This work develops a novel framework which can automatically detect, parameterize and interpolate periodic motion patterns obtained from a motion capture sequence. Using our framework, periodic motions such as walking and running gaits or any motion sequence with periodic structure such as cleaning, dancing etc. can be detected automatically and without manual marking of the period start and end points. Our approach constructs an intrinsic parameterization of the motion and is computationally fast. Using this parameterization, we are able generate prototypical periodic motions. Additionally, we are able to interpolate between various motions, yielding a rich class of 'mixed' periodic actions. Our approach is based on ideas from applied algebraic topology. In particular, we apply a novel persistent cohomology based method for the first time in a graphics application which enables us to recover circular coordinates of motions. We also develop a suitable notion of homotopy which can be used to interpolate between periodic motion patterns. Our framework is directly applicable to the construction of walk cycles for animating character motions with motion graphs or state machine driven animation engines and processed our examples at an average speed of 11.78 frames per second.