In this paper, the kinematic synthesis for the proposed in-vessel remote maintenance system (IVRMS) in the fusion experiment (IGNITEX) is presented based on a convenient coordinate system. The inverse kinematic problem is solved by using a fast, efficient algorithm. The algorithm is especially suitable for the elongated tokamak vacuum vessel geometry required for a fusion ignition experiment. The results of numerical and graphical simulation are presented. Also, a computer animation of this motion has been done. The ideal trajectories are approximated by a set of piece-wise linear functions. The performance of the motion planning is evaluated. The problem of control of the manipulator to accomplish the required maintenance tasks are discussed. The errors caused by the motion planning and the joint mechanisms are analyzed. The preliminary study of the dynamics underlying the design is presented. The analysis in this paper provides an analytical basis for improvement of the design of the IVRMS's manipulator.