论文信息 - Automated generation of Kempe linkages for algebraic curves and surfaces

Automated generation of Kempe linkages for algebraic curves and surfaces

Abstract The well-known Peaucellier linkage converts a circular motion into a linear motion. A more shocking result by Kempe [Proc. LMS (1876) 213] shows that any plane algebraic curve can be delineated by a linkage. In this paper, we improve Kempe's result to give a precise algorithm for generating the Kempe linkage. We prove that for an algebraic plane curve of degree n , the corresponding Kempe linkage uses at most O( n 4 ) links. We extend Kempe's result to the 3D case: any algebraic surface can be delineated by a 3D linkage. We implement a program which can construct the Kempe linkage and animate the drawing process for a given plane curve.

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