Concerning cranks and rockers

Abstract

The paper starts from the fact that, for a general mechanism M of mobilty 1, the space of all configurations can be viewed as an algebraic curve V in a higher-dimensional space. Using techniques from algebraic geometry it is shown how the topology of V can be deduced from the geometry of the natural projection to the corresponding curve V′, for an appropriately chosen submechanism M′. These ideas are applied to the planar and spherical 4-bar mechanisms.