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We present a framework for authoring three-dimensional virtual scenes for Augmented Reality (AR) which is based on hand sketching. Sketches consisting of multiple components are used to construct a 3D virtual scene augmented on top of the real drawing. Model structure and properties can be modified by editing the sketch itself and printed content can be combined with hand sketches to form a single scene. Authoring by sketching opens up new forms of interaction that have not been previously explored in Augmented Reality. To demonstrate the technology, we implemented an application that constructs 3D AR scenes of mechanical systems from freehand sketches, and animates the scenes using a physics engine. We provide examples of scenes composed from trihedral solid models, forces, and springs. Finally, we describe how sketch interaction can be used to author complicated physics experiments in a natural way.