Geometric analysis of antagonistic stiffness in redundantly actuated parallel mechanisms

Abstract

Abstract 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.