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The hinge angle is the angle between the bat and the lead forearm. Ideally the angle should be 90 degrees up until contact. Notice the bat/forearm relationship in Manny Ramirez's swing. As Manny rotates the triangle, his hinge angle remains at 90 degrees.
Many swing and weight shift problems can be traced back to this area. Having a player maintain the hinge angle and work to release it more out front can be a great working cue to shift weight.