During the first 3 months of life, babies’ hands and arms develop rapidly. Initially their hands are often tightly clenched with the thumb curled inside the fingers. They can grasp objects automatically but are not yet capable of shaking them or bringing them to their mouths. Within a month or two, the hands and arms will relax. During the third month, hands will be half open most of the time, and babies begin opening and shutting hands on their own. Babies are now able to grip and shake a rattle placed in the palm.
Shelov, S. P. (Editor-in-Chief). (2004.) Caring for Your Baby and Young Child: Birth to Age 5. The American Association of Pediatrics. Revised edition. New York: Bantam Books.