This paper proposes a procedure to extract the kinetic model from the geometric model of a fixture to reduce the modeling time and effort. Since most of the fixtures in industry follow the same kinetic mechanism, the so-called a slider-crank mechanism; this is a four-axis system of three revolute and one prismatic joint. The prismatic axis of a fixture represents a pneumatic actuator involving a piston and a cylinder. It is very important to identify the prismatic axis from a given geometric model to extract the kinetic model of a fixture. The focus of this paper is to extract a common axis from contact surface between distinguishable links. To do so, we use the concept of the ‘Gauss map’.