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.

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: 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,

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.

Video of Symmetrical Coupler Curve.

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.