ABSTRACT
This chapter discusses body-bar-hinge frameworks which are abstract models of structures consisting of rigid bodies connected by bars and hinges. The constructions of equivalent bar-joint frameworks are also extendable, and hence the rigidity question for body-bar-hinge frameworks can be answered by looking at corresponding equivalent bar-joint frameworks. The study of body-bar frameworks was initiated by T. S. Tay, where he proposed a rigidity matrix written in terms of the Plucker coordinates of bars. As in the case of body-bar frameworks, the rigidity property of body-hinge frameworks can be captured by looking at equivalent bar-joint frameworks, obtained by replacing each body by a bar-joint realization of a large enough complete graph. In rigidity theory, a structure is commonly understood by using a pinned framework, where pinned points are fixed in the ambient space. The combined notion of body-bar frameworks and body-hinge frameworks are useful in some applications.
