This paper proposes design strategies and a comparative study of two antagonistically actuated tensegrity joints: a revolute (R) joint and an anti-parallelogram (X) joint. Geometrically, the R-joint has a fixed center of rotation while the X-joint has a moving center of rotation. Both joints are equipped with two lateral springs and are actuated by cables passing through these springs. Such tensegrity joints can be of interest for developing lightweight manipulators. They are designed to reach a prescribed wrench-feasible workspace (WFW) with a minimum desired stiffness throughout. The design strategy relies on the determination of the complete feasible design space for the problem, rather than resorting to a numerical optimizer for a particular solution. This approach provides more insight into the problem and also presents the designer with all the feasible designs. Several case studies are considered with different WFW specifications and design objectives for the R-and X-joints. The optimal designs obtained for the two joints are compared in terms of their actuation forces, stiffness, geometry, and mass.

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This paper compares the static performances of two types of antagonistically actuated joints: a revolute (R) joint and an antiparallelogram (X) joint. Both joints are equipped with lateral springs and actuated with two opposite cables running through the springs. The comparative study is conducted on the basis of their wrench-feasible workspace and stiffness. A methodology is proposed for the optimal design of each joint. Eventually, an R-joint and an X-joint, optimized for the same prescribed wrench-feasible workspace, are compared on the basis of their maximal actuation forces.

In biological systems, the joints are actuated antagonistically by muscles that can be moved coherently to achieve the desired displacement and co-activated with appropriate forces to increase the joint stiffness. Taking inspiration from this, there is an interest to develop bio-inspired robots that are suitable for both low-stiffness and high-stiffness tasks. Mechanisms actuated by antagonist cables can be a reasonable approximation of biological joints. A study on the antiparallelogram mechanism showed that the antagonistic forces (> 0) have a positive influence on its stiffness, similar to the biological joints. In this work, more general symmetric four-bar mechanisms with crossed/regular limbs, larger/smaller top and base bars are investigated for this property. Totally, six different types of mechanisms were identified and the limits of movement were determined in each case. Inside these limits, it was found through numerical simulations that the cable forces have a positive (resp. negative) influence on the stiffness of the mechanism when its limbs are crossed (resp. regular). This shows that the symmetric fourbar mechanisms with crossed limbs are suitable for building bio-inspired joints/robots, while their counterparts cannot serve this purpose. Among these, the anti-parallelogram mechanism offers the largest orientation range of ] − π, π[ for the top bar w.r.t. its base and is thus the best choice.