We extend a model for the morphology and dynamics of a crawling eukaryotic cell to describe cells on micro patterned substrates. This model couples cell morphology, adhesion, and cytoskeletal flow in response to active stresses induced by actin and myosin. We propose that protrusive stresses are only generated where the cells adheres, leading to the cell’s effective confinement to the pattern. Simulated cells exhibit a broad range of behaviors, including steady motion, turning, bipedal motion and periodic migration. We further extensively study the turning instability by simplifying the full PDE model into a minimal one. By using the minimal model, we also study the persistent rotational motion (PRM) of small numbers of mammalian cells crawling on micropatterned substrates.