The motion and internal loads induced on an object manipulated by two or more robotic mechanisms are considered. In particular, for a desired motion trajectory of the object, the question of load distribution among the arms is analyzed, with particular attention given to the internal loading of the object. A new representation of the load distribution problem is given by the introduction of a particular "nonsqueezing" pseudoinverse, which is shown to possess properties that expose the underlying structure of the problem. It is expected that by using this pseudoinverse new insight will be gained and necessary analysis simplified in a number of aspects of multiple manipulator research. A number of these aspects are detailed and illustrated using a two-armed example.

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Parallel closed‐chain mechanical architectures allow for redundant actuation in the force domain. Antagonistic actuation, afforded by this input force redundancy, in conjunction with nonlinear linkage geometry creates an effective stiffness directly analogous to that of a wound metal spring. A general stiffness model for such systems is derived and it is shown that the constitutive relationship between actuation effort and active stiffness is the second‐order kinematic constraint set relating the actuation sites. The extent of stiffness modulation possible is then evaluated and necessary conditions for full stiffness modulation are obtained. Configuration‐dependent, second‐order, geometric singularities affecting stiffness generation are illustrated in terms of a three‐degree‐of‐freedom parallel spherical mechanism example and discussed in relation to their more commonly investigated first‐order counterparts that affect force and velocity transmission. Finally, a load distribution methodology for simultaneous motion and stiffness generation is introduced, and it is shown that with hyperredundant actuation the internal load state of the mechanism can be controlled independent of its motion and effective stiffness. © 1993 John Wiley & Sons, Inc.

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This work suggests a new (novel) approach for the control of taskspace stiffness characteristics in systems consisting of a superabundance of kinematically dependent inputs. When there are more input actuations than operational degrees off", intemal preloads can be generated that produce effective restoring farces in the face of displacement or disturbances imposed on the system. Examples of this excessive actuation can be found in cutain modes of structurally ovenxnstrained parallel manipulators and in antagonistically structured serial manipulators. The input loads are synthesized off-line (prior to operation) and entered as a feedforward component so that the desired effective loads on objects are obtained and simultaneously significant disturbances at the task level can be largely rejected in an open-loop fashion. This reduces the burden and shortcomings of standard feedback schemes. Moreover, a layered feedback scheme is employed to compensate for small perturbations and unmodeled dynamics. The open-loop task-based stiffness control scheme as applied to structurally parallel mechanisdrobotic lhkage systems is investigated. The scheme's applicability as a programmable active RCC devices is also discussed.