Symmetrical Coupler Curves

Symmetrical Coupler Curves are frequently useful. For example, you can find a coupler curve to give two straight lines. These are often 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 = B0B = BK

Axis-of-Symmetry

Symmetrical Coupler Curves must have an Axis-of-Symmetry.

The 'axis-of-symmetry' is the ray: B0.J

The angle direction of the axis-of-symmetry, relative to the frame, from B0 is given by:

∠A0B0J  (Θ)= ∠ ABK / 2  (External Angle ∠ABK )

Coupler Point on the Axis-of-Symmetry

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

Video of Symmetrical Coupler Curve and Axis-of-Symmetry

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

The mechanism is a standard four-bar mechanism. The length of the Coupler and the Rocker are equal. The distance from joint B to the Coupler Point, K, is equal to the length of the Rocker and Coupler. Thus, the Coupler Curve will be symmetrical.

The videos shows,

shows a stationary 4-bar
the coupler curve for the full cycle of the mechanism [but we are not moving the mechanism]
the Crank-Angle, α [BoAoA] is fixed at 180º .
the angle ABK changes from 0 to 360

Thus, everything is fixed, but we move the coupler point, K, by rotating it about joint B

Because AB, BoB, and BK have equal lengths, the coupler curve is be symmetrical.

the axis-of-symmetry changes and rotates about Bo as we change the angle ABK[2Θ]

Video of Symmetrical Coupler Curve.

 

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

A Symmetrical Coupler can be applied to index a Geneva Wheel. See videos below.

Video of a Geneva Indexer controlled with a Symmetrical Coupler Curve.

 

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