Abstract: We present a space-time abstraction for the sketch-based design of character animation. It allows animators to draft a full coordinated motion using a single stroke called the space-time curve (STC). From the STC we compute a dynamic line of action (DLOA) that drives the motion of a 3D character through projective constraints. Our dynamic models for the line's motion are entirely geometric, require no pre-existing data, and allow full artistic control. The resulting DLOA can be refined by over-sketching strokes along the space-time curve, or by composing another DLOA on top leading to control over complex motions with few strokes. Additionally, the resulting dynamic line of action can be applied to arbitrary body parts or characters. To match a 3D character to the 2D line over time, we introduce a robust matching algorithm based on closed-form solutions, yielding a tight match while allowing squash and stretch of the character's skeleton. Our experiments show that space-time sketching has the potential of bringing animation design within the reach of beginners while saving time for skilled artists.