This thesis will form part of a system for the design of spatial mechanisms presently being developed at Virginia Polytechnic Institute and State University. The major areas covered by this thesis arc the synthesis and analysis of the RRSS spatial mechanism. The RRSS mechanism is a four-link mechanism composed of two revolute (R) joints and two spheric (S) joints. The notation RRSS indicates the order of connection of the joints. A computer program in FORTRAN 77 has been written for three to seven positions synthesis, as well as analyses of the RRSS mechanism. Linear equations are involved in the synthesis of R-R dyad for three and four positions. For five to seven positions, non-linear equations arc involved and the R-R dyads arc synthesized using a least-squares algorithm. For S-S dyad synthesis, all equations arc non-linear. The analysis section of this thesis includes both kinematics and input-link rotatability analyses. A synthesized RRSS mechanism has been included as an example. Miscellaneous design considerations and recommendations for future research are discussed. / M.S.