Symmetrical Coupler Curves

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Symmetrical Coupler Curves

Symmetrical Coupler Curves

Symmetrical Coupler Curves are frequently useful. For example, you can find a coupler curve with two straight lines that may be useful for Dwell Mechanisms.

Mechanisms with symmetrical coupler curves are easy to design with MechDesigner.

Design Parameters of a Four-Bar Mechanism to give a Symmetrical Coupler-Curve.

Design Parameters of a Four-Bar Mechanism to give a Symmetrical Coupler-Curve.

The four-bar mechanism to the left is defined by the Points: AoA (Crank), BoB (Output Rocker), AB (Coupler), Point K (Symmetrical Coupler Point on Part AB).

Symmetrical Coupler Curves

A Coupler Curve becomes symmetrical when:

AB = BOB = BK

Axis-of-Symmetry

The Axis-of-Symmetry is the ray: BOJ

The angle of the axis-of-symmetry, relative to the frame, from BO is:

∠AOBOJ(Θ)= ∠ABK / 2  (External Angle =∠ABK )

The Coupler Point is on the Axis-of-Symmetry when the Input Crank angle, α, is 0 and 180

Video of Symmetrical Coupler Curve and Axis-of-Symmetry

It is worth watching this video two or three times to understand the mechanism design.

In the video:

the 4-bar is stationary, as we edit the angle ABK from 0 to 360  

the Coupler-Curve is the path of K for a complete a rotation of the Crank, AOA

the Crank-Angle, α (BOAOA) is fixed at 180º .

Because the lengths of AB, BOB, and BK are equal, the Coupler-Curve is be symmetrical.

the axis-of-symmetry ∠AOBOJ, increases as we increase ∠ABK

Video of Symmetrical Coupler Curve.

 

Symmetrical Coupler Curves

Video of Symmetrical Coupler Curve.

Application of Symmetrical Coupler Curve with two straight lines: Geneva Indexer

 

Symmetrical Coupler Curves

Video of a Geneva Indexing Mechanism controlled with a Symmetrical Coupler Curve.