title: Specificity of the Darboux mechanism rectilinear motion
metadata.name: dc.contributor.author
metadata.value: Burian, Sergei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-12-13T14:41:29Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-12-13T14:41:29Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Burian S.N. Specificity of the Darboux mechanism rectilinear motion. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 4, pp. 658–669.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.412
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/15134
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Mechanisms of a parallel structure may have singularities in configuration space in which
  system controllability may be lost or additional instantaneous degrees of freedom may
  appear. These features have kinematic base. But interest is also represented by geometric
  singularities, when the mechanism in some configuration could change the type of motion.
  The example of a mechanism with branch points, the Darboux mechanism, is considered. It
  is proved that this hinged mechanism can transform the rotational motion of one rod into
  a (strictly) rectilinear motion of its vertex H. The rods of Darboux’s mechanism can form
  geometric figures, such as triangles and a square (with diagonals drawn). In the “square”
  configuration of the mechanism the branch point arises: the vertex H can move both along
  the straight line L and along the curve γ. The rank of the holonomic constraints of the
  system in singular point falls by one. For a rectilinear motion of the vertex H, the Lagrange
  equation of the second kind is written in terms of the coordinate of H. The coefficients of
  this equation smoothly extend through the branch point. The “limiting” behavior of reaction
  forces in rods is analyzed when the mechanism moves to the branch point. An external force
  that does not work on the point H leads to unlimited reactions in the rods. Kinematics at
  the branch point are studied. The inverse problem of dynamics at a point where the rank
  of holonomic constraints is not maximal is solvable. The Lagrange multipliers of Λi at the
  branch point are not uniquely determined, but the forces corresponding to them acting on
  the vertices of the mechanism are uniquely determined.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5 (63); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Darboux mechanism
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: singular point
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: inverse problem of dynamics
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Specificity of the Darboux mechanism rectilinear motion
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 12-Burjan.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/15134/1/12-Burjan.pdf
resources.format: Adobe PDF
resources.size: 763,52 kB