Human shoulder movements involve motions at four different articulations, one of which is the contact between the scapula bone and the ribcage. The shoulder biomechanical models become less reliable when the scapulothoracic (ST) contact, which is not a joint in the anatomical sense, is not considered. On the other hand, constraints posed by the ST contact reduce the number of degrees of freedom (DOF) and introduce the interdependencies between the joint coordinates which in turn complicates the motion planning. However, a minimal parameterization that incorporates the constraints, notably simplifies costly computational procedure related to the model predictions. In this paper, the complex kinematics of the human shoulder is analyzed considering the point-contact model between scapula bone and thorax. Later, replacing the contact constraint with an equivalent kinematic chain and adding parallel kinematic links, the human shoulder girdle is modelled as a 6-4 parallel mechanism. A novel minimal set of independent parameters equal to the number of degrees of freedom is then devised in terms of the parallel mechanism's link lengths and the shoulder joint angles. The proposed parallel mechanism can also emulate the moving ST contact point during the shoulder motions. Finally, the shoulder motion planning method in terms of the time-dependent minimal coordinates is presented.