An exercising machine is provided that has a head engaging member that can provide a hemispherical movement. The head engaging member is attached to rollers that can roll on a pivotable arcuate track. As an exerciser moves the head engaging member in the X-Y plane, the machine forces movement in the Z plane such that the head engaging member can maintain a point of contact on the user's head as the exerciser rotates his head during exercise. The track can be arced or formed in a radius such that the head engaging member traverses a motion approximate to a radius of a neck rotation as measured from the forehead to the base of the neck.