Mathematics BSc
Course description
2013.

Applied module: Geometric transformations and their applications
Hours
lect+pc
Credits
lect+pc
Assessment Specialization Course code
lect/pc
Semester Status
2 + 2 2 + 3 exam +
term grade
applied math. mm1c1mg4a
mm1c2mg4a
4 optional
Strong Weak Prerequisites
Practice class
Strong:
Geometry1L (mm1c1ge2)
Strong:
Algebra2L (mm1c1al2)
Lecture
Weak:
practice class
Weak:
Analysis2L (mm1c1an2) or
Foundations of analysisL (mm1c1ap2)
Prerequisites
Basic geometry, linear algebra, multivariable calculus, linear algebra, topology.
Literature
  • B. Csikós: Projective Geometry. Lecture notes.
  • M. W. Spong, S. Hutchinson, M. Vidyasagar: Robot Modeling and Control. John-Wiley & Sons, Inc., 2006.
  • M. Berger: Geometry I. Universitext. Springer-Verlag, 1987.
Syllabus
  • Basic notions of projective geometry. Points at infinity. Cross-ratio. Projective transformations. Reconstructing real size and position of objects from photographs.
  • Canonical form of isometries and Killing fields (infinitesimal isometries) of a Euclidean space. Rigid motions in the plane and space. Quaternion representation of elements of SO(3). Instantaneous centers of rotation. Centrodes. Rolling of the moving centrode on the fixed one. Cog wheel tooth design. Instantaneous axis of rotation. Hyperboloid gears.
  • Robot geometry. Joint types. Denavit-Hartenberg convention. Direct and inverse kinematical problems.