1 Introduction: lockable and non-holonomic joints -- 1.1 Motivation -- 1.2 Precursors -- 1.3 Organization of this book -- References -- 2 Parallel robots with lockable revolute joints -- 2.1 Kinematics of the 4RbRPS parallel robot -- 2.2 Maneuvers -- 2.3 Motion planning -- 2.4 Hardware implementation -- 2.5 Software implementation -- References -- 3 Spherical non-holonomic joints -- 3.1 Under-actuated parallel robots with spherical non-holonomic joints -- 3.2 Implementation of spherical non-holonomic joints -- References -- 4 Kinematics of the 3SnPU spatial robot -- 4.1 The 3SnPU robot -- 4.2 Instantaneous kinematics -- 4.3 Statics analysis -- 4.4 Singularities -- 4.5 Controllability -- 4.6 Example -- References -- 5 Motion planning for the 3SnPU robot -- 5.1 Motion planning -- 5.2 Using truncated series -- 5.3 Example -- References -- 6 Kinematics of the Sn-2UPS spherical robot -- 6.1 Kinematic model -- 6.2 Deriving a bilinear model -- 6.3 Singularities -- 6.4 A, B, and rotations in R4 -- 6.5 Workspace computation -- 7 Motion planning for the Sn-2UPS robot -- 7.1 Kinematic model -- 7.2 Three-move motion planner -- 7.3 Two-move motion planner -- 7.4 Single-move motion planner -- 7.5 Example -- 7.6 Implementation -- References -- 8 Conclusions.

This book shows how, through certain geometric transformations, some of the standard joints used in parallel robots can be replaced with lockable or non-holonomic joints. These substitutions allow for reducing the number of legs, and hence the number of actuators needed to control the robot, without losing the robot's ability to bring its mobile platform to the desired configuration. The kinematics of the most representative examples of these new designs are analyzed and their theoretical features verified through simulations and practical implementations. .