Graphical linkage synthesis 4 bar kinematic chain · Synthesis of slider crank mechanism Stavba...

Ing. Šimon Kovář, Ph.D.

Graphical linkage synthesis

4 bar kinematic chain

4 bar kinematic chain synthesis

Engaged: A1, A2, B1, B2

Detect: D1, D2, C1, C2

Choose: D0, C0


Step 1.

connecting line A1 –A2, B1 – B2


Step 2.

symetrals a12, b12

Pole P12

Angle 12 /2


Step 3.

Choose C0, D0

symetrals s1, s2


Step 4.

Angles 12 /2 from s1 and s2

4 bar kinematic chain synthesisStep 5.

Choose points C1 and D1

Points C2 and D2 as symetrical by s1 or s2


Step 6.

First version


Step 7.

Second version

Synthesis of slider crank mechanism

𝐴1 −2.0; 5.5 , 𝐵1 1.5; 6.0

𝐴2 1.0; 2.5 , 𝐵2 4.0; 0.7

Stavba Mechanismů| 20.10.2015

A1

B1

C0

D0

C1

A2

B2

e

𝑒 = 2.0 𝑐𝑚

𝐶0 0.0; 0.0 , 𝐷0 0.5; −5.0

Engaged: A1, A2, B1, B2

C0 , D0, e

Detect: C1, C2



Step 1.



Step 2.

joints A1 A2, B1 B2

symmetrals o1, o2



Step 3.

Cross o1 and o2– motion pole P12

Angle 12 /2

Symmetrals c12, d12

Angles 12 /2 od c12 a d12 – c1, d1, c2, d2



Step 4.

Tangent t1 to k together perpendicular to d1

Tangent t2 to k together perpendicular to d2

Point C1 as cross t1 and c1

Point C2 as cross t2 and c2



First version of mechanism



Second version of mechanism

Slider crank synthesis version I

Engaged: 𝐴0, 𝐵1, 𝑒, 𝐵2, 𝜑12, 𝜑0

Detect: 𝐴1, 𝐴2

𝐴0 0; 0𝐵1 7;−1.5

𝑒 = 1.5 𝑚𝑚𝐵1 9.5; −1.5

𝜑12 = 40°𝜑0 = 55°

Slider crank synthesis version I

Result:

Slider crank synthesis version II

𝐴0𝐴1, 𝐴0𝐴2, 𝑃, 𝑙12, 𝜑0, 𝜑12

𝐵1, 𝐵2

Engaged:

Detect:

𝐴0 0; 0

𝑒 = 1 𝑐𝑚𝜑12 = 65°

𝜑0 = 25°

𝐴0𝐴1 = 4 𝑐𝑚𝐴0𝐴2 = 4 𝑐𝑚

Slider crank synthesis version II

𝐴0𝐴1, 𝐴0𝐴2, 𝑃, 𝑙12, 𝜑0, 𝜑12

𝐵1, 𝐵2

Engaged:

Detect:

Synthesis of 4 bar mechanism 2 prescribed

parallel positions of general member

Engaged:

C0 [0;0]

D0 [9;0]

A1 [3;8]

A2 [7;8]

= 45

rc = 3 cm

= 60

Detect:

C1 ,D1 , C2 , D2



Step 1.

Create sA and sC , sD



Step 2.

Create sC1 , sC2 , sD1 , sD2

Cross points C1, C2, D1, D2



Step 3.



Synthesis of 4 bar mechanism 2 prescribed parallel positions of

general member and transformation

Engaged:

C0 [0;0]D0 [10;0]A1 [3;5]A2 [7;4]= 45AB = 4 cm24

(1)=24(2)=2/4

Detect:

C1 ,D1 , C2 , D2



Step 1.

Create sA and sC , sD



Step 2.





Transformation

Definition of transformation

P42 42 = 43 + 32

42 = 41 +12

𝜇24(1)

=𝑥1

𝑥1 + 𝑑

𝜇24(2)

=𝑥2

𝑥2 + 𝑑

𝑥1 =𝜇24(1)

∙ 𝑑

1 − 𝜇24(1)

𝑥2 =𝜇24(2)

∙ 𝑑

1 − 𝜇24(2)



Step 3.

Transmission in position 1 (local

transmission) is same as transmission in

position 2



Step 4.

Create pole line and cross between

the line and SC1 and SD1



Step 5.

Kinematic chain C0C1D1D0, C0C2D2D0,

Synthesis of 4 bar mechanism 2 prescribed infinite nearly positions of

general members and for prescribed direction of motion from position 1

Engaged:

C0 [0;0]

D0 [9;0]

A1 [3;8]

A2 [7;8]

tA and tB



Step 1.

Create SA, SB

P12 -

Step 2.

Create SA

Create SC and SD



Step 3.

Choice point C1 and D1

Points D1 and D2



Graphical linkage synthesis 4 bar kinematic chain · Synthesis of slider crank mechanism Stavba...

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