Its easy for the triceps to get complacent in the close grip bench press. Its important that you focus on slow rep timing and feel the triceps stretch and contract during the set. Its this mind-muscle connection that can make the difference between your triceps doing the work and your chest/shoulders doing the work.
Keep your elbows tucked in at your sides, and dont let them flare as you raise the weight.
And finally, you need to keep the tension on your triceps during the entire set so dont lock your elbows out at the top of the movement.
Instructions
Set up for the smith machine close grip bench press by placing a flat bench in the smith machine, lowering the bar and adding the weight you want to use to the bar.
Lay back on the bench and grasp the bar with an overhand grip (palms facing your feet) at around 6-12 inches apart.
Take the weight off the rack by twisting the bar.
Keeping your elbows tucked in at your sides, slowly lower the weight focusing on your triceps as the prime movers.
Lower the weight until it almost touches your chest, and then slowly raise it up, pushing the weight with your triceps.
Do not lock your elbows out at the top of the exercise, and then repeat.