Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN....

21
Ing. Šimon Kovář, Ph.D. Mechanism building CREATING OF KINEMATIC CHAIN

Transcript of Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN....

Page 1: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Ing. Šimon Kovář, Ph.D.

Mechanism building

CREATING OF KINEMATIC CHAIN

Page 2: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

GEOMETRICAL PRECISION OF MECHANISMS

Slider crank mechanism

manufacturing tolerance - Δr

error in the position of the slider - Δs=?

Analytical determine slider position error.

crank

slider

coupler

frame

Mechanism Building| 12.11.2015

Page 3: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Slider crank mechanism

For small dimensions is possible: 𝑑𝑟 = Δ𝑟

𝑑𝑠 = Δ𝑠

Mechanism Building| 12.11.2015

Page 4: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Swinging mechanism

For small dimensions is possible:

𝑑𝐻 = Δ𝐻

𝑑𝜓 = Δ𝜓

Mechanism Building| 12.11.2015

Page 5: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Swinging mechanism

manufacturing tolerance - ΔH

error in the position of the

slider - ΔΨ = ?

Analytical determine rocker

position error.

crank

slider

rocker

frame

Mechanism Building| 12.11.2015

Page 6: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Swinging mechanism

Δ𝜓 = −Δ𝐻 ∗ 𝑟 ∗ 𝑠𝑖𝑛𝜑

(𝐻 − 𝑟 ∗ 𝑐𝑜𝑠𝜑)2+𝑟2 ∗ 𝑠𝑖𝑛2𝜑

𝑐𝑜𝑠2𝜓 =(𝐻 − 𝑟 ∗ 𝑐𝑜𝑠𝜑)2

(𝐻 − 𝑟 ∗ 𝑐𝑜𝑠𝜑)2+𝑟2 ∗ 𝑠𝑖𝑛2𝜑

Mechanism Building| 12.11.2015

Page 7: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanism

Transfer function

manufacturing tolerance - Δb

error in the position of the

rocker - Δ=?

Analytical determine slider

position error.

Mechanism Building| 12.11.2015

Page 8: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanism

For small dimensions is possible:

𝑑𝑏 = Δ𝑏

𝑑𝜓 = Δ𝜓

Δ𝜓𝐶 = Δ𝜓𝑎 + Δ𝜓𝑏 + Δ𝜓𝑐 + Δ𝜓𝑑For finish error valid:

Mechanism Building| 12.11.2015

Page 9: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

TRNASFORMATION OF MECHANISMS

Definition for transformation angle

The angle between the direction

of absolute motion and direction

of the relative motion of the

point in which the driven

member gets the motion impulse

Mechanism Building| 12.11.2015

Page 10: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanism

Mechanism Building| 12.11.2015

Page 11: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanism

Important limits for analysis: maximal and minimal values of transformation angle

𝑎𝑝𝑝𝑜𝑖𝑛𝑡 𝜓1 = 0° 𝑎𝑛𝑑 𝜓2 = 180° to

Mechanism Building| 12.11.2015

Page 12: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanism

Ideal transfer between the driving and the driven parts is 90°. Optimal transformation angle is 90°.

Mechanism Building| 12.11.2015

Page 13: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanisms

Very important milestone is transformation in reversal points of mechanism.

Mechanism Building| 12.11.2015

Page 14: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanisms - example

𝜇 1,2 =?

a

d

b

c

Mechanism Building| 12.11.2015

Page 15: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanisms - example

𝜇 1,2 =?

Mechanism Building| 12.11.2015

Page 16: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

4 bar mechanisms - example

Results: 𝜇1 = 𝜇𝑚𝑖𝑛 = 104°00´

𝜇2 = 𝜇𝑚𝑎𝑥 = 81°50´

𝜓𝑂𝑃𝑇1 = 105°20´

𝜓𝑂𝑃𝑇2 = 254°40´

𝜇𝑈1 = 87°10´

𝜇𝑈2 = 98°40´

𝜓𝑈1 = 121°40´

𝜓𝑈2 = 302°00´

Mechanism Building| 12.11.2015

Page 17: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Slider – crank mechanism

Mechanism Building| 12.11.2015

Page 18: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Slider – crank mechanism

Valid for maximum and

minimum

reversal points

Mechanism Building| 12.11.2015

Page 19: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Slider – crank mechanism

example

r= 13 mml= 39 mme= 3 mm

𝜇 1,2 =?e

l

r

Mechanism Building| 12.11.2015

Page 20: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Slider – crank mechanism - example

r= 13 mml= 39 mme= 3 mm

𝜇 1,2 =?

Mechanism Building| 12.11.2015

Page 21: Mechanism building CREATING OF KINEMATIC CHAIN · 2015-11-12 · CREATING OF KINEMATIC CHAIN. GEOMETRICAL PRECISION OF MECHANISMS Slider crank mechanism ... TRNASFORMATION OF MECHANISMS

Slider – crank mechanism - example

Results: 𝜇1 = 𝜇𝑚𝑖𝑛 = 64°40´

𝜇2 = 𝜇𝑚𝑎𝑥 = 104°50´

𝜓𝑂𝑃𝑇1 = 193°20´

𝜓𝑂𝑃𝑇2 = 346°40´

𝜇𝑈1 = 86°40´

𝜇𝑈2 = 83°20´

𝜓𝑈1 = 183°20´

𝜓𝑈2 = 6°40´

Mechanism Building| 12.11.2015