29 research outputs found
Factorization of Rational Curves in the Study Quadric and Revolute Linkages
Given a generic rational curve in the group of Euclidean displacements we
construct a linkage such that the constrained motion of one of the links is
exactly . Our construction is based on the factorization of polynomials over
dual quaternions. Low degree examples include the Bennett mechanisms and
contain new types of overconstrained 6R-chains as sub-mechanisms.Comment: Changed arxiv abstract, corrected some type
The Theory of Bonds: A New Method for the Analysis of Linkages
In this paper we introduce a new technique, based on dual quaternions, for
the analysis of closed linkages with revolute joints: the theory of bonds. The
bond structure comprises a lot of information on closed revolute chains with a
one-parametric mobility. We demonstrate the usefulness of bond theory by giving
a new and transparent proof for the well-known classification of
overconstrained 5R linkages.Comment: more detailed explanations and additional reference
The Kinematic Image of 2R Dyads and Exact Synthesis of 5R Linkages
We characterise the kinematic image of the constraint variety of a 2R dyad as
a regular ruled quadric in a 3-space that contains a "null quadrilateral".
Three prescribed poses determine, in general, two such quadrics. This allows us
to modify a recent algorithm for the synthesis of 6R linkages in such a way
that two consecutive revolute axes coincide, thus producing a 5R linkage. Using
the classical geometry of twisted cubics on a quadric, we explain some of the
peculiar properties of the the resulting synthesis procedure for 5R linkages.Comment: Accepted for publication in the proceedings of the IMA Conference on
Mathematics of Robotics, Oxford, 201