To add a bit to what others have written above, gokyo is otherwise known as "ude nobashi" or "arm stretch" and ikkyo is also known as "ude osae" or "arm pin." Rokyo is known as "ude hishigi" (basically, "arm breaking"), hijishime ("elbow squeeze"), and wakigatame ("cementing against the side").
I hear that rokkyo is the only technique commonly done in aikido that goes "against" the joint (ie trying to bend a joint in the opposite direction that it was meant to bend).
In my experience, just like the rest of aikido, trusting that causing pain will make a technique effective is unreliable. Rather than pressing down on the elbow, I try to break uke's balance through the "straight arm."
Just my thoughts...