When designing new devices, engineers seldomly start their design from scratch. Instead, they redesign or compose existing ones. Finding candidate devices based on their properties is thus an essential design subtask. To be effective, future intelligent computer-aided design (CAD) systems must be able to compare and evaluate existing devices. Due to the large number of known devices, such systems must create and maintain a devices' knowledge base, indexed by the properties of the devices. This paper presents a new method to compare and classify mechanical devices according to their kinematic properties. Mechanism comparison determines when two mechanisms are kinematically equivalent. Mechanism classification organizes classes of equivalent mechanisms for efficient retrieval. Both tasks require describing mechanisms' behaviors from various perspectives and at multiple levels of abstraction. To produce such descriptions, we develop a set of operators to simplify and abstract kinematic descriptions derived from configuration spaces. Simplification operators ignore irrelevant information by incorporating constraints and assumptions. Abstraction operators ignore detail by defining multiple levels of resolution. The resulting hierarchy supports the design process throughout its evolution, from the conceptual to the detailed phase. It provides an explicit link between behavioral specifications and part geometry. © 1990 Springer-Verlag New York Inc.