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Two-Position Synthesis

Two-position synthesis is used to design a four-bar linkage that moves a body between two specified positions. There are two common cases: Crank Output and Coupler Output.

Crank Output​

In crank output synthesis, you design a four-bar linkage where the output link (rocker) rotates between two angular positions.

  1. Use a reference image to define the start and end positions
  2. Place points P1 and P2 at the start and end positions
  3. Draw a Segment connecting P1 and P2
  4. Construct the Perpendicular Bisector of the segment
  5. Place a point P3 at the intersection
  1. Choose a point P4 on the perpendicular bisector as the crank fixed pivot
  2. Draw a Line through P1 and P2
  3. Choose a point P5 on this line as the rocker fixed pivot
  1. Use Compass with P1 and P3 as radius, and P5 as center
  2. Place a point P6 at the intersection of the compass circle and the line P1-P2 (the rocker moving pivot)
  1. Sketch the linkage on top of the geometry construction

Coupler Output​

In coupler output synthesis, you design a four-bar linkage where the coupler moves between two positions.

  1. Use a reference image to define the two coupler positions
  2. Draw a Segment with points P1 and P2 on top of the first coupler position
  3. Use Compass with P1 and P2 as radius
  4. Place the compass center at the first point of the second coupler position (P3)
  5. Draw a Segment from P3 to P4, where P4 is on the compass circle
  6. Rotate segment P3-P4 to align with the second coupler position
  7. (Optional) Hide the compass circle
  1. Draw a Segment between P1 and P3
  2. Construct the Perpendicular Bisector of the segment
  3. Choose a point P5 on the bisector as the first fixed pivot
  1. Draw a Segment between P2 and P4
  2. Construct the Perpendicular Bisector of the segment
  3. Choose a point P6 on the bisector as the second fixed pivot
  1. Sketch the linkage on top of the geometry construction