If you're going to do direct arm training, you need to be locking in your technique, tapping into the mind-muscle connection, and chasing a searing pump. Triceps particularly don't respond well to heavy loaded movement with half-assed form involving momentum at the torso.
A great example of a commonly butchered movement is the traditional standing rope pushdown. These get sloppy quickly, taking tension away from the muscles and placing stress on the elbows and shoulders. Here's a really good, really bad example:
Rope Pushdown, Bad Form
Look at those shoulders! That's an example of direct arm training that leads to AC joint separations. Instead, tighten up and set your ego aside. Drop down to the tall kneeling position and use a slightly longer rope. (If you don't have a long rope, put two ropes on the same cable setup.)
Kneeling Rope Pushdown
From the tall kneeling position, your torso angle will stay constant and your range of motion and tension at the bottom is increased to contract harder. And harder, more calculated contractions lead to gains.
Give these a try, and make sure to move slowly and challenge yourself with higher reps that leave your arms burning.