This book focuses on the synthesis of lower-mobility parallel manipulators, presenting a group-theory-based method that has the advantage of being geometrically intrinsic. Rotations and translations of a rigid body as well as a combination of the two can be expressed and handled elegantly using the group algebraic structure of the set of rigid-body displacements. The book gathers the authors' research results, which were previously scattered in various journals and conference proceedings, presenting them in a unified form. Using the presented method, it reveals numerous novel architectures of lower-mobility parallel manipulators, which are of interest to those in the robotics community. More importantly, readers can use the method and tool to develop new types of lower-mobility parallel manipulators independently.