The derivation of kinematic formulae for mandibular movement

The theoretic basis for developing mathematical formulae that describe the motion of the mandible in relation to the maxillae is presented. The authors present kinematic formulae that compute the three-dimensional displacement of any point on the mandible with an error of less than 0.04 mm and determine the inclinations and azimuth of the orbit of the incisal point with an error of 0.8 degrees. The formulae have been used to develop an electronic pantography system.