Parallel closed-chainmechanical architectures allow for redundant actuation in the force domain. Antagonistic actuation, afforded by this input force redundancy, in conjunction with nonlinear linkage geometry createsan effective stiffnessdirectlyanalogous to that of a wound metal spring. A general stiffness modelfor such systems is derived and it is shown that the constitutive relationshipbetweenactuationeffortand active stiffness is the second-order kinematic constraint(s) relating the actuation sites. The extent of stiffness modulation possible is then evaluated and necessaly conditions for fill stiffness modulation are obtained. Configuration dependent, second-order, geometricsingularitiesaffectingstiffnessgeneration are illustrated in termsof a three degree-of-freedomparallel spherical mechanismexample,and discussedin relalion to their more commonly investigated first-order counterparts.
Byung-Ju Yi, Robert A. Freeman