On the elliptic curves arising from 4-bar mechanisms. (English) Zbl 1254.14036

C. G. Gibson and P. E. Newstead [Acta Appl. Math. 7, 113–135 (1986; Zbl 0629.70002)] investigated the algebraic geometry of the residual curve (configuration curve minus spurious components) of a planar 4-bar mechanism in the constructable case, where at least one real configuration exists. One result states that the residual curve and the mechanism’s Darboux cubic are isomorphic over the complex numbers.
In the article under review, the authors ask whether a real isomorphism between residual curve and Darboux cubic exists. In the generic non-constructable case this is not the case. For the constructable case, the question remains open.


14H52 Elliptic curves
14P25 Topology of real algebraic varieties
70B15 Kinematics of mechanisms and robots


Zbl 0629.70002


Full Text: DOI Euclid


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