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Peaucellier-Lipkin Linkage

Sad Little Mechanical Engineering Laboratory
7-Bar Linkage
Straight-Line Motion
Exact Straight-Line Motion Without Sliding Joints
Animation Controls
Speed 0.40x
Phase 0%
Easing Function
Linkage Parameters
Crank Radius (r) 80
Long Link (L) 215
Rhombus Side (a) 100
Presets
Display Options
View Controls
Zoom 100%
Current State
Angle
0.0°
Direction
→
Phase
0%
Eased
0%
Color Legend
Crank (AQ)
Long Links (OB, OC)
Rhombus (BQCP)
Valid Arc
Output Trace

Circle Inversion Principle

Key relationship: OQ · OP = L² - a² = k²

Points Q and P are inverses with respect to a circle centered at O.

Seven-Bar Structure

• Bar 1: AQ (Crank)
• Bars 2-3: OB, OC (Long links)
• Bars 4-7: BQ, QC, CP, PB (Rhombus)

Historical Note

Invented by Charles-Nicolas Peaucellier (1864) and Yom Tov Lipman Lipkin (1871), this was the first planar linkage to achieve exact straight-line motion using only revolute joints.