ABSTRACT

Describing, exploring, and sampling the realization space of a linkage is a difficult problem that arises in many classical areas of mathematics and computer science and has a wide variety of applications in computer aided design for mechanical engineering, robotics, and molecular modeling. This chapter gives the characterization of graphs in 2D that have convex Aurthur Cayley's configuration spaces. For a graph, the choice of Cayley parameter nonedges is important, as this determines whether the resulting Cayley configuration space is convex or not. In cases where there are multiple Cayley parameters, they additionally show that the order in which Cayley parameters are fixed have an effect on the efficiency of the range computation. The Optimal Cayley Modification problem asks if the system to be realized can be modified, by dropping some constraints and adding certain others, so as to make the system easily realizable.