Pullups are a compound exercise that work every muscle in your upper body. They are a hard exercise to replace, but if you don't have access to a pullup bar or a lat pulldown machine, you can do a workout with dumbbells that trains all the muscles you use to do pullups. Training those muscles with dumbbells will also make you better at doing pullups.
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Bent Over Rows
Bent over rows are the dumbbell exercise that simulates pullups the most. They work your trapezius, latissimus dorsi, teres major and minor, rhomboid major, posterior deltoid and biceps. Stand with your feet shoulder-width apart, holding a dumbbell in each hand. Bend your knees slightly and bend forward at the waist 45 degrees. Inhale and pull the dumbbells up to your chest. Exhale and lower the, back to the starting position.
Dumbbell pullovers work you triceps, lats, seratus anterior and pecs. You need a bench or an exercise ball to do this exercise. Lie on your back on a weight bench with your feet flat on the floor. Hold one dumbbell with both of your hands, gripping the handle with your palms like you're holding a bat. Inhale and lower the dumbbell behind your head. Exhale and extend the dumbbell over your head.
Bicep curls strengthen your biceps, which are the primary muscles you use when you do chinups -- pullups with an underhand grip. Stand with your feet shoulder-width apart, holding a dumbbell in each hand with your palms facing out. Inhale, then curl the dumbbells up to your shoulders, exhaling at the end of the motion. Inhale and lower the dumbbells back to the starting position. You can curl both dumbbells at the same time or alternate between arms.
Reverse curls strengthen your biceps but place more emphasis on your forearms. This is important because pullups require a lot of forearm strength to maintain your grip on the bar. Reverse curls are performed the same way as biceps curls, except instead of holding the dumbbells with your palms facing out, rotate your hands 180 degrees so your palms are facing behind you.