Optimization and experimental verification for the antagonistic stiffness in redundantly actuated mechanisms: a five-bar example

A closed-chain mechanism having redundancy in force domain can produce an effective spring effect by proper internal load distribution. The so-called antagonistic stiffness is provided by redundant actuation in conjunction with nonlinear geometric constraints. The objective of this study is twofold. The first one is to propose a methodology for optimal kinematic design of antagonistic stiffness and the second one is to verify the phenomenon of the antagonistic stiffness through experimentation. In this work, a five-bar mechanism that can modulate antagonistic stiffness by using redundant actuators is employed as an exemplary system. The optimal structure of the five-bar mechanism that can maximize efficiency in generation of antagonistic stiffness is evaluated and analyzed. A measure of stiffness isotropy and the gradient property of the measure are employed as the performance indices in optimization. To deal with multi-criteria based design, a composite design index based on max-min principle of fuzzy theory is used as an objective function. Two optimization results are obtained. Furthermore, a five-bar mechanism has been developed for experimental verification. The phenomenon of antagonistic stiffness has been successfully demonstrated by free vibration and indirect force control experimentation.