Abstract: Physical reasoning often involves approximating or abstracting the situation or the theory at hand. This paper studies the nature of approximation and abstraction as applied to the kinematic theory of rigid solid objects.

Five categories of approximation are considered: 1. Geometric approximation. 2. Abstraction of a complex kinematic structure by a simpler kinematic structure. For example, the abstraction of a collection of tightly-linked objects as a single object. 3. Abstraction of a kinematic structure by a simpler theory. For example, the abstraction by a connectivity graph in configuration space. 4. Approximation of a complex kinematic structure by a simpler structure in a more complex theory. For example, the approximation of a chain by a string. 5. Approximation of a more complex theory by a kinematic theory. For example, the approximation of solid object dynamics by kinematics.

We discuss how some of these types of approximation can be implemented and combined. We conclude that abstraction and approximation are open-ended styles of reasoning, rather than neatly categorizable meta-relationships.