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Even though you may play golf right handed, you only actually involve your right hand in the swing as you strike the golf ball. Your dominant side, if you play golf right handed, is actually your left hand side.
As you swing the golf club away from the golf ball, your left arm should be straight and the dominant force as you turn your shoulders into your back swing position. Your right arm should remain very passive, with your elbow pointing downwards and tucking in close to your body.
You need to initiate your down swing movement back towards the golf ball, with your lower body rotating towards the target and you want to work on pulling the handle of the golf club down with your left hand and arm. Your right arm and hand should remain passive for the majority of your down swing. Your right hand should only become active during the golf swing, to release the club head at the very last second towards the golf ball as you strike it. If you become too dominant with your right hand, it simply means that you are activating your right hand before the ideal time on your down swing.
To illustrate the position that you should achieve before you use your right hand, set up ready to hit the golf ball. Hinge your wrists to the right so that the club becomes horizontal and parallel to the target line. This will create a right angle between the club shaft and your left arm. This is the basic position that you need to swing the golf club back down into as you are approaching the golf ball and you need to get to the position before you use your right hand.
If you achieve this position and then release the club head towards the golf ball by allowing your right hand to make a “slapping” action towards the golf ball as you release the lever of your right wrist, you will impart maximum club head speed into the golf ball and achieve maximum shot length. Using your right hand before this position will result in a loss of power and also result in the club face turning to the left, or closing, making it difficult to hit accurate shots at the target.
A great drill to help you learn how to pull the golf club down correctly with your left arm and hand is as follows. Set up to hit the golf ball. Instead of holding with your usual grip, allow your right hand to lower down on the handle so that you split your hands apart. Swing the club back and as you begin your down swing, let go with your right hand so that you use your left hand and arm only to pull the club back down.
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Casting the golf club means that you are extremely dominant with your right hand as you initiate your down swing action. Casting involves flicking your right wrist to move the golf club around your wrists as you swing down towards the golf ball. Doing this makes you extremely dominant with your right hand.
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If you practise making one arm golf swings with your right arm only, you will teach yourself to feel your right side. If you are already dominant with your right side, you need to work on swinging the club with your left arm only to actually learn the feeling of using this side of your body.
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A stronger grip will only serve to make the right hand even more dominant during the swing. Try to grip in a neutral fashion.