This is a question that many people often ask when studying Claudius as a personality. The historian Suetonious gives a decent writing about the physical traits of Claudius. He stated that his knees were weak and would often limp and that his head shook. In addition, he had a stutter and would often confuse his words which gives us reason to think he had a speech impediment. He is noted to get a runny nose when excited. Later emperor Nero's tutor, Seneca, wrote quite a rude and demeaning work mocking Claudius stating things such as the God's did not know what beast he was and even asked Hercules if this is his 13th labour! Although all these accounts of Claudius' faults, Suetonious did note that he showed no physical deformities and was actually a tall, well built figure. Prior to recent studies, it was widely accepted that his condition was polio but many of the symptoms Claudius had does not support the theory of polio. A more recent plausible theory is that he suffered from cerebral palsy. In addition, tourette syndrome has been a recent possibility from his symptoms. Sorry if I didn't answer the question straight away but I thought some context would be interesting!