Just about every guy who decides to start weight training wants bigger arms. Every time you wear a t-shirt or tank top your arms are on display and people can tell that you work out if you have big arms. Large arm muscles will give that look of strength every weight trainer covets.
To build big arms and shoulders you need to perform intense weight training workouts for them without overtraining them. The shoulders and triceps assist on most pectoral weight training exercises and the biceps assists on most upper back exercises. On the other hand smaller muscle groups do tend to recover quicker than larger ones, so you should do almost as many sets and exercises for the arms as you would for the major muscle groups.
When you are training to build larger arms you should do higher reps on your shoulder, biceps, and triceps exercises than you do with chest, back, and quadricep exercises. Even if you do light, medium, and heavy training day you should do around 5 more reps on arm exercise sets than the larger muscle groups. Don't be overly concerned about how much weight you can curl or use on triceps extensions, if you're strong on chest and back exercises you'll certainly have strong arms. You should focus on getting a nice pump from shoulder, bicep, and tricep exercises to build bigger arm muscles.
To gain arm size you need to do at least as many, if not more, exercises and sets for the triceps as you do for the biceps. The triceps muscles are larger than the biceps and make up more upper arm size. Many weight trainers tend to do more biceps training than triceps training, but for optimal muscle gains in the upper arms you need to work the triceps as hard as the biceps.
You also need to hit the brachialis muscle that is located between the bicep and tricep muscles on the outsides of the upper arms. You can train the brachialis more directly with hammer curls (curls with your palms facing your body throughout the entire rep) and reverse grip barbell curls. Building the brachialis muscle will add thickness to your arms.
Assuming you train arms at their own workout, you could try a routine like this:
Shoulders: 2-3 sets of military or dumbbell presses
2-3 sets of side lateral raises
2-3 sets of rear lateral raises
2-3 sets of shrugs
Biceps: 2-3 sets of cheat barbell curls
2-3 sets of dumbbell curls
2-3 sets of hammer curls
2-3 drop sets of preacher or cable curls to finish
Triceps: 2-3 sets of reverse- or close-grip bench presses
2-3 sets of seated, standing, or lying tricep extensions
2-3 sets of cable triceps pushdowns with a bar or a rope
2-3 drop sets of various triceps exercises to finish
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An arm weight training routine like this one allows you to do many different exercises during different workouts to keep your training from getting boring. Switch which exercises you do regularly. Another thing you may want to try would be to do a set of a biceps exercise followed by a tricep exercise. If you do this you won't have to worry about not being able to muster up enough intensity for your triceps training if you do it after your biceps training and vise versa. Switch your rep ranges often to keep your body guessing and you'll be on your way to building bigger arms.