Offset crank slider mechanism connecting rod analysis

In summary, the angle θ (measured from vertical) when the angular velocity of link AB a maximum is 8.1289°. The maximum angular velocity of link AB is 13.6329 rads-1.
  • #1
sponsoraw
43
1

Homework Statement



A) Determine the value of the angle θ (measured from vertical) when the angular velocity of link AB a maximum.

B) What is the maximum angular velocity of link AB.

slider crank.JPG


Homework Equations

The Attempt at a Solution


This is a part of a bigger question. I've managed to answer all other part apart of those two. Can anyone point me in the right direction. I'm not an expert in this subject. Just let me know if you require any more data.
 
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  • #2
sponsoraw said:

Homework Statement



A) Determine the value of the angle θ (measured from vertical) when the angular velocity of link AB a maximum.

B) What is the maximum angular velocity of link AB.

View attachment 86939

Homework Equations

The Attempt at a Solution


This is a part of a bigger question. I've managed to answer all other part apart of those two. Can anyone point me in the right direction. I'm not an expert in this subject. Just let me know if you require any more data.
It's likely that the other parts of the problem will help answer these.

Also, as you should know by now, you need to make an attempt at a solution.
 
  • #3
No problem SammyS, I will include the full question and all my workings done so far.
 
  • #4
1) For the mechanism shown in the figure included within the #1 post determine for the angle θ=45°:

a) the velocity of the piston relative to the fixed point O (VBO)
b) the angular velocity of AB about point A (i.e. ωAB)
c) the acceleration of point B relative to A (αBA)

Note: Link AB is horizontal when θ=45°.

2) Determine the value of the angle θ (measured from vertical) when:

a) the velocity of point B=0
b) the angular velocity of link AB a maximum

3) What is the maximum angular velocity of link AB?

ANSWER:
ωOA=300 revsmin-1=10π rads-1
lOA=0.05m
lAB=0.2m

1)
a)
VAO=lOAOA=0.05*10π=1.5708 ms-1
using velocity triangle
cosθ=VBO/VAO
VBO=cos45°*VAO=(√2/2)*1.5708=1.1107 ms-1

b)
sinθ=VBA/VAO
VBA=sin45°*VAO=(√2/2)*1.5708=1.1107 ms-1
VBA=lABAB
ωAB=VBA/lAB=1.1107/0.2=5.5535 rads-1

c)
αBA(r)=lABAB2=0.2*5.55352=6.1683 ms-2
ωOA=VAO/lOA=1.5708/0.05=31.416 rads-1
αAO(r)=lOAOA2=0.05*31.4162=49.3482 ms-2

drawing acceleration diagram using following scale (see acceleration diagram attachment)
1 cm=20 mm
1 cm=5 ms-2

measured from the graph
αBA(t)=6.9cm=34.5 ms-2

2)
a)
The velocity of point B=0 occurs at maximum and minimum piston displacement.

calculating the offset height lOD (see the graph attachment)
cosθ=lOD/lOA
lOD=cos45°*lOA=(√2/2)*50=35.3553 mm

calculating at max displacement.
lOB=lOA+lAB=50+200=250 mm
let the angle symmetry line through O and the crank-connection rod at max piston displacement be γ
sinγ=lOD/lOB=35.3553/250=0.1414
γ=arcsin(0.1414)=8.1289°
so θ at max piston displacement (measured from vertical) is θ=90°=8.1289°=81.8711°

calculating at min displacement.
let the angle symmetry line through O and the crank-connection rod at min piston displacement be β
sinβ=lOD/(lAB-lOA)=35.3553/150=0.2357
β=arcsin(0.2357)=13.6329°
so θ at min piston displacement (measured from vertical) is θ=270°-13.6329°=256.3671°

b)
To be able to determine the value of the angle θ (measured from vertical) when the angular velocity of link AB a maximum I need to work out at which position the link AB has the max angular velocity.

3)
Once I know the answer to 2b) I should be using either trigonometry or velocity diagram calculate that velocity. At least I think/hope so.
 

Attachments

  • graph.jpg
    graph.jpg
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  • acceleration diagram.jpg
    acceleration diagram.jpg
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  • #5
Guys, can anyone help me with question 2b and 3 - see post #4. Much appreciated.
 
  • #6
sponsoraw said:
Guys, can anyone help me with question 2b and 3 - see post #4. Much appreciated.
I'm sorry about not getting back to you sooner. I was off traveling.

I will try to wade through that material.

One thing I noticed on drawing for this problem, the angle that OA makes with the horizontal is not θ. It's (π/2) - θ , i.e. 90° - θ. It's only equal to θ for θ = 45° .

graph-jpg.86968.jpg
 
  • #7
Good Morning SammyS,

I believe you don't have any further information on my question? Thanks for trying anyway. I think the connection rod is at the max velocity when is perpendicular to the crank. I will use this assumption and try to work out the angle and the velocity.
 

Related to Offset crank slider mechanism connecting rod analysis

1. What is an offset crank slider mechanism connecting rod?

An offset crank slider mechanism connecting rod is a mechanism used in engines to convert the linear motion of a piston into rotational motion. It consists of a crankshaft, connecting rod, and piston. The offset crank slider mechanism helps to reduce vibrations and improve engine efficiency.

2. How does the offset crank slider mechanism work?

The offset crank slider mechanism works by using a crankshaft to convert the linear motion of a piston into rotational motion. The connecting rod connects the piston to the crankshaft at an offset angle, allowing the piston to move up and down while the crankshaft rotates. This rotation is then used to power other parts of the engine.

3. What are the advantages of using an offset crank slider mechanism?

The offset crank slider mechanism has several advantages, including reducing vibrations, improving engine efficiency, and allowing for a more compact engine design. It also helps to reduce wear and tear on engine components, resulting in a longer lifespan for the engine.

4. How is the connecting rod analyzed in an offset crank slider mechanism?

The connecting rod is analyzed in an offset crank slider mechanism by considering the forces and torques acting on it. This includes analyzing the motion of the piston and the rotation of the crankshaft, as well as the forces exerted on the connecting rod by these motions. This analysis helps to determine the strength and durability of the connecting rod.

5. What are some applications of offset crank slider mechanism connecting rods?

The offset crank slider mechanism connecting rod is commonly used in internal combustion engines, such as those found in cars, motorcycles, and lawnmowers. It is also used in some types of pumps and compressors. Additionally, the offset crank slider mechanism can be found in some industrial machinery and agricultural equipment.

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