When switching from arthritis medicines meloxicam to diclofenac sodium would you expect a period of ineffectiveness as one medicine wears off and before the other starts working. if the area was already being treated with topical diclofenac sodium?

Assuming you are taking the new medication as prescribed, there is always a short period of time needed for the drug to reach adequate, ie. therapeutic, blood levels. Once these levels are reached, you should start to experience the effect of the new drug, diclofenac in this case. However, do not anticipate some type of "instant" change in your joint symptoms... it will take several months.