The curtate cycloid illusion is an illusory perception where a cycloidal trajectory is perceived as curtate cycloid. Previous studies imply that this illusory perception occurs because we could fail to process two motion components (rotation and translation) simultaneously, and this particularly occurs at the instant center of the wheel's rotation. The present study examined the factors of the curtate cycloid illusion by decomposing the wheel's center and rim, where the former causes the vector decomposition of the rotation and translation motion and the latter creates an instant center on a rolling wheel. The results showed that the vector decomposition caused a strong bias in the perception of the trajectory toward a curtate cycloid, while adding an instant center did caused such a bias, but rather caused difficulty in the trajectory perception. These results indicate that the curtate cycloid illusion could occur when a point moving along a cycloidal (or prorate cycloidal) trajectory is perceptually decomposed into its rotational and translational motions by seen as moving relative to a common reference frame with a rectilinearly moving object (e.g., the hub of a wheel).