tangential acceleration ie join A with N and you will get resultant acceleration of connecting rod.
through cg draw a horizontal line parallel to line of stroke to cut previously drawn line AN. name that point g.
the length Og will give you cceleration of center of gravity of connecting rod .             

The calculation part

The answers are
velocity of connecting rod.=4.929 m/s
velocity of piston.=3.3196 m/s
angular velocity of connecting rod.=10.953 rad/s

radial acceleration of connecting rod.=54.243 m/s៱2
tangential acceleration of connecting rod.=173.03 m/s៱2
acceleration of piston.=344.408 m/s៱2
angular acceleration of connecting rod.=384.51 rad/s៱2
acceleration of CG of connecting rod=339.553 m/s


Ques 2. In a single slider crank mechanism having stroke length of 30 cm and obliquity ratio of 4. angular velocity of crank is 52 rad/sec  in anticlockwise direction and crank angle from IDC= 48.45 deg. Determine by using Klein's Construction method .

1. velocity of slider
2. acceleration of slider
3. angular velocity of connecting rod
4. angular acceleration of connecting rod
Crank angle from IDC= 48.45 deg.

Ans.
        the stroke length = 2 x crank length
                              2*r=30 cm
⇒    crank length r = 15 cm
     
       obliquity ratio n =length of  connecting rod / length of crank=l /r.
       4=l/15
⇒    l= 4*15= 60 cm.

as the given dimensions are quite large we need to scale it down.
let 60 mm=20 cm on paper
and 15 mm= 5 cm on paper
hence we have scaled down by 3

This is configuration diagram of given question

Velocity and Acceleration diagrams

The calculation

The answers are

velocity of slider= 6.82 m/s
angular velocity of connecting rod= 8.77 rad/s
acceleration of slider= 265.58 m/s៱2
angular acceleration of connecting rod= 449.94 rad/s៱

If you have any doubts you can ask here.

Thanks for reading :)

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