The swash-plate mechanism is used to transfer rotational motion into translational motion and vice versa. Using transformation matrices to describe each joint, the displacements of the swash-plate mechanism were analyzed. The general transformation matrix model for the plane joint, not previously developed using transformation matrices, was presented. The solution was tested using a computer program. Examples of three different swash-plate angles; 10, 45, and 25' were considered. The solution was found to agree with previous solutions while offering a more complete description of the mechanism. Future work in this area could include a complete static, velocity, and/or dynamic analysis of the swash-plate mechanism based on the solution presented.