Authors: Brigitte Servatius

Reference: in “Geometry at Work”, C. Gorini, Ed., MAA Notes Number 53, pp. 81-88.

Selected Figures:

- Infinitesimal Motions of Plane Designs
- A Point Passing to Infinity
- Generic Direction-Length Cycles on $4$ vertices.
- A direction length construction

Abstract: This paper is a short self-contained introduction to the the study of constrained geometric structures suitable for non-specialists and undergraduate students. The motion and rigidity of frameworks of rods and joints is examined, and connections are drawn to other constrained structures that are useful in many applications, in particular to Computer Aided Design.

In the first section, elementary geometry is used to study the motion and rigidity of frameworks. In the second section rigidity and strong rigidity are contrasted. In the third section, the linear algebra of infinitesimal rigidity is studied and applied as well to the direction constraints of parallel drawings. The purely combinatorial concept of generic rigidity is intruduced, and lastly these ideas are applied to the theory of Computer Aided Design (CAD).