Kinematics Lecture: Design of a Linkage System to Draw a Curve

Kempe’s Universality Theorem states that every algebraic curve has an associated linkage that draws the curve. A popular phrasing of this theorem is “a linkage exists that can sign your name”. This lecture summarizes our efforts to find simplified versions of curve-drawing linkages. A remarkable outcome is the ability to mechanically draw Bézier curves, which yields a linkage system that can sign your name, and even write cursive Chinese. I was honored to return to the University of Pennsylvania’s Grasp Lab after over 30 years to make this presentation. This highlights the excellent work Yang Liu.

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