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 FourBar Mechanism to give a Symmetrical CouplerCurve. 
The fourbar 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 AxisofSymmetry Symmetrical Coupler Curves must have an AxisofSymmetry. The 'axisofsymmetry' is the ray: B0.J The angle direction of the axisofsymmetry, relative to the frame, from B0 is given by: ∠A0B0J (Θ)= ∠ ABK / 2 (External Angle ∠ABK ) 
Coupler Point on the AxisofSymmetry The Coupler Point happens to be on the AxisofSymmetry 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 fourbar 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.
