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.