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  • 70B10  (2)
  • 70B15  (1)
  • Springer  (3)
  • Oxford University Press
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  • Springer  (3)
  • Oxford University Press
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  • 1
    Electronic Resource
    Electronic Resource
    First-order invariants of Euclidean motions (1991)
    Springer
    Acta applicandae mathematicae 24 (1991), S. 233-251 
    Details
    ISSN: 1572-9036
    Keywords: 70B10 ; Kinematics ; invariants ; screws
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let E(n) be the lie group of proper rigid motions of Euclidean n-space. The paper is concerned with the adjoint action of E(n) on its Lie algebra e(n), and the induced action on the Grassmannian of subspaces of e(n) of a given dimension. For the adjoint action, the authors list explicit generators for the ring of invariant polynomials. In the case n=3, of greatest physical interest, explicit finite invariant stratifications are given for the Grassmannians, providing a formal listing of the screw-systems familiar in theoretical kinematics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047045
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the Hierarchy of screw systems (1993)
    Springer
    Acta applicandae mathematicae 32 (1993), S. 267-296 
    Details
    ISSN: 1572-9036
    Keywords: 70B10 ; Screw ; kinematics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetE(3) be the Lie group of proper rigid motions of Euclidean 3-space. The adjoint action ofE(3) on its Lie algebrae(3) induces an action on the Grassmannian of subspaces of given dimensiond. Projectively, these subspaces are the screw systems of classical kinematics. The authors show that existing classifications of screw systems give rise to Whitney regular stratifications of the Grassmannians, and establish diagrams of specialisations for the strata. A list is given of the screw systems which can appear generically for motions of 3-space with at most three degrees of freedom.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01082452
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  • 3
    Electronic Resource
    Electronic Resource
    On the geometry of the planar 4-bar mechanism (1986)
    Springer
    Acta applicandae mathematicae 7 (1986), S. 113-135 
    Details
    ISSN: 1572-9036
    Keywords: 70B15 ; Mechanism ; algebraic curve ; real elliptic curve ; Morse Theory ; Segre quartic surface
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper seeks to elucidate the geometry of a simple engineering mechanism, comprising four bars smoothly jointed together to form a movable quadrilateral with one fixed side. The configurations of this mechanism correspond to the points of an elliptic curve, to which is associated interesting geometry and Morse theory. By appropriate projection, this curve yields the 2-parameter family of plane curves described by points rigidly attached to the side of the quadrilateral opposite the fixed side: the geometry of the general projection is related to the configuration of lines on a Segre quartic surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051348
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