%0 Journal Article %1 819.52018 %A Crapo, Henry %A Whiteley, Walter %D 1994 %J Beitr. Algebra Geom. %K frameworks; infinitesimal motions; oriented polyhedra projection; %N 2 %P 259-281 %T Spaces of stresses, projections and parallel drawings for spherical polyhedra. %V 35 %X Our first paper Topology Struct. 20, 55-79 (1993; Zbl. 793.52006) analyzed the basic three way connection among static self stresses of plane frameworks, reciprocal diagrams and spatial oriented polyhedra. We extend this pattern to describe new: \par(i) isomorphisms between (a) the affine space of polyhedra with a fixed projection; \par (b) the vector space of self stresses of the framework; and \par (c) the space of reciprocal figures of the framework (with one fixed vertex); (ii) and dually, appropriate maps between (d) the vector space of parallel drawings of spatial polyhedral surfaces, (e) the space of frameworks with a fixed reciprocal, and \par (f) the space of parallel drawings (infinitesimal motions) of the projections.

@article{819.52018, abstract = {Our first paper [Topology Struct. 20, 55-79 (1993; Zbl. 793.52006)] analyzed the basic three way connection among static self stresses of plane frameworks, reciprocal diagrams and spatial oriented polyhedra. We extend this pattern to describe new: \par(i) isomorphisms between \par (a) the affine space of polyhedra with a fixed projection; \par (b) the vector space of self stresses of the framework; and \par (c) the space of reciprocal figures of the framework (with one fixed vertex); \par (ii) and dually, appropriate maps between \par (d) the vector space of parallel drawings of spatial polyhedral surfaces, \par (e) the space of frameworks with a fixed reciprocal, and \par (f) the space of parallel drawings (infinitesimal motions) of the projections. }, added-at = {2008-03-02T02:12:02.000+0100}, author = {Crapo, Henry and Whiteley, Walter}, biburl = {https://www.bibsonomy.org/bibtex/252040cddbd351524da1123fa7cdcd3f7/dmartins}, classmath = {*52C25 Rigidity and flexibility of structures}, description = {robotica-bib}, interhash = {dce69e98deddb9e895ba125c80189659}, intrahash = {52040cddbd351524da1123fa7cdcd3f7}, journal = {Beitr. Algebra Geom.}, keywords = {frameworks; infinitesimal motions; oriented polyhedra projection;}, language = {English}, number = 2, pages = {259-281}, timestamp = {2008-03-02T02:12:37.000+0100}, title = {Spaces of stresses, projections and parallel drawings for spherical polyhedra. }, volume = 35, year = 1994 }