In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism
spaces) are introduced. This provides a common schema for many kinds of problems that …

Written by the founders of the new and expanding field of numerical algebraic geometry, this
is the first book that uses an algebraic-geometric approach to the numerical solution of …

The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …

Many polynomial systems have solution sets comprised of multiple irreducible components,
possibly of different dimensions. A fundamental problem of numerical algebraic geometry is …

Precision-point synthesis problems for design of four-bar linkages have typically been
formulated using two approaches. The exclusive use of path-points is known as “path …

The mobility of a mechanism is the number of degrees of freedom (DOF) with which it may
move. This notion is mathematically equivalent to the dimension of the solution set of the …

This overview paper is a collection of several papers (Husty and Schröcker, Nonlinear
Computational Geometry, The IMA Volumes in Mathematics and Its Applications, vol. 151 …

In this overview paper we show how problems in computational kinematics can be
translated into the language of algebraic geometry and subsequently solved using …

We present an algorithm which robustly computes the intersection curve (s) of an under-
constrained piecewise polynomial system consisting of n equations with n+ 1 unknowns …

In the vein of recent algorithmic advances in polynomial factorization based on lifting and
recombination techniques, we present new faster algorithms for computing the absolute …