This dissertation is a treatise on “wrapping cam mechanisms.” This intriguing mechanism is composed of a cam wrapped by a belt, chain, or other flexible follower. Such devices have also been referred to as band mechanisms. The flexible follower is assumed to be constrained such that there is no relative sliding between it and the cam. This dissertation provides the first comprehensive kinematic study of wrapping cam mechanisms. Different forms of this mechanism are enumerated, and two forms believed to be of particular importance are identified. Kinematic analysis techniques are developed to determine the relative positions and internal forces in the mechanism as it moves. Kinematic synthesis methods are developed to generate the surface of a cam to produce a desired displacement or mechanical advantage. These original closed-form techniques are developed from the basic laws of conjugate geometry. While wrapping cams are far less common than cams that generate a specified follower displacement functions, applications exist in archery, counter-balancing mechanisms, exercise equipment, clamping and locking mechanisms, and process machines. / Ph. D.