The objective of this project is to develop a technique for the geometric design of a spatial mechanism to guarantee interference free motion for its links. The technique employs the top down design method rather than conventional trial and error. To design the geometry of a link in a spatial mechanism, the space domain, called a swept solid, which identifies the potential region of conflict between the link and other members of the mechanism, is generated. Placing the link geometry outside of this domain guarantees that it will be free of interference. Although this study focuses on spatial linkages, implementation of the technique should yield valuable insights for the geometric design of other mechanical systems. Results can also be used to study spatial motion between any two objects which may result in conflict.