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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 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 = BOB = BK AxisofSymmetry The AxisofSymmetry is the ray: BOJ The angle of the axisofsymmetry, relative to the frame, from BO is: ∠AOBOJ(Θ)= ∠ABK / 2 (External Angle =∠ABK ) The Coupler Point is on the AxisofSymmetry when the Input Crank angle, α, is 0 and 180 
Video of Symmetrical Coupler Curve and AxisofSymmetry
It is worth watching this video two or three times to understand the mechanism design. In the video: •the 4bar is stationary, as we edit the angle ABK from 0 to 360 •the CouplerCurve is the path of K for a complete a rotation of the Crank, AOA •the CrankAngle, α (BOAOA) is fixed at 180º . Because the lengths of AB, BOB, and BK are equal, the CouplerCurve is be symmetrical. •the axisofsymmetry ∠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. 