Geometric characteristics of antagonistic stiffness in redundantly actuated mechanisms

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(s) relating the actuation sites. The extent of stiffness modulation possible is 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 first-order counterparts