To make your forearm muscle bigger, you need to curl with your palm facing inward, not up.
Evidence from Studies
Supporting (1)
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When you lift something with your palm facing sideways (neutral grip), your brachioradialis muscle works harder than when your palm is facing up (supinated grip), and this study proved it by measuring muscle activity.
Contradicting (2)
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The function of brachioradialis.
The study found that the brachioradialis muscle works just as hard whether your palm is up, down, or sideways during elbow bending — so it doesn’t prefer the hammer grip like the claim says.
Muscular coordination of biceps brachii and brachioradialis in elbow flexion with respect to hand position
The study found that when you hold your hand like you're holding a hammer (neutral), your forearm muscle doesn't work harder than when your palm is facing up — in fact, it works the most when your palm is facing down.