The design of geometric constraints to guide a body through a specified movement is called kinematic synthesis. If the geometric constraints are in the form of an open or closed chain of rigid links and joints such as a robot manipulator, the device is called a linkage. The kinematic synthesis of a linkage formulates the geometric constraint equations associated with the joints of the system and then solves for the dimensions of the chain that ensure its movement through a prescribed task. This project focuses on the kinematic synthesis of spatial chains formed by a pair of revolute joints, the RR dyad. Planar and spherical RR dyads form the basic elements for the construction of planar and spherical linkages. Spatial RR dyads are found as elements in most all robot manipulators. However, the synthesis theory for general RR chains is theoretically challenging and has not been implemented in Engineering practice. This project presents a new formulation of the synthesis equations for a spatial RR chain that simplifies the design process