Duality and reciprocity between twist and wrench systems is the essence of screw theory. The power of these concepts lies in the idea that once a result is obtained for one type of system it can immediately be applied to the dual system provided the appropriate physical interpretation is also translated. The interrelation between serial and parallel mechanisms is a consequence of this twist/wrench duality. The purpose of this investigation is to focus on some fundamental configurations of serial and parallel robot manipulators in an attempt to further elucidate the various correspondences that exist between their geometries and their kinematic equations. The focus is on zero-pitch screw systems, namely revolute joints for serial manipulators and force producing sub-chains in parallel manipulators. Solutions for twist/wrench distributions will be discussed for both proper and redundant systems.

Force-reflected teleoperation with in-parallel devices are gaining prominence in robotics applications. Although their development has been limited primarily to Stewart-platform type devices, many other in-parallel hand controllers hold promise for force-reflected manipulation. One factor prohibiting a full exploration involves their singularity analyses-use of conventional rank determining methods are overly complicated. Singularity analysis complications arise because the Jacobian matrix has several functionally dependent variables. In this analysis, we first derive the Jacobian matrix and then show its six columns can be viewed as zero-pitch wrenches (lines) acting on the top platform. We then show how line geometry and rank determining geometric constructions can be used to obtain all configuration singularities.>

The authors discuss the kinematics of a serial/parallel six degree-of-freedom generalized hand controller for teleoperation. A description of the device is presented with equations needed for control of a remote manipulator. The pantograph linkages extend the workspace of traditional platform designs, while the parallel structure provides force regulation at the platform that is well suited for force-feedback to a teleoperator. The generalized teleoperator controller described will be part of a larger telerobotics system comprising a radio-controlled robotic arm module with appropriate end-effectors and a general-purpose supervisory controlled system. The robotic system is planned for remote handling of toxic solid and liquid debris.>

The authors present an inverse kinematic algorithm for a four-revolute-joint (4-R) spherical wrist that provides for a complete set of spatial orientations, is nonsingular, and is simple to implement with existing technology. The algorithm is a rate-controlled method that depends on the required Cartesian rate. In the process of presenting the algorithm, the authors have developed the fundamentals of differential motion with n-revolute-joint spherical wrists. The method is outlined and applied to a 4-R regional structure. The goal is to combine the 4-R spherical wrist with the 4-R regional structure to develop an 8-R manipulator that is free of internal singularities.>