Analysis and Design of a Two Degree of Freedom Hoeckens-Pantograph Leg Mechanism

Hoeckens and Chebychev linkages have been widely discussed in the literature as design solutions to build single degree of freedom (DOF) leg mechanisms. Compared to fully actuated legs, often bio-inspired, they offer an unmatched simplicity. However, due to their limited motion capability, they can only be used when the traversed terrain is of limited difficulty. In order to alleviate this drawback, a novel design with a second DOF is proposed in this paper. The introduced mechanism is composed of a Hoeckens linkage augmented by a Pantograph for which the position of the pivot can be changed through an additional rotating link. Screw theory is used to determine the kinematic equations of the mechanism, its singular configurations, and its attainable workspace. Subsequently, an optimization of the geometric parameters is performed to maximize performance indices pertaining to the size of the mechanism’s workspace. Finally, possible use of compliant joints is discussed.